Stochastic Geometry Based Modelling and Analysis of Uplink Cooperative Satellite-Aerial-Terrestrial Networks for Nomadic Communications with Weak Satellite Coverage

TL;DR

This work addresses uplink performance in cooperative satellite-aerial-terrestrial networks where terrestrial terminals are confined to a finite region. It introduces a stochastic geometry framework combining a binomial point process for terrestrial terminals and a type-II Matérn hard-core process for aerial relays, to derive distance distributions and end-to-end coverage and ergodic-rate metrics for two-hop T-A and A-S links under Nakagami and shadowed-Rician fading, respectively, with directional beamforming. The paper provides (semi-)closed-form expressions for P_cov^T-A and P_cov^A-S, as well as for the average ergodic rate of each link, and validates them through extensive Monte Carlo simulations while analyzing how aerial coverage, altitude, node densities, and beamforming affect performance. The results offer practical guidance for CSATN planning and deployment in finite regions and highlight how nomadic aerial relays can bolster connectivity when satellite coverage is weak. Future work includes extending the analysis to uplink ergodic sum-rate optimization for the studied CSATN framework.

Abstract

Cooperative satellite-aerial-terrestrial networks (CSATNs), where unmanned aerial vehicles (UAVs) are utilized as nomadic aerial relays (A), are highly valuable for many important applications, such as post-disaster urban reconstruction. In this scenario, direct communication between terrestrial terminals (T) and satellites (S) is often unavailable due to poor propagation conditions for satellite signals, and users tend to congregate in regions of finite size. There is a current dearth in the open literature regarding the uplink performance analysis of CSATN operating under the above constraints, and the few contributions on the uplink model terrestrial terminals by a Poisson point process (PPP) relying on the unrealistic assumption of an infinite area. This paper aims to fill the above research gap. First, we propose a stochastic geometry based innovative model to characterize the impact of the finite-size distribution region of terrestrial terminals in the CSATN by jointly using a binomial point process (BPP) and a type-II Mat{é}rn hard-core point process (MHCPP). Then, we analyze the relationship between the spatial distribution of the coverage areas of aerial nodes and the finite-size distribution region of terrestrial terminals, thereby deriving the distance distribution of the T-A links. Furthermore, we consider the stochastic nature of the spatial distributions of terrestrial terminals and UAVs, and conduct a thorough analysis of the coverage probability and average ergodic rate of the T-A links under Nakagami fading and the A-S links under shadowed-Rician fading. Finally, the accuracy of our theoretical derivations are confirmed by Monte Carlo simulations. Our research offers fundamental insights into the system-level performance optimization for the realistic CSATNs involving nomadic aerial relays and terrestrial terminals confined in a finite-size region.

Figures (16)

• Figure 1: Illustration of the CSATN system.
• Figure 2: The positional relationship between ${\color{black}\mathcal{S}_{\textrm{A}}'}$ and ${\color{black}\mathcal{S_{\textrm{U}}}}$, where $\bm{o}$ is the ground projection position of the AN considered.
• Figure 3: Coverage probability of the terrestrial-aerial link as the function of SINR threshold $T_{h_1}$ given three different $H_{\textrm{A}}$.
• Figure 4: Coverage probability of the terrestrial-aerial link as the function of SINR threshold $T_{h_1}$ given three different ${\color{black}\lambda_{\textrm{T}}}$.
• Figure 5: Coverage probability of the terrestrial-aerial link as the function of SINR threshold $T_{h_1}$ given three different $R_{\textrm{A}}$.

Theorems & Definitions (24)

• Lemma 1
• proof
• Remark 1
• Lemma 2
• proof
• Theorem 1
• proof
• Lemma 3
• proof
• Theorem 2