Parameter Mapping of Distribution Substitution for Inter-Point Distances in Random Networks

Statistical models of inter-point distances are pivotal for analyzing and optimizing wireless communication networks and other spatial systems, such as vehicular swarms and distributed sensing networks. However, the analytical intractability of exact distance distributions often hinders closed-form performance evaluations and obscures parameter-performance relationships. To address these challenges, this paper introduces a low-complexity polynomial substitute for inter-point distance distributions and a systematic framework for parameter mapping. The framework employs two complementary mapping schemes, Relative Entropy Minimization (REM) which promotes fidelity to the original distribution in the Kullback–Leibler sense, and Mean Square Error Minimization (MSEM) which minimizes the mean squared error between the two distributions. These mappings yield parameter correspondences between the original and substitute distributions, enabling efficient and accurate approximations. The substitutes are validated on representative spatial models, preserving fidelity to the original distributions while using a low-complexity polynomial representation. This advancement facilitates closed-form evaluations and optimizations in random networks, enhancing the analytical toolkit for stochastic geometry and control theory.