Large-scale Fading Decoding aided User-centric Cell-free Massive MIMO: Uplink Error Probability Analysis and Detector Design

User-centric cell-free massive MIMO (CFmMIMO), where only partial access points (APs) are selected to serve a specific user equipment (UE), is a scalable extension of CFmMIMO. Existing works have studied the spectral efficiency of large-scale fading decoding (LSFD) aided user-centric CFmMIMO that includes local combining at each AP and statistical channel state information (S-CSI) based fusion in the central processing unit (CPU). However, few efforts have so far been paid to analyze the error probability bound, and existing detectors fail to balance the error probability and fusion complexity. In this paper, we analyze the symbol error rate (SER) and design low-complexity near-optimal detectors for uplink user-centric CFmMIMO systems. Considering non-identical large-scale fading coefficients and local channel estimation errors, we first leverage the pairwise error probability to derive an SER upper bound for optimal linear fusion (OLF) in the CPU, which is suitable to different local combining methods at the APs. Then, by combining local normalization methods and S-CSI based UE grouping or error correction, we design improved detectors for local maximum-ratio and local minimum mean squared error combining successively. Simulation results verify the correctness of the derived SER bound, and show that the proposed detectors are capable of approaching the SER performance of conventional OLF based counterparts with reduced fusion complexity even in scenarios with pilot contamination.