A BP–MF–EP Based Iterative Receiver for Joint Phase Noise Estimation, Equalization, and Decoding

Abstract

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.

Auxiliary Variable-Aided Hybrid Message Passing for Joint Channel, Phase Noise Estimation and Detection for Multi-User MIMO Systems

“…Considering the discrete nature of the coded symbols, Gaussian assumption for the channel and the Gaussian approximation to PN, it is expected to come up with some messages in Gaussian mixture form and some other messages in exponential form that is computational intractable. We adopt the approximate inference combining BP-EP to update the former as in [5] [23] and the MF to update the latter as in [5] [21]. We firstly denote the prior LLR of the coded bits at the nth soft decoder as L a (c t n,q ), the soft mapping operation below is needed to carry out to obtain the prior p.m.f of transmitted symbols P a (x t n ) as below ( [25], [26]):…”

“…L a (c t n,q ) = 0, ∀n, q and t ∈ In the simulations, we evaluate the BER performance of the proposed algorithm and compare it with that of the softinput EKS [9], the auxiliary variable-aided hybrid message passing algorithm (AVA-HMP) [17] and the matched filter bound (MFB). Note that BP-MF is used for detection as in [5] when using soft-input EKS. The PN and channel are aggregated as an equivalent time-varying channel when using the AVA-HMP that was designed for joint channel estimation and decoding.…”

“…Most uplink MU-MIMO detection methods are based on the linear observation model y = Hx + w, which assumes ideal hardware components. When PN is modelled as a Random Walk (Wiener) process as in [3]- [5], the presence of PN results in a non-linear observation model. Conventionally, the non-linear observation model with PN can be linearized by using the first-order Taylor expansion and resolved by the soft-input extended Kalman smoothing (Soft-input EKS) algorithm to track time-varying PN over a frame.…”

“…To deal with complex problems, combinations of these inference techniques can be used, so that their advantages can be exploited while drawbacks be avoided. For example, BP, EP and MF have been jointly used to design receivers, such as the work based on BP-MF [12], [21], BP-EP [23] and BP-MF-EP [5], [22]. Inspired by these hybrid message passing schemes and with the aid of auxiliary variables, we extend the work in [10] to MU-MIMO systems.…”

Nonlinear Channel Equalization Approach for Microwave Communication Systems

“…An iterative receiver is designed [17] for joint phase noise estimation, equalization, and decoding in a coded communication system with combined belief propagation, mean field, and expectation propagation (BP-MF-EP). In the frequency domain-based equalization, many important contributions are made recently, for example, in Ref.…”