Orthogonality Deficiency of Massive MIMO Channels: Distribution and Relationship with Performance

In this letter, we examine orthogonality deficiency (od) of massive multi-input multi-output (mMIMO) channels. The Weibull distribution is adopted for modeling the fading envelopes, and various propagation channels are simulated by varying the Weibull parameters. By studying the statistics of od, we offer insights on the mMIMO size for linear detectors (LDs) to achieve desirable performance. By proposing an approximate distribution of od, we show that for various propagation channels, if the number of receive antennas exceeds a certain number while the number of transmit antennas is fixed, LDs achieve the same diversity as that of the maximum likelihood detector with high probability in practice. Theoretical analysis is validated by simulations.