基于随机投影思想的MWC亚奈奎斯特采样重构算法

针对现有调制宽带转换器（Modulated Wideband Converter，MWC）亚奈奎斯特采样重构算法性能不高问题，提出了一种基于随机投影思想的重构算法.该算法首先将MWC所获得的测量值矩阵通过随机投影方法压缩成具有较少向量的新的测量值矩阵，然后利用所提出的求解器求解多测量向量问题，通过检验和重复尝试性求解过程提高MWC的重构性能.从理论和实验两个方面验证了所提出的算法的有效性.实验结果表明，与著名的ReMBo算法相比，该算法有效提高了重构成功率；当信号的频带数相同时，精确重构所需的硬件通道数更小；在相同的硬件通道数前提下，可重构的信号频带数更高.该算法与ReMBo相比运算时间并没有大幅度增加，当信号频带数较大时，不仅重构性能高，而且运算时间比ReMBo小.

A Recovery Algorithm of MWC Sub-Nyquist Sampling Based on Random Projection Method

The existing recovery algorithm of modulated wideband converter (MWC)-based sub-Nyquist sampling is far from satisfactory.Aiming at this problem,a recovery algorithm for MWC based on random projection method is proposed.This algorithm projects the measurement value matrix of MWC onto a random matrix with lower dimension to form a new measurement value matrix,and then solves a multiple measurement vector problem using a solver proposed.The recovery performance is enhanced through examining and repeating the tentative solving processes.This paper validates the effectiveness of the algorithm from both theoretical and experimental perspectives.Numerical experiments demonstrate that,compared with the popular ReMBo algorithm,the proposed algorithm significantly improves the success rate of recovery.From the same number of channels a signal with more spectral bands can be recovered by this algorithm,and a signal with the same number of bands can be recovered using fewer channels.Furthermore,the run time of this algorithm does not increase greatly.In contrast,compared with ReMBo,this algorithm can use a lower time cost to achieve a higher recovery performance when the spectral bands of the signal exceed a specific number.