Support Recovery for MWC Based on Random Reduction and Null Space

摘要

The recently proposed Modulated Wideband Converter (MWC) sampling method, for sparse wideband signals, can implement sampling without distortion at a rate lower than that prescribed by Nyquist, which alleviates the pressure from high sampling rate. However, the existing recovery algorithm of MWC is far from satisfactory in terms of recovery performance. In this paper, a high-performance recovery algorithm for support is proposed, combining null space and random dimensionality reduction methods. The proposed algorithm firstly uses random transform to convert the sampling equation to a multiple-measurement-vector problem with low dimension, and then utilizes the orthogonal relation between null space and the sampling matrix to judge the support set. Finally the accurate reconstruction is performed by pseudo-inverse operation. The experimental results show that this algorithm can significantly improve the success rate of recovery compared with the traditional OMPMMV algorithm.