Linear Precoding for MIMO Broadcast Channels With Finite-Alphabet Constraints

We investigate the design of linear transmit precoder for multiple-input multiple-output (MIMO) broadcast channels (BC) with finite alphabet input signals. We first derive an explicit expression for the achievable rate region of the MIMO BC with discrete constellation inputs, which is generally applicable to cases involving arbitrary user number and arbitrary antenna number. We further present a weighted sum rate upper bound of the MIMO BC with identical transmit precoding matrices. The resulting bound exhibits a serious performance loss because of the non-uniquely decodable transmit signals for MIMO BC with finite alphabet inputs in high signal-to-noise ratio (SNR) region. This performance loss motivates the use of a simple precoding to combat the non-unique decodability. Based on a constrained optimization problem formulation, we apply the Karush-Kuhn-Tucker analysis to derive necessary conditions for MIMO BC precoders to maximize the weighted sum-rate. We then propose an iterative gradient descent algorithm with backtracking line search to optimize the linear precoders for each user. Our { simulation} results under the practical transmit symbols of discrete constellations demonstrate significant gains by the proposed algorithm over other precoding schemes including the traditional iterative water-filling (WF) design for the Gaussian input signals. For the low-density parity-check coded systems, our precoder provides considerably coded BER improvement through iterative decoding and detection.