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).@en

This paper concerns wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs). We rely on the assumption that the power spectrum of the wideband sources is the same up to a scaling factor, which could in theory allow us to resolve not only more sources than the number of antennas but also more sources than the number of degrees of freedom (DoF) of the difference co-array of the SLA. We resort to the Jacobi-Anger approximation to transform the coarray response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. Based on the obtained model, two super-resolution DoA estimation approaches based on atomic norm minimization (ANM) are proposed, one with and one without prior knowledge of the power spectrum. Simulation results show that our proposed methods outperform the state of the art and are indeed capable of resolving more sources than the number of DoF of the difference co-array.@en