The Fading Number of Multiple-Input Multiple-Output Fading Channels With Memory

The fading number of a general (not necessarily Gaussian) regular multiple-input multiple-output (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be noncoherent, i.e., neither receiver nor transmitter have knowledge about the channel state, but they only know the probability law of the fading process. The fading number is the second term in the asymptotic expansion of channel capacity when the signal-to-noise ratio (SNR) tends to infinity. It is related to the border of the high-SNR region with double-logarithmic capacity growth.