A Tutorial on Mathematical Modeling of 5G/6G Millimeter Wave and Terahertz Cellular Systems

Millimeter wave (mmWave) and terahertz (THz) radio access technologies (RAT) are expected to become a critical part of the future cellular ecosystem providing an abundant amount of bandwidth in areas with high traffic demands. However, extremely directional antenna radiation patterns that need to be utilized at both transmit and receive sides of a link to overcome severe path losses, dynamic blockage of propagation paths by large static and small dynamic objects, macro- and micromobility of user equipment (UE) makes provisioning of reliable service over THz/mmWave RATs an extremely complex task. This challenge is further complicated by the type of applications envisioned for these systems inherently requiring guaranteed bitrates at the air interface. This tutorial aims to introduce a versatile mathematical methodology for assessing performance reliability improvement algorithms for mmWave and THz systems. Our methodology accounts for both radio interface specifics as well as service process of sessions at mmWave/THz base stations (BS) and is capable of evaluating the performance of systems with multiconnectivity operation, resource reservation mechanisms, priorities between multiple traffic types having different service requirements. The framework is logically separated into two parts: (i) parameterization part that abstracts the specifics of deployment and radio mechanisms, and (ii) queuing part, accounting for details of the service process at mmWave/THz BSs. The modular decoupled structure of the framework allows for further extensions to advanced service mechanisms in prospective mmWave/THz cellular deployments while keeping the complexity manageable and thus making it attractive for system analysts.