Off-grid sparse DOA estimation based iterative reweighted linear interpolation in spatial coloured noise

An off-grid sparse direction-of-arrival (DOA) estimation algorithm, namely, iterative reweighted linear interpolation (IRLI), is proposed to avoid the declination of the DOA estimation precision present in unknown spatial coloured noise. The authors start by developing an off-grid sparse model based on linear interpolation with reweighted coefficient, which is a trade-off between tangent and secant offset, to guarantee an optimal approximation for off-grid signals. Next, the authors formulate the DOA estimation problem as solving the off-grid sparse model and, finally, the off-grid sparse model is addressed under the general framework of sparse Bayesian learning (SBL). Additional noise in IRLI is spatially coloured for calculating its statistical properties, which is different from SBL relying on the spatial white noise assumption. Numerical results with the limited snapshots and the low signal-to-noise ratio validate the algorithm by comparing with other algorithms.