On the capacity of MIMO wireless channels with dynamic CSIT

Transmit channel side information (CSIT) can significantly increase MIMO wireless capacity. Due to delay in acquiring this information, however, the time-selective fading wireless channel often induces incomplete, or partial, CSIT. In this paper, we first construct a dynamic CSIT model that takes into account channel temporal variation. It does so by using a potentially outdated channel measurement and the channel statistics, including the mean, covariance, and temporal correlation. The dynamic CSIT model consists of an effective channel mean and an effective channel covariance, derived as a channel estimate and its error covariance. Both parameters are functions of the temporal correlation factor, which indicates the CSIT quality. Depending on this quality, the model covers smoothly from perfect to statistical CSIT. We then summarize and further analyze the capacity gains and the optimal input with dynamic CSIT, asymptotically at low and high SNRs. At low SNRs, dynamic CSIT often multiplicatively increases the capacity for all multi-input systems. The optimal input is typically simple single-mode beamforming. At high SNRs, for systems with equal or fewer transmit than receive antennas, it is well-known that the capacity gain diminishes to zero because of equi-power optimal input. With more transmit than receive antennas, however, the capacity gain is additive. The optimal input then is highly dependent on the CSIT. In contrast to equi-power, it can drop modes for channels with a strong mean or strongly correlated transmit antennas. For such mode-dropping at high SNRs in special cases, simple conditions on the channel K factor or the transmit covariance condition number are subsequently quantified. Next, using a convex optimization program, we study the MIMO capacity with dynamic CSIT non-asymptotically. Particularly, we numerically analyze effects on the capacity of the CSIT quality, the relative number of transmit and receive antennas, and the channel K factor. For example, the capacity gain based on dynamic CSIT is more sensitive to the CSIT quality at higher qualities. The program also helps to evaluate a simple, analytical capacity lower-bound based on the Jensen optimal input. The bound is tight at all SNRs for systems with equal or fewer transmit than receive antennas, and at low SNRs for others.