This paper studies the performance trade-off in a multi-user backscatter communication (BackCom) system for integrated sensing and communications (ISAC), where the multi-antenna ISAC transmitter sends excitation signals to power multiple single-antenna passive backscatter devices (BD), and the multi-antenna ISAC receiver performs joint sensing (localization) and communication tasks based on the backscattered signals from all BDs. Specifically, the localization performance is measured by the Cram\'{e}r-Rao bound (CRB) on the transmission delay and direction of arrival (DoA) of the backscattered signals, whose closed-form expression is obtained by deriving the corresponding Fisher information matrix (FIM), and the communication performance is characterized by the sum transmission rate of all BDs. Then, to characterize the trade-off between the localization and communication performances, the CRB minimization problem with the communication rate constraint is formulated, and is shown to be non-convex in general. By exploiting the hidden convexity, we propose an approach that combines fractional programming (FP) and Schur complement techniques to transform the original problem into an equivalent convex form. Finally, numerical results reveal the trade-off between the CRB and sum transmission rate achieved by our proposed method.

翻译：本文研究集成感知与通信（ISAC）多用户反向散射通信（BackCom）系统的性能权衡问题。在该系统中，多天线ISAC发射机发送激励信号为多个单天线无源反向散射设备（BD）供电，多天线ISAC接收机则基于所有BD反射的信号执行联合感知（定位）与通信任务。具体而言，定位性能通过反向散射信号传输时延与到达方向（DoA）的克拉美-罗下界（CRB）来度量，其闭式表达式通过推导相应的费舍尔信息矩阵（FIM）获得；通信性能则以所有BD的总传输速率为表征。为刻画定位与通信性能间的权衡关系，本文建立了通信速率约束下的CRB最小化问题，并证明该问题通常具有非凸性。通过挖掘隐藏凸性，我们提出一种结合分式规划（FP）与舒尔补技术的方案，将原问题转化为等效凸形式。最终，数值结果揭示了所提方法实现的CRB与总传输速率之间的权衡关系。