A Bayesian estimator for correlation parameters of the multivariate nakagami-m distribution

In this report, we presented a novel Bayesian estimator for the correlation parameters of the multivariate Nakagami-m distributions. The proposed estimator has a two-stage structure. First, a generalized Gibbs sampler - the group-based sampler is constructed to analyze the posterior distributions of the parameters, which leads to a lower time complexity compared to the traditional Gibbs sampler. Second, a multi-proposal Metropolis-Hastings algorithm is implemented within the group-based sampler. In the Metropolis-Hastings stage, estimation values are obtained by computing the weighted mean of both accepted and rejected states. It makes the estimation variance lower compared to the traditional methods using only the accepted states. Numerical simulation results demonstrate that our new estimator is practically unbiased except some points and it offers a relatively small estimation variance.