Spatial-Temporal Discretization Optimization in the Modeling of Optical and RF Wireless Networks

Many optimization frameworks and mathematical models have been proposed for standalone optical and radio frequency (RF) wireless networks, as well as their integration. These models typically discretize the time horizon into fixed intervals, inherently introducing spatial discretization when network nodes are mobile. Spatial discretization is also widely applied in reinforcement learning approaches. While temporal and spatial discretizations reduce computational complexity, they may introduce inaccuracies, especially in highly dynamic systems. This paper presents analytical upper bounds for the relative deviation in signal-to-noise ratio (SNR) in both optical wireless communication (OWC) and RF, focusing on how grid granularity affects SNR accuracy through theoretical analysis. The results show that, under identical grid conditions and ideal node orientation, OWC experiences up to 45% higher relative SNR deviation than RF. Furthermore, an upper bound is derived as a function of node velocity and time interval, indicating that OWC requires 31% shorter time intervals than RF to achieve comparable SNR accuracy. Simulations validate the model, confirming that the theoretical upper bounds closely align with empirical results.