Expectation propagation (EP) is a powerful algorithm for signal recovery in compressed sensing. This letter proposes correction of a variance message before denoising to improve the performance of EP in the high signal-to-noise ratio (SNR) regime for finite-sized systems. The variance massage is replaced by an observation-dependent consistent estimator of the mean-square error in estimation before denoising. Massive multiple-input multiple-output (MIMO) is considered to verify the effectiveness of the proposed correction. Numerical simulations show that the proposed variance correction improves the high SNR performance of EP for massive MIMO with a few hundred transmit and receive antennas.

This paper addresses pilot contamination in massive multiple-input multiple-output (MIMO) uplink. Pilot contamination is caused by reuse of identical pilot sequences in adjacent cells. To solve pilot contamination, the base station utilizes differences between the transmission frames of different users, which are detected via joint channel and data estimation. The joint estimation is regarded as a bilinear inference problem in compressed sensing. Expectation propagation (EP) is used to propose an iterative channel and data estimation algorithm. Initial channel estimates are attained via time-shifted pilots without exploiting information about large scale fading. The proposed EP modifies two points in conventional bilinear adaptive vector approximate message-passing (BAd-VAMP). One is that EP utilizes data estimates after soft decision in the channel estimation while BAd-VAMP uses them before soft decision. The other point is that EP can utilize the prior distribution of the channel matrix while BAd-VAMP cannot in principle. Numerical simulations show that EP converges much faster than BAd-VAMP in spatially correlated MIMO, in which approximate message-passing fails to converge toward the same fixed-point as EP and BAd-VAMP.

Sparse orthogonal matrices are proposed to improve the convergence property of expectation propagation (EP) for sparse signal recovery from compressed linear measurements subject to known dense and ill-conditioned multiplicative noise. As a typical problem, this letter addresses generalized spatial modulation (GSM) in over-loaded and spatially correlated multiple-input multiple-output (MIMO) systems. The proposed sparse orthogonal matrices are used in precoding and constructed efficiently via a generalization of the fast Walsh-Hadamard transform. Numerical simulations show that the proposed sparse orthogonal precoding improves the convergence property of EP in over-loaded GSM MIMO systems with known spatially correlated channel matrices.

Expectation propagation (EP) decoding is proposed for sparse superposition coding in orthogonal frequency division multiplexing (OFDM) systems. When a randomized discrete Fourier transform (DFT) dictionary matrix is used, the EP decoding has the same complexity as approximate message-passing (AMP) decoding, which is a low-complexity and powerful decoding algorithm for the additive white Gaussian noise (AWGN) channel. Numerical simulations show that the EP decoding achieves comparable performance to AMP decoding for the AWGN channel. For OFDM systems, on the other hand, the EP decoding is much superior to the AMP decoding while the AMP decoding has an error-floor in high signal-to-noise ratio regime.