MIMO outage capacity in the high SNR regime

We consider a multi-input multi-output (MIMO) fading channel with coherent reception and provide a sharp characterization of the outage capacity in the form of an asymptotically tight (in the limit of high signal-to-noise ratio) affine lower bound, under only mild assumptions on the fading distribution. The bound is simpler to compute than the original capacity and succinctly captures the various features particular to the channel. For systems where both the transmitter and the receiver have perfect channel state information, we derive asymptotically tight affine lower bounds on the outage capacities under a long-term and a short-term power constraint as well as on the delay-limited capacity. Further, when only the receiver has perfect channel state information, and when the rank of the channel matrix is equal to the number of transmit antennas with probability one, we show that an isotropic Gaussian input is asymptotically optimal. Moreover, for Ricean channels the asymptotic effect of the Rice factor on the delay-limited capacity is also characterized