On precoding for constant K-user MIMO Gaussian interference channel with finite constellation inputs

Abstract

This paper considers linear precoding for constant channel-coefficient K-User MIMO Gaussian Interference Channel(MIMO GIC) where each transmitter-i (Tx-i), requires to send d_i independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution,to receiver-i(Rxi) for i = 1,2, · · · , K. We define the maximum rate achieved by Txi using any linear precoder, when the interference channel-coefficients are zero, as the signal to noise ratio (SNR) tends to infinity to be the Constellation Constrained Saturation Capacity (CCSC) for Tx-i.We derive a high SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I[X_i; Y_i]. A set of necessary and sufficient conditions on the precoders under which I[X_i; Y_i] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Further, we propose gradient-ascent based algorithms to optimize the sum-rate achieved by precoding with finite constellation inputs and treating interference as noise. Simulation study using the proposed algorithms for a 3-user MIMO GIC with two antennas at each node with d_i = 1 for all i, and with BPSK and QPSK inputs, show more than 0.1 bits/sec/Hz gain in the ergodic sum-rate over that yielded by precoders obtained from some known IA algorithms, at moderate SNRs.