时-空欠采样下多个信号的频率和DOA联合估计
|
摘要
针对时-空欠采样条件下多个入射信号的频率和波达方向(DOA)联合估计问题,提出了基于中国余数定理(CRT)的估计算法。利用稀疏分布的非均匀线阵对同时到达的多个入射信号进行多路的并行欠采样,借助AM估计器的谱校正,得到精确的谱峰位置余数和相位差余数。通过改进的重构多个整数的中国余数定理得到频率的估计值,并且根据该频率估计值和频率估计过程中的谱峰位置余数对多个信号和多组相位差余数进行配对,再通过闭式中国余数定理解决相位模糊问题,完成DOA估计。仿真结果验证了该算法的顽健性和高精度,并且阵列一次并行欠采样的样本同时为频率和DOA估计所用,算法耗时短,表明了其实际工程应用前景。
Aiming at the joint estimation of frequency and direction of arrival(DOA) of multiple incident signals under spatio-temporal undersampling condition, this paper proposes an estimation algorithm based on Chinese remainder theorem(CRT). Firstly, multi-path parallel undersampling is performed on multiple incident signals arriving at the same time by sparsely distributed non-uniform linear array. By means of spectrum correction of AM estimator, accurate spectral peak position remainder and phase difference remainder are obtained, and by the improved Chinese remainder theorem of the reconstructed multiple integers an estimate of frequency is obtained. And according to the frequency estimation value and the spectral peak position remainder in the process of frequency estimation, multiple signals and multiple sets of phase difference residues are paired, and then the phase ambiguity problem is solved by the closed Chinese remainder theorem, and thereby DOA estimation is completed. The simulation results verify the robustness and high precision of the algorithm, and the samples of one parallel under-sampling are used for both frequency and DOA estimation. The algorithm takes less time, which indicates its practical engineering application prospects.
Aiming at the joint estimation of frequency and direction of arrival(DOA) of multiple incident signals under spatio-temporal undersampling condition, this paper proposes an estimation algorithm based on Chinese remainder theorem(CRT). Firstly, multi-path parallel undersampling is performed on multiple incident signals arriving at the same time by sparsely distributed non-uniform linear array. By means of spectrum correction of AM estimator, accurate spectral peak position remainder and phase difference remainder are obtained, and by the improved Chinese remainder theorem of the reconstructed multiple integers an estimate of frequency is obtained. And according to the frequency estimation value and the spectral peak position remainder in the process of frequency estimation, multiple signals and multiple sets of phase difference residues are paired, and then the phase ambiguity problem is solved by the closed Chinese remainder theorem, and thereby DOA estimation is completed. The simulation results verify the robustness and high precision of the algorithm, and the samples of one parallel under-sampling are used for both frequency and DOA estimation. The algorithm takes less time, which indicates its practical engineering application prospects.
引文
[1]孙晓颖,陈建,林琳.基于时空处理的频率与二维DOA联合估计算法[J].通信学报,2009,30(8):39-44.
[2]KUMAR A A,RAZUL S G,SEE C M S.Carrier frequency and direction of arrival estimation with nested sub-nyquist sensor array receiver[C]//Proceedings of 2015 23rd European Signal Processing Conference(EUSIPCO).Nice,France,2015:1167-1171.
[3]LEMMA A N,VAN DER VEEN A J,DEPRETTERE E F.Analysis of joint angle-frequency estimation using ESPRIT[J].IEEE transactions on signal processing,2003,51(5):1264-1283.
[4]LIN J D,FANG W H,WANG Y Y,et al.FSF MUSIC for joint DOA and frequency estimation and its performance analysis[J].IEEE transactions on signal processing,2006,54(12):4529-4542.
[5]黄翔东,冼弘宇,闫子阳,等.时-空欠采样下的频率和DOA联合估计算法[J].通信学报,2016,37(5):21-28.
[6]梁红,张琦,杨长生.广义稳健的中国剩余定理及其在欠采样率下频率估计的应用[J].电子与信息学报,2010,32(8):1802-1805.
[7]冼弘宇.时空欠采样下基于中国余数定理的频率和DOA估计方法研究[D].天津:天津大学,2015:43-45.
[8]XIAO Hanshen,XIAO Guoqiang.Notes on CRT-based robust frequency estimation[J].Signal processing,2017,133:13-17.
[9]XIA Xianggen.On estimation of multiple frequencies in undersampled complex valued waveforms[J].IEEEtransactions on signal processing,1999,47(12):3417-3419.
[10]WANG Wenjie,XIA Xianggen.A closed-form robust Chinese remainder theorem and its performance analysis[J].IEEE transactions on signal processing,2010,58(11):5655-5666.
[11]XIAO Li,XIA Xianggen,WANG Wenjie.Multi-stage robust Chinese remainder theorem[J].IEEE transactions on signal processing,2014,62(18):4772-4785.
[12]CHESSA S,MAESTRINI P.Robust distributed storage of residue encoded data[J].IEEE transactions on information theory,2012,58(12):7280-7294.
[13]LIANG Hong,ZHANG Heng,JIA Ning.A generalized robust Chinese remainder theorem for multiple numbers and its application in multiple frequency estimation with low sampling rates[C]//Proceeding of the 2011 IEEEInternational Conference on Signal Processing,Communi cations and Computing(ICSPCC).Xi'an,China,2011.
[2]KUMAR A A,RAZUL S G,SEE C M S.Carrier frequency and direction of arrival estimation with nested sub-nyquist sensor array receiver[C]//Proceedings of 2015 23rd European Signal Processing Conference(EUSIPCO).Nice,France,2015:1167-1171.
[3]LEMMA A N,VAN DER VEEN A J,DEPRETTERE E F.Analysis of joint angle-frequency estimation using ESPRIT[J].IEEE transactions on signal processing,2003,51(5):1264-1283.
[4]LIN J D,FANG W H,WANG Y Y,et al.FSF MUSIC for joint DOA and frequency estimation and its performance analysis[J].IEEE transactions on signal processing,2006,54(12):4529-4542.
[5]黄翔东,冼弘宇,闫子阳,等.时-空欠采样下的频率和DOA联合估计算法[J].通信学报,2016,37(5):21-28.
[6]梁红,张琦,杨长生.广义稳健的中国剩余定理及其在欠采样率下频率估计的应用[J].电子与信息学报,2010,32(8):1802-1805.
[7]冼弘宇.时空欠采样下基于中国余数定理的频率和DOA估计方法研究[D].天津:天津大学,2015:43-45.
[8]XIAO Hanshen,XIAO Guoqiang.Notes on CRT-based robust frequency estimation[J].Signal processing,2017,133:13-17.
[9]XIA Xianggen.On estimation of multiple frequencies in undersampled complex valued waveforms[J].IEEEtransactions on signal processing,1999,47(12):3417-3419.
[10]WANG Wenjie,XIA Xianggen.A closed-form robust Chinese remainder theorem and its performance analysis[J].IEEE transactions on signal processing,2010,58(11):5655-5666.
[11]XIAO Li,XIA Xianggen,WANG Wenjie.Multi-stage robust Chinese remainder theorem[J].IEEE transactions on signal processing,2014,62(18):4772-4785.
[12]CHESSA S,MAESTRINI P.Robust distributed storage of residue encoded data[J].IEEE transactions on information theory,2012,58(12):7280-7294.
[13]LIANG Hong,ZHANG Heng,JIA Ning.A generalized robust Chinese remainder theorem for multiple numbers and its application in multiple frequency estimation with low sampling rates[C]//Proceeding of the 2011 IEEEInternational Conference on Signal Processing,Communi cations and Computing(ICSPCC).Xi'an,China,2011.