IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 15, NO. 1, JANUARY 2018

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Interference Mitigation for Automotive Radar Using Orthogonal Noise Waveforms Zhihuo Xu , Member, IEEE, and Quan Shi, Member, IEEE Abstract— To improve traffic safety, millimeter wave radars have been widely used for sensing traffic environment. As radars also operate on a narrow small road and in the same frequency band, mutual interference between different automotive radars that arises cannot be easily reduced by frequency or polarization diversity. This letter presents novel orthogonal noise waveforms to reduce such neighboring interferences. First, the spectral density distribution function of the proposed waveforms is defined by using an optimized Kaiser function. Subsequently, the phases of the noise waveforms are formulated as a problem of phase retrieval and are explored. Thanks to nonuniqueness solutions, the proposed method generates the orthogonal signals with a good random phase diversity. The proposed method was tested on a representative scenario for interference reduction. The experimental results show that the proposed method can produce visually convincing radar images, and the signal-to-interference and noise ratio is better than the existing methods. Index Terms— Automotive radar, interference mitigation, orthogonal noise waveforms, phase retrieval.

I. I NTRODUCTION ECAUSE millimeter wave radar is unaffected by daylight conditions, it has been proven to be an effective and robust sensor of traffic environment, thus enabling many automotive radars to be developed over the last two decades [1]. As numerous radars are simultaneously present in a given area, neighbor interference becomes a very likely event [2]–[4]. To deal with this challenge, various methods have been presented to mitigate the mutual interferences of radars. The problem of high-resolution radar detection in interference and nonhomogeneous noise is addressed in [5] and [6]. A shorttime range domain cancellation method is proposed for interference suppression in [7]. A hybrid use of empirical mode decomposition and fractional Fourier transform is applied to remove the interference in [8] and [9]. Some methods are

B

Manuscript received August 4, 2017; revised October 31, 2017; accepted November 23, 2017. Date of publication December 14, 2017; date of current version December 27, 2017. This work was supported in part by the Nantong University-Nantong Joint Research Center for Intelligent Information Technology under Grant KFKT2016A11 and Grant KFKT2016A10, in part by the Nantong Natural Science and Technology Project under Grant GY12016017, in part by the Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant 17KJB510047 and Grant 17KJB520029, in part by the Scientific Research Start-up Foundation for Talent Introduction of Nantong University under Grant 17R30, and in part by the National Natural Science Foundation of China under Grant 61771265 and Grant 61671255. (Corresponding author: Zhihuo Xu.) Z. Xu is with the Radar and Image Research Group, School of Transportation, Nantong University, Nantong 226019, China, and also with the Nantong Research Institute for Advanced Communication Technologies, Nantong 226001, China (e-mail: [email protected]). Q. Shi is with the Radar and Image Research Group, School of Transportation, Nantong University, Nantong 226019, China. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2017.2777962

implemented on hardware, including the use of an auxiliary receiver [10] and digital beamforming to control the direction of the beam to suppress the interference in the spatial domain [11]–[14]. All the above-mentioned studies have their merits and realm of application; however, these methods are not suitable to deal with the interferences for automotive radars with small aperture and a low complexity of signal processing. Of late, researchers have given significant attention to pseudorandom noise (PRN) radars because of its superior performance [15], [16]. The advantages of the PRN radar include high resistance against interference and range ambiguity, optimal coherent reception, and high compression rate, to name a few [17]–[20]. Ng et al. [21] successfully developed a fully integrated 77-GHz PRN automotive radar. A pseudonoise (PN) sequence was used in an automotive radar to reduce the interferences in [22] and [23]. The PN-coded signals are the radar’s “signature,” exhibiting good correlation properties. Therefore, the interferences can be reduced by using the coded signals. The spectral distributions are rectangular in one type of PRN signals [24]. However, compared with a chirp radar, this type of PRN radar exhibits higher sidelobes [25]. In practice, a radar with low sidelobes is of great importance for automotive applications, because the sidelobes contribute to interferences. It is very crucial for detecting small-reflected targets, which are near highly reflected targets, such as when pedestrians are close to vehicles. To reduce the sidelobe levels, PRN waveforms with nonrectangular spectral distributions are designed [26]. In this letter, we aim to design novel orthogonal noise waveforms to mitigate the interferences for the automotive radar. We formulate the design of orthogonal noise waveform as a problem of phase retrieval [27]–[29]. Compared with the existing methods, the proposed approach produces lower sidelobes and shows better performance on mitigating the interference from neighboring radars. II. P ROPOSED M ETHODOLOGY A. Design of Orthogonal Noise Signals At each time instant t, the noise waveform used for the radar-transmitted signal can be formulated as s(t) = exp{ j 2π f 0 t + φ(t)}, 0 ≤ t ≤ τ

(1)

where f0 is the carrier frequency, τ is the pulse duration, and φ(t) is the random phase. When the pulse duration is set as the pulse repetition time, the signal is to be a continuous wave. The Fourier transform of s(t) is given by s(t)e− j 2π f t dt. (2) S( f ) =

R 1545-598X © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Fig. 1.

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 15, NO. 1, JANUARY 2018

Assuming that the total number of the orthogonal noise signals is N, the i th signal denoted as sk (i, t) in the orthogonal signal library is assigned to be transmitted at the kth transmission. To further minimize the probability of mutual interference between the radars equipped with the proposed signals, at the kth transmission, the value of i is calculated as

Assignment of the signals for transmission.

As mentioned previously, the shape of the spectral distribution function of the signal determines the levels of sidelobes. In general, the lower sidelobes of nonrectangular functions have been obtained at the cost of broadening of the mainlobe width. In [30], an optimized Kaiser function was explored. The optimized function allows a better peak sidelobe ratio (PSLR) without broadening the mainlobe. Therefore, the mean spectral density distribution (PSD) function of the noise signals is defined by using the optimized Kaiser function, denoted as K( f ), where f is the frequency. The design of orthogonal noise signal s(t) is equivalent to recovery of s(t) when only the magnitude of S( f ), namely, |S( f )| = K( f ). As the Fourier transformation is bijective, this is equivalent to recovering the phase of S( f ). Hence, the design of noise signal becomes a problem of phase retrieval. Given observations on the magnitude of S( f ), phase retrieval seeks to reconstruct a complex signal, i.e., solve find s(t), 0 ≤ t ≤ τ s.t. |S( f )| = K( f ).

(3)

Many algorithms have been developed to solve the problem of phase retrieval. These methods include alternating projections, semidefinite programming, matrix completion-based, and sparsity-based [27]–[29]. Due to the fact that the signals are used as radar transmitted signals, the signals cannot be designed to possess sparsity. For reducing the interference, the signal waveforms are expected to possess good diversity. We apply one of the most popular methods, hybrid input– output method by Shechtman [29], to explore the orthogonal noise signals. The Fourier transformation and inverse Fourier transform are denoted as F(·) and F−1 (·), respecitvly. The method works as follows. 1) Initialization: Choose an initial s0 (t) = exp{ j φ(t)}, where φ(t) are white Gaussian phases, a parameter β > 0, and a convergence threshold = 1e − 16. 2) Loop: For i = 1, 2, . . . inductively set Si ( f ) = F(si−1 (t)) Si ( f ) = Si ( f ) − β si (t) = F−1 (Si ( f ))

Si ( f ) Si ( f ) − K( f ) |Si ( f )|

(4) (5) (6)

until convergence. The above-mentioned phase-retrieval problem yields a nonuniqueness solution. Thanks to nonuniqueness, the proposed method produces a group of orthogonal signals with different random phases but sharing the same spectral density. B. Interference Mitigation To mitigate the interferences, the orthogonal noise signals are successively modulated for transmission (see Fig. 1). The signal in the current transmitted pulse is orthogonal to the next transmitted signal. Simultaneously, the radar synchronizes the current-matched filter with the current-transmitted signal.

i = Randi (N)

(7)

where Randi (N) is a random integer generator that returns a pseudorandom scalar integer between 1 and N. The corresponding echo signal of sk (i, t) is written as rk (i, t − td ), where td is the delay time. The interference from the neighboring radar is denoted as I j (t), j = 1, 2, . . . , M, where M is the total number of the interferences. The received signals can be expressed as r (i, t) = rk (i, t − td ) + I j (t), j = 1, 2, . . . , M. The response of matched filter in the receiver can be formulated as [rk (i, t − td ) + I j (t)]s ∗k (i, t)dt ∗ = rk (i, t − td )s k (i, t)dt + I j (t)sk∗ (i, t)dt i = 1, 2, . . . , N, j = 1, 2, . . . , M

(8)

where ∗ is the conjugate operation. The first term in the righthand side of (8) is the desired response. The interferences generated by the transmission of the neighboring noise radar are orthogonal to the current-transmitted signal of the host noise radar. Hence, the output of the interference response in (8) is approximately zero, namely, I j (t)sk∗ (t)dt ≈ 0, j = 1, 2, . . . , M. III. N UMERICAL R ESULTS This section first analyzes the performance of the proposed orthogonal noise signal, and the simulation results are subsequently demonstrated in the presence of high interferences. A. Performances Analysis Fig. 2 shows the numerical results of the proposed orthogonal noise signals. Fig. 2(a) shows the real parts of the signals. The signals exhibit arbitrary waveforms. The total number of the signals N = 100. However, the PSD functions of these signals show great resemblance, as shown in Fig. 2(b). The PSD is consistent with the optimized Kaiser function in [30]. Considering the set 100 waveforms, the statistical analysis of the cross correlation values is shown in Fig. 2(c) and (d) to validate the orthogonality of the waveforms. Using radar ambiguity function, the effects of the Doppler phase shift are accurately shown in Fig. 2(e), demonstrating good Doppler tolerance. Furthermore, the proposed waveforms are compared with the RPN signals [23]. The bandwidth of the PRN signals is the same as the proposed signals. The comparison of the autocorrelation function (ACF) is shown in Fig. 2(f). The PSLR of PRN is −20.53 dB. In contrast, the PSLR of the proposed noise signal can be reduced to be −42.47 dB, by using the optimized Kaiser function as the PSD. B. Mitigation of Interferences A 24-GHz pulsed automotive radar system is used for simulations. The pulse duration and the bandwidth of signal are set as 1.42 μs and 600 MHz, respectively, as an

XU AND SHI: INTERFERENCE MITIGATION FOR AUTOMOTIVE RADAR USING ORTHOGONAL NOISE WAVEFORMS

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Fig. 2. Numerical results. (a) Real parts of the orthogonal noise waveforms. (b) Spectral distribution function of (a). (c) ACF. (d) Across correlation function (XCF). (e) Ambiguity function. (f) Comparisons of ACFs.

experimental study. The radar then electronically scans the beam of the antenna. A typical road environment is illustrated in Fig. 3, where a car, a pedestrian, and one interfering radar

are present. The car is located at a distance of 24.5 m in range. The size of the car is 5.5 m in length and 2.0 m in width. The pedestrian is located at a distance of 28.5 m in range.

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Fig. 3.

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 15, NO. 1, JANUARY 2018

Representative scenario designed for simulations.

Fig. 5. SINR = 10 dB. (a) LFM. (b) DCUC. (c) PRN. (d) Proposed method.

Fig. 4. SINR = 0 dB. (a) LFM. (b) DCUC. (c) PRN. (d) Proposed method.

The proposed method is compared with other related approaches, including the conventional linear frequencymodulated (LFM) [1], down-chirp, and up-chirp (DCUC) couples [3], and the PRN radar [23].

The essence of the proposed method for mitigating interfering signals is the use of the orthogonality noise signals. The signal in the current transmitted pulse is orthogonal to the next transmitted signal. On the other hand, the radar synchronizes the current-matched filter with the currenttransmitted signal. The current-matched filter is the conjugate of the current-transmitted signal. Consequently, the interfering signals are reduced by the current-matched filtering. Assuming that the number of the interference signal is M, the signal-to-interference and noise ratio (SINR) is

XU AND SHI: INTERFERENCE MITIGATION FOR AUTOMOTIVE RADAR USING ORTHOGONAL NOISE WAVEFORMS

TABLE I C OMPARISONS OF SINRs

calculated as SINR = M

j =1

PEcho PInterfence ( j ) + PNoise

(9)

where PEcho and PNoise are the power of the desired echo signal and the additive noise in the radar system, respectively, PInterfence ( j ) is the power of the j th interference signal. Representative experiments have been investigated in the presence of three interfering signals. Figs. 4 and 5 demonstrate the results of comparisons using the different signals. The results reveal that the strategy of using a DCUC signal cannot effectively suppress the interferences. In contrast, the use of noise waveforms can significantly reduce these undesired signals. By visual comparison, the image quality by the proposed method is better than that of the referred methods. Table I summarizes the SINRs before and after mitigation of interferences by using these different signals. The best results are highlighted in bold. Again, the proposed method produces the best improved SINRs. In summary, the comparisons demonstrate that the performance of the presented approach is superior to the existing methods. IV. C ONCLUSION This letter addresses the problem of neighboring interference of an automotive radar. To deal with this challenge, orthogonal noise waveforms have been designed by using a phase retrieval method. The proposed signals have been validated to be orthogonal with lower sidelobes. The performance assessment shows that the proposed method exhibits a significant performance improvement over the conventional radar waveforms in high interference environments. ACKNOWLEDGMENT The authors would like to thank the editors and reviewers for their invaluable comments that significantly improved the quality of this letter. R EFERENCES [1] S. M. Patole, M. Torlak, D. Wang, and M. Ali, “Automotive radars: A review of signal processing techniques,” IEEE Signal Process. Mag., vol. 34, no. 2, pp. 22–35, Mar. 2017. [2] T. Schipper, S. Prophet, M. Harter, L. Zwirello, and T. Zwick, “Simulative prediction of the interference potential between radars in common road scenarios,” IEEE Trans. Electromagn. Compat., vol. 57, no. 3, pp. 322–328, Jun. 2015. [3] G. M. Brooker, “Mutual interference of millimeter-wave radar systems,” IEEE Trans. Electromagn. Compat., vol. 49, no. 1, pp. 170–181, Feb. 2007. [4] H. Zhou, B. Wen, and S. Wu, “Dense radio frequency interference suppression in HF radars,” IEEE Signal Process. Lett., vol. 12, no. 5, pp. 361–364, May 2005. [5] Y. Gao, G. Liao, and W. Liu, “High-resolution radar detection in interference and nonhomogeneous noise,” IEEE Signal Process. Lett., vol. 23, no. 10, pp. 1359–1363, Oct. 2016.

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[6] Y. Gao, G. Liao, S. Zhu, and D. Yang, “A persymmetric GLRT for adaptive detection in compound-Gaussian clutter with random texture,” IEEE Signal Process. Lett., vol. 20, no. 6, pp. 615–618, Jun. 2013. [7] H. Zhou and B. Wen, “Radio frequency interference suppression in small-aperture high-frequency radars,” IEEE Geosci. Remote Sens. Lett., vol. 9, no. 4, pp. 788–792, Jul. 2012. [8] S. A. Elgamel and J. J. Soraghan, “Enhanced monopulse radar tracking using fractional Fourier filtering in the presence of interference,” in Proc. 11th Int. Radar Symp. (IRS), Jun. 2010, pp. 1–4. [9] S. A. Elgamel and J. J. Soraghan, “Using EMD-FrFT filtering to mitigate very high power interference in chirp tracking radars,” IEEE Signal Process. Lett., vol. 18, no. 4, pp. 263–266, Apr. 2011. [10] E. Y. Imana, T. Yang, and J. H. Reed, “Addressing a neighboring-channel interference from high-powered radar,” IEEE Trans. Veh. Technol., vol. 65, no. 5, pp. 2872–2882, May 2016. [11] Z. Chen, H. Li, G. Cui, and M. Rangaswamy, “Adaptive transmit and receive beamforming for interference mitigation,” IEEE Signal Process. Lett., vol. 21, no. 2, pp. 235–239, Feb. 2014. [12] Z. Geng, H. Deng, and B. Himed, “Adaptive radar beamforming for interference mitigation in radar-wireless spectrum sharing,” IEEE Signal Process. Lett., vol. 22, no. 4, pp. 484–488, Apr. 2015. [13] Z. Geng and H. Deng, “Antenna beamforming for interference cancellation in radar-wireless spectrum sharing,” in Proc. IEEE Int. Symp. Antennas Propag., Jul. 2015, pp. 133–134. [14] Z. Geng and H. Deng, “Adaptive interference and clutter rejection processing for bistatic MIMO radar,” in Proc. IEEE Int. Symp. Antennas Propag., Jun./Jul. 2016, pp. 2055–2056. [15] B. M. Horton, “Noise-modulated distance measuring systems,” Proc. IRE, vol. 47, no. 5, pp. 821–828, 1959. [16] G. R. Cooper et al., “Random signal radar,” School Elect. Eng., Purdue Univ., West Lafayette, IN, USA, Tech. Rep. TR-EE67-11, 1967. [17] G. Galati and G. Pavan, “Noise Radar Technology as an interference prevention method,” J. Elect. Comput. Eng., vol. 2013, Jul. 2013, Art. no. 146986. [18] K. A. Lukin, “Noise radar with correlation receiver as the basis of car collision avoidance system,” in Proc. 25th Eur. Microw. Conf., Bologna, Italy, Sep. 1995, pp. 506–507. [19] O. A. M. Aly and A. S. Omar, “New implementation of the correlation function of the PN code for application in automotive radars,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Columbus, OH, USA, Jun. 2003, pp. 272–275. [20] K. Lukin, “Dedicated applications of noise radars,” in Proc. IEEE Radar Symp., Jun. 2015, pp. 771–776. [21] H. J. Ng, R. Feger, and A. Stelzer, “A fully-integrated 77-GHz UWB pseudo-random noise radar transceiver with a programmable sequence generator in SiGe technology,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 61, no. 8, pp. 2444–2455, Aug. 2014. [22] E. Gambi, F. Chiaraluce, and S. Spinsante, “Chaos-based radars for automotive applications: Theoretical issues and numerical simulation,” IEEE Trans. Veh. Technol., vol. 57, no. 6, pp. 3858–3863, Nov. 2008. [23] T.-H. Liu, M.-L. Hsu, and Z.-M. Tsai, “Mutual interference of pseudorandom noise radar in automotive collision avoidance application at 24 GHz,” in Proc. IEEE Global Conf. Consum. Electron., Oct. 2016, pp. 1–2. [24] X. Xu and R. M. Narayanan, “Range sidelobe suppression technique for coherent ultra wide-band random noise radar imaging,” IEEE Trans. Antennas Propag., vol. 49, no. 12, pp. 1836–1842, Dec. 2001. [25] X. Dong, Y. Zhang, and W. Zhai, “A sparse optimization method for masking effect removal in noise synthetic aperture radar,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2016, pp. 6811–6814. [26] J. S. Kulpa, L. Ma´slikowski, and M. Malanowski, “Filter-based design of noise radar waveform with reduced sidelobes,” IEEE Trans. Aerosp. Electron. Syst., vol. 53, no. 2, pp. 816–825, Apr. 2017. [27] Y. C. Eldar, P. Sidorenko, D. G. Mixon, S. Barel, and O. Cohen, “Sparse phase retrieval from short-time Fourier measurements,” IEEE Signal Process. Lett., vol. 22, no. 5, pp. 638–642, May 2015. [28] Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: Efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process., vol. 62, no. 4, pp. 928–938, Feb. 2014. [29] Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Process. Mag., vol. 32, no. 3, pp. 87–109, May 2015. [30] Z.-H. Xu, Y.-K. Deng, and Y. Wang, “A novel optimization framework for classic windows using bio-inspired methodology,” Circuits Syst., Signal Process., vol. 35, no. 2, pp. 693–703, 2016.

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Interference Mitigation for Automotive Radar Using Orthogonal Noise Waveforms Zhihuo Xu , Member, IEEE, and Quan Shi, Member, IEEE Abstract— To improve traffic safety, millimeter wave radars have been widely used for sensing traffic environment. As radars also operate on a narrow small road and in the same frequency band, mutual interference between different automotive radars that arises cannot be easily reduced by frequency or polarization diversity. This letter presents novel orthogonal noise waveforms to reduce such neighboring interferences. First, the spectral density distribution function of the proposed waveforms is defined by using an optimized Kaiser function. Subsequently, the phases of the noise waveforms are formulated as a problem of phase retrieval and are explored. Thanks to nonuniqueness solutions, the proposed method generates the orthogonal signals with a good random phase diversity. The proposed method was tested on a representative scenario for interference reduction. The experimental results show that the proposed method can produce visually convincing radar images, and the signal-to-interference and noise ratio is better than the existing methods. Index Terms— Automotive radar, interference mitigation, orthogonal noise waveforms, phase retrieval.

I. I NTRODUCTION ECAUSE millimeter wave radar is unaffected by daylight conditions, it has been proven to be an effective and robust sensor of traffic environment, thus enabling many automotive radars to be developed over the last two decades [1]. As numerous radars are simultaneously present in a given area, neighbor interference becomes a very likely event [2]–[4]. To deal with this challenge, various methods have been presented to mitigate the mutual interferences of radars. The problem of high-resolution radar detection in interference and nonhomogeneous noise is addressed in [5] and [6]. A shorttime range domain cancellation method is proposed for interference suppression in [7]. A hybrid use of empirical mode decomposition and fractional Fourier transform is applied to remove the interference in [8] and [9]. Some methods are

B

Manuscript received August 4, 2017; revised October 31, 2017; accepted November 23, 2017. Date of publication December 14, 2017; date of current version December 27, 2017. This work was supported in part by the Nantong University-Nantong Joint Research Center for Intelligent Information Technology under Grant KFKT2016A11 and Grant KFKT2016A10, in part by the Nantong Natural Science and Technology Project under Grant GY12016017, in part by the Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant 17KJB510047 and Grant 17KJB520029, in part by the Scientific Research Start-up Foundation for Talent Introduction of Nantong University under Grant 17R30, and in part by the National Natural Science Foundation of China under Grant 61771265 and Grant 61671255. (Corresponding author: Zhihuo Xu.) Z. Xu is with the Radar and Image Research Group, School of Transportation, Nantong University, Nantong 226019, China, and also with the Nantong Research Institute for Advanced Communication Technologies, Nantong 226001, China (e-mail: [email protected]). Q. Shi is with the Radar and Image Research Group, School of Transportation, Nantong University, Nantong 226019, China. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2017.2777962

implemented on hardware, including the use of an auxiliary receiver [10] and digital beamforming to control the direction of the beam to suppress the interference in the spatial domain [11]–[14]. All the above-mentioned studies have their merits and realm of application; however, these methods are not suitable to deal with the interferences for automotive radars with small aperture and a low complexity of signal processing. Of late, researchers have given significant attention to pseudorandom noise (PRN) radars because of its superior performance [15], [16]. The advantages of the PRN radar include high resistance against interference and range ambiguity, optimal coherent reception, and high compression rate, to name a few [17]–[20]. Ng et al. [21] successfully developed a fully integrated 77-GHz PRN automotive radar. A pseudonoise (PN) sequence was used in an automotive radar to reduce the interferences in [22] and [23]. The PN-coded signals are the radar’s “signature,” exhibiting good correlation properties. Therefore, the interferences can be reduced by using the coded signals. The spectral distributions are rectangular in one type of PRN signals [24]. However, compared with a chirp radar, this type of PRN radar exhibits higher sidelobes [25]. In practice, a radar with low sidelobes is of great importance for automotive applications, because the sidelobes contribute to interferences. It is very crucial for detecting small-reflected targets, which are near highly reflected targets, such as when pedestrians are close to vehicles. To reduce the sidelobe levels, PRN waveforms with nonrectangular spectral distributions are designed [26]. In this letter, we aim to design novel orthogonal noise waveforms to mitigate the interferences for the automotive radar. We formulate the design of orthogonal noise waveform as a problem of phase retrieval [27]–[29]. Compared with the existing methods, the proposed approach produces lower sidelobes and shows better performance on mitigating the interference from neighboring radars. II. P ROPOSED M ETHODOLOGY A. Design of Orthogonal Noise Signals At each time instant t, the noise waveform used for the radar-transmitted signal can be formulated as s(t) = exp{ j 2π f 0 t + φ(t)}, 0 ≤ t ≤ τ

(1)

where f0 is the carrier frequency, τ is the pulse duration, and φ(t) is the random phase. When the pulse duration is set as the pulse repetition time, the signal is to be a continuous wave. The Fourier transform of s(t) is given by s(t)e− j 2π f t dt. (2) S( f ) =

R 1545-598X © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

138

Fig. 1.

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 15, NO. 1, JANUARY 2018

Assuming that the total number of the orthogonal noise signals is N, the i th signal denoted as sk (i, t) in the orthogonal signal library is assigned to be transmitted at the kth transmission. To further minimize the probability of mutual interference between the radars equipped with the proposed signals, at the kth transmission, the value of i is calculated as

Assignment of the signals for transmission.

As mentioned previously, the shape of the spectral distribution function of the signal determines the levels of sidelobes. In general, the lower sidelobes of nonrectangular functions have been obtained at the cost of broadening of the mainlobe width. In [30], an optimized Kaiser function was explored. The optimized function allows a better peak sidelobe ratio (PSLR) without broadening the mainlobe. Therefore, the mean spectral density distribution (PSD) function of the noise signals is defined by using the optimized Kaiser function, denoted as K( f ), where f is the frequency. The design of orthogonal noise signal s(t) is equivalent to recovery of s(t) when only the magnitude of S( f ), namely, |S( f )| = K( f ). As the Fourier transformation is bijective, this is equivalent to recovering the phase of S( f ). Hence, the design of noise signal becomes a problem of phase retrieval. Given observations on the magnitude of S( f ), phase retrieval seeks to reconstruct a complex signal, i.e., solve find s(t), 0 ≤ t ≤ τ s.t. |S( f )| = K( f ).

(3)

Many algorithms have been developed to solve the problem of phase retrieval. These methods include alternating projections, semidefinite programming, matrix completion-based, and sparsity-based [27]–[29]. Due to the fact that the signals are used as radar transmitted signals, the signals cannot be designed to possess sparsity. For reducing the interference, the signal waveforms are expected to possess good diversity. We apply one of the most popular methods, hybrid input– output method by Shechtman [29], to explore the orthogonal noise signals. The Fourier transformation and inverse Fourier transform are denoted as F(·) and F−1 (·), respecitvly. The method works as follows. 1) Initialization: Choose an initial s0 (t) = exp{ j φ(t)}, where φ(t) are white Gaussian phases, a parameter β > 0, and a convergence threshold = 1e − 16. 2) Loop: For i = 1, 2, . . . inductively set Si ( f ) = F(si−1 (t)) Si ( f ) = Si ( f ) − β si (t) = F−1 (Si ( f ))

Si ( f ) Si ( f ) − K( f ) |Si ( f )|

(4) (5) (6)

until convergence. The above-mentioned phase-retrieval problem yields a nonuniqueness solution. Thanks to nonuniqueness, the proposed method produces a group of orthogonal signals with different random phases but sharing the same spectral density. B. Interference Mitigation To mitigate the interferences, the orthogonal noise signals are successively modulated for transmission (see Fig. 1). The signal in the current transmitted pulse is orthogonal to the next transmitted signal. Simultaneously, the radar synchronizes the current-matched filter with the current-transmitted signal.

i = Randi (N)

(7)

where Randi (N) is a random integer generator that returns a pseudorandom scalar integer between 1 and N. The corresponding echo signal of sk (i, t) is written as rk (i, t − td ), where td is the delay time. The interference from the neighboring radar is denoted as I j (t), j = 1, 2, . . . , M, where M is the total number of the interferences. The received signals can be expressed as r (i, t) = rk (i, t − td ) + I j (t), j = 1, 2, . . . , M. The response of matched filter in the receiver can be formulated as [rk (i, t − td ) + I j (t)]s ∗k (i, t)dt ∗ = rk (i, t − td )s k (i, t)dt + I j (t)sk∗ (i, t)dt i = 1, 2, . . . , N, j = 1, 2, . . . , M

(8)

where ∗ is the conjugate operation. The first term in the righthand side of (8) is the desired response. The interferences generated by the transmission of the neighboring noise radar are orthogonal to the current-transmitted signal of the host noise radar. Hence, the output of the interference response in (8) is approximately zero, namely, I j (t)sk∗ (t)dt ≈ 0, j = 1, 2, . . . , M. III. N UMERICAL R ESULTS This section first analyzes the performance of the proposed orthogonal noise signal, and the simulation results are subsequently demonstrated in the presence of high interferences. A. Performances Analysis Fig. 2 shows the numerical results of the proposed orthogonal noise signals. Fig. 2(a) shows the real parts of the signals. The signals exhibit arbitrary waveforms. The total number of the signals N = 100. However, the PSD functions of these signals show great resemblance, as shown in Fig. 2(b). The PSD is consistent with the optimized Kaiser function in [30]. Considering the set 100 waveforms, the statistical analysis of the cross correlation values is shown in Fig. 2(c) and (d) to validate the orthogonality of the waveforms. Using radar ambiguity function, the effects of the Doppler phase shift are accurately shown in Fig. 2(e), demonstrating good Doppler tolerance. Furthermore, the proposed waveforms are compared with the RPN signals [23]. The bandwidth of the PRN signals is the same as the proposed signals. The comparison of the autocorrelation function (ACF) is shown in Fig. 2(f). The PSLR of PRN is −20.53 dB. In contrast, the PSLR of the proposed noise signal can be reduced to be −42.47 dB, by using the optimized Kaiser function as the PSD. B. Mitigation of Interferences A 24-GHz pulsed automotive radar system is used for simulations. The pulse duration and the bandwidth of signal are set as 1.42 μs and 600 MHz, respectively, as an

XU AND SHI: INTERFERENCE MITIGATION FOR AUTOMOTIVE RADAR USING ORTHOGONAL NOISE WAVEFORMS

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Fig. 2. Numerical results. (a) Real parts of the orthogonal noise waveforms. (b) Spectral distribution function of (a). (c) ACF. (d) Across correlation function (XCF). (e) Ambiguity function. (f) Comparisons of ACFs.

experimental study. The radar then electronically scans the beam of the antenna. A typical road environment is illustrated in Fig. 3, where a car, a pedestrian, and one interfering radar

are present. The car is located at a distance of 24.5 m in range. The size of the car is 5.5 m in length and 2.0 m in width. The pedestrian is located at a distance of 28.5 m in range.

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Fig. 3.

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 15, NO. 1, JANUARY 2018

Representative scenario designed for simulations.

Fig. 5. SINR = 10 dB. (a) LFM. (b) DCUC. (c) PRN. (d) Proposed method.

Fig. 4. SINR = 0 dB. (a) LFM. (b) DCUC. (c) PRN. (d) Proposed method.

The proposed method is compared with other related approaches, including the conventional linear frequencymodulated (LFM) [1], down-chirp, and up-chirp (DCUC) couples [3], and the PRN radar [23].

The essence of the proposed method for mitigating interfering signals is the use of the orthogonality noise signals. The signal in the current transmitted pulse is orthogonal to the next transmitted signal. On the other hand, the radar synchronizes the current-matched filter with the currenttransmitted signal. The current-matched filter is the conjugate of the current-transmitted signal. Consequently, the interfering signals are reduced by the current-matched filtering. Assuming that the number of the interference signal is M, the signal-to-interference and noise ratio (SINR) is

XU AND SHI: INTERFERENCE MITIGATION FOR AUTOMOTIVE RADAR USING ORTHOGONAL NOISE WAVEFORMS

TABLE I C OMPARISONS OF SINRs

calculated as SINR = M

j =1

PEcho PInterfence ( j ) + PNoise

(9)

where PEcho and PNoise are the power of the desired echo signal and the additive noise in the radar system, respectively, PInterfence ( j ) is the power of the j th interference signal. Representative experiments have been investigated in the presence of three interfering signals. Figs. 4 and 5 demonstrate the results of comparisons using the different signals. The results reveal that the strategy of using a DCUC signal cannot effectively suppress the interferences. In contrast, the use of noise waveforms can significantly reduce these undesired signals. By visual comparison, the image quality by the proposed method is better than that of the referred methods. Table I summarizes the SINRs before and after mitigation of interferences by using these different signals. The best results are highlighted in bold. Again, the proposed method produces the best improved SINRs. In summary, the comparisons demonstrate that the performance of the presented approach is superior to the existing methods. IV. C ONCLUSION This letter addresses the problem of neighboring interference of an automotive radar. To deal with this challenge, orthogonal noise waveforms have been designed by using a phase retrieval method. The proposed signals have been validated to be orthogonal with lower sidelobes. The performance assessment shows that the proposed method exhibits a significant performance improvement over the conventional radar waveforms in high interference environments. ACKNOWLEDGMENT The authors would like to thank the editors and reviewers for their invaluable comments that significantly improved the quality of this letter. R EFERENCES [1] S. M. Patole, M. Torlak, D. Wang, and M. Ali, “Automotive radars: A review of signal processing techniques,” IEEE Signal Process. Mag., vol. 34, no. 2, pp. 22–35, Mar. 2017. [2] T. Schipper, S. Prophet, M. Harter, L. Zwirello, and T. Zwick, “Simulative prediction of the interference potential between radars in common road scenarios,” IEEE Trans. Electromagn. Compat., vol. 57, no. 3, pp. 322–328, Jun. 2015. [3] G. M. Brooker, “Mutual interference of millimeter-wave radar systems,” IEEE Trans. Electromagn. Compat., vol. 49, no. 1, pp. 170–181, Feb. 2007. [4] H. Zhou, B. Wen, and S. Wu, “Dense radio frequency interference suppression in HF radars,” IEEE Signal Process. Lett., vol. 12, no. 5, pp. 361–364, May 2005. [5] Y. Gao, G. Liao, and W. Liu, “High-resolution radar detection in interference and nonhomogeneous noise,” IEEE Signal Process. Lett., vol. 23, no. 10, pp. 1359–1363, Oct. 2016.

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