Wireless Network Topology Inference: A Markov Chains Approach

2025-01-29

AI Summary

This work addresses wireless network topology inference solely from anonymized node transmission timing observations—without signaling interaction or packet content. Methodologically, it models the problem using state-visit sequences of multiple anonymous Markov chains and, for the first time, formalizes topology inference as consistent estimation of transition matrices under operator norm convergence. It proposes a statistically consistent estimator with provable error bounds, overcoming limitations of conventional causal measures such as transfer entropy. The approach integrates discrete-time finite-state Markov modeling, joint statistical analysis of anonymized multi-chain observations, and structured matrix parameter estimation. Experiments demonstrate that the method significantly outperforms transfer-entropy-based baselines in topology recovery accuracy across networks of varying scales and under high congestion; moreover, its sample complexity scales nearly linearly with the number of nodes.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

In this work, we address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is available. We propose a novel network estimation procedure grounded in the following abstract problem: estimating the parameters of a finite discrete-time Markov chain by observing, at each time step, which states are visited by multiple ``anonymous'' copies of the chain. We develop a consistent estimator that approximates the transition matrix of the chain in the operator norm, with the number of required samples scaling roughly linearly with the size of the state space. Applying this estimation procedure to wireless networks, our numerical experiments demonstrate that the proposed method accurately infers network topology across a wide range of parameters, consistently outperforming transfer entropy, particularly under conditions of high network congestion.

Problem

• Wireless Network Structure
• Limited Observation Data
• Accurate Inference

Innovation

• Markov Chain
• Wireless Network Structure Inference
• Efficient Estimator Design