Multiband grid-free compressive beamforming

Recently, the grid-free compressive beamforming approach was proposed to perform direction-of-arrival (DOA) of sources using observations collected from an array of sensors; however, it is limited to sources with a single frequency. This paper extends it by considering a wideband signal impinging an array and introduces a continuous formulation of the discretized multiband representation of the impinging signal. Next, a sparsity measure is proposed to promote the continuous variable's sparsity. In turn, the DOA estimation problem with infinite unknowns is derived and solved over a few optimization variables with the semidefinite programming. Further, it is demonstrated that the derived problem possesses properties that can be exploited. Accordingly, when the absolute frequency differences phrased in wavelengths are larger than twice the array spacing, an aliased-free DOA estimation can be achieved. Results from simulation and experimental example confirms that at aliasing condition, with sufficient sensors, the proposed approach provides improved DOA estimation using a small number of continuous multiband frequencies compared to other methods using discrete signal model formulation.