Synthesizing Shaped Power Patterns for Linear and Planar Antenna Arrays Including Mutual Coupling by Refined Joint Rotation/Phase Optimization

In this article, a novel strategy based on refined joint element rotation/phase optimization is presented to obtain vectorial shaped power patterns for antenna arrays with arbitrary element structures including mutual coupling. The active element pattern (AEP) is used for each antenna element, and then the rotation of an element is approximately described by mathematically rotating its AEP under the assumption that the mutual coupling variation does not change the AEP considerably. Optimal element rotations and phases for an array can be found by solving a vectorial shaped pattern synthesis problem such that the obtained array pattern has the desired co-polarization mainlobe shape while maintaining constrained sidelobe and cross-polarization levels. However, due to the variation of mutual coupling, this synthesized pattern may deviate from the real array pattern. To reduce the pattern discrepancy, successive refined joint element rotation/phase optimizations are adopted. As the number of refining steps increases, the allowable element rotation range is set to be smaller and smaller so that the synthesized array pattern can get closer and closer to the real one. Such a shaped power pattern synthesis technique does not need nonuniform amplitude weighting, thus saving many unequal power dividers. Three examples for synthesizing rotated linear and planar arrays with different antenna structures and different pattern shape requirements are provided to validate the effectiveness and advantages of the proposed method.