Spatially Asymptotic Behavior of Structured Covariance Matrix Estimation for Massive MIMO

In this letter, the truncated redundancy averaging (TRA) method for structured covariance matrix estimation and its spatially asymptotic behavior for massive MIMO are studied. The TRA method can be applied to the antenna arrays exhibiting correlation redundancy, including linear and non-linear arrays. Resorting to Khinchin's statement on the law of large numbers for correlated random variables, it is derived that, for a uniform array, if its physical size is a strictly increasing linear or sub-linear function of the number of antenna elements, the convergence of the TRA estimate to the true covariance matrix occurs within one single channel realization. We also derive and demonstrate that lower spatial correlation leads to increased estimation performance.