A Novel Method for Maximum Directivity Synthesis of Irregular Phased Arrays

A novel and effective method for the design of maximum directivity irregular phased arrays is proposed in this article. By decomposing the radiation pattern of irregular arrays (IAs) into the product of subarray pattern and subarray array factor, the principal factor for the reduction of directivity and the appearance of high sidelobes is analyzed. Aimed at maximizing directivity of IAs, a binary quadratic optimization problem (BQOP) is established for the design of subarray tiling configuration, where the directivities at considered scanning angles satisfying given peak sidelobes level (SLL) is maximized. To consider the directivities at all the scanning angles within given scan ranges, a concept of “generalized directivity” is introduced and defined. Meanwhile, it is known that high directivity usually enables to suppress high SLL to a great extent. Therefore, the BQOP is reduced to a simplified binary quadratic problem (SBQP) for the maximization of the “generalized directivity” without the high-dimensional constraint on SLL. The associated complex excitations at subarray level are solved using convex optimization after the subarray tiling configuration is determined. By comparing to the reported state-of-the-art methods, several representative numerical examples are implemented to assess the effectiveness of the proposed method.