Optimal array pattern synthesis with desired magnitude response

In most applications of arrays in sonar, radar and wireless communications, we have only the magnitude requirement on the beam response. Thus, the existing techniques, which synthesize the array patterns so that both the magnitude and phase responses approximate the desired ones, lead to sub-optimal designs. A new method is introduced in this paper to synthesize the array patterns with only desired mainlobe magnitude response and prescribed sidelobe level. The resulting optimization problem is nonconvex and is implemented via iterative algorithms of convex optimization, which can be solved using the second-order cone programming method at each iteration. Results of computer simulation for a nonuniform linear array show that the method developed in this paper can obtain the less synthesized magnitude error in the mainlobe region in comparison to the existing methods, and can guarantee that the sidelobes are strictly below the prescribed threshold.