Multi-source off-grid DOA estimation with single snapshot using non-uniform linear arrays

Direction of arrival (DOA) estimation methods suffer from the well-known off-grid problem, that shows up when the true DOAs are not located exactly on the discretized sampling grid points. Existing estimation algorithms should be designed by taking into account the trade-off between density of sampling grids and computational complexity. Moreover, most of the computationally efficient DOA methods cannot be applied to non-uniform linear arrays (NLAs). In order to overcome these drawbacks, we propose a simple but effective off-grid DOA (OGDOA) estimation method that adopts an “estimate and subtract” strategy and then iteratively corrects the DOA estimate of each source based on a closed-form estimator that does not suffer from the off-grid problem. We derived the analytical expression of the mean square error (MSE) of the proposed method and verified that the MSE approaches the Crame´r-Rao lower Bound (CRB) when the signal-to-noise ratio (SNR) increases. We also analyzed the convergence of the proposed OGDOA algorithm. Numerical analyses demonstrated the goodness of the proposed method for OGDOA estimation for single snapshot and NLAs over some existing methods.