Soft-feedback OMP for the recovery of discrete-valued sparse signals

In Compressed Sensing, a real-valued sparse vector has to be reconstructed from an underdetermined system of linear equations. However, in many applications of digital communications the elements of the unknown sparse vector are drawn from a finite set. The standard reconstruction algorithms of Compressed Sensing do not take this knowledge into account, hence, enhanced algorithms are required to achieve optimum performance. In this paper, we propose a new approach for the reconstruction of discrete-valued sparse signals. On the one hand, the algorithm is tailored to the discrete nature of the signal. On the other hand, reliability information is utilized within the successive reconstruction procedure. Via numerical simulations it is shown that the proposed variant of the Orthogonal Matching Pursuit clearly outperforms the well-known standard versions.