Joint channel and impulse noise estimation based on compressed sensing and Kalman filter for OFDM system

Abstract Impulse noise (IN) widely exists in many communication systems, which seriously affects the performance of OFDM communication systems. A joint channel and IN estimation method based on all subcarriers is designed. This method uses a sparse Bayesian learning (SBL) algorithm incorporating forward–backward Kalman filter (FB-Kalman) to tackle the problem of joint channel and IN estimation and data detection for OFDM systems. Firstly, the channel impulse response and IN are regarded as unknown sparse vectors, and a SBL framework using all subcarriers is proposed to estimate the unknown vector. The SBL theory is used based on the prior distribution of variables, and then the forward–backward joint system is established, which applies the data detection simultaneously. We also propose the FB-Kalman implementation algorithm by using the expectation maximization updates. Explicit expressions of mean and covariance matrix of the posterior distribution are derived in the E-step. Simulation results show that the proposed algorithm improves the normalized mean square error and bit error rate performance of OFDM system in the presence of IN communication environment.