International audienceThis paper addresses the problem of decoding in large scale MIMO systems. In this case, the optimal maximum likelihood detector becomes impractical due to an exponential increase of the complexity with the signal and the constellation dimensions. Our work introduces an iterative decoding strategy with a tolerable complexity order. We consider a MIMO system with finite constellation and model it as a system with sparse signal sources. We propose an ML relaxed detector that minimizes the euclidean distance with the received signal while preserving a constant l1-norm of the decoded signal. We also show that the detection problem is equivalent to a convex optimization problem which is solvable in polynomial time. Two applications are proposed, and simulation results illustrate the efficiency of the proposed detector

We consider the problem of estimating a deterministic finite alphabet vector f from underdetermined measurements y = Af , where A is a given (random) n × N matrix. Two new convex optimization methods are introduced for the recovery of finite alphabet signals via 1-norm minimization. The first method is based on regularization. In the second approach, the problem is formulated as the recovery of sparse signals after a suitable sparse transform. The regularization-based method is less complex than the transform-based one. When the alphabet size p equals 2 and (n, N) grows proportionally, the conditions under which the signal will be recovered with high probability are the same for the two methods. When p > 2, the behavior of the transform-based method is established. Experimental results support this theoretical result and show that the transform method outperforms the regularization-based one.