Sparsity-aware DOA estimation of quasi-stationary signals using nested arrays

Direction of arrival (DOA) estimation of quasi-stationary signals (QSS) impinging on a nested array in the context of sparse representation is addressed in this paper. By exploiting the quasi-stationarity and extended virtual array structure provided inherently in the nested array, a new narrowband signal model can be obtained, achieving more degrees of freedom (DOFs) than the existing solutions. A sparsity-based recovery algorithm is proposed to fully utilise these DOFs. The suggested method is based on the sparse reconstruction for multiple measurement vector (MMV) which results from the signal subspace of the new signal model. Specifically, the notable advantages of the developed approach can be attributed to the following aspects. First, through a linear transformation, the redundant components in the signal subspace can be eliminated effectively and a covariance matrix with a reduced dimension is constructed, which saves the computational load in sparse signal reconstruction. Second, to further enhance the sparsity and fit the sampled and the actual signal subspace better, we formulate a sparse reconstruction problem that includes a reweighted ℓ1-norm minimisation subject to a weighted error-constrained Frobenius norm. Meanwhile, an explicit upper bound for error-suppression is provided for robust signal recovery. Additionally, the proposed sparsity-aware DOA estimation technique is extended to the wideband signal scenario by performing a group sparse recovery across multiple frequency bins. Last, upper bounds of the resolvable signals are derived for multiple array geometries. Extensive simulation results demonstrate the validity and efficiency of the proposed method in terms of DOA estimation accuracy and resolution over the existing techniques.