Low-complexity detector for very large and massive MIMO transmission

Maximum-Likelihood (ML) joint detection has been proposed as an optimal strategy that detects simultaneously the transmitted signals. In very large multiple-input-multiple output (MIMO) systems, the ML detector becomes intractable due the computational cost that increases exponentially with the antenna dimensions. In this paper, we propose a relaxed ML detector based on an iterative decoding strategy that reduces the computational cost. We exploit the fact that the transmit constellation is discrete, and remodel the channel as a MIMO channel with sparse input belonging to the binary set {0, 1}. The sparsity property allows us to relax the ML problem as a quadratic minimization under linear and ℓ
₁
-norm constraint. We then prove the equivalence of the relaxed problem to a convex optimization problem solvable in polynomial time. Simulation results illustrate the efficiency of the low-complexity proposed detector compared to other existing ones in very large and massive MIMO context.