In order to reduce the complexity and cost of an N×M large planar array from a practical point of view, firstly, the array matrix is divided into four equal N/4×M/4 quarter regions, and then only one quarter is selected to be optimized. After that, this selected quarter region is tiled with a few irregular polyomino clusters (IPC) and then rotating it to the other three-quarter regions. This method is called Quarter Region Rotational Symmetry (QRRS). The copy from the selected region is rotated by three angles 90,180 and 270 degrees respectively until the main planar array is filled. Two methods of feeding clusters based on amplitude only and phase only were used to reduce the complexity further. In addition, the complexity can bereduced more by applying the thinning technique with clusters or building clusters for a part of the planar array. A genetic algorithm (GA) is used to implement these ideas until a radiation pattern (RP) useful for modern applications. An additional constraint is included in the optimization process represented by a mask to cover the pattern according to the desired shape. The simulation results showed that the RP can be fully controlled by applying the QRRS technique successfully while reducing the complexity of the feeding network to only 2.25% in the amplitude-only and phase-only cases, and 1.75% and 1.5% in the thinning and partially tiling cases, respectively. Moreover, a detailed design of the feeding network circuit of the main planar array based on IPCis given for practical implementation.
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