发表机构
Politecnico di Milano; Qualcomm Inc.; Technical University of Berlin（米兰理工大学; 高通公司; 柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对动态集成感知与通信问题，提出基于率失真和平稳策略的框架，利用PCRB构造外部界，证明高斯信号在渐近最优性下平衡跟踪与通信性能。
AI 中文摘要
我们研究了一个动态集成感知与通信问题，其中多天线发射机与接收机通信，同时跟踪由稳定高斯-马尔可夫模型支配的运动目标。我们将感知-通信权衡表述为率失真问题，其中通信速率通过Verdú-Han信息谱定义，感知失真通过角度和距离上的长期最小均方跟踪误差衡量。我们通过后验Cramér-Rao界（PCRB）对该失真进行下界约束，构造了一个易处理的可行外部区域。由于目标状态对发射机不可直接获得，该控制问题是部分可观测的。因此，我们引入信念增强信息状态，并在所述正则性假设下证明，对于外部界中使用的基于协方差的标量化问题，平稳随机化马尔可夫策略是充分的。然后，在所述大块条件下，我们推导出高斯协方差控制外部界，证明在大块机制中，感知信念转移渐近地成为协方差充分的；因此，具有相同平稳协方差策略的高斯信号在渐近意义上保持平稳PCRB，同时为每个发射协方差最大化通信奖励。数值实验比较了基于扩展卡尔曼滤波的可实现前沿与基于PCRB的高斯协方差控制外部前沿。
英文摘要
We study a dynamic integrated sensing-and-communication problem in which a multi-antenna transmitter communicates with a receiver while simultaneously tracking a moving target governed by a stable Gauss--Markov model. We formulate the sensing--communication trade-off as a rate--distortion problem, where the communication rate is defined through the Verdú--Han information spectrum and the sensing distortion is measured by the long-run minimum mean square tracking error in angle and distance. We construct a tractable outer region by lower bounding this distortion through the posterior Cramér--Rao bound (PCRB). The control problem is partially observed because the target state is not directly available to the transmitter. We therefore introduce a belief-augmented information state and show, under the stated regularity assumptions, that stationary randomized Markov policies suffice for the covariance-based scalarized problem used in the outer bound. We then derive, under the stated large-block conditions, a Gaussian covariance-control outer bound by showing that, in the large-block regime, the sensing belief transition becomes asymptotically covariance sufficient; consequently, Gaussian signaling with the same stationary covariance policy preserves the stationary PCRB asymptotically while maximizing the communication reward for each transmit covariance. Numerical experiments compare an extended Kalman filter-based achievable frontier with a PCRB-based Gaussian covariance-control outer frontier.
Comments17 pages, 5 figures, submitted to IEEE Transactions on Information Theory
