DOA estimation with planar array via spatial finite rate of innovation reconstruction

Recently, a new DOA estimation algorithm called FRIDA was proposed. It is based on spatial finite rate of innovation (FRI) reconstruction and exhibits some attractive features. In this paper, we propose a variation of FRIDA which is called FRIDA-V (suffix “-V” means variation) . FRIDA-V improves FRIDA in three aspects. Firstly, a multiple measurement vectors (MMV) spatial FRI model is built in the direct data domain rather than the covariance domain, which avoids the model residual error in FRIDA and makes the new method capable of handling both incoherent and coherent sources. Secondly, the full column rank constraint on the mapping matrix is relaxed by adopting the pseudo-inverse technique, which makes it possible to reduce the Bessel function approximation error to a negligible level. Thirdly, the multiple random initializations in the iterative calculations are replaced by a single straightforward initialization, which will speed up the convergence to the optimal solution and save the computational resource. Theoretical derivations and numerical simulation results are given to demonstrate the effectiveness of the proposed method. Compared with the representative methods, the new method is gridless and possesses higher performance with closely-spaced sources and under low signal-to-noise ratio (SNR), small number of snapshots scenarios.