Steerable Sparse Linear Array Synthesis using Second Order Cone Programming

We present the design of steerable Sparse Linear Array (SLA) for 2D forward looking sonar imaging system in this paper. The mathematical model includes constraints for multiple steering directions in the Field Of View (FOV) and this model is based on the Compressive Sensing (CS) theory. The sparsity in this model is introduced by considering oversampled linear aperture (i.e. densely populated aperture by sensors). This model defines the Main Lobe Width (MLW) constraints indirectly by matching the beam pattern of the synthesized SLA with the desired beam pattern in the main lobe region for all steering direction. The Side Lobe Peak (SLP) constraints in this model are defined directly for all steering directions. This optimization problem is a disciplined convex program and its equivalent formulation is a second order cone programming problem. The SLA synthesized using this method has separate weights for each steering directions. The SLA synthesized using this method is compared with the SLA designed using Multiple beam, Measurement Vectors (MMV) CS method. The performance of the synthesized SLAs is compared in terms of reduction of sensors with half wavelength spacing Uniform Linear Array (ULA) and MLW % error. We present the design results of forward looking sonar imaging system for frequencies 37.5 kHz and 75 kHz having angular resolution 6.4 degrees and 3.2 degrees respectively, with 11 and 19 beams in FOV.