This paper investigates the system model and the transmit beamforming design for the Cell-Free massive multi-input multi-output (MIMO) integrated sensing and communication (ISAC) system. The impact of the uncertainty of the target locations on the propagation of wireless signals is considered during both uplink and downlink phases, and especially, the main statistics of the MIMO channel estimation error are theoretically derived in the closed-form fashion. A fundamental performance metric, termed communication-sensing (C-S) region, is defined for the considered system via three cases, i.e., the sensing-only case, the communication-only case and the ISAC case. The transmit beamforming design problems for the three cases are respectively carried out through different reformulations, e.g., the Lagrangian dual transform and the quadratic fractional transform, and some combinations of the block coordinate descent method and the successive convex approximation method. Numerical results present a 3-dimensional C-S region with a dynamic number of access points to illustrate the trade-off between communication and radar sensing. The advantage for radar sensing of the Cell-Free massive MIMO system is also studied via a comparison with the traditional cellular system. Finally, the efficacy of the proposed beamforming scheme is validated in comparison with zero-forcing and maximum ratio transmission schemes.

翻译：本文研究了无蜂窝大规模多输入多输出（MIMO）通感一体化（ISAC）系统的系统模型与发射波束赋形设计。在上行和下行阶段中，考虑了目标位置不确定性对无线信号传播的影响，并特别以闭式形式从理论上推导了MIMO信道估计误差的主要统计特性。针对所研究系统，通过三种情形（即纯感知情形、纯通信情形和通感一体化情形）定义了一项基础性能指标——通信-感知（C-S）区域。分别通过不同的重构方法（例如拉格朗日对偶变换和二次分式变换）以及块坐标下降法与逐次凸近似法的组合，对三种情形下的发射波束赋形设计问题进行了求解。数值结果展示了随接入点数量动态变化的三维C-S区域，揭示了通信与雷达感知之间的权衡关系。通过与传统蜂窝系统的对比，还研究了无蜂窝大规模MIMO系统在雷达感知方面的优势。最后，通过与迫零和最大比传输方案的对比验证了所提波束赋形方案的有效性。