Impulse Noise Suppression for Single-Carrier Coded Systems by Monte Carlo Expectation Maximization

An efficient approach to alleviating performance loss caused by unknown (non-stationary) impulse noise, which is typically sparse and whose statistics are difficult to model accurately, was made possible in power line communications systems when the clipping operation is properly implemented. As reported in numerous papers, the clipping threshold, which impacts system performance profoundly, is closely related with the probability of impulse occurrence and the strength of the background noise. This paper first highlights that the least-absolute-shrinkage-and-selection-operator (LASSO) algorithm, aimed at estimating the regularization parameter λ and sparse vector of regression coefficients, can be interpreted as an effective clipping operation. Subsequently, a hybrid of the Bayesian LASSO and the maximum a posteriori algorithm using the Monte Carlo expectation maximization (MCEM) is proposed to simultaneously estimate the regularization parameter and detect the convolutional codeword in single-carrier coded systems subject to the impulse noise. Moreover, by exploiting information exchangeable between those two aforementioned entities, a novel termination rule on the EM iteration stage is devised. Numerical results attest the efficacy of the proposed scheme, despite a lack of statistical knowledge on impulse noise models.