Variational Sparse Bayesian Learning for Estimation of Gaussian Mixture Distributed Wireless Channels

In this paper, variational sparse Bayesian learning is utilized to estimate the multipath parameters for wireless channels. Due to its flexibility to fit any probability density function (PDF), the Gaussian mixture model (GMM) is introduced to represent the complicated fading phenomena in various communication scenarios. First, the expectation-maximization (EM) algorithm is applied to the parameter initialization. Then, the variational update scheme is proposed and implemented for the channel parameters' posterior PDF approximation. Finally, in order to prevent the derived channel model from overfitting, an effective pruning criterion is designed to eliminate the virtual multipath components. The numerical results show that the proposed method outperforms the variational Bayesian scheme with Gaussian prior in terms of root mean squared error (RMSE) and selection accuracy of model order.