Iteratively reweighted two-stage LASSO for block-sparse signal recovery under finite-alphabet constraints

In this paper, we derive an efficient iterative algorithm for the recovery of block-sparse signals given the finite data alphabet and the non-zero block probability. The non-zero block number is supposed to be far smaller than the total block number (block-sparse). The key principle is the separation of the unknown signal vector into an unknown support vector s and an unknown data symbol vector a. Both number (parallel to s parallel to(0)) and positions (s(i) is an element of{0, 1}) of non-zero blocks are unknown. The proposed algorithms use an iterative two-stage LASSO procedure consisting in optimizing the recovery problem alternatively with respect to a and with respect to s. The first algorithm resorts on l(1)-norm of the support vector and the second one applies reweighted l(1)-norm, which further improves the recovery performance. Performance of proposed algorithms is illustrated in the context of sporadic multiuser communications. Simulations show that the reweighted-l(1) algorithm performs close to its lower bound (perfect knowledge of the support vector). (C) 2018 Elsevier B.V. All rights reserved.