Compressive Spectrum Sensing Using Blind-Block Orthogonal Least Squares in Cognitive Sensor Networks

In cognitive sensor networks (CSNs), compressive spectrum sensing (CSS) has been shown as a promising candidate for improving the recovery performance based on the signal sparsity. However, most current works need to know the sparsity or the noise information in advance for reliable reconstruction, where such information is usually unavailable in practical applications. In this article, we propose a blind-block orthogonal least squares-based CSS (B-BOLS-CSS) algorithm, which utilizes a novel blind stopping rule to cut the cords to these prior information. Specifically, we first present both the noiseless and noisy recovery guarantees for the BOLS algorithm based on the mutual incoherence property (MIP). Motivated by them, we then formulate the blind stopping rule, which exploits an
$\ell _{{2},\infty }$
sufficient statistic to blindly test the support atoms in the remaining measurement matrix. We further evaluate the theoretical performance analysis of the holistic B-BOLS-CSS algorithm by developing a lower bound of the signal-to-noise ratio (SNR) to ensure that the probability of recovery is no lower than a given threshold. Simulations not only demonstrate the improvement of our derived theoretical results but also illustrate that B-BOLS-CSS works well in both low and high SNR environments.