Impulsive Noise Suppression Based on ℓq-norm and Graph Laplacian Regularization for NOMA System

This letter proposes a method for impulsive noise (IN) suppression in non-orthogonal multiple access (NOMA) downlink system by leveraging the graph signal processing (GSP) and ℓq-norm-based sparse signal recovery theories. Within GSP framework, we propose a graph-based representation to characterize the underlying structure of the sub-carriers. Accordingly, the graph Laplacian regularization (GLR) is defined to capture the similarities between sub-carriers. Then, the IN suppression problem is formulated as a constraint optimization problem, incorporating the ℓq-norm and GLR, which can efficiently characterize the sparsity of IN and the underlying structure of the sub-carriers. Finally, an augment Lagrange multiplier (ALM) framework is introduced to solve the optimization problem. Numerical experiment results illustrate the effectiveness of the proposed method in comparison with existing methods.