Synthesis of Multibeam Sparse Circular-Arc Antenna Arrays Employing Refined Extended Alternating Convex Optimization

A refined extended alternating convex optimization (REACO) method is presented to synthesize multibeam sparse circular-arc antenna arrays with minimum element spacing control by considering real antenna array structure characteristics. This method consists of the initial step and a few refining steps. At the initial step, an initial array with dense elements distributed on a circular-arc is considered, and its array manifold vector is described by rotating a simulated isolated element pattern (IEP) without considering element mutual coupling. The collective excitation coefficient vector (CECV) and its energy bound are introduced for each element, and consequently, the common element positions for generating desired multibeam patterns can be found by minimizing the number of active CECVs under multiple constraints. This minimization problem is further formulated as performing a sequence of alternating convex optimization (ACO) in which the CECV and an auxiliary weighting vector are alternately chosen as the optimization variables so that the minimum element spacing constraint can be easily dealt with. Once the initial optimization step is finished, a few refining steps are performed in which the element positions and excitations are successively updated in each step by renewing the array manifold vector through rotating the simulated nearby active element patterns (AEPs) of the antenna array obtained at the previous step. In such a way, the mutual coupling can be incorporated into the multibeam sparse array synthesis. An example of synthesizing a sparse circular-arc conformal array with 23 beams covering the space from −63.25° to 63.25° is conducted to validate the effectiveness and advantage of the proposed method.