A Subspace Searching Approximation Message Passing Algorithm for Single Snapshot DOA Estimation
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摘要: 压缩感知（Compressed sensing，CS）技术应用于单快拍波达方向（Direction of arrival，DOA）估计中可以实现相关信号的超分辨估计，但会遇到感知矩阵高相干性以及对噪声敏感的问题.本文提出一种基于近似消息传递的子空间搜索算法以解决上述问题.该算法首先通过近似消息传递算法得到一个粗解，随后利用该粗解划分子空间，最后在子空间中寻找精确解.仿真结果验证了所提算法的有效性.文章最后通过理论分析了该算法性能并讨论了算法在信号数未知时的扩展应用.Abstract: When compressed sensing (CS) is applied to single snapshot direction of arrival (DOA) estimation, super-resolution reconstruction of the correlated signals becomes possible. However, problems such as high coherent sensing matrix and noise sensitivity come into being at the same time. In order to solve these problems, an approximate message passing based subspace search algorithm is proposed. Firstly, a rough solution is obtained by approximate message passing algorithm. Secondly, subspaces are divided according to the rough solution. Thirdly, an exact solution is found by searching the subspaces. Simulation results show the effectiveness of the proposed approach. Finally, the performance of the proposed algorithm is analzed, and the application in which the number of signals is unknown is discussed as well the performance.1) 本文责任编委 辛景民
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表 1 SSAMP算法伪代码
Table 1 SSAMP algorithm pseudocode
输入: $A$, ${\pmb y}$, ${\tau_0}$, $K$ 输出: ${\widehat {\pmb x}}$ 初始化: ${\pmb x}^0, {\pmb z}^0, {\tau}^0, res1, res1_{\rm old}$ 求粗解: while($res1 < res1_{\rm old}$) $res1_{\rm old}=res1$ 由AMP算法公式更新${\pmb x}^t, {\pmb z}^t, {\tau }^t, res1$ end ${\pmb x}_{\rm rough}={\pmb x}^t$ 划分子空间: for $\forall {\pmb x}_{{\rm rough}, i} \ne 0$ if ${\pmb x}_{{\rm rough}, i-1} =0: r=r+1, Supp_r \leftarrow i $ elseif ${\pmb x}_{{\rm rough}, i-1} \ne 0: r=r, Supp_r \leftarrow i$ end end $S_r=Supp_r$的中位数 求精确解: 尝试解支撑集$S=\bigcup\limits_{r = 1}^{{N_R}} {{S_r}}$, $N_{sol}=K-N_r+1$ for $r=1:N_r$ for $p=1:N_{sol}$ $T=$所有$Supp_r$中$p$元备选支撑集组合 遍历$T$, 找出$p$元最优解$S_r^{(p)}$及相应残差$res2_r^{(p)}$ if $res2_r^{(p)}>res2_r^{(p-1)}$且$p \ge 2$ break end end 更新$S$, $N_{sol}=K-{\rm size}(S)+1$ end 求最终解: ${\widehat {\pmb x}}=A_S^*{\pmb y}$ 
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[1] Schmidt R. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 1986, 34(3):276-280 doi: 10.1109/TAP.1986.1143830 [2] Roy R, Paulraj A, Kailath T. ESPRIT-a subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986, 34(5):1340-1342 doi: 10.1109/TASSP.1986.1164935 [3] Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306 doi: 10.1109/TIT.2006.871582 [4] Malioutov D, Cetin M, Willsky A S. A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Transactions on Signal Processing, 2005, 53(8):3010-3022 doi: 10.1109/TSP.2005.850882 [5] Kim J M, Lee O K, and Ye J C. Compressive MUSIC:revisiting the link between compressive sensing and array signal processing. IEEE Transactions on Information Theory, 2012, 58(1):278-301 doi: 10.1109/TIT.2011.2171529 [6] 王秀红, 毛兴鹏, 张乃通.基于CS的脉冲压缩雷达单快拍DOA估计.系统工程与电子技术, 2014, 36(9):1737-1743 doi: 10.3969/j.issn.1001-506X.2014.09.11Wang Xiu-Hong, Mao Xing-Peng, Zhang Nai-Tong. Single-snap DOA estimation based on compressed sensing in pulse compression radar system. Systems Engineering and Electronics, 2014, 36(9):1737-1743 doi: 10.3969/j.issn.1001-506X.2014.09.11 [7] Liu J, Mallick M, Han C Z, Yao X H, Lian F. Similar sensing matrix pursuit:an efficient reconstruction algorithm to cope with deterministic sensing matrix. Signal Processing, 2014, 95:101-110 doi: 10.1016/j.sigpro.2013.08.009 [8] Liu J, Mallick M, Lian F, Han C Z, Sheng M X, Yao X H. General similar sensing matrix pursuit:An efficient and rigorous reconstruction algorithm to cope with deterministic sensing matrix with high coherence. Signal Processing, 2015, 114:150-163 doi: 10.1016/j.sigpro.2015.03.002 [9] Donoho D L, Maleki A, Montanari A. Message passing algorithms for compressed sensing: Ⅰ. Motivation and construction. In: Proceedings of the 2010 Information Theory Workshop on Information Theory. Cairo, Egypt: IEEE, 2010. 1-5 [10] Donoho D L, Maleki A, Montanari A. Message passing algorithms for compressed sensing: Ⅱ. Analysis and Validation. In: Proceedings of the 2010 IEEE Information Theory Workshop on Information Theory. Cairo, Egypt: IEEE, 2010. 6-10 http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5503228 [11] Rangan S. Generalized approximate message passing for estimation with random linear mixing. In: Proceedings of the 2011 IEEE International Symposium on Information Theory Proceedings (ISIT). St Petersburg, Russia: IEEE, 2011. 2168-2172 http://arxiv.org/abs/1010.5141 [12] Vila J P, Schniter P. Expectation-maximization Gaussian-mixture approximate message passing. IEEE Transactions on Signal Processing, 2013, 61(19):4658-4672 doi: 10.1109/TSP.2013.2272287 [13] Tan J, Ma Y T, Baron D. Compressive imaging via approximate message passing with image denoising. IEEE Transactions on Signal Processing, 2015, 63(8):2085-2092 doi: 10.1109/TSP.2015.2408558 [14] 任越美, 张艳宁, 李映.压缩感知及其图像处理应用研究进展与展望.自动化学报, 2014, 40(8):1563-1575 http://www.aas.net.cn/CN/abstract/abstract18426.shtmlRen Yue-Mei, Zhang Yan-Ning, Li Ying. Advances and perspective on compressed sensing and application on image processing. Acta Automatica Sinica, 2014, 40(8):1563-1575 http://www.aas.net.cn/CN/abstract/abstract18426.shtml [15] Ziniel J, Schniter P. Dynamic compressive sensing of time-varying signals via approximate message passing. IEEE Transactions on Signal Processing, 2013, 61(21):5270-5284 doi: 10.1109/TSP.2013.2273196 [16] Orlando D, Venturino L, Lops M, Ricci G. Track-before-detect strategies for STAP radar. IEEE Transactions on Signal Processing, 2010, 58(2):933-938 doi: 10.1109/TSP.2009.2032991 [17] Richards M A. Fundamentals of Radar Signal Processing. New York:McGraw-Hill, 2005. 88-92 [18] Maleki A, Montanari A. Analysis of approximate message passing algorithm. In: Proceedings of Information Sciences and Systems. Princeton, USA: IEEE, 2010. 1-7 http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5464887 [19] Elad M. Sparse and Redundant Representations. New York:Springer, 2010. 65-68 [20] Wei D, Milenkovic O. Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 2009, 55(5):2230-2249 doi: 10.1109/TIT.2009.2016006 -
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