The performance analysis of maritime communication networks is frequently constrained by the widespread yet unrealistic assumption of a uniform spatial distribution of vessels. This paper presents a unified stochastic geometry framework that integrates high-fidelity physical channel models with nonhomogeneous vessel topologies to provide a more accurate analytical foundation. We first systematically demonstrate that the macroscopic geographical distribution of vessels is a dominant factor governing overall network performance, with significant performance variations observed across different deployment scenarios. Subsequently, to analyze the spatial origins of this performance, we introduce the coverage probability density function (Cpdf) as a novel metric. The Cpdf enables a finegrained spatial decomposition of the total coverage probability, thereby identifying key geographical areas that contribute most to network performance and quantifying the precise spatial impact of physical phenomena, such as multipath fading nulls. Our results affirm the primacy of realistic spatial modeling and provide a new analytical tool for the design and optimization of next-generation maritime networks.

The growing demand for reliable and extensive connectivity has made low Earth orbit (LEO) satellites aided Internet of Things (IoT) systems a critical area of research. However, current theoretical studies on IoT-over-LEO satellite systems often rely on unrealistic assumptions, such as infinite terrestrial areas and omnidirectional satellite coverage, leaving significant gaps in theoretical analysis for more realistic operational constraints. These constraints involve finite terrestrial area, limited satellite coverage, Earth curvature effect, integral uplink and downlink analysis, and link-dependent interference. To address these gaps, this paper proposes a novel stochastic geometry based model to rigorously analyze the performance of IoT-over-LEO satellite systems. By adopting a binomial point process (BPP) instead of the conventional Poisson point process (PPP), our model accurately characterizes the geographical distribution of a fixed number of IoT devices in a finite terrestrial region. This modeling framework enables the derivation of distance distribution functions for both the links from the terrestrial IoT devices to the satellites (T-S) and from the satellites to the Earth station (S-ES), while also accounting for limited satellite coverage and Earth curvature effects. To realistically represent channel conditions, the Nakagami fading model is employed for the T-S links to characterize diverse small-scale fading environments, while the shadowed-Rician fading model is used for the S-ES links to capture the combined effects of shadowing and dominant line-of-sight paths. Furthermore, the analysis incorporates uplink and downlink interference, ensuring a comprehensive evaluation of system performance. The accuracy and effectiveness of our theoretical framework are validated through extensive Monte Carlo simulations. These results provide insights into key performance metrics, such as coverage probability and average ergodic rate, for both individual links and the overall system. Our study also offers an important analytical tool for optimizing the design and performance of IoT-over-LEO satellite systems with the operational constraints that are more realistic.

In harsh environments, such as mountainous terrain, dense vegetation and urban landscapes, a single type of unmanned aerial vehicles (UAVs) may encounter challenges like flight restrictions, difficulty in task execution or increased risk. Therefore, employing multiple types of UAVs to collaborate along with satellite assistance, becomes essential in such scenarios. In this context, we present a stochastic geometry based approach for modeling the heterogeneous non-terrestrial networks (NTNs) by using the classical binomial point process and introducing a novel point process, called Matérn hard-core cluster process (MHCCP) which possesses both properties of exclusivity and clustering. Through simulations, MHCCP has been validated as a more suitable model for UAV groups composed of multiple clusters, compared with traditional point processes such as Poisson point process, binomial point process, and Poisson cluster process. This is because MHCCP ensures inter-cluster repulsion while effectively capturing the clustered distribution observed in practical scenarios. Then, taking into account the influence of terrain shadows on the aerial-satellite links in low-altitude harsh environments, we derive closed-form expressions of the outage probability and average ergodic rate for the aerial-to-satellite uplink of heterogeneous NTNs. Unlike existing studies, our analysis adopts an advanced system configuration that combines beamforming with frequency division multiple access and incorporates a shadowed-Rician fading model to accurately capture signal fading under complex environmental conditions. Furthermore, we investigate link performance in the presence of co-channel interference. Monte Carlo simulations validate that the derived closed-form solutions of the outage probability and the average ergodic rate provide a precise quantitative tool for evaluating the reliability and transmission efficiency of the aerial-satellite links, offering deeper insights into system performance in complex environments.

In harsh environments such as mountainous terrain, dense vegetation areas, or urban landscapes, a single type of unmanned aerial vehicles (UAVs) may encounter challenges like flight restrictions, difficulty in task execution, or increased risk. Therefore, employing multiple types of UAVs, along with satellite assistance, to collaborate becomes essential in such scenarios. In this context, we present a stochastic geometry based approach for modeling the heterogeneous non-terrestrial networks (NTNs) by using the classical nbinomial point process and introducing a novel point process, called Matérn hard-core cluster process (MHCCP). Our MHCCP possesses both the exclusivity and the clustering properties, thus it can better model the aircraft group composed of multiple clusters. Then, we derive closed-form expressions of the outage probability (OP) for the uplink (aerial-to-satellite) of heterogeneous NTNs. Unlike existing studies, our analysis relies on a more advanced system configuration, where the integration of beamforming and frequency division multiple access, and the shadowed-Rician (SR) fading model for interference power, are considered. The accuracy of our theoretical derivation is confirmed by Monte Carlo simulations. Our research offers fundamental insights into the system-level performance optimization of NTNs.

In this paper, we propose a stochastic geometry based innovative model to characterize the impact of the limited-size distribution region of terrestrial terminals in terrestrial-to-aerial networks by jointly using a binomial point process (BPP) and a type-II Matérn hard-core point process (MHCPP). Then, we analyze the relationship between the spatial distribution of the coverage areas of aerial nodes and the limited-size distribution region of terrestrial terminals, thereby deriving the distance distribution of the terrestrial-aerial (T-A) links. Furthermore, we consider the stochastic nature of the spatial distributions of terrestrial terminals and unmanned aerial vehicles (UAVs), and conduct a thorough analysis of the coverage probability of the T-A links under Nakagami 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 terrestrial-to-aerial networks involving nomadic aerial base-stations and terrestrial terminals confined in a limited-size region.

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 Matérn 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.