Velocity-Aware Statistical Analysis of Peak AoI for Ground and Aerial Users

TL;DR

This paper develops a velocity-aware framework for analyzing peak age-of-information (PAoI) in uplink cellular networks using a dominant interferer-based approximation. By expressing the SINR meta-distribution as a function of the distances to the serving base station $R_0$ and the dominant interferer $R_1$, and by modeling spatio-temporal correlations through these distances, the authors quantify how user velocity impacts PAoI for both ground and aerial UEs. A Nakagami-$m$ fading setting is accommodated via an indicator-function approach, enabling tractable joint distributions of the conditional success probability and PAoI; results show ground UEs exhibit stronger spatio-temporal correlations than aerial UEs, and velocity broadens the PAoI distribution while leaving the mean PAoI largely unchanged. The framework offers a low-complexity tool for velocity-aware network design and trajectory optimization in UAV-enabled systems, with potential extensions to alternative handover strategies and interference-management techniques.

Abstract

In this paper, we present a framework to analyze the impact of user velocity on the distribution of the peak age-of-information (PAoI) for both ground and aerial users by using the dominant interferer-based approximation. We first approximate the SINR meta distribution for the uplink transmission using the distances between the serving base station (BS) and each of the user of interest and the dominant interfering user, which is the interferer that provides the strongest average received power at the tagged BS. We then analyze the spatio-temporal correlation coefficient of the conditional success probability by studying the correlation between the aforementioned two distances. Finally, we choose PAoI as a performance metric to showcase how spatio-temporal correlation or user velocity affect system performance. Our results reveal that ground users exhibit higher spatio-temporal correlations compared to aerial users, resulting in a more pronounced impact of velocity on system performance, such as joint probability of the conditional success probability and distribution of PAoI. Furthermore, our work demonstrates that the dominant interferer-based approximation for the SINR meta distribution delivers good matching performance in complex scenarios, such as Nakagami-m fading model, and it can also be effectively utilized in computing spatio-temporal correlation, as this approximation is derived from the distances to the serving BS and the dominant interferer.

Figures (6)

• Figure 1: Illustration of the distances based on UE displacement. (a) (i) Illustration of the spatial correlation between the distances to the nearest interferer and the serving UE when no handover happens (the BS has the same nearest interferer UE). (a) (ii) Illustration of the distance to the serving BS when no handover happens. (b) Illustration of the spatial correlation between the distances to the nearest interferer and the serving UE when handover happens (BSs have two different nearest interferer UE).
• Figure 2: Illustration of the system model. (a) Illustration of the conditional success probability along the UE trajectory. (b) Illustration of AoI, which is composed of two transmission time, $T_1$ and $T_2$, and one data generation time, $\Delta T$.
• Figure 3: Analysis results and simulation results of the SINR meta distribution of aerial users under the dominant interferer-based approximation: (a) suburban regions $(a,b) = (4.88,0.43)$, (b) urban regions $(a,b) = (9.6,0.16)$, (c) dense urban regions $(a,b) = (12,0.11)$, and (a) highrise urban regions $(a,b) = (27,0.08)$.
• Figure 4: Analysis and simulation results of the correlation coefficient of the conditional success probability of aerial and ground users versus different velocities.
• Figure 5: Analysis and simulation results of the joint distribution of the conditional success probability of (a) ground users, (b) aerial users in highrise urban regions $(a,b) = (27,0.08)$, and (c) aerial users in suburban regions $(a,b) = (4.88,0.43)$.

Theorems & Definitions (17)

• Definition 1: Spatio-temporal Correlation Coefficient of $P_s(\theta)$
• Definition 2: Distribution of PAoI
• Lemma 1: Distance Distribution
• Lemma 2: Approximation of the Interference.
• Theorem 1: Joint Distribution of the Conditional Success Probability
• Lemma 3: Distance Distribution
• Lemma 4: Approximated Interference for Aerial UE
• Lemma 5: Approximated Conditional Success Probability of Aerial Users
• Lemma 6: Association Probability
• Theorem 2: Approximated SINR Meta Distribution of Aerial Users