Pattern Synthesis for Large Planar Arrays Using a Modified Alternating Projection Method in an Affine Coordinate System

A pattern synthesis approach based on a modified alternating projection method in an affine coordinate system is proposed in this paper. The approach is suitable for large planar arrays with skewed element layout. According to the affine transformation theory, the radiation pattern of the array with a periodic parallelogram element layout could be written down immediately from that of a conventional one with rectangle cells when a pattern invariant group is defined. Just as known, the conventional alternating projection method is sensitive to the starting point and easy to fall into local optimum; in this paper we introduce a modified alternating projection method with a variable projection operator. To verify the rationality of the proposed method, several examples have been performed on our personal computer. Results show that the method could quickly synthesize the array patterns to the required with high accuracy. In addition, if the array has a triangle or parallelogram element layout, the required antennas to fill up the aperture is reduced when compared with the conventional one with antennas arranged along a rectangle grid. In our examples, the maximum reduction is about 18.09%, which is quite beneficial to reduce the weight and cost of the array.