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The impulsive noise can deteriorate sharply the performance of orthogonal frequency division multiplexing (OFDM) systems. In this paper, we propose a novel joint channel impulse response estimation and impulsive noise mitigation algorithm based on compressed sensing theory. In this algorithm, both the channel impulse response and the impulsive noise are treated as a joint sparse vector. Then, the sparse Bayesian learning framework is adopted to jointly estimate the channel impulse response, the impulsive noise, and the data symbols, in which the data symbols are regarded as unknown parameters. The Cramér-Rao Bound is derived for the benchmark. Unlike the previous impulsive noise mitigation methods, the proposed algorithm utilizes all subcarriers without any a priori information of the channel and impulsive noise. The simulation results show that the proposed algorithm achieves significant performance improvement on the channel estimation and bit error rate performance.INDEX TERMS Orthogonal frequency division multiplexing (OFDM), channel estimation, impulsive noise mitigation, sparse Bayesian learning (SBL), compressed sensing.

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 ℓ 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 4-QAM and 16-QAM demonstrate the practical advantages of the proposed algorithm over the other algorithms in bit error rate performance gains.