Sparse Array Synthesis Including Mutual Coupling for MU-MIMO Average Capacity Maximization

A hybrid optimization algorithm, including mutual coupling (MC), is proposed to synthesize an irregular sparse array (ISA) for average capacity maximization in a multiuser multiple-input–multiple-output (MU-MIMO) system. The hybrid approach is composed of two phases to suboptimally determine the location of a fixed number of omnidirectional thin dipole antennas in an arbitrary sparse aperture via a diagonal antenna selection matrix. In Phase I, the problem is relaxed to a convex optimization by ignoring the MC and weakening the constraints. The output of Phase I is accounted as a reliable initial guess for the genetic algorithm (GA) in Phase II, which incorporates the MC effects through the coupling matrix and avoids the convex relaxation technique. The proposed approach outperforms the conventional GA with a random initial population, while it avoids trying several starting positions. Meanwhile, the undesirable appearance of grating lobes, due to the undersampling, and the degrading MC effects are suppressed by aperiodicity. It is observed that doubling the conventional interelement spacing (half-wavelength) and finding the location of eight dipoles in a sparse aperture by the proposed method improve the average capacity by 3.27%–11.9% when the number of users varies from two to eight, and the signal-to-noise ratio (SNR) is 30 dB.