Joint channel and impulsive noise estimation method based on approximate message passing for NOMA systems

To address the channel estimation problem for non-orthogonal multiple access (NOMA) systems under non-Gaussian impulsive noise, a joint channel and impulsive noise estimation method based on approximate message passing was proposed, by exploiting the joint sparsity of the channel and impulsive noise. Firstly, based on sparse Bayesian learning theory, a compressed sensing equation was constructed by using all subcarriers, and then a joint estimation optimization problem for the channel, impulsive noise, and data symbols was proposed. To address this hyperparameter nonlinear non-convex problem, an expectation maximization (EM) implementation algorithm based on Gaussian generalized approximation message passing and sparse Bayesian learning (SBL) theory was designed. Simulation results show that compared to the SBL method based on EM, the proposed algorithm exhibited a slight degradation in terms of mean square error (MSE) for channel and impulsive noise estimation, bit error rate (BER). However, the complexity of the proposed algorithm was reduced by one order of magnitude.