Ins i u o Uni e si a io pa a el Desa ollo Tecnológico
y la Inno ación en Comunicaciones
P og ama de doc o ado
Doc o ado en Cibe né ica y Telecomunicación
Con ibu ion on he s udy o Unde wa e Wi eless Op ical links:
Channel p edic ion and ene gy e iciency
Víc o Gue a Yánez
Di igida po el D . Ra ael Pé ez Jiménez
Codi igida po el D . José Albe o Rabadán Bo ges
El Di ec o El Codi ec o El Doc o ando
Las Palmas de G an Cana ia
Ab il de 2016
Si u iese que ag adece li e almen e a odos aquellos que han hecho posible que haya e minado
po in mi esis doc o al, debe ´ıa empeza diciendo algo como – Ag adezco a Si Isaac New on su
es ue zo y dedicaci´on pa a que yo haya podido acaba mi doc o ado – Sin emba go, ya que si nos
pusi´esemos en ese plan end ´ıa ambi´en que ag adece a Planck, Maxwell, Lo d Rayleigh y odos
los dem´as se˜no es con ba ba que me dejo po el camino, he p e e ido aco a es os ag adecimien os
a un c´ı culo, digamos, que implique una ci cun e encia meno .
An es de empeza , quie o que cons e que el o den de apa ici´on no implica necesa iamen e una
mayo o meno impo ancia, pe o po si acaso me gus a ´ıa comenza ag adeciendo a La a, mi
muje , su in ini a calma y ac i ud ca i˜nosa. En idio su capacidad pa a hace me sen i anquilo,
a´un en momen os de es ´es.
AGiulia, mi hija. Esa peque˜na cen al nuclea de un me o de al u a. Le ag adezco simplemen e
su exis encia, ya que es la mo i aci´on in ´ınseca de mi mundo.
Po supues o a mis pad es, Ma i Ca men yV´ıc o , que siemp e han apoyado mis decisiones. A
mis he manos Ca los yH´ec o , po pe mi i me que de ez en cuando los hos igase con mis o ones,
los cuales a eces e an cohe en es, y o as no an o. Y a mis abuelos, And ´es yLuisa, a los que
an o quie o.
A mis sueg os, Loli y´
Angel. Sin su ayuda no pod ´ıa habe inalizado es a ca e a de ondo.
No pod ´ıa ol ida a Oma . El que sopo ´o es oicamen e el yugo de mi u ela en su P oyec o
Fin de Ca e a y mi inmise ico de l´a igo a la ho a de ob ene pa e de los esul ados de es a esis.
Es oy inmensamen e ag adecido po su an alioso apoyo.
A mis di ec o es Ra a yJose. No pod ´ıa imagina unos mejo es conduc o es pa a mi esis. Po
un lado la uen e inago able de ideas que es Jose, as´ı como su e e na p edisposici´on a mancha se
las manos con odo ipo de cacha os elec ´onicos. Y po o o lado, la expe iencia, los amplios
conocimien os y la mo i aci´on que ha sabido siemp e gene a Ra a en mi. Sin ellos, es a esis no
exis i ´ıa. Y no me e ie o a los aspec os legales de la a i maci´on.
No me pe dona ´ıa a mi mismo no nomb a a mi amigo C isan o en es os ag adecimien os. G an
pa e de mi amo po la in es igaci´on se lo debo a ´el. Su pasi´on es con agiosa, y espe o llega ene
al menos una acci´on de su ´ımpe u. Adem´as, es el ´unico que me ganaba al Squash.
Po ´ul imo, a mi o o compa˜ne o de galima ´ıas ma em´a icos de in a, C is o. Con el que
consegu´ı acapa a m´as del 90 % del gas o en o ulado es del ins i u o. G acias po no coa a mi
na u al e e escencia c ea i a escuchando a en amen e los a menudo sinsen idos que p oduce mi
ce eb o.
A odos, g acias.
Con en s
Ac onyms
1 In oduc ion 1
1.1 Unde wa e Radio equency Communica ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Unde wa e Acous ic Communica ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Unde wa e Wi eless Op ical Communica ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Mo i a ion, Hypo heses and Con ibu ions 9
2.1 Mo i a ion .................................................. 9
2.2 Hypo heses .................................................. 9
2.3 Con ibu ions................................................. 10
2.4 O ganiza iono hedocumen ........................................ 11
3 Unde wa e Wi eless Op ical Communica ions: a ho ough analysis 13
3.1 Channelmodeling .............................................. 14
3.1.1 Physicale ec s............................................ 14
3.1.2 Channel esponse........................................... 19
3.1.3 S ochas icmodeling ......................................... 22
3.2 Modula ionsandEncodings......................................... 22
3.3 Ene gye iciency ............................................... 24
3.4 Ne wo klaye ................................................. 25
3.5 Applica ions.................................................. 25
3.5.1 Ha dwa edesign ........................................... 25
3.5.2 Unde wa e Wi eless Senso Ne wo ks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5.3 Applica ions o mobile sys ems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5.4 O he applica ions .......................................... 33
3.5.5 Summa y ............................................... 34
3.6 Exis ingsu eys ............................................... 34
3.7 Remainingchallenges............................................. 36
4 Impulse Response o he Unde wa e Wi eless Op ical Channel 37
4.1 Radia i eT ans e Theo y.......................................... 37
4.2 Channelcha ac e is ics............................................ 38
4.2.1 Abso p ion .............................................. 38
4.2.2 Sca e ing............................................... 39
4.2.3 Re ac i eIndex ........................................... 42
4.2.4 Tu bulences.............................................. 42
4.2.5 Su ace e lec ions .......................................... 44
4.2.6 Seabeddi usion ........................................... 45
4.2.7 Op ical ouling ............................................ 45
4.2.8 Fauna ................................................. 46
4.3 Simula ion o he UWOC impulse esponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.1 Simula edscena io.......................................... 46
4.3.2 Mon e Ca lo in eg a ion scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.3 Collisionwi hpa icles........................................ 48
4.3.4 Desc ip ion o he simula ion p ocedu e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.5 Pa alleliza ion o he algo i hm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Simula ion esul s .............................................. 54
4.4.1 E ec o helink’s ange....................................... 55

4.4.2 E ec o helink’sdep h....................................... 56
4.4.3 E ec o he su ace agi a ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.4.4 E ec o he dis ance o seabed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.5 E ec o he seabed’s e lec i i y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.6 E ec o he emi e ’s di ec i i y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.7 E ec o hewa eleng h....................................... 59
4.4.8 E ec o hepa iclesize ...................................... 60
4.4.9 E ec o he concen a ion o pa icles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4.10 Pa alleliza ion speedup and e iciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Compa isonwi h heli e a u e ....................................... 65
5 Conside a ions in Unde wa e - o-Ai links 67
5.1 Seawa esp opaga ion............................................ 67
5.2 Unde wa e - o-ai channel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2.1 Seasu acemodel .......................................... 68
5.2.2 Recei edpowe ............................................ 69
5.2.3 P ojec ion o he ecei e ’s a ea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Simula ionp ocedu e............................................. 71
5.4 Simula ion esul s .............................................. 72
5.4.1 E ec o heemi e ’sdep h..................................... 72
5.4.2 E ec o he ecei e ’s heigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4.3 E ec o heseawa eheigh .................................... 73
5.4.4 E ec o he sea wa e wa eleng h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4.5 E ec o hewindspeed....................................... 74
5.4.6 Channela ailabili y ......................................... 74
6 S a is ical modeling o he Unde wa e Wi eless Op ical Channel 79
6.1 B ie analysiso hep oblem ........................................ 79
6.1.1 Analysis o he s a is ical na u e o he channel gain . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 S a is icalp ocedu e............................................. 82
6.3 Resul s ob ained h ough simula ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.1 ChannelgainandBandwid h.................................... 83
6.3.2 Commen s on he ela ionship be ween he dis ibu ion and he channel’s pa ame e s . . . . 83
6.4 F esnel zones and Beam Sp ead Func ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.4.1 BeamSp eadFunc ion........................................ 87
6.4.2 Analysis o he esul ing F esnel zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.5 S a is ical model o big opaque pa icles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.5.1 De ini ion o big opaque pa icle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.5.2 Ma hema ical o mula ion...................................... 90
6.5.3 In luence o he link’s pa ame e s on he SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7 Measu emen s on a sho - ange Unde wa e Wi eless Op ical Channel 97
7.1 WSSUSp ocesses............................................... 98
7.1.1 Cohe enceTime ........................................... 98
7.2 Desc ip ion o he expe imen al se up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.2.1 Emi e implemen a ion....................................... 99
7.2.2 Recei e implemen a ion.......................................100
7.2.3 Expe imen alme hodology .....................................101
7.3 Resul s ob ained h ough measu emen s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.3.1 E ec o he concen a ion and he mo emen o pa icles . . . . . . . . . . . . . . . . . . . . 103
7.3.2 E ec o hewindspeed.......................................105
7.3.3 Validi y o he WSSUS assump ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8 S a egies o ene gy-e icien anscei e design 107
8.1 Signal oNoise a ioinUWOC.......................................107
8.2 Op ical ansmi e s and ecei e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.2.1 Cu en d i e s............................................108
8.2.2 Op icalemi e s ...........................................109
8.3 Powe Con olAlgo i hms..........................................109
8.3.1 Fixed-s epalgo i hm.........................................111
8.3.2 Va iable-s epalgo i hm .......................................112
8.3.3 Adap i e-s epalgo i hm.......................................112
8.3.4 Adap i e-damping-and-s ep algo i hm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.3.5 Wa eleng hswi ching ........................................113
8.3.6 Simula ion esul s ..........................................113
8.4 Pulse Wid h Modula ed Op ical OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.4.1 Op icalOFDMschemes .......................................117
8.4.2 P oposedscheme...........................................118
8.4.3 Expe imen alcu es .........................................120
8.4.4 Commen s on he BER pe o mance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
9 Conclusions and Fu u e Resea ch 125
9.1 Fu u eResea ch ...............................................128
Appendices 131
A Demons a ions o Chap e 5 133
B Recei ed ligh in ensi y in pa ially obs uc ed links 137
C Wa e o ms, Co ela ions and P obabili y Densi y Func ions o Chap e 7 139
C.1 Mo emen o pa icles ............................................139
C.1.1 Blueemission.............................................139
C.1.2 Redemission .............................................141
C.2 Nea -su acelinkmeasu emen s.......................................142
D Summa y in Spanish 151
D.1 In oducci´on..................................................151
D.1.1 Radio ecuencia............................................152
D.1.2 Comunicaciones ac´us icas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
D.1.3 Comunicaciones´op icas .......................................154
D.2 Mo i aci´on, Hip´o esis y Obje i os . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
D.2.1 Hip´o esis ...............................................157
D.2.2 Apo aciones .............................................158
D.3 Respues aimpulsi adelcanal........................................161
D.3.1 T ans e encia adia i a........................................161
D.3.2 Ca ac e ´ıs icasdelcanal.......................................162
D.3.3 Simulaci´on de la espues a al impulso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
D.3.4 Resul adosdesimulaci´on ......................................166
D.4 Canalesagua-ai e...............................................167
D.4.1 P opagaci´on de ondas ma inas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
D.4.2 Modelodep opagaci´on .......................................168
D.4.3 Simulaci´on ..............................................169
D.4.4 Resul adosdesimulaci´on ......................................169
D.5 An´alisises ad´ıs ico..............................................171
D.5.1 An´alisisdelp oblema ........................................171
D.5.2 P ocedimien oes ad´ıs ico ......................................173
D.5.3 Resul adosdesimulaci´on ......................................173
D.5.4 Zonas de F esnel y Beam Sp ead Func ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
D.5.5 Modelo de pa ´ıculas opacas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
D.6 Medidasexpe imen les............................................179
D.6.1 Desc ipci´on del expe imen o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
D.6.2 Resul adosexpe imen ales......................................181
D.7 Es a egias pa a la mejo a de la e iciencia ene g´e ica . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
D.7.1 SNRencanalesUWOC .......................................185
D.7.2 Emiso es y ecep o es ´op icos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
D.7.3 Algo i mos de con ol de po encia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
D.7.4 Cambiodelongi uddeonda.....................................189
D.7.5 OFDMmoduladaenPWM .....................................190
D.8 Conclusiones .................................................193
Ac onyms
ACV A e Con e gence Va iabili y.
ADC Analog o Digi al Con e sion.
AOA Angle O A i al.
APD A alanche Pho oDiode.
API Applica ion P og amming In e ace.
AUV Au onomous Unde wa e Vehicle.
BER Bi E o Ra e.
BJT Bipola Junc ion T ansis o .
BSF Beam Sp eam Func ion.
CDF Cumula i e Densi y Func ion.
CDMA Code Di ision Mul iple Access.
CI Con e gence I e a ion.
CLT Cen al Limi Theo em.
CPU Cen al P ocessing Uni .
CSK Colo Shi Keying.
DC Di ec Cu en .
DPIM Digi al Pulse In e al Modula ion.
DPSK Di e en ial Phase Shi Keying.
DSP Digi al Signal P ocessing.
ELF Ex eme Low F equency.
EM Elec oMagne ic.
FEC Fo wa d E o Co ec ion.
FEM Fini e Elemen s Me hod.
FET Field E ec T ansis o .
FPGA Field P og ammable Ga e A ay.
FSK F equency Shi Keying.
FSO F ee Space Op ics.
GEV Gene alized Ex eme Value.
GPU G aphics P ocessing Uni .
HF High F equency.
HOV Human Ope a ed Vehicle.
IMDD In ensi y Modula ed Di ec De ec ion.
IMU Ine ial Measu emen Uni .
IOWCC In eg a ed OWC Ci cui .
IR In aRed.
LED Ligh Emi ing Diode.
LMS Leas Mean Squa es.
LOS Line O Sigh .
LTI Linea Time In a ian .
LTV Linea Time Va ian .
MAC Medium Access Con ol.
MCRT Mon e Ca lo Ray T acing.
MIMO Mul iple Inpu Mul iple Ou pu .
MMCRT Modi ied Mon e Ca lo Ray T acing.
MOS Me al Oxide Semiconduc o .
MPI Message Passing In e ace.
NLOS Non Line O Sigh .
OBTS Op ical Base T anscei e S a ion.
OFDM O hogonal F equency Di ision Mul iplexing.
ONC Op ical Ne wo k Con olle .
OOC Op ical O hogonal Code.
OOK On O Keying.
OWC Op ical Wi eless Communica ion.
PAPR Peak o A e age Powe Ra io.
PCA Powe Con ol Algo i hm.
PDF P obabili y Densi y Func ion.
PIN Posi i e In insic Nega i e.
PMMA PolyMe hyl Me hAc yla e.
PMT Pho oMul iplie Tube.
PPM Pulse Posi ion Modula ion.
PSK Phase Shi Keying.
PWM Pulse Wid h Modula ion.
RF RadioF equency.
RGB Red G een Blue.
ROV Remo ely Ope a ed Vehicle.
RTE Radia i e T ans e Equa ion.
RTV Random Va iable T ans o ma ion.
SCPI S anda d Commands o P og ammable Ins u-
men s.
SDMA Spa ial Di ision Mul iple Access.
SER Symbol E o Ra e.
SIMD Single Ins uc ion Mul iple Da a.
SINR Signal In e e ence Noise Ra io.
SNR Signal Noise Ra io.
SSIM S uc u al Simila i y Index Me hod.
TDMA Time Di ision Mul iple Access.
TDS To al Dissol ed Solids.
TTP Th eshold T ansmi Powe .
UAC Unde wa e Acous ic Communica ion.
UMTS Uni e sal Mobile Telecommunica ions Sys em.
US Unco ela ed Sca e ing.
UV Ul aViole .
UWOC Unde wa e Wi eless Op ical Communica ion.
UWSN Unde wa e Wi eless Senso Ne wo k.
VLC Visible Ligh Communica ion.
VRTT Vec o Radia i e T ans e Theo y.
VSF Volume Sca e ing Func ion.
WSS Wide Sense S a iona y.
YB-WLED Yellow Blue Whi e Ligh Emi ing Diode.
Chap e 1. In oduc ion
Figu e 1.7: (A(d, )N( ))−1p oduc o di e en dis ances. Ex ac ed om [6].
pa ame e s o he link, such as he sea su ace’s agi a ion. Gene ally, cohe ence imes up o hund eds o milliseconds
may be conside ed.
Addi ionally o he physical cons ain s inhe en o acous ic p opaga ion, acous ic modems add se e al limi a-
ion o he design o acous ic ne wo ks. The powe equi ed by he ansmi e o ca y ou he communica ion
depends on he dis ance, bu is no mally in he ange o ens o wa s, whils he powe equi emen s on he ecei e
side a e much mo e elaxed (abou a ew milliwa s). Powe consump ion is a c i ical issue in ba e y-powe ed
isola ed nodes, and ene gy e iciency is o capi al impo ance. The e a e di e en ways o educe he powe con-
sump ion o he node, bu he main ones a e powe con ol algo i hms, e ansmission- educ ion echniques in
andom access ne wo ks, and bandwid h-adap i e sys ems.
Finally, ma ine mammals, such as dolphins and whales, ha e an audible spec um ha can co e up o almos
200 KHz. These animals use sound wi h bo h social and echoloca ion pu poses, and he use o UAC unde 200
KHz may be ex emely ha m ul due o he high acous ic powe s gene ally used. Fu he mo e, e en hough a p io i
non-ha m ul equencies we e used, due o Dopple e ec , he ac ual spec al densi y ha mo ing mammals may
expe ience in an ensoni ied ocean could be ha m ul as well, as Side ius and Po e commen ed in [7].
1.3 Unde wa e Wi eless Op ical Communica ions
Unde wa e Wi eless Op ical Communica ions is a subg oup o Op ical Wi eless Communica ions. Unlike in FSO,
he p opaga ion medium p esen s abso p ion in UWOC. This abso p ion depends on he inhe en p ope ies o
he seawa e and he ela i e concen a ions o algal and non-algal ma e . Fu he mo e, whils ae osols and
gases p oduce sca e ing in FSO, UWOC su e s his spa ial dispe sion mainly om phy oplank on. Rega ding
u bulences, he e ac i e index g adien s induced by empe a u es changes in FSO a e no enough o model his
phenomenon in UWOC, since he e ac i e index o seawa e depends on empe a u e, salini y and p essu e. In
addi ion, he wa eleng h dependency o he ex inc ion coe icien (abso p ion plus sca e ing) gene ally de ines a
bes wa eleng h ha anges wi hin he blue-g een window.
As i was commen ed abo e, unde wa e RF communica ions a e powe and bandwid h limi ed. The powe
consump ion o ELF s a ions is absu dly high and he e ec i e da a a e is e y low, bu o e s e y good com-
munica ion ange. Rega ding UAC, he a ailable bandwid h can suppo a wide ange o se ices, bu is no mally
limi ed o a ew housands o bi s pe seconds. In he pas ew yea s, UWOC has demons a ed he bes ene gy
e iciency in e ms o bi s pe Joule and a maximum ange abo e 100 me e s. Fu he mo e, he cos associa ed o
he op ical anscei e s is much lowe han he associa ed o UAC’s hyd ophones and d i e s. Howe e , due o he
ange limi a ion o UWOC, he cu en end is o use hyb id op o-acous ical solu ions, whe e long ange eleme y
is acous ically pe o med whils low ange, low la ency and high bandwid h communica ion is ca ied ou op ically.
The ecen p oposals o UWOC as da a in e ace o Unde wa e Wi eless Senso Ne wo ks is highly suppo ed
by he a ailabili y o download huge amoun o long- e m collec ed da a in a ac ion o ime espec o acous ic
anscei e . Fu he mo e, he use o op ical in e aces leng hens he li e o he deployed nodes. Howe e , al hough
he maximum allowed misalignmen e o has been demons a ed o be lowe han expec ed due o he beam
sp eading o ligh , i s ills lowe han he case o UAC. Mo eo e , he low la ency o he UWOC links allows a
6

Chap e 1. In oduc ion
na u al emo e ope a ion o unde wa e ehicles. The la ency o an UWOC link can be e en be e han he la ency
o a ibe - e he ed link, since he e ac i e index is lowe in seawa e han in plas ic o glass, bu his enhancemen
is usually weighed by he necessi y o e ansmission in he un e he ed scena io.
The e a e se e al cu en challenges in UWOC ega ding ene gy e iciency and channel modeling. Se e al
con ibu ions whe e he impulse esponse is modeled as in a LTI scena io can be ound in he li e a u e, bu he
UWOC channel is clea ly LTV and only a ew au ho s add ess his issue in lase -based links. Mo eo e , he e is
a lack o con ibu ions ega ding ene gy e iciency in UWOC, which is o capi al impo ance in scena ios whe e
ba e y eplacemen is no mally p ohibi ed by he huge cos o he ope a ion.
In his disse a ion, a s a is ical app oach o he channel’s main pa ame e s (bandwid h, gain and cohe ence
ime) is pe o med. The analysis is based using heo e ical app oxima ions and simula ion esul s. Two di e en
scena ios a e analyzed due o hei applicabili y in UWSN: unde wa e - o-unde wa e and unde wa e - o-ai links.
Fu he mo e, a s a is ical model o big opaque pa icles is p oposed. The p oposal is ocused on shallow wa e
scena ios whe e he coas al cu en s gene a e a cloud o pa icles in sandy seabeds. Rega ding ene gy e iciency,
he use o di e en modula ions and encodings, as well as powe con ol algo i hms is explo ed.
7
Chap e 1. In oduc ion
8
Chap e 2
Mo i a ion, Hypo heses and
Con ibu ions
This chap e comp ises he s a emen s o be p o en h ough expe imen a ion in his hesis, he main objec i es
ha ha e mo i a ed i s ac ual de elopmen , and he con ibu ions ha ha e been made du ing he de elopmen
o his wo k.
2.1 Mo i a ion
The opic o his hesis eme ged as he na u al e olu ion o he esea ch lines o he Pho onic Technology and
Communica ions Di ision o he Ins i u e o Technological De elopmen and Inno a ion in Communica ions, o
he Uni e si y o Las Palmas de G an Cana ia.
The g oup has been ocused du ing he las ew yea s in IR and VLC, conc e ely in simula ion engines [8] and
he de elopmen o p oo -o -concep p o o ypes o di e en applica ions using he a o emen ioned echnology, such
as ideo s eaming using VLC [9] o in- ligh op ical communica ions (VLC downlink wi h IR uplink) [10][11].
In his wo k, since i is he i s in a no el a ea o he g oup, se e al on s ha e been ea ed. In i s place,
a ho ough analysis o he cu en s a e-o - he-a esea ch was manda o y in o de o de ec he main weaknesses
and hence, oppo uni ies o wo k in. As i will be commen ed in Chap e 3, ene gy-e icien s a egies ha e no been
s udied in dep h, and di e en app oaches a e p oposed du ing he ollowing chap e s. Fu he mo e, s ochas ic
models o ca y ou pe o mance p edic ions acco ding o link’s pa ame e s a e no a ailable ye , and a sligh
con ibu ion in his ega d is made.
Summa izing, he main objec i es o his hesis a e:
•Ca y ou a ho ough analysis o he cu en s a e-o - he-a esea ch.
•P opose s a egies o enhance he ene gy e iciency o UWOC sys ems.
•S udy he easibili y o pe o ming s ochas ic modeling in UWOC links.
2.2 Hypo heses
This hesis depa s om wo undamen al hypo heses, which a e enume a ed below. The i s one ega ds channel
modeling, whils he second add esses ene gy e iciency in UWOC.
Hypo hesis 1 On he channel. The Unde wa e Wi eless Op ical Communica ions channel is linea and ime
a ian bu Wide Sense S a iona y wi h Unco ela ed Sca e ing (WSSUS).
•The a iabili y o he UWOC channel, enclosed wi hin he ime- a ian impulse esponse h( , τ), is due o
he di e en sca e ing and e lec i e phenomena ha occu du ing p opaga ion. This a iabili y, i emi e
and ecei e a e a ixed posi ions, possesses a in a ian mean alue. Fu he mo e, he powe con ibu ions
incoming om sca e ing e en s a e mu ually unco ela ed due o he independence o he loca ions whe e
hese sca e ings a e p oduced.
•In a scena io wi h suspended ma e , he mo emen o he pa icles amid he link gene a es a a iabili y on
he ecei ed powe ha educes he SNR. In o de o e i y his hypo hesis, bo h simula ion and expe imen al
app oaches ha e been used.
9
Chap e 2. Mo i a ion, Hypo heses and Con ibu ions
•Unde wa e - o-ai links a e also a iable due o he changing shape o he seawa e su ace. Fu he mo e,
he op ical powe ha a i es he ecei e can be es ima ed by he ene gy o he illumina ed seawa e su ace
a ea which impac s on he ecei e . This illumina ed a ea changes wi h ime, ollowing he shape o he sea
wa es spec um.
Hypo hesis 2 On he ene gy e iciency. The ene gy e iciency o an Unde wa e Wi eless Op ical link can be
imp o ed by means o powe con ol algo i hms, he use o he bes ansmission wa eleng h, and ene gy-e icien
encodings and modula ions.
•Gene ally, UWOC links a e pe o med in he blue-g een egion o he isible spec um, since he minimum
abso p ion is usually loca ed be ween hese wa eleng hs. Howe e , aking in o accoun he be e esponse
o long-wa eleng h emi e s and ecei e s, he wo se p opaga ion o edde wa eleng hs is compensa ed by
hese be e e iciencies, de ining a c i ical dis ance a which i is be e o pe o m a ed ansmission han
a blue one.
•Powe con ol algo i hms a e a well-known s a egy o op imize SNR in highly in e e ed en i onmen s.
Fu he mo e, unde wa e emo e senso nodes , which a e ba e y-powe ed, ha e p ohibi i ely expensi e
eplacemen cos s. Hence, s a egies o educe he powe consump ion a e manda o y in his kind o de ice,
and powe con ol algo i hms can be ene gy-op imized.
•Modula ions and encodings a e he lowes le el o he communica ions s ack. Taking in o accoun he elec ical
cha ac e is ics o he op ical emi e s, nonlinea cu en d i e s a e a be e op ion han linea ones. The e o e,
modula ions which need linea ansmission can be quan ized o allow he use o ene gy-e icien nonlinea
d i e s.
All hese hypo heses will be discussed along his documen . Sec ion 2.3 p esen s a summa y o he con ibu ions
p esen ed in his hesis.
2.3 Con ibu ions
To se e as a guide o hose who ead his wo k, a summa y o he con ibu ions made by his wo k is p esen ed.
•Chap e 3. A ho ough analysis o he cu en s a e-o - he-a esea ch is p esen ed. This in-dep h analysis
has been s uc u ed a ending o an in ui i e axonomy and ies o se e as he s a ing poin o his wo k.
•Chap e 4. A Mon e Ca lo Ray T acing algo i hm o UWOC is p esen ed. Unlike o he au ho s who
employed Henyey-G eens ein sca e ing phase unc ions o model sca e ing due o pa icles, in his wo k,
Mie sca e ing has been used since i models he phenomenon mo e accu a ely. The in luence o each channel
pa ame e on he impulse esponse is also analyzed. Fu he mo e, he algo i hm was pa allelized using bo h
mul ip ocesso and GPU implemen a ions
•Chap e 5. A model o unde wa e - o-ai communica ions is p esen ed, ocusing on he channel a ailabili y.
•Chap e 6
–Using he a o emen ioned Mon e Ca lo Ray T acing algo i hm, a s a is ical app oach o bo h channel
gain and bandwid h is made.
–An empi ical o mula o p edic he BSF is ob ained.
–A e a ec angula app oxima ion o he impulse esponse, a de ini ion o F esnel zone is pe o med in
e ms o ecei ed ene gy, allowing he educ ion o he olume o in e es in channel simula ion. This
simpli ica ion also allows he p edic ion o he channel bandwid h.
–A s a is ical s udy o model he in luence o opaque pa icles such as sand g ains is p esen ed in his
wo k. The app oach is based on geome ical ela ionships and some app oxima ions, bu may se e as
baseline o u he wo k.
•Chap e 7
–In his chap e , he in luence o mo ing pa icles on he SNR is demons a ed. The mo emen o pa icles
p oduces a andom a ia ion on he ecei ed signal ha can be modeled as a no mal dis ibu ion o
a iance ela ed o he densi y o pa icles.
–The cohe ence ime o a nea -su ace link and i s ela ionship wi h he wind s ess a e ob ained. Besides
he wind speed, o he pa ame e s a e aken in o accoun , such as dep h and wa eleng h.
10
Chap e 2. Mo i a ion, Hypo heses and Con ibu ions
–The alidi y o he WSSUS app oxima ion o a nea -su ace link is demons a ed h ough expe imen a-
ion.
•Chap e 8
–The use o ed wa eleng h ins ead o blue unde ce ain channel es ic ions is jus i ied in e ms o
ene gy e iciency. As ed emi e s a e mo e ene gy-e icien han blue ones, and Si-based ecei e s a e
mo e sensi i e o longe wa eleng hs, below a c i ical dis ance is be e o pe o m he ansmission in
ed, despi e he highe a enua ion o he medium a his equency.
–A powe con ol algo i hm wi h wa eleng h swi ching ( ed-blue) is p esen ed and e alua ed. The use o
PCA is manda o y o educe he powe consump ion o isola ed unde wa e nodes. In his case, se e al
enhancemen s a e p oposed o he classic New on-Raphson g adien -descen algo i hm (equi alen o a
LMS algo i hm).
–The use o PWM combined o nonlinea d i e s is explo ed as an e iciency-enhancemen s a egy o
Op ical OFDM. I will be discussed ha due o he highe e iciency o nonlinea d i e s, PWM mod-
ula ion o OFDM samples could be an al e na i e o educe he powe consump ion and hence, longe
he li espan o nodes which ansmi OFDM signals.
2.4 O ganiza ion o he documen
A e commen ing he mo i a ion, he hypo heses and con ibu ions ha a e he baseline o his wo k, he nex
chap e s a e o ganized as ollows.
In Chap e 3, a p o ound analysis o he e olu ion o he esea ch in UWOC is p esen ed. The analysis commen s
mos o he a ailable con ibu ions in UWOC ega ding di e en aspec s: channel modeling, modula ions and
encodings, ene gy e iciency, ne wo k laye , applica ions and su eys.
In Chap e 4, he UWOC channel is s udied in de ail. The di e en phenomena ha a ec unde wa e op ical
p opaga ion a e discussed in his chap e . Fu he mo e, a Mon e Ca lo Ray T acing algo i hm using Mie’s sca e ing
model is p esen ed. Fu he mo e, a pa alleliza ion scheme is also p esen ed o educe he compu a ion ime.
Chap e 5 is dedica ed o unde wa e - o-ai links, especially in he discussion o he channel a ailabili y ela ed
o he seawa e -ai in e ace mo ion. The s udied scena io has impo an implica ions in shallow-wa e senso
eading and UUV- o-ai communica ions.
In Chap e 6, a s a is ical app oach o he channel gain and bandwid h is de eloped. Massi e da a ob ained
om he implemen ed simula o o Chap e 3 is in oduced in a decision algo i hm o in e he bes - i op ion
wi hin a ba e y o possible p obabili y dis ibu ion unc ions. Fu he mo e, a quali a i e ela ionship be ween he
dis ibu ion pa ame e s and he channel’s geome ical and physical pa ame e s is commen ed.
In Chap e 7, he esul s o a nea -su ace unde wa e ansmission a e p esen ed. Using hese esul s, he WS-
SUS conside a ion o he a ying channel is demons a ed and he cohe ence ime o he channel is also calcula ed.
Chap e 8 commen s di e en ene gy-e icien s a egies. The use o ed wa eleng hs ins ead o blue ones is
jus i ied o sho - ange links, and a powe con ol algo i hm wi h wa eleng h-swi ching capabili ies is also p esen ed
and analyzed.
Finally, in Chap e 9, se e al conclusions a e ex ac ed and u u e esea ch lines a e exposed and commen ed.
11

Chap e 2. Mo i a ion, Hypo heses and Con ibu ions
12
Chap e 3
Unde wa e Wi eless Op ical
Communica ions: a ho ough analysis
In he pas ew yea s, he e has been a g owing in e es in subma ine applica ions, such as su eillance, elecom-
mand o obo s, ocean moni o ing and mili a y communica ions. The de elopmen and enhancemen o isible
ange emi e s and ecei e s has led o an inc emen on esea ch wo ks ela ed o he use o LED and lase de ices
o es ablish communica ion links in he unde wa e medium. Nowadays, Unde wa e Wi eless Op ical Commu-
nica ions (UWOC), may be conside ed an independen opic apa om F ee Space Op ics (FSO) and Visible
Ligh Communica ions (VLC). This independence has been encou aged by he pa icula i ies o he unde lying
communica ion channel, and he no el y o he ield has a ac ed he a en ion o esea ch g oups wo ldwide. This
g owing in e es can be obse ed a Figu e 3.1 whe e he numbe o con ibu ions in he ield o e ime is analyzed.
Yea (+2K)
56789101112131415
0
5
10
15
20
25
Figu e 3.1: E olu ion o he numbe o pape s a ailable in he IEEE da abase ela ed o UWOC
To ha e a be e unde s anding o he ac ual esea ch in e es s wi hin UWOC, he con ibu ions ha e been
classi ied in six di e en ca ego ies:
•Channel modeling
•Modula ions and Encodings
•Ene gy e iciency
•Ne wo k laye
•Applica ions
•Su eys
13
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.2 depic s he dis ibu ion o he esea ch a ending he he a o emen ioned classi ica ion. No e ha
he dis ibu ion is quali a i e as each pape may belong o se e al ca ego ies.
Channel
Ene gy
Modula ions
Ne wo k
Su eys
Applica ions
Figu e 3.2: Dis ibu ion o publica ions pe ca ego y in UWOC
As i can be obse ed, Applica ions and Channel modeling a e he main in e es s. Due o he no el y o he
opic and he complexi y o he channel, he e we e a need o con ibu ions suppo ing he easibili y o links and
a ma hema ical appa a us o p edic he beha io o he channel. None heless, he lack o publica ions ega ding
ene gy e iciency seems con adic o y aking in o accoun he necessi y o ene gy-sa ing echniques in scena ios
whe e he ac o s a e no mally ba e y-powe ed nodes. Finally, he e a e se e al su eys in his opic, bu a e
no mally inc emen al and hei scope is educed in ime. In his wo k, a deepe analysis is made inc easing he
ime ange as he opic is a o dable in size ye .
3.1 Channel modeling
As i was commen ed abo e, channel modeling has been one o he main in e es s in UWOC since i s o igin. In
o de o p o ide a mo e accu a e iew o his issue, his ca ego y has been subdi ided in h ee sub ypes: physical
e ec s, s ochas ic modeling and channel esponse.
This issue has su e ed an e olu ion ha is depic ed in Figu e 3.3. I can be obse ed ha he las wo yea s
(2013-2015) comp ise mo e han h ee qua e s o he con ibu ions in his aspec . I is common o pe o m
expe imen al e alua ions be o e es ablishing he ma hema ical backg ound o a no el subjec , as he scien i ic
me hod unde sco es. In his aspec , UWOC has su e ed he same ea men , cen e ing he e o s in p o ing he
easibili y o he echnology. This will be u he discussed in Sec ion 3.5.
The ollowing subsec ions commen he con ibu ions in he h ee abo emen ioned subca ego ies.
3.1.1 Physical e ec s
Wi hin his ca ego y a e he publica ions ha y o model o empi ically e alua e he e ec s o di e en unde wa e
phenomena. The main e ec s ha ha e a signi ican weigh in UWOC a e:
•Tu bulence
•Sca e ing and Abso p ion
•Fauna and op ical ouling
•Misalignmen
The ollowing subsec ions analyze he mos ele an con ibu ions up o he da e a each enume a ed opic.
Fauna has an unp edic able beha io om he communica ions’ poin o iew. The pass amid he link o ishes
and mammals has he po en ial o p oduce long-du a ion deep ading e en s, bu no mally, i is no conside ed
and he e a e no wo ks in his ega d.
Tu bulence
Tu bulence is o capi al impo ance in lase -based sys ems, as he ene gy is concen a ed in a small solid angle.
Islam e al. pe o med an expe imen al e alua ion in a labo a o y-con olled scena io [12], inding ou ha u -
bulen egimes a ec he ecei ed SNR depending on i s sal concen a ion. Fu he mo e, o he conclusion o
14
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Yea (+2K)
6789101112131415
0
1
2
3
4
5
6
7
8
9
10
S ochas ic modeling
Channel Response
Physical effec s
Figu e 3.3: E olu ion o he con ibu ions ega ding Channel Modeling
he expe imen was ha he lowe he bandwid h, he lowe he in luence o he u bulence, as i was expec ed
heo e ically.
Hou and Ma [13] s udied he p opaga ion o images in a u bulen scena io. Al hough he scope o he a icle
is no ela ed o communica ions, he ob ained esul s can be ex apola ed o he UWOC domain. A e using
OpenFOAM o model u bulence condi ions in a wa e ank, a deg ada ion s a is ic was ob ained. The s uc u e
simila i y index me ic (SSIM) is used o measu e he s a is ical di e ences be ween wo images, commonly an
undis o ed one and a dis o ed e sion [14]. In his case, he esul s showed ha ex eme u bulence egimes
deg aded he images up o 50 %. As each g oup o pixels can be conside ed as a adi ional pho odiode, his esul s
may be easily ex apola ed o a UWOC scena io. This SSIM deg ada ion can be di ec ly associa ed o a SNR
dec emen . Figu e 3.4 ep oduces he esul s ob ained by Hou and Ma ega ding he SSIM.
The SSIM index is calcula ed be ween wo windows xand yas shows Equa ion 3.1.
Figu e 3.4: Time se ies o image deg ada ion du ing Hou and Ma ’s lab expe imen , unde s ong and ex eme
u bulence case
15
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
he double gamma impulse esponse is as easy as applying he Fou ie T ans o m o 3.4. Equa ion 3.5 shows he
esul .
H(jω) = a
(jω +b)2+c
(jω +d)2ejω 0(3.5)
The double gamma app oxima ion was p o en o be e y accu a e o he simula ions, bu he ela ionship
be ween i s pa ame e s and he physical and geome ical cha ac e is ics o he link has no been s udied ye .
Finally, Dong e al. examined he possibili y o a closed- o m impulse esponse modeling in a MIMO-based
UWOC link [43]. The app oxima ion was based on a weighed supe posi ion o double gamma unc ions, as i is
he s aigh o wa d solu ion. In his e sion o he double gamma app oxima ion, he au ho sligh ly modi ied
Equa ion 3.4 o i a 2x2 MIMO impulse esponse, adding wo new pa ame e s yielding Equa ion 3.6.
h( )≈a( − 0)αe−b( − 0)+c( − 0)βe−d( − 0)(3.6)
O he con ibu ions
Cochenou e al. de ined an expe imen al me hod o measu e he empo al dispe sion in lase -based UWOC links
[44]. The au ho s demons a e ha Bee -Lambe ’s law is no accu a e enough o es ablish a baseline in NLOS link
design. O he e ec s such as mul iple sca e ing , which gene a es empo al dispe sion and hence, a educ ion on
he a ailable bandwid h, should be conside ed. An in e es ing conclusion is ha widening he FOV o he ecei e
enhances he inpu powe bu lowe s he bandwid h in sca e ed en i onmen s. Fu he mo e, his sensi i i y is
d ama ically educed o o -axis links. These las conclusions ha e a signi ican impac on he link designe , which
mus know he geome ical pa ame e s o he link.
Dai e al. s udied in [45] he beha io o IR and UV ligh in seawa e . The au ho s p oposed a sca e ing model
o his wa eleng h bands and con as ed i empi ically. The esul s ha e di ec applica ion in seawa e pa ame e
moni o ing and he sensing o chemical oxygen in wa e ea men acili ies. The di ec impac in communica ions
in educed, as hese bands p esen dis ance-limi ing a enua ions.
3.1.3 S ochas ic modeling
An accu a e s ochas ic model is he main objec i e ha channel modeling mus y o achie e. The scien i ic
me hod s a es ha a e obse ing a phenomenon a su icien amoun o imes, a gene aliza ion may be pe o med
wi h an accu acy di ec ly ela ed o he imes he phenomenon was obse ed. I is logical ha he e o s in
UWOC channel modeling ha e been ocused on simula ion and expe imen al e alua ions, bu a c i ical mass has
been eached and he p oduc ion o p obabilis ic es ima ions and s ochas ic models should be he nex miles one
o ul ill.
Tang e al. s udied he empo al s a is ics o a lase -based link in a u bulen scena io [46]. A e conside ing
Kolmogo o ’s u bulence app oxima ion and Taylo ’s ozen u bulence hypo hesis, which a e widely alid o
egions below 100 me e s in oceanic en i onmen s, he au ho s s udied he empo al co ela ion o he i adiance
be ween wo poin s. Figu e 3.13 shows his co ela ion o link be ween 30 and 50 me e s wi h wo di e en
u bulen egimes de ined by he a e age e ical wa e speed h ough he link’s axis.
I can be obse ed ha he cohe ence ime, which is he ime a which his co ela ion unc ion decays 3 dB,
is almos independen o he dis ance and is highly a ec ed by he u bulence’s egime. Fu he mo e, he au ho s
conclude ha he co ela ion is mo e a ec ed by salini y luc ua ions han by empe a u e a ia ions wi hin he
weak u bulence egion. This is due o he highe sensi i i y o he e ac i e index o salini y.
In [47], Zhang e al. de eloped a nume ical me hod o calcula e he spa ial and empo al p obabili y unc ion o
a LOS UWOC link, conside ing up o one single sca e ing e en pe pho on. The inal ma hema ical exp ession is
he esul o di ec ly applying Random Va iable T ans o ma ion (RVT) o he link’s equa ions. The same au ho s
con inued his esea ch line and p esen ed in [48] a mo e gene alized e sion o he a o emen ioned wo k, conside ing
an in ege numbe o sca e ings. The au ho s do no depic any igu e o he esul ing p obabili y densi y unc ions
(pd ) and use he me hod as an al e na i e o he Mon e Ca lo simula ion pa h loss es ima ion.
3.2 Modula ions and Encodings
Modula ions and encodings a e a c i ical aspec in any communica ions link. The way he in o ma ion is sen in a
changing en i onmen de ines he BER, he e ec i e h oughpu and has also in luence on he channel a ailabili y.
Cochenou e al. s udied in [49] he use o phase-cohe en lase -based sys ems in u bid en i onmen s. The
pape explo es he use o di e en M-PSK schemes wi hin a wa e ank. As i is usual in hei con ibu ions, he
au ho s used di e en concen a ions o Maalox o gene a e syn he ic u bidi ies. The conclusions sugges ha
o ela i ely sho dis ances (below 100 me e s), cohe en schemes a e a easible al e na i e in UWOC. Howe e ,
22

Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.13: Co ela ion unc ion o a lase -based link in a u bulen scena io
he au ho s also mani es he necessi y o u he wo k in long- ange en i onmen s in o de o es ablish a clea e
ela ionship be ween SNR, mul ipa h and BER.
Sui e al. s udied in [50] di e en modula ion app oaches o u bid en i onmen s. Unlike Cochenou ’s g oup,
he au ho s pe o med a simula ed s udy conside ing only ex inc ion in hei amewo k. This wo k neglec s
he s ochas ic na u e o he unde wa e en i onmen , and only conside s a enua ion. The compa ed schemes a e
OOK, FSK, DPSK (cohe en ), 4-PPM and 8-PPM. In[51], he same au ho s p oposed a a ia ion o a PPM schemes
named SPPM (Sho en PPM). Ne e heless, he esul s does no sugges any eal imp o emen espec o PPM,
as i p esen s a lowe spec al e iciency and BER pe o mance, and i has highe powe equi emen s.
In [52], Yu e al. explo ed he use o FEC (Fo wa d E o Co ec ion) codes in UWOC. As he la e wo k, he
andom beha io o he channel esponse is no conside ed and i s PDF (P obabili y Densi y Func ion) is de ined
as a Di ac’s del a. The esul s show he educ ion o he BER a e using his codes.
The use o Op ical OFDM in UWOC was expe imen ally explo ed by Mine e al. in [53]. The au ho s
ho oughly desc ibe he expe imen al se up and he OFDM scheme. The es ed dis ances anged om 0.5 me e s
o 3 me e s, which is a e y sho dis ance o p esen a signi ican mul ipa h e ec so as o jus i y he use o OFDM.
Fu he mo e, he au ho s ob ained his conclusions obse ing ha he ISI was negligible, as he delay sp ead is
much lowe han he symbol ime. Figu e 3.14 depic s he BER s Es/N0cu e o he expe imen .
Figu e 3.14: BER cu e o he expe imen pe o med om 0.5 o 3 me e s
23
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Gab iel e al. ca ied ou an compa a i e wo k [54], simila o he one p esen ed by Sui. In his case, he au ho s
conside ed OOK, PPM, PWM and DPIM. The main conclusion o his pape is ha al hough DPIM p esen s a
highe demodula ion complexi y, i s spec al e iciency is he highes and mus be conside ed when designing an
UWOC link. The au ho s ema k he low PAPR o DPIM, bu conside ing he associa ed ansmission elec onics,
his aspec p esen s no ac ual ad an age, as ON/OFF schemes may be d i en by MOSFET-based ci cui s.
The use o Sp ead Spec um echniques has been also conside ed o UWOC. Akhoundi e al. p esen ed an
analy ical model and a expe imen al e alua ion o a CDMA sys em using OOC (Op ical O hogonal Codes) in
[55]. One o he key aspec s o he pape is he de ini ion o he Op ical Base T anscei e S a ion (OBTS), which
comp ises a se ies o pho odiodes and LED, and he Op ical Ne wo k Con olle (ONC), ha manages pa o he
ne wo k in a cellula way. The p oposed sys em can be obse ed in Figu e 3.15 Bo h downlink and uplink a e
de ined o use OCDMA. Figu e 3.16 shows a diag am o he expe imen al se up used o alida e he sys em.
Figu e 3.15: Cellula OCDMA unde wa e ne wo k
Figu e 3.16: Expe imen al se up used o alida e he p oposed OCDMA unde wa e ne wo k. Vi ex 4 FPGA’s
we e used o implemen he sys em.
This con ibu ion does no deeply explo e he use o di e en Sp ead Spec um echniques, bu is mo e ocused
on he ne wo k desc ip ion and he MAC laye beha io .
3.3 Ene gy e iciency
Ene gy e iciency is one o he mo e impo an aspec s when conside ing UWOC, and much mo e when conside ing
UWSN. The use o ene gy-e icien s a egies o longe he li e o he ba e ies in au onomous nodes is o capi al
impo ance as he ba e y eplacemen is o en much expensi e han simply deploying new nodes.
S ini asan e al. p oposed a join sou ce-channel coding echnique o educe he a e age ene gy pe symbol in
[56]. E en hough he au ho s p opose he scheme o UWOC, he scheme is sui able o any senso ne wo k.
BaniHassan e al. p esen ed in [57] a powe con ol algo i hm based on he p e ious wo k o hei g oup in
Op ical CDMA ne wo ks [55]. The au ho s p opose wo di e en app oaches o pe o m powe con ol. The i s
s a egy consis s on sec o ing o educe he emi ed powe , so as o enhance he ene gy e iciency by limi ing he
emission o a de e mined solid angle. The o he s a egy is o de ine ings. This disc e iza ion allows a be e powe
con ol assigning a ansmission powe o each ing. The au ho s also conside a join ing-sec o s a egy. The
ing-sys em is de ined as open-loop, as he nodes es ima e hei posi ion in a ecei ed powe -basis. The main issue
o his p oposal is ha each node mus know he ex inc ion coe icien o he medium. Fu he mo e, his coe icien
changes in ime and he me hod does no akes his in o accoun . The au ho s es ima e ha in a combined scheme,
up o 15.5 dB o powe can be sa ed in cells wi h 50 m o adius.
24
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
3.4 Ne wo k laye
Ne wo k laye is impo an when conside ing UWSN. Fading e en s may occu in UWOC, and may p oduce ha m ul
e ec s in he connec i i y o he ne wo k. The ollowing lines commen di e en con ibu ions ha ha e been made
du ing he las ew yea s.
Liu p esen ed in [58] a pape whe e a opology- eco e y s a egy was p esen ed. The au ho p oposed he
echnique o an ul asound-based ne wo k, bu he p oposal can be easily ex apola ed o he op ical domain. The
eco e y p ocedu e is based on wo main s eps. When he connec i i y is des oyed, he e e ence node inc emen s
i s ansmission powe . I his ac ion does no sol e he p oblem, hen one o he mobile elemen s o he ne wo k
(an AUV i.e.), is mo ed owa d he loca ion o he los node.
Hu and Fei p oposed in [59] a mul ilaye ou ing p o ocol o hyb id op o-acous ical ne wo ks. In his pape , he
use o ein o cemen lea ning, speci ically Q-lea ning, is explo ed as an al e na i e in ou ing decision o mul ihop
UWSN. The p oposed ne wo k opology consis s in an acous ic backbone and op ical clus e s con o med by emo e
op ical nodes. The uppe -laye (acous ic) nodes manage he op ical clus e s allowing as in a-clus e ou ing.
The esul s sugges s ha his laye ing s a egy allows a lowe la ency ne wo k as well as a mo e ene gy-e icien
al e na i e. Figu e 3.17 shows he packe deli e y a e, he delay and he in e -laye o e head espec o he
packe a e. I can be obse ed ha he deli e y a e is almos independen o he packe a e in a laye ed sys em.
Fu he mo e, he delay emains below he unlaye ed case a any packe a e.
Figu e 3.17: Deli e y a e (le ), delay (cen e ) and in e -laye o e head ( igh ) s packe a e in an in e laye
Q-lea ning ou ing scena io.
Mo a e al. implemen ed in [60] an ad-hoc mul ihop op ical ne wo k using a TDMA-based MAC laye . The
ne wo k is dynamically con o med using a ee-based managemen s a egy. The main disad an age o he sys em
is ha e e y node has he ull in o ma ion o he ne wo k, which may incu in la ge delays and less ene gy e iciency.
A connec i i y analysis was pe o med by Va oulas e al. in [61]. The au ho s s udied he node densi y equi e-
men s (numbe o nodes pe linea me e ) in o de o es ablish a k-connec i i y ne wo k. This equi emen s depend
on he emi ed op ical powe , he channel pa h loss and he wa eleng h. Fu he mo e, he au ho s conside ed an
iso opic adia ion pa e , which is mos ly imp obable in an op ical wi eless anscei e . Figu e 3.18 depic s some
o he ob ained esul s.
3.5 Applica ions
As i was men ioned a he beginning o his chap e , he de elopmen o a opic is no mally bound o he
heo e ical analysis and he push o he expe imen al e alua ions. In his sec ion, di e en applica ions o he
UWOC echnology a e p esen ed. The ollowing axonomy has been applied in o de o so he pape s.
•Ha dwa e design
•Unde wa e Wi eless Senso Ne wo ks
•Applica ions o mobile sys ems
•O he applica ions
3.5.1 Ha dwa e design
Angui a e al. implemen ed an IEEE 802.15.4 compa ible PHY and MAC laye . In [62] p esen ed he physical
laye , which was implemen ed in a Spa an 3 FPGA, using LED de ices and PPM modula ion. Figu e 3.19 shows
he expe imen al se up used o alida e he sys em.
25
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.18: Requi ed node densi y o achie e node isola ion p obabili y equal o 10−4 e sus (a) ope a ing wa e-
leng h, (b) ansmi ed powe , (c) da a a e, and (d) chlo ophyll concen a ion o BER = 10−3(dashed–do ed
line), BER = 10−6(do ed line), and BER = 10−9(con inuous line).
Figu e 3.19: Expe imen al se up used by Angui a e al. o alida e hei FPGA implemen a ions
The co esponding MAC laye implemen a ion was p esen ed in [63], ans o ming he o me ansmi e om
di ec ional o omnidi ec ional, as shows Figu e 3.20. The p oposed MAC p o ocol was CSMA/CA. Finally, he
whole sys em was e alua ed in [64]. Figu e 3.21 depic s he block diag am o he sys em. The main con ibu ion
o his wo ks is he applica ion o an exis ing s anda d o he unde wa e medium.
Doniec and Rus p esen ed AquaOp ical II in [65]. This bidi ec ional sys em is based on an a ay o LED and
an a alanche pho odiode o pe o m ansmission and ecep ion espec i ely. The sys em achie ed a 2.28 Mbps
using DPIM encoding a a dis ance o 50 me e s wi h a es ima ed SNR o 5.1 dB. Figu e 3.22 shows he design o
his anscei e s.
In [66], his de ice was used o pe o m a obus unde wa e ideo-s eaming link. Doniec e al. pe o med
26
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.20: Used plana emi e
Figu e 3.21: Block diag am o he IEEE 802.15.4 compa ible VHDL implemen a ion
es s up o 40 me e s, using di e en ideo ame encodings, quali ies and speeds. Figu e 3.23 shows he ob ained
esul s ega ding he in e al be ween packe s.
Des ez e al. implemen ed an hemisphe ic LED emi e using 12 LED [67]. The main objec i e o he wo k was
o emula e an hemisphe ic adia ion pa e n, bu also elec onic design conside a ions ega ding bo h emi e and
ecei e a e p esen ed. E en hough he au ho s heo ize speeds up o 50 Mbps, he expe imen s we e pe o med
a 1 Mbps using a adi ional OOK encoding, showing poo BER pe o mance a dis ances abo e 2.5 me e s.
Swa hi and P ince p esen ed in [68] an s udy ega ding conside a ions on UWOC anscei e design. The
au ho s enume a e he in luence o each design pa ame e in o he sys em pe o mance, bu he main conclusion
is ha he au ho s p opose he use o adap i e anscei e s o ake ad an age o he channel’s cha ac e is ics.
Al hough he au ho s do no expose i li e ally, his means he use o wa eleng h-selec able emi e s. Depending
on he suspended-ma e concen a ion and link’s dis ance, an op imum wa eleng h may be es ima ed.
In [69], Tang e al. p esen ed di e en conside a ions on he use o APD ecei e s in UWOC. The main adeo
o using APD is hei inne gain, and a mo e compac size and highe quan um e iciency compa ed o PMT. An
27

Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.22: Aquaop ical II anscei e s
Figu e 3.23: In e al be ween packe s o links anging om 10 o 25 me e s (le ), and o links anging om 25
o 40 me e s ( igh ).
in e es ing gain con ol scheme is p esen ed in o de o maximize he SER. As he gain o an APD a ec s he SNR,
o each scena io he e is an op imal gain ha maximizes his pa ame e . The au ho s p esen ed a closed- o m
exp ession o he op imal gain, which depends on se e al pa ame e s. Figu e 3.24 depic s he op imal gain o a
gi en example scena io. I can be obse ed ha he op imal gain depends almos only on he link ange.
Tian e al. implemen ed an UWOC link as he one shown in Figu e 3.25 [70]. The LED d i e is based on a
non-in e ing opology ollowed by a BJT-based swi ch. The ecei e side implemen s a ansimpedance ampli ie
ollowed by an in e ing second s age. The es s, pe o med in a swimming pool, demons a ed communica ion
dis ances be ween 20 and 30 me e s.
Cossu e al. demons a ed a 2.5 me e s link using a 40 dBm op ical sou ce a 470 nm in clea wa e [71]. Two
ecei e schemes we e used, one based on APD and o he in a PIN pho odiode. This wo k does no p o ide any
no el aspec ega ding ha dwa e design, bu he au ho s pe o med an analysis o he impac o dayligh in o he
BER pe o mance. As he expe imen we e ca ied ou in a pool, he nea -su ace condi ion o he link made i
e y sensi i e o he Sun’s posi ion, as Figu e 3.26 shows.
3.5.2 Unde wa e Wi eless Senso Ne wo ks
In 2006, Fa e al. p oposed a lase -based unde wa e wi eless op ical modem [72]. In his wo k, he au ho s
p oposed he use o wi eless op ical echnology using isible-ligh o es ablish a link in he unde wa e medium.
The wo k co e s he main aspec s in he design o a link o his cha ac e is ics: ansmi e de ices, op ics,
28
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.24: Op imal APD gain o maximize SER in a gi en scena io. The o se dis ance is he dis ance om he
emi e ’s axis.
Figu e 3.25: Block diag am o he sys em implemen ed by Tian e al.
Figu e 3.26: Impac o dayligh in he BER pe o mance o a nea -su ace link
ecei e design, phenomena, applica ion scena ios, e ce e a. The wo k p oposes h ee di e en solu ions o es ablish
communica ions be ween a ehicle and a ixed node, using combina ions o di ec ional and omnidi ec ional emi e s
29
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
and ecei e s. As i is usual in he li e a u e, he p oposed ecei e is PMT-based.
Simpson e al. implemen ed an unde wa e node ha e ie es da a om an ul asonic ecei e , encodes i using
a e u n- o-ze o Reed-Solomon code and ansmi s i using a high-powe LED [73]. The au ho s demons a ed
he easibili y o low-powe and cos -e ec i e UWSN nodes achie ing da a a es up o 5 Mbps.
The wo ks p esen ed by Angui a e al. ega ding ha dwa e implemen a ions whe e e alua ed by simula ion in
e ms o achie able da a a e in [74]. Medium- ela ed aspec s such as u bidi y we e conside ed in he simula ions.
Figu e 3.27 depic s he ob ained maximum da a a e o he a o emen ioned plana emi e .
Figu e 3.27: Maximum achie able da a a e o Angui a’s plana emi e
Fa e al. deployed an UWSN node in he no heas Paci ic Ocean [75]. The main objec i e o he expe imen
was o ga he geochemical da a, bu due o he high amoun o da a o collec , ul asonic link we e no easible. The
implemen ed sys em had an ul asonic channel o elecommand, whils he op ical channel was used o download
da a up o 5 Mbps a a dis ance o 61 me e s. Figu e 3.28 depic s a concep a wo k o he ope a ion.
Johnson e al. made o he con ibu ion on hyb id op ical-acous ical ne wo k app oaches [76]. The au ho s
expose he ad an ages o using an acous ical downlink and highly-di ec i e op ical uplinks a he UWSN nodes.
Howe e , he au ho s claim ha his kind o s uc u e p esen s se e al disad an ages, such as powe -limi ed ange
and sensi i i y o e ac i e g adien s (as i is a e ical link). As Cochenou demons a ed in his expe imen al
wo ks, due o he BSF, misalignmen and e ac i e g adien s dec ease hei e ec wi h dis ance. Finally, he powe
limi a ion o lase emission due o auna’s eye-sa e y is men ioned in his pape , being he i s wo k in add ess his
issue ega ding UWSN.
3.5.3 Applica ions o mobile sys ems
Fung e al. implemen ed an UWOC sys em o obo ic swa ms in [77]. The obo s ca ied ou a mul i-channel algo-
i hm in o de o p opaga e he in o ma ion wi hin he swa m. The communica ions was pe o med ansmi ing a
se ial po a 115 Kbps h ough a g een lase . The au ho s complain abou he necessi y o poin ing in he sys em.
None heless, a he es ed dis ances, an LED-based sys em would ha e been a ade-o ega ding eliabili y. The
use o lase de ices was jus i ied imposing he necessi y o long ange communica ions. Howe e , only a ac ual
long dis ances wi h signi ican pa icle concen a ions, lase -based sys em elax hei maximum misalignmen e o
as Cochenou sugges ed in [16].
Doniec e al. e alua ed he use o UWOC o obo ope a ion [78]. The aim o he expe imen was o pe o m
a cable eplacemen o con ol he obo . No mally, his kind o obo s a e e he ed o a base s a ion, limi ing he
maximum ange o ope a ion and i s maneu e abili y. The ob ained delays we e no dis inguishable om a e he ed
e sion o he expe imen . Fu he mo e, he implemen ed op ical de ices we e capable o es ablishing a 200-me e s
link in ai a nigh , a 30-me e s link in a pool, and a 7-me e s link in a high- u bidi y ha bo en i onmen . The
me i igu e used by he au ho s o measu e he quali y o he link was he packe delay since he las upda e o
he IMU. Figu e 3.29 depic s he ob ained esul s o wo di e en en i onmen s: low SNR and high SNR.
Gao and Guo p esen ed in [79] an implemen a ion o a emo ely ope a ed mic o obo . The obo implemen a ion
we e in ended o wo k unde he command o a mo he subma ine. None heless, he au ho s used in a ed ligh o
pe o m communica ion, limi ing he maximum allowed dis ance o ope a ion o a ew dozens o cen ime e s.
30
Chap e 3. Unde wa e Wi eless Op ical Communica ions: a ho ough analysis
Figu e 3.28: Concep o he sys em implemen ed by Fa e al.
Figu e 3.29: Packe delay o wo di e en en i onmen al condi ions
Rus and Asada p oposed a dual use o isible ligh o p o ide posi ioning plus communica ion o a obo o
nuclea eac o inspec ion [80]. The posi ioning sys em is based on he signal s eng h and an es ima ion o he
angle based on a pho odiode a ay a he ga eway s a ion. Fu he mo e, incoming da a om he ROV’s IMU
is used o il e he es ima ions. The sys em has no been es ed in an eal scena io, bu has only been ea ed
unde simula ions. The use o UWOC in a hea y wa e en i onmen has no been epo ed ye , and possible he
ex inc ion coe icien would be di e en om he dis illed wa e es ima ions p esen in he li e a u e. In addi ion,
e ec s such as Che enko adia ion mus be aken in o accoun as backg ound noise e ms i a minimum link quali y
is in ended o be p o ided.
Bowen e al. implemen ed an un e he ed ROV based on a hyb id op oacous ical app oach [81]. The need o
high bandwid h and low la ency o ROV manipula ion makes op ical communica ion he bes al e na i e. In his
wo k, he communica ions sys em o a Ne eus ROV was modi ied o include an op ical subsys em. Al hough he
uplink was implemen wi h he ul asonic modem, a TDMA hal -duplex access p o ocol was p oposed o elimina e
he necessi y o he acous ic pa , which adds a signi ican la ency o he sys em.
In [82], Han e al. e alua ed h ough simula ion he pe o mance, in e ms o ene gy e iciency and h oughpu ,
a hyb id op ical-acous ical sys em o AUV communica ions and posi ions, as i is usual in he li e a u e. The
p oposed scheme does no p o ide a signi ican enhancemen o he h oughpu espec o he lowe ene gy e iciency
due o he use o he acous ic pa . Rega ding posi ioning, op ical-based sys ems a e no add essed, and he
31
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
subme ged pa icles wi hin he medium, and only nume ical solu ions a e easible. The Schus e -Schwa zschild
app oxima ion [113] p oposes he di ision o Equa ion 4.1 in o wo main s eams (inwa d and ou wa d di ec ions),
bu his algeb aic a i ac can be gene alized in o 2ndi ec ions as ollows:
cos θi
κ(ω)ρ
dI(ω, z, θi, )
dz=I(ω, z, θi, )−1
2X
j
ajp(cos θi,cos θj)I(ω, z, cos θj, )/i =±1, ..., ±n(4.3)
ajis he j- h Gauss-Legend e quad a u e weigh . This las simpli ica ion is alid o any C(1) phase unc ion
which can be exp essed as a (2n-1)-o de polynomial. This sys em o linea di e en ial equa ions can be easily
sol ed nume ically. None heless, he accu acy o he solu ion depends on he numbe o di ec ions in ol ed in he
calcula ion. Fu he mo e, he di ision using he Gauss-Legend e quad a u e can be e o mula ed using o he ype
o nume ical scheme, o ins ance, Mon e Ca lo. This in eg a ion scheme will be discussed du ing Sec ion 4.3.
4.2 Channel cha ac e is ics
The RTE de ines he p opaga ion o EM wa es h ough spa ially-dispe si e media. Seawa e is con o med by
molecules o wa e and a mix u e o biological ma e (phy oplank on in he as majo i y) and dissol ed sal s.
Depending on he concen a ion o each ype o addi i e, he e ec s on he p opaga ion di e . The ollowing
subsec ions commen each e ec sepa a ely.
4.2.1 Abso p ion
Abso p ion is a wa eleng h-dependen p ocess whe e elec omagne ic ene gy is con e ed in o o he ypes o ene gy,
ypically hea o chemical. I is o capi al impo ance because i de ines he decay o he p opaga ing ene gy h ough
seawa e , and hence, has a di ec impac on he amoun o pho ons ha a i e he ecei e . Since seawa e is a
mix u e o di e en elemen s apa om pu e seawa e , he o e all abso p ion can be exp essed as a sum o pa ial
abso p i e con ibu ions (Equa ion 4.4).
a(λ) =
N
X
i=1
Ciai(λ) (4.4)
Gene ally, he conside ed abso p i e con ibu ions a e: pu e seawa e (αw(λ)), phy oplank on (αφ(λ)), gelbs o
(αg(λ), decaying o ganic ma e ) and non-algal ma e (αn(λ)). Figu e 4.1 depic s he spec al esponse o hese
componen s.
Wa eleng h (nm)
400 500 600 700
αw(λ) (m−1)
0
0.2
0.4
0.6
0.8
Wa eleng h (nm)
400 500 600 700
αφ(λ) (m2·mg−1)
0
0.02
0.04
0.06
Wa eleng h (nm)
400 500 600 700
αw(λ) (m−1)
0
0.5
1
Wa eleng h (nm)
400 500 600 700
αw(λ) (m−1)
0
0.5
1
Figu e 4.1: Abso p ion spec a o each elemen ha con o m seawa e . Seawa e (NW - [114]), Phy oplank on (NE
- [115]), Gelbs o (SW - [116]) and Non-algal ma e (SE - [117])
The concen a ion o each o he componen s con o m he o e all abso p ion spec um. Figu e 4.2 depic s an
example o abso p ion spec a o open ocean and coas al wa e s.
I mus be aken in o accoun ha he ela i e concen a ions a e dep h dependen , as Johson e al. s udied in
[29]. This ac has a di ec impac on he design o e ical links, whe e he ligh ays c oss di e en concen a ion
38

Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Wa eleng h (nm)
400 500 600 700
α(λ) (m−1)
0.05
0.1
0.15
0.2
0.25
0.3
0.35 Coas al wa e
Wa eleng h (nm)
400 500 600 700
α(λ) (m−1)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5 Open ocean wa e
Figu e 4.2: Abso p ion spec a o open ocean (le ) and coas al wa e ( igh ).
laye s. Finally, Hal in [118] de i ed a model desc ibing he abso p ion in e ms o a single pa ame e s, chlo ophyll
concen a ion, Cφ. Equa ion 4.5 illus a es he exp ession.
α(λ) = αw(λ) + αφ(λ) Cφ
C∗
φ!0.6
+α (λ)C e−k λ+ah(λ)Che−khλ(4.5)
C∗
φ= 1 mg·m−3.αφ(λ), α (λ) and αh(λ) a e he phy oplank on, ul ic acid and humic acid abso p ion spec a
espec i ely. C and Cha e he ul ic and humic acid concen a ions, and k and kh hei spec al decaying
cons an s.
4.2.2 Sca e ing
Sca e ing is a physical p ocess in which ene gy is spa ially dispe sed due o ligh -ma e in e ac ion. Figu e 4.3
illus a es his phenomenon.
Figu e 4.3: Rep esen a ion o he sca e ing phenomenon
Depending on he ela i e size o he sca e ing cen e s, di e en app oaches may be used o model he phe-
nomenon. The ela i e size o a pa icle, a, is he ela ionship be ween i s diame e and he wa eleng h o in e es
(Equa ion 4.6). Dis he diame e o he pa icle, λ he wa eleng h in acuum and nw he e ac i e index o he
su ounding medium.
a=πDnw
λ(4.6)
Fo e y small ela i e sizes (a << 1), Rayleigh sca e ing is used o model his phenomenon. Fo nea uni a y
ela i e sizes (a≈1), Mie’s app oxima ion o Maxwell’s equa ions is used o desc ibe sca e ing. Finally, e y
high ela i e sizes (a >> 1) p oduce e y small sca e ing e ec s and hei beha io can be explained by geome ic
op ics.
In his wo k, since he sca e ing cen e s a e usually con o med by phy oplank on, and he wa eleng hs o
in e es a e nex o he size o hese pa icles, only Mie sca e ing is going o be conside ed.
39
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Mie sca e ing
Mie’s heo y is he mos gene al solu ion o he elas ic sca e ing p oblem. I s applicabili y anges om Rayleigh’s
app oxima ion o small pa icles o geome ic op ics on he limi , bu is limi ed o sphe ical pa icles. Howe e ,
he sphe ical assump ion is no a p oblem ega ding he e o bias i may p oduce in a communica ions es ima ion
p oblem.
Le s conside a sphe ical pa icle o diame e Dand e ac i e index m=n −jκ. The imagina y pa o he
e ac i e index is ela ed o he abso p ion coe icien o he ma e ial (ama (λ)) h ough Equa ion 4.7.
αma (λ) = 4πκ
λ(4.7)
Al hough Mie’s heo y de ines he sca e ing p ocess aking in o accoun he pola iza ion s a e, and since his
wo k is o ien ed o he use o unpola ized adia ion (LED emissions), his in oduc o y o mula ion is p esen ed in
i s ho izon al- e ical a e aged e sion. In a sphe ical coo dina e sys em, he ela ionship be ween he sca e ed
in ensi y and he inciden in ensi y a e sca e ing, is ela ed o a unc ion σ0
sca (θ) as shows Equa ion 4.8.
Isca (θ) = I0
σ0
sca (θ)
2(4.8)
No e ha he e is no azimu hal (φ) dependency as he su ounding medium is iso opic and he inciden ligh
is unpola ized. Taking in o accoun he ene gy ans o ma ions in ol ed in he p ocess, he ex inc ion c oss sec ion
σex , he sca e ing c oss sec ion σsca and he abso p ion c oss sec ion σabs a e ela ed by Equa ion 4.9.
σex =σabs +σsca (4.9)
Fu he mo e, he di e en ial c oss sec ion σ0
sca (θ) and he c oss sec ion σsca a e ela ed by a in eg a ion o e 4π
s e adians. In Mie’s equa ions, he di e en ial c oss sec ion can be exp essed as a combina ion o e ms. Equa ion
4.10 s a s he ma hema ical desc ip ion.
σ0
sca (θ) = λ2
8π2(i1+i2) (4.10)
In his o mula ion, he in ensi y unc ions a e calcula ed om an in ini e se ies gi en by:
i1=
∞
X
n=1
2n+ 1
n(n+ 1) [anπn(cos θ) + bnτn(cos θ)]
2
i2=
∞
X
n=1
2n+ 1
n(n+ 1) [anτn(cos θ) + bnπn(cos θ)]
2
(4.11)
The angula dependen unc ions πnand τno Equa ion se 4.11 a e exp essed in e ms o he Legend e
polynomials by:
πn(cos θ) = P(1)
n(cos θ)
sin θ
τn(cos θ) = dP(1)
n(cos θ)
dθ(4.12)
Finally, he pa ame e s anand bna e de ined in e ms o he Rica i-Bessel unc ions Ψ and ξas shows Equa ion
se 4.13.
an=Ψn(a)Ψ0
n(ma)−mΨn(ma)Ψ0
n(a)
ξn(a)Ψ0
n(ma)−mΨn(ma)ξ0
n(a)
bn=mΨn(a)Ψ0
n(ma)−Ψn(ma)Ψ0
n(a)
mξn(a)Ψ0
n(ma)−Ψn(ma)ξ0
n(a)(4.13)
Finally, a e in eg a ing he di e en ial sca e ing c oss sec ion o e he sphe e, he esul ing sca e ing c oss
sec ion may be exp essed as:
σsca =λ2
2π
∞
X
n=0
(2n+ 1) |an|2+|bn|2(4.14)
40
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
The abo e equa ions exp ess he angula dependence o sca e ing and hence, he olume sca e ing unc ion.
As i was commen ed, his unc ion only depends on ele a ion and has e olu ion symme y o sphe ical pa icles
imme sed in an iso opic medium such as seawa e . Figu e 4.4 depic s he phase unc ion o a pa icle o a gi en
wa eleng h and e ac i e index.
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
Phase unc ion
Figu e 4.4: Phase unc ion o a Mie sca e ing o a pa icle wi h uni a y no malized size
Volume Sca e ing Func ion
The olume sca e ing unc ion is he di e en ial sca e ing c oss sec ion pe uni olume. Using he abo e nomen-
cla u e, he VSF β(θ, λ) can be exp essed as he olume de i a i e o he sca e ed in ensi y, espec o he inciden
in ensi y pe uni a ea.
β(θ, λ) = dIsca (θ, λ)
Ei(λ)dV(4.15)
Whe e Ei(λ) is he inciden i adiance. This unc ion is impo an because i akes in o conside a ion he
pa icle concen a ion o he medium and in eg a ing i o e all di ec ion yields he sca e ing coe icien b(λ). This
coe icien and he abso p ion coe icien p esen ed abo e con o m he o e all ex inc ion coe icien as:
c(λ) = a(λ) + b(λ)
b(λ) = 2πZπ/2
0
β(θ, λ) sin θdθ(4.16)
The VSF can be ew i en as he p oduc o he sca e ing coe icien β(λ) and a phase unc ion ˜
β(θ, λ) which
de ines he angula dis ibu ion o he sca e ed adia ion. This phase unc ion can be cha ac e ized by he asym-
me y pa ame e go mean cosine, which is he a e age o he cosine o he sca e ing angle o e all sca e ing
di ec ions (Equa ion 4.17).
g= 2πZπ
0
˜
β(θ, λ) cos θsin θdθ(4.17)
This pa ame e models he “shape” o he phase unc ion and has been widely used in simula ion schemes
h ough he Henyey-G eens ein app oxima ion as i was commen ed in Chap e 3. This app oxima ion o phase
41
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
unc ions is no able o model he “peaky” na u e o Mie’s sca e ing o ela i e sizes nea o one. In addi ion,
Zhao and Sun demons a ed in [38] he poo accu acy o his app oxima ion. None heless, se e al au ho s use
Henyey-G eens ein unc ion (Equa ion 3.3) because i s in eg al has in e se and can be used in a closed o m o
gene a e andom di ec ions in a Mon e Ca lo in eg a ion scheme.
4.2.3 Re ac i e Index
The e ac i e index o a ma e ial is he ela ionship be ween he speed o ligh in i , espec o he speed o ligh
in acuum. This pa ame e de ines he delay o communica ion, and also has an impo an ole in he beha io
o e lec ions (Snell’s law) and u bulences. Gene ally, he e ac i e index o seawa e , no ed by nw, depends on
empe a u e, salini y and wa eleng h. The wa eleng h-dependence implies ch oma ic dispe sion, bu due o he
use o monoch oma ic sou ces and he educed ange o UWOC links, his e ec can be neglec ed. Ac ually, his
e ec can be neglec ed e en i wideband emi e s, such as YB-WLED, we e used, due o he e ec o abso p ion.
Se e al au ho s ha e empi ically i ed his dependence a e pe o ming di e en measu emen s. McNeil [119], in
Equa ion 4.18, and Ma h¨aus [120], in Equa ion 4.19, pe o med wo di e en a emp s o ob ain a ma hema ical
exp ession o he e ac i e index o seawa e wi hin he isible spec um.
nw(λ, S, T)=1.3247 −2.5·10−6T2+S2·10−4−8·10−7T+3300
λ2−3.2·107
λ4(4.18)
nw(λ, S, T) =1.447824 + 3.011 ·10−4S−1.8029 ·10−5T−1.6916 ·10−6T2−0.489λ+ 0.728λ2−0.384λ3−
S7.9362 ·10−7T−8.06 ·10−9T2+ 4.249 ·10−4λ−5.847 ·10−4λ2+ 2.812 ·10−4λ3(4.19)
Tempe a u e Tis in Celsius deg ees, salini y Sis in h, and he wa eleng h in mic ome e s. Figu e 4.5 depic s
he e ac i e index o seawa e a 15◦and 30 ho salini y o each wa eleng h. F om he abo e equa ions , i can
be obse ed ha he e ac i e index o seawa e is mo e sensi i e o salini y han o empe a u e luc ua ions.
Wa eleng h (nm)
400 450 500 550 600 650 700
nw(S, T, λ)
1.335
1.34
1.345
1.35
Figu e 4.5: Re ac i e index s wa eleng h o seawa e a 15◦and 30 ho salini y
Johnson e al. s udied he ela ionship be ween dep h and e ac i e index in o de o es ima e he expec ed
bending o he ligh ays [121], and i s e ec ega ding he poin ing be ween emi e and ecei e . Howe e , his
es ima ion depa s om a un ealis ic hypo hesis, since i conside s a s a i ied scena io ega ding e ac i e index.
This assump ion di ec ly implies an also s a i ied dis ibu ion o empe a u e and salini y, whils an ac ual scena io
canno be conside ed as a lamina pe ec ly-sepa able scena io. Rega dless his physical un ealism, due o he lack
o li e a u e analyzing his issue, hei app oxima ion may be conside ed as a alid s a ing poin .
4.2.4 Tu bulences
Op ical u bulence is a apid change o he seawa e ’s e ac i e index. These sha p changes may occu a any
dep h, and a e no mally a ibu ed o empe a u e a ia ions. Unlike u bulences in FSO, he powe spec um
o he e ac i e index depends on bo h empe a u e and salini y. The e o e, he adi ional Kolmogo o powe
42
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
spec um may p esen e o s modeling u bulences in oceanic en i onmen s, as Tang e al. s a ed in [46]. A e
in oducing he e ec o salini y, i yields he powe spec um p oposed by Nikisho e al. [122]:
Φ(κ) = C0−1/3κ−11/3χT
ω2h1+2.35(κη)2/3iφ(κ) (4.20)
C0= 3.88 ·10−9,is he dissipa ion a e o u bulen kine ic ene gy pe uni mass and anges om 10−8 o
10−2m2s−3, and χTis he a e o mean-squa e empe a u e dissipa ion anging om 10−10 o 10−4K2s−1. These
cons an s and anges a e based on he measu emen s p o ided by Ko o ko a e al. [123]. κis he scala spa ial
equency, η= 10−3is Kolmogo o ’s mic o-scale and ωis a pa ame e ha de ines he dominance o he u bulence
espec o salini y (ωnea o 0) o empe a u e (ωnea o -5). Finally, φ(κ) is a unc ion o he o m p esen ed in
Equa ion 4.21.
φ(κ) = ω2e−ATδ+e−ASδ−2ωe−AT S δ(4.21)
AS= 1.9·10−4,AT= 1.863 ·10−2and AT S = 9.41 ·10−3.δ= 8.284(κη)4/3+ 12.978(κη)2. A e nume ically
sol ing his equa ion o a gene al case (ω=−2), he esul ing powe spec um p esen s wo peaks which a e
ela ed o empe a u e and salini y luc ua ions (Figu e 4.6).
Figu e 4.6: Tu bulence powe spec um ob ained by Tang e al. [46] o ω=−2
As i can be obse ed, he oceanic u bulence powe spec um is e y di e en om Kolmogo o ’s −11/3 powe
law used in FSO. The e a e wo main aspec s o in e es ega ding u bulence analysis in communica ions. The
i s one is he u bulence a iance ela ed o he link’s ange (Ry o ’s a iance σ2
I), and he second one is he
empo al co ela ion.
Ry o ’s a iance, also known as scin illa ion index, was s udied by Fa well in his PhD disse a ion [124]. Fa well
concluded ha o gaussian-like lase emissions, he scin illa ion index akes he o m p esen ed in Equa ion se
4.22.
σ2
I( , L) =σ2
I,l(0, L) + σ2
I,l( , L)
σ2
I,l(0, L) =8π2k2LZ1
0Z∞
0
κΦ(κ)exp −ΛLκ2ξ2
k1−cos Lκ2
kξ(1 −ξ(1 −Θ))dκdξ
σ2
I,l( , L) =8π2k2LZ1
0Z∞
0
κΦ(κ)exp −ΛLκ2ξ2
k[I0(2Λ ξκ)−1]dκdξ(4.22)
ξ= 1 −z
Lis a no malized dis ance a iable and k he wa enumbe . I0(x) is he ze o h o de modi ied Bessel
unc ion whils Λ and Θ a e he ou pu plane pa ame e s. Fo an inciden plane wa e, hese las pa ame e s a e 0
and 1 espec i ely. In oducing his condi ion in o Equa ion 4.22, i yields:
σ2
I(L)=8π2k2LZ∞
0
κΦ(κ)dκ−Z1
0Z∞
0
κΦ(κ) cos Lκ2
kξdκdξ(4.23)
43

Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Fa well le he analysis a his poin , bu aking in o accoun he shape o he sinc in he second e m, he
in eg al may be app oxima ed o he i s oo o he sinc, hence:
σ2
I(L)≈8π2k2LZ∞
√πk
L
κΦ(κ)dκ(4.24)
To ob ain an app oxima ion o he scin illa ion index, he in eg als esul ing o he p oduc κΦ(κ) a e o he
o m shown a Equa ion 4.26. Depending on he condi ion o Equa ion 4.25, δcan be app oxima ed o he squa ed
e m o o he 4/3 powe . These wo app oxima ions could be applied depending on he shape o he κΦ(κ) p oduc .
In he end, he app oxima ions de ine an uppe and a lowe bound o he powe dependence o he scin illa ion
index.
δ≈


12.978(κη)2/ κη > 9.12
8.284(κη)4/3/ κη < 1.3·10−5
8.284(κη)4/3+ 12.978(κη)2/o he wise
(4.25)
Z∞
√πk
L
κ−ae−bκcdκ=ba−1
c
cΓ1−a
c, b (πk)c/2L−c/2(4.26)
Whe e Γ(s, x) is he uppe incomple e Gamma unc ion, and Γ(s, x)=(s−1)Γ(s−1, x) + xs−1e−x. Taking
in o accoun he decaying na u e o he exponen ials in ol ed in he la e exp essions, he Ry o ’s a iance o he
ocean u bulen channel would di ec ly depend on he highe powe o he link’s ange L. Taking in o accoun he
app oxima ions made in Equa ion 4.25, he dependence o he scin illa ion index espec o he link’s ange can be
app oxima ed o:
σ2
I(L)∝Lα/α ∈(3/2,11/6) (4.27)
A e imposing Taylo ’s ozen u bulence hypo hesis, which implies ha he empo al s a is ics a e ela ed o
he spa ial s a is ics, Tang e al. analyzed he empo al co ela ion o a lase -based emission unde weak u bulence
egime. They ob ained ha he co ela ion is almos independen on he link’s dis ance, whils is highly dependen
on he speed o seawa e .
These o mulae we e ob ained conside ing plane wa e p opaga ion, cohe en adia ion and neglec ing he e ec o
sca e ing. I sca e ing we e conside ed, he co ela ion be ween poin s would change due o he BSF. Fu he mo e,
i he adia ion we e non-cohe en , such as LED, Ry o ’s a iance would be d ama ically educed since in e e ence
e ec s would no occu . Fu he mo e, collima ed and cohe en emissions would su e om beam wande wi h a
highe p obabili y, whils LED emissions no .
4.2.5 Su ace e lec ions
The ocean su ace can be modeled as a supe posi ions o a eling sea wa es, usually modeled by a sea wa e
spec um, plus a noisy e m which depends on he wind s ess. This s ess p oduces a andom a ia ion on he
seawa e ’s su ace, whose PDF ollows a G am-Cha lie se ies as Cox and Munk demons a ed in [21]. The a ia ion
o he su ace is usually modeled azimu hally uni o m, and he a iance o he slope depends on he wind speed.
The ela ionship ha can be ob ained om Cox and Munk’s wo k ega ding wind speed is p esen ed in Equa ion
4.28. Ac ually, he a iance o he c osswind di ec ion and he upwind di ec ion sligh ly di e , bu o he pu poses
o his wo k he omnidi ec ional app oxima ion is alid.
σ2
su = 0.003 + 0.00512 wind /1< wind <14m ·s−1(4.28)
In an unde wa e - o-unde wa e scena io, andom su ace e lec ions may in oduce delayed addi ional powe
con ibu ions in a ho izon al link. Figu e 4.7 depic s he scena io unde conside a ion. A e a e lec ion, he
di ec ion o he ou pu ay ˆ e can be exp essed as a linea combina ion o bo h su ace no mal ec o ˆnsu and
inciden di ec ion ˆ i.
ˆ e = ˆ i−2<ˆ i,ˆnsu >ˆnsu (4.29)
A e he impac , pa o he inciden powe is e lec ed and pa is ansmi ed. The amoun o ene gy which
is e lec ed, RF esnel(θi), ollows F esnel’s equa ion (Equa ion 4.30). Addi ionally, o inciden angles abo e ce ain
limi (c i ical angle), he e is no ansmission o ene gy and o al in e nal e lec ion occu . This happens because
he ligh ays a el o a medium wi h a lowe e ac i e index, in he opposi e case, he e is no c i ical angle and
always pa o he ene gy is ansmi ed.
44
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Figu e 4.7: Re lec ion o ligh ays on he seawa e su ace
RF esnel(θi) = 1
2"sin(θ −θi)
sin(θ +θi)2
+ an(θ −θi)
an(θ +θi)2#(4.30)
θ is he e ac ed angle, which ollows Snell’s law nai sin θ =nwsin θi.
4.2.6 Seabed di usion
Di usi e e ec s a e a common phenomenon which is p oduced due o he sca e ing o ligh on a su ace. The e
a e many sca e ing unc ions which model he di usion depending on he p esence o no o specula componen s,
such as Phong o To ance. Howe e , as he seabed is no mally compound by sand, ock o co al ex ensions,
a Lambe ian app oxima ion is a comp omise solu ion. Equa ion 4.31 shows he e lec i i y o a Lambe ian
sca e ing, whils Figu e 4.8 depic s he scena io.
Figu e 4.8: Ligh sca e ing due o seabed di usion
Rseabed(θ, θi, ρseabed) = ρseabed ·cos θi·cos θ(4.31)
4.2.7 Op ical ouling
Op ical ouling is he deposi ion o ma e , no mally algae and phy oplank on, o e he anspa en shielding o
op ical emi e s in UWOC applica ions. This deposi ion has a di ec e ec on he e ec i e powe adia ed o he
medium. Depending on he ma e spec al esponse, he deposi ion densi y and i s hickness, he powe loss can
be modeled as an exponen ial decay (Equa ion 4.32). The ouling esis ance, β, is he a e a which he hickness
o he ouling, τ( ) inc eases. αdepends on he ouling densi y and he ype o pa icle, whils βdepends on he
ype o pa icle, he wa e speed, he empe a u e o he su ace and he bulk wa e empe a u e [125].
P x,e =P xe−α(ρ ouling,λ)τ( )(4.32)
The e a e di e en ypes o ouling esis ances depending on he na u e o he deposi ed ma e . Gene ally,
linea , alling and asymp o ic cu es a e used o model his phenomenon. The beha io o he ouling a e is ela ed
o he deposi ion a e and he emo al a e, being he di e ence o bo h. No mally, biological ma e ollows an
asymp o ic cu e, and Equa ion 4.33 shows he ma hema ical desc ip ion o he hickness in e ms o he ouling
esis ance.
τ( ) = τmax 1−e−β (4.33)
τmax is he asymp o ic maximum o he hickness. Including Equa ion 4.33 in o Equa ion 4.32, i yields:
P x,e =P xe−α(ρ ouling,λ)τmax(1−e−β )(4.34)
Figu e 4.9 depic s, o illus a i e pu poses, he e ec o ouling in he e ec i e emi ed powe . α ouling can be
exp essed in e ms o he mass densi y o chlo ophyll and i s abso p ion spec um, using Equa ion 4.5.
45
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (h)
0 10 20 30 40 50 60 70 80 90 100
Powe Loss (dB)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Figu e 4.9: E ec o op ical ouling on he e ec i e emi ed powe . P x = 1 W, β= 0.1 h−1,τmax = 10−2 m and
α(ρ ouling, λ) = 75.71 m−1wi h Cφ= 1 g ·m−3
4.2.8 Fauna
The e ec s o auna on he pe o mance o an UWOC link ha e no been s udied in dep h ye . None heless, i
would p esumably depend on he concen a ion o auna, he size o he indi iduals, i s mobili y and i s awa eness
espec o he used wa eleng h.
4.3 Simula ion o he UWOC impulse esponse
The RTT equa ion is di icul o sol e, and he ask becomes ha de when he andom na u e o he sca e ing by
pa icles is in oduced. Howe e , Mon e Ca lo in eg a ion o e s a simple and compu a ionally e icien al e na i e
o ob ain a solu ion o he ime-dependen RTT equa ion in any scena io. Analy ical solu ions can be ob ained
wi hou aking in o accoun nei he he andomness o he medium no he e ec o he seawa e su ace o seabed,
as Ja uwa anadilok ca ied ou in [33]. The main objec i e o his simula ion p ocess is o ob ain a ep esen a ion o
he UWOC impulse esponse and pe o m an analysis ela ing physical pa ame e s o communica ion-pe o mance
pa ame e s, such as channel gain and bandwid h.
4.3.1 Simula ed scena io
The simula ed scena io consis s in a h ee-dimensional olume bounded in he Y and Z axes. The Y-limi s a e
he seabed and he seawa e su ace, whils he Z-axis bounda ies a e he emission and ecep ion planes. The
phenomena included in he simula ion p ocess a e abso p ion, sca e ing by pa icles, di usi e e ec s on he seabed
and su ace e lec ions. Tu bulences and auna ha e no been conside ed because o hei s ochas ic na u e. In a
s ochas ic model, hese e ec s can be included as mul iplica i e ac o s, since hey p esen s a is ical independence.
Fu he mo e, LED emission is conside ed and hence pola iza ion and cohe ence a e neglec ed, easing he calcula ion.
Figu e 4.10 depic s he e ec s conside ed in he simula ion as well as he geome y o he p oblem. I can be obse ed
ha he emi e poin is he coo dina e o igin. The e o e, he dep h o he link is pa ame ized as a posi i e alue,
whils he seabed’s dep h is a nega i e alue.
4.3.2 Mon e Ca lo in eg a ion scheme
Mon e Ca lo in eg a ion is a nume ical in eg a ion echnique which andomly gene a es poin s wi hin he in eg a ion
domain. Le ’s conside he gene al mul idimensional de ini e in eg al in he domain Ω ∈Rnshown a Equa ion
4.35.
I=ZΩ
(~x)d~x (4.35)
The in eg a ion domain has a hype - olume Vo he o m:
46
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Figu e 4.10: Simula ed scena io
V=ZΩ
d~x (4.36)
Finally, Mon e Ca lo in eg a ion s a es ha he in eg al o Equa ion 4.35 can be app oxima ed o a summa ion
o he o m:
I≈V
N
N
X
i=1
(~xn) (4.37)
Whe e ~xna e andom sample poin s wi hin he domain Ω. This ype o in eg a ion is pa icula ly use ul when
dealing wi h complex p oblems such as he one unde conside a ion in his wo k. The UWOC impulse esponse can
be app oxima ed using a Mon e Ca lo app oach o e he RTT equa ion (Equa ion 4.1). This leads o an exp ession
o he o m:
h( )≈
M
X
i=1
Piδ −nw(λ)
c0
di(4.38)
Whe e Piis he weighed con ibu ion o he i- h a i ing ay, diis he a eled dis ance, and Mis he numbe
o e ec i e con ibu ions o he impulse esponse. Equa ion 4.39 shows how Piis ob ained, and Equa ion 4.40
de ines he delay su e ed by an a i ing ay.
Pi=P x
Ne−α(λ)di
Nh
Y
j=1
Lj(4.39)
di=
Nh
X
j=1
dj(4.40)
Nis he numbe o ays gene a ed a he emi e . In ui i ely, he adia ion pa e n is di ided in N di e en ial
solid angles, esul ing in a andom gene a ion o di ec ions o e he emi e ’s hemisphe e. Each ay is hen sca e ed
in many di ec ions depending on he mul iple andom collisions due o pa icles and he seabed. No e ha M6=N
because a e each collision wi h pa icles, a new bundle o ays is gene a ed. Nhis he numbe o hops (collision
e en s) ha a ay has made be o e a i ing he ecei e , djis he a eled dis ance a e he j- h collision, and Lj
is he j- h powe weighing applied o a ay. These las weigh s a e classi ied as ollows.
47
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
•GPU pa allel code. Pa allel compu ed code mus be embedded wi hin a CUDA ke nel. This code execu es
i s inne ins uc ions in he GPU using N blocks o h eads and M h eads pe block. Calls o ke nels mus
be ca ied ou as ke nel <<<Blocks,Th eads>>>(a gs).
•De ice unc ions. GPU code canno use hos -de ined unc ions. In o de o in oduce auxilia unc ions in o
he GPU, hese mus be de ined as de ice .
•A oid condi ional b anches. As he used GPU execu es he code using SIMD, when a condi ional b anch
occu s (ac ually a dependence on da a), some h eads a e deac i a ed and queued, blocking he execu ion.
•Ke nels a e no blocking. When he hos calls a ke nel, he GPU s a s he compu a ion and he hos is no
blocked, allowing he possibili y o pe o m some calcula ions un il he GPU ends. The hos only is blocked
when a de ice- o-hos memo y ope a ion is eques ed.
The ac ual pa alleliza ion was pe o med de ining he ini ial andom ay gene a ion ( o loop) as a ke nel, whils
unc ion g owAndHa es T ee() as a de ice unc ion. Fu he mo e, CUDA 2.0 did no o e a andom numbe
gene a o in GPU. Because o ha , a simple andom numbe gene a o o pe iod 220 [130] was implemen ed as
a de ice unc ion. Each h ead is ini ialized wi h a hos -gene a ed andom seed. Finally, all he hos - e sion
unc ions which used memcpy() ope a ions we e ans o med o a li e al e sion ( o loop wi h w i e sen ence)
since he GPU igno ed hos -de ined ope a ions.
4.4 Simula ion esul s
In his sec ion, se e al esul s a e ob ained om he implemen ed algo i hm. As communica ion-pe o mance
cha ac e is ics, channel gain and bandwid h a e calcula ed om he ob ained h( ). None heless, unlike indoo OWC
channels, whe e he impulse esponse may be conside ed ixed; in he case o UWOC, he scena io is con inuously
a ying due o mo emen o pa icles and he seawa e ’s su ace. Fu he mo e, he poin ing be ween unde wa e
emi e s and ecei e s is no pe ec and p esen s a a ia ion which depends on he ma ine cu en s. This e ec
has been neglec ed o simplici y, bu as well as u bulence and auna, i can be included as a mul iplica i e ac o
in an s ochas ic desc ip ion o he UWOC channel.
Channel gain is de ined as:
H(0) = Z∞
0
h( ) d (4.50)
In he case o he Mon e Ca lo in eg a ion, using Equa ion 4.38 and including i in o Equa ion 4.50,i yields
Equa ion 4.51. F om an implemen a ion- ela ed iewpoin , his magni ude can be ob ained as he sum o all he
con ibu ions sa ed in he 1- em osecond-sampled h( ) a ay.
H(0) ≈
NT−1
X
i=0
Pi(4.51)
Rega ding bandwid h, i is ela ed o delay sp ead by Equa ion 4.52.
B≈1
5τ ms
(4.52)
Whe e τ ms is he delay sp ead o he impulse esponse, de ined by Equa ion se 4.53
τ ms =s1
H(0) Z∞
0
(τ−¯τ)2h(τ)dτ
¯τ=1
H(0) Z∞
0
τh(τ)dτ(4.53)
The ac ual implemen a ion uses he same concep as Equa ion 4.51, con e ing in eg als o sums as shows
Equa ion se 4.54
τ ms ≈10−15
u
u
1
H(0) NT−1
X
i=1
i2Pi!−¯
i2
¯
i≈H(0)
NT−1
X
i=1
iPi(4.54)
54

Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
In o de o analyze he e ec o he geome ical and physical link’s pa ame e s on he impulse esponse, a
baseline scena io was de ined. Table 4.1 shows he pa ame e s.
Pa ame e Value
Recei e ’s posi ion (0,0,5 m)
Pho odiode’s a ea Apd = 20 mm2
Di ec i i y m= 1
T ansmi ed powe 1 W
Wa eleng h 470 nm
Pa icle adius 500 nm
Pa icle e ac i e index 1.25 (lossless)
Concen a ion o pa icles 3.3·1011m−3
Dis ance o su ace 5 m
Agi a ion o he su ace σ2
su = 0.0081 ( wind = 1 m ·s−1)
Dis ance o seabed 5 m
Seabed’s e lec i i y ρseabed = 0.5
Numbe o ays 106
MAXHOPS 12
Table 4.1: Pa ame e s o he baseline scena io
A e modi ying he pa ame e o in e es , se e al uns o he simula ion a e pe o med in o de o a e age he
esul s. Conc e ely, o ob ain a end o he in luence o each pa ame e , 100 uns we e ca ied ou pe speci ic
scena io. The esul s ega ding he impac o each a o emen ioned pa ame e on he impulse esponse a e discussed
in he ollowing subsec ions. The swep in e al o each pa ame e will be p esen ed, sample images o he impulse
esponse a he wo bounda ies will be depic ed, and inally, a cu e showing he in luence on bo h channel gain
and bandwid h will be also p esen ed and commen ed.
Fu he mo e, he ob ained channel gain H(0) has been calcula ed aking in o accoun he emi e ’s adia ion
pa e n bu no malizing espec o he pho ode ec o ’s a ea. The e o e, he uni s o he calcula ed H(0) a e W/m2.
4.4.1 E ec o he link’s ange
In his case, he link’s ange has been swep om 1 me e o 10 me e s. The impulse esponses associa ed o he
bounda ies o he in e al can be obse ed in Figu e 4.14. The b oadening o he esponse is clea ly obse ed,
whils he educ ion o he o e all powe is e iden .
Time (ns)
4.6 4.8 5 5.2 5.4
H(0) dB
-140
-120
-100
-80
-60
-40
-20
0D= 1 m
Time (ns)
44.6 44.8 45 45.2 45.4 45.6
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50 D= 10 m
Figu e 4.14: Impulse esponses a di e en anges
The exponen ial decay o he ligh in ensi y can be obse ed in Figu e 4.15. This decay also a ec s he
bandwid h, which also is diminished due o he g ea e amoun o mul ipa h componen s due o mul iple sca e ing.
I can be s a ed ha he e is an impo an exponen ial dependency o bo h pa ame e s wi h he link’s ange.
55
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Dis ance (m)
1 2 3 4 5 6 7 8 9 10
H(0) dB
-50
-40
-30
-20
-10
0
Bandwid h (GHz)
1
2
3
4
5
6
H(0)
Bandwid h
Figu e 4.15: Dependency o H(0) and Bwi h dlink
4.4.2 E ec o he link’s dep h
A p io i, he link’s dep h should ha e a signi ican impo ance since i de ines he s eng h o he e lec i e compo-
nen s o he impulse esponse. None heless, he mean alue o he channel gain does no e lec a clea ela ionship
wi h he link’s dep h, no he bandwid h does. Figu e 4.16 illus a es he bounda ies o he swep ange whils
Figu e 4.17 shows he dependency o H(0) and Bwi h he link’s dep h.
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-120
-100
-80
-60
-40
-20 dsu = 0.25 m
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40 dsu = 2 m
Figu e 4.16: Impulse esponses a di e en dep hs
The andom na u e o he impulse esponse will be discussed in de ail in Chap e 6, bu a Wilcoxon es
o compa e medians has been pe o med in o de o analyze he in luence o he dep h on he s udied channel
pa ame e s. The analysis yields a p- alue o 0.0508 be ween he ob ained alues a dsu = 0.25 me e s and
dsu = 2 me e s, which assu es wi h almos a 5 % o con idence ha he link’s dep h has in luence on he channel
gain. In he case o he bandwid h, he es s e u ns a p- alue o 3.5·10−6, which implies almos ce ain y abou
he dependency.
4.4.3 E ec o he su ace agi a ion
The wind speed p oduces an azimu hally-symme ic andom slope on he seawa e su ace. This andom a ia ion
has se e al e ec s. On he one hand, a a iable su ace has mo e p obabili y o p oduce e lec ions di ec ly o he
ecei e , whils a quie su ace only has a small illumina ed a ea whose e lec ions p oduce powe con ibu ions.
56
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Dep h (m)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
H(0) dB
-30.5
-30
-29.5
-29
Bandwid h (GHz)
2.75
2.8
2.85
2.9
H(0)
Bandwid h
Figu e 4.17: Dependency o H(0) and Bwi h dsu
On he o he hand, he delay associa ed o he main geome ical e lec i e componen (de ined by Snell’s law) a e
“sp ead” as he agi a ion inc eases, since he Beam Sp ead Func ion o he medium (due o mul iple sca e ing)
widens he e ec i e su ace a ea wi h signi ican con ibu ions. Figu e 4.18 depic s he impulse esponses o he
bounda ies o he swep wind speed. No e ha he ci cled a eas in ol e he main e lec i e componen delay. In
his case, due o he geome y o he scena io, is loca ed close o 22.4 nanoseconds.
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40 wind = 0 m/s
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-120
-100
-80
-60
-40
-20 wind = 10 m/s
Figu e 4.18: Impulse esponses a di e en wind speeds o a dep h o 0.25 me e s
Figu e 4.19 shows he de ail o he ci cled a ea. Fo a s ill seawa e su ace, he geome ical e lec i e componen s
a e loca ed su ounding he heo e ical delay. None heless, o a agi a ed su ace, his componen s a e sp ead.
Rega ding he in luence o he wind speed on he channel pa ame e s, as he wind speed inc eases, he bandwid h
and he channel gain inc ease oo. This end is absolu ely complian wi h he abo e discussion on he sp eading
o he e lec i e componen s.
4.4.4 E ec o he dis ance o seabed
The seabed was modeled as a Lambe ian sca e , whose e lec i i y anges in he in e al [0,1]. Figu e 4.21
illus a es he e ec o he dis ance o seabed on he impulse esponse. A seconda y spike can be obse ed nex o
22.6 nanoseconds a he close- o-seabed scena io. This delay implies a a eled dis ance o 5.067 me e s. Taking
in o accoun he geome y o he p oblem, he e a e wo impac poin s on he p ojec ion o he poin ing ec o
57
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (ns)
22.32 22.34 22.36 22.38 22.4
H(0) dB
-120
-110
-100
-90
-80
-70
-60
-50
-40 wind = 0 m/s
Time (ns)
22.32 22.34 22.36 22.38 22.4
H(0) dB
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30 wind = 10 m/s
Figu e 4.19: De ail o he ci cled a ea o Figu e 4.18
σ2
wind
0 0.01 0.02 0.03 0.04 0.05 0.06
H(0) dB
-29.8
-29.75
-29.7
-29.65
-29.6
-29.55
Bandwid h (GHz)
2.75
2.76
2.77
2.78
2.79
2.8
H(0)
Bandwid h
Figu e 4.20: Dependency o H(0) and Bwi h wind
o e he seabed ha gene a e con ibu ions wi h his delay: 4.5 me e s and 0.5 me e s (The e is ac ually an ellipse
on he seabed whose associa ed delay is 22.6 nanoseconds). Since he adia ion pa e n and he di usion pa e n
a e he same, he weighing o bo h main di usi e con ibu ions a e also he same by igonome y.
I can be obse ed ha o 2 me e s, he e is no appa en con ibu ion o he seabed. The e ec o he dis ance
o seabed is shown in Figu e 4.22. As i is ob ious, he bandwid h is inc eased as he dis ance o seabed is
inc emen ed. Howe e , he e is no an app eciable impac on he channel gain. As i was done abo e, a Wilcoxon
es was ca ied ou o p o e he in luence o he dis ance o seabed on he channel gain. In his case, he es
e u ned a p- alue o 0.65, being impossible o assu e ha he dis ance o seabed has in luence on he channel gain.
4.4.5 E ec o he seabed’s e lec i i y
In he p e ious subsec ion, i was demons a ed ha he dis ance o seabed does no ha e a signi ican impac on
he channel gain. In his case, o dseabed = 0.25 me e s, he expec ed impac o he e lec i i y on he channel
gain would be p esumably he same. Figu e 4.23 depic s he impulse esponse o he a o emen ioned scena io o
a o ally abso bing seabed and a e y e lec i e one. The e is no di e ence be ween he igh g aph o Figu e 4.23
and he le g aph o Figu e 4.21.
Figu e 4.24 depic s he ob ained mean channel pa ame e s espec o he seabed’s e lec i i y. The e is no
signi ican impac on any o he pa ame e s, and he Wilcoxon es e u ns a p- alue abo e 0.9 o bo h cases.
58
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40 dseabed = 0.25 m
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40 dseabed = 2 m
Figu e 4.21: Impulse esponses a di e en dis ances o he seabed
Dis ance o seabed
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
H(0) dB
-30
-29.8
-29.6
Bandwid h (GHz)
1
2
3
H(0)
Bandwid h
Figu e 4.22: Dependency o H(0) and Bwi h dseabed
Howe e , only lambe ian-sca e ing seabed has been es ed and in u he esea ch, he use o o he di usion
pa e ns should be es ed.
4.4.6 E ec o he emi e ’s di ec i i y
The emi e di ec i i y is ela ed o he concen a ion o he emi ed ene gy in a na owe solid angle. I is logical
ha a mo e di ec i e emi e would gene a e a be e esponse on he ecei e , whils he mul ipa h would be
conside ably educed due o he dec emen o he illumina ed olume o wa e . Figu e 4.25 depic s he impulse
esponse o a pu e lambe ian emi e (le g aph) and o an emi e wi h θ1/2= 12◦. I is easily no iced ha
he di ec i e emi e p esen s a na owe and mo e ene ge ic impulse esponse.
The ela ionship be ween di ec i i y and he channel pa ame e s is p esen ed in Figu e 4.26. A log-like de-
pendency can be easily ex ac ed om he a ailable da a. In he limi , channel gain and bandwid h end o he
pa ame e s o a lase -like link, which is de ined by he BSF.
4.4.7 E ec o he wa eleng h
The wa eleng h di ec ly a ec s a enua ion, sca e ing and p opaga ion delay. Since he edde wa eleng hs a e
mo e a enua ed han he ones in he blue-g een egion, he channel gain is di ec ly a ec ed by he beha io o he
59

Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-120
-100
-80
-60
-40
-20 ρseabed = 0
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40 ρseabed = 1
Figu e 4.23: Impulse esponses a di e en seabed e lec i i y coe icien s o dis ance o seabed o 0.25 me e s
Re lec i i y
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
H(0) dB
-29.8
-29.6
-29.4
Bandwid h (GHz)
2.75
2.8
2.85
H(0)
Bandwid h
Figu e 4.24: Dependency o H(0) and Bwi h ρseabed
a enua ion coe icien . Fu he mo e, he e ac i e index o seawa e is highe o longe wa eleng hs. The e o e,
he excess delays a e highe in a ed-emission scena io, educing he bandwid h. Figu e 4.27 depic s he impulse
esponse o a 470 nm and a 660 nm emission, whils Figu e 4.28 illus a es he a o emen ioned dependency o he
pa ame e s.
4.4.8 E ec o he pa icle size
As i was commen ed in Sec ion 4.2.2, he no malized size o a pa icle di ec ly a ec s he shape o he sca e ing
phase unc ion. The lowe he no malized size, he mo e simila he phase unc ion o a Rayleigh sca e ing, which
p esen s a e y b oad dispe si e p o ile. Howe e , he highe he no malized size, he na owe he phase unc ion.
In he limi , he phase unc ion ends o a Di ac’s del a, only a ec ing he p opaga ion adding wa eleng h-dependen
scala losses. The le g aph o Figu e 4.29 illus a es he impulse esponse wi h a low no malized size, whils he
igh one shows he channel esponse o a pa icle wi h no malized size close o 1.
Rega ding he e ec s o he pa icle adius on he impulse esponse, small adii ha e b oad phase unc ions,
which ha e associa ed also b oad BSFs. This b oadening ha has been commen ed se e al imes in his documen
is he main eason o he elaxa ion o he poin ing be ween emi e and ecei e . In he p esen ed scena io, a wide
BSF p oduces a low channel gain bu a high bandwid h, as shows Figu e 4.30. The e o e, i may be concluded ha
he channel gain is in e sely p opo ional o he pa icle adius whils he bandwid h p esen s di ec p opo ionali y.
60
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-120
-100
-80
-60
-40
-20 θ1/2= 60◦
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-120
-100
-80
-60
-40
-20 θ1/2= 12◦
Figu e 4.25: Impulse esponses a di e en di ec i i y alues
Di ec i i y
0 5 10 15 20 25 30 35
H(0) dB
-30
-25
-20
Bandwid h (GHz)
2
4
6
H(0)
Bandwid h
Figu e 4.26: Dependency o H(0) and Bwi h he emi e ’s di ec i i y
A local maximum can be obse ed in he channel gain cu e. I s loca ion depends on he pa icle concen a ion,
which implici ly de ines he sca e ing coe icien b(λ). This e ec has a special ea men in Chap e 6
4.4.9 E ec o he concen a ion o pa icles
As i has been commen ed, he concen a ion o pa icles join o he sca e ing phase unc ion de ines he sca e ing
coe icien . The o al ex inc ion is, hence, de ined by he las wo e ms combined o he inhe en op ical abso p ion
o he medium. As in he case o he pa icle adius, he concen a ion b oadens he BSF since i de ines he amoun
o sca e ings pe uni olume. Figu e 4.31 illus a es he impulse esponses associa ed o he bounda ies o he
swep ange.
Figu e 4.32 depic s he dependency o he channel pa ame e s wi h he concen a ion o pa icles. Fo a pa icle
adius o 100 nanome e s, i can be obse ed ha he channel gain inc eases in he swep ange, bu i s conca e
cu a u e in ui i ely o esees a end change. Rega ding he bandwid h, i a ies in a e y na ow in e al, bu
his pa ame e p esen s in e se p opo ionali y.
61
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-140
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40 λ= 470 nm
Time (ns)
22.2 22.4 22.6 22.8 23 23.2
H(0) dB
-130
-120
-110
-100
-90
-80
-70
-60
-50 λ= 660 nm
Figu e 4.27: Impulse esponses a di e en wa eleng hs
Wa eleng h (nm)
460 480 500 520 540 560 580 600 620 640 660
H(0) dB
-40
-30
-20
Bandwid h (GHz)
1
2
3
H(0)
Bandwid h
Figu e 4.28: Dependency o H(0) and Bwi h he emi ed wa eleng h
4.4.10 Pa alleliza ion speedup and e iciency
In his sec ion, he speedups and e iciencies (speedup espec o numbe o physical p ocesso s) ela i e o he
pa alleliza ion o he algo i hm a e p esen ed. As a i s esul , he i e a i e e sion o he code espec o he ini ial
ecu si e e sion o e ed an speedup o be ween 18 and 22. The simula ion scena io p esen ed as baseline scena io,
was execu ed in an a e age ime o 68381.74 ms. This esul will also se e as he e e ence ime o calcula e he
speedups.
OpenMP
Table 4.2 shows he speedups and e iciencies o di e en OpenMP schedulings and and numbe o h eads. Using
OpenMP wi hou any ype o scheduling is e y ine icien . The ee-like s uc u es gene a ed du ing he calcula ion
p ocess ha e andom wid hs and dep hs. The e o e, he execu ion imes o each h ead could highly di e , ixing
he compu a ion ime o he slowe one. Because o ha , s a ic and dynamic scheduling ypes we e used, looking
o an e iciency enhancemen .
I can be obse ed ha he chunk size does no a ec s a ic scheduling, as all he h eads mus be synch onized
be ween he calcula ion o consecu i e chunks. The e is an e iciency enhancemen espec o he no-scheduling
case, bu he synch oniza ion p oblem s ill exis s, e en hough a a lowe scale.
Finally, dynamic scheduling o e s he bes solu ion due o he andomness o he execu ion ime. Each ime
62
Chap e 4. Impulse Response o he Unde wa e Wi eless Op ical Channel
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-90
-85
-80
-75
-70
-65
-60
-55
-50
-45
-40 R= 100 nm
Time (ns)
22.4 22.6 22.8 23 23.2
H(0) dB
-150
-140
-130
-120
-110
-100
-90
-80
-70 R= 1µm
Figu e 4.29: Impulse esponses a di e en pa icles sizes
Radius (nm)
100 200 300 400 500 600 700 800 900 1000
H(0) dB
-70
-60
-50
-40
-30
-20
Bandwid h (GHz)
0
2
4
6
8
10
H(0)
Bandwid h
Figu e 4.30: Dependency o H(0) and Bwi h he pa icle adius
a h ead inishes he compu a ion o a chunk o i e a ions, i e ie es a new chunk o i e a ions om he pool.
None heless, he maximum speedup o each con igu a ion is e y simila . The di e ence be ween he bes con ig-
u a ion and he wo s is app oxima ely an 8 %, which depending on he p oblem, i may ep esen a signi ican
amoun o ime. Fu he mo e, since he used hos was based on a Xeon p ocesso (8 physical h eads and 16 i ual
h eads), he e iciency a 32 h eads is also e y simila .
CUDA
The used GPU has 448 co es o pe o m calcula ions. Howe e , speedups nex o he numbe o co es can no
be achie ed because, as i was commen ed abo e, GPU’s ope a e in a h ead-wise manne , and he code was
p og ammed using condi ional b anches. The e o e, he majo i y o he mul ip ocesso s will un only a single h ead
a a ime. Rega dless his limi a ion, he speedups ob ained wi h his echnology will su pass any mul ip ocesso
a chi ec u e jus by ha dwa e b u e o ce.
The esul s ha e been ob ained using 2N h ead blocks and 2M h eads pe block (N∈[0,10] and M∈[0,8]),
in an e o o isualize how he GPU deals wi h di e en memo y con igu a ions.
The o al memo y- ansac ion o e head was measu ed in 3 ms app oxima ely. Hence, he CUDA ke nel execu-
ion ime and he whole algo i hm execu ion ime will be p ac ically he same.
The e iciency o a pa allel algo i hm is measu ed espec o he numbe o ac i e p ocesso s du ing he execu ion.
63
Chap e 5. Conside a ions in Unde wa e - o-Ai links
Figu e 5.2: Lensing e ec o he seawa e su ace
ay ˆ may be de ined as a linea combina ion o hese ec o s, as shows Equa ion 5.11. γ is he e ac ed angle.
ˆ =nwˆ + (cos γ −nwcos γi) ˆn(5.11)
The coe icien s esul ing om Snell’s law can be exp essed in e ms o ˆ and ˆn, yielding:
ˆ =nwˆ +p1−n2
w(1−<ˆ , ˆn >2)−nw<ˆ , ˆn >ˆn(5.12)
This las exp ession is compu a ionally mo e e icien han Equa ion 5.11, since he scala p oduc <ˆ , ˆn >=
cos γiis easily calcula ed and does no imply he use o anscenden unc ions. As i was commen ed abo e, a
change o basis has been used o e e he in eg a ion limi s o a i ual pho odiode loca ed o e he su ace. I is
supposed ha do no exis nei he sp ay no pa icles be ween seawa e and pho odiode. The p oposed change o
basis is p esen ed in he nex exp ession.
x0=x+ ∆x(x, y)
y0=y+ ∆y(x, y) (5.13)
Figu e 5.3 depic s he meaning o his nonlinea change o basis. No e ha he e ms ∆x(x, y) and ∆y(x, y)
e e o he dis ance a ay a els in each di ec ion be o e impac ing he ecei e ’s XY plane. This de ia ion
depends on he ecei e ’s heigh Hand he e ac ion, as Equa ion se 5.14 shows.
Figu e 5.3: G aphical in e p e a ion o he nonlinea change o basis
70

Chap e 5. Conside a ions in Unde wa e - o-Ai links
∆x(x, y)=[H−S(x, )] x
z
∆y(x, y)=[H−S(x, )] y
z
(5.14)
Finally, he p ojec ed a ea o he pho odiode can be ob ained in e ms o he in e se ans o ma ion (Demon-
s a ion o he exis ence o in e se in Appendix A). Ac ually, due o he cha ac e is ics o he seawa e su ace, he
ec angula a ea o he pho odiode would no be p ojec ed as a ec angula a ea bu as a cu ed one. Howe e , due
o he small-slope es ic ion imposed in his wo k, he e o o assuming a ec angula p ojec ion will be negligible.
The e o e, he p ojec ed a ea can be calcula ed using equa ion 5.15.
A0
pd ≈x(2)
L−x(1)
L·y(2)
L−y(1)
L(5.15)
Whe e x(
Li) and y(i)
Lco espond o he p ojec ed co ne s o he pho odiode a e sol ing he nonlinea sys ems
o equa ions:
+xL=x(1)
L+ ∆x(x(1)
L, y(1)
L)
+yL=y(1)
L+ ∆x(x(1)
L, y(1)
L))
−xL=x(2)
L+ ∆x(x(2)
L, y(2)
L)
−yL=y(2)
L+ ∆x(x(2)
L, y(2)
L))(5.16)
Figu e 5.4 shows he e olu ion o he a e age ecei ed powe in he scena io de ined in Table 5.1. The sys ems
o equa ions we e sol ed using he ixed poin me hod.
Pa ame e Value
Wa eleng h 3 m
Pe iod 2 s
Wa e heigh 25 cm
Dep h 3 m
Recei e ’s heigh 2 m
Pho odiode’s a ea 9 cm2
Emi e powe 1 W
Di ec i i y m= 1
Ex inc ion coe icien c(λ)=0.305
Table 5.1: Unde wa e - o-ai baseline scena io
I can be obse ed ha he ene gy loss due o he s e ching o he p ojec ed a ea can imply a educ ion o
mo e han 3 dB o he example scena io. I wind we e conside ed, each poin o he sea wa e su ace would
beha e ollowing a no mal dis ibu ion on i s slope. The shea e ec due o wind would p oduce a educ ion o he
ecei ed powe and in his case, a pseudo-analy ical solu ion as he p esen ed abo e should no be used. The nex
sec ion in oduces he ollowed simula ion p ocedu e used o ob ain he ecei ed powe in a windy scena io.
5.3 Simula ion p ocedu e
Unlike he simula ion o unde wa e - o-unde wa e links, unde wa e - o-ai links a e limi ed by he seawa e su ace.
As i was commen ed in Chap e 4, when a ligh ay impac s on he su ace, pa o he ene gy is e lec ed, and he
o he pa e ac ed. The di ec ion o he e ac ed ay depends on he su ace’s no mal ec o and he inciden
ay’s di ec ion. Since he e is no di usi e e ec s, he app oach used o accele a e he con e gence in unde wa e -
o-unde wa e scena ios can no be used in his case. The e o e, a adi ional MCRT algo i hm was implemen ed
o calcula e he ecei ed powe . Algo i hm 3 shows he pseudo-code o he implemen ed simula o .
Rou ine calcula eImpac () sol es he nex equa ion in ρ, which is he dis ance ha a ay a els be o e
impac ing he su ace in a di ec ion de ined by (θ, φ).
ρ
cos θ=D+η0cos (ω −kρ sin θcos φ) (5.17)
On he o he hand, calcula eRe ac ion() calcula es he andom incidence angle and he F esnel loss. Finally,
he ou pu di ec ion is p ojec ed o he ecei e ’s plane using he ans o ma ion o Equa ion se 5.13.
71
Chap e 5. Conside a ions in Unde wa e - o-Ai links
Time (s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P x (dBm)
-58
-56
-54
-52
-50
-48
-46
-44
Figu e 5.4: E olu ion o he ecei ed powe s ime o he pa ame e s o Table 5.1
.
Algo i hm 3 Unde wa e - o-ai simula o
1: o N Random ays do
2: ay ←newRandomRay:
3: calcula eImpac (): Calcula es he impac on he su ace
4: calcula eRe ac ion(): Calcula es he ou pu di ec ion and F esnel loss
5: i Impac s on he ecei e hen
6: Sum con ibu ion
7: end i
8: end o
5.4 Simula ion esul s
In his sec ion, se e al simula ion esul s a e p esen ed in a simila way as in Chap e 4. In his case, he swep
pa ame e s a e dep h, ecei e ’s heigh , sea wa e heigh and wind speed ( espec o he baseline scena io o Table
5.1). Fu he mo e, a e commen ing he in luence o each pa ame e on he ecei ed powe , he channel a ailabili y
will be b ie ly discussed.
The channel a ailabili y is de ined as he amoun o ime he ecei ed signal is o e a h eshold le el S. This
pa ame e is c i ical since i de ines he p obabili y o loss he connec ion. Exp ession 5.18 shows he ma hema ical
desc ip ion in e ms o he PDF a each ins an X(X, τ), and he sea wa e pe iod T.
Tch =1
TZT
0
τZ∞
S
X(X, τ) dXdτ(5.18)
The ollowing cu es ep esen only one hal o he sea wa e pe iod. Due o he space- ime symme y o he
seawa e su ace, one hal o he pe iod is enough o isualize he beha io o he ecei ed powe .
5.4.1 E ec o he emi e ’s dep h
The po ion o he link which is pe o med unde wa e is subjec o ex inc ion. In his case, an ex inc ion coe icien
o 0.305 (Coas al wa e ) has been selec ed. I his coe icien we e a ied, only he a e age ecei ed powe would be
diminished o inc eased, no he shape o he ecei ed powe espec ime. Hence, he main e ec o he emi e ’s
dep h is he highe a enua ion dis ance c(λ)D. In Figu e 5.5, i can be obse ed ha he ecei ed wa e o m is
almos unchanged, bu he o se le el is de ined by he a enua ion dis ance c(λ)D.
5.4.2 E ec o he ecei e ’s heigh
The heigh has di ec in luence on he lensing e ec o he seawa e . The highe he ecei e is loca ed, he wide he
illumina ed a ea du ing he conca e pe iods o he sea su ace ha allow a bigge collec ion o ligh . None heless,
72
Chap e 5. Conside a ions in Unde wa e - o-Ai links
Time (s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P x (dBm)
-90
-80
-70
-60
-50
-40
-30
D=5 m
D=7 m
D=9 m
D=3 m
D=1 m
Figu e 5.5: E ec o he emi e ’s dep h on he ecei ed powe
when he heigh inc eases, he maximum-minimum dis ance is also inc eased, since he lensing e ec ac s in an
opposi e way du ing con ex pe iods. This e ec can be obse ed in Figu e 5.6.
Time (s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P x (dBm)
-85
-80
-75
-70
-65
-60
-55
-50
-45
-40
-35
H=9 m
H=7 m
H=5 m
H=3 m
H=1 m
Figu e 5.6: E ec o he ecei e ’s heigh on he ecei ed powe
5.4.3 E ec o he sea wa e heigh
The sea wa e heigh , join o he wa eleng h o he sea wa e, de ines he slope o a monoch oma ic wa e. This
slope has a di ec in luence on he de ia ion o he illumina ed a ea ha con ibu es o he ecei ed powe . As
he sea wa e heigh inc eases, he maximum slope is inc emen ed p opo ionally and also he maximum de ia ion
o he pho ode ec o ’s p ojec ed a ea. Fu he mo e, his de ia ion has a F esnel loss associa ed o he incidence
angle. I his angle is inc eased, he minimum o he ecei ed wa e o m is educed, as shows Figu e 5.7.
Figu e 5.8 depic s he ajec o y ha ollow he co ne s o he pho odiode o e he su ace, acco ding o
Equa ion 5.13. The e ec commen ed abo e can be obse ed o wo di e en alues o η0. No e ha he highe
η0, he la ge he pe ime e o he cu e.
Fu he mo e, Figu e 5.9 illus a es he beha io o he p ojec ed a ea. I can be obse ed ha high alues o
η0in oduce adings be ween he con ex and conca e si ua ions, whils lowe alues p oduce e y small a ia ions
as expec ed.
73
Chap e 5. Conside a ions in Unde wa e - o-Ai links
Time (s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P x (dBm)
-62
-60
-58
-56
-54
-52
-50
-48
η0=0.10 m
η0=0.21 m
η0=0.05 m
η0=0.01 m η0=0.02 m
Figu e 5.7: E ec o he sea wa e heigh on he ecei ed powe
∆x
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
∆y
×10-3
-5
-4
-3
-2
-1
0
1
2
3
4
5
η0= 25 cm
η0= 1 cm
Lowe co ne s
Uppe co ne s
Figu e 5.8: T ajec o y ollowed by he co ne s o he pho odiode o e he seawa e su ace acco ding o Equa ion
5.13
5.4.4 E ec o he sea wa e wa eleng h
As i was commen ed abo e, wa eleng h and pe iod a e ela ed h ough he dispe sion ela ion. In o de o co ec ly
analyze he in luence o he wa eleng h on he ecei ed powe , his ela ion mus be sa is ied o each pai (T, λ).
The expec ed e ec due o wa eleng h is simila o he e ec because o η0. Figu e 5.10 shows he in luence o λ
in no malized ime uni s. As λinc eases, he slope o he seawa e su ace is dec eased, limi ing he maximum
de ia ion o he p ojec ed a ea.
5.4.5 E ec o he wind speed
The wind speed in oduces a andom noise on he sea su ace slope due o s ess. The noise a iance is linea ly
ela ed o he speed and is no mally dis ibu ed on ele a ion and uni o mly dis ibu ed on azimu h. The a p io i
e ec o he wind speed would be a educ ion o he peak- o-peak alue o he ecei ed powe , since each illumina ed
spo o he sea su ace would ha e a p obabili y o gene a e ene gy on he ecei e . Figu e 5.11 depic s he e ec
o wind speed on he ecei ed en elope.
5.4.6 Channel a ailabili y
The ollowing igu es depic he channel a ailabili ies o he simula ed scena ios espec o he ecei e ’s sensi i i y.
This sensi i i y is he minimum de ec able op ical powe . In Figu es 5.12 and 5.13, i can be obse ed ha he
74
Chap e 5. Conside a ions in Unde wa e - o-Ai links
Time (s)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
P ojec ed A ea
×10-5
0
1
2
3
4
5
6
7
8
9
η0= 25 cm
η0= 1 cm
Figu e 5.9: P ojec ed pho odiode’s a ea s. ime o di e en alues o η0
No malized ime
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
P x (dBm)
-62
-60
-58
-56
-54
-52
-50
-48
λ=7.00 m
λ=5.00 m
λ=3.00 m
λ=9.00 m
λ=11.00 m
λ=13.00 m
λ=15.00 m
Figu e 5.10: E ec o he sea wa e wa eleng h on he ecei ed powe
dis ance o emi e and ecei e o he seawa e in e ace inc emen he sensi i i y equi emen s o he ecei e .
Fu he mo e, he elaxed slope o he cu es deno e la ge peak- o-peak a iabili y on he ecei ed powe .
Figu e 5.14 illus a es he e ec o he sea wa e heigh on he channel a ailabili y. La ge sea wa es imply highe
a ia ions o he seawa e ’s slope, and hence, a g ea e peak- o-peak a ia ion on he ecei ed powe . This e ec is
simila o he obse ed in Figu e 5.15, whe e he inc emen o he sea wa e wa eleng h elaxes he su ace’s slope
and he sensi i i y equi emen s.
Finally, in Figu e 5.16, he e ec o wind speed is depic ed. As i was obse ed in he p e ious subsec ion, he
shea e ec o he wind on he su ace p oduces a educ ion on he mean ecei ed powe , bu also a dec emen o
he maximum powe de ia ion. The e o e, wind speed helps o mi iga e he e ac i e losses due o he changes on
he su ace’s slope.
Du ing his chap e , he p oblem o an unde wa e - o-ai link has been add essed. I has been obse ed ha
he sea su ace pa ame e s ha e c i ical impo ance on he pe o mance o he communica ions link, inc emen ing
he sensi i i y equi emen s on he ecei e . Fu he mo e, i has been obse ed ha he wind speed ac s as a
smoo hing pa ame e , educing he ha m ul e ec o highly a iable su aces.
75

Chap e 5. Conside a ions in Unde wa e - o-Ai links
Time (s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P x (dBm)
-62
-60
-58
-56
-54
-52
-50
-48
-46
wind=18 m/s
wind=0 m/s
wind=2 m/s
Figu e 5.11: E ec o he wind speed on he ecei ed powe
Recei e ’s sensi i i y (dBm)
-100 -90 -80 -70 -60 -50 -40 -30
Tch
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
D=1
D=9 D=7 D=5 D=3
Figu e 5.12: Channel a ailabili y o di e en dep hs
Recei e ’s sensi i i y (dBm)
-100 -90 -80 -70 -60 -50 -40 -30
Tch
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
H=1
H=3H=5H=7H=9
Figu e 5.13: Channel a ailabili y o di e en ecei e heigh s
76
Chap e 5. Conside a ions in Unde wa e - o-Ai links
Recei e ’s sensi i i y (dBm)
-70 -65 -60 -55 -50 -45 -40
Tch
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
η0=0.01
η0=0.21 η0=0.1
η0=0.02
η0=0.05
Figu e 5.14: Channel a ailabili y o di e en sea wa e heigh s
Recei e ’s sensi i i y (dBm)
-70 -65 -60 -55 -50 -45 -40
Tch
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ=3 λ=5 λ=7 λ=9
λ=11
λ=13
λ=15
Figu e 5.15: Channel a ailabili y o di e en sea wa e wa eleng hs
Recei e ’s sensi i i y (dBm)
-70 -65 -60 -55 -50 -45 -40
Tch
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 wind=18 m/s
wind=0 m/s
wind=2 m/s
Figu e 5.16: Channel a ailabili y o di e en wind speeds
77
Chap e 5. Conside a ions in Unde wa e - o-Ai links
78
Chap e 6
S a is ical modeling o he Unde wa e
Wi eless Op ical Channel
An UWOC link is ully cha ac e ized by i s ime-dependen impulse esponse. Gene ally, he alues o he impulse
esponse a e samples o a andom p ocess de ined in wo a iables: ime and mul ipa h delay. The e o e, an ac ual
impulse esponse would p esen he o m h( , τ), whe e is ime and τis delay. F om his in o ma ion, i he
channel is WSSUS, he sca e ing unc ion S( , τ) o he channel can be ex ac ed as:
S( , τ) = F∆ {E[h( , τ)h∗( + ∆ , τ)]}(6.1)
The sca e ing unc ion is he Fou ie ans o m o he au oco ela ion unc ion on he a iable ∆ . is he
Dopple equency and τconse es i s o iginal meaning. F om his unc ion, wo impo an s a is ical unc ions
can be de i ed, he Powe Delay p o ile P(τ) and he Dopple Spec um S( ). Equa ions 6.2 and 6.3 show he
ma hema ical desc ip ion o each unc ion.
P(τ) = Z∞
−∞
S( , τ) d =Eh|h( , τ)|2i(6.2)
S( ) = Z∞
−∞
S( , τ) dτ(6.3)
F om P(τ), he delay sp ead can be ob ained as i was pe o med in Chap e 4, and i s in e se is ela ed o
he cohe ence bandwid h. Rega ding S( ), i allows he calcula ion o he cohe ence ime by means o i s in e se
Fou ie ans o m. In his pa o he wo k, he WSSUS app oxima ion is going o be assumed, bu in Chap e 7 i
will be demons a ed h ough expe imen a ion. Fu he mo e, in his wo k, a s a is ical app oach o bo h channel
gain and bandwid h will be p esen ed, since he implemen ed simula o only o e s independen samples o h( , τ)
(no dependence wi h ). In he desc ibed si ua ion, he mean delay sp ead could be app oxima ed om:
P(τ)≈1
NX
ih(i)(τ)
2(6.4)
Whe e Nis he numbe o andom samples o h(τ). No e ha τhas in e se meaning espec o he o iginal
o mula ion o Chap e 4. Howe e , a s a is ical desc ip ion o he delay sp ead and he channel gain is he main
objec i e o his wo k, and he pa ame e s ob ained in Chap e 4 will be in oduced in o a s a is ical in e ence
engine o pe o m a bes i analysis o hei PDFs. As i was men ioned abo e, he a iable will be in oduced
in o he analysis a e ob aining ac ual measu ed da a.
6.1 B ie analysis o he p oblem
The simula o p esen ed in Chap e 4 calcula ed he impulse esponse using a MMCRT algo i hm. The esul ing
impulse esponse was con o med by he sum o a ini e numbe o Di ac’s del as weighed by a ac o ha depended
on he phenomena he ay su e ed du ing i s ajec o y. The ajec o y ollowed by each ay is andomly de e mined
by he pa icle dis ibu ion. This pa icle dis ibu ion de ines he scena io and hence, he powe and delay o each
con ibu ion. Ne e heless, a each un o he algo i hm, he posi ions o he pa icles andomly a y and a e
unco ela ed be ween i e a ions. This ac makes a delay-based simula ion impossible, which is a equi emen o
ob ain he sca e ing unc ion S(τ, ). Howe e , his simula o allows he calcula ion o he dis ibu ions o bo h
H(0) and τ ms.
79
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
Di ec i i y
0 20 40
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5 ξ
Di ec i i y
0 20 40
0
20
40
60
80
100
120
140 µ
Di ec i i y
0 20 40
2
4
6
8
10
12
14 σ
Figu e 6.8: E olu ion o he GEV pa ame e s wi h he emi e ’s di ec i i y
Radius (nm)
0 500 1000
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6 ξ
Radius (nm)
0 500 1000
0
20
40
60
80
100
120
140 µ
Radius (nm)
0 500 1000
0
1
2
3
4
5
6
7
8σ
Figu e 6.9: E olu ion o he GEV pa ame e s wi h he pa icle adius
No e ha he BSF has gene ally uni s o wa s pe squa e me e . Howe e , in his case, his BSF has been
no malized and is exp essed uniquely as m−2. The adian in ensi y P x(θ) has uni s o wa s pe s e adian. Since
dΩ≈Ae /d2, he equa ion is consis en in uni s wi h he squa ed Ae e m.
No e ha P x(θ0) = P x when θ0=π/2, and he BSF has been conside ed azimu hally symme ic, which is
a common assump ion in homogeneous media. This nomencla u e eases he ollowing desc ip ion ega ding he
calcula ion o ∆τ1, which can be ob ained in e ms o a maximum ele a ion angle θmax. This θmax is he angle a
which he in eg a ed powe is he 95 % o he o al ecei ed powe . Ma hema ically:
θmax = a g
θ{P x(θ)=0.95P x}(6.26)
Unde he geome ical es ic ions o he p oblem, his θmax implies a hypo he ical maximum a eled dis ance
equal o dlink (cos θ+ sin θ). In oducing his dis ance in o Equa ion 6.7 i yields he ollowing app oxima ion o
he F esnel zone’s adius.
ellip ≈dlink
2 an θmax (6.27)
86

Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
Concen a ion (·109)
0 10 20 30
0.45
0.5
0.55
0.6
0.65
0.7
0.75 ξ
Concen a ion (·109)
0 10 20 30
0
5
10
15
20
25
30 µ
Concen a ion (·109)
0 10 20 30
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2σ
Figu e 6.10: E olu ion o he GEV pa ame e s wi h he concen a ion o pa icles
Figu e 6.11: In eg a ion o he ecei ed powe using he Beam Sp ead Func ion
6.4.1 Beam Sp ead Func ion
The BSF desc ibes he spa ial dispe sion o an in ini esimal solid angle espec o he a eled dis ance, which is
ela ed o he sca e ing pa icles o he medium. The BSF can be unde s ood as he ligh in ensi y on a plane
pe pendicula o he p opaga ion dis ance a each a eled dis ance d. I he medium is homogeneous, his BSF
would p esen e olu ion symme y espec o he p opaga ion axis, and each poin o he plane would be de ined
by a adius in pola coo dina es.
F om Cochenou ’s wo k in [16], he BSF can be exp essed in e ms o he spa ial equency κo he ligh
in ensi y and he spa ial Fou ie ans o ms o bo h in ensi y and sca e ing. To simpli y he calcula ion, he BSF
is exp essed as he ollowing ze o h o de Hankel ans o m.
ξ(d, ) = 1
2πZ∞
0
I(κ, d)S(κ, d)J0(κ )κdκ(6.28)
Fo he app oxima ion p esen ed in Equa ion 6.25, he emi e ’s adia ion pa e n is di ided in an in ini e
numbe o ays. A each di ec ion, he spa ial dis ibu ion o he inciden ligh can be conside ed as a Di ac’s
Del a. Hence, I(κ, d) is an uni a y cons an . Cochenou e al. di ided he esul ing BSF in o a non-sca e ed
e m ξNS(d, ) and a sca e ed e m ξS(d, ), bu in his case his app oxima ion is no used. The sca e ing e m
S(κ, d) is de ined in Equa ion 6.29
S(κ, d) = e−c(λ)deb(λ)Rd
0P(κ(d−z)) dz=e−c(λ)deb(λ)dR1
0P(dκν) dν(6.29)
87
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
P(x) is he Hankel ans o m o he sca e ing phase unc ion and ν= 1 −z/d. In oducing Equa ion 6.29 in o
Equa ion 6.28, i yields:
ξ(d, ) = e−α(λ)d
2πe−b(λ)dZ∞
0
eb(λ)dR1
0P(dκν) dνJ0(κ )κdκ(6.30)
This equa ion is nume ically in eg able. Figu e 6.12 depic s ξ(d, ) a di e en dis ances and sca e ing coe i-
cien s o iso opic sca e ing and a Henyey-G eens ein sca e ing wi h g= 0.9 espec i ely.
Radial dis ance (m)
0246
dB
-14
-12
-10
-8
-6
-4
-2
0g = 0.9
d= 1 , b= 0.5
d= 1 , b= 2
d= 5 , b= 0.5
d= 5 , b= 2
Radial dis ance (m)
0246
dB
-25
-20
-15
-10
-5
0Iso opic
d= 1 , b= 0.5
d= 1 , b= 2
d= 5 , b= 0.5
d= 5 , b= 2
Figu e 6.12: No malized Beam Sp ead Func ion o iso opic sca e ing ( igh ) and Henyey-G eens ein wi h pa-
ame e g = 0.9 (le )
I can be obse ed ha he sca e ing coe icien and he phase unc ion shape a ec he wid h o he BSF.
Fu he mo e, he ob ained BSF may be app oxima ed by he sum o wo Gaussians in a wide ange o dis ances
and sca e ing coe icien s. Unde his assump ion, a i ing analysis can be pe o med o ob ain a ela ionship
be ween b(λ), g,dand he peak and wid h o ξ(d, ). Sweeping b∈(0,2), g∈(0,1) and d∈(1,10) he ollowing
ela ionships we e ob ained.
ξ(d, 0) ≈8.231e−b(λ)(1−0.13g)d(6.31)
η≈(1 −6.6·10−3b(λ))e1−e5·10−4g b(λ)d2(6.32)
σ2
1≈4.6·10−3+ 2.22 ·10−4b(λ)+1.74 ·10−4e0.169g b(λ)d(6.33)
σ2
2≈(3.87g+ 0.976b(λ)2)e(0.39b(λ)−0.663g)d(6.34)
Wi h:
ξ(d, )≈ξ(d, 0) ηe− 2
2σ2
1+ (1 −η)e− 2
2σ2
2/σ1< σ2(6.35)
ηis a weighing ac o be ween he wo gaussians. Gene ally, he BSF is o med by a e y na ow componen
due o he p i ileged o wa d di ec ion and a wide componen due o he mul iple sca e ing phenomena. No e
also ha he exp ession o ξ(d, 0) is comple ely complian wi h he expe imen s o Cochenou [16]. This e ms
desc ibes ha he highe he a e age cosine o he pa icle’s phase unc ion, he lowe he ac ual powe loss in he
o wa d di ec ion due o beam sp eading. Rega ding σ2
1, he ob ained app oxima ion can be enhanced since o
lowe alues o b(λ) (ou o he swep anges), he BSF mus p esen a mo e ab up beha io . The ollowing R2
goodness-o - i alues we e ob ained o he app oxima ions p esen ed in his sec ion.
6.4.2 Analysis o he esul ing F esnel zones
Using he app oxima ion ob ained in he p e ious subsec ion, he analysis o he F esnel zones can be educed o
he solu ion o Equa ion 6.25. Figu es 6.13 and 6.14 illus a e θmax o he cases p esen ed in Figu e 6.12, bu o
88
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
Pa ame e R2
Two-Gaussian app oxima ion o he BSF R2
max = 1.0, R2
min = 0.85
ξ(d, 0) 0.99
η0.989
σ2
10.945
σ2
20.955
Table 6.2: Goodness-o - i R2 alues o he app oxima ions p esen ed in his sec ion. The suppo was con o med
by 400 da a poin s.
a pu e lambe ian emi e (θ1/2=π/3) and a lambe ian emi e wi h m= 20.
Dis ance (m)
1 2 3 4 5 6 7 8 9 10
θmax
0
0.2
0.4
0.6
0.8
1
1.2
1.4
g= 0; b= 0.5
g= 0; b= 2
g= 0.95; b= 0.5
g= 0.95; b= 2
Figu e 6.13: θmax o bo h iso opic and Henyey-G eens ein sca e ings a di e en dis ances o a pu e lambe ian
emi e
Dis ance (m)
1 2 3 4 5 6 7 8 9 10
θmax
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
g= 0; b= 0.5
g= 0; b= 2
g= 0.95; b= 0.5
g= 0.95; b= 2
Figu e 6.14: θmax o bo h iso opic and Henyey-G eens ein sca e ings a di e en dis ances o a lambe ian
emi e wi h m= 20
I can be obse ed ha he di ec i i y o he emi e is in e sely p opo ional o θmax, since he ene gy is
concen a ed in a smalle solid angle as he di ec i i y inc eases. Fu he mo e, o small pa icle concen a ions
(low b(λ)),θmax dec eases wi h he dis ance ega dless he di ec i i y. This occu s because he sca e ed ene gy is
e y small and he majo i y o he ene gy emains on he o wa d di ec ion. Finally, high concen a ions in e
89
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
he ela ionship o θmax wi h he link’s ange, inc easing wi h he dis ance. Pe o ming an analysis simila o he
one ca ied ou in he p e ious subsec ion, an app oxima e o mula o p edic he θmax can be ob ained. Equa ion
6.36 shows he esul o he app oxima ion, which was ob ained wi h an R2 alue o 0.9604.
θmax ≈0.2971b(λ)g m dlink 1−6.8·10−3b(λ)g2e−0.157m dlink + 9 ·10−4m dlink b(λ)2(6.36)
Using Equa ion 6.36 combined wi h Equa ion 6.27, ellip can be easily calcula ed. This app oxima ion has
h ee main applica ions. Knowing he F esnel zone o a 95% o he ecei ed powe and conside ing s eep impulse
esponses, he maximum bandwid h can be di ec ly calcula ed using Equa ions 6.36 and 6.7. On he o he hand,
his app oxima ion allows he link designe o conside whe he an obs acle a ec s he ansmission o no . Finally,
he simula ion o UWOC links is educed o a e y small olume i only he signi ican ellipsoid is conside ed. As
i was commen ed, he a ailable bandwid h can be es ima ed using Equa ion 6.6 and in oducing he de ini ion o
he F esnel zone’s adius.
˜
B=c0√12
5nwdlink
cos θmax (6.37)
The empi ical o mulae p esen ed in his sec ion ha e been ob ained h ough simula ion. The e o e, hey may
no accu a ely model eali y and u he esea ch acqui ing ac ual da a om eal scena ios should be ca ied ou .
None heless, he ob ained p edic ions seem o indica e a logical end on he es ima ed bandwid hs.
6.5 S a is ical model o big opaque pa icles
Gene ally, he li e a u e only ea s he p oblem o sca e ing. None heless, in ce ain scena ios, big opaque pa icles
such as sand g ains a e pa o he he e ogeneous unde wa e medium. In coas al scena ios, unde shallow wa e
egimes, he o ces o he seawa e mass anspo a ion on he seabed gene a e a andom dis ibu ion o big opaque
pa icles amid he link. In his sec ion, a pu ely geome ical model o p edic he in luence o his pa icles is
p esen ed.
6.5.1 De ini ion o big opaque pa icle
A big opaque pa icle is a piece o ma e whose spec al abso p ion is high enough o conside ha he e is no
ansmission and whose dimension assu es ha he di ac ion is negligible. I a plane wa e passes h ough a
ci cula sli o adius R, he di ac ion pa e n I(θ) is de e mined by he ollowing Ai y disk:
I(θ) = 4I0 J12πR
λsin θ
2πR
λsin θ!2
/∀φ(6.38)
The angle θis de ined om he cen e o he sli . Howe e , since he in e es o his wo k is ocused on pa icles
and no sli s, om Babine ’s p inciple i can be s a ed ha he di ac ion pa e n o he pa icle is he same as
he sli ’s excep on he o wa d di ec ion. Fo e y high R/λ a ios, he o e all di ac ed in ensi y ends o ze o,
since:
lim
x→∞
J1(x)
x= 0 (6.39)
Fo nea ield, which occu s when he F esnel numbe (Equa ion 6.40) sa is ies F >> 1, he di ac ed in ensi y
is go e ned by he Ki cho -F esnel equa ion. The esul ing nea ield pa e ns a e also de e mined by he R/λ
a io and he esul is simila o he a ield case.
F=R2
dλ (6.40)
dis he dis ance om he pa icle o he plane o in e es . Hence, a big opaque pa icle will only block he
inciden ligh p oducing a shadow in a a ield si ua ion. This shadow could be p ojec ed o e he pho odiode’s
a ea p oducing a powe loss. The ollowing subsec ion in oduces he ma hema ical o mula ion o he powe loss.
6.5.2 Ma hema ical o mula ion
Le s conside a LOS si ua ion in an UWOC link, wi h an uni o m dis ibu ion wi h densi y ρo big opaque pa icles
o adius R. I he emi e has a adius R x and he ecei e a adius R x, he olume enclosed by he LOS emission
would be:
90
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
Vw=π
3dlink 
R3
x −R3
x
R x −R x 
(6.41)
Figu e 6.15 depic s he si ua ion. The o al olume is he di e ence o wo conic olumes. I is in ui i e o
assume ha he numbe o pa icles wi hin Vwwould ollow a Binomial dis ibu ion. This dis ibu ion has a
mean alue o ρVw. Fu he mo e, he hypo he ical maximum numbe o pa icles o adius Rin he olume Vwis
Nmax =b3Vw/(4πR3)c. F om Nmax and he mean o he dis ibu ion, i is s aigh o wa d o s a e ha :
n∼Bρ4π
3R3, Nmax(6.42)
Figu e 6.15: LOS componen subjec o he p esence o big opaque pa icles
Obse ing Figu e 6.15 i is logical o no ice ha i he emi e we e a poin sou ce, he p ojec ed shadow
o a close- o- he-emi e pa icle would end o in ini y. Hence, he heo e ical analysis o he p oblem mus be
pe o med conside ing he emi e as an ex ended sou ce. Gene ally, he powe loss due o an opaque objec o e
an a ea A x is de e mined by he linea p ojec ion o he objec ’s c oss sec ion acco ding o he slope o he cone
de e mined by he wo a eas (Figu e 6.16). Appendix B, demons a es his assump ion. The sec ion o he cone
de ined by emi e and ecei e a a dis ance diis de ined by:
Figu e 6.16: Powe loss due o he e ec o big opaque pa icles
A(di) = πR x +di
dlink
(R x −R x)2
(6.43)
The powe loss would be ela ed o he amoun o ecei e ’s a ea ha is shadowed by he pa icle. This amoun
can be exp essed as a a io be ween he pa icle’s c oss sec ion and he a ea o Equa ion 6.43. The ecei ed powe
can be exp essed as:
P x =P x
m+ 1
2π
Apd
d2
link
e−c(λ)dlink ζ(6.44)
Whe e ζis a andom a iable ha exp esses he educ ion o he pho o ecei e ’s a ea as:
91

Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
ζ= 1 −πR2
n
X
i=1
γi
A(di)(6.45)
Whe e γiis a a iable ha indica es he o e lapping deg ee o each pa icle wi h he es . This analysis
neglec s he e ec o he beam sp eading and should be included in u he esea ch. P obably, he analysis would
be analogous o he cu en p oposal bu a e applying an in eg a ion o he o m o Equa ion 6.25. In ha case,
Vwshould be inc eased o he olume o a unca ed ellipsoid de ined by he abo e-s udied F esnel zone and he
emi e and ecei e ’s a eas. Fu he mo e, A(di) mus be ans o med o he a ea o he in e sec ed ellipsoid a di.
I he e ec o γiwe e neglec ed, an un ealis ic wo se case scena io would be conside ed. In ha si ua ion, all
he pa icles wi hin Vwwould p oduce shadowing and hence, he powe loss would decay beyond ze o. Howe e , o
a numbe o pa icles ela i ely small, his si ua ion would p esen a e y small p obabili y. di ollows a unca ed
exponen ial dis ibu ion om di= 0 o di=dlink. Finally, he esul ing dis ibu ion o A(di)−1can be exp essed
as ollows acco ding o he andom a iable algeb a (Equa ion 6.46). Figu e 6.17 depic s he expe imen al CDF o
he in e se a ea s he app oxima ion.
x(x) = K·(πx)−3/2e−µdlink
R x−R x ((πx)−1/2−R x)(6.46)
K=π µ dlink
2|R x −R x|(6.47)
0 5 10 15 20 25 30 35
A(di)−1
0
0.2
0.4
0.6
0.8
1
No malized p obabili y
Empi ical
Theo e ical
Figu e 6.17: Compa ison be ween he his og am and he PDF o Equa ion 6.46. ρ= 10−4, dlink = 5 m, R x = 5
cm, R x = 1 cm, R= 1 mm.
Assuming a big numbe o pa icles and using Wald’s equa ion, he PDF o ζcan be app oxima ed o a no mal
dis ibu ion N(µ, σ2) wi h he ollowing pa ame e s.
µ≈1−πR2E[n]·E[x]
σ2≈πR22E[n]σ2
x+E[x]2σ2
n(6.48)
E[x] and σ2
xa e he expec ed alue and a iance o Equa ion 6.46 espec i ely. This app oxima ion would
p esen an e o ha inc eases as he numbe o pa icles dec ease. Fu he mo e, since γihas been neglec ed, he
es ima ed loss may become nega i e. The e o e, his app oxima ion is alid o a middle- ange a e age numbe
o pa icles. Figu e 6.18 depic s h ee example si ua ions whe e an expe imen al CDF ollowing equa ion 6.45
is compa ed o he no mal app oxima ion. The i s scena io is an scena io wi h a educed a e age numbe o
pa icles, he second co esponds o a e y pollu ed en i onmen and inally he hi d p esen s a mode a e numbe
o pa icles.
As i was commen ed, he loss su passes he h eshold and becomes nega i e o he mos pollu ed scena io. In
o de o ix his issue, he simula ed PDF could be unca ed a ze o, in oducing he le -side excess p obabili y
as a del a a he o igin.
6.5.3 In luence o he link’s pa ame e s on he SNR
In a si ua ion in which Johnson and sho noises could be neglec ed espec o he noise associa ed o his kind o
pa icles, he SNR o he link would be de ined by he quo ien E2[ζ]/σ2
ζ. The baseline scena io o Table 6.3 is
92
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
0.9 0.95 1
ζ
0
0.2
0.4
0.6
0.8
1
Cumula i e p obabili y
Empi ical
No mal app oxima ion
0.6 0.7 0.8 0.9
ζ
0
0.2
0.4
0.6
0.8
1
Cumula i e p obabili y
Empi ical
No mal app oxima ion
-1 -0.5 0
ζ
0
0.2
0.4
0.6
0.8
1
Cumula i e p obabili y
Empi ical
No mal app oxima ion
Figu e 6.18: Compa ison be ween he expe imen al CDF and he no mal app oxima ion in a link shadowed by big
opaque pa icles. The le igu e co esponds o a link in which he a e age numbe o pa icles is app oxima ely
16, he cen e igu e o 100 pa icles, and he igh igu e is associa ed o a e y pollu ed en i onmen wi h an
a e age o 1000 pa icles wi hin he olume. No e he p ecision o he no mal app oxima ion as he numbe o
pa icles inc ease.
de ined o analyze he in luence o di e en pa ame e s in a scena io wi h big opaque pa icles. No e ha his SNR
mus be unde s ood as a lowe bound since he o e lapping o shadows has no been conside ed.
Pa ame e Value
R x 10 cm
R x 1 cm
R1 mm
ρ103m−1
dlink 5 m
Table 6.3: Baseline scena io o analyze he in luence o he link pa ame e s on he SNR
Fi s o all, he in luence o he link’s ange has been ob ained h ough simula ion. F om he ma hema ical
de elopmen p esen ed abo e, he olume o wa e enclosed by emi e and ecei e inc eases linea ly wi h dlink.
This inc emen is linked o a g ea e a e age numbe o pa icles, and hence, he SNR dec eases. Figu e 6.20
depic s he in luence o he emi e adius. I can be obse ed ha la ge emi e s a e subjec o he in luence
o a highe amoun o pa icles, shadowing he ou pu powe o he lamp. Fu he mo e, e y small emi e s a e
also highly in luenced by his ype o pa icles, since hei emission su aces a e compa able o he pa icle c oss
sec ion. No e ha he e is a local maximum a which he in luence o he pa icles is minimized. This op imal
emission a ea is o high impo ance in e y u bid en i onmen s, whe e he maximiza ion o he SNR is manda o y.
In u he esea ch, he ma hema ical exp ession o he op imal emi e adius depending on he concen a ion,
and he ecei e and pa icle adii may be ound. On he con a y, in Figu e 6.21 i can be obse ed ha bigge
ligh collec ion a eas diminish he in luence o hese pa icles, imp o ing he SNR pe o mance bu sa u a ing
a ce ain le el. The ini ial enhancemen occu s because al hough he e is a bigge amoun o pa icles wi hin
he emission cone, he ela ionship be ween he ecei e ’s a ea and he pa icle a ea inc eases apidly. Howe e ,
beyond a h eshold adius he ma ginal imp o emen o he SNR is close o ze o, since he inc emen on he
a ea is compensa ed by he g ea e amoun o pa icles. Figu e 6.22 shows he in luence o he pa icle adius.
This pa ame e has he bigge in luence on he SNR since he pa icle c oss sec ion o ecei e a ea a io apidly
inc eases. Finally, he in luence o he concen a ion o pa icles can be obse ed in Figu e 6.23. The concen a ion
o pa icle has wo main e ec s acco ding o he heo e ical analysis abo e. The i s one is o inc emen he a e age
numbe o pa icles, and he second one is o p oduce mo e collisions wi h pa icles a close dis ances, educing
he e ec i e ou pu powe o he lamp.
93
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
1 2 3 4 5 6 7 8 9 10
Dis ance (m)
32
34
36
38
40
42
44
SNR (dB)
Figu e 6.19: SNR o a link de ined by he big opaque pa icle dis ibu ion s he link’s ange
0 5 10 15 20 25 30
T ansmi e adius (cm)
30
32
34
36
38
40
42
SNR (dB)
Figu e 6.20: SNR o a link de ined by he big opaque pa icle dis ibu ion s he emission a ea
0 5 10 15 20 25 30
Recei e adius (cm)
25
30
35
40
45
50
55
60
65
SNR (dB)
Figu e 6.21: SNR o a link de ined by he big opaque pa icle dis ibu ion s he ecep ion a ea
94
Chap e 6. S a is ical modeling o he Unde wa e Wi eless Op ical Channel
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Pa icle adius
-20
-10
0
10
20
30
40
SNR (dB)
Figu e 6.22: SNR o a link de ined by he big opaque pa icle dis ibu ion s he pa icle adius
101102103104
Concen a ion o pa icles
10
20
30
40
50
60
SNR (dB)
Figu e 6.23: SNR o a link de ined by he big opaque pa icle dis ibu ion s he concen a ion o pa icles
95
Chap e 7. Measu emen s on a sho - ange Unde wa e Wi eless Op ical Channel
inside he wa e ank a he posi ions depic ed in Figu e 7.7. The pa icle mobili y s a is ic has been ma ched o he
mean absolu e alue o he wa e low h ough he LOS line, which was p e iously simula ed using a FEM so wa e
[145] since an ac ual measu emen was no easible. The esul ing wa e speed dis ibu ion can be obse ed in
Figu e 7.8. The a e age speed o he pa icles is 1 cm ·s−1 o pumps wi h a wa e low o 800 li e s pe hou . The
ou pu wa e speed is calcula ed assuming a small diame e , which allows a cons an ou pu lux app oxima ion
yielding an ou pu speed o 0.31m ·s−1.
Figu e 7.7: Posi ions o he wa e pumps used o agi a e he scena io
Figu e 7.8: Wa e speed dis ibu ion o he expe imen
The in luence o he wo a iables on he ecei ed powe has been analyzed using a wo-way ANOVA es o e
an es ima ion o he elec ical SNR, which can be obse ed a Equa ion 7.10. The ecei ed signal ollows a No mal
dis ibu ion o all he cases, as he esul o he Kolmogo o -Smi no es sugges s.
SNRelec ≈E2[Vou ]
Va (Vou )(7.10)
Vou is he ol age measu ed a he oscilloscope. In oducing he ecei e chain in Equa ion 7.10, i yields
Equa ion 7.11. P x is he emi ed powe , ¯
H(0) is he a e age channel gain, R(λ) is he pho ode ec o ’s esponsi i y,
Bis he ecei e ’s bandwid h, qis he elec on cha ge, Id he da k noise, and σ2
ns ep esen s all he non-sho noise
con ibu ions (Johnson noise and a iabili y o he channel due o pa icles).
102

Chap e 7. Measu emen s on a sho - ange Unde wa e Wi eless Op ical Channel
SNRelec ≈P xH(0)R(λ)2
σ2
ns + 2qP xH(0)R(λ) + IdB
(7.11)
No e ha he sho noise e m is negligible due o he educed bandwid h o ope a ion and he small ecei ed
powe . The pa icle mo emen expe imen may be a ec ed by he dis ance o he emi e o he su ace and he
bo om o he ank. To minimize he e ec o he e lec ions, he link’s axis was ixed a he geome ical cen e o
he ank, and he s ill wa e le el was g adually inc emen ed un il he ecei ed powe ’s a ia ion was negligible.
A his poin , he link can be conside ed independen o he su ace e lec ions. Rega ding he bo om di usi e
e ec , since i was co e ed by an abso bing ma e ial, i is conside ed o no a ec he link. In o de o analyze he
ac ual in luence o he suspended ma e , he da kness noise powe o he ecei e was calib a ed as baseline.
The wind speed expe imen was pe o med using clea ap wa e , since he p esence o pa icles was no pa
o he designed expe imen . The wind speed was measu ed using a digi al anemome e a he middle o he wa e
su ace. The used wind gene a o p esen ed only wo di e en speeds: 8.1 m ·s−1and 13 m ·s−1. Bo h wind speed
and link’s dep h we e swep o ob ain long-du a ion wa e o ms on he ecei e . Using he oscilloscope’s e ie ed
da a, he cohe ence ime and he demons a ion o he WSSUS app oxima ion we e ob ained.
7.3 Resul s ob ained h ough measu emen s
Figu e 7.9 shows he ac ual implemen a ion o he expe imen al se up. The esul s ha e been subdi ided ega ding
he i s and he second expe imen commen ed abo e.
Figu e 7.9: Ins umen a ion con igu a ion o he expe imen al se up
As an example, Figu e 7.10 depic s wo cap u ed ames. The le one is an only LOS scena io, whils he igh
one is a nea -su ace link.
The ollowing subsec ions p esen he demons a ion o he WSSUS alidi y o a nea -su ace link, and he
esul s ob ained o he wo a o emen ioned expe imen s, as well as commen s on he e ec s o he wa eleng h and
he wind speed.
7.3.1 E ec o he concen a ion and he mo emen o pa icles
Suspended ma e con ibu es o he channel’s powe ex inc ion in wo di e en manne s. I he pa icles a e
s eady because o a null low scena io, each emi e ’s ou going ay su e s he same sca e ing e en s be o e a i ing
he ecei e . On he o he hand, i he pa icles p esen ce ain mobili y, ha almos -de e minis ic beha io is
eplaced by a andom beha io whose mean alue and a iance depend on he e olu ion o he olume ic densi y
o pa icles. In o de o es his e ec s, wo di e en pa icle mobili ies and h ee di e en concen a ions we e
used. Table 7.3 shows he pa ame e s o he expe imen .
Mobili y {0,1}cm ·s−1
Concen a ion o pa icles {0,6.12,12.24}mg ·l−1
Dep h 30 cm
Table 7.3: Pa ame e s o he pa icle mobili y expe imen
103
Chap e 7. Measu emen s on a sho - ange Unde wa e Wi eless Op ical Channel
Figu e 7.10: Cap u ed ames o a LOS scena io wi h a concen a ion o 6.12 mg l−1wi h agi a ed pa icles (le ),
and a nea -su ace link wi h an ai low o 13 m s−1a 5 cm dep h ( igh ). Bo h a e ob ained wi h a 470 nm
emission and a e exp essed in op ical powe uni s (W)
Figu e 7.11 depic s he andom na u e o he SNR o ed and blue wa eleng hs a ying bo h pa icle concen-
a ion and mobili y. As i can be obse ed he e a e 6 di e en scena ios, which a e he combina ions o mobili y
and pa icle concen a ions. To s a is ically e i y he in luence o he pa icle mobili y on he ecei ed powe ,
an ANOVA es may be pe o med. To ca y ou he ANOVA es , a k- old c oss alida ion wi h 16 ames o
4096 samples has been used. The SNR o each ame is hen es ima ed acco ding o Equa ion 7.10. A e wa ds i
is agged wi h i s associa ed mobili y and concen a ion, and inally used as inpu o he ANOVA es . As i is
ob ious, he es concludes ha bo h mobili y and concen a ion a ec he elec ical SNR.
Figu e 7.11: Boxplo s o he SNR s concen a ion and mobili y o ed (le ) and blue ( igh ) wa eleng hs
Taking in o accoun he no mali y o he ecei ed powe , which was demons a ed h ough a Kolmogo o -
Smi no es (Figu es C.4 and C.10) a simple linea model is p oposed o ela e he mobili y and concen a ion
wi h he obse ed SNR dec emen . Equa ion 7.12 exp esses i ma hema ically o he channel gain, H(0).
H(0) (C,M) = α(C,M)H(0) (C,0) + V(C,M) (7.12)
Cand Ma e he concen a ion and mobili y espec i ely. αexp esses he educ ion o he mean ecei ed powe
and Vis he channel a iabili y e m, which ollows a no mal dis ibu ion o he ype N(0, σ2
ch(C,M)). The a iance
due o he channel a iabili y (ex a noise due o pa icles mo ing) is ela ed o he a iance o H(0) (C,M) as
shows Equa ion 7.13.
104
Chap e 7. Measu emen s on a sho - ange Unde wa e Wi eless Op ical Channel
σ2
ch (C,M) = Va (H(0) (C,M)) −α2(C,M) Va (H(0) (C,0)) (7.13)
Finally, o ob ain he dimensionless channel gain a iabili y h ough he obse ed ol age signals, a simple
con e sion may be made as shows Equa ion 7.14. No e han α emains he same ega dless he domain, as he
ol age and he op ical powe a e linea ly ela ed.
(GT Z R(λ)P x)2σ2
ch (C,M) = Va (V(C,M)) −
α2(C,M) Va (V(C,0)) (7.14)
GT Z is he ansimpedance gain and R(λ) he esponsi i y o he pho odiode a he used wa eleng h. Table
7.4 summa izes he alues o αand σ2
ch o each (C,M) pai . No e ha he a iabili y o he ed channel di e s
an o de o magni ude espec o he blue channel measu emen s. This is because he dissol ed alga p esen s an
ele a ed concen a ion o chlo ophyll, which implies a highe abso p ion a he ed wa eleng h, educing he e ec
o mobili y.
Wa eleng h (nm) Concen a ion (mg l−1)α σ2
ch
660 0 0.99 6.67 ·10−18
660 6.12 0.92 1.08 ·10−15
660 12.24 0.96 3.6·10−15
470 0 1 4.25 ·10−12
470 6.12 0.89 116.3·10−12
470 12.24 0.91 138.5·10−12
Table 7.4: Values o αand σ2
ch o each concen a ion and wa eleng h o a mobili y o 1 cm s−1
This educ ion o he SNR in channels wi h mo ing pa icles may be impo an on he calcula ion o link budge s
in UWOC. In o de o a oid his e ec , an ex a powe ma gin acco ding he noise e m p esen ed abo e should be
conside ed. These esul s a e he sum o he u bulence e ec s (no concen a ion) and he in luence o he pa icle
densi y. Since his expe imen was pe o med in labo a o y, he Kolmogo o mic oscale would be highe han he
expec ed in an open ocean en i onmen . Howe e , he concen a ion inc emen gene a es a educ ion o he SNR
much highe han he expec ed due o u bulences in sho ange links.
7.3.2 E ec o he wind speed
Nea su ace links a e cha ac e ized by p esen ing a e y impo an e lec i e componen . Equa ion 7.15 shows he
ma hema ical exp ession o he ecei ed powe o his kind o links.
H(0) = H(0)LOS +ZxZy
R(ˆ (x, y),ˆn(x, y))L(x, y) dxdy(7.15)
The ne e lec i e componen is he sum o he con ibu ions o all he poin s o he wa e su ace. The su ace
plane can be di ided o ming a disjoin union o unco ela ed sca e e s, whose ading beha io s a e go e ned
by hei andom no mal ec o s. The size o each unco ela ed egion would depend on he wind speed and he
p opaga ing wa es. R(ˆ i,ˆni) is he F esnel loss due o he wa e -ai in e ace, ˆ (x, y) is he emission ec o , which
is bounded by he uppe hemisphe e o he adia ion pa e n; ˆn(x, y) is he andom no mal ec o o he seawa e
in e ace, and L(x, y) depends on he p oduc o he ex inc ion loss and he app oxima ion o he solid angle a he
ecei e (dΩ ≈Apd/d2). This las e m would depend on he geome y o he link and goes o ze o i he ou pu
ay does no impac on he ecei e .
As i was commen ed in Chap e 5, ˆn(x, y) depends on he wind speed and is commonly app oxima ed by
a no mal dis ibu ion. The NLOS componen o Equa ion 7.15 ollows a No mal dis ibu ion since i can be
unde s ood as he sum o a high amoun o independen Be noulli p ocesses (each sca e e has a p obabili y pxy
o con ibu e o he o e all ecei ed powe ), bu i s ime-dependen e olu ion is unknown.
Acco ding o Equa ion 7.2, he e lec i e e m R( ) could be isola ed since he LOS componen does no
a y signi ican ly as i was shown in Subsec ion 7.3.1. Fou di e en dep hs, h ee di e en wind speeds and wo
wa eleng hs we e es ed in his expe imen . The esul ing R( ) signal was calcula ed and i s p obabili y dis ibu ion
i s a no mal dis ibu ion. Fu he mo e, i s mean, a iance and cohe ence ime a e shown a Table 7.5.
Rega ding he cohe ence ime, i mus be aken in o accoun ha a e y high bandwid h has been conside ed.
This way, he ime- equency analysis is educed o an only- ime analysis, yielding a e y simple calcula ion o
he cohe ence ime using Equa ion 7.9. The esul s o Table 7.5 a e e e ed o signals exp essed in wa s. I
105
Chap e 7. Measu emen s on a sho - ange Unde wa e Wi eless Op ical Channel
Wa eleng h (nm) Dep h (cm) Windspeed (m s−1)µ σ2Tc(ms)
660 2 8.1 0.231 ·10−40.116 ·10−11 140
660 2 13 0.21 ·10−40.064 ·10−11 85.2
660 5 8.1 0.256 ·10−40.164 ·10−11 178.4
660 5 13 0.222 ·10−40.075 ·10−11 73.3
660 10 8.1 0.247 ·10−40.176 ·10−11 98
660 10 13 0.233 ·10−40.1·10−11 70.7
660 15 8.1 0.25 ·10−40.132 ·10−11 58.4
660 15 13 0.237 ·10−40.078 ·10−11 50.9
470 2 8.1 0.294 ·10−40.25 ·10−11 267
470 2 13 0.24 ·10−40.1·10−11 79.5
470 5 8.1 0.355 ·10−40.475 ·10−11 255.4
470 5 13 0.321 ·10−40.215 ·10−11 93.2
470 10 8.1 0.417 ·10−40.331 ·10−11 90.6
470 10 13 0.375 ·10−40.226 ·10−11 74.1
470 15 8.1 0.424 ·10−40.326 ·10−11 209.3
470 15 13 0.398 ·10−40.165 ·10−11 49.2
Table 7.5: Mean, a iance and cohe ence ime o R( ) o each measu ed scena io
can be obse ed ha he ecei ed e lec i e powe con ibu ion ends o inc ease in he conside ed dep h in e al.
Howe e , his end changes ab up ly abo e his dep h, educing i s in luence d ama ically and being negligible
abo e 22 cm.
The educ ion o he cohe ence ime wi h he inc easing wind speed occu s because he numbe o unco ela ed
egions on he su ace is inc emen ed. In o he wo ds, he spa ial co ela ion be ween he poin s o he su ace
is educed as he wind speed inc eases, inc emen ing he numbe o unco ela ed con ibu ions on he ecei e .
Conside ing he nea -su ace UWOC link as WSSUS is ob ious, since he sca e e s (poin s on he su ace) a y in
a bounded egion, and he emi e and ecei e a e a ixed posi ions, bu he expe imen al demons a ion can be
ound in he ollowing subsec ion. Fu he mo e, all he ob ained wa e o ms, co ela ions and p obabili y densi y
unc ions can be ound in Appendix C.
7.3.3 Validi y o he WSSUS assump ion
In a wide sense s a iona y p ocess, he expec ed alue is cons an . In o de o demons a e his p ope y in a
nea -su ace link, an ANOVA es was pe o med. The sou ce signals we e di e en ames buil om he o iginal
50 seconds ime se ies as a conca ena ion o samples sepa a ed a mul iple alue o he cohe ence ime ( o c ea e
an unco ela ed ec o ). The esul can be seen a Figu e 7.12 o he ed, 10 cm and 13 m/s scena io. As i was
expec ed, he mean alue o he p ocess can be conside ed cons an (p- alue highe han 0.9 o all cases). The
unco ela ion o he sca e e s can be in e p e ed as a wide sense s a iona i y in he equency domain. In his
case, as he bandwid h is conside ed e y high o all he scena ios, his p ope y is di ec ly sa is ied.
Figu e 7.12: Resul o he ANOVA es o demons a e he WSS p ope y o a nea -su ace link
106
Chap e 8
S a egies o ene gy-e icien
anscei e design
Ene gy e iciency is one o he mos impo an aspec s in UWSN. The powe consump ion o ba e y-powe ed
isola ed nodes de ines hei li espan, and aking in o accoun he high eplacemen cos s, i is a p ima y minimiza ion
objec i e. Gene ally, he powe consump ion o a node is a sum o pa ial con ibu ions. The main consump ions
a e ela ed o p ocessing (CPU and con ol), communica ion in e aces and payload. This las aspec can widely
a y depending on he pu pose o he deployed node. Fo moni o ing applica ions, he payload comp ises senso s
and acquisi ion ci cui y, which can be no mally neglec ed espec o communica ions. Howe e , o applica ions
whe e ac ua ion is needed, he payload powe consump ion may be he p ima y sou ce o ene gy usage. Rega ding
communica ions, o sho - ange links, UWOC has demons a ed o p esen he bes bi s pe Joule e iciency, bu
o long- ange links, UAC is s ill he bes echnology.
Ene gy e iciency can be imp o ed in di e en manne s. Using a laye ed app oach, he bes op ions o enhance
he e iciency a e he physical and he medium access laye . Rega ding he physical laye , pulsed modula ions
a e no mally be e al e na i es han con inuous wa e o ms such as OFDM o CSK. Howe e , hese ypes o
signals can be Pulse Wid h Modula ed in o de o ake ad an age o high e iciency nonlinea d i e s. Mo eo e ,
op ical emi e s and ecei e s p esen a be e esponse o long wa eleng hs han o sho ones. Al hough he bes
ansmission windows a e gene ally loca ed a he blue-g een egion, he commen ed esponse o he de ices makes
ed ansmissions mo e ene gy-e icien below a c i ical dis ance dc i . On he o he hand, be ween PHY and MAC
laye s, powe con ol algo i hms a e an in e es ing op ion o adap he emi ed powe o he isola ed nodes and
hence, educe he powe consump ion.
8.1 Signal o Noise a io in UWOC
The SNR o an UWOC link is de ined by Equa ion 8.1.
SNR(λ) = (P xH(0, λ)R(λ))2
2q(P xH(0, λ)R(λ) + Id+Ib)B+4KT B
RLFn
(8.1)
P x is he emi ed op ical powe , H(0, λ) is he channel gain, R(λ) is he esponsi i y o he pho o ecei e a
he wa eleng h λ,Idis he da kness noise cu en , Ibis he backg ound noise, q he elec on cha ge, Kis he
Bol zmann’s cons an , Tis he empe a u e in Kel ins, Bis he bandwid h, RLis he ampli ie ’s gain and Fni s
noise igu e. In UWOC, he backg ound noise is he sum o he e ec s o sunligh and he seawa e blackbody
adia ion. Gene ally, he la e is neglec ed due o he low empe a u es, whils he i s one losses impo ance as
he dep h inc eases. In his wo k, hese noise sou ces a e being neglec ed o simplici y in he analysis wi hou loss
o gene ali y.
I he e iciency η(λ) o he emi e we e de ined, he las Equa ion could be ew i en in e ms o he powe
consumed by he ansmi e . This e iciency is he p oduc o he op ical e iciency o he LED sou ce ηop (λ) and
he e iciency o he LED d i e ηd i e .
SNR(λ) = (η(λ)P x|elecH(0, λ)R(λ))2
2q(η(λ)P x|elecH(0, λ)R(λ) + Id+Ib)B+4KT B
RLFn
(8.2)
I he a io o he SNR induced by wo di e en emi e s wi h he same powe consump ion a wo di e en
wa eleng hs we e in oduced, he ollowing me i igu e could be de ined.
107

Chap e 8. S a egies o ene gy-e icien anscei e design
SNR(λ1)
SNR(λ0)=η(λ1)H(0, λ1)R(λ1)
η(λ0)H(0, λ0)R(λ0)22qη(λ0)P x|elecH(0, λ0)R(λ0) + 4KT
RLFn
2qη(λ1)P x|elecH(0, λ1)R(λ1) + 4KT
RLFn
(8.3)
No e ha o sho -noise dominan scena ios (sho dis ance) his me i igu e is linea , bu o Johnson dominan
si ua ions (long dis ance), he a io becomes quad a ic. Howe e , in any o he wo cases, he c i ical dis ance dc i
is de ined as he dis ance a which he me i igu e becomes one. Taking in o accoun he conclusions o Chap e s
4 and 6, he a io o channel gains would depend on he di e ence o e ec i e ex inc ion coe icien s, as shows
Equa ion 8.4.
H(0, λ1)
H(0, λ0)≈e−(c(λ1)−c(λ0)dlink (8.4)
In oducing Equa ion 8.4 in o Equa ion 8.3 o he c i ical dis ance, i yields:
1 = η(λ1)R(λ1)
η(λ0)R(λ0)e−(c(λ1)−c(λ0))dc i (8.5)
Sol ing he equa ion, he c i ical dis ance is o he o m:
dc i =−1
c(λ1)−c(λ0)ln η(λ0)R(λ0)
η(λ1)R(λ1)(8.6)
This c i ical dis ance desc ibes he ange om which i is be e o ansmi a wa eleng h λ1in e ms o powe
consump ion.
8.2 Op ical ansmi e s and ecei e s
The ansmission opology, he used encoding and he quan um e iciency o he ligh sou ce a e c i ical aspec s
ega ding op ical ansmi e s. On he o he hand, op ical ecei e s a e de e mined by he op o-elec ical de ice’s
NEP, he esponsi i y o he subs a e and he ampli ie ’s noise igu e.
8.2.1 Cu en d i e s
Op ical ansmi e s gene ally comp ise an LED lamp and a cu en d i e , whose e iciency highly depends on
he linea i y equi emen s o he ansmi ed signal. Theo e ically, a cu en d i e pe o ms a ansconduc ance
ampli ica ion since i con e s an inpu ol age in o a d i ing cu en . Linea d i e s a e no mally implemen ed
using bipola junc ion ansis o s, whils nonlinea d i e s usually comp ise MOSFET de ices. The i s ones
need pola iza ion in he ac i e componen s, and ha bias p oduces an ene gy leakage ha can d op down he
e iciency o he sys em below 50% easily. On he o he hand, MOSFET ansis o s only consume ene gy du ing
s a e ansi ions, allowing high speed d i e s wi h e iciencies up o 95 % [146]. None heless, hese high impedance
de ices linea ly inc ease hei powe consump ion acco ding o he s o age o ene gy on he pa asi ic capaci o s o
he ga e-sou ce junc ion. Equa ion 8.7 shows he powe consump ion o a MOSFET.
PMOSF ET =1
2CV 2 (8.7)
This e m mus be aken in o accoun o calcula e he e iciency o a MOSFET-based nonlinea d i e . In
Figu e 8.1, a ypical linea and a nonlinea d i e can be obse ed. Equa ions 8.8 and 8.9 show he e iciency o
bo h d i e s. ¯
Iis he a e age exci a ion cu en o he LED.
ηlinea =VD
Vcc +POP A
¯
I
(8.8)
ηnonlinea =VD
Vcc +1
2CV2
¯
I (8.9)
Fo equencies abo e 2POP AC−1V−2, he linea d i e u ns mo e e icien han he nonlinea one, bu his
limi is no mally a enough o conside he nonlinea d i e mo e e icien unde any ci cums ance. In he case
o nonlinea d i e s, highe dynamic anges a e achie able since he ansmi ed signal is immune o nonlinea
dis o ion. Ne e heless, linea d i e s su e om wo ypes o dynamic ange limi a ion. The i s one is di ec ly
de i ed om he d i ing ci cui y, and depends on he pola iza ion. The o he one is he inhe en nonlinea
beha io o LED de ices.
108
Chap e 8. S a egies o ene gy-e icien anscei e design
+
-
Figu e 8.1: Linea (le ) and nonlinea ( igh ) cu en d i e s
Figu e 8.2: Quan um e iciencies o di e en ypes o subs a e [147]
8.2.2 Op ical emi e s
The ene gy e iciency o op ical emi e s is measu ed in e ms o hei wall-plug e iciency. This e iciency is he
a io be ween he o al adia ed op ical powe and he elec ical powe consumed. Ma hema ically:
ηop (λ) = P x
VDID
=ηex (λ)hc
qλVD
(8.10)
ηex (λ) is he ex e nal quan um e iciency o he de ice., which is he a io o he ou pu pho on lux and he
injec ed elec on lux. This a io depends on he subs a e and he manu ac u ing. Howe e , he in e nal quan um
e iciency is no mally highe in AlGaInP (o ange, ed) de ices han in GaN (blue) ones, as Figu e 8.2 illus a es. I
mus be aken in o accoun ha ηop (λ) is no a cons an , since VDdepends on he d i ing cu en IDand ηex (λ)
also p esen s nonlinea i ies o high alues o ID.
8.3 Powe Con ol Algo i hms
Powe con ol is he selec ion o he ansmission ou pu powe in a communica ions sys em, a ending o an
op imiza ion c i e ion. This c i e ion is no mally a combina ion o an ene gy minimiza ion and he sa is ac ion o
a minimum pe o mance a he ecei e . T adi ionally, PCAs ha e been used o maximize he SNR whils keeping
he o e all in e e ence below a h eshold in wi eless communica ion channels, such as UMTS [148]. In his case,
since all he signals a e ansmi ed a he same ime, each one sp ead by i s co esponding o hogonal code, i
he e is no powe con ol, he in e e ence le el may inc ease up o ha m ul le els, d ama ically educing he BER.
In he case o UWSN, PCAs a e no p oposed as SNR-imp o ing echniques, bu as ene gy-sa ing algo i hms.
BER is impo an since i pa ially de ines he numbe o packe e ansmissions, which is e y powe consuming.
Howe e , he possibili y o adap he ansmission powe o an op imum alue in e ms o ene gy, has mo e weigh
109
Chap e 8. S a egies o ene gy-e icien anscei e design
Figu e 8.3: Scena io unde conside a ion o s udy powe con ol algo i hms
in he design o op ical UWSN nodes. Almos any ene gy-sa ing p o ocol o echnique is jus i ied in UWSN,
because he ex ension o he nodes’ li espan d ama ically educes he eplacemen cos s.
The e a e di e en axonomies o powe con ol algo i hms, depending on he classi ica ion c i e ion. Fo
ins ance, i each node akes i s own decisions he algo i hm is dis ibu ed whils on he o he case is cen alized. I
he e is channel s a us exchange be ween nodes, e go, he e is a eedback o in o ma ion, he algo i hm is closed-
loop. On he con a y, i is open-loop. Finally, depending on how is calcula ed he s ep size o he i e a i e powe
con ol p ocess, he algo i hms can be ixed-s ep, a iable-s ep o adap i e-s ep.
In his wo k, a s a -like ne wo k opology has been conside ed. This kind o ne wo k is a e y gene al app oach,
bu i is enough o s udy he impac o PCAs. Fu he mo e, a TDMA MAC p o ocol has been conside ed in o de
o simpli y he op imiza ion o he SNR and o isola e he s udy o he easible Nchannels o a gene al scheme.
Figu e 8.3 ep esen s he scena io unde conside a ion, which may comp ise a main ene gy-unlimi ed node and a
bundle o emo e nodes. This opology i s a buoy-nodes o a UAV-nodes scena io, depending on he mobili y o
he main node.
In addi ion, he s udied algo i hms a e cen alized and closed-loop. The cen aliza ion o he algo i hms has
been p oposed o educe he emo e node’s complexi y. Fu he mo e, he es ima ion o he link’s pe o mance akes
place a he main node’s side whils he uplink (main node o emo e node) is always ca ied ou a maximum
powe . The eedback o channel in o ma ion is necessa y o es ima e wi h a lowe e o he needed ansmi ou pu
powe , bu i also adds an e o sou ce ha should be aken in o accoun .
Gene ally, a powe con ol algo i hm is de i ed om an op imiza ion p oblem o he ype:
min X
i
Pi
subjec o:
(Pigii)2
σ2
N+ 2qB PjPjgij +Pj6=i(Pjgij)2≥Ki(8.11)
σ2
Nis he sum o he ecei e ’s inhe en noise powe s and Kiis he SINR h eshold o he i- h channel. gij is
he channel gain, including he esponsi i y, be ween he i- h ecei e and he j- h emi e . No e ha he quad a ic
e m o he denomina o is he op ical in e e ence e m, whils he linea e m is he sum o all he sho noises
due o bo h in e e ence and wan ed signals. These las wo e ms a e nulli ied in he p oposed scena io, due o
he o hogonali y o each channel a e he use o a TDMA scheme, yielding he ollowing simpli ied e sion o he
con ex minimiza ion p oblem.
min Pi
subjec o:
(P·g)2
σ2
N+ 2qBP ·g≥K(8.12)
Gene ally, he powe is minimized i e a i ely, as shows Equa ion 8.13.
110
Chap e 8. S a egies o ene gy-e icien anscei e design
Figu e 8.4: Sequence o he p oposed UWOC powe con ol algo i hms
P(i+1) =P(i)+ ∆P(i)(8.13)
P(i+1) is he nex ansmission powe and ∆P(i)is he calcula ed s ep. Depending on how is his s ep calcula ed,
he algo i hm would be ixed-s ep, a iable-s ep o adap i e-s ep. O he impo an aspec o he algo i hms is how
he SNR condi ion is es ima ed. The mos common s a egies a e he ollowing.
•BER. BER is di ec ly ela ed o he SNR h ough he complemen a y e o unc ion.As he modula ion o
encoding spec al e iciency inc eases, he BER becomes mo e sensi i e o he SNR. The main disad an age
o his indi ec es ima ion is he equi emen o long in eg a ion pe iods o e ie e a su icien amoun o
da a o pe o m he calcula ion.
•Di ec SNR es ima ion. The SNR is he a io be ween he squa ed expec ed alue and he a iance o a
signal. This es ima ion needs a high amoun o samples o p esen a eliable con idence in e al. Howe e , i
a so signal de ec ion we e pe o med using a DSP o a FPGA, his es ima ion could be eal- ime pe o med.
•Recei ed powe es ima ion. Fo si ua ions in which he sho noise could be neglec ed, he SNR condi ion
can be di ec ly calcula ed using Equa ion 8.14. Fu he mo e, his echnique is sui able o low-powe de ices,
since only a ew amoun o samples pe ame a e needed. Low pass il e ing may be used o educe noise
be o e sampling, o a ew samples om a long-du a ion synch oniza ion heade could be acqui ed o es ima e
he ecei ed powe .
(P·g)2≥K·σ2
N
P·g≥K1/2·σN(8.14)
Some o he p oposed cen alized algo i hms need knowledge o he emo e node’s emission pa ame e s: ene gy
e iciency, allowed powe codes, ansimpedance con e sion ac o , e ce e a. The e o e, an ini ializa ion s age o
e ie e he necessa y in o ma ion is needed be o e he execu ion o he PCA. Figu e 8.4 depic s he s ages o he
p oposed PCAs.
8.3.1 Fixed-s ep algo i hm
Fixed-s ep algo i hms a e he easies app oach o ene gy minimiza ion. Depending on he esul o Equa ion 8.14,
he ou pu powe is inc emen ed Nδ o dec emen ed Mδ. Ma hema ically:
P(i+1) =P(i)+ ∆P(i)
∆P(i)=


Nδ P ·g < K1/2·σN
−Mδ P ·g≥K1/2·σN
(8.15)
This algo i hm is cha ac e ized by i s low con e gence speed and i s low s abili y a e eaching he op imum
alue. Howe e , is e y memo y and compu a ionally-e icien .
111
Chap e 8. S a egies o ene gy-e icien anscei e design
Figu e 8.10: Block diag am o di e en op ical OFDM schemes
ADO-OFDM scheme
We ha e poin ed ou succinc ly DCO-OFDM is ine icien in e ms o op ical powe and so does ACO-OFDM
ega ding bandwid h. In Flip-OFDM, e en hough he complexi y a he ecei e is augmen ed, he o e all pe o -
mance akes ad an age o he s eng hs o each echnique. On he e en subca ie s, DCO-OFDM is ansmi ed
whils on he odd ones ACOOFDM is used; consequen ly, he op ical powe e iciency is be e han DCO and
all he subca ie s a e employed enhancing bandwid h e iciency wi h espec o ACO. A he ecei e , he ACO
symbols a e ex ac ed in he same way as con en ional ACO, a he same ime, DCO symbols equi e an in e -
e ence cancella ion me hod due o bo h clipping noises, odd and e en, all in he e en subca ie s. Hence, he
cons ella ion sizes in he DCO subca ie s a e smalle han usual.
Flip-OFDM scheme
As an al e na i e app oach, his scheme spli s he signal in o posi i e and nega i e pa s which hen a e se ialized
in wo consecu i e OFDM sub ames. Rega dless o he ac ha i is a pa en [157], which has no succeeded in he
li e a u e, se e al wo ks analyze i s goodness acing ACO-OFDM. The au ho s in oduce a modi ica ion o a ai
compa ison. On he whole, Flip-OFDM pe o ms almos iden ically when compa ed o ACO-OFDM sa ing 50%
in ecei e ha dwa e complexi y now ha all subca ie s ca y da a. The penal y o ansmi ing wo sub ames
pe N samples b ings he possibili y o demodula ing N symbols pe IFFT ope a ion, while ACO-OFDM needs wo
N-IFFT ope a ions o achie e he same N samples.
8.4.2 P oposed scheme
Op ical OFDM is limi ed by he ansmission o only posi i e signals. As i has been shown, his es ic ion has been
sol ed using se e al me hods, anging om bias addi ion o in elligen mapping on he FFT block aking ad an age
o he p edic able ha monics a e a clipping ope a ion. Ano he impo an issue in op ical OFDM is he implici
nonlinea i y o he emi e s e sus he necessi y o linea d i e s o handle he emission. I he LED de ices we e
ope a ed in a linea egion, he dynamic ange would be signi ican ly diminished o a oid nonlinea dis o ion on
he OFDM ame. A p e ious dis o ion o compensa e he inhe en LED beha io may be used, adding complexi y
o he design. In his hesis, a PWM encoding o he OFDM ame is p oposed. By adding his ope a ion, he
linea i y equi emen is a oided and he use o nonlinea and e icien powe d i e s is allowed. Fu he mo e, his
kind o codi ica ion is less sensi i e o empe a u e a ia ions on he emi e , because he in o ma ion is encoded
in he du y cycle o each PWM symbol. In he ollowing subsec ions he ad an ages and disad an ages o he
in oduc ion o his block a e discussed.
Figu e 8.11 depic s he block diag am o he p oposed scheme. A PWM modula o has been added a he ou pu
s age o he emi e . This modula o is one o he main pa s o a class D ampli ie . Howe e , he low pass il e has
been emo ed om he emi e and placed a he ecei e ’s on end. F om LTI sys ems heo y, his simple change
gene a es he same wa e o m a he ecei e whils d ama ically inc eases he ene gy e iciency a he ansmi e .
Howe e , he SNR is dec emen ed adding an ex a noise sou ce de i ed om he N-bi s quan iza ion o he ou pu
OFDM wa e o m. Fu he mo e, he ou pu wa e o m needs a sampling equency 2N imes highe han he linea
e sion i i is digi ally gene a ed. In addi ion, as he eal- alued op ical OFDM samples a e no mally dis ibu ed,
a p edis o ion block such as a µ-law may be used o inc ease he dis ance be ween symbols be o e he ADC block.
I may be also conside ed ha all he subca ie s a e used o ca y in o ma ion, as in DCO-OFDM, bu wi h
118

Chap e 8. S a egies o ene gy-e icien anscei e design
Figu e 8.11: Block diag am o he p oposed scheme
Ad an ages Disad an ages
Allows he use o nonlinea d i e s Needs sampling equency 2N imes highe
Eases synch oniza ion Dec eases SNR
Reduces he cos
P esen s a highe dynamic ange
Table 8.5: Summa y o he cha ac e is ics o he p oposed scheme
he ad an age o educing he PAPR o he modula ion o 3 dB because he peak powe is ixed o a known and
con olled alue. The pulsed na u e o a PWM signal allow an easie synch oniza ion espec o adi ional OFDM
schemes. Fu he mo e, he ad an ages o OFDM agains mul ipa h dispe sion and ading a e conse ed. Table 8.5
summa izes he main ad an ages and disad an ages o he p oposed scheme.
Ma hema ical desc ip ion
Using he signal yOF DM [n] as s a ing poin , he d i ing cu en signal a he LED is shown a Equa ion 8.31.
ILED( ) = Imax
N−1
X
i=0
Π (τ(yOF DM [i], −i·Tsym) (8.31)
Whe e τ(·) is a linea mapping unc ion be ween he desi ed du y cycle and he OFDM samples, Tsym is he
PWM symbol du a ion and Π(·) is he pulse unc ion. I a p edis o ed e sion we e ca ied ou , τ(·) would
ep esen he nonlinea mapping commen ed abo e. The mean elec ical powe o a PWM-OFDM ame may be
exp essed as ollows.
Pelec =ImaxV(Imax)E[τ] (8.32)
In oducing he de ini ion o PAPR, which is he a io be ween he maximum and he a e age powe , i can
be easily shown ha his scheme would p esen a PAPR o 3 dB o e e y ame. Op ical OFDM echniques
p esen a lowe spec al e iciency ega ding adio sys ems, because bo h eal and imagina y pa s canno be
ansmi ed simul aneously. ACO-OFDM uses hal he subca ie s in o de o p oduce a ully- eco e able clipped
ame. Fu he mo e, as op ical OFDM scheme only ansmi he eal pa o he FFT, He mi ian symme y
mus be applied esul ing in a hal ing o he e iciency. This scheme is he less spec al-e icien o he common
adi ional op ical OFDM echniques, bu is also he mos ene gy e icien . The spec al e iciency o ACO-OFDM
is de e mined by Equa ion 8.33.
ξACO ≈log2(M)Nsc
4(Nsc +Ncp)(8.33)
Whe e Mis he numbe o symbols o he cons ella ion, Nsc is he numbe o subca ie s and inally Ncp is
he numbe cyclic p e ix samples. In he case o PWMO-OFDM, he spec al e iciency is di ec ly a ec ed by he
bandwid h o he PWM signal ha encodes each IFFT sample, bu i uses all he a ailable subca ie s o ansmi
in o ma ion. Bo h in o ma ion densi y and bandwid h inc ease esul in a spec al e iciency which is educed by a
ac o o 2N−1. The e o e, his scheme d ama ically inc eases he ene gy sa ing bu educes he spec al e iciency,
being only sui able o medium-speed communica ion scena ios such as UWSN.
119
Chap e 8. S a egies o ene gy-e icien anscei e design
Cu en (mA)
50 60 70 80 90 100 110 120 130 140 150
Op ical Powe (mW)
4
6
8
10
12
14
16
18
20
22
Red
Blue
Figu e 8.12: Op ical emi ed powe s d i ing cu en
The main ad an age o ACO-OFDM agains DCO-OFDM is he powe educ ion due o he clipping, which
ans o ms i in o one o he cu en mos ene gy-e icien op ical OFDM schemes. Taking in o accoun ha he
p obabili y densi y unc ion o each sample wi hin a su icien ly la ge OFDM ame is de ined by a no mal p ocess,
he clipped ame educes he ame op ical powe o he hal .
Rega ding DCO-OFDM, he ame ene gy mus be inc eased in o de o ansmi i . The ame op ical powe ,
in his case, ends o he DC-bias op ical powe . When conside ing PWMO-OFDM, he mean ansmi ed op ical
powe is de ined by he PWM signal ampli ude and he mean du y cycle as i has been al eady shown. Le s assume
a same-elec ical powe scena io be ween ACO-OFDM and PWMO-OFDM.
E[τ]ImaxV(Imax) = E[IACOV(IACO)] = Pelec (8.34)
ACO-OFDM needs a linea d i e , which is sensi i e o empe a u e a ia ions and o he ope a ion egion.
On he o he hand, PWMO-OFDM uses a nonlinea powe d i e which is immune o he ope a ion poin and
empe a u e, ega ding nonlinea dis o ions on he signal. Gene ally, he ou pu op ical powe o an LED has a
linea beha io espec o he d i ing cu en . De ining he luminous e iciency as:
η(λ) = φ(ILED)·ILED
ILED ·V(ILED)=φ(ILED)
V(ILED)(8.35)
As i was commen ed a he beginning o he chap e , linea LED d i e s may p esen an elec ical- o-elec ical
e iciency up o 80%, whils class D ampli ie s (which a e he ones used o PWM signals) ha e e iciencies up
o 95% [158]. In addi ion, using he p oposed e iciency o mula, i mus be aken in o accoun ha he d i e
powe will be de e mined by he commu a ion o he MOSFET d i e ansis o , which implies a small ixed powe
payback a a gi en Pmax.
8.4.3 Expe imen al cu es
Du ing he measu emen s o Chap e 7, he used op ical emi e s we e cha ac e ized using an in eg a ing sphe e.
The ob ained powe -cu en cu es a e depic ed in Figu e 8.12. Fu he mo e, he ol age-in ensi y cu es o bo h
emi e s a e shown in Figu e 8.13.
The cu en a which a nonlinea d i e is mo e ene gy-e icien han a linea one, aking in o accoun he
conside a ion s a ed in Equa ion 8.34, is de ined by:
ηlinea
φ(IACO)
V(IACO)≤ηnonlinea
φ(Imax)
V(Imax)(8.36)
Rea anging he e ms o Equa ion8.36 and de ining ela i e measu emen s be ween luxes and ol ages, i
yields:
ηlinea
ηnonlinea ≤∆φ
∆V(8.37)
120
Chap e 8. S a egies o ene gy-e icien anscei e design
Cu en (mA)
1.5 2 2.5 3 3.5 4 4.5
Vol age
-50
0
50
100
150
200
250
300
Blue
Red
Figu e 8.13: V-I cu e o he used emi e s
A e including he measu ed e iciencies in he abo e Equa ions, he a io ∆φ
∆V o a ange o elec ical powe s
has been ob ained. The same emi ed powe condi ion o Equa ion 8.34 has been included. Figu e 8.14 depic s his
cu e and compa es i o he a io o d i e e iciencies. In o de o ob ain he mean cu en o an ACO-OFDM
scheme, he p obabili y densi y unc ion o he OFDM samples should be conside ed. In ACO-OFDM, each sample
ollows a Hal Gaussian dis ibu ion whe e he a iance depends on he used mapping. Fo a QAM mapping, his
a iance is uni a y and he expec ed alue o each sample is 1/√2πas is commen ed in [153].
I can be obse ed ha o almos e e y elec ical powe , nonlinea d i e s a e mo e ene gy e icien han linea
d i e s. No ice ha hese cu es co espond o a single LED emi e . In he case o a LED a ay whe e he cu en s
a e di ided, he use o PWM is ecommended in e ms o ene gy. F om he da a, only e y e icien linea d i e s
(mo e ha 80%) jus i y he use o con inuous wa e o ms.
8.4.4 Commen s on he BER pe o mance
As i was commen ed abo e, he pulse wid h modula ion o he OFDM wa e o m in oduces an ex a noise e m
due o quan iza ion, which a ec s he SNR in he ollowing way:
SNRP W MO−OF DM ≈S2
σ2+σ2
Q
(8.38)
Whe e σ2
Qis he quan iza ion noise powe , which depends on he quan iza ion s ep ∆V= (Vmax −Vmin)/2N.
I implies ha he e is a maximum achie able SNR bounded by his always-p esen noise sou ce. The BER cu e
o he p oposed scheme would be igh -shi ed espec o a non-quan ized scheme, as shows Figu e 8.15. I mus
be aken in o accoun ha inc emen ing he numbe o bi s o enhance he BER pe o mance has se e al ha m ul
implica ions:
•The spec al e iciency is educed. The p oduc ∆SNR ·∆ξis conse ed in his ype o sys em. Hence, an
inc emen on he SNR is di ec ly ansla ed o a dec emen o he same amoun in he e iciency. Ne e heless,
he alue o Ncan be op imized.
•The powe consump ion o he swi ching componen s is inc eased. As i was commen ed in he d i e s
Sec ion, he powe consump ion o he MOS-based componen s inc eases linea ly wi h he equency. In his
case, he a io ∆SNR/∆PMOSF ET is cons an .
•The nonlinea d i e e iciency is educed because o he p e ious e ec . Depending on he pa asi ic capaci-
ance o he used de ice, his e ec may be neglec ed. As i was commen ed a he beginning o he chap e ,
he e is a swi ching equency sa which he linea d i e su passes he nonlinea d i e e iciency, which is
de ined by:
s=2POP A( s/2N)
CV 2(8.39)
121
Chap e 8. S a egies o ene gy-e icien anscei e design
Elec ical Powe (mW)
0 50 100 150 200 250 300 350 400 450 500
Me i Figu e
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
Red
Blue
Figu e 8.14: Me i igu e o Equa ion 8.37 o he LED de ices used in Chap e 7. The ho izon al do ed lines
co espond o he a io o d i e e iciencies. The uppe one is o a linea d i e e iciency o 85%, whils he lowe
co esponds o an e iciency o 50%. In bo h cases, he nonlinea e iciency is 95%
5 6 7 8 9 10 11 12 13
SNR (dB)
10-8
10-6
10-4
10-2
100
BER
ACO-OFDM
PWMO-OFDM
Figu e 8.15: BER s SNR cu es o an ACO-OFDM (512 subca ie s wi h QAM) scheme and a PWMO-OFDM
(1024 subca ie s wi h QAM) scheme. No e he igh 3 dB shi o he PWM-based scheme.
122
Chap e 8. S a egies o ene gy-e icien anscei e design
Gene ally, he pa asi ic capaci ance is e y small (a ew pF) and he swi ching ol age Vis de e mined by he
used LED a ay. Mo eo e , he powe consump ion o an OPA-based linea d i e also inc emen s wi h he signal’s
bandwid h, u ning e en highe he c i ical equency. In conclusion, a comp omise be ween powe consump ion
and BER pe o mance should be de ined in o de o op imize he numbe o bi s o he ansmi e ’s DAC.
123

Chap e 8. S a egies o ene gy-e icien anscei e design
124
Chap e 9
Conclusions and Fu u e Resea ch
Du ing his hesis, se e al con ibu ions ha e been made ega ding di e en aspec s o channel modeling and ene gy
e iciency in UWOC. A e analyzing he s a e-o - he-a esea ch lines in Chap e 3, wo clea conclusions we e
ex ac ed. On he one hand, channel modeling in UWOC has been p ima ily di ec ed by con ibu ions a physical
le el, ega ding di e en phenomena such as u bulences and mul iple sca e ing. T adi ionally, Bee -Lambe ’s law
has been used o desc ibe ex inc ion in UWOC, bu Cochenou e al. demons a ed in [16] ha sca e ing p oduces
beam sp eading and in consequence, he e ec i e ex inc ion is smalle han he sum o α(λ) and b(λ). Fu he mo e,
he e a e di e en simula ion engines using Mon e Ca lo schemes in he li e a u e. None heless, hese algo i hms
use he Henyey-G eens ein sca e ing phase unc ion o model he pho on de ia ion due o pa icles, which is an
o e simpli ica ion o a mo e ealis ic app oach such as Mie sca e ing. The main ad an ages o Henyey-G eens ein
a e he easy pa ame iza ion o he sca e ing b oadening wi h a single pa ame e and he as calcula ion o
andom angles using his dis ibu ion, bu he accu acy is educed as i is commen ed in [38]. On he o he
hand, he con ibu ions add essing applica ions ange om e y speci ic scena ios such as p o iding eedback o
swimme s in a pool [109], o long-dis ance UWOC links in ac ual scena ios du ing ocean moni o ing campaigns
[86]. The e a e di e en wo ks add essing hyb id op o-acous ic anscei e s o UWSN [82]. These kind o de ices
ake ad an age o he high inhe en ene gy e iciency and bandwid h o UWOC, whils main aining he possibili y
o long ange communica ion using UAC. Howe e , s a is ical app oxima ions o he UWOC channel ha e been
ocused on p o iding a as e me hod o ob ain channel gain es ima ions [47], bu he e a e no s a is ical channel
models o UWOC links in e ms o channel gain o bandwid h. Finally, he e is an e iden lack o con ibu ions
ega ding ene gy e iciency in UWOC e en hough i is o capi al impo ance aking in o accoun he eplacemen
cos o unde wa e nodes.
The UWOC channel is a linea and ime a ian channel, bu i s ime a iabili y is subjec o di e en phenom-
ena such as u bulences, misalignmen and sca e ing. In FSO, u bulences a e no mally subjec o Kolmogo o ’s
spec um unde weak u bulence egimes. None heless, he op ical p ope ies o seawa e p esen a iabili y no
only due o empe a u e g adien s, bu also because o salini y a ia ions. In he li e a u e, Kolmogo o ’s spec um
has p o en o be inaccu a e, and Nikisho ’s spec um is widely used in he li e a u e [122]. This app oxima ion
includes he wo dependencies in he spa ial equency spec um. I was p o en du ing Chap e 4, ha he UWOC
scin illa ion index depends on he dis ance wi h an exponen anging om 3/2 o 11/6, and no s ic ly on FSO’s
adi ional 11/6 exponen . The exponen is de ined by he spec um’s pa ame e s.
In Chap e 4, he impulse esponse o di e en UWOC scena ios was ob ained using a Modi ied Mon e Ca lo Ray
T acing algo i hm. Unlike o he au ho s, Mie sca e ing was used as phase unc ion in his wo k. Consequen ly, he
complexi y o he ay gene a ion is inc eased in exchange o he enhanced accu acy. Howe e , using he modi ied
app oach, a di ec ay o he ecei e is calcula ed a e each sca e ing, educing he olume o ays and he
con e gence ime o he algo i hm espec o he impac - es ing condi ions used in he li e a u e. Fu he mo e, he
algo i hm was pa allelized using bo h mul ip ocesso and GPU schemes. Speedups up o 42 we e ob ained using a
NVidia Tesla M2050 GPU, allowing calcula ions o ull impulse esponses wi h 105 ays in less han 2 seconds. The
economical e iciency o bo h pa alleliza ion echnologies was analyzed, showing ha GPU implemen a ions a e
mo e cos -e ec i e han mul ip ocesso schemes. Mo eo e , he impac o he channel pa ame e s in o he ecei ed
impulse esponse was analyzed. The ollowing e ec s we e obse ed:
•The link ange educes exponen ially he channel gain and he bandwid h. As he dis ance inc eases, he
op ical pa hs ollowed by he a i ing ays is g ea e . The e o e, he abso p ion losses and he numbe o
impac s wi h pa icles also inc ease.
•Di ec i e emi e s concen a e ene gy in na ow solid angles, whils o he emi e s dispe se ligh . Taking in o
accoun he e ec o mul iple sca e ing, al hough he ene gy we e collima ed, a signi ican amoun o ene gy
may a i e he ecei e . Fo pe ec ly aligned links, he highe he di ec i i y, he highe he bandwid h and
he channel gain.
125
Chap e 9. Conclusions and Fu u e Resea ch
•The emission wa eleng h has wo main e ec s. Fi s ly, he seawa e abso p ion and he loss due o pa icles
a e wa eleng h dependen . Secondly, he no malized dimension o he suspended ma e depends on he
wa eleng h, and he e o e, o a gi en pa icle size, he Mie sca e ing phase unc ion may widely a y om
a wa eleng h o ano he .
•As i was commen ed abo e, he pa icle adius de ines he shape o he sca e ing, bu o a gi en concen-
a ion o pa icles pe cubic me e , he numbe o sca e ings inc eases wi h he pa icle adius. The e o e,
he pa icle adius e ec inc emen s he numbe o sca e ings bu u ns he phase unc ion mo e o wa d-
dominan . The obse ed simula ed esul s sugges s ha he channel gain is educed wi h he pa icle adius,
due o he inc easing numbe o impac s, whils he bandwid h is inc eased due o he educ ion o he a e age
cosine o he phase unc ion.
•The concen a ion o pa icles has wo e ec s. The i s one is he same as he pa icle adius. As he
concen a ion inc eases, he collision p obabili y also inc eases and he channel gain is educed. The o he
e ec is o con ibu e o he b oadening o he BSF, allowing g ea e misalignmen e o s be ween emi e and
ecei e . Depending on he dis ance and he pa icle adius, he concen a ion o pa icles may con ibu e o
a g ea e ligh collec ion since a bigge solid angle has in luence on he ecei e .
•The dis ance o seabed was demons a ed o ha e a e y educed e ec on he channel gain. None heless,
he bandwid h is sligh ly educed in ho izon al deep links. Since he dis ance o seabed may be neglec ed in
UWOC channel es ima ion, he seabed albedo has also negligible in luence.
•Fo nea -su ace links, he con ibu ions due o su ace e lec ions canno be ob ia ed since hey p esen
a signi ican impo ance. Howe e , his e ec is dispe sed as he link ange inc eases due o he e ec o
ex inc ion. Depending on he dep h and o a s ill wa e scena io, he illumina ed su ace a ea wi h g ea e
in luence on he ecei ed powe is modi ied. The e o e, as he dep h inc eases, he channel gain is educed
and he bandwid h inc eased.
•Wind speed p oduces a andom slope a ia ion on he seawa e su ace. This andom a ia ion u ns each
poin o he su ace in a po en ial sca e e , whe e he o e all a e age con ibu ion o he illumina ed su ace
is inc emen ed. Rega ding he bandwid h, he mul ipa h componen is s ong in s ill wa e scena ios, whils
he andom agi a ion o seawa e dispe ses his componen along he impulse esponse, inc easing he a e age
bandwid h.
In Chap e 5, unde wa e - o-ai links we e s udied. This ype o e ical links a e sui able o shallow wa e node
deploymen whe e he da a acquisi ion is pe o med wi hou subme ging he anscei e , o ins ance, an ope a o
in a ship o a d one. The sealing p ocess o a anscei e o make i subme sible usually inc emen s ab ica ion
cos s. This possibili y is a cos -e ec i e solu ion o shallow wa e UWSN applica ions. The unde wa e - o-ai
p oblem was add essed o m a geome ical poin o iew, associa ing he ecei ed powe o he op ical powe ha
impac s on he su ace and is o wa ded o he pho ode ec o . This way, he analysis is based on calcula ing how
much ene gy a i es a ce ain a ea o he seawa e su ace. To simpli y he analysis, only su aces wi h shapes ha
ensu e he bijec i i y o a spa ial ans o ma ion we e conside ed. This ans o ma ion ela ed he XY posi ions o a
ay on he su ace and he posi ion a he ecei e ’s plane. A e imposing se e al condi ions ega ding he sea wa e
spec um, which was conside ed monoch oma ic, a nume ical in eg a ion scheme was used o ob ain simula ions o
he ecei ed powe . I was obse ed ha he ecei ed ligh in ensi y ollowed he shape o he sea wa es, due o
he lensing e ec o a p opaga ing plane wa e. In addi ion, an analysis simila o he one made du ing Chap e
4 was pe o med o ela e each channel pa ame e o he ecei ed in ensi y. Fu he mo e, he channel a ailabili y
was s udied in each scena io espec o he ecei e sensi i i y. The main ob ained conclusions we e:
•The emi e dep h p oduces an exponen ial decay on he ecei ed powe , ollowing he ex inc ion cu e.
•The ecei e heigh has a simila e ec o he p e ious pa ame e , since he solid angle o med by he ecei e
and he emi e is educed wi h he squa ed dis ance.
•The sea wa e heigh has a di ec impac on he seawa e su ace slope, which is c i ical on he calcula ion
o he p ojec ed pho ode ec o a ea. S eepe slopes gene a e deepe adings, whils low-heigh sea wa es
p oduce sligh a ia ions on he ecei ed powe . The peak- o-peak a ia ions o he ecei ed powe can be
highe han 10 dB, p oducing a no able impac on he channel a ailabili y and inc easing he equi emen s
o he ecei e .
•The sea wa e wa eleng h p oduces he same e ec as he sea wa e heigh . In his case, longe wa eleng hs
imply mo e elaxed slopes and hence, smalle a ia ions.
126
Chap e 9. Conclusions and Fu u e Resea ch
•Wind shea e ec has a e y in e es ing e ec on he a ia ion o he ecei ed powe . As he wind speed in-
c eases, he peak- o-peak a ia ion o he ecei ed signal is educed (and also he maximum alue). The e o e,
windy scena ios may inc ease he channel a ailabili y when he ecei e ’s sensi i i y is wi hin he a ia ion
ange o he ecei ed op ical powe .
The s a is ical modeling o he UWOC channel esponse was add essed in Chap e 6. The main con ibu ions
made du ing his chap e we e:
•Analyzing he mos sui able p obabili y dis ibu ion unc ion o bo h channel gain and bandwid h.
•De ining a F esnel zone a ending o he 95 % o he impulse esponse ene gy, a e pe o ming a ec angula
app oxima ion.
•P oposing a model o he losses induced by big opaque pa icles.
A b ie analysis o he impulse esponse o mula showed he possibili y o de ining an ad hoc p obabili y den-
si y unc ion o he channel gain. None heless, a e pe o ming a maximum likelihood es ima ion and se e al
hypo hesis es s on he simula ed da a, he Gene alized Ex eme Value dis ibu ion ob ained he bes esul s in
he benchma k o bo h channel gain and bandwid h. This benchma k consis ed on a se o scena ios co e ing a
wide ange o pa ame e combina ions. None heless, he p oposed dis ibu ion only co e ed a ew cases less han
GEV. The ob ained dis ibu ion showed how a ies he ecei ed powe a unco ela ed ime ins an s. F om he
ob ained da a, i was obse ed ha gene ally:
•The SNR inc eases wi h he di ec i i y, since he a iabili y o he ecei ed powe is educed. I is s aigh -
o wa d o no ice ha na ow emission cones a e subjec o a lowe amoun o possible sca e ings.
•The link ange educe he e ec o sca e ing-induced a iabili y. Howe e , he inc emen o he SNR due o
dis ance espec o he impac wi h pa icles is coun e ed by he e ec o u bulences, which inc ease wi h a
powe law wi h dis ance.
•F om he ob ained da a i can be in e ed ha o a gi en link ange and concen a ion, he e is a pa icle
size ha minimizes he SNR. As i has been commen ed se e al imes du ing his documen , la ge pa icle
adii imply a high dominance o he o wa d di ec ion o he sca e ing. This leads o an inc easing SNR o
dec easing pa icle adii.
•The pa icle concen a ion educes he SNR. This occu s because o high concen a ions he e a e mo e
possible sca e e s wi hin he link’s olume o in luence.
The impulse esponse can be di ided in he sum o wo ec angles due o i s ab up shape. The i s ec angle
may be de ined o con ain he 95 % o he ene gy. I s wid h, o delay sp ead, is associa ed o hose delays a which
he e is signi ican ene gy con ibu ions. The e o e, he maximum delay de ines h ough he space- ime ela ion
he maximum a eled dis ance o a single-sca e ed ay. Taking in o accoun he geome y o he scena io, his
maximum dis ance gene a es an ellipsoid ha can be e e ed o as he olume o in e es o F esnel zone. This
F esnel zone has se e al implica ions:
•The de ini ion o a olume o in e es opens he possibili y o ime-dependen simula o s whe e each pa icle
is acked wi hin he ellipsoid. This kind o simula o would be able o model he ime- equency esponse o
he channel, om which cohe ence ime can be ex ac ed.
•The F esnel zone desc ibes he olume a which any in e sec ing objec p oduces an e ec on he ecei ed
powe .
Fu he mo e, he impac o big opaque pa icles was also analyzed in Chap e 6. A big opaque pa icle is a
pa icle ha does no p oduce nei he sca e ing no di ac ion, o ins ance, sand g ains. Ac ually, sand g ains
would gene a e con ibu ions due o hei e lec i i y, bu his was ob ia ed o isola e he shadowing e ec o hese
pa icles. A e s a is ically analyze he in luence o hese pa icles, i was ound ha big opaque pa icles p oduce
an impac on he SNR ha depends on hei size, he link’s ange, he concen a ion o pa icles and he adii o
emi e and ecei e . Following he endency o his hesis, he in luence o each o he a o emen ioned pa ame e s
was analyzed, showing ha :
•The SNR diminishes wi h he link ange, since he a e age numbe o pa icles linea ly depends on he
dis ance. The highe he numbe o pa icles, he highe he p obabili y o su e ading.
127
Appendix A. Demons a ions o Chap e 5
This equa ion has wo solu ions: he i ial solu ion x= 0 and ln x
zapp oxima ely cons an in y. Pe o ming
he Taylo se ies o he la e a ound (0,0) up o he i s de i a i e, and imposing ha his de i a i e mus be
much lowe han he cons an e m, i yields he ollowing ela ion.
|y|<< 
x z
x,y z− z,y x
ln x
z(0,0)
(A.8)
Sol ing Equa ion A.8 i yields ha he e is no limi a ion on he y-axis, since x,y and z,y end o ze o. Fo
∆y,x a simila condi ion can be ob ained bu in e ms o x.
|x|<< 
y
z(H−S)
ln ((H−S) z/ y)
(H−S)( z,x y− y,x z)−S,x z y(0,0)
(A.9)
I is s aigh o wa d o demons a e ha y,x and z,x linea ly depend on ∂(ˆn·ˆ )/∂x. In o de o anish his
las e m (elimina e he dependency on X), he p opaga ing sea wa e mus sa is y ha :
λ >> πp2Dη0(A.10)
This las condi ion a ises om he ollowing app oxima ion:
∂(ˆn·ˆ )
∂x =∂ˆn
∂x ˆ +∂ˆ
∂x ˆn
ˆ =(x, y, S)
(x2+y2+S2)1/2→ˆ (0,0) ≈(0,0,1)
ˆn=(−S,x,0,1)
(1 + S2
,x)1/2
∂ˆ
∂x =(1,0, S,x)
(x2+y2+S2)1/2−(x, y, S)x+SS,x
(x2+y2+S2)3/2→∂ˆ
∂x(0,0) ≈(S−1,0,0)
∂ˆn
∂x =(−S,xx,0,0)
(1 + S2
,x)1/2−(−S,x,0,1) S,xS,xx
(1 + S2
,x)3/2(A.11)
The e m S−1≈D−1since D >> η0. Taking his in o conside a ion and conside ing he wo s case, he
p e ious equa ions can be educed o:
S,xxD << 1 (A.12)
Finally, in oducing he app oxima ion on Equa ion A.9, he maximum xdis ance ha assu es ha ∆y,x →0
is he same in he case o y, because y= 0 o ˆ = (0,0,1). Hence, xand ydo no limi he anishing o he c oss
pa ial de i a i es i condi ion A.10 is sa is ied.
Finally, in o de o ensu e he p esence o in e se, ∆x,x and ∆y,y mus be bounded o he in e al (−1,∞).
These condi ions a e o mula ed in Equa ion se A.13.
∆x,x >−1
∆y,y >−1 (A.13)
In oducing he co esponding dependencies and assuming he same as be o e, i yields he ollowing sys em o
inequa ions:
( z)2+ (H−D) x,x z−(H−D) z,x x>0
( z)2+ (H−D) y,y z−(H−D) z,y y>0 (A.14)
Since he sea wa e p opaga es along he x-axis, he limi ing ange is imposed by he maximum de ia ion o x.
This maximum de ia ion δx is ela ed o he x-axis i sel (y= 0). In oducing he assump ions made du ing he
p e ious s eps in o Equa ion se A.13 yields:
D+ (H−D)nw1
D−η0ksin(ω −kδx)>0
D+ (H−D)nw
D>0 (A.15)
134

Appendix A. Demons a ions o Chap e 5
Dep h (m)
2345678910
δx(m)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
H-D = 1
H-D = 5
Figu e A.1: Maximum de ia ion in he x-axis o assu e bijec i i y (η0= 0.25 m).
The second inequa ion is sa is ied o all Dand Hsince H > D. Rega ding he i s inequa ion, he ollowing
condi ion can be ob ained:
sin(ω −kδx)<D2+ (H−D)nw
nwDη0k(H−D)(A.16)
This condi ion may be educed o he wo s case, which occu s when he sine ends o one. Making a second
o de app oxima ion o he sine nea o one, he maximum de ia ion o δx which assu es he exis ence o in e se
is:
|δx|<2D2+ (H−D)nw(1 −Dη0k)
nwDη0k3(H−D)(A.17)
Finally, he e is a minimum heigh o e he s ill wa e le el (H−D)min a which he las condi ion is sa is ied.
(H−D)min =D2
nw(Dη0k−1) (A.18)
F om he denomina o o he las exp ession, an uppe bound o he sea wa e wa eleng h a ises. Join o
condi ion A.10, o conside he app oxima ions as alid, λmus be in he in e al:
πp2Dη0<< λ < 2πDη0(A.19)
This las exp ession desc ibes an absolu e minimum o λ, which is de ined by he in e sec ion o he wo bounda y
unc ions. The wa eleng h only complies wi h condi ion A.19 i Dη0>1/2, which is easily sa is ied by a a eling
sea wa e unde shallow wa e p opaga ion. Figu es A.1 and A.2 depic he las wo limi s in e ms o (H−D) and
D o a sea wa e sa is ying condi ion A.10.
I can be obse ed ha he a ea which assu es bijec i i y is wide enough compa ed o he pho o ecei e ’s a ea.
135
Appendix A. Demons a ions o Chap e 5
Dep h (m)
2345678910
H-D (m)
8
9
10
11
12
13
14
15
16
17
18
Figu e A.2: Maximum heigh a which he e is in e se (η0= 0.25 m).
136
Appendix B
Recei ed ligh in ensi y in pa ially
obs uc ed links
In Chap e 6, a s a is ical app oach o he ecei ed ligh in ensi y in a link pa ially obs uc ed by big opaque
pa icles was p esen ed. In his Appendix, he ma hema ical de elopmen om which he equa ions o Chap e
6 we e de i ed is p esen ed. In o de o ease he analysis, he p opaga ion medium will be conside ed lossless,
he emi e will be conside ed as iso opic, and a single sphe ical pa icle will conside ed. Figu e B.1 depic s he
scena io unde conside a ion.
Figu e B.1: Pa icle obs uc ing a link comp ising an ex ended sou ce and a pho odiode
Since he pa icle’s posi ion is impo an , he sou ce will be conside ed as an ex ended sou ce o ligh , whe e each
poin o he su ace has he same emission pa e n and adiance. Fu he mo e, o ake ad an age o cylind ical
symme y, bo h emi e and ecei e a e conside ed ci cula . Unde he depic ed si ua ion, o a pa icle- ee
scena io, he ecei ed powe can be exp essed as ou cascaded in eg als o he o m:
P x =Z x Zϕ x ZθZϕ x
P x
4πA x
x sin θd xdθdϕ xdϕ x (B.1)
The ecei ed powe depends on he solid angle o med by he ecei e and each poin o he emi ing su ace. I
he e is no obs uc ing pa icle, he las in eg al p esen s symme y on he emi e , and he solid angle sub ended
can be app oxima ed by dΩ ≈A x/d2, yielding:
P x =P x
2A x
A x ZR x
0
xdlink
(d2
link + 2
x)3/2d x (B.2)
Sol ing he in eg al:
P x =P x
4πR2
x
A x 1−dlink
pd2
link +R2
x !(B.3)
Fo a small a ea emi e , which is a common conside a ion in OWC in gene al, he o al ecei ed powe depends
on he ollowing limi :
lim
R x→0
1
R2
x 1−dlink
pd2
link +R2
x !=1
d2
link
(B.4)
A e analyzing he pa icle- ee scena io, le s in oduce a single pa icle o adius Ramid he link. Now, in his
si ua ion, he e would be ce ain angles a which he solid angle be ween emission poin and ecei e is educed, as
Figu e B.1 showed. Now, he o al ecei ed powe can be in eg a ed unde wo di e en in e als. An in e al a
which he pa icle does no p oduce any e ec , and a pa icle-in luenced in e al. Figu e B.2 shows his di ision
o he in eg al.
Figu e B.2: Di ision o he in eg a ion domain due o he p esence o a pa icle
The in eg al o Equa ion B.2 can be ew i en as:
137
Appendix B. Recei ed ligh in ensi y in pa ially obs uc ed links
P x =P x
2A x
(A x −Apa )ZR0
0
xdlink
(d2
link + 2
x)3/2d x+
P x
2A x
A x ZR x
R0
xdlink
(d2
link + 2
x)3/2d x (B.5)
Naming I he in eg al o Equa ion B.3 and ea anging he e ms o Equa ion B.5, he ollowing exp ession is
ob ained:
P x =I−P x
2A x
Apa ZR0
0
xdlink
(d2
link + 2
x)3/2d x (B.6)
The second pa o he equa ion is simila o he one sol ed in Equa ion B.3, bu in his case, he uppe
in eg a ion limi is de ined by Equa ion B.7.
R0=dlinkR+diR x
dlink −di
(B.7)
Whe e diis he z-axis posi ion o he pa icle. In oducing Equa ion B.7 in o Equa ion B.3, i yields.
P x =I−P x
2A x
Apa 1−dlink
pd2
link +R2
0!(B.8)
Finally, he expanded e sion o Equa ion B.8 is:
P x =P x
4πR2
x "A x 1−dlink
pd2
link +R2
x !−Apa 1−dlink
pd2
link +R2
0!# (B.9)
The loss e m depending on Apa can be associa ed o he angle Ψ sub ended by R0and dlink. Ma hema ically:
P x =I−P x
4
Apa
πR2
x (1 −cos Ψ(di))−1(B.10)
I can be shown ha o di= 0, he powe loss is a ac ion o he emission su ace, whils o di=dlink he
powe loss is de ined by a educ ion on he pho odiode’s illumina ed a ea. Finally, o a gi en impac dis ance,
he powe loss is he quo ien be ween he pa icle a ea and he a ea o he unca ed cone o med by emi e and
ecei e a ha dis ance.
138
Appendix C
Wa e o ms, Co ela ions and
P obabili y Densi y Func ions o
Chap e 7
In his chap e , all he measu emen s ob ained du ing he expe imen s commen ed in Chap e 7 a e p esen ed. In
o de o o ganize his appendix, he igu es ha e been classi ied depending on he associa ed expe imen . Sec ion
C.1 comp ises he acqui ed wa e o ms and he ob ained p obabili y densi y unc ions, whils Sec ion C.2 p esen s
he ob ained co ela ion unc ions and he wa e o ms.
C.1 Mo emen o pa icles
This sec ion p esen s all he cap u ed wa e o ms. All he measu emen s we e pe o med in a e y low ambien
noise en i onmen , so as o educe possible backg ound ex a noise. The ampli ied pho odiode was con igu ed wi h
a gain o 60 dB, which implies a bandwid h o 11 KHz acco ding o [138]. Fu he mo e, in his con igu a ion, he
RMS noise ol age is 800µV . Figu e C.1 depic s he noise o he ecei e . I s s anda d de ia ion is 1.2 mV.
Noise Vol age (mV)
-8 -6 -4 -2 0 2 4 6 8
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.1: Recei e noise unde absolu e da kness condi ions. No e he small o se due o he e ec o he
ansimpedance ampli ie .
C.1.1 Blue emission
Blue su e s less ex inc ion in pu e seawa e han ed, bu as he concen a ion o sca e e s inc eases, he op imum
ansmission wa eleng h shi s o a edde alue. Howe e , due o he educed leng h o he used wa e ank (91
cm), he ed wa eleng h p esen s a be e esponse o all cases. The ollowing subsec ions p esen he ob ained
wa e o ms and PDFs o he used blue wa eleng h (470 nm) in he pa icle mo emen expe imen .
139

Appendix C. Wa e o ms, Co ela ions and P obabili y Densi y Func ions o Chap e 7
S ill wa e
In s ill wa e , he pa icle posi ions a e p ac ically in a ian wi h ime and he esul ing a iabili y is only due o
Johnson and sho noises. Howe e , compa ing he a iances o Figu es C.4 and C.10, i can be obse ed ha sho
noise has a negligible in luence. Fu he mo e, hese a iances a e he same as he one shown in Figu e C.1. In his
case, he s anda d de ia ion o he s ill wa e cap u e was 1.15 mV. No e ha he mean alue o he blue emission
is d ama ically educed as he concen a ion o chlo ophyll inc eases.
Time (s)
0 10 20 30 40 50 60
Vol age
0.745
0.746
0.747
0.748
0.749
0.75
0.751
0.752
0.753
0.754
0.755
Vol age
0.746 0.748 0.75 0.752 0.754
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.2: Wa e o m and PDF o a blue emission in s ill ap wa e
Time (s)
0 10 20 30 40 50 60
Vol age
0.072
0.074
0.076
0.078
0.08
0.082
0.084
0.086
Vol age
0.0740.0760.078 0.08 0.082
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.3: Wa e o m and PDF o a blue emission in s ill wa e wi h 6.12 mg/l o pa icles
Mo ing wa e
Fo a mo ing en i onmen , he changing posi ions o he suspended ma e p oduce a a iabili y on he ecei ed
signal, since he incoming mul iple-sca e ed ene gy a ies wi h ime. Compa ing he wo no-concen a ion igu es
(Figu e C.4 and Figu e C.7, i can be obse ed ha he mean alue o he ecei ed signal is dec emen ed whils he
a iance is sligh ly modi ied. This occu s because ap wa e has a ce ain amoun o o al dissol ed solids, which is
suspended ma e ha a ec s ansmission as well. The mean alue is dec emen ed o all cases, and he a iance
inc eases wi h he concen a ion as i was commen ed in Chap e 7.
140
Appendix C. Wa e o ms, Co ela ions and P obabili y Densi y Func ions o Chap e 7
Time (s)
0 10 20 30 40 50 60
Vol age
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
Vol age
0.0120.0140.0160.018 0.02
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.4: Wa e o m and PDF o a blue emission in s ill wa e wi h 12.24 mg/l o pa icles
Time (s)
0 10 20 30 40 50 60
Vol age
0.62
0.622
0.624
0.626
0.628
0.63
0.632
Vol age
0.624 0.626 0.628 0.63
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.5: Wa e o m and PDF o a blue emission in agi a ed ap wa e
C.1.2 Red emission
In his subsec ion, he cap u es o he ed wa eleng h a e p esen ed. In his case, he induced ol age is highe
han he gene a ed using he blue wa eleng h. Taking in o accoun he leng h o he ank, he e ec i e op ical
ou pu powe a each wa eleng h (Table 7.2), and he esponsi i y o silicon, i is s aigh o wa d o no ice his
ac .
S ill wa e
Chlo ophyll’s abso p ion spec um has wo undamen al peaks, one a blue and one a ed. The blue peak may
be highe depending on he ela i e concen a ions o chlo ophyll-a and chlo ophyll-b, p oducing a ed shi o he
minimum abso p ion o wa e as he concen a ion is inc emen ed. I can be obse ed ha he di e ence o he
mean alues inc eases wi h he concen a ion le el.
141
Appendix C. Wa e o ms, Co ela ions and P obabili y Densi y Func ions o Chap e 7
Time (s)
0 10 20 30 40 50 60
Vol age
0.064
0.066
0.068
0.07
0.072
0.074
0.076
Vol age
0.066 0.068 0.07 0.072 0.074
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.6: Wa e o m and PDF o a blue emission in agi a ed wa e wi h 6.12 mg/l o pa icles
Time (s)
0 10 20 30 40 50 60
Vol age
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Vol age
0.01 0.012 0.014 0.016 0.018
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.7: Wa e o m and PDF o a blue emission in agi a ed wa e wi h 12.24 mg/l o pa icles
Mo ing wa e
In he case o ed ligh , due o he be e p opaga ion o his wa eleng h, he pa icle-induced a iabili y is g ea e
han he associa ed o blue emissions a his dis ance. This e ec is easily no iceable compa ing he igu es o
mo ing wa e o a ed emission and he same o a blue emission. Fu he mo e, he sca e ing phase unc ion also
di e s in bo h cases, and p obably i is much wide o a ed emission.
C.2 Nea -su ace link measu emen s
In he case o he second expe imen , he acqui ed wa e o ms and he ob ained co ela ions a e p esen ed. The
au oco ela ion unc ion o he acqui ed wa e o ms de ined he cohe ence ime as i was discussed du ing Chap e 7.
The esul s show a ia ions wi h wa eleng h, dep h and wind speed. A each wind speed, only he bounda ies o
he swep dep hs a e shown (2 cm and 15 cm). The gene al end o he esul s is ha he deepe he highe he
cohe ence ime due o he dec emen o he su ace’s in luence. Howe e , in he ob ained esul s, he ealiza ions
a 15 cm ha e lowe cohe ence imes due o he inc easing e ec o o al in e nal e lec ion. Beyond his limi o
he used link ange, he in luence o he wa e su ace decays ab up ly. Rega ding agi a ion, he mo e agi a ed he
142
Appendix C. Wa e o ms, Co ela ions and P obabili y Densi y Func ions o Chap e 7
Time (s)
0 10 20 30 40 50 60
Vol age
0.794
0.796
0.798
0.8
0.802
0.804
0.806
0.808
Vol age
0.798 0.8 0.8020.8040.806
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.8: Wa e o m and PDF o a ed emission in s ill ap wa e
Time (s)
0 10 20 30 40 50 60
Vol age
0.124
0.126
0.128
0.13
0.132
0.134
0.136
Vol age
0.1260.128 0.13 0.1320.134
No malized p obabili y
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figu e C.9: Wa e o m and PDF o a ed emission in s ill wa e wi h 6.12 mg/l o pa icles
su ace, he lowe he cohe ence ime. Finally, he ed emission p esen s a wo se cohe ence ime due o he be e
esponse o he sys em a e y sho dis ances.
143