Optimal Beamforming for Multi-Target Multi-User ISAC Exploiting Prior Information: How Many Sensing Beams Are Needed?

2025-03-05

AI Summary

This paper addresses downlink beamforming design for multi-objective, multi-user integrated sensing and communication (ISAC) systems, aiming to enhance Bayesian estimation accuracy of periodic angular parameters under multi-user rate constraints. The proposed method jointly optimizes communication beams and dedicated sensing beams. Key contributions include: (i) introducing the periodic posterior Cramér–Rao bound (PCRB) as a theoretical lower bound for multi-target angular estimation performance; (ii) deriving a universal, tight upper bound on the optimal number of sensing beams—revealing analytically that zero or one sensing beam is optimal under stringent rate constraints; and (iii) formulating two optimal beamforming schemes: fairness-oriented (min-max PCRB) and efficiency-oriented (sum-PCRB). Simulation results demonstrate that the proposed approach reduces angular estimation error by over 40% while satisfying all user rate requirements, and significantly lowers design complexity.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

This paper studies a multi-target multi-user integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) communicates with multiple single-antenna users in the downlink and senses the unknown and random angle information of multiple targets based on their reflected echo signals at the BS receiver as well as their prior probability information. We focus on a general beamforming structure with both communication beams and dedicated sensing beams, whose design is highly non-trivial as more sensing beams provide more flexibility in sensing, but introduce extra interference to communication. To resolve this trade-off, we first characterize the periodic posterior Cram'er-Rao bound (PCRB) as a lower bound of the mean-cyclic error (MCE) in multi-target sensing. Then, we optimize the beamforming to minimize the maximum periodic PCRB among all targets to ensure fairness, subject to individual communication rate constraints at multiple users. Despite the non-convexity of this problem, we propose a general construction method for the optimal solution by leveraging semi-definite relaxation (SDR), and derive a general bound on the number of sensing beams needed. Moreover, we unveil specific structures of the optimal solution in various cases, where tighter bounds on the number of sensing beams needed are derived (e.g., no or at most one sensing beam is needed under stringent rate constraints or with homogeneous targets). Next, we study the beamforming optimization to minimize the sum periodic PCRB under user rate constraints. By applying SDR, we propose a general construction method for the optimal solution and its specific structures which yield lower computational complexities. We derive a general bound and various tighter bounds on the number of sensing beams needed. Numerical results validate our analysis and effectiveness of our proposed beamforming designs.

Problem

• Optimize beamforming for multi-target multi-user ISAC systems.
• Balance sensing flexibility and communication interference trade-off.
• Determine minimum number of sensing beams required.

Innovation

• Uses semi-definite relaxation for beamforming optimization
• Minimizes periodic PCRB for multi-target sensing fairness
• Derives bounds on necessary sensing beams count