Distributed Convex Optimization Compressed Sensing Method for Sparse Planar Array Synthesis in 3-D Imaging Sonar Systems

Synthesis of sparse planar arrays can effectively reduce hardware costs and computational complexity in phased array 3-D imaging sonar systems. Traditional stochastic methods, such as simulated annealing, require multiple experiments and parameter adjustments to obtain optimal results. Methods based on compressed sensing (CS) can overcome this defect. However, when applied to large arrays, CS methods require vast computational complexity and may not obtain optimal sparse results because of violating the restricted isometry property. To make CS methods more practical, a distributed convex optimization CS method is proposed here for the sparse planar array synthesis in 3-D imaging sonar systems. This method is based on the CS theory, solving the minimum number of active elements under certain beam pattern constraints using the iterative reweighted l₁-norm minimization algorithm. Then, a multistage distributed framework is proposed to decompose the array into multistage subarrays, and the array synthesis is performed sequentially for each stage subarray to reduce computational complexity and obtain higher sparsity rates. Some applications of sparse planar array synthesis are employed to evaluate the efficiency of the proposed method.