Iterative recovery algorithms for compressed sensing of wideband block sparse spectrums

Abstract

A major task in cognitive radios (CRs) is spectrum sensing. In a wide-band regime, this is a challenging task requiring very high-speed analog-to-digital converters (ADCs), operating at or above the Nyquist rate. Compressed sensing is recognized as an effective technique to significantly reduce the sampling rate in wideband spectrum sensing, taking advantage of the sparsity of the spectrum. The recovery of the spectrum from the samples at sub-Nyquist rates is usually achieved through the so-called ℓ₁-norm minimization. A more effective recovery technique for block sparse signals, called ℓ₂/ℓ₁-norm minimization, can be used as a replacement for ℓ₁-norm minimization to reduce the sampling rate and consequently simplify the implementation of ADCs even further. In this paper, we propose two iterative ℓ₂/ ℓ₁-norm minimization algorithms for the recovery of block sparse spectrums. Similar to the standard ℓ₂/ℓ₁-norm minimization, the proposed algorithms require the side information about the boundaries of the spectral blocks. We evaluate the performance of the proposed algorithms both in the absence and in the presence of noise, and demonstrate that for both cases, the proposed algorithms significantly outperform the existing ℓ₁-minimization-based and standard ℓ₂/ℓ₁ minimization recovery algorithms. The improvement in performance comes at a small cost in complexity increase.