Linear Precoding for MIMO Multiple Access Channels with Finite Discrete Inputs

In this paper, we study linear precoding for multiple-input multiple-output (MIMO) multiple access channels (MAC) with finite discrete inputs. We derive the constellation-constrained capacity region for the MIMO MAC with an arbitrary number of users and find that the boundary can be achieved by solving the problem of weighted sum rate maximization with constellation and individual power constraints. Due to the non-concavity of the objective function, we obtain a set of necessary conditions for the optimization problem through Karush-Kuhn-Tucker analysis. To find the optimal precoding matrices for all users, we propose an iterative algorithm utilizing alternating optimization strategy. In particular, each iteration of the algorithm involves the gradient descent update with backtracking line search. Numerical results show that when inputs are digital modulated signals and the signal-to-noise ratio is in the medium range, our proposed algorithm offers considerably higher sum rate than non-precoding and the traditional method which maximizes Gaussian-input sum capacity. Furthermore, a low-density parity-check coded system with iterative detection and decoding for MAC is presented to evaluate the bit error rate (BER) performance of precoders. BER results also indicate that the system with the proposed linear precoder achieves significant gains over the non-precoding system and the precoder designed for Gaussian inputs.