Pattern synthesis with desired magnitude response for arbitrary arrays

A pattern synthesis with desired magnitude response based on the combination of genetic algorithm and convex optimization is proposed. The phase in mainlobe is used as the optimization variables for genetic algorithm, and the fitness function is constructed with the desired magnitude of mainlobe. The optimal fitness degree for the corresponding individual can be obtained through solving the fitness function with the convex optimization, which improves the algorithm search performance with great efficiency. The optimization design in phase makes the synthesis result has no relation to the array reference point and the proposed algorithm is suit for the array synthesis with arbitrary element positions. The validity of method is confirmed by the result of the simulate data.