Capacity of fading MIMO channels with channel estimation error

In this paper, we investigate the effect of channel estimation error on the capacity of multiple input multiple output (MIMO) systems in i.i.d. Rayleigh flat-fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. It is seen that the mutual information increases with the number of antennas, but is limited by channel estimation error at high SNR. We also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (subchannel) and temporal (fading) domain. For the outage capacity, it is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance.