Technology Category
Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsIntelligent Robots: Motion and Path PlanningSearch and Optimization: Evaluation and Analysis
Reflected wireless signals under random spatial sampling
🤖 AI Summary
This study investigates the singularities and non-classical fading phenomena in received power distributions of wireless signals under random spatial sampling, caused by multipath reflections. Focusing on a canonical scenario between two parallel walls, the work attributes—for the first time—the unbounded peaks observed in power histograms to the non-monotonic path loss inherent in deterministic propagation models. A closed-form analytical framework is established by integrating wave propagation theory, stochastic spatial sampling, and the Lerch transcendent special function. Notably, a closed-form expression for received power is derived for the case of transmission from the midpoint between the walls, revealing the oscillatory mechanism induced by reflections. This research provides a foundational theoretical basis for the deployment of intelligent reflecting surfaces in urban environments.
Technology Category
Application Category
📝 Abstract
We present a propagation model showing that a transmitter randomly positioned in space generates unbounded peaks in the histogram of the resulting power, provided the signal strength is an oscillating or non-monotonic function of distance. Specifically, these peaks are singularities in the empirical probability density that occur at turning point values of the deterministic propagation model. We explain the underlying mechanism of this phenomenon through a concise mathematical argument. This observation has direct implications for estimating random propagation effects such as fading, particularly when reflections off walls are involved. Motivated by understanding intelligent surfaces, we apply this fundamental result to a physical model consisting of a single transmitter between two parallel passive walls. We analyze signal fading due to reflections and observe power oscillations resulting from wall reflections -- a phenomenon long studied in waveguides but relatively unexplored in wireless networks. For the special case where the transmitter is placed halfway between the walls, we present a compact closed-form expression for the received signal involving the Lerch transcendent function. The insights from this work can inform design decisions for intelligent surfaces deployed in cities.
Problem
Research questions and friction points this paper is trying to address.
wireless propagation
signal fading
spatial randomness
wall reflections
power oscillations
Innovation
Methods, ideas, or system contributions that make the work stand out.
random spatial sampling
power singularities
non-monotonic propagation
wall reflections
Lerch transcendent
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