Reconfigurable sparse concentric ring arrays with optimized number of rings and elements

A method for synthesizing sparse reconfigurable concentric ring arrays is introduced. The method is based on convex optimization and group sparsity. In particular, the algorithm iteratively minimizes the ℓ1 norm of auxiliary variables. Each auxiliary variable defines the upper bound on the ℓ2 norm of the excitations at the same ring for all the patterns. Using this method, the ring radii and excitations for all the patterns are optimized simultaneously to ensure that all the patterns share the same set of ring radii with a different set of excitations for each pattern. This allows us to achieve all the requirements on the radiation patterns using a minimum number of rings. Also, a change to the weighting scheme during the iterative process is introduced to ensure that the optimized array has an acceptable minimum radial distance between the rings for practical implementation. Simulations were conducted to validate the proposed method. Results show that the proposed scheme saves 50% of rings compared to the phase differentiated arrays optimized using evolutionary optimization technique.