This paper formulates a closed-form expression for the full MIMO spatial covariance matrix based on knowledge of the propagation environment PAS and the antenna radiation patterns. It then uses the CMD to compare the results of this calculation with what is obtained when estimating the covariance from a sample mean taken over a finite set of observed channel measurements. Example computations based on a simple two-ring propagation model reveal that the window over which this sample mean should be computed can be estimated based on knowledge of the average distance to the scatterers. This framework provides a capability that allows us to better understand practical computation of covariance matrices for channel modeling and MIMO signal processing applications.
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