Stochastic optimization of linear sparse arrays

In conventional beamforming systems, the use of aperiodic arrays is a powerful way to obtain high resolution employing few elements and avoiding the presence of grating lobes. The optimized design of such arrays is a required task in order to control the side-lobe level and distribution. In this paper, an optimization method aimed at designing aperiodic linear sparse arrays with great flexibility is proposed. Simulated annealing, which is a stochastic optimization methodology, has been utilized to synthesize the positions and the weight coefficients of the elements of a linear array in order to minimize the peak of the sidelobes and to obtain a beam pattern that meets given requirements. An important novelty is the fact that the latter goal can be achieved in parallel to the minimization of both the number of elements and the spatial aperture, resulting in a “global” optimization of the array characteristics. The great freedom that simulated annealing allows in defining the energy function to be minimized is the main reason for the notable versatility and the good results of the proposed method. Such results show an improvement in the array characteristics and performances over those reported in the literature