Compressed Sensing of Block Sparse Signals with Application to Wideband Spectrum Sensing

In many applications of compressed sensing, the signal is block sparse. Here, we propose a family of iterative algorithms for the recovery of block sparse signals, referred to as iterative reweighted $\ell_2/\ell_1$ minimization algorithms (IR-$\ell_2/\ell_1$).As an example, we apply the proposed algorithms to wideband spectrum sensing (WSS). Our simulation and analytical results on the recovery of both ideally and approximately block sparse signals show that the proposed iterative algorithms have significant advantages in terms of accuracy and the number of required measurements over the existing methods.We also propose a of reweighting scheme for the recovery block sparse signals with known borders to improve the performance of the so-called approximate message passing (AMP) algorithm.For the case of unknown borders, we propose an iterative algorithm which combines a border detection scheme with a recovery algorithm for block sparse signals with known borders. Simulation results, both in noiseless and noisy scenarios, show a considerably better performance/complexity trade-off compared to other state-of-the-art recovery algorithms.WSS is a significant challenge in cognitive radios (CRs) due to requiring very high-speed analog-to-digital converters (ADCs), operating at or above the Nyquist rate. Here, we first propose a very low-complexity zero-block detection scheme that can detect a large fraction of spectrum holes from the sub-Nyquist samples, even when the undersampling ratio is very small.We then propose an iterative low-complexity scheme for the reliable detection of zero blocks in a block sparse signal.This scheme is based on the application of verification based (VB) recovery algorithms in compressed sensing to block sparse signals. To apply both schemes to WSS, we devise a block sparse sensing matrix by designing a novel analog-to-information converter (AIC). The AIC, the sensing matrix and the VB algorithms can be optimized such that the largest number of zero blocks for a given number of measurements can be detected. These works introduce a paradigm in the recovery of block sparse signals, where one is interested in partial detection of the complement of the support set, reliably, rather than the full recovery of the signal or its support.