Steerable Sparse Linear Array Synthesis using Alternating Direction Method of Multipliers

In this paper, we present the Sparse Linear Array (SLA) synthesis using Alternating Directional Method of Multipliers (ADMM). The array has been synthesized for 2D Underwater Forward Looking Sonar (FLS) imaging system. The steerable SLA has been synthesized earlier using Multiple Measurement Vectors (MMV) Compressive Sensing (CS) method in far-field as well as in near-field. Synthesizing steerable SLA using MMV CS method for a high angular resolution imaging system with very fine resolution beam spacing pose challenges in terms of execution time and amount of requirement of the system memory. The ADMM algorithm includes steps which involve multiplication of vector and matrices and thus, reduces the execution time in synthesis of SLA and overcome the requirement of a very large system memory. The synthesized SLA using ADMM achieves similar sparsity and beampattern characteristics as achieved by MMV CS method and, allows to synthesize steerable SLA for very high angular resolution and fine beam spacing. We present the design of FLS operating at 300 kHz in far-field, 600 kHz and 1.2 MHz in near-field having angular resolution 0.86°, 0.44° and 0.22° in the broadside respectively. The beam spacing are 0.8°, 0.8° and l° in the field of view -30° to 30° for the SLA operating at 300 kHz, 600 kHz and 1.2 MHz. We also present the design of SLA operating at 1.2 MHz having angular resolution same as above but beam spacing is 0.25° instead 1°, which shows that the limitation imposed by MMV method in terms of large system memory has been overcome by ADMM method.