Optimal Transmit Beamforming for MIMO ISAC with Unknown Target and User Locations

2026-02-09

AI Summary

This work addresses beamforming design in MIMO integrated sensing and communication (ISAC) systems under uncertainty, where both target and user locations are unknown but characterized by known probability distributions. The authors formulate an optimization framework that jointly considers statistical sensing and communication performance by minimizing the posterior Cramér–Rao bound (PCRB) subject to a constraint on the expected communication rate. Leveraging location distribution information, they derive a theoretical upper bound on the rank of the optimal transmit covariance matrix and prove that static beamforming suffices to achieve optimality, obviating the need for time-varying designs. Furthermore, they show that ISAC performance improves as the spatial distributions of the target and user become more similar. Numerical simulations corroborate the theoretical findings and offer practical guidance for base station deployment and user–target association.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper studies a challenging scenario in a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system where the locations of the sensing target and the communication user are both unknown and random, while only their probability distribution information is known. In this case, how to fully utilize the spatial resources by designing the transmit beamforming such that both sensing and communication can achieve satisfactory performance statistically is a difficult problem, which motivates the study in this paper. Moreover, we aim to reveal if it is desirable to have similar probability distributions for the target and user locations in terms of the ISAC performance. Firstly, based on only probability distribution information, we establish communication and sensing performance metrics via deriving the expected rate or posterior Cram\'{e}r-Rao bound (PCRB). Then, we formulate the transmit beamforming optimization problem to minimize the PCRB subject to the expected rate constraint, for which the optimal solution is derived. It is unveiled that the rank of the optimal transmit covariance matrix is upper bounded by the summation of MIMO communication channel matrices for all possible user locations. Furthermore, due to the need to cater to multiple target/user locations, we investigate whether dynamically employing different beamforming designs over different time slots improves the performance. It is proven that using a static beamforming strategy is sufficient for achieving the optimal performance. Numerical results validate our analysis, show that ISAC performance improves as the target/user location distributions become similar, and provide useful insights on the BS-user/-target association strategy.

Problem

• MIMO ISAC
• unknown target location
• unknown user location
• transmit beamforming
• probability distribution

Innovation

• MIMO ISAC
• transmit beamforming
• unknown locations
• posterior Cramér-Rao bound
• static beamforming optimality