Subsampled circulant matrix based analogue compressed sensing

The modulated wideband converter (MWC) is an attractive analogue compressed sensing technique proposed recently. Unfortunately, the MWC has high hardware complexity owing to its parallel structure. To reduce the complexity, proposed is a novel subsampled circulant matrix based analogue compressed sensing (SCM-ACS) scheme. Using the cyclic shifts of the Zadoff-Chu sequence, the SCM-ACS scheme reduces the number of physical parallel channels from m to 1 with larger processing time, where m ranges from several dozen to several hundred. It is proved that when m=O(r log²M log³r) the measurement matrix of the SCM-ACS scheme satisfies the restricted isometry property condition with probability 1-M^-O(1), where M is the length of the Zadoff-Chu sequence, and r is the sparsity of the input signal. Simulation results show that the SCM-ACS scheme outperforms the MWC on recovery performance.