Performance Trade-off of Integrated Sensing and Communications for Multi-User Backscatter Systems

TL;DR

This work addresses a multi-user backscatter ISAC system by deriving closed-form CRB expressions for the transmission delay and DoA and a sum-rate bound for BD communications, both dependent on the transmitter covariance $\mathbf{R}_x$. It formulates a non-convex CRB-minimization problem under a rate constraint and introduces a FP–Schur complement framework to recast it as a convex optimization, enabling efficient design of $\mathbf{R}_x$. The results quantify the fundamental trade-off between localization precision and communication throughput, and demonstrate how pulse shapes, power budgets, and antenna configurations shape the boundary of achievable performance. The proposed approach offers practical guidance for jointly optimizing sensing and communication in ISAC-enabled BackCom systems.

Abstract

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 Cramér-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.

Figures (9)

• Figure 1: System model of multi-user BackCom system for ISAC.
• Figure 2: Frame structure of multi-user BackCom signals.
• Figure 3: Geometric model for estimating the location of the $l$-th BD via the ISAC transmitter and receiver.
• Figure 4: Experimental scenarios of the considered BackCom system for ISAC.
• Figure 5: Trade-off curve between CRB and minimum sum transmission rate with different transmit pulses, with $P_0=30$ dBm and $M_t=M_r=8$.