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Gaussian mixture model approximation of total spatial power spectral density for multiple incoherently distributed sources

Practically, the spatial power spectral density (PSD) of single or multiple incoherently distributed (ID) sources is often unknown, and the total spatial PSD is suitable to model the spatial distribution characteristic of signals if the number of multiple ID sources is also unknown. In this study, the Gaussian mixture model (GMM) is employed to characterise the total spatial PSD of multiple ID sources, and two algorithms are proposed to estimate the parameters of the GMM. The first one is the covariance fitting method for multiple ID sources with Gaussian PSD, and the other is the iterative expectation maximisation (EM) algorithm. Simulation studies demonstrate that the EM algorithm outperforms other methods in approximating the shape of the total spatial PSD, especially for small spatial spread.