A Blind Recovery Algorithm Based on SPG for Multiband Signals

Multiband signal is a typical signal in the realm of modern communication, whose spectrum is the sum of several narrow bands in frequency domain. Modulated Wideband Converter (MWC) system, which is based on the emerging theory of Compressed Sensing (CS), can sample multiband signals at sub-Nyquist rate. However, classical reconstruction algorithm for MWC requires the number of carrier frequencies of the original signal in advance, which is a very difficult condition to satisfy. In this paper, a Spectral Projection Gradient (SPG) Ll,l algorithm for MWC is proposed. We use the l1,1 norm of the matrix to measure the sparsity of the matrix, and transforms the sparse solution problem into a class of constrained extremum problems by minimizing l-norm. Then it is transformed into a linear programming problem which is solved by SPG. The sparsity is determined by assessing the numerical differential iteratively. The algorithm can realize blind reconstruction for MWC without requiring the number of carrier frequencies at the expense of minor increased complexity. Simulations demonstrate that the proposed algorithm has good reconstruction performance, which is superior to the classical Simultaneous Orthogonal Matching Pursuit (SOMP).