Bayesian inference for amplitude distribution with application to radar clutter

Abstract

The performance of telecommunication systems is significantly subject to scattered signals superposed at the receivers. Notably, if the superposed scattered signals are impulsive in nature, this leads to burst effect on the communicated symbols. Thus, attaining an accurate estimate of the parameters of the underlying statistical model of the aggregate scattered signals becomes more important. More specifically, in the case of radar applications, finding efficient estimators for the amplitude distribution has been found to be of highly importance. In this article, the Bayesian approach has been adopted for parameter estimation of the amplitude distribution. To this end, within a Gibbs sampling framework, this would be done by the sampling from four full conditionals which can be performed in a straightforward manner. Depending on the size of sample, two types of priors, i.e. Jeffreys (small size) and conjugate (non-small size), are considered for the scale parameter of the amplitude distribution. While using the conjugate prior, hyperparameters can be found through the empirical Bayes. For the purpose of validation of the proposed approach, performance of the adopted Bayesian paradigm will be demonstrated through the simulation study. Furthermore, analysis through real datasets of radar signals reveals that the proposed Bayesian approach outperforms the known moment and log-moment estimators of the amplitude distribution and works better than the maximum likelihood estimator when sample size is small.