Design of high performance compact linear ultra-wideband arrays with the CMA evolutionary strategy

Many high-performance ultra-wideband array topologies have recently arisen that utilize mathematical constructs such as fractals or simple mathematical expressions to determine element locations [1] - [2]. The main motivation of these methods is to reduce the scale of the optimization problem such that it is feasible for the evolutionary strategy. In this manner, large arrays can be successfully optimized with a reasonably small set of controlling parameters. However, for an array with a small number of elements, these methods can be constraining and lead to less than acceptable peak sidelobe level performances and poor bandwidths. For these small arrays, the element locations can be directly specified with the optimization tool if it is capable of handling the large parameter set. Previous attempts using the genetic algorithm (GA) [3] with array sizes of eight to 24 elements and large scan angles (analogous to a small bandwidth) were preformed in [4]. With a more powerful evolutionary strategy, problems with large parameter sets become much more practical and yield better results. The covariance matrix adaptation evolutionary strategy (CMA-ES) is a recently developed and extremely powerful optimization tool that has shown itself to be a leader in speed and possesses an excellent capacity for handling problems of large dimensions [5]. It is applied here to the direct optimization of element spacings for relatively small to moderate size ultrawideband antenna arrays in order to extract the best performance possible from a limited number of antenna elements.