Dynamic tracking and communication limits using stationary policies
Fundamental Limits of Dynamic Tracking and Communication: A Stationary Policy Formulation
Information Theory
Summary
This work looks at how to send information while also tracking a moving object, like a person or car, using a multi-antenna transmitter. The authors study the trade-off between communicating data and accurately tracking the object's position over time. They use mathematical tools to find the outer performance limits and show that certain stationary policies are enough to capture these limits. Their analysis relies on models that assume large time scales and stable target movements. They also compare their theoretical limits to practical algorithms to see how close real systems can get.
What this means in practice
- •For wireless communication engineers: Design integrated systems that jointly track moving targets and communicate data efficiently using stable stationary policies characterized by theoretical performance limits.
- •For radar system developers: Evaluate achievable tracking accuracy against fundamental bounds when combining sensing and communication under partial observations with multi-antenna setups.
Authors
Mohammadreza Bakhshizadeh Mohajer, Luca Barletta, Alex Dytso, Giuseppe Caire
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.