Abstract
A shaped beam synthesis from a concentric ring array has been presented. Two different cases are considered. In the first case, a flat-top beam pattern and, in the second case, a cosec<sup >2</sup> beam pattern have been generated. In both the cases, it has been ensured that the obtained beam patterns are not restricted in any single predefined <svg style="vertical-align:-2.29482pt;width:10.0125px;" id="M1" height="12.325" version="1.1" viewBox="0 0 10.0125 12.325" width="10.0125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,7.825)"><path id="x1D711" d="M559 271q0 -109 -83 -187t-189 -89l-36 -213q-16 -30 -86 -43l-7 9q10 36 53 242q-91 11 -139.5 63.5t-48.5 132.5q0 186 242 271l11 -28q-76 -34 -119.5 -91.5t-43.5 -136.5q0 -66 29 -108.5t77 -55.5q39 205 56 260q21 71 65 111t93 40q50 0 88 -45.5t38 -131.5z
M484 273q0 65 -26.5 99t-52.5 34q-37 0 -53 -75l-59 -298q80 5 135.5 74.5t55.5 165.5z" /></g> </svg>-cut of the patterns; rather, their characteristics are retaining within a range of predefined <svg style="vertical-align:-2.29482pt;width:10.0125px;" id="M2" height="12.325" version="1.1" viewBox="0 0 10.0125 12.325" width="10.0125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,7.825)"><use xlink:href="#x1D711"/></g> </svg>-planes with some minor variations. The desired beam pattern under each of the individual case is obtained by finding optimum discrete excitations of the array elements. The optimum 4-bit amplitudes generated by four-bit digital attenuators and 5-bit phases generated by 5-bit digital phase shifters are computed using Differential Evolution (DE) Algorithm. To illustrate the effectiveness of DE, the two beam patterns with specified characteristics are computed from the same array using Particle Swarm Optimization (PSO) algorithm and Genetic algorithm (GA) by finding out optimum discrete excitations among the elements. Results clearly show the superiority of DE over PSO and GA to handle the presented problem.
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