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Hybrid MMSE-VP precoding for multi-user massive MIMO systems

This paper examines design of mixed-timescale hybrid precoding with vector perturbation (VP) to achieve minimum mean square errors (MMSE) for multi-user massive multiple-input multiple-output (MIMO) systems. In particular, equipped with the perfect effective channel state information (CSI)-based MMSE-VP solution at the baseband, we derive partial CSI-based linear radio frequency (RF) precoding as the solution to a stochastic programming problem. In the scenario of single-cluster transmission, RF eigen-beamforming in the transmit correlated subspace is proved to be optimality-achieving. In the multi-cluster case, by approximating the discrete constellation as uniformly distributed, we establish a closed-form lower bound for the objective function. A critical point to this bound is found by a trust-region method on a smooth Riemannian manifold. Simulation results demonstrate that in the former case, a limited number of RF chains suffices for the nonlinear hybrid scheme to outperform the fully digital linear solution, and approaches the performance of the traditional MMSE-VP solution in terms of bit error rate. In the latter case, the proposed solution delivers a superior error performance to the state-of-the-art baselines.