Breaking the CP Limit: Robust Long-Range OFDM Sensing via Interference Cleaning

1 Breaking the CP Limit: Rob ust Long-Range OFDM Sensing via Interfer ence Cleaning Umut Utku Erdem, Graduate Student Member , I EEE , Lucas Giroto, Member , IEEE , Benedikt Geiger , Graduate Student Member , IEEE , T aewon Jeong, Gradua te Student Member , IEEE , Silvio Mande lli, Member , IEEE , Christian Karle, Graduate Stude nt Membe r , IEEE , Benjamin Nuss, Senior Member , IEEE , Laurent Schmalen, F ellow , IEEE , a nd T homas Z w ick , F e llow , IEEE Abstract —In orthogonal fre quency-division multiplexing-based radar and integrated sensing a nd communication systems, the sensing range is traditionally limited by the r ound-trip time corres ponding to the cyclic prefix duration. T ar gets whose echoes arriv e after this duration induce intersymbol interference (IS I) and associa ted intercarrier int erference (ICI), which significantly degrade detection p erf ormance, elevate the i nterference-noise floor in the radar image, and reduce the useful signal power due to win dow mismatch. Existing methods face a trade-off between re cov ering useful signal and suppressing in terference, particularly in multi-target scenarios. This paper proposes two framewo rks to resolv e thi s d ilemma, offering a flexible trade-off between computational cost and tar get detection perform ance. First, a si gnal m odel is d eriv ed, demonstrating t h at ISI and ICI-oriented interference often dominates therma l noise in high-dynamic-range scenarios. T o combat the ISI and ICI-based interference-noise floor increase, joint-interference cancellation with coherent compensation is proposed. This approa ch is an efficient evolution of the successive-interference cancellation algorithm, utilizing high-precision chirp Z-transfo rm estimation and fr equency-domain coherent compensation t o recov er weak distant tar gets. F or scenarios requiring maximum pr ecision, the full reconstruction-based sli ding window scheme is presented, which shifts the recei ve window to capture optimal signal energy while perfo rming full-signal reconstruction f or all detected targets. Numerical results show th at both meth ods outp erf orm state-of-the-art benchmarks. Index T erms —Coherent compensation (CC), cyclic prefix (CP), integrated sensing and communication (ISA C), OFDM radar . The authors ackno w ledge the financial support by the Federal Ministry of Researc h, T echnology and Spac e of German y in the projects “K OMSENS-6G” (grant number: 16KISK123), “SENSA TION” (grant number: 16KI S2528) and “Open6GHub” (grant number: 16KISK010). (Correspondi ng author: Umut Utku Erdem.) U. U. Erdem, T . Jeong, and T . Zwick are with the Institute of Radio Frequency E nginee ring and Electronic s (IHE), Karlsruhe Institute of T echnolog y (KIT), 76131 Karl sruhe, Germany (e-mail: umut.erdem@kit .edu, tae won.jeong@kit .edu, thomas.zwick@ki t.edu). L. Giroto was with the Institute of Radio Frequenc y Engineering and Electroni cs (IHE), Karlsruhe Institute of T echnology (KIT), 76131 Karlsruhe, Germany . He i s no w with Nokia Be ll Labs, 70469 Stuttga rt, Germany ( e-mail: lucas.giro to@nokia -bell-labs.com). B. Geiger and L. Schmalen are with the Communicati ons Engineering Laboratory (CEL), Ka rlsruhe Institute of T echnolog y (KIT), 76187 Karlsruhe, Germany (e-mail : benedikt .geiger@ki t.edu, laurent.schmale n@kit.edu ). S. Mandelli is with Nokia Bell Labs, 70469 Stuttgar t, Germany (e-mail: silvio.mande lli@nok ia-bell-labs.com). C. Karle is with the Institute for Information Processing T echnology (ITIV), Karlsruhe Institute of T echnology (KIT), 76131 Karlsruhe, German y (e-mail: christia n.karle@k it.edu ). B. Nuss was with the Institut e of Radio Frequency Engineering and Electroni cs (IHE), Karlsruhe Institute of T echnology (KIT), 76131 Karlsruhe, Germany . He is now with the Professorship of Micro wav e Sensors and Sensor Systems, T echnica l Univ ersity of Munich, 80333 Munich, Germany . (e-mail: benjamin .nuss@tum.de). I . I N T RO D U C T I O N I NTEGRA TED sensing and commu nication (ISAC) has emerged as a pivotal technology for Sixth Generation (6G) cellular networks [1], pr omising to unify sensing and data transmission in to a single hardware [2]. Among various wa vefo rm ca ndidates, orth ogonal frequen cy-division multiplexing (OFDM) presen ts itself as a ro bust candidate for integrated sensing and communicatio n (ISAC ) application s [3], of f ering key advantages such as spectral efficiency and flexibility , alon gside n ati ve support within existing frameworks inclu ding Fifth Gen eration New Radio (5G NR) and IEEE 802.1 1ad [ 4]. Th e compatibility of OFDM with curr ent infra structure allows I SA C systems to deploy sensing capabilities without sign ificant h ardware chang es. Furthermo re, recent 3rd Generation Partnership Project (3GPP) Radio Access Network (RAN) agr eements ha ve established th at OFDM will be retained as the fo undation a l downlink wav eform for 6G, reaffirming its critica l role in next-genera tio n standardiza tions [5]. The du al functio n ality o f OFDM comes with a fundam ental design conflict in wa veform: th e duratio n of the cyclic prefix ( CP). In commun ication systems, the CP acts as a guard interval that prevents intersymb o l interference (ISI) by absorbing multipath compo nents within its dura tion. It also enab les c ircular conv o lu tion, which allows one-tap frequen cy-domain channel equalizatio n . Howev er , since the CP does not carr y any new infor mation, it in troduces overhead. T o minim ize th is overhead and maintain a high spectral efficiency , the CP is typically kept as short as possible, since CP redu c es the tim e available for pay load transmission, thereby d irectly imp acting the throug hput of the system. In con trast, radar sensing requ ir es the detection of targets at ranges that may correspon d to delays significan tly exceeding the CP dur ation. When the rou nd-trip delay o f a target echo exceeds th e CP length, two detrimen tal effects oc cur: (i) ISI arises as the previous OFDM symbol spills into the curren t detection window , and (ii) intercar r ier interferenc e (ICI) destroys the subcarrier or thogonality requ ir ed f o r accurate parameter estimation. Standard OFDM rad ar processing assumes that the ma x imum d e lay fo r ech oes is strictly limited by th e CP dur ation, which d etermines the ISI-f ree ran g e. T o overcome this limitation , r ecent research has diverged into two p rimary methodo logies: coher ent compensatio n (CC) an d su ccessi ve-interference c a ncellation ( SIC). Th e CC This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. approa c h , exemplified by [6], attempts to recover the ICI-b ased processing g ain loss by a dding the capture d signal for the next symbol to the curren t sy mbol. While CC effecti vely improves the signal- to -interferen ce-plus-noise ratio (SINR) for a single distan t target, it exhibits se vere d rawbacks in multi-target scen arios. As dem onstrated in [7], conventional coheren t co mpensation techniqu es g enerate strong interference and raise the interferen ce-noise floor level in m u lti-target cases. Conversely , th e SIC-based appro aches propo sed in [8 ] focus on estimating an d subtracting these interf erence terms iterativ ely to clean the radar ima g e. While SI C excels at lowering the in ter ference-n oise floor , it faces a d etection threshold dilemma: it relies on the initial d etection of a target to estimate interfer e nce effects for cancellation. If a distant target suffers from significant p r ocessing gain lo ss due to window mismatch, it may r emain below the noise floo r in the initial stage, renderin g the SIC algo rithm u nable to detect or can cel it. Recently , sliding window techniq u es ha ve been investigated for this scenario. N o tably , [9] pro posed a sliding wind ow detection scheme combined with time-d omain inte r ference removal. While th is method mitiga te s power degrad ation, it typically reconstru cts signals o nly within the ISI-fr ee region for each win d ow step. This p artial r econstruction can lead to the late removal of in te r ference effects, poten tially preventing target detection in certain scenarios. Additionally , signal reconstruction tech niques have been propo sed in th e literatu re to ad dress off-grid targets and ICI supp r ession. Notably , a low-comp lexity sup er-resolution algorithm is developed in [ 1 0] that mod els the r ange-Dop pler map via 2D local surface fitting to supp ress ICI and off-grid effects. While th is approach effectiv ely mitigates spectral leaka g e, it formu lates the par ameter estimatio n a s an o ptimization prob lem, requ iring iterativ e numeric a l solvers (e.g., N e lder-Mead [11] or Trust-Re gion [12] me thods). Consequently , th e co mputationa l co st scales with the number of d etected targets an d the requir ed co n vergence iter a tions. In co ntrast, our pro posed framework elimin ates the need for iterativ e fitting and any n umerical solver . By leveraging the computatio nally efficient chir p Z-transfo rm (CZT) [13], we achieve precise off-grid target detection and cance llation. Furthermo re, a cr itical oversight in th e existing literature [8], [9] is the unr ealistic assumption that targets are lo cated on the range-Do ppler g rid. This would allow n eglecting the necessity of windowing fun ctions (e.g., Ha m ming or Chebyshev) used in pr actice to sup press sidelobes. I n realistic scena rios, the absence o f win dowing leads to high sidelo bes th at can mask some o f th e targets, wh ile o f f-grid targets in troduce spec tr al leakage that se verely degrades the accu racy of standard reconstruc tion-based can cellation algor ithms. This work pr esents a robust fra m e work f or extend ing the sensing range of OFDM- based I SAC systems under practical no n-idealities, including off-grid target location s and windowing effects. T wo comp lementary algo rithms are introd u ced, enab ling a trade-off between computatio nal complexity and sensing capab ility . The main contributions ar e summarized as f o llows: • Interference analy sis under practica l noise limitations: While existing mod els captu re the effects o f excessive delay [6]–[9], a c o mprehen si ve ana lysis is for mulated in this pap er in c o rporating windowing an d off-grid targets. By explicitly co mparing interference p ower against thermal and quantization noise limits fo r p ractical systems, it is a nalytically shown that ISI and ICI fro m strong distant targets are th e p rimary bottleneck in high-d ynamic-ran ge scen arios, establishing the n ecessity for the mitig a tion schemes. • Joint-interfe rence cancellation with coherent compensation a lgorithm: An enhanced interferen ce cancellation algorithm is propo sed by embedd ing frequen cy do main coh erent compensation (FDCC) into a joint interf e rence can cellation scheme. This ap p roach, named joint-inte r ference ca ncellation with coh erent compen satio n ( JIC-CC), enab les recovery of weak distant targets by restor in g processing gain using FDCC, while precise cance llation of off-grid strong interferer s is ensured throug h high-r esolution CZT-based p arameter estimation. • Full reconstruction-based sliding window a lgorithm: A high-p recision full r econstruction -based sliding window (FR-SW) techniqu e is d eveloped for scen arios requirin g maximum dyn amic range. Unlike prior approa c h es such as [9] that partially mitigate interferen c e within the ISI-free ran g e, FR-SW adap ti vely shif ts th e receive win dow to cap ture o ptimal signal e nergy and perf orms fu ll re c onstruction o f all d etected targets, effecti vely min imizing residual interfer e n ce and r evealing weak targets. • Perf ormance-complex ity trade-of f analysis: A compara tive complexity analy sis is provided that ev alua te s b oth comp utational cost and har dware mem ory requirem ents. It is shown that while FR-SW achieves superior inter ference cancellatio n and target detectability , JIC-CC offers com petiti ve perf o rmance with sub stan tially reduced com putational comp lexity and lower buf fering demand s, offering a practical option for real-time or memory -constrained systems. The r emainder of this paper is organized as follows. Section II establishes the OFDM-ISAC system mod el and analytically derives the im pact of excessive delay on interferen ce and usefu l sign a l power . Section III revie ws the mathematical model with ISI and ICI. Section IV introdu c es the pro posed interferen c e cleaning frameworks, including the JIC-CC and the FR-SW alg orithms. Sectio n V presents th e compu tational com plexity analysis an d provides com prehensive simulation resu lts comparing th e propo sed metho ds against existing mitigation techniqu es and benchm a rks. Section VI verifies the p roposed algorithms via verification m easurements. Finally , Section VII conclu d es th e paper . I I . S Y S T E M M O D E L A N D P RO B L E M F O R M U L A T I O N This study co nsiders a monostatic CP-OFDM-ISAC system transmitting an OFDM frame c o mposed of M OFDM 2 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. Fig. 1: Consider ed ISA C system model. symbols, each co n sisting of N sub carriers. Th e baseba nd time-dom a in transmit sign al of the m th OFDM sy m bol is x m ( t ) = r P tx N N − 1 X k =0 X m ( k ) e j2 π k ∆ f t u ( t ) , (1) where X m ( k ) ∈ C denotes the unit power com plex-valued data symbo l modulated onto th e k th subcarr ier o f the m th OFDM symb ol and en tr y o f X ∈ C N × M , P tx is th e total av erage transmit p ower per OFDM sym bol, ∆ f d e notes the subcarrier spacing 1 . The function u ( t ) repre sen ts a r e c tangular pulse win d ow that incor p orates the CP u ( t ) = ( 1 , − T cp ≤ t < T d 0 , o therwise , (2) where T cp denotes the cyclic prefix duration, while T d represents th e data-carry ing part of the OFDM symbol excluding the CP. Accordin gly , the total du ration of one OFDM symbol is T = T cp + T d . The transmit signa l x ( t ) correspo n ds to a frame co nsisting of M OFDM symbo ls and is the n given by x ( t ) = M − 1 X m =0 x m ( t − mT ) = r P tx N M − 1 X m =0 N − 1 X k =0 X m ( k ) e j2 π k ∆ f ( t − mT ) u ( t − mT ) . (3) The sensing ch annel is mo d eled with H targets present in the en vironm e nt, alon gside multiple I SA C no des, a s illustrated in Fig. 1. It is assume d that the co mmunicatio n signal from ISA C N o de #2 is perfectly can celled prio r to sensing processing at the receiver of ISAC Node #1. This assump tion isolates th e sensing reflection s and enables a focused analysis of r a dar , i.e., sensing perfor mance. 1 For notatio nal con venience, the baseband s ignal in this mathematic al model is defined over the frequency interv al [0 , B ] , effe cti vely centered at B / 2 . In actual hardware realizat ions, the complex discrete -time baseband signal is gene rated symmetrica lly aroun d 0 Hz before upco n version. Consequen tly , applying this practic al symmetric representati on direct ly to the radar signal processing framewo rk detailed in Section III would necessita te appropria te subcarrier reinde xing and slight modifications to the subsequent mathemati cal formulations. Furthermore, the expli cit transformation of these time-disc rete symbols into a contin uous-time wa vefor m via a digital- to-anal og con verter (DA C) is omitted for brevity . Under this assump tion, the received sensing signal can be expressed as y ( t ) = H − 1 X h =0 α h x ( t − τ h )e j2 π f D ,h t + w ( t ) , (4) where α h ∈ C is complex attenu ation factor o f target h , τ h is the delay of target h , f D ,h denotes the Do ppler f requency for target h , and w ( t ) denotes additive white Gau ssian noise (A WGN) w ( t ) ∼ C N (0 , σ 2 ) with noise p ower σ 2 . For completen e ss, | α h | f ollows fro m the [14], [15], | a h | = s G tx G rx σ RCS ,h λ 2 (4 π ) 3 R 4 h , (5) where G tx and G rx are the transmitter and r eceiv er anten na gains, respectively , σ RCS ,h is the r a dar cross section of target h , R h represents the distance to target h , an d λ = c/ f c is the wavelength of the transmitted signal, with c d enoting the speed o f light. In an ideal scenario, it is assumed that (i) targets are perfectly separated by the resolution limits, (ii) target de la y s are bo unded by the CP du r ation av o iding ISI and I CI, and (iii) the an alog-to-d igital converter (ADC) reso lution is high enoug h , meaning qu a ntization noise is negligible and therm al noise is th e sole limiting factor . Under these ideal assumption s, the resulting radar image exhibits the h th target as a distinct signal peak. Th e cor respondin g signal- to-noise ratio (SNR) for target h , denote d a s SNR ideal image ,h , can b e compu ted with respect to the p o st-processing noise variance as [15] SNR ideal image ,h = P tx G tx G rx σ RCS ,h λ 2 G p (4 π ) 3 R 4 h k B B T th NF , (6) with proce ssing gain G p . The term k B represents Boltzmann ’ s constant, T th is the standard room temperature in Kelvin, and NF is the overall receiver n oise figure. Con sequently , the produ ct k B B T th NF in the denomin ator accounts for the effectiv e power of th e samp led version of th e A WGN w ( t ) . However , this idealized formu la fails to capture the perfor mance b ottlenecks o f p ractical systems. In reality , the dynamic r ange is severely constraine d b y q uantization n oise, as well as I SI and ICI from targets exceed ing the CP d uration. T o quantify these effects, the exp r ession in (6) must be extended. For OFDM- based radar systems, the CP duration determ ines the max imum ISI-f ree range R max,ISI = c · T cp 2 . (7) The targets that ar e in this I SI-free region do not indu ce any ISI and ICI due to delay . On the o th er h and, target mo tion induces a Dop pler shift th at inher e ntly results in I CI. T o ensure th at subcarrier orthog onality is appro ximately preserved an d the resulting ICI r emains negligible, the Doppler shift is typ ically constrained to f D < 0 . 1 ∆ f , which d efines th e maximu m ICI-limited velocity v max,ICI [15], [ 16]. While this velo c ity limit is n ecessary to mitigate drastic Doppler-induced interferen ce, the primary stru ctural constraint regarding ISI is impo sed by the CP du ration. This is visua lize d 3 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. Fig. 2: Recei ved OFDM signal for two dif ferent targets, upper is for the target in the ISI free region and lowe r is for the non-ISI free region. in Fig. 2, wh ich illustrates the recep tion timing relative to the transmit time t tx for two distinct scenarios. For target h − 1 , the round -trip delay is shorter than the CP duratio n , therefore, the received ech o remains fu lly aligned within th e ISI-free region, av oid ing delay-in duced inter ference. In co ntrast, the ech o fro m target h a rriv es with a delay exceed ing th e CP d uration. T h is misalignment d estroys subcarrier o rthogo n ality , r esulting in both ISI and ICI. Conseque n tly , the target h suffers from a redu ction in effecti ve useful signal p ower due to window mismatch. Th is scenario leads to bo th I SI and ICI, re su lting in interference and loss in useful signal power . T o quantify th is power lo ss, the captu red signal fr action for target h is defined as η h = max  0 , min  1 − τ h − T cp T d , 1  . (8) Accountin g f or th e imp a ct of window m ism a tch and interferen ce, the actual po st-p rocessing SINR f or target h is giv en by SINR actual image ,h = P tx G tx G rx σ RCS ,h λ 2 G p η 2 h (4 π ) 3 R 4 h P dom n , (9) where P dom n denotes the dominan t n o ise or interference term over thermal noise, quantization n oise, a n d interference limiting th e system dyn amic range. In practical mono static ISA C sy stem s, a strong self-interfer e nce arises due to the spillover between the transmit an d r ecei ve chains. Since this cou p led signal is typically much stronger th an the reflected target ech o es [15], it dictates the r equired full-scale ran ge of the ADC to prevent sign al clipping. Consequ ently , th e quantization noise floor is character ized by the signal-to - quantization -noise ratio (SQNR), wh ic h mu st accoun t f or the peak -to-average power ratio (P APR) o f the OFDM wav eform. Specifically , th e SQNR can b e expre ssed a s [1 7] SQNR = 6 . 0 2 N bit + 10 lo g 10 (3 F ) , (10) where N bit denotes the n umber of bits used in the A DC and F represents th e ratio of the average signal power to the squar ed peak amp litude. In this study , the quan tization n oise p ower is determined relative to th e peak spillover le vel, ensuring it is accurately m odeled alon g side thermal noise an d interf erence. Beyond har dware-induced thermal noise and quan tization noise limits, th e system is also limited by excessive delay-ind uced interferen ce. Specifically , th e interferenc e T ABLE I C O N S I D E R E D S I M U L AT I O N P A R A M E T E R S Parame ters Symbol V alue Carrier frequency f c 3 . 5 GHz Frequenc y bandwidth B 200 MHz Number of s ubcarri ers N 6652 Cyclic prefix length N cp 458 OFDM symbols per frame M 280 Tra nsmit power P tx 49 dBm Antenna gain G tx , G rx 25 . 8 dBi Noise Figure NF 8 dB 22.7 dB 22.6 dB Range (m) Power (dBm) 0 0 1000 2000 3000 4000 5000 100 80 60 40 20 - 100 - 80 - 60 - 40 - 20 Fig. 3: Recei ved power profile versus range for a tar get with 20 dBsm radar cross section (RCS). The effect i ve recei ved po wer is s ho wn as ( ). The maximum ISI range R max,ISI is indicated by ( ). Noise floors are depict ed as follows: Thermal noise is shown as ( ), and 12-bit quanti zatio n noise as ( ). The interferenc e power is indicat ed by ( ). T he ef fecti ve recei ved signal, including processing gain, is represente d by ( ), and the peak powe r in the radar image by ( ). power resulting from a target that is outside th e I SI-fr ee region can b e calcu lated as P int ,h = P tx G tx G rx σ RCS ,h λ 2 (1 − η 2 h ) (4 π ) 3 R 4 h , (11) where P int ,h denotes th e interfere n ce power level resulting from target h . T o fo rmulate the problem and motivate the n e c essity of the pro posed in terference canc ellation frameworks prior to the detailed sign al model deriv ations, a prelimin ary nu m erical system-level analysis is condu cted. T o identify th e dominan t noise or interf erence con tr ibution in p r actical systems am ong thermal, quan tization, and interfer ence in p ractical sy stem s, the system p a rameters repor ted in [2] and [7] are c o nsidered, which are summa r ized in T able I. For a n aggregate Tx- Rx isolation of 60 d B, which is achiev able throug h a combin ation of physical antenna separation and analog self-interf erence cancellation [1 8], th e q uantization no ise lev el is c omputed based o n the spillover level an d (1 0). Using the pa r ameters in T ab le I, an example scenario is considered in wh ich a target with 20 dBs m RCS is genera ted, and its range is swept u p to the maximu m unamb iguous range. The corr esponding r esults ar e shown in Fig. 3. When a strong target (e.g., a auto mobile or truck with 2 0 dBsm RCS 4 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. Interferer RCS (dBsm) Interferer RCS (dBsm) Power (dBm) Maximum range (km) (a) (b) 10 10 20 20 30 30 - 85 - 80 - 75 - 70 - 65 - 60 - 55 - 50 - 45 - 40 0 0 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 Fig. 4: Analy sis of noise, interferenc e le vel s, and maximum dete ctable range versus interferenc e source RCS. (a) Comparison of noise and interfere nce po wer le vel s. Interference powe r is represe nted by ( ), thermal noise by ( ), and quantizat ion noise by ( ). (b) Maximum detect able range for targ et RCS values of 0 dBsm ( ), 10 dBsm ( ), and 20 dBsm ( ). The maximum unambiguous range limit is indicat ed by ( ), and the ISI-free range limit by ( ). [19]) m oves ou tside the I SI-free r ange, it introduces significan t interferen ce as illustra ted in Fig. 3. This inter f erence results in an interferenc e-induced floor in the radar ima ge that exceeds both the quantization noise an d the therm al noise lev els. As an notated in Fig. 3, the noise le vel d ifference between the in terference noise and the larger of th e th ermal and quantizatio n n oise co mponen ts can reach up to 22 . 6 dB , depend ing on the rang e of the in terferer . Furth ermore, as the target range app roaches the maximum una m biguou s r ange, the received power in the rad ar imag e decrea ses due to the reduced overlap betwe en the d elayed echo and the p rocessing window of th e receiver . For the considere d system p arameters in T able I , th is power loss can reach u p to 22 . 7 dB . T o e valuate the system limits, a worst-case scen a r io is analyzed where th e interferin g target is po sitioned at a ran ge that max imizes interf erence power . I n this config uration, the RCS o f the interfer e r is swep t to comp are the r esulting no ise lev els, as illustrated in Fig. 4 (a). The re su lts demonstra te that interferen ce-induced no ise consistently exceed s o ther no ise sources acr oss all consid e r ed cases. Con sequently , inter ference is ide ntified as the domin ant factor that determ ines the floor lev el in the r adar image and is u tilized in (9) f or p e r formanc e estimation. Based on th e m inimum target RCS and th e r equired SNR th reshold of 17 dB fo r reliable detectio n o f a target [2], the m aximum de te c ta b le rang e is calculated and plotted as a fun ction of the RCS o f interfer er in Fig. 4(b) . It is evident that th e de tectable range is drastically redu ced when a target or m ultiple targets exist beyond the ISI- free range. This su bstantial d egradation h ighlights the critical necessity for r obust interfe r ence cancellation an d coheren t co mpensation mechanisms. I I I . S I G N A L M O D E L The r eceiv ed signal associated with target h , de n oted as y h ( t ) , is a nalyzed und er two distinct d elay scenarios, as illustrated in Fig . 2 . The first case consid e rs a target who se round -trip d elay τ h is shorter than the CP duration . As a result, the corresp o nding echo doe s n o t expe r ience ISI or I CI d u e to excessi ve delay , as d epicted in the upp er part of Fig. 2. For this scenario, if i ∈ { 0 , . . . , N − 1 } is used to deno te th e sample index at the m th OFDM symb ol in terval, the r e cei ved samples can b e written as y h m ( i ) = r 1 N N − 1 X k =0 ˜ α h · X m ( k ) · e j 2 π k ∆ f ( iT s − τ h ) · e j 2 πf D ,h iT s · u ( iT s − τ h ) , (12) where | ˜ α h | 2 = P tx | α h | 2 . Apply ing a discrete Fourier transform (DFT) on (12), th e resulting fr equency domain sign a l is given by Y h m ( p ) = ˜ α h X m ( p )e − j2 πpτ h N T s e j2 π f D ,h mT , (13) where p ∈ { 0 , . . . N − 1 } . Next, the excessive delay scenario is considere d , in which the ro und-trip delay of target h exceeds the CP duration . In such cases, the received samples co r respondin g to target h are influenced by two consecutive OFDM symbols, resulting in both ISI and ICI. The received signal un der this condition is expressed as (14) [6], in which w m ( i ) deno tes the A WGN at the i th sample of the m th received OFDM symb ol. Follo wing the a nalysis in [6], the average p ower of the useful signal can be calculated under the assumption of low Doppler shifts, i.e., f D ,h < ∆ f 10 . By app lying the DFT to (14), the resulting e xpression c an be comp uted as in (15). By rearrang ing ( 1 5), the received signal can be expressed as [ 8] Y h m ( p ) = ˜ α h X m ( p ) e − j 2 π p ∆ f τ h e j 2 πm f D ,h T s | {z } Y free m,h + ˜ α h e j2 π ( m − 1) f D ,h T s N − 1 X k =0 X m − 1 ( k )e j2 π k ∆ f ( T cp − τ h ) φ h p,k | {z } Y ISI m,h − ˜ α h e j2 π mf D ,h T s N − 1 X k =0 X m ( k )e − j2 π k ∆ f τ h φ h p,k | {z } Y ICI m,h , (16) where φ h p,k = 1 N P N − 1 i = N h − N cp e j2 π ( k − p ) i N represents th e interferen ce comp onent, wh ich also d enotes the elem ent at row p and c olumn k of the interferen ce matrix Φ h ∈ C N × N . Let the steering vectors fo r the d elay , Doppler, and Jacobian matrix be de fined as [8] b ( τ h ) = h 1 , e − j π ∆ f τ h , . . . , e − j2 π ( N − 1)∆ f τ h i T , (17) c ( f D ,h ) = h 1 , e j2 π f D ,h T , . . . , e j2 π ( M − 1) f D ,h T i T , (18) J =  0 ( M − 1) × 1 I M − 1 0 0 1 × ( M − 1)  , (19) where I M − 1 is the identity m atrix, 0 ( M − 1) × 1 and 0 1 × ( M − 1) are zero c o lumn an d row vector s with size M − 1 , respectively . Based o n th ese steering vectors, an d the Jacobian matrix, 5 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. y h m ( i ) = r 1 N N − 1 X k =0 ˜ α h · X m ( k ) · e j2 π k ∆ f ( iT s − τ h ) · e j2 π f D ,h ( mT + iT s ) · u ( iT s − τ h ) + r 1 N N − 1 X k =0 ˜ α h · X m − 1 ( k ) · e j2 π k ∆ f ( T + iT s − τ h ) · e j2 π f D ,h ( mT + iT s ) · u ( T + i T s − τ h ) + w m ( i ) (14) Y h m ( p ) =  1 − N h − N cp N  ˜ α h X m ( p )e − j2 πpτ h N T s e j2 π f D ,h mT + 1 N N − 1 X k =0   ˜ α h X m − 1 ( k )e j2 πk ( T cp − τ h ) N T s   N h − N cp − 1 X i =0 e j 2 π ( k − p ) i N     e j2 π f D ,h mT + 1 N N − 1 X k =0 ,k 6 = p   ˜ α h X m ( k )e − j2 πkτ N T s   N − 1 X i = N h − N cp e j2 π ( k − p ) i N     e j2 π f D ,h mT + W m ( p ) . (15) and (16), the signal contribution f rom each target in the frequen cy domain can b e expr essed as Y h ( ˜ α h , τ h , f D ,h ) = ˜ α h "  b ( τ h ) c T ( f D ,h ) ⊙ X  + Φ h  b ( τ h − T cp ) c T ( f D ,h ) ⊙ X  J + Φ h  b ( τ h ) c T ( f D ,h ) ⊙ X  # . (20) where ⊙ deno tes the Hadam ard p roduct. Finally , the received frequen cy-domain frame withou t no ise Y ∈ C N × M can be expressed as the superp osition of all target reflectio n s as Y = H − 1 X h =0 Y h ( ˜ α h , τ h , f D ,h ) . (21) The estimate d channel m a trix H with zero -forcing equalization and 2 D windowing is given by H = ([ Y ⊘ X ]) ⊙ H window , ( 22) where ⊘ de n otes the element-wise d ivision. The 2D windowing matrix is d efined as the oute r prod uct H window = w r w T d , where w r ∈ R N and w d ∈ R M are the w in dowing coefficient vector s for the de lay and Dopp ler dimension s. Finally , the r ange-velocity ima ge I rv is ob tained v ia standard range-Do ppler pr ocessing I rv = F M  F − 1 N { H }  Π M , (23) where F − 1 N , F M , an d I rv ∈ C N × M denote the energy preserving in verse discrete Fourier transform (IDFT) along the subcarriers, th e DFT along the symbols, an d the complex r adar image, resp e cti vely . The matrix Π M ∈ { 0 , 1 } M × M is a block permutatio n matrix that ensures th e zero -velocity compo nent is alig n ed to the center of th e im age. Assuming M is ev en, Π is d e fin ed as Π M =  0 M / 2 I M / 2 I M / 2 0 M / 2  , (24) where 0 M / 2 denote the ze ro matr ix with size M / 2 . Follo wing a coarse ta rget detection in th e r ange-velocity image | I rv | 2 by the con stan t false alarm rate (CF AR) algorithm , a 2D CZT can be employed to refine the r ange an d velocity estimates. Unlike th e standard fast Fourier tran sform (FFT), which is limited to a fixed grid re so lution of ∆ f = f s / N (where f s denotes the sampling f r equency), the CZT allows for the evaluation of the Z- transform along a spiral co ntour . This effecti vely z ooms in to a specific spectral r egion of in ter est (R OI) with an arbitr a ry resolution factor L . Let ( ˆ n h , ˆ m h ) deno te the co arse rang e and Do ppler indices of a detected peak f or target h wher e ˆ n h ∈ { 0 , . . . , N − 1 } a n d ˆ m h ∈ { 0 , . . . , M − 1 } . A local search window o f wid th B roi bins is defined aroun d these indices. Th e refinem e n t pr ocedure is carr ie d out by ran ge interpolatio n f ollowed by Doppler interpolatio n. In the first stage, CZT is applied alon g the first dimension of the pre-pr ocessed, wind owed ch annel response H . The zoom ope ration is con trolled b y th e starting contour point A r and the conto ur step scala r W r , which are defined as A r = e − j 2 π N  ˆ n h − B roi 2  , W r = e j 2 π L · N . (25) The intermediate r ange-refin e d matrix Z r is computed by ev alua tin g the CZT alo n g the defined contour Z r ( k , m ) = N − 1 X n =0 H ( n, m ) A n r W nk r , (26) where N czt = B roi · L and k ∈ { 0 , . . . , N czt − 1 } . Next, the CZT is app lied along th e secon d dimensio n of Z r to r efine th e velocity estimate. The Dop pler contour parameter s a re defined similarly ar ound the coarse Doppler index ˆ m h as A d = e j 2 π M  ˆ m h − M + B roi 2  , W d = e − j 2 π L · M . (27) The fin a l 2D high - resolution image Z rd is obtained by Z rd ( k , p ) = M − 1 X m =0 Z r ( k , m ) A m d W mp d , (28) where p ∈ { 0 , . . . , N czt − 1 } . The sub-b in p eak lo cation ( k ∗ h , p ∗ h ) for target h is iden tified by max im izing the magn itude of th e high -resolution ima g e 6 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. | Z rd | 2 . T o facilitate the p h ysical param eter mapp in g, the fractional index offsets ∆ k h and ∆ p h are defined r elati ve to the center of th e zoom ed window as follows ∆ k h = k ∗ h − N czt / 2 L , ∆ p h = p ∗ h − N czt / 2 L . (29) These offsets represent th e deviation from th e coarse indices ( ˆ n h , ˆ m h ) in units of th e o riginal bin width. The prec ise physical delay ˆ τ h and the Do ppler frequ ency ˆ f D,h are then calculated as ˆ τ h = ˆ n h + ∆ k h B , ˆ f D,h = ˆ m h + ∆ p h T , (30) where B is the signal bandwid th. Additionally , the option al q uadratic interp olation techniqu e described in [2 0] can be applied to fu rther refine the peak estimates obta in ed f rom the CZT. By app roximating the main lobe of the window fu nction as a two-dimen sional p arabola, fractional co r rections to the CZT p eak indic e s ( k ∗ h , p ∗ h ) can be compu ted. T o simplify the no tation, let us define the fine-resolutio n power at indices ( k , p ) as S [ k , p ] = | Z rd [ k , p ] | 2 . The r efined rang e index ˜ k h and Dop pler index ˜ p h are g iven by [ 20], ˜ k h = k ∗ h + S ( k ∗ h − 1 , p ∗ h ) − S ( k ∗ h + 1 , p ∗ h ) 2 ( S ( k ∗ h − 1 , p ∗ h ) + S ( k ∗ h + 1 , p ∗ h ) − 2 S ( k ∗ h , p ∗ h )) , (31) ˜ p h = p ∗ h + S ( k ∗ h , p ∗ h − 1) − S ( k ∗ h , p ∗ h + 1) 2 ( S ( k ∗ h , p ∗ h − 1) + S ( k ∗ h , p ∗ h + 1) − 2 S ( k ∗ h , p ∗ h )) , (32) to have continuo us estimation. However , as it is shown in measurem ent r esults, e ven with out this o ptional p r ocess, interferen ce cancellation a nd weak target detection ca n be done succe ssfu lly . I V . P RO P O S E D I N T E R F E R E N C E M I T I G A T I O N A L G O R I T H M S Based on c omputation al com plexity difference, we prop ose two distinct frameworks. Each f ramew ork reconstructs target’ s echo based on delay , Do ppler and c omplex attenuation factor estimates. Befor e m oving o n to the d etails of each algor ith m, the calcu lation of the attenuation factor mag nitude, which is used b y both meth o ds, is explain ed. T o e stimate the c o mplex attenuation factor α h , th e signal amplitu de is r econstructed by compen satin g for sign al-depend ent losses as well as system processing gains. In (15), the useful signal comp o nent is initially de ri ved under th e assum ption of a moder ate Do ppler shift. More gen erally , the useful signal p ower can be expressed for arbitrary Doppler shifts by explicitly accounting for both Doppler-induced atten uation an d excess delay . Using the Dirichlet kernel rep resentation, the u seful signal p ower is given by P h u = η h 2 |{z} L ISI ( ˆ τ h ) ·         sin  π f D ,h η h ∆ f  N · sin  π f D ,h η h N ∆ f          2 | {z } L Dop ( ˆ τ h , ˆ f D ,h ) ·| ˜ α h | 2 . (33) For targets tha t correspo nd to the delay smaller than the cyclic prefix, η h = 1 , and the signal is lossless. For excessiv e delays, η h decreases lin early , introd ucing an ISI p ower lo ss factor of L ISI = η 2 h and a Dop pler spreading loss L Dop characterized by the widen ed Dirich let kernel in (33). W e utilize the fine-r esolution peak power | Z rd [ k ∗ h , p ∗ h ] | 2 obtained fro m the CZT, wh ic h p r ovides a better estimate th an the coarse grid peak . T he magn itude estimate | ˆ α h | is der i ved by inverting (33) | ˆ α h | = s | Z rd ( k ∗ h , p ∗ h ) | 2 G p · L win · L ISI ( ˆ τ h ) · L Dop ( ˆ τ h , ˆ f D,h ) , (34) where L win =      1 N M X n,m H window ( n, m )      2 , (35) which den otes the p e ak power loss due to the 2D windowing. Dirichlet kernel term in (33) is the lo ss related to the Dop pler shift but it is a fun ction of η . This broad ening o c c urs because the effectiv e recta n gular window in the time d o main sho rtens as th e delay inc reases, causing the main lob e of the Dirichlet kernel in the f requency d omain to widen. Therefo re, while estimating th e received signal power for each target, we will consider power losses resulting from excessi ve delay and velocity of the target. A. JIC-CC: Efficient Cancellation with Co her en t Recovery The pro posed JIC-CC framework adopts similar cancellation p rocess to the iter ati ve cancel-then - detect architecture of SIC schem e in [ 8], yet it differs in the interferen ce cancellation and p a rameter estimation stages. Specifically , the SIC metho d described in [8] attempts to estimate the c omplex attenua tion factor ˆ α h via a least squares projection , u tilizing the estimated delay ˆ τ h and D o ppler shift ˆ f D ,h . The estima to r is given b y [8], [2 1]: ˆ α h = b T ( ˆ τ h ) ( Y free ⊙ X ∗ ) c ( ˆ f D ,h ) k b ( ˆ τ h ) k 2 k c ( ˆ f D ,h ) k 2 , (36) where X ∗ denote th e conjugate of transmit f rame and Y free h ∈ C N × M is the interferen ce-free observation which is also expressed fo r m th sym bol in (16). Th e app roach in [8] attempts to reconstruc t th e ISI an d ICI terms, Y ISI h and Y ICI h , for targets located outside the ISI- f ree region . By iteratively subtracting th ese com ponents in the frequ ency do main, the m ethod aim s to supp ress the interf e rence-no ise floor and rev eal targets und etectable by co n ventio nal p rocessing. Howe ver, with this ap proach, interfer e nce e f fects ca n be cancelled fo r on -grid targets but, targets that are below interferen ce-noise floor level due to window mismatch will be missed. Add itionally , calculatio n of the c o mplex attenuation factor α h via least squ are estimation can lead to poo r estimations wh e n a target is located in o ff-grid in the rad ar image. T o address these limitation s, the pro p osed JIC-CC framework introd uces a d etection-recovery loop . Spe cifically , the CZT [13] is em p loyed to refine the comp lex amp litude and phase estimates. Furth ermore, inter ference con tributions 7 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. from all dete c te d targets are subtracted jointly as in (20), a n d the resultin g c le a n sign al Y c is utilized in frequ ency-domain coheren t compensation to recover the signal energy for targets with excessi ve dela y in the subsequ ent symbol. 1) Algorithm Description : Upo n d etection of targets with co nventional pro cessing, the proce ss transitions to the estimation stage. T o minimize p arameter errors, the CZT is utilized to estimate ( ˆ τ , ˆ f D ) with super-resolutio n p r ecision. In this algor ith m, signa l cleaning is d irectly d one in the frequen cy domain. Ther efore, estimated p hase ˆ θ h of th e target h can be directly extracted from phase o f Z rd ( k ∗ h , p ∗ h ) . The co mplex attenuation factor ˆ α h is co n structed as ˆ α h = | ˆ α h | · e j ˆ θ h , (37) by co m bining the mag nitude estimation in (34) with the phase estimate ˆ θ h . Let P init denote the dete c ted target list with conventional processing. For detected targets with c on ventional rad ar processing using CF AR, the fr equency d omain signal f or all detected targets in P init can be regenerated based o n delay and Doppler estimations ˆ τ h , ˆ f D ,h and those can be re moved fr om received freq uency do main signal by Y c = Y − X h ∈P init Y h ( ˆ α h , ˆ τ h , ˆ f D ,h ) . (38) Let Y c m ( k ) denote the value in k th subcar rier and m th sym bol in Y c . FDCC can b e a p plied to the resulting signal by [ 7] Y c-FDCC m ( k ) = Y c m ( k ) + C ( k ) Y c m +1 ( k ) , (39) where C ( k ) = e − j2 π kN cp / N . Due to missing CP in frequen cy domain, full compen sation of the signal p ower loss is not possible. Howe ver, with this ap proach, it is p ossible to strengthen signal power f o r targets o utside ISI-free r egio n , especially if N cp ≪ N . Ad ditionally , sin c e n ext OFDM symbol is f u lly added to p revious symbol in this tech nique, additional interfer ence is introduced . Howe ver, since the dominan t echoes from detected targets hav e already been subtracted from the received signal, this residual inter ference is minimal, typ ically falling below the the r mal and quantization noise floor . Consequ e n tly , conventional radar proce ssing can be rep eated by using Y c-FDCC m ( k ) an d the we a k targets in the en vironme nt can be detected. B. FR-SW : Fu ll-Reconstruction Slidin g W in dow While the FDCC appr oach co mpensates for power loss in the freq uency do main, the sliding win dow (SW) approa ch addresses the excessive delay problem in the time dom ain. By explo iting the cyclic natu re of the CP, we can iterati vely shift th e obser vation window to bring distant targets into the ISI- free processing region. T o prevent inter f erence-no ise floor increase d uring this pr ocess, we employ a hybrid joint interferen ce c a ncellation and stitching strategy . 1) Algorithm Description: Th e algorithm first performs standard ra d ar processing on the received time-d omain signal y [ n ] to identify strong targets. For each d e te c ted target h , we refine the ran g e and Do ppler estimates ( ˆ τ h , ˆ f D ,h ) using the CZT method described in Section III. Th e magnitud e of Algorithm 1 JIC-CC with FDCC-Aided Recovery Input: Rece ived fram e Y , referen ce X , CZT pa r ameters ( B roi , L ), H window Output: Reconstructed I m age I f , T arget List P f 1: Initialization: Y canc ← 0 2: Step 1: Strong T arget De t ection 3: I init ← Conv entionalRadar Pr ocessing ( Y , X ) 4: P init ← CF AR ( I init ) 5: Step 2: Precision Cancella tion 6: for each target h ∈ P init do 7: Estimate ˆ τ h , ˆ f D ,h , ˆ θ h using CZT { (30) } 8: Estimate com plex attenuatio n factor ˆ α h { (34) } 9: Construct FD Signal Y h ( ˆ α h , ˆ τ h , ˆ f D ,h ) { (20) } 10: Y canc ← Y canc + Y h ( ˆ α h , ˆ τ h , ˆ f D ,h ) 11: end for 12: Y c ← Y − Y canc 13: Step 3 : FDCC-Aided W eak T arget Det e ction 14: Y c-FDCC ← ApplyFDCC ( Y c ) { (39) } 15: I clean ← Conv entionalRadar Pr ocessing ( Y c-FDCC , X ) 16: P weak ← CF AR ( I clean ) 17: P f ← P init ∪ P weak 18: Step 4 : Final Restoratio n 19: I f ← RestoreT argetsShape ( I clean , P f ) 20: return I f , P f complex attenuation factor | ˆ α h | is estimated by compen sating for the ISI an d wind owing losses as derived in (34). For th e in itial phase estimation, it is critical to reco gnize that the comp lex phase o b served at th e rang e-Doppler p eak does not correspo n d to the target’ s initial phase at t = 0 . Instead, it inclu des a deter ministic r otation caused b y the Do ppler shift up to the effective processing window . Th is a c cumulated rotation is ra n ge-depe n dent, as the effecti ve win dow shif ts for targets subject to delay -induced truncation . The r efore, to en sure precise coheren t cancellation , we app ly a phase correction that explicitly co mpensates for th is Dop pler-induced rotation, rec overing the true phase relative to the glob al time referen ce. Finally , using the f ully estima ted parameter set { ˆ α h , ˆ τ h , ˆ f D ,h , ˆ θ h } , the received signal f or target h is reconstruc ted and subtrac ted fro m the input stream an d this process is d one for all detec ted targets jointly . Sp e c ifically , the interferen ce cancellatio n is p erformed in the time doma in by subtracting the reco nstructed signal estimates for eac h target. Based on d e fined discrete sam p ling times t = nT s , the clean signal is g i ven by y clean [ n ] = y [ n ] − X h ∈P init ˆ α h  x ( t − ˆ τ h )e j2 π ˆ f D ,h t     t = nT s | {z } y h [ n ] , (40 ) where x ( t ) denotes th e continuo u s-time tran smitted wa vefo rm. After cleaning , the residu al sign al y clean contains the weak targets poten tially located beyond the m aximum ISI-fr e e range. T o recover th ese, the final high- range image I f is constructed by stitchin g tog e th er ”fraction a l” ra dar images. 8 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. Algorithm 2 SIC-Aide d Sliding W indow Stitchin g Input: Received time do m ain signal y , refer ence X , CZT parameters ( B roi , L ), H window Output: Final I mage I f , T arget List P f 1: Step 1: Initial Detection & Cleaning 2: I init ← Conv entionalRadar Pr ocessing ( y , X ) 3: P init ← CF AR ( I init ) 4: y clean ← y , P f ← P init 5: for each target h ∈ P init do 6: Estimate ˆ τ h , ˆ f D ,h , ˆ θ h via CZT and phase calibratio n { (30) } 7: Estimate ˆ α h including losses { (34) } 8: Generate y h [ n ] and u pdate: y clean ← y clean − y h [ n ] 9: end for 10: Step 2 : Fract ional Stitching Loop 11: Initialize I f 12: S ← ⌈ N / N cp ⌉ 13: for s = 0 to S − 1 do 14: y s shift ← ShiftSignal ( y clean , s · N cp ) { (41) } 15: I s aux ← FractionalRad a r Processing ( y s shift , X ) 16: P aux ← CF AR ( I s aux ) 17: P f ← P f ∪ P aux 18: Stitch: Extract valid range 19: R start ← s · N cp 20: L seg ← min( N cp , N − R start ) 21: I f [ R start : R start + L seg − 1 , :] ← I s aux [0 : L seg − 1 , :] 22: end for 23: Step 3 : Restora tion 24: I f ← RestoreT argets ( I f , P f ) 25: return I f , P f The algor ithm p erforms S = ⌈ N / N cp ⌉ iteration s. In the s th iteration (wh ere s = 0 , . . . , S − 1 ), the clean time-do m ain signal is sh ifted by s · N cp samples: y s shift [ n ] = y clean [ n + s · N cp ] . (41) Standard OFDM radar pr ocessing is ap plied to this shifted signal to obtain a n a uxiliary range-Do ppler image I s aux . Due to the time sh if t, physical targets loc a te d a t delay τ ≈ s · T cp in the origin al fram e now appear nea r zero delay in I s aux , placin g them in th e high -SNR, ISI-fr ee r egion. The final image is constructed b y extracting the valid ISI-free region from each auxiliary image and mapp in g it to the correspo nding absolute delay indices in the final image. T o handle th e g eneral case where the total num b er of subcarrier s N is no t an integer multiple of N cp , we define the length of the valid segment for the s th window sh ift as L seg = min( N cp , N − s · N cp ) . (42) The stitchin g ope r ation is then p erformed as I f [ r + s · N cp , m ] = I s aux [ r , m ] , (43) valid f or local range in dices r ∈ [0 , L seg − 1] . Th is process effecti vely solves the rang e amb iguity by stitching togeth er locally valid segments of leng th L seg to for m a comp lete, extended radar im a ge up to the unam biguous range. Fina lly , T arget 1 RCS (dBsm) Mean SINR Image (dB) 30 40 50 60 0 0 5 10 10 15 20 − 5 − 10 − 15 Fig. 5: SINR comparison for the weak target agai nst RCS. The empirical detec tion threshol d is indicat ed by ( ). The theoret ical ideal SNR is sho wn in (  ). The exist ing m ethods are shown with lines: SW ( × ), 15 itera tion SIC (  ), TDCC ( △ ), FDCC ( ▽ ), and MT CC ( ♦ ). The proposed methods are shown with: SIC-CC ( ⋆ ) and F R-SW ( ⋆ ). the strong targets rem oved in th e first step are restored to I f to com plete the scene. V . S I M U L AT I O N R E S U LT S A N D C O M P L E X I T Y A N A LY S I S T o bench mark the prop osed algorith ms against the existing literature, the detection p erforman ce for wea k targets near the maximum una mbiguou s r ange is ev aluated. The simulation parameters ar e listed in T able I. T o ensure a fair comp arison, windowing is o m itted for all scheme s and a n d targets are ideally p laced on th e range- Doppler g rid, i.e., in teger m u ltiples of r ange and velocity resolution . Consistent with th e previous analysis, a worst-case scenario is adop te d wherein a stron g interfering target ( 2 0 dBsm) is positioned at the range yielding maximum interfer ence power , as illustrated in Fig. 3. A secondary weak target is placed n ear the unambigu ous range limit where R max,unamb = 4914 m. T o establish a fair baselin e compariso n isolated from spectral leakag e effects, th is target is intentiona lly placed exactly o n th e ra n ge grid at 4 8 39 m. The RCS of this weak target is swept, and the r esulting image SINR le vels are m easured f or all co nsidered algo rithms. Additionally , a detection threshold of 17 dB is ind icated in Fig. 5 to d efine the boun d for reliable target detection [2]. As illustrated in Fig. 5, the pr oposed FR-SW algorithm achieves an SINR pro file tha t closely m atches th e theore tical ideal. This demo nstrates the efficiency o f the sliding window technique combin ed with stron g target cancellatio n in fully recovering wea k targets. Conversely , the prop osed JIC-CC algorithm exhibits slightly subop timal p erforma n ce compar ed to the ideal cu rve. T h is deviation can be attributed to the signal power loss inherent to the FDCC op e ration wh en the CP is absent an d therm al no ise power increase during this process. In the high RCS regime ( > − 5 dBsm), the SIC algo rithm from [8] outp erforms slightly JIC-CC but r emains inferior to FR-SW. Th is beh avior is expected; while th e alg orithm used 15 iter ations, further increasin g this n umber could theoretically allow convergence to the ideal boun d, but at the cost of p rohibitive computatio nal complexity . A more critical 9 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. Amplitude MAE (dB) Range offset (m) Range offset (m) Interference-noise floor (dBm) Phase MAE ( ◦ ) 5 4 3 2 1 0 0 0 0 - 0 . 2 - 0 . 2 - 0 . 4 - 0 . 4 0 . 1 0 . 2 0 . 2 0 . 2 0 . 3 0 . 4 0 . 4 0 . 4 0 . 5 - 55 - 60 - 65 - 70 - 75 - 80 Fig. 6: Performance analysis of parameter estimation and int erferenc e cance llati on under on-grid and off-gri d conditions. (a) Estimation accurac y: Solid lines represent amplitude mean absolute error (MAE) (left axis), and dashed lines represent phase MAE (right axis). (b) Residual interfe rence-n oise floor in comparison to the − 82 . 96 dBm thermal limit. Initia l noise-i nterfere nce floor with con ventional processi ng is indicate d by ( ). Results are shown for the proje ction-b ased estimator (36) at f D = 0 ( ♦ ) and f D = 0 . 1∆ f (  ); and for the CZT-based estimator at f D = 0 ( × ) and 0 . 1∆ f ( ◦ ). limitation of SIC is observed at low RCS values ( ≤ − 10 dBsm). As shown, a sharp perfor m ance disco ntinuity occu rs where the target SINR falls below the detectio n thresh o ld (17 dB). In th is region, the a lg orithm fails to r eliably detect and r e c onstruct th e signal Y free , leading to a breakdown in cancellation p erforman ce. Additionally , SW algo rithm p r oposed in [9] is also in vestigated. As explained ea rlier , ta rgets inside ISI-free region are detected at every iteration and th eir contribution to received signal is removed iteratively and overall radar image is constructed by stitching individual radar processing results u p to R max,ISI at every iteration in [ 9]. Howe ver , this techniqu e leads to h igh inte r ference-n oise floor in e a rlier iteration s until the strong target that is outside ISI-f ree region is de tec ted and removed. Th erefore, m ean SINR image re d uction is also observed with that techniq ue as well. The investigation also e valuates th e mu lti target coher ent compen satio n (MTCC) algo rithm, which is p roposed in [7]. While MT CC imp roves up o n standard techniqu es like FDCC and time dom ain cohere n t com pensation (TDCC) by apply ing th resholding in multi-target scenarios, it still suffers fro m SINR loss. When a strong target lies outside the ISI-fre e region, it encou nters ISI an d ICI that elev ate s the interfer e nce-noise floor . Since M TCC suppresses only the peak power of stron g targets via threshold in g, the residual interferen ce ( e.g., sidelo bes) remains, resulting in the observed degradation. In practical scenarios, off-grid targets introd uce spectral leakage that can fu rther degrade perfo r mance. Consequ ently , this section investigates the necessity o f CZT-based parameter estimation to add ress th e se off-grid effects. This investigation considers a single strong target ( 20 dBsm) located outside the ISI-fre e region. Given a n oise figure o f NF = 8 dB, the theoretical thermal n oise floo r following ideal cancellation is − 8 2 . 96 dBm. T o e valuate robustness again st off-grid effects, the target range is swep t across the inte r val [ R − ∆ R / 2 , R + ∆ R/ 2] centered at R = 750 m. W e analyze the MAE of the estima te d attenu ation factor | ˆ α h | in dB scale and phase ˆ θ h for both the proje c tio n-based techn ique (via (36)) with iterative cleanin g p rocess describ ed in [8] an d the T ABLE II C O M P U TA T I O N A L C O M P L E X I T Y C O M PA R I S O N O F A L G O R I T H M S Algorithm Computational Complexit y TDCC / FDCC [6] O ( M N log( M N )) MTCC [7] O (3 M N log ( M N )) SIC [8] O ( N iter ( M N log( M N ) + H M N )) SW [9] O (( S + 1) M N log( M N ) + H M ( N + N cp )) Proposed JIC-CC O (2 M N log ( M N ) + H d ( C czt + M N )) Proposed F R-SW O (( S + 1) M N log( M N ) + H d ( C czt + C tdr )) Note: The term H d accoun ts for number of detect ed targets with initial radar processing. CZT-based estimation describ ed in this paper . The estimation a n d cancellatio n p erforman ces are presented in Fig . 6. As shown in Fig. 6(a), th e CZT-b ased metho d achieves near-perfect estimation regardless of grid alignment. Con versely , the p rojection-b ased estimator exhibits high er amplitude MAE, which degrades sign ificantly with velocity and off-grid offsets. Add itionally , both estimation tech n iques demonstra te high precision in terms of phase MAE with errors rem aining below 0 . 05 ◦ for the c onsidered system configur ation and scen arios. Fig. 6(b) demon strates that these discrepancies, co mbined with d e lay and Doppler estimation errors inheren t to o ff-grid scenario s in the pro jec tion-based technique , translate into significant residua l interfe r ence. Specifically , the projection appro ach fails to reach the thermal noise floo r for any scenario oth e r than static, on-g rid targets. Furthermo re, while the results in Fig. 6 omit the windowing pro cess, the applica tio n of a practical wind ow function to supp ress sidelob es would lead to an offset in the attenuatio n factor estimation via th e projection -based approa c h . Consequen tly , any app lied windowing fu nction leads to a substantial r esidual interf erence floo r even for o n-grid targets. In contr a st, the prop osed framew orks inherently mitigate th is offset by explicitly com pensating fo r the 2D wind owing loss factor L win , as deriv ed in (34), ensuring robust cancellation under f ully pr a ctical cond itions. Additionally , th e computationa l costs of the proposed algorithm s are compar ed a g ainst state-of-th e-art tech n iques in T able II. The an a ly sis considers the th ree primary processing stages: (i) the radar pro cessing with 2D-FFT ( O ( M N log ( M N )) ); (ii) the pa rameter estimatio n co st (iterative or CZT- based); (iii) the interfer ence recon stru ction cost. A critical distinction lies in the d omain of recon struction. T ime-domain ap proaches, such as the sliding wind ow methods (SW [ 9] and th e p roposed FR-SW), must gen erate the full signal vector inclu d ing the cyclic prefix to effecti vely mitigate the interfe rence. Th is reconstru ction cost is den oted as C tdr in T able II . In our simula tio ns and measuremen ts, C tdr is mod eled based o n FFT ope r ations to ensure exact fra ctional delay a n d Dop pler calculatio n, scaling as O ( M ( N + N cp ) log ( M ( N + N cp ))) , while real-time h a rdware could reduce th is to linear complexity O ( K · M ( N + N cp )) using K -tap polyp h ase finite imp ulse response (FIR) filters. Since the r e c ei ver must iteratively transform th e signa l betwe e n doma in s for every shift 10 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. S = ⌈ N / N cp ⌉ , slidin g window techniques result in a multiplicative scaling o f th e co mplexity . For the pro posed FR-SW, the co mplexity is detailed in T able II for stand ard 2D FFT impleme ntation whic h is utilized for every sliding window shif t and would result in substantial redun dancy , as the full spectr um is re-calculated despite only a fraction being relevant to the curren t wind ow . The r efore c omplexity can be reduced by emp loying an outpu t-pruned FFT algorithm [22]. Since each iteratio n of the FR-SW framework isolates a spe cific frequency sub-band of size ro ughly N /S , the transfor m can be restricted to ev aluate only these requ ired c o efficients. As der i ved in [22], computing a N /S ou tputs fr om N in puts r educes the co mputationa l cost fro m O ( N log N ) to approx imately O ( N lo g( N /S )) . Consequently , b y targeting o nly the relevant sub- band indices, the comp lexity for the iter ati ve stage can be effectively reduced by u sing pruned FFT in the sliding window architecture . In contr a st, the prop osed JIC-CC algorithm o perates entirely in the frequ ency domain , req uiring only two 2 D FFT opera tio ns a longside the local CZT estimation. By eliminating the multiplicative factor S inher e n t to sliding window app r oaches, JIC-CC a c hiev es the efficient complexity profile shown in T able II, o ffering r obust p erforman ce with a computatio nal burden compar able to existing state-of-the- art algorithm s. Additionally , bo th propo sed alg orithms utilize the CZT to improve parameter estimation and this co st is denoted as C czt . The refinement c ost fo r a single target is determin ed by the 2D Chirp-Z T r a nsform, implem ented via Bluestein’ s FFT-based conv olu tion a lg orithm [23]. Assumin g a single refinem e n t window size N czt that is negligible com pared to the full signal dimensions (i.e., N czt ≪ { N , M } ), the co mplexity of CZT can be expre ssed as C czt ≈ O ( M N log N + N czt M log M ) . In addition to compu tational com plexity , th e ev aluated algorithm s im pose distinct memory and har d ware buffering requirem ents. Frequency-d o main appr oaches, such as the propo sed JIC-CC, a s well as existing meth o ds like SI C [8] and MTCC [7] , operate pred ominantly on the demodu lated signal. Con sequently , the hardware on ly need s to buf fer the standard N × M received symb ol matrix after CP r e m ov al, identical to conventional OFDM ra d ar processing, alon gside the N × M refer ence frame. In contra st, time- domain in terference cancellation and iterativ e window shifting meth o ds, su ch as th e pr o posed FR-SW and the SW algorithm in [9], re q uire buffering the r aw , time- domain baseb a nd signal. Specifically , these technique s necessitate buf fering ( M + 1)( N + N cp ) rec ei ved samples to ac commoda te the sliding win d ow sh if ts, along sid e M ( N + N cp ) samp le s of the ideal transmit signal to a pply precise delay , Dopp ler , and attenuation correc tions du ring the time-d omain removal process. For scenario s requiring large fr ame sizes, this extensive time-do main buffering can increase the on-c h ip memory con sumption compare d to frequen cy-domain ap p roaches. Furth e rmore, while JIC-CC and FR-SW utilize a CZT factor ( L ) fo r precise param e te r estimation, the resulting hig h-resolution ima ge is strictly transient. Th e system simply extracts th e scalar parameter s T ABLE III C O N S I D E R E D M E A S U R E M E N T P A R A M E T E R S Parame ters V alue Carrier frequency ( f c ) 3 . 68 GHz Frequenc y bandwidth ( B ) 500 MHz Number of s ubcarri ers ( N ) 1024 Cyclic prefix length ( N cp ) 256 OFDM symbols per frame ( M ) 1024 Number of targets ( H ) 6 Ranges (m) 72 , 150 , 162 , 222 , 228 , 240 V eloci ties (km/h) 0 , − 220 , 220 , 0 , 0 , 0 Attenua tion factor s (dB) 0 , 0 , 0 , 50 , 50 , 0 CZT factor ( L ) 100 Fig. 7: Measurement setup with ISAC testbe d and radar target simulator . (delay , Dop pler , and attenuation ) f or the detected targets and discards th e interpo lated grid. Th us, the memo ry overhead for the hig h precision pa r ameter estimatio n via CZT adds a negligible burden. V I . V E R I FI C A T I O N M E A S U R E M E N T S T o validate the ef fectiv eness of the proposed JIC-CC and FR-SW frameworks in a practical en vironmen t, proof -of-con cept mea su rements were co nducted using a hardware-in-the - loop setup. The measureme n t setup, illustrated in Fig. 7, comp rises a broad band OFDM-based ISA C testbed an d a Rohd e & Schwarz AREG800A radar target emu la to r . Furth er details regarding the ISA C testbed can b e fo und in [24] an d [2 5]. The AREG8 0 0A is utilized to emulate multiple rad ar targets with pre cise ran ge, velocity , and RCS character istics d irectly in the radio-fr equency ( RF) do main, p roviding a contr ollable and repea table environment for inter ference an a lysis. In this setup, a sing le baseba nd m odule is em p loyed to generate the transmit signal and pro cess the received ech o, ensur in g intrinsic synchro n ization between the tran smitter an d rec ei ver . The system oper ates at a carrier frequ ency of 3 . 68 GHz with 11 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. Fig. 8: Measurement results with (a) con venti onal radar processing, CZT-based (b) JIC-CC, and (c) F R-SW. a bandw id th of 500 MHz . The specific sy stem parameters configur ed for this measurement c a mpaign a r e detailed in T able III. A critical aspect of th is experime n tal d esign is the specific configu ration of the target scenario relative to the CP duration . As shown in T able II I, the cyclic prefix length is set to N cp = 256 samples. Given th e system band width, this correspo n ds to a maximum ISI-free ra n ge of ap p roximately R max,ISI = 76 . 8 m. T o create the severe interf erence condition s th at n ecessitate the pro posed cancellation alg orithms, the AREG8 00A was progr ammed to generate a m u lti-target environment where th e majority of targets fall outside ISI-fr e e range. Specifically , the first target is p ositioned at 72 m , which lies within the ISI-free zone. Howe ver, subsequen t targets are located at rang es such as 150 m , 16 2 m , and 240 m , all o f whic h sign ificantly exceed R max,ISI . T hese distant targets indu ce substantial ISI a n d ICI, which spill over in to the p rocessing window of the first target and elevate the overall interferen ce-noise floor in the r adar image. Furthermo re, to ev aluate the r obustness o f algorithms in high-d ynamic-ran ge scena r ios, th e em u lation inclu des targets with different attenuation factors (e.g., 0 dB versus 50 dB ) . This configuration cr eates a challenging masking scenario where strong distant targets (0 dB attenuation) obscure weaker targets (5 0 d B attenuation) , allowing fo r a rig orous b enchmark of the cancellation accur a cy and d y namic r ange improvement offered by the JI C-CC and FR-SW methods comp ared to conv entional pr ocessing. Furthermo re, to evaluate the robustness of algo rithms in high-d ynamic-ran ge scenar io s, the emu lation parameters were defined in terms of attenuatio n factor rath e r than RCS. This appro ach allows f or the direct contro l of the r eceiv ed signal power in dependen t of the emulated r ange, effectively decoup ling the SNR o f targets fro m the ran ge-depen dent free-space p ath loss. Consequen tly , inter f erence power can be controlled , a n d challen ging masking scenarios can be created easily , whe re distant targets can maintain high interf erence power . The p erforman ce of the propo sed interf erence cancellatio n schemes was validated using a mea surement setu p inv o lving six targets with ranges an d velocities indicated in T able I I I. T ABLE IV M E A S U R E D S I N R I M AG E F O R P R O P O S E D S C H E M E S Proce ssing M ethod Image SINR (dB) Con vention al Processing < 0 Proposed JIC-CC 18.6 Proposed F R-SW 25.5 Fig. 8 illustrates the Rang e-Doppler maps o btained from the conv entional pro cessing and the prop osed algo rithms, wh ile T able IV quantitatively summarizes the fin al SINR of the recovered weak targets. As expe cted, b oth the JIC-CC and the FR-SW de monstrate a significan t capab ility to suppress interferen ce, resultin g in a no ta b ly red uced interfe r ence-noise floor compare d to the conventional pro cessing baseline. A closer inspection of T able IV reveals th at the FR-SW appro a c h ac h ie ves a superio r interferen ce mitigation perfor mance, yielding a cleaner spectru m and a h igher final SINR image com pared to the JIC-CC method. Th is perfor mance gap is dr iven by three in herent characteristics of th e f r equency-do main o p eration utilized in JIC-CC. First, FDCC sums adjacent rece ived symbo ls to recover sign al energy , which statistically doubles the therm al n o ise power, inherently raising th e noise floo r by appro ximately 3 dB. Second, because the CP is discard ed prio r to the FFT, th e frequen cy-domain compe nsation cann ot recover the fraction of sign al energy that fell within the CP wind ow , leading to a slight signal p ower loss. Finally , f o r environmen ts with high-velocity targets, th e pure f r equency-do main cancellatio n does not fu lly r esolve range- Doppler cou pling effects, wh ich can leave minor residua l interfer ence af ter cancellatio n. Howe ver, it is crucial to em phasize that this SINR gap narrows significantly in many practical deploymen ts. For scenarios domina te d by static or low-velocity interferer s, the range- Doppler coupling mismatch be c o mes negligible. Furthermo re, in standard OFDM waveforms where the CP overhead is kept sma ll to max imize spectra l efficiency (i.e. , N cp ≪ N ), the unr ecoverable power loss in the CP window becomes small. Consequ ently , while FR-SW provid e s better dyn amic range and theoretical accuracy , the JIC-CC framework offers a high ly fa vorable trade-o ff. It provides 12 This work has been submitted to the IEEE for possible publicat ion. Copyrig ht may be transferre d without notice, after which this version may no longer be accessible. robust interferen c e suppr e ssion an d reliable we a k target detection with su b stantially lower com putational comp lexity , making it a hig hly attractive solution f o r real-tim e o r resource- c onstrained I SAC application s. V I I . C O N C L U S I O N This pape r addr essed the challenge of extending the sensing range b eyond ISI-free range u p in OFDM-based ISA C systems, particularly und er high- dynamic-r ange condition s an d realistic scen arios such as off-grid targets. T wo algorith ms were pr oposed: JIC-CC , which integrates FDCC with CZT-based estimation for efficient in terference cancellation , and FR-SW, wh ich shifts th e receive window to max imize signal en ergy and su p press residu al interfer ence. Simulation and measur ement results demo n strate that both methods outper f orm existing alg orithms in m ulti-target scenarios. While FR-SW o ffers the high est dy namic range, JIC-CC ac h ie ves compa rable perfo rmance with lower complexity , m aking it suitable fo r real-time ap plications. Future work will explor e extensions o f the alg orithms to multiple-inp ut multiple- output (MIMO) systems and extend ed target mod els. 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