L1-analysis稀疏重构在阵列信号恢复及波达角估计中的应用

通过适当的空域稀疏化构造了可对阵列接收信号进行冗余稀疏表示的阵列流形矩阵，建立了相应的L1-analysis稀疏重构模型用于恢复阵列接收信号，重点证明了该流形矩阵是满足L1-analysis 稀疏重构条件的紧框架，从理论上保证了将L1-analysis 稀疏重构用于阵列接收信号恢复及波达角估计问题的合理性，并推导出信号恢复误差的理论上界。利用在微波暗室环境中采集的实测数据，结合MUSIC算法进行实验验证，结果表明基于L1-analysis 稀疏重构的信号恢复对提高低信噪比环境下的波达角估计性能是有效的。

Reconstruction of array output and Direction-of-Arrival estimation via L1 -analysis sparse recovery

The array manifold matrix was constructed as a redundant dictionary in which the array receiving signals were sparse through the appropriate spatial sparse division, and the corresponding L1-analysis sparse recovery model was established to reconstruct the array output data. The core of this paper is the fact that it was proved that the manifold matrix was a tight frame and satisfied the condition which guaranteed accurate recovery of signals through L1-analysissparse recovery so that it was reasonable enough to use L1-analysissparsity optimization to reconstruct the array output data. The upper bound of reconstruction error was given. The effectiveness of this presented method for improving the performance of DOA estimation with low SNR were verified by the experiments using the actual measurement data received in microwave darkroom through MUSIC algorithm.