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


Thomas L. Marzetta       Bertrand M. Hochwald


Abstract: 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 and unknown; they remain constant for a coherence interval of T symbol periods, after which they change to new 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 an optimization over the joint density of T * M complex transmitted signals. We prove that 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 T x M transmitted signal matrix is equal to the product of two statistically independent matrices: a T x T isotropically distributed unitary matrix times a certain T x M 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.

Status: Appears in IEEE Transactions on Information Theory, Jan. 1999.

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Bert Hochwald <hochwald@bell-labs.com>