Clifford Poisson Point Process for Structured StochasticGeometry Modeling of 6G Wireless Systems

Poisson point process (PPP) is fundamental in stochastic geometry for modeling random node locations in wireless networks. Classical PPP is inherently scalar and isotropic. Although they capture spatial randomness, other important information in 6G wireless communication, such as orientation, polarization, and geometric semantics of electromagnetic (EM) fields, is not considered. Existing extensions, such as marked PPP, Boolean models, and determinantal point processes, remain limited because they lack an internal algebraic structure capable of representing such information. To bridge the gap, this work introduces an innovative Clifford-algebraic model called the Clifford Poisson Point Process (Clifford PPP), where each point is marked with a Clifford multivector, as shown in Figure 1. In this model, in addition to location, other properties of a node, such as those related to an EM field, including its scalar, vector, bivector and higher multigrade components, are represented by a Clifford structure.