Low-Complexity Variational Bayesian Inference Based Groupwise Detection for Massive MIMO Uplinks

Abstract

This paper proposes a low-complexity groupwise detection scheme for massive multiple-input multiple-output (MIMO) systems based on two key features of massive MIMO channels. First, most inter-user correlations tend to be negligible as the number of antennas <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> at the base station (BS) increases, while some users might have a high correlation that is indistinguishable for linear projection-based detectors. We hence develop a variational Bayesian inference-based groupwise (VBI-G) detector based on a factorization approximation of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> probability of transmitted symbols, which sequentially performs nonlinear detection for small groups of highly correlated users without computations of large-scale matrices. Second, the variation of normalized inter-user correlation is insignificant over a wide range of frequency, thereby user grouping based on correlation coefficients can be performed on a wideband basis. Accordingly, we propose a low-complexity incremental greedy grouping algorithm for minimizing the Kullback-Leibler divergence of the unconditioned posterior probabilities with the constraint of a maximum group size. Theoretical analysis proves that for a BS equipped with a uniform linear array, the maximum group size grows logarithmically with the number of users <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> with high probability in the regime <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M,K</i> → ∞ with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K/M</i> < 1/2 under the worst line-of-sight propagation condition. Simulation results verify that the proposed VBI-G detector achieves superior performance with an extremely low computational overhead for massive MIMO systems.