The fading number of memoryless multiple-input multiple-output fading channels

In this correspondence, we derive the fading number of multiple-input multiple-output (MIMO) flat-fading channels of general (not e channel necessarily Gaussian) regular law without temporal memory. 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, after the double-logarithmic term, of the high signal-to-noise ratio (SNR) expansion of channel capacity. Hence, the asymptotic channel capacity of memory-less MIMO fading channels is derived exactly. The result is then specialized to the known cases of single-input-multiple-output (SIMO), multiple-input single-output (MISO), and single-input-single-output (SISO) fading channels, as well as to the situation of Gaussian fading.