A Forward-Backward Matrix Pencil and Variable Projection Based Method for Reducing the Number of Elements in Shaped-Beam Pattern Linear Arrays

This paper presents a variable projection based method, used along with the forward-backward matrix pencil method, for the synthesis of linear arrays with shaped-beam patterns employing a least number of antenna elements. The forward-backward matrix pencil method has been used previously for this application. However, the array factor obtained using fewer elements may not always provide a satisfactory approximation of the true array factor, as demonstrated by some examples in this work. Therefore, we propose incorporating a variable projection iterative step to enhance the performance of the array derived from the forward-backward matrix pencil method.