Ultra Low-Complexity Detection of Spectrum Holes in Compressed Wideband Spectrum Sensing

Wideband spectrum sensing 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 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. The scheme is based on a block sparse sensing matrix, which is implemented through the design of a novel analog-to- information converter (AIC). The proposed scheme identifies some measurements as being zero and then verifies the sub-channels associated with them as being vacant. Analytical and simulation results are presented that demonstrate the effectiveness of the proposed method in reliable detection of spectrum holes with complexity much lower than existing schemes. This work also introduces a new paradigm in compressed sensing where one is interested in reliable detection of (some of the) zero blocks rather than the recovery of the whole block sparse signal.Comment: 7 pages, 5 figure

Iterative reweighted ℓ<inf>2</inf>/ℓ<inf>1</inf> recovery algorithms for compressed sensing of block sparse signals

In many applications of compressed sensing the signal is block sparse, i.e., the non-zero elements of the sparse signal are clustered in blocks. Here, we propose a family of iterative algorithms for the recovery of block sparse signals. These algorithms, referred to as iterative reweighted ℓ2/ℓ1 minimization algorithms IR 702Dℓ2/ℓ1 , solve a weighted ℓ2/ℓ1 minimization in each iteration. 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 non-iterative approaches as well as existing iterative methods. In particular, we demonstrate that, by increasing the block length, the performance of the proposed algorithms approaches the Wu-Verdú theoretical limit. The improvement in performance comes at a rather small cost in complexity increase. Further improvement in performance is achieved by using a priori information about the location of non-zero blocks, even if such a priori information is not perfectly reliable

Low-complexity detection of zero blocks in wideband spectrum sensing

A low-complexity scheme for the reliable detection of zero blocks in a block sparse signal is proposed. The scheme is based on the application of verification based (VB) recovery algorithms in compressed sensing to block sparse signals, and is described in the context of wideband spectrum sensing (WSS). To apply VB algorithms 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 are then optimized such that the largest number of zero blocks for a given number of measurements can be detected. This work introduces a new 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. The analysis and simulations demonstrate significant improvement in performance/complexity over the existing block sparse recovery schemes within this new framework. An important application of the results would be in cognitive radios with limited computational resources

Iterative recovery algorithms for compressed sensing of wideband block sparse spectrums

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 complexit

On weighting/reweighting schemes for approximate message passing algorithms

In this paper, we propose a number of weighting/reweighting schemes to improve the performance of the so-called approximate message passing (AMP) algorithm of Donoho et al. We consider the application of AMP for the recovery of sparse signals from an under-determined system of linear equations, and variants of AMP for the recovery of block sparse signals. The proposed schemes for block sparse signals cover both cases of known and unknown block borders. Simulation results, both in noiseless and noisy scenarios, show significant performance improvement over the standard AMP algorithm and a considerably better performance/complexity trade-off compared to other state-of-the-art recovery algorithms