Scalable Alternating Projection and Proximal Splitting for Array Pattern Synthesis

Array synthesis with embedded element patterns is a problem of great practical importance. In this paper, an array pattern synthesis method using scalable alternating projection and proximal splitting is proposed which considers the scaling invariance property of design specifications and constraints for the amplitudes of pattern and excitation. Under the framework of alternating projection, the scalable pattern and excitation constraint sets are first defined. Then the scalable pattern projection and iterative procedure for optimum pattern scaling factor are studied in detail. For the scalable excitation projection, it is designed as the solution to a constrained weighted least mean squares optimization, which can be solved by an effective forward-backward splitting iterative process. Finally, the selection of the weighted matrix and computational complexity are discussed briefly. Several typical linear and planar synthesis examples with or without the embedded element patterns are provided to demonstrate the effectiveness and power of the proposed method.