EM independent Gaussian approximate message passing and its application in OFDM impulsive noise mitigation

We propose an empirical compressed learning approach based on generalized approximate message passing (GAMP) for deterministic sensing matrix with low spark. The spark of a matrix is defined as the minimum number of correlated columns. In contrast to previous works, GAMP with independent and non-identically distributed Gaussian prior for the sparse signal to be estimated is used to avoid the over-fitting problem in the original GAMP. Specifically, we consider the discrete Fourier transform (DFT) sub-matrix as part of the sensing matrix which is common used in communication systems. Then we consider using the proposed approach to the estimation and mitigation of impulsive noise in orthogonal frequency division multiplexing (OFDM) systems utilizing null tones. Numerical results show that the performance of the proposed method is close to sparse Bayesian learning (SBL) for low spark DFT matrices and about 1dB performance gain in symbol error rate (SER) is observed over existing GAMP based approaches for Gaussian mixture interferences and more than 5dB gain at symbol error rate (SER) of 0.01 for stable-alpha-symmetric interference. The complexity is only O(Nlog2N), where N is the size of the signal to be estimated.