Multi-beam Synthesis for Reconfigurable Sparse Array via New Consensus PDD Framework

A reconfigurable sparse array radiates multiple patterns from a single array while using fewer array elements through the design of the array structure. To address this array design problem, a new consensus penalty dual decomposition (CPDD) method was proposed in this work based on the concept of consensus computation. The CPDD method is a double-loop iterative algorithm. It employs a virtual star-shaped topology graph network. The central node of the network corresponds to the global variable, i.e. the common array structure, while each of the edge nodes corresponds to a single beam synthesis task. In the outer loop, the algorithm collects excitation vector information from the edge nodes through the center node and then integrates the information to obtain a better common array structure. In the inner loop, each beam is synthesized locally in the corresponding edge node based on the information provided by the central node. Finally, all edge nodes achieve a consistent array structure. Some numerical simulations were performed to verify the effectiveness of the algorithm in different situations. They show that the proposed method CPDD has good performances. It can achieve a satisfactory radiation pattern with fewer antennas in different application cases.