Linear sparse array synthesis via convex optimization

Due to the constraint on half-wavelength inter-element spacing of a uniformly spaced array, sparse arrays are usually designed to be non-uniformly spaced. Through proper design, unequally-spaced sparse arrays can have higher spatial resolution, lower sidelobe and less number of sensors required in comparison with uniformly spaced arrays. However, the synthesis of a sparse array is a non-convex process as the array beampattern is an exponential or trigonometric function of sensor positions. In this paper, we propose a synthesis scheme, where the design of sparse arrays is formulated as a convex optimization problem. The array weights are optimized to achieve minimum Peak Sidelobe Level (PSL) as well as maximizing the sparsity of the array by optimizing an objective function that includes two terms, one measures the PSL and the other measures the sparsity of array. Sparse array is then obtained by removing those sensors with weights approximately equal to zero. The proposed design scheme eliminates the need of optimization according to sensor positions, which consequently solves the problem in non-convex optimization that cannot guarantee to find the optimum solution with reasonable computation time. Numerical studies show that it can be successfully applied to sparse array synthesis with low computational complexity. Moreover, lower PSL and higher resolution of mainlobe can be achieved in comparison with a uniformly spaced array.