Abstract-The least square method has been widely applied in many fields. However, when the approach is used for antenna array pattern synthesis, it is not excellent. In this paper, the least square method is used to synthesize antenna array pattern, and its performance is reviewed. Then contraposing to the shortcoming of the least square method, a new steerable least square (SLS) method is put forward. For an antenna array whose manifold matrix has been determined, the projection matrix equation can be derived from array manifold matrix easily. In order to get premium solution of array element excitation, a novel projection matrix equation with adjustable matrices is adopted. The results of simulations show that the pattern synthesized by the traditional least square method fits the targeted pattern badly and is worse in the key performance indicators of peak level of side-lobe and null beam level than the targeted pattern; however, the pattern synthesized by the new SLS method fits the targeted pattern well in zero point and local peak distribution and is better in the key performance indicators of peak level of side-lobe and null beam level than the targeted pattern.
Rotationally symmetric sparse circular arrays are synthesized under multiple constraints. By combining the modified differential evolution algorithm based on the harmony search (in short HSDE) with the vector mapping (VM) method, a hybrid algorithm, called VM-HSDE, is proposed for synthesizing sparse circular arrays with low sidelobe levels. Due to the array's specific geometry, the number of optimization variables is reduced, and the constrained optimization problem is simplified. Moreover, infeasible solutions are avoided, and the problem is effectively solved by the VM-HSDE algorithm. Finally, three pattern optimization results verify the effectiveness and reliability of the VM-HSDE algorithm.
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