Minimal antenna-subset selection under capacity constraint for power-efficient MIMO systems: A relaxed ℓ1 minimization approach

This paper addresses the minimal subset selection of antennas achieving designated channel capacity. This is one of the most natural approaches to alleviating the power consumption in MIMO systems, while it is a mathematically challenging nonlinearly-constrained sparse optimization (ℓ₀-norm minimization) problem. We present an efficient algorithmic solution, to this highly combinatorial problem, using convex and differentiable relaxations of the (ℓ₀-norm. The proposed algorithm is based on the hybrid steepest descent method for the subgradient projection operator together with the soft-thresholding technique, minimizing the Moreau envelope of the (ℓ₁-norm subject to the capacity constraint. The simulation results show that the proposed algorithm realizes a near optimal solution to the original nonlinearly-constrained sparse optimization problem.