Progressive evolution of fractal random arrays by generator mitosis

In an effort to design robust low side-lobe antenna arrays, a new class of arrays, called the fractal random array, has been proposed that includes both fractal and random features (Kim, Y. and Jaggard, D.L., 1996; Werner. D.H. and Mittra, R., 2000). A deterministic fractal array can be created through the repeated application and scaling of a simple motif known as the generator pattern. A fractal random array is created similarly; however, multiple generator patterns are used and chosen randomly. The fractal aspects of the array provide radiation characteristics similar to periodic arrays, and the random aspects provide characteristics similar to random arrays. Thus, fractal random arrays are able to bridge the gap between completely deterministic (i.e., periodic) and completely random arrays by combining the good qualities of both. The paper describes a genetic algorithm approach used to evolve an optimized linear fractal random array with 848 elements and a side-lobe level of approximately -20 dB. The fitness function for the genetic algorithm is the sum of the maximum side-lobe level and a window function. Three separate mitosis processes are used to double the number of generators in each array, one initial mitosis process and two additional mitosis processes when the genetic algorithm seems to reach an evolutionary minimum. These mitosis processes result in a staircase pattern in the evolutionary diagram.