Alternating projection method applied to indefinite correlation matrices for generation of synthetic MIMO channels

Complex correlation multiple-input multiple-output (MIMO) matrices estimated from measurements under realistic propagation conditions occasionally have positive, zero and negative eigenvalues, converting them to indefinite matrices. In this framework, this paper presents a novel correction procedure (CP) based on the alternating projection (AP) method to find the Hermitian and positive definite matrix closest to an estimated indefinite full spatial correlation (FSC) MIMO matrix. This corrected matrix allows the Cholesky factorisation usually used for generation of synthetic MIMO channel samples. The applicability of the CP has been analysed using real data from non-line-of-sight (NLOS) indoor measurements. The results reported in this paper show that a proper selection of the CP parameters has not a sensitive impact on the cumulative distribution function (CDF) of the eigenvalues of the estimated FSC MIMO matrices. This characteristic makes the CP useful for channel characterisation, allowing to assess the performance of a MIMO system. As an example of the CP application, a study of ergodic and outage MIMO capacities for different array configurations is presented .