Capacity of a Mobile Multiple-Antenna Communication Link in a Rayleigh Flat-Fading Environment

We analyze a mobile wireless link comprising M transmitter and N receiver antennas operating in a Rayleigh flat-fading environment. The propagation coefficients between every pair of transmitter and receiver antennas are statistically independent values which they maintain for another T symbol periods, and so on. Computing the link capacity, associated with channel coding over multiple fading intervals, requires optimizing the joint density of the T-M complex transmitted signals. We prove taht there is no point in making the number of transmitter antennas greater than the length of the coherence interval: the capacity for M>T is equal to the capacity for M=T. Capacity is achieved when the TxM transmitted signal matrix is equal to the product of two statistically independent matrices: a TxT isotropically distributed unitary matrix times a TxM random matrix that is diagonal, real, and nonnegative. This result enables us to determine capacity for many interesting cases. We conclude that, for a fixed number of antennas, as the length of the coherence interval increases, the capacity approaches the capacity obtained as if the receiver knew the propagation coefficients.