Efficient Impulsive Noise Mitigation for OFDM Systems Using the Alternating Direction Method of Multipliers

Abstract

An efficient impulsive noise estimation algorithm based on alternating direction method of multipliers (ADMM) is proposed for OFDM systems using quadrature amplitude modulation (QAM). Firstly, we adopt the compressed sensing (CS) method based on the ${\mathcal{l}}^{\mathrm{1}}$-norm optimization to estimate impulsive noise. Instead of the conventional methods that exploit only the received signal in null tones as constraint, we add the received signal of data tones and QAM constellations as constraints. Then a relaxation approach is introduced to convert the discrete constellations to the convex box constraints. After that a linear programming is used to solve the optimization problem. Finally, a framework of ADMM is developed to solve the problem in order to reduce the computation complexity. Simulation results for $\mathrm{4}$-QAM and $\mathrm{16}$-QAM demonstrate the practical advantages of the proposed algorithm over the other algorithms in bit error rate performance gains.