Wireless Network Topology Inference: A Markov Chains Approach

TL;DR

This paper introduces a Markov chain-based method for inferring wireless network topology from limited transmission detection data, demonstrating high accuracy and outperforming existing methods like transfer entropy.

Contribution

The paper presents a novel Markov chain estimation approach for wireless topology inference, with a consistent estimator that scales efficiently with network size.

Findings

Accurately infers network topology in various scenarios.

Outperforms transfer entropy under high congestion.

Requires samples scaling linearly with network size.

Abstract

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.