Estimação de parâmetros por máxima verossimilhança para ambientes generalizados do canal sem fio

Abstract

In this Master thesis, Maximum Likelihood (ML) estimators for the parameters of the a-k-u and a-n-u distributions are proposed. These general distributions have been used to model the envelope of the received signal in different scenarios, and they have been considered applicable from a practical point of view. The a-k-u and a-n-u distributions have parameters that characterize specifically the behavior of the envelope of the signal that propagates through communication channels modeled by them. That way, in the modeling of the communication systems that operate in a-k-u and a-n-u environments, it is necessary to know the values of the parameters of the distributions. Hence, efficient estimators are used to infer them from samples of the signal’s envelope, aiming to provide an exchange of information with quality and in a reliable way. The ML parameter estimators for the a-k-u and a-n-u distributions are proposed and verified against true values of the parameters by means of simulations. The samples used in the estimation are generated by three different random sequence generators, and a comparison of the performance of the estimators for the samples generated by different methods is done. Besides, this work presents a comparison of the theoretical and estimated probability density functions of the signal’s envelope and an analysis of the variances of the estimators considering a lower bound. The results show that the estimators obtained were capable of predicting, with a good performance, the behavior of the envelope of the signal that propagates in the mobile channel. As an original contribution of this research, the simplified expressions for the log-likelihood function of the a-k-u and a-n-u distributions were found, as well as their derivatives in respect to the parameters of the distributions. Besides, the Smith Spectrum method for random numbers generation was adapted to generate random samples following the distributions regarding this thesis.