DOA estimation with channel gain‐phase uncertainties via Schur‐product and RARE algorithm

Direction‐of‐arrival (DOA) estimation for L‐shaped array with channel gain‐phase uncertainties is addressed in this study. The channel gain uncertainties are estimated and removed by the method proposed by Wylie et al., and the phase uncertainties are eliminated by Schur‐product of the covariance matrix of received data and the corresponding conjugate. The newly constructed matrix based on Schur‐product can be regarded as the virtual covariance matrix corresponding to non‐coherent virtual 2D sources, whose 2D DOAs are associated with the original sources’, impinging on a virtual L‐shaped array. This finding can provide the chance of the usage of propagator‐method‐rank‐reduction (PM‐RARE) algorithm proposed in this study for the virtual L‐shaped array to obtain 2D DOAs of virtual sources. With the uncertainties removed, 1 component due to the Schur‐product of the steering vector and its conjugate should be eliminated via a novel rank reduction (RARE) method. Otherwise, it may interfere in distinguishing the adjacent sources. Then the DOAs can be estimated with PM‐RARE, which decouples and estimates two parameters related to elevation and azimuth of virtual 2D sources via RARE and eigendecomposition, respectively, without pairing parameters. This proposed on‐line method avoids multi‐dimensional parameter search occurring in the alternative iteration method. Numerical examples verify its effectiveness.