Stochastic optimization methods for angle of arrival estimation

The difficulty for accurate determination of the angles of arrival (AOA) of signals arises from the optimization of likelihood functions of high dimension. Usually, a gradient-based technique is employed to find the optimum of the function. However, this method requires heavy computational work and the differentiability of the likelihood function. This paper presents two gradient-free methods: One is based on the Markov Chain Monte Carlo (MCMC) method and the other applies particle swarm optimization (PSO) to estimate the AOA. The main difference between the two methods is that the PSO-based method exploits multiple random search paths, while the MCMC-based method only employs undirected random search along a single path. A practical search space is also proposed for the case of symmetric objective functions to reduce the computational work in a manner that the traditional PSO stopping criteria is still applicable. To illustrate these techniques, a uniform linear antenna array is considered under the influence of additive complex Gaussian noise.