Distance Analysis in Regular OWC Deployments

Abstract

For future wireless networks, including 6G, the ability to accurately model and predict network behaviour is essential for meeting stringent quality of service (QoS) requirements. This paper addresses a critical need in future wireless communication systems, particularly for 6G networks, by providing a comprehensive mathematical framework for modelling network geometry in regular cell deployments. Accurate modelling of network geometry is essential for ensuring high QoS and precise localization. While both regular (e.g., square) and irregular (e.g. Poisson Point Process (PPP)) cell-deployment models have been studied, regular deployments, which are crucial for wireless and optical wireless communications (OWC), have received less attention. This paper proposes a mathematical framework to analyse the distance distribution in various regular cell deployments, including line, square, and hexagon configurations. It derives the probability density function (pdf) of the horizontal (2D) and vertical (3D) distances between a user equipment (UE) and the closest node. The framework reveals inaccuracies in previous assumptions made in the literature regarding distance distribution. The exact pdf of the 2D distance between a randomly located UE and the closest node is derived, considering parameters such as inter-node distance and system dimensions (e.g., width). The framework is extended to study the 3D distance, accounting for both fixed and random height differences between the UE and nodes. The coverage probability (CP) is also derived using the proposed framework, providing a more accurate representation of network performance. The results confirm the accuracy of the proposed analysis and compare it with existing works in the literature. The paper highlights that some of assumptions in these works lead to significant errors, such as a 4dB error in signal to noise ratio (SNR) in square deployments. The proposed framework offers a more precise approach to capturing the system characteristics, leading to better network planning and performance optimization.

Keywords

• Coverage probability (CP)
• distance distribution
• hexagon deployment
• line deployment
• optical wireless communications (OWC)
• regular deployment