Beyond Multiplexing Gain in Large MIMO Systems

Given the common technical assumptions in the literature on MIMO system modeling, we derive elementary results for the mutual information of a MIMO system at high SNR in the large system limit. Consider a MIMO system with R receive and φR transmit antennas. When φ < 1, removing as many receive antennas as to obtain a square system results in a mutual information loss per receive antenna that is solely given by the binary entropy function of φ. Furthermore, we calculate the deviation of the growth of mutual information from linear growth versus the number of antennas. We show that this deviation is additive for MIMO compound channels and can be easily expressed in terms of the S-transform of the spectrum of the channel matrix.