Ci a ion: Pe ez-Po e o, A.; Que ol, J.;
Camps, A. Resou ce-E icien FPGA
A chi ec u e o Real-Time RFI
Mi iga ion in In e e ome ic
Radiome e s. Senso s 2024,24, 8001.
h ps://doi.o g/10.3390/s24248001
Academic Edi o : Ja i Nu mi
Recei ed: 28 No embe 2024
Re ised: 9 Decembe 2024
Accep ed: 12 Decembe 2024
Published: 14 Decembe 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
senso s
A icle
Resou ce-E icien FPGA A chi ec u e o Real-Time RFI
Mi iga ion in In e e ome ic Radiome e s
Ad ian Pe ez-Po e o 1,2,3,* , Jo ge Que ol 1,3,4 and Ad iano Camps 1,2,3,5
1CommSensLab—UPC, Uni e si a Poli ècnica de Ca alunya—Ba celonaTech, 08034 Ba celona, Spain
2Ins i u e o Space S udies o Ca alonia (IEEC)—CTE-UPC, 08860 Cas ellde els, Spain
3MITIC Solu ions S.L., 08017 Ba celona, Spain
4In e disciplina y Cen e o Secu i y, Reliabili y and T us (SnT), Uni e si y o Luxembou g,
1855 Luxembou g, Luxembou g
5College o Enginee ing, Uni ed A ab Emi a es Uni e si y, Al Ain 15551, Uni ed A ab Emi a es
*Co espondence: ad ian.pe ez.po e [email p o ec ed]
Abs ac : In e e ome ic adiome e s ope a ing a L-band, such as ESA’s SMOS mission, enable
c ucial Ea h obse a ions p o iding high- esolu ion measu emen s o soil mois u e, ocean salini y,
and o he geophysical pa ame e s. Howe e , he inc easing elec omagne ic spec um u iliza ion
has led o signi ican Radio F equency In e e ence (RFI) challenges, pa icula ly c i ical gi en he
senso s’ ine empe a u e esolu ion equi emen s o less han 1 K. This wo k p esen s he ha dwa e
implemen a ion o an ad anced RFI de ec ion and mi iga ion algo i hm speci ically designed o
in e e ome ic adiome e s, a ge ing u u e L-band missions. The implemen a ion p ocesses 1-bi
quan ized signals a 57.69375 MHz om mul iple ecei e s, employing ime- equency analysis
and pola ime ic de ec ion echniques while op imizing Field P og ammable Ga e A ay (FPGA)
esou ce u iliza ion. No el op imiza ion s a egies include o e clocked p ocessing co es ope a ing
a
230.775 MHz
, e icien esou ce sha ing h ough ope a ion se ializa ion, and s a egic memo y
managemen . The sys em achie es eal- ime p ocessing capabili ies while main aining de ec ion p ob-
abili ies abo e 63% wi h alse ala m a es below 1% o ypical in e e ence scena ios. Pe o mance
alida ion using syn he ic da ase s demons a es obus ope a ion ac oss a ious RFI condi ions,
making his implemen a ion sui able as pa o he RFI de ec ion and mi iga ion e o s o u u e
in e e ome ic adiome e missions beyond SMOS.
Keywo ds: adio equency in e e ece; RFI; FPGA; Ea h obse a ion; in e e ome ic adiome e s;
pola ime y
1. In oduc ion
Mic owa e adiome y has es ablished i sel as a co ne s one o Ea h Obse a ion
(EO) sys ems, p o iding p ecise da a o moni o ing c i ical en i onmen al pa ame e s
such as soil mois u e, ocean salini y, and a mosphe ic condi ions [
1
]. Cu en ope a ional
sa elli es employing mic owa e adiome e s, including Soil Mois u e and Ocean Salini y
(SMOS) [
2
] and
Soil Mois u e Ac i e Passi e (SMAP) [3]
, ha e demons a ed he echnol-
ogy’s capabili ies o global en i onmen al moni o ing. These ins umen s ope a e in
p o ec ed equency bands heo e ically ese ed o passi e obse a ions. Howe e , he
exponen ial g ow h o wi eless communica ions, coupled wi h unau ho ized ansmissions
and ou -o -band emissions, has led o an inc ease in Radio F equency In e e ence (RFI)
inciden s [
4
–
6
]. The p oli e a ion o RFI sou ces comp omises da a quali y and scien i ic
obse a ions, p esen ing a signi ican challenge o cu en and u u e Ea h obse a ion
missions. RFI can o igina e bo h om ex e nal sou ces and om conduc ed o adia ed
in e e ence wi hin he sa elli e i sel [7]. The impac o RFI on adiome ic measu emen s
mani es s in a ious o ms, anging om sub le biases ha dis o scien i ic da a o com-
ple e da a loss in se e ely a ec ed egions. Analysis o SMOS mission da a has e ealed
Senso s 2024,24, 8001. h ps://doi.o g/10.3390/s24248001 h ps://www.mdpi.com/jou nal/senso s
Senso s 2024,24, 8001 2 o 14
signi ican RFI con amina ion pa e ns, pa icula ly o e densely popula ed egions in
Asia and Eu ope [
8
]. In some a eas, pe sis en in e e ence has ende ed measu emen s
comple ely unusable, necessi a ing ex ensi e da a il e ing and co ec ion p ocedu es [
9
].
Simila challenges ha e been documen ed o he SMAP mission [
10
] and o he adiome ic
sys ems, highligh ing RFI as a c i ical conce n ha mus be add essed o ensu e he iabili y
o u u e Ea h obse a ion missions [11].
The scien i ic communi y has esponded o hese challenges by de eloping inc easingly
sophis ica ed RFI de ec ion and mi iga ion s a egies [
12
–
14
]. These app oaches ha e e ol ed
om simple h eshold-based echniques o complex mul i-domain analysis me hods.
A e he key lessons lea n om SMOS [
15
], a new a chi ec u e o ad anced L-band
adiome e s using 1-bi quan iza ion a a highe sampling a e was p oposed [
16
]. As pa
o he echnology ac i i ies, he RFI de ec ion algo i hm p esen ed in [
17
] was de eloped.
The algo i hm p ocesses he 1-bi quan ized signals and employs inno a i e echniques
such as equency-domain c oss-co ela ion compu a ion and Pola ime ic Ku osis, o e -
ing p omising esul s in heo e ical and simula ion s udies. The challenges o RFI de ec ion
wi h highly quan ized da a a e illus a ed in Figu e 1, which shows a chi p in e e ence
signal be o e and a e 1-bi quan iza ion. The quan iza ion p ocess in oduces se e al
c i ical e ec s: signal clipping undamen ally al e s bo h empo al and spec al p ope ies,
gene a ing ha monics a in ege mul iples o he RFI’s undamen al equency, some o
which mani es as aliases in he equency domain. Despi e hese dis o ions, he empo al
and spec al signa u es o he RFI emain de ec able, mo i a ing de ec ion algo i hms ha
exploi hese p ese ed cha ac e is ics while accoun ing o quan iza ion e ec s. Mic owa e
adiome e s mus de ec ex emely weak signals, o en below
−
100 dBm [
18
], making hem
pa icula ly suscep ible o elec omagne ic in e e ence. The loss o sensi i i y due o he
1-bi sampling, since he ha d decision h eshold be ween 0 and 1 means ha any in e e -
ence abo e he noise loo can di ec ly impac he quan iza ion decision, can po en ially
co up measu emen s mo e se e ely han in sys ems wi h highe bi dep h ha p o ide
ampli ude in o ma ion.
(a) (b)
Figu e 1. E ec s o 1-bi quan iza ion on a 15,000 K chi p RFI signal wi h he mal noise. (a) O iginal
unquan ized spec og am showing he chi p’s na u al equency p og ession. (b) A e 1-bi quan i-
za ion, e ealing ha monic gene a ion and aliasing e ec s, among o he s.
Howe e , he ansi ion om heo e ical algo i hms o space-quali ied implemen a-
ions p esen s a o midable se o challenges. Space missions demand highly op imized
ha dwa e implemen a ions ha mus ope a e eliably o yea s wi h minimal in e en ion.
Field P og ammable Ga e A ay (FPGA) implemen a ions mus balance complex ade-
o s be ween p ocessing capabili ies, esou ce u iliza ion, and powe consump ion [
19
].
Real- ime p ocessing equi emen s necessi a e ca e ul op imiza ion o da a low and com-
pu a ional esou ces, while space ope a ion demands obus e o handling and aul
ole ance mechanisms [
20
]. These implemen a ion challenges become pa icula ly ha d o
in e e ome ic adiome e s, whe e nume ous ecei e s mus be p ocessed simul aneously.
Some examples o such implemen a ions can be ound in [
13
,
21
,
22
] o mul i-bi inpu s.
Con en ional app oaches o en ely on dedica ed FPGAs o each ecei e o ecei e pai ,
leading o inc eased sys em complexi y, powe consump ion, and mission cos s. Space-
g ade FPGAs p esen addi ional cons ain s, ypically o e ing ewe esou ces han hei
comme cial coun e pa s while demanding mo e obus design p ac ices and ho ough
Senso s 2024,24, 8001 3 o 14
alida ion p ocedu es. Implemen a ion conside a ions ex end beyond basic esou ce al-
loca ion o encompass complex sys em-le el challenges. Clock domain managemen and
synch oniza ion become c i ical when dealing wi h mul iple da a s eams and p ocessing
s ages. Fixed-poin a i hme ic mus be ca e ully designed o main ain p ecision h oughou
he p ocessing chain while minimizing esou ce usage. Memo y bandwid h op imiza ion
equi es s a egic bu e ing and e icien da a mo emen s a egies. Pipeline design mus
balance h oughpu equi emen s agains esou ce cons ain s, o en necessi a ing c ea i e
app oaches o esou ce sha ing and ope a ion se ializa ion.
The wo k p esen ed he ein add esses hese implemen a ion challenges, desc ibing a
p ac ical ealiza ion o ad anced RFI de ec ion and mi iga ion algo i hms speci ically op i-
mized o space-based in e e ome ic adiome e s explo ed in [
17
]. Th ough inno a i e
app oaches o o e clocking, esou ce sha ing, and ope a ion se ializa ion, he implemen-
a ion achie es signi ican educ ions in FPGA esou ce equi emen s while main aining
eal- ime p ocessing capabili ies. The design emphasizes eliabili y and lexibili y, allowing
pa ame e adjus men du ing mission li e ime while main aining obus ope a ion in he
space en i onmen . The ollowing sec ions de ail he de elopmen and alida ion o his
implemen a ion. Sec ion 2p esen s a comp ehensi e block design, examining he da a low
a chi ec u e and p ocessing s ages. Sec ion 3explo es implemen a ion op imiza ion s a e-
gies, de ailing no el app oaches o o e clocking, se ializa ion echniques, and esou ce
u iliza ion imp o emen s. Sec ion 4desc ibes he alida ion me hodology, p esen ing
esul s om syn he ic da a es ing, ha dwa e-in- he-loop alida ion, and pe o mance
measu emen s. Finally, Sec ion 5o e s conclusions and examines po en ial pa hways o
u u e implemen a ion imp o emen s.
2. Algo i hm Desc ip ion
This sec ion desc ibes an RFI de ec ion and mi iga ion algo i hm op imized o in e -
e ome ic adiome e s wi h 1-bi digi iza ion. The algo i hm combines s a is ical analysis
h ough ku osis es ima ion wi h pola ime ic measu emen s o iden i y and emo e RFI
con amina ion. I p ocesses bo h ime and equency domains o p o ide wi h a wide
ange o de ec ion oppo uni ies. The de ec ion s a egy makes use o he non-Gaussian
cha ac e is ics o RFI signals and hei impac on signal pola iza ion, allowing o e ec i e
iden i ica ion e en wi h highly quan ized inpu da a.
The Ha dwa e Design Language (HDL) a chi ec u e has been s uc u ed o minimize
esou ce u iliza ion o allow o mul iple ecei e s o be ins an ia ed in he same FPGA,
while main aining p ocessing capabili ies. The RFI Mi iga ion algo i hm implemen a ion is
sepa a ed in h ee dis inc p ocessing s ages (Figu e 2), each add essing speci ic aspec s o
he de ec ion and mi iga ion p ocess: i s , he Obse able Gene a ion s age p oduces he
in e media e p oduc s necessa y o RFI de ec ion. This s age implemen s he heo e ical
amewo k desc ibed in [
17
], compu ing he ime- equency ep esen a ions and pola i-
me ic pa ame e s while managing he s ic esou ce cons ain s o space-g ade FPGAs.
The s age handles he c i ical 1-bi quan ized inpu signals, p ocessing hem om he base
sampling a e o 57.69375 MHz, h ough an o e clocked Sho -Time Fou ie T ans o m
(STFT), while p epa ing he da a o subsequen analysis. Second, he RFI De ec ion s age
p ocesses he obse ables o iden i y in e e ence in bo h ime and equency domains.
This s age implemen s he mul i-domain analysis app oach, gene a ing blanking masks a
he sample le el. The de ec ion p ocess inco po a es bo h he s a is ical and pola ime ic
es s. Thi d, he PMS Blanking s age applies he gene a ed masks o mi iga e RFI in bo h
he 1-bi quan ized signals and he Powe Measu emen Sys em (PMS) da a. This inal
s age ensu es he cleaned signals main ain p ope synch oniza ion o he subsequen
co ela ion p ocessing.
The implemen a ion adop s a modula a chi ec u e whe e hese h ee p ocessing
s ages a e encapsula ed in sepa a e HDL blocks. The design enables con olled da a low
managemen be ween p ocessing s ages, c ucial o main aining eal- ime p ocessing capa-
bili ies. Ex e nal bu e ing handles he 3-bi unca ed STFT ou pu s and 1-bi pola iza ion
Senso s 2024,24, 8001 4 o 14
signals, ensu ing p ope synch oniza ion wi h he co ela o iming equi emen s. The
bu e ing s a egy op imizes memo y usage while main aining he necessa y h oughpu
o eal- ime ope a ion. A key a chi ec u al decision in ol es p ocessing each ecei e inde-
penden ly. The design p ocesses a single ecei e ’s da a pa h, allowing ho izon al scaling
h ough mul iple ins an ia ions o he RFI Mi iga ion block. The abili y o scale ho izon ally
by eplica ing p ocessing blocks p o ides lexibili y in adap ing he implemen a ion o
di e en mission equi emen s and ha dwa e cons ain s.
x
y
calib a ion
Obse able
gene a ion RFI De ec ion PMS Blanking
h esholding
pmsx
pmsy
T unca ed STFT
Equalized STFT
Blanking Masks
gammax
gammay
mpmsx
mpmsy
apmsx
apmsy
unca ed_s blank_mask
Figu e 2. Simpli ied o e iew o he RFI Mi iga ion algo i hm implemen a ion showing he h ee main
p ocessing s ages and da a low pa hs. Con igu able o ex e nal inpu s a e shown wi h ed a ows.
Resou ce-in ensi e ope a ions, pa icula ly he Fas Fou ie T ans o m (FFT) compu a-
ion and wide-wo d di isions, ha e been speci ically op imized. The FFT implemen a ion
employs se ializa ion echniques and esou ce sha ing s a egies o minimize Digi al Signal
P ocessing (DSP) block usage while main aining h oughpu equi emen s. Simila ly, di i-
sion ope a ions a e op imized h ough Au oma ic Gain Con ol (AGC) uni s ha educe he
wid h o he ope ands. Memo y managemen emphasizes he use o Block RAM (BRAM)
o e dis ibu ed memo y and egis e s. This s a egy educes he o e all logic elemen us-
age while p o iding he necessa y s o age capaci y o in e media e esul s and p ocessing
bu e s. The ollowing sec ions p o ide de ailed block diag ams and in o ma ion o each
p ocessing s age, examining he speci ic op imiza ion s a egies employed o mee space
implemen a ion equi emen s while main aining algo i hm e ec i eness.
2.1. In e ace De ini ion
The RFI de ec ion and mi iga ion sys em in e aces wi h mul iple da a s eams and
con ol signals, as illus a ed in Figu e 2. Each in e ace se es a speci ic pu pose in he
p ocessing chain.
The sys em’s p ima y inpu s a e wo 1-bi quan ized da a s eams (xand y) ep esen -
ing he in-phase and quad a u e componen s om each ecei e ’s X and Y pola iza ions.
These signals a e sampled a 57.69375 MHz and eed di ec ly in o he Obse able Gene a-
ion block. In pa allel, he sys em ecei es PMS measu emen s (pmsx,pmsy) a a lowe a e
o app oxima ely 28 kS/s, which p o ide o al powe in o ma ion o each pola iza ion
channel. The inal s age applies he gene a ed blanking masks o bo h he high-speed signal
pa h and he PMS measu emen s. The ou pu s include gain-co ec ed PMS measu emen s
o bo h pola iza ions (gammax,gammay), mi iga ed and a e aged PMS alues (mpmsx,
mpmsy), and unmi iga ed and a e aged PMS alues (apmsx,apmsy). These ou pu s p o ide
bo h debug and clean measu emen s o subsequen adiome ic p ocessing.
2.2. Obse able Gene a ion
The Obse able Gene a ion subblock (Figu e 3) gene a es in e media e signals ha
a e hen used in he RFI De ec ion and PMS Blanking subblocks o u he p ocessing, as
well as he inpu unca ed signals o he ad anced co ela o . These in e media e signals
co espond o he unca ed and equalized STFT, ob ained om he X- and Y-pola iza ion
inpu signals. This subblock includes a calib a ion p ocedu e o ex ac s a is ical in o ma-
ion om he inpu signals o equalize he gene a ed STFT. The unca ed signals can also
be con igu ed ex e nally wi h a unca ion ac o (
δp
). The main pu pose o his block is o
con e he X- and Y-pola iza ion eal and imagina y samples o a sui able o ma o RFI
Senso s 2024,24, 8001 5 o 14
de ec ion. This in e media e o ma includes a 3-bi unca ed STFT ou pu , and a 16-bi
equalized STFT ou pu .
x
O e clocked
STFT
230.775 MHz 125 MHz
Calib a ion
y
xe
ye
T unca ion
Equaliza ion
x
y
CPU
Co-p ocesso
Obse able Gene a ion
Figu e 3. Obse able Gene a ion block diag am de ailing he p ocessing chain om 1 o bi inpu s
h ough windowing and FFT s ages o unca ed and equalized ou pu s. The di e en clock domains
a e higligh ed in ed and o ange.
2.2.1. Calib a ion
The calib a ion p ocedu e allows he pa ial compu a ion o he equaliza ion coe -
icien s, wi h he help o an ex e nal p ocesso o pe o m he cos lie s eps. By de aul ,
da aEq is se o 1, hus applying no equaliza ion. In o de o ob ain he p ope alues o use
in he da aEq ield, he calib a ion p ocedu e is necessa y. The p ocedu e in ol es se ing
MCalSe o a numbe o ime slo s ha wan o be in eg a ed. Once s a Cal is se o ue,
he block will s a in eg a ing he Powe Spec al Densi y (PSD) o he da a in X and Y.
When MCalSe ime slo s ha e passed (calDone is ue), he accumula o will be ou pu
h ough he da aCal po when alidCal is ue. I is impo an o no e ha he eal pa o
his po co esponds o he alues o X-pol, and he imagina y pa o Y-pol. I is possible
o speci y an add ess o his alue o be ou pu o, by using he add Cal po , oge he
wi h he add Cal lag. Wi h his alue, he Equaliza ion coe icien s can be calcula ed by
di iding hem by MCalSe , pe o ming he squa e oo and in e ing he alue. The esul
o his ope a ion will be se o he da aEq po o comple e he calib a ion.
2.2.2. Equaliza ion and T unca ion
The 3-bi unca ion applied by he Obse able Gene a ion block can be con igu ed by
means o he δpinpu a iable. δpis a scaling ac o used du ing unca ion, de ined as:
δp=2Nbi s−1−1
Aclip
=2Nbi s−1−1
δ·√2, (1)
whe e he numbe o quan iza ion bi s is
Nbi s
= 3, and he scaling ac o is
δ
= 2 [
23
]. In
p inciple,
δ
mus be selec ed so ha he clipping e ec s a e negligible. This ac o is applied
o he signal p io o unca ion as:
X =ℜ(X)·δp(2)
Xi =ℑ(X)·δp(3)
Y =ℜ(Y)·δp(4)
Yi =ℑ(Y)·δp, (5)
and i con ols he clipping poin o he unca ion. A deepe s udy on he e ec s o he δ
pa ame e can be ound in Appendix A o [17].
2.3. RFI De ec ion
The RFI De ec ion subblock (Figu e 4) uses he in e media e ou pu s gene a ed by he
Obse able Gene a ion block and c ea es blanking masks o allow mi iga ion o he inpu
signals i hey a e con amina ed by RFI. The main inpu s o his subblock a e he Equalized

Senso s 2024,24, 8001 6 o 14
STFT ou pu s ob ained om he Obse able Gene a ion block, and he ou pu s co espond
o me ics on he p ocess and he blanking masks o be used when mi iga ing he inpu
obse ables. The h esholds used in he de ec ion o RFI signals can be uned by changing
he Th eshold po s, bo h in ime and equency.
S a is ical
Pola ime y F eq. Mask
OR MaskTime Mask
bx
by
Me ics Blanking Mask
h es
xe
xei
ye
yei
e_ alid
m_de
m_blank
b_ alid
AND Mask
Figu e 4. RFI De ec ion a chi ec u e showing pa allel compu a ion o s a is ical and pola ime ic
pa ame e s in ime and equency domains. The de ec ion logic combines mul iple me ics o gene a e
blanking masks o RFI mi iga ion. Con igu able o ex e nal inpu s, and debug ou pu s, a e shown
wi h ed a ows.
Th eshold Calcula ion
The ime and equency h esholds a e he de ec ion h esholds o s a is ical and
pola ime y me ics o de e mine ha an RFI signal is p esen . The alue o hese h esholds
may ake wo di e en speci ic alues whe he hey a e used o empo al o spec al
momen s. Fo he alues
K=
1024,
M=
4096, and
PFA =
1
·
10
−8
, he ime h eshold is
0.3582, and he equency h eshold is 0.1791. These heo e ical h esholds a e ob ained as:
α = 4
M·√2·e −1(1−PFA)(6)
α = 4
K·√2·e −1(1−PFA), (7)
whe e
α
,
α
co espond o he equency and ime h esholds, espec i ely,
M
,
K
co espond
o he numbe o samples in he equency and ime domains, espec i ely, e is he e o
unc ion, and PFA is he P obabili y o False Ala m.
A di e en h eshold, he be a h eshold (
β
) o maximum blanking h eshold, is used
o adjus he amoun o posi i e de ec ions in he masks ha is allowable so as o no excise
a signi ican pa o he desi ed signal. Mo e in o ma ion on his p ocedu e can be ound
in Sec ion 2.1.6 o [
17
]. The RFI mi iga ion is based on he excision o he con amina ed
samples ou o he se o all ans o med samples. The RFI mi iga ion ope a es e icien ly i
ew samples con ain he la ges ac ion o he RFI powe . Howe e , his may no be he
case when he RFI powe is well-sp ead ac oss he ime- equency space. In hese cases, i
may happen ha almos all samples a e disca ded and, he e o e, no signal emains a he
ou pu o he RFI mi iga ion algo i hm. The alue o
β
de e mines which ype o mi iga ion
app oach is applied o he signal. A ypical alue o he be a h eshold is 1.
2.4. PMS Blanking
The PMS Blanking subblock (Figu e 5) pe o ms he inal mi iga ion o he de ec ed
RFI om he inpu PMS signals, using he masks p o ided by he RFI De ec ion subblock,
and he T unca ed STFT signals p o ided by he Obse able Gene a ion block, o p o ide
he X- and Y-pola iza ion a e aged (and mi iga ed) PMS signals. The ou pu o his block
includes he Gamma pa ame e s used o scale he inal mi iga ed signal.
Senso s 2024,24, 8001 7 o 14
g_ alid
gy1
gy2
mapmsx
mapmsy
apmsx
apmsy
pmsb_ alid
gx1
gx2
Gamma
Calcula ion
pmsx
pmsy
x
x i
y
y i
_ alid
bx
by
b_ alid
pms_ alid PMS A e aging
Figu e 5. PMS Blanking implemen a ion illus a ing he applica ion o blanking masks o bo h high-
speed signals and PMS measu emen s. Ra e con e sion and gain co ec ion s ages ensu e p ope
synch oniza ion and calib a ion.
The mi iga ion o he powe measu emen s ollows a pulse blanking app oach (mi -
iga ion in he ime domain), bu ins ead o using jus he ins an aneous powe alue o
in e he p esence o RFI i i is abo e a gi en alue ( ypically se e al imes he s anda d
de ia ion o he powe i sel , assuming i is RFI- ee), he blanking mask is calcula ed
di ec ly om he empo al momen s o he pola ime ic ku osis (
bx[m]
and
by[m]
). The
a ios,
γx
and
γy
, a e calcula ed o each ecei e
, ep esen ing he a io be ween he
powe o he bins a e mi iga ion and be o e, as:
γx, =∑M−1
m=0∑K−1
k=0|Xmi
[m,k]|2
∑M−1
m=0∑K−1
k=0|X [m,k]|2, (8)
γy, =∑M−1
m=0∑K−1
k=0|Ymi
[m,k]|2
∑M−1
m=0∑K−1
k=0|Y [m,k]|2., (9)
whe e
Xmi
[m
,
k]
and
Ymi
[m
,
k]
a e he di e en mi iga ed ime and equency obse ables
o he X and Y pola iza ions, whe eas
X [m
,
k]
and
Y [m
,
k]
a e unmi iga ed. These a ios a e
used o compensa e o he bias in oduced by he RFI signal in o he PMS measu emen s.
No e ha , ideally, ou pu PMS signal should be ob ained di ec ly om he mi iga ed STFT
i he inpu signal had mul iple quan iza ion bi s. A e he mi iga ion o he co up ed
PMS, he sum o PMS samples ha a e no disca ded has o be no malized by he gamma
ac o , in o de o es ima e p ope ly he powe in each channel/pola iza ion, as:
Pmi
x, =∑
b ime
x[m]=1
Px, [m]·γx, , (10)
Pmi
y, =∑
b ime
y[m]=1
Py, [m]·γy, ., (11)
whe e
Pmi
x,
,
Pmi
y,
a e he mi iga ed powe s o he X and Y pola iza ions and ecei e
,
Px,
,
Py,
a e he unmi iga ed powe s, and he
b ime
x[m] = 1
and
b ime
x[m] = 1
sums i e a e o e
he blanking masks, whe e hey a e equal o 1.
3. Implemen a ion Op imiza ion
The implemen a ion o any DSP algo i hms in FPGAs equi es ca e ul op imiza ion o
mee eal- ime p ocessing equi emen s while e icien ly u ilizing a ailable esou ces. This
sec ion discusses he key op imiza ion s a egies employed h ough he implemen a ion o
he RFI mi iga ion algo i hm.
Senso s 2024,24, 8001 8 o 14
3.1. Fixed-Poin Design
The da a p ocessing chain (Figu e 6) shows cha ac e is ic bi -wid h changes h ough
ixed-poin ope a ions. I demons a es s a egic ixed-poin scaling choices, wi h bi -
wid h expansion in mul iplica ion-hea y ope a ions (windowing, S okes), and con olled
educ ion in s a is ical compu a ions (ku osis) and powe measu emen s (PMS).
Gamma
Calcula ion
i(0,16,0)
X/Y PMS
i(0,12,0)
PMS
A e aging
i(1,32,8)
X/Y Pola iza ion
Radiome ic da a Windowing FFT Equaliza ion S okes
Pa ame e s
Time Ku osis
F equency
Ku osis
i(0,1,0) i(0,16,15) i(1,16,11) i(0,16,11) i(0,68,44)
i(0,16,12)
i(0,16,12)
T unca ion
Th esholding
i(0,1,0)
i(1,3,0)
Inpu
Ou pu
Gamma
coe icien s
A e aged /
Mi iga ed PMS
Blanking
masks
Figu e 6. Fixed-poin implemen a ion o adiome ic da a p ocessing chain. The diag am shows
bi -wid h e olu ion h ough signal p ocessing s ages. Block colo s indica e inpu s and ou pu s (blue),
lossless p ocessing (g ay), and p ecision loss: g een o low, yellow o medium, and o ange o
signi ican p ecision educ ion.
As p e iously in oduced, he adiome ic signal is quan ized a 1 bi . The e ec s o
his choice in e ms o adiome ic sensi i i y ha e been discussed in he in oduc ion, bu
con e sely, i also o e s subs an ial ha dwa e e iciency ad an ages. The educed bi wid h
di ec ly ansla es o smalle ha dwa e oo p in s in c i ical componen s, including adde s,
accumula o s, and associa ed ou ing esou ces. This a chi ec u al choice cascades in o
p ac ical sys em-le el bene i s: dec eased memo y equi emen s, op imized FPGA esou ce
u iliza ion, enhanced iming pe o mance h ough simpli ied logic pa hs, and educed
o e all powe consump ion.
The adiome ic da a p ocessing chain in he Obse able Gene a ion block begins wi h
windowing, applying a Hamming window o shape he empo al esponse o subsequen
STFT analysis. The window unc ion educes spec al leakage and imp o es equency
esolu ion, hough expanding he wo d leng h o
i(0,16,15)
due o he mul iplica ion
wi h window coe icien s. The FFT s age in oduces bi g ow h p opo ional o
log2(N)
h ough i s bu e ly addi ions, bu a e scaling by
√N
, i se les a
i(1,15,11)
. This
ollows om he heo e ical maximum g ow h in FFT p ocessing, whe e he widdle ac o
mul iplica ions in oduce nega i e alues in o he compu a ion. The ac ion leng h is
educed o a oid excessi e g ow h in la e s ages.
The RFI De ec ion block implemen s wo key ope a ions: he compu a ion o S okes
pa ame e s and he es ima ion o spec al ku osis in bo h ime and equency domains. The
S okes pa ame e s compu a ion equi es ca e ul managemen o nume ical g ow h h ough
he p ocessing chain. S a ing om an ini ial ixed-poin ep esen a ion o
i(0,16,11)
o
he inpu samples, he wo d leng h expands signi ican ly due o he successi e mul iplica-
ion ope a ions. The mos demanding case occu s in he compu a ion o he S4pa ame e ,
whe e he bi -wid h g ows up o
i(1,68,44)
o main ain p ecision h ough he complex
p oduc s. This expansion is necessa y o p e en a i hme ic o e low and p ese e he de-
ec ion sensi i i y ac oss he ull dynamic ange o he inpu signals. The mos nume ically
challenging aspec lies in he ku osis compu a ion, which equi es ex ensi e accumula ion
o ou h-o de momen s. While his accumula ion inhe en ly demands high nume ical
p ecision du ing in e media e calcula ions, he inal ku osis alues a e ep esen ed us-
ing ixed-poin o ma
i(0,16,12)
. This educed p ecision is jus i ied by he de ec ion
mechanism i sel : ku osis-based RFI de ec ion elies on h eshold compa ison a he han
p ecise magni ude es ima ion. When he ku osis de ia es signi ican ly om i s heo e ical
alue o Gaussian signals, indica ing he p esence o RFI, he exac magni ude o his
de ia ion becomes i ele an o de ec ion pu poses. This implemen a ion conside a ion
Senso s 2024,24, 8001 9 o 14
signi ican ly educes ha dwa e esou ces while main aining de ec ion e ec i eness. Finally,
he h esholding s age con e s he ku osis alues in o bina y decisions, esul ing in he
bina y blanking masks.
In he PMS Blanking block, he implemen a ion o gamma calcula ions (Equa ions
(8)
and
(9)
) is op imized o FPGA esou ces by sepa a ing he nume a o and denomina o
compu a ions, a oiding di ec di ision ope a ions in ha dwa e. Bo h he nume a o and
denomina o a e ep esen ed in ixed-poin o ma
i(0,16,0)
, wi h he ac ual di ision
pe o med in pos -p ocessing. This design choice signi ican ly educes ha dwa e complex-
i y while main aining he necessa y p ecision o he powe a io es ima ion. The PMS
a e aging compu a ion (Equa ions
(10)
and
(11)
) uses a wide ixed-poin ep esen a ion
o
i(1,32,8)
o accommoda e he accumula ion o powe measu emen s and ensu e
su icien dynamic ange o bo h s ong and weak signal condi ions. The second pa h
pe o ms he a e aging o bo h he mi iga ed and unmi iga ed PMS measu emen s. The
inal powe es ima ion is ob ained by no malizing he sum o non-disca ded PMS samples
by hei co esponding gamma ac o s, ensu ing accu a e powe measu emen s e en in he
p esence o RFI blanking.
3.2. Resou ce Op imiza ion and Th oughpu Enhancemen
The implemen a ion employs se ializa ion o he pa allel X/Y pola iza ion inpu s,
in e lea ing he da a s eams be o e en e ing he p ocessing chain. By con e ing pa allel
da a pa hs in o a single se ialized s eam, he a chi ec u e euses c i ical blocks including
windowing and FFT p ocesso s. This se ializa ion s a egy educes FPGA esou ce u i-
liza ion by app oxima ely 50% compa ed o a ully pa allel implemen a ion, as iden ical
ope a ions o bo h pola iza ions sha e he same ha dwa e blocks. The esou ce op imiza-
ion becomes pa icula ly ele an in FPGA pla o ms whe e DSP blocks and memo y
ep esen cons ained esou ces.
To main ain p ocessing h oughpu despi e se ializa ion, he sys em implemen s a 4x
o e clocking scheme in he FFT p ocessing block. The inpu da a a i es wi h a 1
/
4 du y
cycle, p o iding iming ma gins ha enable clock a e mul iplica ion. By ope a ing he FFT
a ou imes he inpu clock equency, he sys em achie es he same e ec i e h oughpu
as a pa allel implemen a ion while u ilizing ewe ha dwa e esou ces. This o e clocking
s a egy ensu es ha he se ialized da a pa h can p ocess bo h X and Y pola iza ion samples
wi hin he equi ed ime cons ain s, ma ching he pe o mance o a dual-pa h a chi ec u e.
Table 1p o ides an es ima ion o he FPGA esou ces used by he en i e RFI Mi iga ion
block once implemen ed in he FPGA. The es ima ion is pe o med by Vi ado wi h knowl-
edge o he a chi ec u e o he FPGA whe e he block will be implemen ed in, bu is s ill
missing u he op imiza ions ha can only be pe o med once he block is implemen ed
wi h he es o he sys em, ins ead o isola ed.
Table 1. Resou ce u iliza ion compa ed wi h he a ailable esou ces in he Xilinx KU040 a chi ec u e.
LUT Logic
LUT Memo y La ch BRAM DSP
ObsGen STFT 3838 785 7388 7 16
ObsGen EqT unc 625 0 743 6.5 12
RFI De 9260 99 5782 30 48
PMS Blank 2755 84 2631 3 0
To al 16,478 968 16,544 46.5 76
KU040 242,400 484,800 1200 1920
Pe cen 6.80 % 3.41 % 3.88 % 3.96 %
4. Valida ion and Tes ing
The alida ion o RFI de ec ion and mi iga ion implemen a ions equi es a sys ema ic
app oach o e i y bo h unc ional co ec ness and pe o mance unde a ious ope a ing
condi ions. The es ing s a egy consis s o mul iple s ages, om syn he ic da a alida ion
o ull sys em in eg a ion es ing, ensu ing he implemen a ion mee s i s design speci ica-
ions while main aining eal- ime pe o mance. The simula ion was pe o med ei he by