Synthesis of Sparse Array via Convex Optimization

Design of sparse array antenna that can create the desired radiation patterns with minimum number of elements, is a favorite research area. The synthesis sparse array problem can be modeled with appropriate constraints on the number of solve space members, namely l_0-norm of the weight elements. But it is a non-convex problem that requires to solving a NP-hard problem. An interesting ideas is mentioned to relax problem to convex problem. The proposed solution is based l_1-norm; The algorithm used here, first determines the optimal radiation pattern with convex optimization. then by using iterative weighting l_1-norm, sparse array is obtained by removing those elements that weights of them are almost zero and optimally determines the position of the element. As a result, by solving the non-convexity property of the problem, the optimal solution is provided with a reasonable computational time. The purpose of the optimization method is to minimize the number of elements, observe the constraints related to the requirements of the radiation pattern and reduce the calculation time. This research, in its case study, was able to sparse the 11×11 array (121 elements) to 42 elements (increase PSL) and 37 elements (increase mainlobe beamwidth) by adjusting the relevant parameters such as DRR, γ and ε.