Hidden Markov blind source separation of post-nonlinear mixture

In this paper, a novel solution is developed to solve the problem of separating noisy and post-nonlinearly distorted mixture. In the proposed work, the source signals are nonstationary and temporally correlated. A generative model based on hidden Markov model (HMM) is derived to track the nonstationarity of the source signal while the source signal itself is modeled by temporally correlated generalized Gaussian distribution (GGD) model. The maximum likelihood (ML) approach is developed to estimate the parameters of the proposed model by using the expectation maximization (EM) algorithm and the source signals are estimated by maximum a posteriori (MAP) approach. The strength of the proposed approach lies in the tracking of the nonstationarity of the source signal by HMM and the temporal correlation by the autoregressive (AR) source model. This has resulted in high performance accuracy, fast convergence and efficient implementation of the estimation algorithm. Simulations have been investigated to verify the effectiveness of the proposed algorithm and the results have shown significant improvement has been obtained when compared with nonlinear algorithm without using HMM.