Multibit Quantized Precoding for MU-mMIMO

We propose a novel multibit quantized precoding method for the downlink of multi-user massive MIMO systems with low-resolution digital-to-analog converters. The new method, termed multibit quantized precoding (MQP), enforces the finite-alphabet constraint through an l0-norm penalty, approximated by a smooth surrogate so as to yield a reformulated problem, which is then convexized via fractional programming, ultimately extending quantized precoding beyond 1-bit alphabets. The regularization parameter of the proposed method is selected via a discrepancy principle integrated with graduated non-convexity continuation, resulting in a principled and reproducible hyperparameter tuning method and an efficient iterative algorithm with a closed-form, least-squares-type update per iteration. In order to further reduce the computational complexity of the method, we include a Gaussian belief propagation (GaBP) step for turning the least-squares update in linear-time. Simulations performed for systems with different sizes demonstrate that both methods, namely the MQP with and without GaBP, achieve competitive or superior error-rate performance compared to state-of-the-art quantized precoding algorithms under various channel conditions.