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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