Array design is the primary consideration for array signal processing, and sparse array design is an important and challenging task. In underwater acoustic environments, the vector hydrophone array contains more information than the scalar hydrophone array, but there are few articles focused on the design of the vector hydrophone array. The difference between the vector hydrophone array and the scalar hydrophone array is that each vector hydrophone has three or four channels. When designing a sparse vector hydrophone array, these channels need to be optimized at the same time to ensure the sparsity of the array elements' number. To solve this problem, this paper introduced the compressed sensing (CS) theory into the vector hydrophone array design, constructed the vector hydrophone array design problem into a globally solvable optimization problem, proposed a CS-based algorithm with the L1 norm suitable for vector hydrophone array, and realized the simultaneous optimization of multiple channels from the same vector hydrophone. At the same time, the off-grid algorithm was added to obtain higher design accuracy. Two design examples verify the effectiveness of the proposed method. The theoretical analysis and simulation results show that compared with the conventional compressed sensing algorithm with the same aperture, the algorithm proposed in this paper used fewer vector hydrophone elements to obtain better fitting of the desired beam pattern.
Keywords: array design; beam pattern; compressed sensing; off-grid.