Fundamental Limits of Dynamic Tracking and Communication: A Stationary Policy Formulation
Abstract
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.
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BibTeX
@misc{mohajer2026fundamental,
title = {{Fundamental Limits of Dynamic Tracking and Communication: A Stationary Policy Formulation}},
author = {Mohammadreza Bakhshizadeh Mohajer and Luca Barletta and Alex Dytso and Giuseppe Caire},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36143},
eprint = {2609.36143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fundamental Limits of Dynamic Tracking and Communication: A Stationary Policy Formulation
AU - Mohammadreza Bakhshizadeh Mohajer
AU - Luca Barletta
AU - Alex Dytso
AU - Giuseppe Caire
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36143
UR - https://arxiv.org/abs/2609.36143
AB - 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.
ER -