非准确先验知识下认知雷达低峰均比稳健波形设计
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摘要
针对目标和杂波先验知识不准确时认知雷达的检测波形设计问题,同时兼顾功率放大器对低峰均比(PAR)波形的需求,该文提出一种信号相关杂波背景下认知雷达低PAR稳健波形设计方法。首先,在目标和杂波不确定集范围内,基于极大极小化准则构造关于输出信干噪比(SINR)的优化模型;然后将不确定性参数代入该模型,给出最差SINR下对应杂波协方差矩阵和目标Toeplitz矩阵的取值;在此基础上,利用半正定松弛,将非凸的优化模型转化为关于发射波形半正定矩阵的凸问题进行求解;最后,通过秩1近似法结合最近邻方法,进一步从波形的最优矩阵解中提取出最优向量解。分析表明,在稳健性能相同的情况下,与现有方法相比该算法具有更低的运算量,仿真结果验证了所提方法的有效性和稳健性。
In view of the detection waveform design for cognitive radar with imprecise prior knowledge of target and clutter, while considering the demand of power amplifier on low Peak-to-Average power Ratio(PAR) waveform, a low-PAR robust waveform design method in presence of signal-dependent clutter is proposed. Firstly, the optimization model of radar's output Signal-to-Interference-plus-Noise Ratio(SINR) is established within the uncertainty of target and clutter via Max-Min method. Secondly, the clutter covariance matrix and Toeplitz matrix of target corresponding to worst-case SINR is obtained. Since the optimization problem of waveform is non-convex, Semi-Definite Relaxation(SDR) is adopted to converse the non-convex problem into a convex problem, which is about the semi-definite matrix of waveform. Finally, the optimal vector solution of waveform can be extracted from the optimal matrix solution by the rank-one approximation method combined with the nearest neighbor method. Compared with the existing methods, the computational complexity of the proposed method is obviously reduced without losing robust performance according to the analysis. The simulation results demonstrate the effectiveness and robustness of the proposed method.
In view of the detection waveform design for cognitive radar with imprecise prior knowledge of target and clutter, while considering the demand of power amplifier on low Peak-to-Average power Ratio(PAR) waveform, a low-PAR robust waveform design method in presence of signal-dependent clutter is proposed. Firstly, the optimization model of radar's output Signal-to-Interference-plus-Noise Ratio(SINR) is established within the uncertainty of target and clutter via Max-Min method. Secondly, the clutter covariance matrix and Toeplitz matrix of target corresponding to worst-case SINR is obtained. Since the optimization problem of waveform is non-convex, Semi-Definite Relaxation(SDR) is adopted to converse the non-convex problem into a convex problem, which is about the semi-definite matrix of waveform. Finally, the optimal vector solution of waveform can be extracted from the optimal matrix solution by the rank-one approximation method combined with the nearest neighbor method. Compared with the existing methods, the computational complexity of the proposed method is obviously reduced without losing robust performance according to the analysis. The simulation results demonstrate the effectiveness and robustness of the proposed method.
引文
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[21]TROPP J A,DHILLON I S,HEATH R W,et al.Designing structured tight frames via an alternating projection method[J].IEEE Transactions on Information Theory,2005,51(1):188-209.doi:10.1109/TIT.2004.839492.
[22]YANG Yang and BLUM R S.MIMO radar waveform design based on mutual information and minimum mean-square error estimation[J].IEEE Transactions on Aerospace and Electronic Systems,2007,43(1):330-343.doi:10.1109/TAES.2007.357137.
[2]GUERCI J R.Cognitive radar:The Knowledge-Aided Fully Adaptive Approach[M].Norwood,MA,Artech House,Inc.,2010:13-30.
[3]冯翔,陈志坤,赵宜楠,等.基于联合优化松弛交替投影的组网雷达恒模波形设计[J].电子与信息学报,2016,38(7):1745-1751.doi:10.11999/JEIT151152.FENG Xiang,CHEN Zhikun,ZHAO Yinan,et al.Unimodular waveforms design for netted radar system via joint optimization relaxed alternating projection[J].Journal of Electronics&Information Technology,2016,38(7):1745-1751.doi:10.11999/JEIT151152.
[4]HE Yan,JIAN Tao,SU Feng,et al.Novel range-spread target detectors in non-gaussian clutter[J].IEEE Transactions on Aerospace and Electronic Systems,2010,46(3):1312-1328.doi:10.1109/TAES.2010.5545191.
[5]CHEN Chunyang and VAIDYANATHAN P P.MIMO radar waveform optimization with prior information of the extended target and clutter[J].IEEE Transactions on Signal Processing,2009,57(9):3533-3544.doi:10.1109/TSP.2009.2021632.
[6]NAGHSH M M,SOLTANALIAN M,PETRE S,et al.A Doppler robust design of transmit sequence and receiver filter in the presence of signal-dependent interference[J].IEEE Transactions on Signal Processing,2014,62(4):772-785.doi:10.1109/TSP.2013.2288082.
[7]ZHU Wei and TANG Jun.Robust design of transmit waveform and receive filter for colocated MIMO radar[J].IEEE Signal Processing Letters,2015,22(11):2112-2116.doi:10.1109/LSP.2015.2461460.
[8]TANG Bo and TANG Jun.Robust waveform design of wideband cognitive radar for extended target detection[C].IEEE International Conference on Acoustics,Speech and Signal Processing,Shanghai,China,2016:3096-3100.doi:10.1109/ICASSP.2016.7472247.
[9]ZHANG Xin and CUI Chen.Robust transmitted waveform and received filter design for cognitive radar in the presence of signal-dependent interference[J].Circuits,Systems,and Signal Processing,2013,32(6):3013-3029.doi:10.1007/s00034-013-9611-6.
[10]JIU Bo,LIU Hongwei,FENG Dazheng,et al.Minimax robust transmission waveform and receiving filter design for extended target detection with imprecise prior knowledge[J].Signal Processing,2012,92(1):210-218.doi:10.1016/j.sigpr.2011.07.008.
[11]KARBASI S M,AUBRY A,MAIO A D,et al.Robust design of transmit code and receive filter for extended targets in clutter[J].IEEE Transactions on Signal Processing,2015,63(8):1965-1976.doi:10.1109/TSP.2015.2404301.
[12]YUE Wenzhen,ZHANG Yan,LIU Yimin,et al.Radar constant-modulus waveform design with prior information of the extended target and clutter[J].Sensors,2016,16(6):889-910.doi:10.3390/s16060889.
[13]ROMERO R A,BAE J H,and GOODMAN N A.Theory and application of SNR and mutual information matched illumination waveforms[J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(2):912-927.doi:10.1109/TAES.2011.5751234.
[14]STOICA P,HE Hao,and LI Jian.Optimization of the receive filter and transmit sequence for active sensing[J].IEEE Transactions on Signal Processing,2012,60(4):1730-1740.doi:10.1109/TSP.2011.2179652.
[15]LI Jian,STOICA P,and WANG Zhisong.On robust capon beamforming and diagonal loading[J].IEEE Transactions on Signal Processin,2003,51(7):1072-1715.doi:10.1109/TSP.2003.812831.
[16]李秀友,薛永华,黄勇,等.基于不确定集的稳健MIMO雷达波形设计算法[J].电子与信息学报,2016,38(10):2445-2452.doi:10.11999/JEIT151425.LI Xiuyou,XUE Yonghua,HUANG Yong,et al.Robust MIMO radar waveform design algorithm based on uncertainty set[J].Journal of Electronics&Information Technology,2016,38(10):2445-2452.doi:10.11999/JEIT151425.
[17]张贤达.矩阵分析与应用[M].第2版,北京:清华大学出版社,2013:447-450.ZHANG Xianda.Matrix Analysis and Application[M].Second Edition,Beijing:Tsinghua University Press,2013:447-450.
[18]HORN R A and JOHNSON C R.Matrix Analysis[M].Cambridge:Cambridge University Press,2012:86-100.
[19]LUO Zhiquan,MA W K,SO A M C,et al.Semidefinite relaxation of quadratic optimization problems[J].IEEE Signal Processing Magazine,2010,27(3):20-34.doi:10.1109/MSP.2010.936019.
[20]PATAKI G.On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues[J].Mathematics of Operations Research,1998,23(2):339-358.
[21]TROPP J A,DHILLON I S,HEATH R W,et al.Designing structured tight frames via an alternating projection method[J].IEEE Transactions on Information Theory,2005,51(1):188-209.doi:10.1109/TIT.2004.839492.
[22]YANG Yang and BLUM R S.MIMO radar waveform design based on mutual information and minimum mean-square error estimation[J].IEEE Transactions on Aerospace and Electronic Systems,2007,43(1):330-343.doi:10.1109/TAES.2007.357137.