Receive beamforming optimization for MIMO system with constant envelope precoding

In this paper, we study the receive beamforming design to minimize the symbol error rate (SER) in a point-to-point multiple-input multiple-output (MIMO) system with constant envelope (CE) precoding. In this case, a constellation is feasible at the combiner output of the receiver if and only if it can be scaled to lie in an annular region, whose boundaries are determined by channel realization, receive beamforming and per-antenna transmit power. By approximating the exact SER with its union bound, we aim to optimize the receive beamforming weights to maximize the minimum Euclidean distance (MED) between any two signal points at the combiner output for any desired constellation and given channel realization, subject to the feasibility constraint of the constellation. We first show that under the assumption of independent and identically distributed (i.i.d.) Rayleigh fading channel, this problem is feasible as long as there are no more transmit antennas than receive antennas. Then, we assume the aforementioned condition holds and reformulate this problem into an equivalent quadratically constrained quadratic program (QCQP), for which we find an approximate solution by applying the semidefinite relaxation (SDR) technique and a customized Gaussian randomization method. Numerical results show that our proposed receive beamforming scheme achieves significantly improved SER performance than other benchmark schemes.