Robust Beamforming for MIMO Radar with Imperfect Prior Distribution Information

2026-04-23

AI Summary

This work addresses the robust beamforming problem for MIMO radar in the presence of bounded perturbations in the prior distribution of target angles. By adopting the worst-case posterior Cramér–Rao bound (PCRB) as the performance metric, the authors formulate an optimization model that minimizes the maximum PCRB. They innovatively model prior uncertainty via a perturbation set and establish, for the first time, a robust beamforming framework based on the worst-case PCRB. Through second-order Taylor expansion and the S-procedure, the originally nonconvex problem with infinitely many constraints is equivalently transformed into a tractable convex optimization problem solvable in polynomial time, yielding a near-globally optimal solution. Numerical experiments demonstrate that the proposed method achieves significantly superior robust sensing performance compared to existing approaches under prior mismatch scenarios.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper studies a multiple-input multiple-output (MIMO) radar system for sensing the unknown and random angular location (angle) of a point target, based on the target-reflected echo signals and known prior distribution information about the target's angle specified by a probability density function (PDF). We consider a challenging yet practical scenario where the knowledge of such PDF is imperfect, due to the inaccuracy in PDF acquisition or unpredicted change of target appearance pattern; while the real (actual) PDF is modeled as an unknown perturbed version of the imperfect known PDF bounded by a given uncertainty radius. Such PDF imperfection motivates us to study the robust transmit beamforming design to optimize the worst-case sensing performance among all possible real PDFs. Since the sensing mean-squared error (MSE) is difficult to be characterized explicitly, we adopt the worst-case posterior Cramér-Rao bound (PCRB) as the performance metric. We formulate the beamforming optimization problem to minimize the maximum PCRB among all possible real PDFs, which is highly non-trivial since the PCRB has a complex intractable expression over the real PDF, and there are infinite constraints corresponding to the continuous set of real PDFs bounded by the uncertainty radius. To address these challenges, we derive a tractable quadratic approximation of the PCRB via second-order Taylor expansion, and leverage the S-procedure to equivalently transform the infinite constraints into a linear matrix inequality, based on which the problem is reformulated into a convex optimization problem solvable with polynomial time complexity. The obtained solution approaches the globally optimal robust beamforming solution as the uncertainty radius decreases. Numerical results validate the effectiveness of our proposed robust beamforming design.

Problem

• MIMO radar
• robust beamforming
• imperfect prior information
• angular estimation
• uncertainty modeling

Innovation

• Robust beamforming
• MIMO radar
• Imperfect prior information
• Posterior Cramér-Rao bound
• Convex optimization