Real‐valued off‐grid DOA estimation based on fourth‐order cumulants using sparse Bayesian learning in spatial coloured noise

In this study, the authors address the problem of off‐grid sparsity‐inducing direction‐of‐arrival (DOA) estimation in the context of real‐valued fourth‐order cumulants (FOC) in the presence of spatially coloured noise. Firstly, a selection matrix is constructed to eliminate the redundant data of FOC and rearrange the data in the de‐redundant FOC matrix to facilitate real processing. Then a new virtual overcomplete dictionary is constructed with coupling symmetric property by linear transform with the selection matrix. Next, the FOC matrix is transformed into a real‐valued matrix via a unitary transformation which can be sparsely represented by a real‐valued virtual overcomplete dictionary. The real‐valued sparse model is vectorised for transforming to a single measurement vector (SMV) model, and the redundant data in the vector model is further removed by another selection matrix. Finally, an off‐grid sparse model based on the real‐valued SMV is established and solved by utilising the SBL strategy. The proposed method not only reduces the computational complexity but also obtains an extended‐aperture array with increased degrees of freedom which yields high resolution, and provides superiority in performance and robustness against coloured noise. The simulation results demonstrate the effectiveness of the proposed method.