Shaped‐Beam Pattern Synthesis Through the Construction of Weighted Generalized Rayleigh Quotient

A novel shaped‐beam pattern synthesis method of generating an arbitrary footprint pattern under an arbitrary array structure is proposed. The embedded element pattern information is included in the pattern model, and a new cost function composed of three optimization items which are sidelobe levels, mainlobe ripples and mainlobe gains is constructed through the model. During the optimization process, to further enhance the performance of the synthesized pattern, a weight matrix is designed and added to the optimization items, then the generalized Rayleigh quotient approximation method is used to obtain the final array element excitations. To illustrate the good performance of the provided method, several synthesis examples with different arrays and footprints are presented. Compared with other algorithms such as Weighted alternating reverse projection (WARP) method, the proposed method can achieve better results with lower sidelobe levels, smaller mainlobe ripples and less computational load.