Message-Passing Receiver for Joint Channel Estimation and Decoding in 3D Massive MIMO-OFDM Systems

Abstract

In this paper, we address the message-passing receiver design for the 3D massive MIMO-OFDM systems. With the aid of the central limit argument and Taylor-series approximation, a computationally efficient receiver that performs joint channel estimation and decoding is devised by the framework of expectation propagation. Specially, the local belief defined at the channel transition function is expanded up to the second order with Wirtinger calculus, to transform the messages sent by the channel transition function to a tractable form. As a result, the channel impulse response (CIR) between each pair of antennas is estimated by Gaussian message passing. In addition, a variational expectation-maximization (EM)-based method is derived to learn the channel power-delay-profile (PDP). The proposed joint Jianhua Lu is with the Department of Electronic Engineering, Tsinghua University, China (e-mail: lhh-dee@mail.tsinghua.edu.cn). 2 algorithm is assessed in 3D massive MIMO systems with spatially correlated channels, and the empirical results corroborate its superiority in terms of performance and complexity.

Message-Passing Receiver Design for Joint Channel Estimation and Data Decoding in Uplink Grant-Free SCMA Systems

“…In this paper, we focus on the design of an iterative messagepassing receiver for uplink SCMA that performs joint channel estimation, data decoding, and active users detection. Iterative receivers for joint channel estimation and data decoding has been studied in [23]- [29] for MIMO-OFDM systems with the assumption that receivers have a perfect knowledge of user activity in the network. Using the framework of expectationmaximization (EM), the authors in [23], [24] addressed the joint detection problem by sparse Bayesian learning (SBL) algorithm.…”

“…Moreover, accurate initialization is often required for BP-MF otherwise it will achieve a local optimal point. In [27]- [29], Gaussian approximation in BP (BP-GA) is considered in MIMO-OFDM system via central-limit theorem and moment matching. While central-limit theorem works well in large scale MIMO, it may have a poor performance in SCMA as the collision users in one resource is limited due to the sparse structure of codewords.…”

“…Using the idea of approximate inference, we approximate the intractable distribution involved in BP with some simple families such as Gaussian distribution. However, unlike the works in [29], the approximation does not rely on centrallimit theorem. Instead, the complex distribution is projected into Gaussian families for each user individually so that the Kullback-Leibler (KL) divergence is minimized.…”

“…Assume that the output information I ftn→u tnk (u tnk ) from function node f tn follows the Gaussian distribution CN (u tnk ; τ ftn→u tnk , υ ftn→u tnk ), the posterior belief of variable u tnk can be calculated in (29) where β(x tnk ), τ u tnk and υ u tnk are computed in (30)- (32) and C is a normalization constant.…”

“…For both parts, the complexity is in the order of O (BN M d c ). With the Gaussian approximation, BP-GA has the same complexity with BP-GA-EP for both data detection and channel estimation, i.e., the complexity is in the order of O(BN M d c ), see (22) and (23) in [29]. The joint maximization step in SBL algorithm has a complexity of O(M K ), which is prohibitively complexity for massive number of connected users.…”