基于Rao检验的信号统计分辨界分析
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摘要
针对基于广义似然比检验(GLRT)的信号统计分辨界(SRL)分析存在计算较复杂、难以得到检测统计量解析表达式等问题,提出了一种基于Rao检测的SRL分析方法。分析了噪声方差已知和未知两种情形下的信号一维方位角SRL以及噪声方差已知时的信号二维方位角及俯仰角SRL,推导得到了Rao检测统计量以及对应SRL所需的最小信噪比(SNR),分析了检测性能、计算复杂度,并与GLRT方法进行了对比。仿真实验验证了Rao检测方法的有效性。
Since the approach of analyzing statistical resolution limit(SRL) based on generalized likelihood ratio test(GLRT) has the problems of high computational complexity and isn't easy to get the analytical formula of the detection statistics, a method for the analysis of the SRL based on Rao test was proposed. The unidimensional SRL of azimuth under the cases of known and unknown noise variance, two-dimensional SRL of azimuth and elevation under the case of known noise variance were analyzed. The Rao test detection statistic and the minimum SNR required for the corresponding SRL were derived, the detection performance and the computational complexity of the Rao test were analyzed and compared with the GLRT method. Simulation results verify the validity of the Rao test.
Since the approach of analyzing statistical resolution limit(SRL) based on generalized likelihood ratio test(GLRT) has the problems of high computational complexity and isn't easy to get the analytical formula of the detection statistics, a method for the analysis of the SRL based on Rao test was proposed. The unidimensional SRL of azimuth under the cases of known and unknown noise variance, two-dimensional SRL of azimuth and elevation under the case of known noise variance were analyzed. The Rao test detection statistic and the minimum SNR required for the corresponding SRL were derived, the detection performance and the computational complexity of the Rao test were analyzed and compared with the GLRT method. Simulation results verify the validity of the Rao test.
引文
[1]LIU Z,NEHORAI A.Statistical angular resolution limit for point sources[J].IEEE Transactions on Signal Processing,2007,55(11):5521-5527.
[2]COX H.Resolving power and sensitivity to mismatch of optimum array processors[J].Journal of the Acoustical Society of America,1973,54(3):771-785.
[3]SHARMAN K,DURRANI T.Resolving power of signal subspace methods for fnite data lengths[C]//IEEE International Conference on Acoustics,Speech&Signal,April 26-29,1985,Florida,USA.New Jersey:IEEE Press,1985:1501-1504.
[4]LEE H B.The Cramer-Rao bound on frequency estimates of signals closely spaced in frequency(unconditional case)[J].IEEE Transactions on Signal Processing,1994,42(6):1569-1572.
[5]SMITH S T.Statistical resolution limits and the complexified Cramer-Rao bound[J].IEEE Transactions on Signal Processing,2005,53(5):1597-1609.
[6]DING-HONG L U,YANG L I,LIANG C J,et al.Statistical resolution limit for closely spaced targets based on Cramer-Rao bound[J].Transactions of Beijing Institute of Technology,2014.
[7]BAO T,EL KORSO M N,OUSLIMANI H H.Cramér-Rao bound and statistical resolution limit investigation for near-field source localization[J].Digital Signal Processing,2016,48(C):137-147.
[8]XIE N,GUO W,ZHANG L,et al.High resolution DOA estimation method in MIMO radar[J].Wireless Personal Communications,2016,91(1):219-236.
[9]SHAHRAM M,MILANFAR P.Statistical and information-theoretic analysis of resolution in imaging[J].IEEE Transactions on Information Theory,2006,52(8):3411-3437.
[10]ZHU W,TANG J,WAN S.Angular resolution limit of two closely-spaced point sources based on hypothesis testing[C]//IEEE International Conference on Acoustics,Speech and Signal Processing,May 26-31,2013,Vancouver,British Columbia,Canada.New Jersey:IEEE Press,2013:3905-3909.
[11]EL KORSO M N,BOYER R,RENAUX A,et al.On the asymptotic resolvability of two point sources in known subspace interference using a GLRT-based framework[J].Signal Processing,2012,92(10):2471-2483.
[12]SHAHRAM M,MILANFAR P.On the resolvability of sinusoids with nearby frequencies in the presence of noise[J].IEEE Transactions on Signal Processing,2005,53(7):2579-2588.
[13]ZHU W,TANG J,WAN S.Angular resolution limit of two closely-spaced point sources based on information theoretic criteria[C]//IEEE International Conference on Acoustics,Speech and Signal Processing,May 4-9,2014,Florence,Italy.New Jersey:IEEE Press,2014:86-90.
[14]PRIBIC R,COUTINO M,LEUS G.Stochastic resolution analysis of co-prime arrays in radar[C]//IEEE Statistical Signal Processing Workshop,June 26-29,2016,Palma de Mallorca,Spain.New Jersey:IEEE Press,2016:1-5.
[15]PRIBIC R.Stochastic resolution analysis via a GLR test in radar[C]//International Workshop on Compressed Sensing Theory and ITS Applications To Radar,Sonar and Remote Sensing,September 16-22,2016,Aachen,Germany.[S.l.:s.n.],2016:168-172.
[16]GAO Y,LIAO G,LIU W.High-resolution radar detection in interference and nonhomogeneous noise[J].IEEE Signal Processing Letters,2016,23(10):1359-1363.
[17]KORSO M N E,BOYER R,RENAUX A,et al.Statistical resolution limit for the multidimensional harmonic retrieval model:hypothesis test and Cramér-Rao bound approaches[J].EURASIP Journal on Advances in Signal Processing,2011(1):1-14.
[18]ZHOU X,WANG H,CHENG Y,et al.Statistical spatial resolution limit for ultrawideband MIMO noise radar[C]//Statistical Signal Processing,June 29-July 2,2014,Jupiters,Gold Coast,Australia.New Jersey:IEEE Press,2014:440-443.
[19]KORSO M N E,BOYER R,RENAUX A,et al.A GLRT-based framework for the Multidimensional Statistical Resolution Limit[C]//IEEE Statistical Signal Processing Workshop,June 28-30,2011,Nice,France.New Jersey:IEEE Press,2011:453-456.
[20]EL KORSO M N,BOYER R,RENAUX A,et al.Statistical resolution limit for source localization with clutter interference in a MIMO radar context[J].IEEE Transactions on Signal Processing,2012,60(2):987-992.
[21]KAY S M.Fundamentals of statistical signal processing:detection theory volume II[M].London:Prentice-Hall PTR,1998.
[2]COX H.Resolving power and sensitivity to mismatch of optimum array processors[J].Journal of the Acoustical Society of America,1973,54(3):771-785.
[3]SHARMAN K,DURRANI T.Resolving power of signal subspace methods for fnite data lengths[C]//IEEE International Conference on Acoustics,Speech&Signal,April 26-29,1985,Florida,USA.New Jersey:IEEE Press,1985:1501-1504.
[4]LEE H B.The Cramer-Rao bound on frequency estimates of signals closely spaced in frequency(unconditional case)[J].IEEE Transactions on Signal Processing,1994,42(6):1569-1572.
[5]SMITH S T.Statistical resolution limits and the complexified Cramer-Rao bound[J].IEEE Transactions on Signal Processing,2005,53(5):1597-1609.
[6]DING-HONG L U,YANG L I,LIANG C J,et al.Statistical resolution limit for closely spaced targets based on Cramer-Rao bound[J].Transactions of Beijing Institute of Technology,2014.
[7]BAO T,EL KORSO M N,OUSLIMANI H H.Cramér-Rao bound and statistical resolution limit investigation for near-field source localization[J].Digital Signal Processing,2016,48(C):137-147.
[8]XIE N,GUO W,ZHANG L,et al.High resolution DOA estimation method in MIMO radar[J].Wireless Personal Communications,2016,91(1):219-236.
[9]SHAHRAM M,MILANFAR P.Statistical and information-theoretic analysis of resolution in imaging[J].IEEE Transactions on Information Theory,2006,52(8):3411-3437.
[10]ZHU W,TANG J,WAN S.Angular resolution limit of two closely-spaced point sources based on hypothesis testing[C]//IEEE International Conference on Acoustics,Speech and Signal Processing,May 26-31,2013,Vancouver,British Columbia,Canada.New Jersey:IEEE Press,2013:3905-3909.
[11]EL KORSO M N,BOYER R,RENAUX A,et al.On the asymptotic resolvability of two point sources in known subspace interference using a GLRT-based framework[J].Signal Processing,2012,92(10):2471-2483.
[12]SHAHRAM M,MILANFAR P.On the resolvability of sinusoids with nearby frequencies in the presence of noise[J].IEEE Transactions on Signal Processing,2005,53(7):2579-2588.
[13]ZHU W,TANG J,WAN S.Angular resolution limit of two closely-spaced point sources based on information theoretic criteria[C]//IEEE International Conference on Acoustics,Speech and Signal Processing,May 4-9,2014,Florence,Italy.New Jersey:IEEE Press,2014:86-90.
[14]PRIBIC R,COUTINO M,LEUS G.Stochastic resolution analysis of co-prime arrays in radar[C]//IEEE Statistical Signal Processing Workshop,June 26-29,2016,Palma de Mallorca,Spain.New Jersey:IEEE Press,2016:1-5.
[15]PRIBIC R.Stochastic resolution analysis via a GLR test in radar[C]//International Workshop on Compressed Sensing Theory and ITS Applications To Radar,Sonar and Remote Sensing,September 16-22,2016,Aachen,Germany.[S.l.:s.n.],2016:168-172.
[16]GAO Y,LIAO G,LIU W.High-resolution radar detection in interference and nonhomogeneous noise[J].IEEE Signal Processing Letters,2016,23(10):1359-1363.
[17]KORSO M N E,BOYER R,RENAUX A,et al.Statistical resolution limit for the multidimensional harmonic retrieval model:hypothesis test and Cramér-Rao bound approaches[J].EURASIP Journal on Advances in Signal Processing,2011(1):1-14.
[18]ZHOU X,WANG H,CHENG Y,et al.Statistical spatial resolution limit for ultrawideband MIMO noise radar[C]//Statistical Signal Processing,June 29-July 2,2014,Jupiters,Gold Coast,Australia.New Jersey:IEEE Press,2014:440-443.
[19]KORSO M N E,BOYER R,RENAUX A,et al.A GLRT-based framework for the Multidimensional Statistical Resolution Limit[C]//IEEE Statistical Signal Processing Workshop,June 28-30,2011,Nice,France.New Jersey:IEEE Press,2011:453-456.
[20]EL KORSO M N,BOYER R,RENAUX A,et al.Statistical resolution limit for source localization with clutter interference in a MIMO radar context[J].IEEE Transactions on Signal Processing,2012,60(2):987-992.
[21]KAY S M.Fundamentals of statistical signal processing:detection theory volume II[M].London:Prentice-Hall PTR,1998.