On the Outage Capacity of the Massive MIMO Diversity Channel

We consider the massive Multiple Input Multiple Output (MIMO) diversity channel affected by independent and identically distributed Rayleigh fading, with linear processing at both transmitter and receiver sides, and analyze the outage capacity for large number of antennas. We first discuss the classical Single Input Multiple Output (SIMO) diversity channel that uses Maximal Ratio Combining (MRC) or Selection Combining (SC). For MRC, a numerical computation and a Gaussian Approximation (GA) are considered, whereas for SC an exact evaluation is possible. The analysis is then straightforwardly extended to the Multiple Input Single Output (MISO) system that uses Maximal Ratio Transmission (MRT) or transmit antenna selection. The general Multiple Input Multiple Output (MIMO) system that pursues full diversity is finally considered, with both optimal linear processing and simple antenna selection at both transmitter and receiver. If the number of antennas is sufficiently large on at least one side, the outage capacity of each considered diversity channel approaches that of a suitable reference Additive White Gaussian Noise (AWGN) channel with properly defined Signal-to-Noise Ratio (SNR), which provides a performance benchmark. This conclusion is valid for large but realistic number of antennas compatible with the assumption of independent fading.