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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. |
