CFAR-Based Interference Mitigation for FMCW Automotive Radar Systems
JJOURNAL OF L A TEX CLASS FILES, VOL. , NO. , 1
CFAR-Based Interference Mitigation for FMCWAutomotive Radar Systems
Jianping Wang,
Member, IEEE
Abstract —In this paper, constant false alarm rate (CFAR)detector-based approaches are proposed for interference mitiga-tion of Frequency modulated continuous wave (FMCW) radars.The proposed methods exploit the fact that after dechirping andlow-pass filtering operations the targets’ beat signals of FMCWradars are composed of exponential sinusoidal components whileinterferences exhibit short chirp waves within a sweep. Thespectra of interferences in the time-frequency ( t - f ) domainare detected by employing a 1-D CFAR detector along eachfrequency bin and then the detected map is dilated as a maskfor interference suppression. They are applicable to the scenariosin the presence of multiple interferences. Compared to theexisting methods, the proposed methods reduce the power lossof useful signals and are very computationally efficient. Theirinterference mitigation performances are demonstrated throughboth numerical simulations and experimental results. Index Terms —Beat signal, Constant false alarm rate (CFAR)detector, FMCW radar, Interference mitigation, time-frequencyspeatrum.
I. I
NTRODUCTION N OWADAYS frequency modulated continuous wave(FMCW) radars have become a key device for auto-motive assistant/autonomous driving due to its operationalcapability in all day time and all weather conditions as wellas its low cost. With the increase of vehicles equipped withradar sensors, the FMCW radar systems mounted on differentcars in busy area will inevitably suffer from strong interferinginfluence from the radar systems on the neighboring cars aswell as other radars on the same car when they operate at thesame time. The strong interferences would cause significantlyincreased noise floor, weak target mask and reduced proba-bility of target detection. Therefore, to overcome these risks,effectively mitigating interferences from other radars is criticalto high-performance automotive radars.Interference mitigation (IM) for automotive radar is a hottopic in recent years. In the literature, many approaches havebeen proposed and developed to suppress the interferencesamong different automotive radars, which can be classifiedinto three categories: radar system coordination, radar systemdesign and waveform design, and signal processing. For theradar system coordination approaches, a coordination scheme,which is either centralized [1] or distributed [2], [3], amongdifferent operational radars are devised to avoid conflictsby adjusting the operating parameters (i.e.,transmitting time,spectrum, etc.) of each radar within the interfering area.
The author is with the Faculty of Electrical Engineering, Mathematics andComputer Science (EEMCS), Delft University of Technology, Delft, 2628CD,the Netherlands e-mail: [email protected].
Although these coordination schemes originated from commu-nication network could effectively avoid certain interferences,they usually require to introduce an extra coordination unit tothe the existing FMCW radar systems or need communicationwith a coordination center for a local distributed radar network.On the other hand, some new radar system architecturesand waveforms are proposed to benefit the interference miti-gation [4]–[10]. The frequency-hopping random chirp (FHRC)FMCW technique [4], [5] and FMCW radar with randomrepetition interval [6] resets the parameters of the chirp signals(the bandwidth, sweep duration, center frequency, repetitioninterval) every cycle to result in noise-like frequency responsesof mutual interferences after the received signals are down-converted and demodulated. Both techniques would mitigatepartial interferences and avoid the appearance of ghost targetscaused by mutual interferences. However, the randomizedrepetition intervals would cause the Fast Fourier transform,which is conventionally used, inapplicable for the fast Dopplerprocessing. On the other hand, pseudo-random noise signals[8] and chaotic sequences [7] are proposed to mitigate mutualinterferences for automotive radars. For these radar systems,the received signals are processed by the correlation operationand a high sampling frequency is generally required for theAnalog-to-Digital Converter (ADC), which would increase thecost of the radar systems. To exploit the advantages of bothnoise-like signals and the FMCW radar system, phase modu-lated (PM) FMCW radar systems modulate the FMCW wave-forms with orthogonal or random sequences as transmittedsignals [9], [10]. In reception, the received PM-FMCW signalscan be down-converted as the traditional FMCW radars andthen decoded by correlation with the stored sequences usedfor transmission modulation. The scattered signals resultingfrom the transmitted signals generally result in high correlationpeaks while the uncorrelated interferences would spread outand build up the noise floor after decoding. Consequently,the raised noise floor could overwhelm the weak targets andreduce the probability of detection. In addition, PM-FMCWradar requires to design a new radar architecture, which cannotbe easily implemented with the existing FMCW radar chips.Moreover, for the FMCW radars, a number of signalprocessing approaches to interference mitigation have beenpresented, which includes both traditional signal processingmethods and deep-learning based methods. The traditionalsignal processing methods usually address the interferencemitigation by filtering or separating the interferences fromthe received signals in various domains (i.e., space, time,frequency, time-frequency, etc). For array-based radar system,interference mitigation can be achieved by constructing nulls a r X i v : . [ ee ss . SP ] J a n OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 2 in the directions of arrival (DOA) of the interferences throughbeamforming [11]–[13]. However, these approaches wouldsuppress targets’ signals scattered from the same DOAs ofthe interferences. In [14], the interference is detected basedon a threshold and then suppressed by windowing in time. In[15], an iterative modified method based on empirical modedecomposition is proposed to decompose the low-pass filteroutput of an FMCW radar as a series of empirical modes inthe time domain while in [16] the wavelet denoising methodis used to separate interferences from the useful signals.Both approaches implicitly assume interferences are sparsein time in the received signals and their performances woulddegrade with the increase of the proportion of interference-contaminated samples in the acquired signal. By contrast, theAdaptive Noise Canceller (ANC) [17] is utilized to suppressinterferences in the frequency domain. Although it is compu-tationally very efficient, its performance heavily depends onif a proper correlated reference input of the adaptive filter canbe found. Meanwhile, in [18] the interference-contaminatedsignal samples of FMCW radars are first cut out in the short-time-Fourier-transform (STFT) domain and then a Burg-basedmethods is developed to reconstruct the signal in the cut-out region based on an auto-regressive (AR) model alongeach frequency bin. However, with the increase of the cut-outregion in the signal, the accuracy of the recovered signals withthis approach drops rapidly. Moreover, recently some deep-learning approaches are used for interference mitigation ofFMCW radars [19], [20]. These approaches generally requirea large volume of dataset acquired in various situations fortraining.In this paper, we proposed two constant false alarm rate de-tector (CFAR) [21] based approaches to mitigate interferencesfor FMCW radars. In both approaches, the acquired beat signalis transformed into the time-frequency ( t - f ) domain by usingthe STFT. Then a one-dimensional (1-D) CFAR detector isutilized to detect interferences and the detection map is dilatedto generate a mask for interference suppression. Specifically,one approach is to zero out the interference-contaminatedsamples and the other one is to keep their phases unchangedbut correct their amplitudes by the mean of the amplitudes ofthe interference-free samples in the corresponding frequencybin based on the dilated detection map, which are termed asthe CFAR-Zeroing (CFAR-Z) and CFAR-Amplitude Correc-tion (CFAR-AC) approaches in the paper. Compared to theexisting approaches, the proposed approaches are capable tomitigate multiple interferences and minimize the power lossof useful signals. Their interference mitigation performancehave been validated through both numerical simulations andexperimental results. Moreover, they is very efficient andcan be implemented for real-time interference mitigation ofFMCW automotive radars.The rest of the paper is organized as follows. Section IIbriefly describes the signal model of the FMCW radar. Then,the CFAR-based interference mitigation approaches are pre-sented in section III.To demonstrate the interference mitigationperformance of the proposed approach, numerical simulationsand experimental results are shown in sections IV and V.Finally, some conclusions are drawn in section VI. II. S IGNAL MODEL AND
CFAR-
BASED INTERFERENCEMITIGATION METHOD
Assume that the transmitted signal p ( t ) by an FMCW radaris given by p ( t ) = exp (cid:20) j π (cid:18) f t + K t (cid:19)(cid:21) (1)where f is the starting frequency of the FMCW sweep,and K is the sweep slope. Considering the single bouncescattering, then the signals scattered back from point-liketargets are the superposition of the time-delayed transmittedsignals. Meanwhile, assume that the scattered signals fromtargets are contaminated by an interference s int ( t ) during itsreception. After dechirping and low-pass filtering operating onreceiver, the acquired beat signals is represented as s ( t ) = s b ( t ) + ˜ s int ( t ) + n ( t )= M (cid:88) i =1 a i exp ( − j πf b,i t ) + F lp ( s int ( t ) · p ∗ ( t )) + n ( t ) (2)where F lp is the low-pass filtering operator whose cut-offfrequency is determined by the desired maximum detectablerange of targets. s b ( t ) = (cid:80) Mi =1 a i exp ( − j πf b,i t ) is the beatsignals of M scatterers, which is composed of M complexexponentials with the beat frequency f b,i and scattering coef-ficient a i for the i th scatterer. Note here a residual video phaseterm is subsumed by a i for conciseness. ˜ s int ( t ) = F lp ( s int ( t ) · p ∗ ( t )) is the remaining interference after the low-pass filtering,and n ( t ) denotes the noise and measurement errors. Accordingto the analysis in [22], the interference ˜ s int ( t ) in (2) generallyexhibits as some short chirp-like pulses in the time domain.Although FMCW interferences with the same sweep slopeand frequencies falling into the receiving bandwidth wouldresult in ghost targets, its probability is extremely small [23].Therefore, After taking the STFT of s ( t ) , the time-frequency( t - f ) domain counterparts of the beat signals of scatterersshow as straight lines along the corresponding frequency binswhile interferences display as oblique lines, as illustrated inFig. 1(b). These different distributions of useful beat signalsand interferences motive us to proposed the CFAR-basedinterference mitigation approach in the following.III. CFAR- BASED INTERFERENCE MITIGATION APPROACH
Accurately detecting interferences is crucial for effectiveinterference mitigation. Based on the above analysis of dif-ferent distribution features of useful signals and interferencesin the t - f domain, i.e., straight lines for useful signals alongthe frequency bin and oblique lines for interferences, detect-ing interferences can be converted to distinguish the signalsdistributed along oblique lines relative to the frequency axis.Therefore, we propose to utilize a 1-D CFAR detector alongeach frequency bin in the t - f domain to detect interferencesand then suppress them.The complete CFAR-based interference mitigation methodis shown in Algorithm 1. In principle, it contains three majorsteps in implementation, which are described in detail asfollows. OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 3
Algorithm 1:
CFAR-based interference mitigationmethod.
Data:
Complex signal s in a sweep Result:
Complex signal s c after interference mitigation begin S tf = STFT ( s ) ; [ N r , N c ] = size ( S tf ) ; P tf = S tf (cid:12) ¯S tf ; for k = 1 to N r do D ( k, :) = CFARDetector [ P tf ( k, :)] ; end D dl = maskDilate ( D ) ; S tf ( D dl ) = 0 ; s c = ISTFT ( S tf ) ; end A. Time-Frequency Analysis with the STFT
Applying the STFT to the acquired signal in (2), its t - f spectrum is obtained as S ( τ, f ) = (cid:90) ∞−∞ s ( t ) w ( t − τ ) e − j πft dt (3)where w ( τ ) is the window function, for instance, a Gaussianwindow or Hann window. For N discrete signal samples s [ k ] = s ( k ∆ t ) , k = 0 , , · · · , N − , the discrete t - f spectrumsamples over a regular grid are generally computed by S tf [ m, n ] = S ( m ∆ τ, n ∆ f )= N − (cid:88) k =0 s ( k ∆ t ) w ( k ∆ t − m ∆ τ ) e − j πnk ∆ f ∆ t ∆ t (4)where ∆ t is the time sampling interval, ∆ τ is the slidingstep of the window and ∆ f is the step of frequency samples.One can see that for a fixed time delay m ∆ τ of the window,(4) can be efficiently implemented by using the fast Fouriertransform (FFT). For the convenience of computation, gener-ally ∆ τ = l · ∆ t and l ≥ is an integer. Sliding the windowover the signal duration, the t - f spectrum is obtained as atwo-dimensional matrix with dimensions of N t × N f alongthe time and frequency axes, respectively, where N t is thenumber of sliding steps of the time window and N f is thenumber of FFT points.Then, the spectrogram is obtained as the amplitude squaredof the t - f spectrum, given by P tf [ m, n ] = | S tf [ m, n ] | = S tf [ m, n ] · ¯ S tf [ m, n ] (5)where ¯ S tf is the complex conjugate of S tf . B. CFAR Detection and Detection Mask Dilation
In this step, the interference detection is performed. Aftergetting the power spectrogram, a Cell Averaging CFAR (CA-CFAR) detector [21] is utilized to the spectrum density alongeach frequency bin, resulting in a detection matrix D with thesame size as the spectrogram. The detection matrix D has theentries of ones and zeros and the entries of one indicate thepositions of the detected interferences. The numbers of guardcells and training cells, the probability of false alarm and the threshold factor of the CFAR detector can be set based on thedifferent scenarios.After acquiring the detection map with the CFAR detector,in principle it could be employed as a mask to suppressinterferences. However, due to the possible existence of severalinterference-contaminated spectral samples in a frequency bin,a relatively large threshold value would be calculated; thus, itcauses the missed detection of some edge cells of the inter-ferences. To alleviate such problem, a dilation procedure [24],which is widely used for image processing, is introduced toslightly swell the detected mask of interferences. Consideringthe detection map D as a binary image, the one-valued pixelsform a pattern of the detected interferences, denoted as I .To dilate the pattern I , a structuring element B is used andits origin is translated throughout the entire domain of theinput image D . The dilation of the pattern I by the structuringelement B is defined as the set operation I dl = I ⊕ B = (cid:110) z | ( ˆ B ) z ∩ I (cid:54) = ∅ (cid:111) (6)where ˆ B is the reflection of the structuring element B aboutits origin and z indicates the location that the origin of thestructuring element is translated to. So the dilated pattern I dl is the set of pixel locations z , where the reflected structuringelement overlaps with at least one element in I when translatedto z . Accordingly, at these locations of z , the output image D dl is 1, which contains the dilated pattern I dl . Since the detectedpattern of interferences is some oblique thick lines withpossible round ends, the disk-shaped or octagonal structuringelement can be used. C. Interference Mitigation and Signal Recovery
The dilated detection map of interferences can be used asa mask for interference mitigation. With the aid of the dilateddetection map, a simplest interference mitigation approach isto zero out the interference-contaminated signal samples inthe t - f spectrum S tf , denoted as CFAR-Z for conciseness inthe following. However, the zeroing operation suppresses notonly interferences but also the useful signals, thus causing thepower loss of the targets’ signals.To circumvent the signal power loss of the CFAR-Z method,we suggest utilizing the amplitude correction method [25]to the interference-contaminated samples based on the CFARdetection map. The resultant approach is termed as CFAR-AC.The basic idea of this approach is to replace the amplitudesof the interference-contaminated samples with the averageamplitude of the interference-free spectrum samples in the cor-responding frequency bin but keep their phases invariant. Thenew value for a interference-contaminated sample S tf [ m i , n i ] is given by ˜ S tf [ m i , n i ] = A n i e j arg( S tf [ m i ,n i ]) (7)where ˜ S tf [ m i , n i ] is the new sample value at the position [ m i , n i ] obtained after interference mitigation, and arg( x ) takes the phase of a complex number x . A n i is the averageamplitude of the interference-free samples in the n i th fre-quency bin. In this way, the strong power of the interferencesis significantly suppressed. OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 4
TABLE IP
ARAMETERS FOR NUMERICAL SIMULATIONS
Parameter Value
Center frequency
77 GHz
Bandwidth
600 MHz
Sweep duration of FMCW signal µ s Maximum detection range
250 m
Sampling frequency
40 MHz
Distances of three point targets , , and
150 m
After that, an inverse STFT (ISTFT) is applied to theinterference-mitigated t - f spectrum to recover the targets’ beatsignals in the time domain.In addition, we should mention that although the phasesof the new sample values still surfer from the disturbance ofinterferences, their effects are negligible after taking furthercoherent range compression and/or Doppler processing. More-over, for the array signals contaminated simultaneously by thesame interferences, CFAR-AC approach has no impact on thebeamforming performance as the phases of signals are keptunchanged. IV. N UMERICAL SIMULATIONS
Numerical simulations are presented to demonstrate theinterference mitigation performance of the proposed approach.Meanwhile, the results are compared with two the state-of-the-art efficient approaches, i.e., Wavelet Denoising (WD) ap-proach [16] and the Adaptive Noise Canceller (ANC) approach[17].
A. Performance Metrics
To facilitate the comparison among different IM approachesand quantitatively evaluate the accuracy of the beat signalsrecovered by each approach, we use as the metrics the Signalto Interference plus Noise Ratio (SINR) and correlation coef-ficient ( ρ ) [22] of the beat signal obtained after IM processingrelative to the clean reference signal. The SINR is definedin the same way as the relative signal to noise ratio (RSNR)in [22], which is inversely proportional to the error vectormagnitude in [26]. For conciseness, the definition formulas ofthese metrics are omitted here. B. Point Target Simulation
Some typical automotive radar parameters were used fornumerical simulations, as listed in Table I. Three point targetswere placed in the scene of illumination at the distance of
30 m ,
80 m and
150 m , respectively. The amplitudes of thescattered signals from the three targets are set as , . , and . to emulate variations of scattering coefficients of differenttargets. The victim radar transmitted up-sweep FMCW signalsand suffered from some strong FMCW interferences, andcomplex while Gaussian noise was also added to account forthermal noise and measurement errors of the radar system.The acquired signal at the output of the low-pass filter isshown in Fig. 1(a). Its signal to noise ratio (SNR) and signal to interference plus noise ratio (SINR) are and − .
71 dB .Due to the strong interferences, the weak target at the distanceof
80 m is completely overwhelmed by the increased noisefloor of the range profile formed by taking the FFT of theacquired signal (see Fig. 1(k)).Using the proposed approaches to mitigate the interferences,the acquired time-domain signal is first transformed into the t - f domain by using the STFT. For discrete implementation,the length of the window of STFT is 256 sampling points andthe overlap between adjacent window positions is 252 points.The obtained t - f spectrogram is shown in Fig. 1(b), where thestrong spectrum along the oblique lines are the interferenceswhile the three weak horizontal lines represent the useful beatsignals.Then, utilizing the CA-CFAR detector along each frequencybin, the non-horizontal patterns of interferences are detected(see Fig. 1(c)). As the threshold of CA-CFAR detector is com-puted based on the average of training cells and varies for eachCell Under Test (CUT), it causes the missed detection of thecells at the edges of the oblique lines of the interferences (i.e.,the detected lines are thinner than that of the interferences),which leads to only partial mitigation of interferences in thefollowing operations. To overcome this problem, the detectionmap of the CFAR detector was dilated by using the octagonalstructuring element, as shown in Fig. 1(d). It is clear that thedilated detection map is much thicker compared to that inFig. 1(c).Next, the dilated detection map was employed as a maskto zero out the interference-contaminated samples by theCFAR-Z approach or to correct their amplitudes by using theCFAR-AC method. The resultant t - f spectra after interferencemitigation are shown in Fig. 1(e) and (f). Finally, applyingthe ISTFT to the obtained t - f spectra, the correspondingbeat signals are recovered, shown in Fig. 1(g) and (h).For comparison, the IM of the signal was also performedusing the ANC [17] and the WD methods [16]. For theANC method, the length of the adaptive filter was set 80.Meanwhile, for the WD approach, the level of the waveletdecomposition was four which was optimally selected andthe Stein’s unbiased risk estimate was used to determine thethreshold value. The beat signals recovered by the ANC andthe WD methods are presented in Fig. 1(i) and (j). FromFig. 1(g), one can see that the CFAR-Z approach suppressesnot only the interferences but also the targets’ beat signalsat the time instances related to the intersection points of the t - f spectra of the interferences and useful signals. Similarly,the wavelet denoising method causes even more loss of usefulsignals, especially in the period between µ s to µ s inFig. 1(j). By contrast, the CFAR-AC recovers the beat signalsof targets with negligible power loss (Fig. 1(h)). From Fig. 1(i),the ANC method only suppresses part of the interferencesbetween µ s and µ s and some chirp-like pulses of theinterferences are still observed. This could be caused by thefact that the assumption of the complex conjugate symmetryof the interference spectrum around zeros used by the ANCmethod is not valid to the synthetic data. To quantitativelycompare the accuracy of the recovered beat signals relativeto the clean reference, the SINRs of the signals obtained OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 5
20 40 60 80-20-1001020 A m p li t ude Real part (a) (b)
Map of interference detection
20 40 60 80-15-10-505101520 F r equen cy [ M H z ] (c)(d) (e) (f)
20 40 60 80-2-1012 A m p li t ude Beat signal recovered with CFAR-Z (g)
20 40 60 80-3-2-10123 A m p li t ude Beat signal recovered with CFAR-AC (h) (i)(j)
Range [km] -25-20-15-10-50 N o r m a li z ed a m p li t ude [ d B ] Range profile (k)
Range [km] -50-40-30-20-10010 N o r m a li z ed a m p li t ude [ d B ] RP after IM
ANCWDCFAR-ZCFAR-AC
29 30 31-20-100 (l)Fig. 1. Illustration of the CFAR-based interference mitigation and comparisons with the ANC and WD methods. (a) and (b) show the real part of the rawsignal and its t - f spectrum after the STFT. (c) displays the map of the detected interferences and (d) is its dilated version. (e) and (f) are the t - f spectrumafter interference mitigation with CFAR-Z and CFAR-AC approaches. (g) and (h) are the recovered beat signals after taking ISTFT of the spectra in (e) and(f). (i) and (j) show the recovered beat signal after interference mitigation by the ANC and WD methods. (k) and (l) present the range profiles of targetsconstructed by using the acquired raw signal and the recovered signals after IM, respectively. with the ANC, WD, CFAR-Z and CFAR-AC methods are − .
96 dB , .
27 dB , .
03 dB and .
47 dB , respectively. Andthe corresponding correlation coefficients are . e − j . , . e j . , . e − j . , and . e . .Taking the FFT of the recovered beat signals, the targets’range profiles in Fig. 1(l) are obtained. All the approaches OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 6 -25 -20 -15 -10 -5 0 5 10
SNR of Input Signal[dB] -30-20-10010 S I NR A ft e r I M [ d B ] ANCWDCFAR-ZCFAR-AC (a) -25 -20 -15 -10 -5 0 5 10
SNR of Input Signal[dB]
ANCWDCFAR-ZCFAR-AC (b) -25 -20 -15 -10 -5 0 5 10
SNR of Input Signal[dB] -3-2-10123
ANCWDCFAR-ZCFAR-AC (c)Fig. 2. Quantitative comparison of the interference mitigation performance of the ANC, WD, CFAR-Z and CFAR-AC methods at the different SNRs of theinput signals. (a), (b) and (c) show the variations of SINRs, the magnitudes and phase angles of correlation coefficients of the recovered beat signals afterinterference mitigation, respectively. except the ANC method significantly suppress the interfer-ences and reduce the noise floor of the focused range profilecompared to that in Fig. 1(k). The weak target at the distanceof
80 m is clearly visible. However, compared to that of theWD method, the range profiles obtained with the CFAR-Zand CFAR-AC have lower noise floor and thus achieve betterinterference mitigation performance. Moreover, in contrastto CFAR-AC approach, both the WD method and CFAR-Zapproach suppress some targets’ signals after mitigating theinterferences, which not only decreases the signal power butalso causes increased sidelobes in the focused range profile(see the inset in Fig. 1(l)). But as mentioned above, the rangeprofile obtained with the CFAR-Z approach still has smallerpower loss and lower sidelobes than that acquired with the WDmethod. Therefore, in terms of noise floor, power loss andsidelobe levels of the resultant range profile, the CFAR-ACachieves the best interference mitigation performance amongthe three approaches.
C. Effect of SNR on Interference Mitigation
The noise included in the acquired signal impacts thedetection of interferences, thus affecting the interference mit-igation. In this section, we used the same targets’ signalsand the interferences as in section IV-B but changed theadded noise levels to investigate the effect of SNR on theIM performance of the two proposed approaches and theircompeting counterparts, i.e., WD and ANC methods.The noise levels with the SNR ranging from −
25 dB to
10 dB were considered. At each noise level, 500 timesMonte Carlo runs were implemented and the statistics of theperformance metrics achieved by the four IM methods arepresented as the box plot in Fig. 2. The bottom and top ofeach box indicate the th and th percentiles of the sample,respectively. Meanwhile, the lines extending above and belowof each box show the range between the maximum and min-imum values of the sample. From Fig. 2(a), one can see thatthe SINR of the recovered signals after IM increases with theincrease of the SNR of input signal. Generally, the proposedCFAR-Z and CFAR-AC achieve better SINR than the WD andANC approaches except at SNR = −
25 dB in which case the interferences are almost overwhelmed by the noise. A largeportion of the interferences were not detected by the CFAR-Z and CFAR-AC approaches; as a results, the interferencesare not fully suppressed. Meanwhile, the WD method alsofail to extra the interferences and leads to degraded SINRafter IM. By contrast, the ANC method eliminates half ofthe frequency spectrum that does not contain targets’ signalsand uses the complex conjugate symmetry of the interferencespectra to suppress them; thus, it results in better SINR afterIM. In addition, compared to CFAR-AC, the CFAR-Z obtainsslightly higher SINRs when SNR < but lower oneswhen SNR > . This is because that when SNR < the values of targets’ signals at the interference-contaminatedregion are more closer to zero than to the amplitude-correctedvalues in which noise is the dominant component. Therefore,in terms of the SINR obtained after IM, the CFAR-Z approachis a better option than the CFAR-AC when the SNR of theinput signal is lower than .Moreover, Fig. 2(b) shows that the magnitudes of correlationcoefficients of the signals obtained with the CFAR-AC areconstantly larger than that acquired by the other three methods.Moreover, with the rise of the SNRs of input signals, the phaseangles of the correlation coefficients of the recovered signalsby the WD, CFAR-Z and CFAR-AC are all increasinglyconcentrated around zero. So in terms of both the SINR andcorrelation coefficient of the recovered signals after IM, theproposed CFAR-Z and CFAR-AC outperform the other twoapproaches; however, in practice the better choice betweenthem should be determined based on the SNR of the acquiredsignal. D. Computational Time
The computational complexities of the proposed CFAR-Zand CFAR-AC are dominated by the CFAR detection alongeach frequency bin. In section. IV-B, the synthetic beat signalin one sweep contains 3933 samples and was processed withthe ANC, WD, CFAR-Z and CFAR-AC approaches by usingMATLAB 2019b on a computer with Intel i5-3470 CPU and . The computational time of the four IM approaches aresummarized in Table II. One can see that the WD method is
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TABLE IIC
OMPUTATIONAL TIME OF THE
ANC, WD, CFAR-Z
AND
CFAR-AC
APPROACHES FOR INTERFERENCE MITIGATION
ANC WD CFAR-Z CFAR-AC N os N os N os N os Time [ms] 73 9.64 214 109.3 228.5 116.4 N os = 252 , N os = 248 are the number of overlapped samplesof the sliding window at two adjacent positions for the STFT. AggressorradarVictimradar TCR 1 TCR 2TCR : Trihedral cornerreflector6.95m 9.75m . m (a) AWR1642Radar AWR1443Radar TCR 1 TCR 2stationaryvan (b)Fig. 3. Experimental setup for interference mitigation with two TI automotiveradar boards. (a) shows geometrical configuration and (b) the experimentalsetup. the most efficient one compared to the other three approaches.Meanwhile, when the number of overlapped samples of theSTFT window decreases from 252 to 248 (i.e., the sliding stepof the STFT window increases from 4 to 8), the computationaltime of both CFAR-Z and CFAR-AC decreases by about as the number of samples in each frequency bin ishalved for the CFAR detection. So by properly adjusting theprocessing parameter, the computational time of the CFAR-Z and CFAR-AC can be significantly reduced. Moreover, asthe CFAR detection is carried out independently along eachfrequency bin in the t - f domain, these detection operationsalong different frequency bins can be implemented by usingparallel computing, thus further reducing their computationaltime and improving the real-time processing capability.V. E XPERIMENTAL RESULTS
In this section, the experimental results are presented todemonstrate the performance of the proposed approach.One Texas Instruments (TI) AWR1642BOOST radar boardis used as the victim radar while another TI AWR1443BOOSTradar board is utilized as the aggressor radar. Two TrihedralCorner Reflectors (TCRs) are used as targets. The geometricalconfiguration and picture of experimental setup are shown inFig. 3(a) and (b). The system parameters used for the victim
TABLE IIIP
ARAMETERS OF EXPERIMENTAL RADAR SYSTEMS
Parameter Victim radar Aggressor radar Unit
Center frequency 77.69 77.69
GHz
Bandwidth 1380.18 1380
MHz
K 15.015 35
MHz /µ s T 91.92 39.4337 µs Sampling frequency 6.25 5
MHz
No. of Samples 512 256 – and aggressor radars are listed in Table III. The AWR1642radar board is connected with a TI DCA1000EVM datacapture card to collect raw ADC data which is then sent to ahost laptop for data storage.Fig. 4(a) shows the acquired signal in one of the FMCWsweeps. Two large pulses are observed at the the beginning andend of the acquired data, which are caused by the strong in-terferences from the aggressor radar. After range compression,the interference-contaminated signal leads to a range profilewith significantly increased noise floor (see Fig. 4(b)). Forcomparison, the range profile of targets obtained with a cleanreference signal is also presented, where the first three peaksindicate the locations of the aggressor radar and two TCRsat the distance of .
33 m , .
95 m and .
75 m , respectively.One can observe that in the range profile obtained with theinterference-contaminated signal the two TCRs are almostoverwhelmed by the increased noise floor. This made theTCR at the further distance not detectable when a CA-CFARdetector was employed for target detection (see Fig. 5(a)). TheCA-CFAR detector was set with one guard cell and 10 trainingcells on each side of the CUT and the probability of false alarmof × − .To overcome the missed detection of the target caused by thestrong interferences, the proposed approaches are applied tothe acquired signal for interference mitigation. Firstly, the t - f spectrum of the acquired signal is computed through the STFTimplemented by using a sliding Hamming window of length128 with sliding step of one for signal segmentation and thentaking the FFT of each signal segments. The obtained spectrumis shown in Fig. 4(c). One can see that the interferences exhibitas the two thick vertical lines in the t - f domain. Then, a1-D CFAR detector is applied along each frequency bin todetect the interference-contaminated signal spectrum, and thedetection map is presented in Fig. 4(d). Compared to Fig. 4(c),one can see that in Fig. 4(d) some interference-contaminatedspectral samples are not detected, especially the ones at theedges of the two thick spectral lines. To tackle the misseddetection of the interferences, the detection map is dilated withan octagonal structuring element and the result is displayedin Fig. 4(e). Note that three small patches appear between µ s and µ s , which reveals that some isolated spectralsamples are falsely detected as the interference in Fig. 4(d).Next, using the dilated detection map as a mask, the zeroingand amplitude correction can be conducted to substantiallymitigate the inferences, and the results of CFAR-Z and CFAR-AC approaches are given in Fig. 4(f) and (g). Finally, the t - f spectrum obtained after IM is inverted through the ISTFT to OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 8 A m p li t ude Beat signal realimag (a)
Range [m] -30-25-20-15-10-50 N o r m a li z ed a m p li t ude [ d B ] RP interferedref sig (b) (c) Map of interference detection
20 40 60 80 100-3-2-10123 F r equen cy [ M H z ] (d) (e) (f)(g) Range [m] -30-25-20-15-10-50 N o r m a li z ed a m p li t ude [ d B ] RP after IM ref sigWDANC CFAR-ZCFAR-AC (h)
Range [m] -30-25-20-15-10-50 N o r m a li z ed a m p li t ude [ d B ] Zoomed-in RP (i)Fig. 4. Interference mitigation for the experimental radar measured with TI automotive radar. (a) shows the acquired beat signal contaminated by theinterferences and (c) its time-frequency spectrum. (b) presents the range profiles of targets related to the beat signal in (a) and an interference-free reference.(d) shows the CFAR detection map of the interferences and (e) its dilation that will be used for interference mitigation. (f) and (g) give the results ofinterference mitigation with CFAR-Z and CFAR-AC approaches, respectively. (h) displays the range profiles obtained after interference mitigation and (i)shows the zoomed-in view of the range profiles at the distance of . to
11 m . reconstruct the time-domain beat signal.To demonstrate the IM performance of the proposed ap-proaches, the targets’ range profiles resulting from their recov-ered beat signals are presented in Fig. 4(h). For comparison,the range profiles obtained with the reference signal andthe beat signals recovered by the two IM methods, i.e. WDand ANC, are also presented, which are normalized by themaximum value of all the range profiles. From Fig. 4(h),the overall range profiles obtained with the WD, CFAR-Zand CFAR-AC have very good agreement with the referenceone except that the one acquired by the ANC method hashigher sidelobes. However, based on the zoomed-in view ofthe range profiles around the two TRCs (Fig. 4(i)), one cansee that among the four IM methods, the CFAR-AC and ANC methods get the maximum peak values at the distances of twoTCRs, whose values are also closest to the reference ones.However, the WD method results in lower peak amplitudesthan the reference one and the other three methods as thewavelet-based denoising method not only eliminates the stronginterferences but also suppresses part of the useful signalpower. Meanwhile, as expected, the CFAR-Z leads to smallerpeak values of the range profile at the positions of two TCRscompared to the CFAR-AC. So in terms of power conservationof useful signals, the CFAR-AC and ANC methods achievethe best performance in this case. However, the ANC methodassumes strict complex conjugate symmetry of the interfer-ence spectrum in the positive and negative frequency bands.Otherwise, its performance degrades significantly as shown OURNAL OF L A TEX CLASS FILES, VOL. , NO. , 9
Range [m] -30-20-10010 N o r m a li z ed a m p li t ude [ d B ] RP with InterfthresholdCFAR output (a)
Range [m] -30-20-10010 N o r m a li z ed a m p li t ude [ d B ] RP after IM with WD
RP after IMthresholdCFAR output (b)
Range [m] -30-20-10010 N o r m a li z ed a m p li t ude [ d B ] RP after IM with ANC
RP after IMthresholdCFAR output (c)
Range [m] -30-20-10010 N o r m a li z ed a m p li t ude [ d B ] RP after IM with CFAR-Z
RP after IMthresholdCFAR output (d)
Range [m] -30-20-10010 N o r m a li z ed a m p li t ude [ d B ] RP after IM with CFAR-AC
RP after IMthresholdCFAR output (e)Fig. 5. The output results of the CFAR detection of the input range profiles before and after interference mitigation. (a) shows the detected results of therange profiles obtained with interference-contaminated signal. (b), (c), (d) and (e) are the corresponding detection results after taking interference mitigationwith WD, ANC, CFAR-Z and CFAR-AC approaches, respectively. in the simulation. In addition, we want to mention that toavoid the weighting effect of the sliding window of the STFTon the reconstructed signal samples in the beginning and theend, 128 zeros were padded at both sides of the acquiredsignal before computing the STFT and then the extra zeroswere removed after inverting the t - f spectrum through theISTFT. Due to this operation before the STFT, it leads to thevisually “increased” time duration of the t - f domain plots(i.e., Fig. 4(c)-(g)) compared to that of the acquired signal(Fig. 4(a)).To further evaluate the quality of the beat signals recoveredby the four IM approaches, the target detection performanceof the constructed range profiles are tested by employing thesame CFAR detector used for target detection in Fig. 5(a).Fig. 5(b)-(e) show the output results of the CFAR detector. Onecan see that the three peaks related to the aggressor radar andtwo TCRs are all detected after IM with all the four methodswhile the TCR at the further distance was missed based on therange profile before IM (Fig. 5(a)). So the four IM methodsimprove the targets’ probability of detection. Moreover, basedon the range profiles obtained with the CFAR-Z and CFAR-AC, a fourth target, which is a stationary car at a distance of . , is also detected (Fig. 5(d) and (e)) but missed whenthe RPs acquired with the WD and ANC methods were used(Fig. 5(b) and (c)). Therefore, the beat signals obtained withthe CFAR-Z and CFAR-AC IM approaches provide highertarget’s probability of detection than those recovered with theWD and ANC methods.VI. C ONCLUSION
In the paper, we proposed two CFAR-based approaches,i.e., CFAR-Z and CFAR-AC, to mitigate inference for FMCW radars system, which exploit the CFAR detector to detect thelarge chirp-pulse like interferences in the time-frequency do-main and then apply the zeroing and amplitude correction formitigate them, respectively. Compared to the prior art methods,both approaches achieve better interference mitigation perfor-mance in terms of both SINR and correlation coefficient ofthe recovered signal after IM. Moreover, both CFAR-Z andCFAR-AC approaches are computationally efficient and couldbe implemented for real-time processing for automotive radars.A
CKNOWLEDGMENT
The authors would like to thank Ms Y. Lu and Mr I. R.Montero for their help during the experimental measurement.R
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