Computing the Closest Positive Definite Correlation Matrix for Experimental MIMO Channel Analysis

Under realistic propagation conditions in multiple-input-multiple-output (MIMO) wireless channels, some experimental (measured) full-spatial-correlation (FSC) MIMO channel matrices may not be positive definite, especially when the number of antennas elements increases. In this letter, an enhancement technique to solve the problem of non-positiveness for large experimental FSC matrices is proposed. This technique, based on the alternating-projection (AP) method, computes the closest positive definite matrix to the experimental FSC matrix preserving its covariance structure. The proposed technique is useful to evaluate the performance of large array MIMO systems under realistic conditions, allowing the Cholesky factorization of FSC matrices, which is needed for synthetic channel generation.