Underdetermined High-Resolution DOA Estimation: A $2\rho$ th-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 2ρth-order cumulant matrix. The COP solution provides a weight vector to the look direction such that it is constrained to the 2ρth-order source-signal subspace when the look direction is in alignment with the true DOA; otherwise, it is constrained to the 2ρth-order noise subspace. This weight vector is incorporated into the spatial spectrum to determine the degree of orthogonality between itself and either the 2ρth-order source-signal subspace when the number of sources is unknown, or the 2ρth-order noise subspace when the number of sources is known. For a uniform linear array (ULA) of M sensors, the spatial spectrum for known number of sources can theoretically be shown to identify up to 2ρ(M-1) sources. Realizing the difficulty in identifying stationarity in the received sensor signals, the estimate of the noise-eliminated local 2ρth-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 ( ρ = 1, 2), and the proposed algorithms when ρ = 1 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 ρ = 2 is improved by two-folds compared to that for ρ = 1 with an ULA.