Performance Analysis and Pilot Length Optimization for Multi-Dimensional Sensing in Uplink CF-ISAC Systems

The fusion of multi-dimensional communication-sensing signals can significantly raise the theoretical upper limit of integrated sensing and communication (ISAC). Distributed terminals transmit uplink communication signals that provide richer multi-perspective observation information for sensing, effectively enhancing sensing dimensionality. This paper focuses on the uplink sensing process in cell-free ISAC (CF-ISAC) architecture, aiming to integrate pilot signals and data siganls from multiple terminals to achieve efficient spectrum utilization and robust uplink sensing capability. Theoretically, under imperfect decoding conditions, we derive the Cramér-Rao lower bound (CRLB) for uplink sensing accuracy. Building on this foundation, we establish a Pareto boundary model that characterizes the trade-off between communication rate and sensing precision, highlighting the critical role of optimizing the proportion of pilot symbols to data symbols. To further enhance CF-ISAC performance, we propose a pilot optimization algorithm based on a deep Q-network (DQN), which dynamically adjusts pilot length to balance communication rate and sensing precision. Simulation results demonstrate that the proposed algorithm significantly enhances sensing accuracy by integrating pilot and data, while effectively balances the sensing performance and communication performance. Therefore, this uplink ISAC method can simultaneously support high-precision multi-dimensional sensing and reliable communication without additional resource overhead, offering an efficient and scalable solution for CF-ISAC systems.