Selecting an optimal set of transmit antennas for a low rank matrix channel

Previous work has shown that the use of multiple antennas in a fading environment results in a linear increase in capacity. This paper examines the capacity of a multiple antenna element array (MEA) in a quasi-static flat fading environment with a rank deficient channel. We assume that the channel is known at the receiver and the existence of a feedback path to the transmitter. For a particular channel realization, we show that the judicious use of fewer transmit antennas when the channel matrix is ill-conditioned can increase system capacity. We develop a criterion for selecting an optimum set of transmit antennas. This selection is optimal in the sense that the capacity of the resulting MEA system is greater than that for any other configuration with the same number of transmit antennas chosen from the original set. The resulting channel is full rank