Semi-blind joint channel estimation and data detection (JCD) is a promising approach to mitigate pilot contamination in cell-free massive multiple-input multiple-output (CF-MaMIMO) networks. The effectiveness of such methods fundamentally depends on identifiability, i.e., the ability to unambiguously recover the unknown channel coefficients and transmitted data signals from the received uplink observations. In this work, we investigate the identifiability of semi-blind JCD from a large-scale system design perspective. We consider a CF-MaMIMO network in which access points (APs) and user equipments (UEs) are spatially distributed according to Poisson point processes (PPPs). The resulting network topology is modeled as bipartite random geometric graph (BRGG) that captures local connectivity induced by wireless propagation. To enable a tractable analysis, the spatially dependent graph model is approximated by a surrogate independent-edge random graph with matched degree distributions. Building on this model, we develop a recursive probabilistic analysis that characterizes the conditions under which semi-blind recovery succeeds with high probability. The proposed analysis reveals an identifiability region as a function of key system parameters, including AP and UE densities and the connectivity radius beyond which channel coefficients are assumed negligible. Monte Carlo simulations validate the predicted identifiability region and assess the accuracy of the proposed graph approximation. The proposed framework provides system level insights into how network density and connectivity affect identifiability in large-scale CF-MaMIMO systems and offers guidelines for selecting deployment parameters and pilot sequence lengths that enable reliable semi-blind recovery.

翻译：半盲联合信道估计与数据检测（JCD）是缓解无蜂窝大规模多输入多输出（CF-MaMIMO）网络中导频污染的有效方法。此类方法的有效性从根本上取决于可辨识性，即从接收的上行观测中无歧义地恢复未知信道系数与传输数据信号的能力。本文从大规模系统设计视角研究了半盲JCD的可辨识性问题。我们考虑一个接入点（AP）与用户设备（UE）遵循泊松点过程（PPP）空间分布的CF-MaMIMO网络。该网络拓扑被建模为二分随机几何图（BRGG），以刻画无线传播引发的局部连接性。为实现可处理的分析，该空间依赖图模型被近似为具有匹配度分布的独立边随机图。基于此模型，我们发展了一种递归概率分析方法，刻画了半盲恢复以高概率成功的条件。所提出的分析揭示了由关键系统参数（包括AP与UE密度、信道系数可忽略的连通半径）决定的可辨识区域。蒙特卡洛仿真验证了预测的可辨识区域，并评估了所提图近似的准确性。该框架从系统层面揭示了网络密度与连通性如何影响大规模CF-MaMIMO系统中的可辨识性，为选择能够实现可靠半盲恢复的部署参数与导频序列长度提供了指导准则。