Coverage and Rate of Joint Communication and Parameter Estimation in Wireless Networks

TL;DR

This paper develops a rigorous, information-theoretic and stochastic-geometry framework for joint communication and sensing (JCAS) in mmWave networks with a shared waveform. Sensing performance is captured via mutual information $I(Y; obreak oldsymbol{ heta})$ and bounded through the Bayesian Cramér–Rao framework, yielding tractable lower bounds on the sensing rate that relate to an effective SINR for sensing. The authors define JCAS coverage and ergodic rate as mixtures of conventional communication metrics and radar-sensing metrics, enabling separate yet integrated analysis via Palm measures and independent UE/SO point processes. They derive upper and lower bounds on the Laplace transforms of Poisson shot-noise interference, establish AM/GM/HM-based bounding models for the sensing SINR, and obtain integral closed-form expressions for bound-based radar and communication performance. Numerical results reveal that network densification improves sensing performance more than communications, offering practical guidance for designing JCAS deployments and waveform-sharing strategies in urban mmWave environments.

Abstract

From an information theoretic perspective, joint communication and sensing (JCAS) represents a natural generalization of communication network functionality. However, it requires the re-evaluation of network performance from a multi-objective perspective. We develop a novel mathematical framework for characterizing the sensing and communication coverage probability and ergodic rate in JCAS networks. We employ a formulation of sensing parameter estimation based on mutual information to extend the notions of coverage probability and ergodic rate to the radar setting. We define sensing coverage probability as the probability that the rate of information extracted about the parameters of interest associated with a typical radar target exceeds some threshold, and sensing ergodic rate as the spatial average of the aforementioned rate of information. Using this framework, we analyze the downlink sensing and communication coverage and rate of a mmWave JCAS network employing a shared waveform, directional beamforming, and monostatic sensing. Leveraging tools from stochastic geometry, we derive upper and lower bounds for these quantities. We also develop several general technical results including: i) a generic method for obtaining closed form upper and lower bounds on the Laplace Transform of a shot noise process, ii) a new analog of H{ö}lder's Inequality to the setting of harmonic means, and iii) a relation between the Laplace and Mellin Transforms of a non-negative random variable. We use the derived bounds to numerically investigate the performance of JCAS networks under varying base station and blockage density. Among several insights, our numerical analysis indicates that network densification improves sensing SINR performance -- in contrast to communications.

Figures (5)

• Figure 1: This figure depicts analytical upper and lower bounds and simulated CCDFs for various radar SINR models. These indicate that a) the analytical bounds are tight in most cases, and b) the approximate radar SINR model, $\normalfont{\text{ SINR}_\text{GM}}$, is a close fit to the true model, $\normalfont{\text{ SINR}_\text{rad}}$.
• Figure 2: This figure depicts analytical upper and lower bounds and simulated CCDFs for the communication SINR models. Like the radar case, these indicate that the analytical bounds are tight.
• Figure 3: This figure depicts lower (a) and upper (b) bounds for the ergodic estimation efficiency of the JCAS network with respect to various SINR models as well as bounds on the ergodic communication efficiency (c) in the high blockage regime with $\beta^{-1} = 360.67$.
• Figure 4: This figure depicts lower (a) and upper (b) bounds for the ergodic estimation efficiency of the JCAS network with respect to various SINR models as well as bounds on the ergodic communication efficiency (c) in the low blockage regime with $\beta^{-1} = 72.13$.
• Figure 5: This figure depicts how the sensing and communication ergodic efficiencies vary jointly with the network density and the LoS pathloss exponent, $\alpha_\text{L}$, in the high blockage regime. Lower bounds for the ergodic efficiencies are depicted for sensing with respect to the lower bounding model, $\normalfont{\text{ SINR}_\text{AM}}$, (a) and communications (b). Similarly, upper bounds for the ergodic efficiencies are depicted for sensing with respect to the upper bounding model, $\normalfont{\text{ SINR}_\text{HM}}$, (c) and communications (d). A few representative level sets for these surfaces are shown as block lines to improve clarity.