In e na ional Jou nal on AdHoc Ne wo king Sys ems (IJANS) Vol. 13, No. 4, Oc obe 2023
DOI:10.5121/ijans.2023.13402 21
PAPR, SPECTRAL EFFICIENCY, BER AND SNR
ANALYSIS OF OFDM : A NOVEL PARTIAL
TRANSMIT SEQUENCE-PARTICLE SWARM
OPTIMIZATION TECHNIQUE
Ka hik Kuma Vaigandla, Ranji h Kuma Siddoju, Madhu Kuma Van e u,
Malo hu De singh, Dudime la P asad
Depa men o ECE, Balaji Ins i u e o Technology & Science, Wa angal, Telangana,
India
ABSTRACT
O hogonal equency di ision mul iplexing (OFDM) is a widely used mul ica ie modula ion (MCM)
echnique in he ield o wi eless communica ions, speci ically designed o acili a e high-speed da a
ansmission. The use o se e al subca ie s inside an OFDM sys em o he ansmission o modula ed
symbols esul s in he gene a ion o OFDM signals wi h a signi ican peak- o-a e age powe a io (PAPR).
In his s udy, we p opose a no el app oach o mi iga ing he high PAPR in wi eless communica ion
sys ems (WCS). Ou me hod u ilizes a pa ial ansmi sequence (PTS) s a egy, which is enhanced by
using an adap i e pa icle swa m op imiza ion (PSO) algo i hm. In his s udy, we p esen a desc ip ion o
an OFDM sys em employing he s anda d PTS echnique in conjunc ion wi h PSO. To mi iga e
compu a ional complexi y, he sugges ed me hodology e icien ly explo es he op imal amalgama ion o
phase o a ion componen s. Expe imen al indings demons a e ha he compu a ional complexi y and
PAPR ha e been g ea ly minimized by he sugges ed me hod.
KEYWORDS
BER, CCDF, compu a ional complexi y, communica ion, OFDM, PAPR, PTS, PSO, SNR.
1. INTRODUCTION
In nowadays days, he digi al landscape is eple e wi h wi eless echnologies ha acili a e he
seamless execu ion o daily asks, hence enhancing he quali y o li e o indi iduals. The
p oli e a ion o wi eless echnology has led o a subs an ial inc ease in he popula ion's awa eness
and p o icien use o his echnology. The inc easing numbe o ac i e use s has led o a s ong
demand o se ices such as high-de ini ion ele ision, mobile ideo, high-speed in e ne , and
ideo con e encing [1-4]. OFDM is widely ecognized as a undamen al ansmission s a egy o
mul ica ie (MC) due o i s abili y o spli he channel in o sub-channels, enabling pa allel da a
ans e wi h ex ended symbol leng hs. This cha ac e is ic makes OFDM a highly e icien and
s aigh o wa d op ion o wideband communica ion. The p oblem o es ima ing in e -symbol
in e e ence (ISI) is add essed, and a me hod is p oposed o ans o m a speci ied equency
ading channel in o a la ading channel [5-6]. One o he MCM echniques o en employed in
wi eless communica ions is OFDM [7]. The use o he OFDM echnique is a common s a egy in
achie ing high-speed ansmission ac oss equency-selec i e ading channels [9]. OFDM signals
commonly demons a e ampli ude a ia ion in he ime domain and possess a no able dynamic
ange, also known as PAPR, owing o hei MC s uc u e [8], as he PAPR o an OFDM signal is
high, i unde goes clipping as i passes h ough a nonlinea high powe ampli ie (HPA). This
In e na ional Jou nal on AdHoc Ne wo king Sys ems (IJANS) Vol. 13, No. 4, Oc obe 2023
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esul s in a dec ease in pe o mance and leads o he gene a ion o ou -o -band (OoB) adia ion
and in-band dis o ion. The e o e, he use o expensi e linea HPA wi h a wide dynamic ange is
impo an o OFDM ansmi e s [10]. An ele a ed PAPR has a de imen al e ec on he
e iciency o adio- equency (RF) powe ampli ie s, esul ing in inc eased cos s. Nume ous
app oaches ha e been de eloped o mi iga e he disad an ages associa ed wi h high PAPR. In he
con ex o OFDM sys ems, he e exis many echniques aimed a educing he PAPR. These
me hods encompass clipping, coding, non-linea companding, one ese a ion (TR) and
injec ion, selec i e mapping (SLM), and PTS [11]. Among he many ways, he PTS app oach
eme ges as he mos success ul and dis o ion- ee echnique o minimizing PAPR in OFDM
sys ems. One o he mos e ec i e echniques o educing PAPR is PTS. One o he challenges
associa ed wi h he PTS s a egy is i s signi ican compu a ional bu den in es ablishing he
op imal phase ac o s. Addi ionally, he equi emen o gi e an excessi e amoun o phase ac o s
as side in o ma ion o he ecei e side poses ano he issue [12]. The op imal selec ion o phase
ac o s was achie ed by he applica ion o se e al op imiza ion app oaches, including PSO,
Simula ed Annealing (SA), Gene ic Algo i hms (GA). These s a egies we e employed o
o e come he es ic ions associa ed wi h he use o PTS [13]. In he PTS echnique, he inpu
da a block is di ided in o many dis inc sub-blocks, each o which is independen . P io o
mul iplying each ela ed ime signal wi h a phase o a ion ac o , an IFFT ope a ion is pe o med
on each independen sub-block. The objec i e o he PTS app oach is o selec app op ia e phase
ac o s in o de o minimize he PAPR o he combined signal gene a ed by all sub-blocks [14].
The complexi y o conduc ing an exhaus i e sea ch o he op imal phase ac o s in he PTS
echnique inc eases as due o he numbe o sub-blocks and phase o a ion a iables in ol ed.
P e ious s udies [15-17] ha e examined many subop imal ways o minimize he sea ch
complexi y in he con ex o PTS.
The PSO-PTS Scheme u ilized in he OFDM sys em, as desc ibed in he wo k o Wen, Ho ng, e
al. [18], u ilizes heu is ic echniques o de e mine he op imal combina ion o basic phase
a iables. This app oach leads o a dec ease in compu a ional complexi y, bu wi h a li le ade-
o o inc eased PAPR. In hei s udy, he esea che s in e e ence [19] in oduced an OFDM
sys em ha u ilizes a sub-op imal PTS echnique based on PSO o de e mine he ideal phase
weigh ing ac o s. The esul s p oduced om his app oach demons a ed good pe o mance in
e ms o PAPR and compu a ional complexi y, while using only a limi ed numbe o i e a ions.
Addi ionally, au ho s wo ked on he PTS-OFDM echnique in [20], which p o ided a no el
s a egy o educing compu a ional complexi y using PSO, wi h he app oach's ou pu coming
close o being achie ed bu equi ing he use o PAPR. The lowe PAPR ecei ed, bu he
complexi y load was s ill somewha abo e a e age, in acco dance wi h GA-PTS and pa heno-
c osso e ope a o combina ion(PCGA)[21]. Addi ionally, he GA and Op imiza ion algo i hms
in PTS-OFDM we e analyzed, and he esul s indica ed ha while he GA educed PAPR a he
expense o compu a ional complexi y, he PSO app oach achie ed he ice e sa[23]. The eade
may ead [24] o mo e de ails on ano he app oach called i ewo ks algo i hm (FWA) ha
ou pe o med he wo echniques men ioned abo e. PSO and GA we e sugges ed as some
e olu iona y PTS-based op imiza ion echniques o lowe ing sea ch numbe s[22]. In o de o
sol e he compu a ionally challenging PAPR minimiza ion p oblem in he PTS echnique, a no el
PSO-based app oach is p esen ed in his a icle. The sugges ed app oach dec eases PAPR wi h a
be e con e gence a e and a educed compu a ional complexi y.
The emaining o he a icle is a anged as ollows. The OFDM anscei e model is desc ibed in
Sec ion 2. The PSO algo i hm and PTS app oach a e desc ibed in Sec ion 3. Sec ion 4
summa izes he discussion and simula ion ou pu s. Sec ion 5 p o ides conclusions.
In e na ional Jou nal on AdHoc Ne wo king Sys ems (IJANS) Vol. 13, No. 4, Oc obe 2023
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2. OFDM SYSTEM MODEL
All he elecommunica ions s anda ds, such as hose o WLANs, DTT, and DRT in much o he
wo ld, a e based on OFDM, a Commonly employed modula ion and mul iplexing
echnology[25]. The li e a u e has e e ed o OFDM in he pas and p esen as MC, Mul i- one,
and Fou ie T ans o m. The idea o OFDM is o dis ibu e he da a o be b oadcas among a lo o
ca ie s ha a e all modula ed a a low a e. By ca e ully deciding on hei equency spacing, he
ca ie s a e made o hogonal o one ano he [26]. The comple e amoun o spec um bandwid h is
di ided in o sub-bands using a mul ica ie sys em like FDM so ha many ca ie s can b oadcas
simul aneously. I c ea es a composi e high speed communica ion sys em by combining a lo o
low da a a e ca ie s [27]. The ca ie s can be igh ly spaced wi h o e lapping and no ICI
because o o hogonali y. The need o g ea e da a a e se ices, such as mul imedia, audio, and
da a ac oss wi ed and wi eless lines, is ising along wi h communica ions echnologies. To
anspo he as quan i y o da a ha con en ional app oaches canno handle, new modula ion
me hods a e needed. High da a a e, accep able bi e o a e(BER), and mo e la ency mus be
p o ided by hese me hods[28]. One o hem is OFDM. In Eu ope, OFDM has been u ilized o
la ge da a a e wi ed ne wo ks like ADSL, DAB, and DVB.
Figu e 1. Signals o a ious equencies a e added ia an OFDM modula o
An e ec i e modula ion scheme named OFDM is employed in cu en wi eless communica ion
sys ems, such as 5G. The de elopmen o a high-speed communica ion sys em in ol es he
in eg a ion o FDM and QAM in he OFDM echnique [29]. BPSK, QPSK, 16QAM, and
64QAM a e a ew o he a ious modula ion ypes e e ed o as QAM. R. W. Chang was he i s
o sugges he undamen al idea o OFDM, ealizing ha band limi ed o hogonal signals migh
be mixed wi h subs an ial o e lap while minimizing ICI. Using OFDM, we could c ea e a
ne wo k o subca ie s ha wo k oge he o ans e da a ac oss se e al equencies. These
subca ie s mus ca y ou o hogonal unc ions. Fo wo unc ions o be e med o hogonal in
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ma hema ics, he in eg al o hei p oduc o e he chosen ime ange mus be ze o[29]. In a
b oade sense, o hogonal unc ions can be o med o as s a is ically unconnec ed.
The signal ep esen a ion is gi en by
12
0
() k
Mj
n
k
s c e
(1)
He e, k = 0 + k. ∆ (2)
Figu e 1 demons a es how M subca ie s wi h iden ical spacing can be me ged o c ea e an a ay
o pa allel signals. QAM is used o modi y each subca ie . Al hough hese modula ed subca ie s
can suppo sepa a e baseband signals, hey a e o en me ged o o e he highes da a h oughpu
o a single s eam o da a. These subca ie s can be ma hema ically ep esen ed by u ilizing a
complex o m ha is compa ible wi h he usage o QAM. A ansmi e and ecei e combine up
he undamen al block diag am o OFDM sys em in Figu e 2. A he ansmi e side, he inpu bi
s eam en e s in o he sys em. No mally, his inpu bi s eam is de-mul iplexed in o smalle bi
s eams ha a e gi en o each o he M-QAM modula o s indi idually.
Figu e 2. A basic OFDM sys em
The p oduc ion o he ime domain signal om he a ay o modula ed subca ie s using he IFFT
is a c ucial ac o ha acili a es he implemen a ion o OFDM. The digi al OFDM signal
ob ained is subsequen ly applied o he DAC o con e sion in o an analogue wa e o m [30]. The
baseband signal is equen ly subjec ed o up-con e sion o a highe equency p io o i s
ansmission ac oss he channel. A he ecipien , he p ocess is e e sed. The unc ion o an
analogue down-con e e (DN) is o pe o m a equency shi on he OFDM signal, b inging i
back o he baseband. The ADC is esponsible o con e ing he incoming signal in o a digi al
ep esen a ion p io o ansmi ing i o he FFT block. The FFT module pe o ms a con e sion
o he inpu signal om he ime domain o a collec ion o subca ie s in he equency domain,
which a e hen modula ed using QAM. Upon he comple ion o QAM demodula ion, he bi
s eam om each subca ie is ep oduced. Subsequen ly, he o iginal single da a s eam is
In e na ional Jou nal on AdHoc Ne wo king Sys ems (IJANS) Vol. 13, No. 4, Oc obe 2023
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econs uc ed by he p ocess o mul iplexing [31]. Figu e 3 illus a es he empo al and spec al
ep esen a ion o an OFDM ansmission signal.
Figu e 3. combined iew o he OFDM signal in he ime and equency domains
Figu e 3 illus a es he ime plus equency domain isualiza ion o an OFDM signal. A se o
OFDM subca ie s is ep esen ed by each symbol in he diag am and is ansmi ed along he
channel. Th ough he applica ion o a digi al modula ion echnique, he ini ial bina y sequence
unde goes a con e sion p ocess esul ing in a limi ed numbe o cons ella ion poin s. The
u iliza ion o a se ial o pa allel (S/P) con e e is employed in o de o di ide he baseband
modula ed symbols ha ha e been success ully acqui ed in o M- ames o iden ical leng h p io
o pe o ming an IFFT ope a ion. The gene a ion o he baseband OFDM signal in ol es he
ansmission o a sequence o baseband modula ed symbols Sk ia an IFFT block [32,35]. The
disc e e- ime ansmi ed OFDM signal, consis ing o M subca ie s, can be ep esen ed by n
samples, gi en below:
2
1
0
1;0 1
j kn
MM
nk
k
s S e n M
M
(3)
The PAPR o he signals is he a io o maximum powe o a e age powe and is gene ally
exp essed as:
2
2
n
n
Max s
PAPR Es
(4)
2
10 2
10log n
dB
n
Max s
PAPR Es
(5)
The e iciency o he PAPR minimiza ion me hod is o en examined using he complemen a y
cumula i e dis ibu ion unc ion(CCDF). The CCDF may be de ined as: "The p obabili y ha an
OFDM signal's PAPR will exceed a h eshold le el. ρ"
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( ) 1 1 M
CCDF P PAPR e
(6)
3. PTS AND PSO-PTS METHOD
In he PTS app oach, he inpu sequence is pa i ioned in o many subsequences. Subsequen ly,
e e y subsequence o symbols unde goes an IFFT, and he esul an subsequences o signals a e
combined by mul iplica ion wi h a se o dis inc o a ing ec o s [11]. The signal sequence
exhibi ing he minimum PAPR is he ea e sen a e e alua ing he PAPR o each esul ing
sequence. When he numbe o subca ie s and he sequence o modula ion inc ease, p io i izing
he educ ion o compu a ional complexi y is mo e impo an han minimizing edundancy.
The inpu da a block, consis ing o M symbols, is di ided in o N dis inc sub-blocks using he
PTS echnique. The IFFT is subsequen ly pe o med on each sub-block indi idually and is
mul iplied by he co esponding complex phase ac o
m
i
n
pe
. In o de o mi iga e he PAPR
o he agg ega e signal o igina ing om all sub-blocks, app op ia e phase ac o s a e used. Figu e
4 is a schema ic diag am o he OFDM ansmi e ha inco po a es he PTS echnique. The inpu
da a s eam, deno ed as S, is pa i ioned in o N dis inc sub blocks, e e ed o as Sn. Each sub
block unde goes an IFFT ope a ion, and i s associa ed weigh ed phase ac o , pn, is app op ia ely
modi ied. The objec i e is o de e mine he se o phase ac o s pn ha minimizes he PAPR o he
composi e ime-domain signals.
1
Nnn
n
s p s
(7)
1
IFFT
Nnn
n
s p S
(8)
~
1
Nnn
n
s p x
(9)
The phase ac o s a e selec ed o educe he PAPR, which is exp essed as ollows:
~ ~ ~
1
12
, ,...., a gmin max Nnn
n
nps
p p p
(10)
The ime-domain signal wi h he associa ed minimal PAPR is ep esen ed by:
~
1
Nnn
n
s p s
(11)
I needs o be no ed ha choosing he bes phase ac o s needs a ho ough sea ch o all possible
combina ions o phase ac o s, which inc eases compu ing complexi y. In o de o dec ease he
complexi y o he sea ch, a ce ain se o elemen s a e limi ed by phase ac o pn. The bes se o
phase ec o s should be ound by sea ching 4N se s o phase ac o s as he ange o pe mi ed
In e na ional Jou nal on AdHoc Ne wo king Sys ems (IJANS) Vol. 13, No. 4, Oc obe 2023
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phase ac o s is p={±1, ±j}. Wi h mo e sub-blocks, he sea ch complexi y is ob iously
conside ably mo e di icul .
Figu e 4. PTS me hod o OFDM PAPR minimiza ion
PSO is a s ochas ic op imiza ion app oach ha elies on he mo emen and beha iou o swa ms.
In PSO, he u iliza ion o social in e ac ion is employed as a means o ackle a ious challenges.
The p oposed me hod employs a collec ion o pa icles, e e ed o as agen s, which na iga e
inside he sea ch egion wi h he objec i e o loca ing he mos op imum solu ion. E e y
indi idual inside he swa m ac i ely seeks he posi ional coo dina es wi hin he solu ion space
ha co espond o he mos op imal solu ion hey ha e gene a ed hus a . The e m commonly
e e ed o as a pe sonal bes is deno ed as pbes . The PSO algo i hm also conside s he global
bes (gbes ) as a signi ican me ic. The maximum alue is de e mined by he pa icle nex o i .
In he ini ializa ion phase o he PSO algo i hm, a andom eloci y is assigned o each possible
solu ion wi hin he popula ion o andomized solu ions. The anspo a ion o po en ial solu ions
occu s inside he issue space in he o m o pa icles. Pa icles ha e been shown o be associa ed
wi h he mos op imal esul o highes deg ee o physical i ness seen hus a . Fu he mo e, he
i ness alue is also kep . The designa ed nomencla u e o his pa icula alue is "pbes ".
Ano he signi ican measu e iden i ied by he in e na ional i e a ion o he PSO algo i hm is he
collec i e bes alue a ained by each pa icle inside he popula ion, oge he wi h i s
co esponding loca ion. The e m used o e e o his numbe is o en known as "gbes ." The
a o emen ioned is he wo ldwide mani es a ion o PSO. Du ing each i e a ion, he pa icle
modi ies i s eloci y and mo es close o i s pe sonal bes (pbes ) and he global bes (gbes )
posi ions. The echnique being e e ed o is commonly e e ed o as he local a ian o PSO. In
his app oach, each indi idual pa icle in he swa m keeps no e o he bes solu ion i has seen,
known as he neighbou hood bes (nbes ) o local bes (lbes ). This is achie ed by conside ing a
small opological neighbou hood o pa icles [33]. One o he s a egies employed in e olu iona y
compu ing is he PSO algo i hm. The p ima y objec i e was o demons a e he s ochas ic
locomo ion pa e ns o a collec i e o a ian o ganisms. An enhanced PSO algo i hm is p oposed
in his s udy o minimize he high PAPR o an OFDM sys em using he PTS echnique [34],
while educing compu a ional complexi y. A collec ion o ac o s can be seen as a speci ic poin
o place inside he ex ensi e space o phase ac o s, whe e each alue along a dimension
co esponds o a dis inc componen . The sugges ed PSO echnique use a p ima y se o solu ions
e e ed o as "pa icles" as he i s s a ing poin . Each pa icle is loca ed a a speci ic posi ion
inside he N-dimensional space. To cla i y, i may be said ha e e y pa icle possesses an N-
dimensional phase ec o , whe eby each componen is selec ed om a se o phase ac o s.
Pa icles a e se ac oss space in sea ch o he mos a o able loca ion, and hei inal posi ions
a e de e mined by he in e play o hei in e ac ions. Consequen ly, indi iduals seek ou
oppo uni ies o op imiza ion a bo h local and global le els. Ul ima ely, each indi idual pa icle
In e na ional Jou nal on AdHoc Ne wo king Sys ems (IJANS) Vol. 13, No. 4, Oc obe 2023
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achie es mo ion owa ds he op imal loca ion. Pa icles possess he inhe en po en ial o explo e
and, as a esul , hey engage in a sea ch p ocess o iden i y he mos a o able sequence o phase
ac o s.
Le Lj = (lj1, lj2,..., ljN) is he loca ion/ ec o o he j h pa icle, Pj = (pj1, pj2,..., pjN) is he bes place
(pbes ) ound by he j h pa icle and he bes place disco e ed by all pa icles wi h he gbes index is
shown. Vj =(ϑj1,ϑj2,..,ϑjN) is used o deno e he j h pa icle's eloci y (V). By using Eq.(12) and
(13), pa icles mo e.
12
( 1) ( )
jb jb
k k Q Q
(12)
He e ,
1 1 1 ( ) ( ) ( )
b jb jb
Q a k p k l k
, and
2 2 2 ( ) ( ) ( )
b jb jb
Q a k p k l k
( 1) ( ) ( 1)
jb jb jb
l k l k k
(13)
He e, k indica es he numbe o i e a ions and b = 1, 2,..., N; ω s ands o he ine ia weigh ,
which has a posi i e alue in e ms o a ime- a ying linea unc ion. The igh ine ia weigh
es ablishes a balance be ween local and global explo a ion, which speeds up he algo i hm's
abili y o loca e he bes esponse.
ω = I e a ion Numbe /Max I e a ion (14)
The coe icien s, a1 and a2, show how quickly each pa icle app oaches i s espec i e indi idual
and global op imal places. When hese accele a ions a e low, pa icles ci cle he a ge egion
wi hou a emp ing o app oach i , and when hey a e s ong, pa icles a el owa d he a ge
a ea a as speeds and may e en pass h ough i . Two uni o mly dis ibu ed andom numbe s in
he ange (0,1) a e 1 and 2, espec i ely. The maximum eloci y(Vmax) se s a limi on he pa icle
eloci ies. The g ea es mo emen a pa icle can make in he sea ch space is de e mined by his
ec o . The pa icles canno be in es iga ed ou side o he semi-op imal egions i he Vmax is low.
Pa icles may go h ough he op imal solu ion i Vmax is high. The di e ence in pa icle posi ions
a he wo poin s de e mines he eloci y. The new pa icle eloci y is de e mined by applying Eq.
(12). The p io eloci y is used o calcula e he new eloci y. The sepa a ion be ween he
pa icle's ac ual loca ion and bes loca ion and he bes loca ion can be de e mined by he g oup.
The pa icle a els o he new posi ion in acco dance wi h Eq. (13) a e compu ing i s eloci y.
The i ness o pa icles has been e alua ed using he ollowing e alua ion:
1
() ()
i ness s PAPR s
(15)
Algo i hm
Ini ialize all pa ame e s;
a1, a2, Max. i e a ion, p, pa icles, 1, 2, Vmax, ω
Ini ialize pa icles wi h andom posi ions in he space
Le k=1
While(k ≤ Max. i e a ion)
k=k+1
Fo each pa icle do
Compu e he posi ion o he pa icle using ω
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Upda e pbes o he pa icle
End
Selec he bes posi ion ind by all pa icles as a gbes o swa m
Fo each pa icle do
E alua e he eloci y o he pa icle using Vjb(k+1)
Upda e posi ion o he pa icle using ljb(k+1)
End
End While
Re u n he phase ac o se wi h lowe PAPR as he solu ion.
Figu e 5. Flowcha : PSO-PTS p ocess
4. RESULTS
Va ious simula ions ha e been pe o med o analyze he e ec i eness o he PSO-PTS algo i hm
o PAPR minimiza ion in OFDM. MATLAB R2018a so wa e was used o pe o m simula ions.
Table 1. Simula ion pa ame e s
Pa ame e s
Value
No. o subca ie s
512
No. o symbols
1e4
Modula ion
QPSK
No. o sub-blocks
2,4,8,16
O e sample a e
4
Pa i ion
adjacency pa i ion
No. o pa icles pe gene a ion
10
I e a ion numbe s
[1 4 8 10 20 30]
Max i e a ion numbe
30
Lea ning ac o s
a1 = 2; a2 = 2
Max eloci y
Vmax = 0.2
Leng h o weigh ing ac o se
1,2,3
Min ine ia weigh ec o
wmin = 0.4
Max ine ia weigh ec o
wmax = 0.9
