This paper presents a novel optimization framework for beamforming design in integrated sensing and communication systems where a base station seeks to minimize the Bayesian Cram\'er-Rao bound of a sensing problem while satisfying quality of service constraints for the communication users. Prior approaches formulate the design problem as a semidefinite program for which acquiring a beamforming solution is computationally expensive. In this work, we show that the computational burden can be considerably alleviated. To achieve this, we transform the design problem to a tractable form that not only provides a new understanding of Cram\'er-Rao bound optimization, but also allows for an uplink-downlink duality relation to be developed. Such a duality result gives rise to an efficient algorithm that enables the beamforming design problem to be solved at a much lower complexity as compared to the-state-of-the-art methods.

翻译：本文提出了一种面向集成感知与通信系统波束赋形设计的新型优化框架，其中基站旨在在满足通信用户服务质量约束的同时最小化感知问题的贝叶斯克拉美-罗界。现有方法将该设计问题建模为半定规划，求解波束赋形方案的计算开销较大。本研究证明该计算负担可显著降低。为此，我们将设计问题转化为易于处理的形式，不仅为克拉美-罗界优化提供了新见解，还推导出上下行对偶关系。基于该对偶结果，我们开发了一种高效算法，能够以远低于现有方法的复杂度求解波束赋形设计问题。