Coverage and Rate Analysis for Integrated Sensing and Communication Networks

TL;DR

A generalized stochastic geometry framework is introduced in ISAC networks by defining and calculating the coverage and ergodic rate of sensing and communication performance under resource constraints, and shed light on the fundamental limits of ISAC networks by presenting theoretical results.

Abstract

Integrated sensing and communication (ISAC) is increasingly recognized as a pivotal technology for next-generation cellular networks, offering mutual benefits in both sensing and communication capabilities. This advancement necessitates a re-examination of the fundamental limits within networks where these two functions coexist via shared spectrum and infrastructures. However, traditional stochastic geometry-based performance analyses are confined to either communication or sensing networks separately. This paper bridges this gap by introducing a generalized stochastic geometry framework in ISAC networks. Based on this framework, we define and calculate the coverage and ergodic rate of sensing and communication performance under resource constraints. Then, we shed light on the fundamental limits of ISAC networks by presenting theoretical results for the coverage rate of the unified performance, taking into account the coupling effects of dual functions in coexistence networks. Further, we obtain the analytical formulations for evaluating the ergodic sensing rate constrained by the maximum communication rate, and the ergodic communication rate constrained by the maximum sensing rate. Extensive numerical results validate the accuracy of all theoretical derivations, and also indicate that denser networks significantly enhance ISAC coverage. Specifically, increasing the base station density from $1$ $\text{km}^{-2}$ to $10$ $\text{km}^{-2}$ can boost the ISAC coverage rate from $1.4\%$ to $39.8\%$. Further, results also reveal that with the increase of the constrained sensing rate, the ergodic communication rate improves significantly, but the reverse is not obvious.

Figures (14)

• Figure 1: An implementation of an ISAC network, where the triangles represent BSs, and the red and green triangles represent the nearest BS and the $\mathcal{L}$-th nearest BS ($\mathcal{L}=4$ in this figure), respectively. The point represents the typical user, and the locations of the remaining users are omitted for brevity.
• Figure 2: The coverage rate of $\mathcal{L}$-conditional positioning function, derived in Lemma 2, versus different accuracy thresholds and scenarios.
• Figure 3: The PMF of $\mathcal{L}$, derived in Lemma 3, versus different path-loss exponents and $\mathcal{L}$-localizability SINR thresholds.
• Figure 4: The coverage rate of positioning performance $P_p(\epsilon_1)$, derived in Theorem 1, versus different accuracy thresholds and $\mathcal{L}$-localizability SINR thresholds.
• Figure 5: The ergodic rate of the positioning process $\mathbb{E}(\underline{\mathcal{C}})$, derived in Theorem 1 and Definition 6, versus different path-loss exponents and BS densities.

Theorems & Definitions (13)

• Lemma 1
• Proposition 1
• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Lemma 2
• Lemma 3