The Meta Distribution of the SIR in Joint Communication and Sensing Networks

TL;DR

This work addresses the variability of joint communication and sensing (JCAS) performance by deriving the $SIR$ meta-distribution in a stochastic-geometry network model. It develops an analytical framework based on three independent PPPs for BSs, UEs, and SOs, introduces LoS/NLoS path-loss, and defines both $SIR_c$ and $SIR_s$ to characterize communication and sensing performance. The key contributions are closed-form-like expressions for the moments $M_b^s$, $M_b^c$, and $M_b^{JCAS}$, the meta-distribution $F(\theta_s, x)$ obtained via Gil-Pelaez from $M_{j\omega}^{JCAS}$, and validation through simulations showing density-induced variations in performance. The results provide a fine-grained performance metric beyond average coverage, offering design insights for balancing sensing and communication in JCAS deployments and highlighting how deployment density impacts reliability across users and radars.

Abstract

In this paper, we introduce a novel mathematical framework for assessing the performance of joint communication and sensing (JCAS) in wireless networks, employing stochastic geometry as an analytical tool. We focus on deriving the meta distribution of the signal-to-interference ratio (SIR) for JCAS networks. This approach enables a fine-grained quantification of individual user or radar performance intrinsic to these networks. Our work involves the modeling of JCAS networks and the derivation of mathematical expressions for the JCAS SIR meta distribution. Through simulations, we validate both our theoretical analysis and illustrate how the JCAS SIR meta distribution varies with the network deployment density.

Figures (4)

• Figure 1: Illustration of the JCAS network considered, with BSs simultaneously sending information packets to UEs and sensing waveforms to the SOs for which they receive radar echoes.
• Figure 2: SIR meta distribution (Theorem \ref{['thrm:momts_Sen_cvrg']}, Theorem \ref{['thrm:momts_com_cvrg']}) and simulations, as a function of the reliability threshold (x-axis) and for different SIR thresholds ($\theta_\mathrm{c},\theta_\mathrm{s}$).
• Figure 3: JCAS SIR meta distribution as a function of the reliability threshold under different UEs and SOs densities. SIR detection threshold is set as $\theta_{\mathrm{c}} = \theta_{\mathrm{s}} = -10$ dB.
• Figure 4: Coverage probability of communication only, sensing only, and JCAS versus SIR threshold.