Amplitude-Only Pattern Synthesis of Nonuniform Linear Arrays Using a Generalized Pattern Search Optimization

Abstract

In this work, synthesis of linear array geometry and excitation amplitudes is first formulated as a linearly constrained multiobjective optimization problem with the goals of minimum sidelobe level, null control and high directivity and then solved by a generalized pattern search (GPS) algorithm for the optimum element locations and excitation amplitudes. The constraints are imposed on the interelement spacing and dynamic range ratio of the amplitude tapering to reduce mutual coupling effects between the elements. GPS methods are newly discovered, derivative-free methods where the current iterate is updated by sampling the fitness function at a finite number of points along a suitable set of search directions to find a decrease in the function value. Thus, GPS methods can be exploited efficiently in solving optimization problems without requiring any information about the gradient of the fitness function which may be even discontinuous, nondifferentiable, stochastic or highly nonlinear. Finally, four worked examples are presented that illustrate the use of the whole GPS synthesis method, and the optimization goal in each example is easily achieved. Furthermore the full-wave simulations of the synthesized arrays are also completed to examine the mutual coupling effects. Finally the results of the GPS algorithm are validated by comparing with results obtained using the genetic algorithm, and the results of the uniform and Dolph - Chebyshev arrays, having the same number of element and the same aperture length. (C) 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE 21:251-262, 2011.