Finite-SNR outage analysis for MIMO channels with imperfect channel state information

In this paper, a point-to-point multiple-input multiple-output (MIMO) channel with imperfect channel state information (CSI) at the receiver and no CSI at the transmitter is considered. Using Monte Carlo simulations, we compute the optimum number of active antennas required at the transmitter (topt) to minimize the outage probability. We show that, apart from the number of transmit antennas, topt depends on the signal to noise ratio (SNR), multiplexing gain, coherence time, and the number of receive antennas. Our results give insights on the behavior of topt with respect to these parameters. Specifically, we show that as the multiplexing gain increases, the value of topt increases from one, and as the multiplexing gain reaches its maxima, the value of topt equals the minimum of the number of transmit and receive antennas. The intermediate behavior of topt with respect to multiplexing gain depends on the MIMO channel configuration. topt for the MIMO channel with perfect CSI at the receiver follows a similar pattern as that with imperfect CSIR. For a multiple-input single-output (MISO) channel with imperfect CSIR, we obtain a tight upper bound on the outage probability. Using this analytical upper bound, we can calculate topt for any fixed channel configuration. For a MISO channel with imperfect CSIR and fixed SNR, topt reduces as multiplexing gain increases; however, for fixed multiplexing gain and fixed SNR, topt monotonically increases with increase in coherence time of the channel.