Approaching the capacity of the MIMO Rayleigh flat-fading channel with QAM constellations, independent across antennas and dimensions

In this study we consider the challenge of reliable communication over a wireless Rayleigh flat-fading channel using multiple transmit and receive antennas. Since modern digital communication systems employ signal sets of finite cardinality, we examine the use of the quadrature amplitude modulation (QAM) constellation to approach the capacity of this channel. By restricting the channel input to the M-QAM subset of the complex-plane, the maximum achievable information rate (C_M-QAM ) is strictly bounded away from the channel capacity (C). We utilize a modified version of the Arimoto-Blahut algorithm to determine C_M-QAM and the probability distribution over the channel input symbols that achieves it. The results of this optimization procedure numerically indicate that the optimal input symbol distribution factors into the product of identical distributions over each real dimension of the transmitted signal. This is shown to vastly reduce the computational complexity of the optimization algorithm. Furthermore, we utilize the computed optimal channel input probability mass function (pmf) to construct capacity approaching trellis codes. These codes are implemented independent across all antennas and symbol dimensions and, if used as inner codes to outer low-density parity check (LDPC) codes, can achieve arbitrarily small error rates at signal-to-noise ratios very close to the channel capacity C_M-QAM . Examples are given for a 2-transmit/2-receive antenna (2 times 2) system