Underdetermined High-Resolution DOA Estimation: A 2ρth-Order Source-Signal/Noise Subspace Constrained Optimization

For estimating the direction of arrival (DOA)s of non-stationary source signals such as speech and audio, a constrained optimization problem (COP) that exploits the spatial diversity provided by an array of sensors is formulated in terms of a noise-eliminated local th-order cumulant matrix. The COP solution provides a weight vector to the look direction such that it is constrained to the th-order source-signal subspace when the look direction is in alignment with the true DOA; otherwise, it is constrained to the th-order noise subspace. This weight vector is incorporated into the spatial spectrum to determine the degree of orthogonality between itself and either the th-order source-signal subspace when the number of sources is unknown, or the th-order noise subspace when the number of sources is known. For a uniform linear array (ULA) of sensors, the spatial spectrum for known number of sources can theoretically be shown to identify up to sources. Realizing the difficulty in identifying stationarity in the received sensor signals, the estimate of the noise-eliminated local th-order cumulant matrix is marginalized over various possible stationary segmentations, for a more robust DOA estimation. In this paper, we focus on the use of local second and fourth order cumulants ( , 2), and the proposed algorithms when outperformed the KR subspace-based algorithms and also the 4-MUSIC for globally non-stationary, non-Gaussian synthetic data and also for speech/audio in various adverse environments. We verified that the identifiability for is improved by two-folds compared to that for with an ULA.