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

We study the joint channel estimation and data detection (JED) problem in cell-free massive MIMO (CF-mMIMO) networks, where access points (APs) forward signals to a central processing unit (CPU) over fronthaul links. Due to bandwidth limitations of these links, especially with a growing number of users, efficient processing becomes challenging. To address this, we propose a variational Bayesian (VB) inference-based method for JED that accommodates low-resolution quantized signals from APs. We consider two approaches: quantization-andestimation (Q-E) and estimation-and-quantization (E-Q). In Q-E, each AP directly quantizes its received signals before forwarding them to the CPU. In E-Q, each AP first estimates channels locally during the pilot phase, then sends quantized versions of both the local channel estimates and received data to the CPU. The final JED process in both Q-E and E-Q is performed at the CPU. We evaluate our proposed approach under perfect fronthaul links (PFL) with unquantized received signals, Q-E, and E-Q, using symbol error rate (SER), channel normalized mean squared error (NMSE), computational complexity, and fronthaul signaling overhead as performance metrics. Our methods are benchmarked against both linear and nonlinear state-of-the-art JED techniques. Numerical results demonstrate that our VB-based approaches consistently outperform the linear baseline by leveraging the nonlinear VB framework. They also surpass existing nonlinear methods due to: i) a fully VB-driven formulation, which performs better than hybrid schemes such as VB combined with expectation maximization; and ii) the stability of our approach under correlated channels, where competing methods may fail to converge or experience performance degradation.