Closed-Form SINR Expression of Precoding Techniques in Cell-Free Massive MIMO Over Rician Fading Channels

Cell-free massive multiple-input multiple-output (CF-MM) is a promising architecture for next-generation wireless networks, offering enhanced capacity, coverage, and spectral efficiency (SE). However, designing scalable, low-complexity CF-MM systems under Rician fading—characterized by both line-of-sight (LoS) and non-line-of-sight (NLoS) components—remains challenging, especially in dense deployments with many distributed access points (APs). This work studies four distributed precoding schemes, namely maximum-ratio transmission (MRT), full-pilot zero-forcing (FZF), partial ZF (PZF), and protective partial ZF (PPZF), highlighting their complexity–interference trade-offs across channel estimators. We evaluate several channel estimation methods, including minimum mean square error (MMSE), linear minimum mean square error (LMS), and least squares (LS). We first derive a closed-form ZF normalization constant that removes per-block norm computations to enable low-complexity per-AP implementation. Building on this, we derive closed-form downlink signal-to-interference-plus-noise ratio (SINR) expressions for all precoder–estimator configurations under Rician fading and validate them via Monte Carlo simulations. Additionally, we propose a distributed power allocation rule and a three-group user-scheduling policy, both driven by closed-form SINR expressions based on large-scale statistics, reducing per-AP precoder computation and fronthaul overhead while preserving fairness. Our results quantify how user density, pilot reuse, and estimator choice shape the trade-off between SE and computational burden, yielding design guidelines for fronthaul-efficient CF-MM deployments that approach centralized performance at much lower complexity.