A blind recovery algorithm for spectrum-sparse signals sub-Nyquist sampling

Abstract

Wideband analog signals push contemporary analog- to-digital conversion systems to their performance limits. The recent development of compressive sensing theory enables direct analog-to-information conversion of sparse (or compressible) signals at sub-Nyquist rate. In this paper, we implement spectrum-sparse signals sub-Nyquist sampling by use of Modulated Wide Converter (MWC). To overcome the drawback of requiring exact sparsity of the existing recovery algorithm, we introduce the Sparsity Adaptive Matching Pursuit (SAMP) method into reconstruction stage to search the support set of unknown signal vectors blindly. The numerical experiments demonstrate that the MWC system with the proposed recovery algorithm can implement spectrum-sparse signals sub-Nyqiust sampling and perfect reconstruction under the condition of not knowing exact sparsity.