Antenna array synthesis using the cross entropy method

This dissertation addresses the synthesis of antenna arrays using the Cross-Entropy (CE) method, marking the first application of the CE method for solving electromagnetic optimization problems. The CE method is a general stochastic optimization technique for solving both continuous and discrete multi-extremal, multi-objective optimization problems. The CE method is an adaptive importance sampling derived from an associated stochastic problem (ASP) for estimating the probability of a rare-event occurrence. The estimation of this probability is determined using a log-likelihood estimator governed by a parameterized probability distribution. The CE method adaptively estimates the parameters of the probability distribution to produce a random variable solution in the neighborhood of the globally best outcome by minimizing cross entropy.;In this work, single and multi-objective optimization using both continuous and combinatorial forms of the CE method are performed to shape the sidelobe power, mainlobe beamwidth, null depths and locations as well as number of active elements of linear array antennas by controlling the spacings and complex array excitations of each element in the array. Specifically, aperiodic arrays are designed through both non-uniform element spacings and thinning active array elements, while phased array antennas are designed by controlling the complex excitation applied to each element of the array. The performance of the CE method is demonstrated by considering different scenarios adopted from literature addressing more popular stochastic optimization techniques such as the Genetic Algorithm (GA) or Particle Swarm Optimization. The primary technical contributions of this dissertation are the simulation results computed using the Cross Entropy method for the different scenarios adopted from literature. Cursory comparisons are made to the results from the literature, but the overall goal of this work is to expose the tendencies of the Cross Entropy method for array synthesis problems and help the reader to make an educated decision when considering the Cross Entropy method for their own problems. Overall, the CE method is a competitive alternative to these more popular techniques, possessing attractive convergence properties, but requiring larger population sizes.