Transmitter optimization for MIMO systems with mutual coupling at high SNR

This paper considers the optimal transmit precoder design for MIMO systems operating with antenna mutual coupling at high signal to noise ratios (SNR). The design problem is formulated as a convex optimization problem with two separate power constraints: a constraint on the available power imposed on a per-amplifier basis, and a sum constraint on the allowable radiated power. To gain insights into the mutual coupling effect and to simplify the optimization problem, sufficient and necessary conditions on the power constraints are derived, under which the dual-constraint problem reduces to a single-constraint problem with a closed-form solution. An efficient suboptimal algorithm is also proposed for the dual constraint problem by relaxing the per-amplifier power constraint to sum power constraint. One interesting conclusion of our analysis is that, with mutual coupling, isotropic inputs are not optimal in general at high SNR. Our proposed optimal precoder design is shown to yield significant improvements compared to conventional techniques which are designed based on one power constraint only.