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Interference Compression and Mitigation for Automotive FMCW Radar Systems

Millimeter-wave (mm-wave) frequency-modu- lated continuous wave (FMCW) radars are increasingly being deployed for scenario perception in various applications. It is expected that the mutual interference between such radars will soon become a significant problem. Therefore, to maintain the reliability of the radar measurements, there must be procedures in place to mitigate this interference. This article proposes a novel interference mitigation technique that utilizes the pulse compression principle for interference compression and mitigation. The interference in the received time-domain signal is compressed using an estimated matched filter. Afterward, the compressed interference is discarded, and the signal is repaired in the pulse-compressed domain using an autoregressive (AR) model. Since the interference spans fewer samples after compression, the signal can be restored more accurately in the compressed domain. Real outdoor measurements show that the interference is effectively suppressed down to the noise floor using the proposed scheme. A signal to interference and noise ratio (SINR) gain of approximately 14 dB was achieved in the experimental data, supporting this study. Moreover, the results indicate that this method is also applicable to situations where multiple interference sources are present.


I. INTRODUCTION
F REQUENCY-modulated continuous wave (FMCW) radars, operating at millimeter-wave (mm-wave), are capable of providing highly accurate position and velocity estimates under most weather conditions [1]. In recent years, thanks to the technological advancements in mmwave technology, these sensors have become low-cost, small-sized, and highly capable. Hence, radar has become an attractive sensor in numerous applications, for example, indoor and outdoor surveillance, industrial, and, most notably, automotive applications [2], [3]. Many advanced driver assistance systems (ADASs) and autonomous driving functions in modern vehicles depend on the automotive radar for 360 • situational awareness. However, the rapidly increasing deployment of automotive radars in modern cars and the shared frequency spectrum are giving rise to concerns regarding mutual interference, which affects the sensor reliability and, consequently, the autonomous vehicle safety [4]. Mutual interference can deteriorate the performance of the victim radar by increasing the noise floor of the receiver, which results in reduced sensitivity and degraded detection performance [5]. This directly impacts the functionality of ADAS and autonomous functions in vehicles, which may lead to hazardous situations considering the safety-related systems. The mutual interference problem can become more challenging if interference mitigation strategies are not developed and standardized. In the past decade, several studies have been conducted to understand interference mechanisms, develop countermeasures, and explore cooperative solutions [6]. However, to this date, thereis no scientific mutual interference mitigation standard for automotive radar or mm-wave radars operating in the 77-81 GHz band, in general [7]. Therefore, it is pertinent to investigate innovative interference mitigation strategies for the existing mm-wave radar systems, predominantly utilizing the FMCW waveform.
Interference mitigation techniques in FMCW radar systems can be classified into three main categories: avoidance, This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ detect-and-repair, and more recent communication-based methods [7]. Interference avoidance methods employ techniques like frequency hopping [8], medium access control [9], and chirp randomization [10] to decrease the probability of occurrence of interference or to minimize its effects during postprocessing. Communication-based methods [11], [12] are based on the idea that radars operating in the same vicinity can communicate with each other and decide on transmit (Tx) intervals. Both avoidance and communication-based methods require changes in the existing radar systems at the hardware level. The existing systems usually drop the corrupted frames or employ detect-and-repair methods based on signal-processing techniques to minimize the effect of interference in the corrupted signal received by the radar [7].
The mutual interference in most cases is time-limited, meaning that the interference appears in short bursts in the received signal. Due to this, there has been an interest in developing time-domain signal-processing methods that mitigate interference by recovering the signal of interest from the corrupted signal. These methods include interference signal estimation and subtraction [13], sparse signal reconstruction using the iterative method with adaptive thresholding (IMAT) [14], inverse Fourier transformation using adaptively selected peaks in the range spectrum [15], Kalman filtering [16], and autoregressive (AR) modeling in fast and slow-time [17]. More recently, deep-learning methods [18], [19] have also been employed to recover the interference-free signal from the corrupted signal. All of the time-domain interference mitigation methods mentioned above show an excellent performance for relatively short interference intervals. For longer interference intervals, where a relatively large number of samples in the received signal get corrupted, the reconstruction performance tends to deteriorate.
This article proposes a novel approach that compresses the interference in the received time-domain signal to improve the signal reconstruction performance. The pulse (interference) compression is performed after detecting the interference and estimating the required interference parameters, that is, duration and chirp slope. As a result, a significant part of the interference spans relatively fewer samples in the compressed domain. These samples are discarded, and the signal is then reconstructed in the compressed domain by predicting the missing samples iteratively. Since fewer samples are predicted, the reconstruction error is reduced compared to the case where the missing samples are predicted directly in the time domain [17].
The main contributions of this study are: 1) estimation of required parameters for estimation of the interference signal; 2) using a combination of pulse compression, signal reconstruction, and pulse decompression for effective interference removal; and 3) verification of the proposed methodology using real measurements.

II. THEORETICAL FRAMEWORK A. FMCW Radar
The Tx signal in an FMCW radar (see Fig. 1) is composed of a sequence of M linear frequency-modulated chirps for simultaneous range and velocity estimation [20]. The chirp where t represents the continuous time and φ 0 is the initial phase. Note that the frequency of the chirp signal increases with time. These types of chirps are often referred to as up-chirps. Using a directional coupler, the Tx signal s RF,Tx is fed to a Tx antenna and a homodyne downconversion mixer. The receive (Rx) signal is a scaled and delayed version of the Tx signal and contains reflections from all targets in the radar's field of view, that is, where K is the number of targets and A (k) and τ (k) denote the scaling factor and the round trip delay corresponding to the kth target, respectively. In the receiver, the Rx signal is mixed (multiplied) with the transmitted signal (1), and the mixer output is downconverted using a low-pass filter, which also acts as an anti-aliasing filter in further processing, to obtain the complex baseband signal of the form The beat frequency f (k) B and the phase φ (k) B in the above expression contain the range and velocity information of the kth target in the radar's field of view. The low-pass filter defines the maximum beat frequency expected by the radar system, which in turn corresponds to the maximum detectable range.
In further processing, a 2-D fast Fourier transform (2D-FFT) is applied to the sampled baseband signal over the sequence of M chirps to obtain a range-Doppler (RD) map, which enables the extraction of the range and the radial velocity of the targets, simultaneously.

B. FMCW-FMCW Interference
A single Tx chirp from the interfering radar has similar form as the ego radar but with bandwidth B int and duration T int (chirp slope k int = B int /T int ). The Tx chirp from the interfering radar is therefore represented as where φ 0,int is the starting phase and f c,int is the carrier frequency. The interference occurs when the Tx chirp falls within the time interval t B Rx defined by the receiver's bandwidth B Rx (see Fig. 2). The interference between FMCW radars can be classified into same-slope (k = k int ) and different-slope (k = k int ) interference. The probability of occurrence of same-slope interference is small compared to the different-slope interference because the time interval T B Rx T CRI (due to B Rx B), where T CRI is the chirp repetition interval [21]. The different-slope interference appears in relatively short bursts in the downconverted baseband signal. The duration of the interference is directly proportional to B Rx and inversely proportional to the difference between chirp slopes of both radars [22], that is, The baseband signal during the interference interval is the sum of the contributions from target reflections and the interfering signal, that is, where t o is the time instance where Tx and interfering chirps cross each other in the time-frequency domain. If τ int is the time delay between the start of the Tx and the interfering chirps, the interference contribution is expressed as where The starting phase of s int (t) in the interference interval is represented by φ offset . The time-domain representation (real part) of an interfered baseband signal and the corresponding instantaneous frequencies are shown in Fig. 3.

C. Pulse Compression
Pulse compression is utilized to improve the resolution as well as the detection and estimation performance of a typical pulse radar [23]. An example of a pulse compression waveform is the linearly frequency-modulated (LFM) waveform, which is defined as where β is the pulse bandwidth and is the pulse duration. The time-domain response of an LFM pulse is plotted in Fig. 4(a), and the instantaneous frequency is plotted in Fig. 4(b). The compression can be performed by filtering the received echo using a matched filter defined as where ( * ) is the complex conjugation operator. This filter choice maximizes the signal-to-noise ratio (SNR) in the output where ( * ) represents the convolution operation. The Tx pulse energy is compressed in the center of the output y(t) (see Fig. 5). In this work, rather than improving the detection performance, pulse compression is utilized to shorten the duration of the interference contribution in the received baseband signal by compressing a significant portion of the interfering signal to a relatively small time interval.  D. AR Modeling AR models [24], [25] can be used to predict future samples in a time series. The underlying assumption is that the time series is wide-sense stationary, which means its mean and autocorrelation functions are time-invariant. If a discrete time signal has some missing samples, the information from previous observations can be used to reconstruct the missing samples [17]. Formally, the kth sample of a signal s(k) is estimated using the AR model coefficients a i as where p denotes the AR model order, and k are residuals with zero mean and variance σ 2 . Several methods of AR coefficient a i estimation [26] and AR model order p selection [27], [28] are found in the literature. In this work, we use the Akaike information criterion (AIC) [29] to select the AR model order.
III. INTERFERENCE MITIGATION Comparing the instantaneous frequency versus time plots for the interfering signal (see Fig. 3) and the LFM waveform [see Fig. 4(b)], it can be observed that both signals have the same frequency versus time characteristics. Moreover, from (8) and (9), it can be seen that the phase progression of the interference in the baseband signal is the same as the phase progression in an LFM pulse. Therefore, similar to the pulse compression principle in the LFM waveform case, it is possible to compress the interference in the received baseband signal, provided that the interference phase φ int (t) is known for the design of the matched filter.
The complete interference mitigation method is composed of the following steps: interference parameter estimation, pulse compression, AR signal reconstruction, and pulse decompression. These steps are described in the sections that follow.

A. Interference Parameter Estimation
Interference parameters (chirp slope, phase, and amplitude) can be estimated using the method described in [13], provided that the interference has a significantly higher amplitude compared to the target echoes and the interference duration is relatively long. In our work, the aim is to design a matched filter for interference compression. If the matched filter is shifted in phase by φ new and scaled in amplitude by A new , that is, then the corresponding compressed output will simply be shifted in phase and scaled in amplitude, that is, (14) and there will be no effect on the SNR in the output. Therefore, contrary to [13], it is not essential to estimate accurate phase offset and amplitude of the interference for the purpose of pulse compression. However, it is still required that the estimation of k int , which determines the interference phase progression, is accurate. The initial estimates of the interference slope are obtained from (5), which can be rewritten as The interference duration T d in (15) is determined by identifying the start and end of the interference burst in the received baseband signal, for example, using the interference detection method described in [30]. The number of consecutive disturbed samples in the received baseband signal gives an estimate of T d . If T d is known, then using own radar parameters (B Rx and k), the slope of the interference is estimated as Consider an own radar with chirp slope k = 800 MHz/40 μs, B Rx = 10 MHz, and analog to digital converter (ADC) sampling rate of 20 Msps. If the number of disturbed samples is 80, then the interference duration is T d = 4 μs, and the interference chirp slope is computed to be k int,+ = 25(MHz/μs) and k int,− = 15(MHz/μs).

B. Interference Compression
Once the interference chirp slope is estimated, the phase progression of the matched filter is determined by (8). Consequently, the matched filter for interference compression is where w(t) denotes a window function applied to the filter. In this work, we use a Kaiser window, which approximates the discrete prolate spheroidal sequence (DPSS) for maximizing the energy concentration in the main lobe [31]. The Kaiser window parameter β determines the tradeoff between the mainlobe width and the sidelobe level. Given the complex baseband signal s CB (t), the compressed waveform is obtained using the following expression: The correct interference chirp slope out of the two estimations from Section III-A can be decided by filtering the received signal using the corresponding filter estimates, which results in two different outputs (see Fig. 6). There is no interference compression in the output corresponding to the first estimation (k int,− ), because the duration of the disturbance in the output is not reduced. However, the interference is compressed in the output signal corresponding to the second estimation (k int,+ ). Therefore, it can be concluded that k int,+ is the correct interference chirp slope.

C. Signal Reconstruction
The interference in the filter output is concentrated in the center of the interference interval. Moreover, more than 90% of the LFM pulse energy is contained in the mainlobe of the compressed waveform [23]. Therefore, it is possible to remove a significant portion of the interference by removing the mainlobe of the compressed waveform. When a windowed matched filter is used, the width of the mainlobe increases. As a result, the energy in the mainlobe increases further. More interference energy can be removed by discarding more samples from the compressed waveform. However, it would lead to a loss of information from the signal of interest. Discarding the interference-affected samples creates gaps in the resulting waveform, which can be filled by inserting new samples to obtain an interference-free waveform.
If the compressed waveform fulfills the wide sense stationarity condition, one option is to predict the missing samples by estimating an AR model for the compressed waveform [17]. Other sample prediction methods may achieve better signal reconstruction performance in the compressed domain. However, in this work, we use the AR-model-based sample prediction in order to compare the signal reconstruction performance in the fast time and the compressed domain using a well-established sample prediction method.
After reconstruction, the next step is to decompress the repaired compressed waveformȳ c (t) to obtain the baseband signals CB (t) without interference. The decompression is performed by dividing the frequency response ofȳ c (t) by the frequency response of h int (t). This is equivalent to deconvolution in the time domain, which is numerically an ill-posed problem and can introduce unwanted effects in the output [32]. To overcome this problem, the matched filter is regularized for the purpose of decompression. In this work, the regularization is performed by modifying the minimum magnitude of H int ( f ) = F (h int (t)) (here F represents the Fourier transform) to a threshold as while the phase is kept unchanged (see Fig. 7). The decompressed signal is obtained by frequency-domain deconvolution where F −1 represents the inverse Fourier transform. The complete interference mitigation process is summarized in Fig. 8 using a simulated received baseband signal with interference. The matched filter is estimated using the duration of the interference in s CB (t) [see Fig. 8(a)]. The interference is concentrated in the mainlobe of the filter output y c (t) [see Fig. 8(b)]. The mainlobe in the filter output is removed, and the remaining signal is repaired by employing an AR model to obtainȳ c (t) [see Fig. 8(c)]. Finally, the repaired signal is decompressed using the regularized matched filter H int,r ( f ) to obtain the baseband signal without interference.

IV. RESULTS
The interference mitigation performance of the proposed method is verified using real radar data. The experimental setup consists of an ego radar mounted on a car moving toward two interfering radars (see Fig. 9). The radar parameters are summarized in Table I.

A. Stationarity Test for AR Modeling
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test [33] is employed to check that the compressed waveforms are stationary and, therefore, can be modeled as AR processes. The test

B. Parameter Selection
In this section, we discuss the selection or estimation of various parameters in the proposed interference mitigation method.
1) Interference Duration T d : In real situations, it might be difficult to accurately estimate the interference duration T d from the received signal, due to the relative amplitude of the interference and low-pass filter characteristics. The initial estimate of T d , in terms of samples, is obtained by counting the number of disturbed samples based on the amplitude of the received signal. This estimate is then improved by comparing the output for a range of filters and selecting one that provides the maximum amplitude of the mainlobe in the compressed output. Using the criteria mentioned above, the number of disturbed samples is 34 for interference-1 and 17 for interference-2. Consequently, the estimated interfering chirp slopes are k int,1 = 13.96 MHz/μs and k int,2 = 10.61 MHz/μs (see Fig. 10).
2) Matched Filter Parameters: Kaiser window parameter β is influenced by the window length and determines the tradeoff between the relative sidelobe attenuation and the mainlobe width. Different values were tested, and it was observed that β = 5 is suitable for the window length 17 and β = 6 is suitable for the window length 34. For lower β values, a significant amount of interference energy started leaking into the sidelobes. For higher β values, a loss in interference compression gain was observed. However, the window parameter selection criteria for the purpose of interference mitigation need to be investigated further.
The threshold for matched filter regularization is determined by computing the mean squared error (mse), which is where C is a set of N c clean samples in the received baseband signal. We selected = −65 dB, because the MSE is not reduced further by increasing the threshold (see Fig. 11).
To illustrate the interference compression achieved in the output of the estimated filter, we compare the magnitudes of a sample interfered frame in the time domain and the corresponding frame in the compressed domain (see Fig. 12).

C. Interference Mitigation-Real Data
The interference mitigation performance of the proposed method is evaluated using real interference data corresponding to three scenarios. In scenario-1, the interference in the received signal is caused by "interfering radar-1," in scenario-2, the interference is caused by "interfering radar-2," and in scenario-3, the interference is caused by both radars. The time-domain baseband signal and the RD maps corresponding to the three scenarios illustrate that the proposed method suppresses the interference while keeping the signal of interest unaffected (see Fig. 13). The target signal-tointerference-and-noise ratio (SINR) is used as a quantitative measure of interference mitigation performance (see Table II).   (21) where n and m are row and column indices of the RD matrix, respectively, T is a set of target cells, and N is a set of noise plus interference cells (see Fig. 14). It can be observed that the interference is removed in the reconstructed signal and target SINRs comparable to the clean signal are obtained. In scenario-3, the interference noise is concentrated at around 4.5 m/s in the Doppler domain; therefore, there is no degradation in target SINRs.
Since the clean versions of the interfered frames are not available, we use the next frame in the sequence of frames as a clean reference. Similarly, in the case of the real baseband signal, we use a clean chirp from the same frame as a reference. In scenario-3, where interference from two sources is observed, both disturbances are removed by sequentially performing the pulse compression, reconstruction, and pulse decompression steps for each interference source.
For further quantitative evaluation of the proposed method (AR model-based signal reconstruction in the compressed domain, abbreviated hereinafter as AR-CD), the worst interference-affected regions in the RD maps corresponding to the three scenarios are identified and the noise levels are compared (see Table III). The first two rows of the table define the worst interference-affected RD map regions and the next three rows show the noise levels.
The signal reconstruction performance of the proposed method is compared with the AR model-based signal reconstruction in the fast-time domain [17] (abbreviated hereinafter  Principal setup of target cells T (green) and noise plus interference cells N (red) for SINR calculation in the RD matrix. Guard cells (gray) are typically used to reduce the effect of target sidelobes or other nearby targets on SINR.  as AR-TD) and the IMAT algorithm-based reconstruction [14]. As proposed in [14], the minimum threshold for the IMAT algorithm is set to 10 dB above the noise floor, which is estimated from the clutter-free image band. A comparison of the time-domain signal frames (see Fig. 15) shows that AR-TD struggles to predict the samples directly in the fast-time domain. We can also observe a clear discontinuity in the sample magnitudes of the frame reconstructed using the IMAT algorithm. The signal reconstruction performance improves with AR-CD since there is no clearly visible discontinuity in the reconstructed frame.
The sidelobe levels in the region highlighted using the orange rectangles in the corresponding RD maps (see Fig. 16) indicate a better signal reconstruction performance using AR-CD and IMAT compared to AR-TD. For strong scatterers, a comparable signal reconstruction performance is achieved with IMAT and AR-CD (see SINR values in Table IV). However, the proposed method is better able to recover the relatively weak scatterers (highlighted with white rectangles in Fig. 16) in the RD map.

V. DISCUSSION
Repairing the received baseband signal by AR reconstruction in the time domain means that all samples of the signal  of interest within the interference duration are lost. The proposed method compresses the interference, but the signal of interest does not undergo any compression. Therefore, when the interference is removed in the compressed domain, only a small portion of the signal of interest is lost. As a consequence, AR-CD outperforms AR-TD, especially when a relatively large percentage of the samples are affected by the interference (see Fig. 17). When a small percentage of the received samples are disturbed, the time-bandwidth product would be small, leading to a lower compression gain. In such situations, it might be better to perform the signal reconstruction directly in the fast-time domain.
An important prerequisite for the proposed method to successfully suppress interference is that the interference is detected and the disturbed samples are identified correctly. This task becomes more complicated when there is interference from multiple sources because the samples identified as interfered have to be assigned to a particular interfering radar. In this study, we use the prior information that there are two interference sources to assign disturbed samples to The difference in the signal reconstruction performance can be seen in the range profiles in (b) and (d). Targets in (b) for the signal reconstructed in TD have lower SINR and higher side lobes, especially the ones further than 10 m. There is no significant difference in the signal reconstruction performance for the short-duration interference, at least in the range profiles. either interference-1 or interference-2 based on the number of consecutive disturbed samples. However, when there is an unknown number of interfering radars, more sophisticated interference detection methods need to be applied.
The performance of the slope estimation method proposed in this study depends directly on the efficiency of the interference detection method used and may have some limitations in certain scenarios. Therefore, more research should be done to find a better method rather than evaluating the performance of the proposed one.

VI. CONCLUSION
This article describes a method for mutual interference mitigation in mm-wave FMCW radar, which is validated using real measurements. After detecting interference in the received signal, the chirp slope of the interfering signal is estimated using the interference dwell time and the receiver bandwidth. A matched filter is designed using the estimated slope, and pulse compression is performed to compress interference in the filter output. In the compressed output, most of the interference energy is concentrated in the center of the interference interval. The interference is mitigated by removing the interference-related mainlobes from the compressed waveform and restoring the missing samples using AR model-based sample prediction. The advantage of performing sample prediction in the compressed domain instead of the time domain is a significant reduction in the number of samples to be predicted. However, if the interference duration is relatively short, it may be better to predict signal samples directly in the time domain. The interference-free baseband signal is retrieved by decompressing the restored compressed waveform using a regularized matched filter, which ensures numerical stability. Results from real outdoor measurements show that interference is effectively suppressed down to the noise floor, and for this particular experiment, the pulse compression-aided AR signal reconstruction achieves a target SINR gain of about 14 dB. The results also demonstrate that this method can be applied to situations where the interference is caused by multiple sources.