Variational Bayesian Channel Estimation and Data Detection for Cell-Free Massive MIMO with Low-Resolution Quantized Fronthaul Links

TL;DR

This paper introduces a variational Bayesian method for joint channel estimation and data detection in cell-free massive MIMO systems with low-resolution fronthaul links, improving performance over traditional linear methods.

Contribution

It proposes two novel VB-based approaches, Q-E and E-Q, for efficient joint estimation and detection under quantized fronthaul constraints, outperforming LMMSE.

Findings

VB approaches outperform LMMSE in SER and NMSE.

VB(Q-E) outperforms VB(E-Q) due to better local channel estimation.

Both methods reduce fronthaul overhead while maintaining high accuracy.

Abstract

We study the joint channel estimation and data detection (JED) problem in a cell-free massive multiple-input multiple-output (CF-mMIMO) network, where access points (APs) communicate with a central processing unit (CPU) over fronthaul links. However, the bandwidth of these links is limited, and thus, presents challenges to the applicability of CF-mMIMO, especially with an ever-increasing number of users. To address this, we propose a method based on variational Bayesian (VB) inference for performing the JED process, where the APs forward low-resolution quantized versions of the signals to the CPU. We consider two approaches: \emph{quantization-and-estimation} (Q-E) and \emph{estimation-and-quantization} (E-Q). In the Q-E approach, each AP uses a low-bit quantizer to quantize the signal before forwarding it to the CPU, while in the E-Q approach, each AP first performs local channel estimation and then sends a low-bit quantized version of the estimated channel to the CPU. We evaluate the performance of our VB-based approach under perfect fronthaul link (PFL) with unquantized received signals, Q-E, and E-Q in terms of symbol error rate (SER), normalized mean square error (NMSE) of the channel estimation, computational complexity, and fronthaul signaling overhead. We also compare these results with those of the linear minimum mean squared error (LMMSE) method under the PFL scenario. Our numerical results show that both the VB(Q-E) and VB(E-Q) approaches achieve superior performance compared to LMMSE(PFL), benefiting from the nonlinear modeling inherent in VB. Furthermore, the VB(Q-E) method outperforms VB(E-Q) due to errors in the local channel estimation process at the APs within the VB(E-Q) approach.