Direction of Arrival Estimation of Wideband Sources Using Sparse Linear Arrays

In this paper, we study the problem of wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs), where a number of uncorrelated wideband signals impinge on an SLA and the data is collected from multiple frequency bins. To boost the performance and perform underdetermined DoA estimation, the difference co-array response matrices for all frequency bins are constructed first. Then, to merge the data from different frequency bins, we resort to the Jacobi-Anger approximation to transform the co-array response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. The major advantage of this approach is that the transformation matrices are all signal independent. For the special case where all sources share an identical distribution of the power spectrum, we develop two super-resolution off-the-grid DoA estimation approaches based on atomic norm minimization (ANM), one with and one without prior knowledge of the power spectrum. Our solution is able to resolve more sources than the number of antennas but also more than the number of degrees of freedom (DoF) of the difference co-array of the SLA. For the general case where each source has an arbitrary power spectrum, we propose a multi-task ANM method to exploit the joint sparsity from all frequency bins. Simulation results show that our proposed methods present a clear performance advantage over existing methods, and achieve an estimation accuracy close to the associated Cramér-Rao bounds (CRBs).