Multiple-input Multiple-output (MIMO) wireless communication systems allow increased spectral efficiency and therefore promise significant improvement in performance. However, because of the rapid variation in channel state information (CSI) in networks with mobile nodes or scatterers, it is difficult both to maintain high communication performance and to create channel models that effectively represent the time-varying behavior of the channels. The spatial covariance of the MIMO channel describes the average power gain on each transmit-receive antenna pair as well as the correlation between the complex link gains and thus provides critical information for understanding the performance of the system and for creating models to accurately describe the interaction of the electromagnetic fields with the antennas. Furthermore, in many cases the MIMO signaling scheme uses knowledge of this spatial covariance. This thesis proposes a closed-form analytical model that allows estimation of the full MIMO channel covariance based on knowledge of the power angular spectrum (PAS) of the channel and the antenna radiation patterns. Comparison of covariance matrices computed using this model with those estimated from observed channel samples reveals the appropriate window over which the covariance should be estimated for non-WSS time-varying channels. Two approaches are developed to compare the covariance matrices in order to determine the appropriate window, both based on a metric, correlation matrix distance (CMD). Simulations based on both a two-ring propagation model and raytracing data in a three dimensional urban environment are included. The results reveal that with the optimal window size, the CMD of the estimated covariance is close to that of the analytical covariance. An average window size normalized by the scatterer circle radius is determined for practical estimation of covariance based on knowledge of the average distance to the scatterers. The impact of the number of scatterers on the optimal window size is analyzed as well. The results based on ray-tracing data show that the CMD of the estimated covariance using a 16 – 17λ window match the CMD of the analytical covariance.