2012/10/14 by Ganesan, Abhinav, Rajan, B. Sundar
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1210.3819
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 di independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution, to receiver-i (Rx-i) for i=1,2,⋯,K. We define the maximum rate achieved by Tx-i 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[Xi;Yi]. A set of necessary and sufficient conditions on the precoders under which I[Xi;Yi] 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 di=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.