Partial Power Control for Slowly Fading MIMO Channels

Transmit power control to minimize the outage probability over a slowly fading multiple-antenna channel utilizing partial channel state information at the transmitter is studied. The optimal power quantizer is shown to have a "circular" structure. The design problem is then explicitly formulated and numerically solved based on a Gaussian approximation. Asymptotic behavior of the outage probability achieved with a finite-size power codebook is investigated. It is shown that the diversity gain of such a system is a K-order polynomial of the product of the number of transmit and receive antennas, where K is the size of the power codebook. The interesting concept of power-control diversity is discussed.