Wideband spectrum sensing is a significant challenge in cognitive radios (CRs) due to requiring very high-speed analogto-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 subNyquist 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.Index Terms -Wideband spectrum sensing, cognitive radios, compressed sensing, 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 2/ 1 minimization algorithms (IR-2/ 1), solve a weighted 2/ 1 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 nonzero blocks, even if such a priori information is not perfectly reliable.Index Terms -Block sparsity, compressed sensing, 2/ 1 minimization, iterative recovery algorithms, iterative reweighted 2/ 1 minimization.
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