On the fading number of multi-antenna systems over flat fading channels with memory and incomplete side information

Upper and lower bounds are derived on the capacity and fading number of multi-antenna systems operating over flat fading channels. The fading process may exhibit memory, and the receiver is assumed to have access to some incomplete (possibly null) side information related to the fading realization. For single-input single-output (SISO) systems these bounds typically yield an exact expression for the system's fading number. This expression is evaluated explicitly in the SISO Gaussian case as a function of the fading mean, its power spectral density, and the mutual information rate between the fading process and side information. In the absence of side information, the fading number of such systems depends only on the mean and variance of the fading process and on the minimum mean squared-error in predicting the present fading from the past; it is not directly related to the Doppler spread or coherence time.