Multi-User ISAC with Heterogeneous Unknown Parameters: Optimal Beamforming based on Distribution Information

2026-04-24

AI Summary

This work addresses the joint optimization of communication and sensing in a multi-user integrated sensing and communication (ISAC) system, where both target angles and reflection coefficients are unknown and lack prior information. The authors investigate a downlink multi-antenna base station that simultaneously serves multiple users and performs angle sensing. They propose a unified transmission architecture combining communication beams with dedicated sensing beams and, for the first time, optimize beamforming based on the periodic posterior Cramér–Rao bound (PCRB) without any prior knowledge of reflection coefficients. It is theoretically shown that achieving optimal performance requires at most one dedicated sensing beam. The non-convex problem is solved via semidefinite relaxation and Lagrangian duality to minimize the PCRB under user communication rate constraints. Simulations confirm that the proposed scheme significantly enhances sensing accuracy while maintaining communication quality, validating the theoretical analysis and algorithmic efficacy.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

This paper studies an 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 a target based on its prior distribution information and the received echo signals. We focus on a challenging scenario with heterogeneous unknown parameters where the target's reflection coefficient is also unknown with no prior information. We consider a general transmit beamforming structure with both communication beams and dedicated sensing beams, where the communication users can cancel the interference caused by the pre-determined sensing signals. By adopting the periodic posterior Cramer-Rao bound (PCRB) to quantify a lower bound of the mean-cyclic error (MCE) for sensing the periodic angle parameter, we optimize the transmit beamforming to minimize the periodic PCRB, subject to individual communication user rate constraints, which is a non-convex problem. By leveraging the semi-definite relaxation (SDR) technique and Lagrange duality theory, we derive the optimal solution and prove that at most one dedicated sensing beam is needed. Numerical results validate our analysis and effectiveness of the proposed beamforming design.

Problem

• Integrated Sensing and Communication
• Heterogeneous Unknown Parameters
• Beamforming
• Posterior Cramer-Rao Bound
• Multi-User ISAC

Innovation

• Integrated Sensing and Communication (ISAC)
• Periodic Posterior Cramer-Rao Bound (PCRB)
• Optimal Beamforming
• Heterogeneous Unknown Parameters
• Semi-Definite Relaxation (SDR)