Abstract-In this letter, a message-passing algorithm that combines belief propagation and expectation propagation is applied to design an iterative receiver for intersymbol interference channels. We detail the derivation of the messages passed along the nodes of a vector-form factor graph representing the underlying probabilistic model. We also present a simple but efficient method to cope with the "negative variance" problem of expectation propagation. Simulation results show that the proposed algorithm outperforms, in terms of bit-error-rate and convergence rate, a LMMSE turbo-equalizer based on Gaussian message passing with the same order of computational complexity.

We propose a fast and near-optimal approach to joint channel-estimation, equalization, and decoding of coded single-carrier (SC) transmissions over frequency-selective channels with few-bit analog-to-digital converters (ADCs). Our approach leverages parametric bilinear generalized approximate message passing (PBiGAMP) to reduce the implementation complexity of joint channel estimation and (soft) symbol decoding to that of a few fast Fourier transforms (FFTs). Furthermore, it learns and exploits sparsity in the channel impulse response. Our work is motivated by millimeter-wave systems with bandwidths on the order of Gsamples/sec, where few-bit ADCs, SC transmissions, and fast processing all lead to significant reductions in power consumption and implementation cost. We numerically demonstrate our approach using signals and channels generated according to the IEEE 802.11ad wireless local area network (LAN) standard, in the case that the receiver uses analog beamforming and a single ADC.Index Terms-Low resolution analog-to-digital converter, millimeter wave, joint channel estimation and equalization, turbo equalization, approximate message passage. P. Sun (sun.1771@osu.edu) and Z. Wang (iezywang@zzu.edu.cn) are with

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Abstract-In this work, with combined belief propagation (BP), mean field (MF) and expectation propagation (EP), an iterative receiver is designed for joint phase noise (PN) estimation, equalization and decoding in a coded communication system. The presence of the PN results in a nonlinear observation model. Conventionally, the nonlinear model is directly linearized by using the first-order Taylor approximation, e.g., in the state-ofthe-art soft-input extended Kalman smoothing approach (soft-in EKS). In this work, MF is used to handle the factor due to the nonlinear model, and a second-order Taylor approximation is used to achieve Gaussian approximation to the MF messages, which is crucial to the low-complexity implementation of the receiver with BP and EP. It turns out that our approximation is more effective than the direct linearization in the soft-in EKS with similar complexity, leading to significant performance improvement as demonstrated by simulation results.

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