Resource-Efficient FPGA Architecture for Real-Time RFI Mitigation in Interferometric Radiometers

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