Passive Wireless Network Topology Inference Using a Multi-Dimensional Hawkes Process

Accurate topology inference plays a key role in the effective management, optimization and security monitoring of wireless networks. However, in non-cooperative scenarios, topology inference of the target network with different communication modes is challenging, because only limited information can be obtained from passive observations. Inspired by some causal inference methods, the wireless communication interaction can be modeled as a multi-dimensional Hawkes process with a Granger causal relationship, and then topology inference can be transformed into a maximum-likelihood based parameter estimation (MLE) problem. To this end, we propose a new framework for passive wireless network topology inference using a multi-dimensional Hawkes Process (PWNTI-MH). First, by modeling the timestamps of Acknowledgement (ACK) packets of communication nodes as a discrete binary event sequence matrix, the communication behavior of each node can be considered as a sub-process of the multi-dimensional Hawkes process. Then, structural constraints, including temporal sparsity, group sparsity, and low-rank constraints, are imposed on the MLE optimization problem to improve inference accuracy. To solve the new objective function, we derived a new maximum likelihood estimation method with sparsity, group sparsity, and low-rank constraints (MLE-SGLR) that shows good convergence behavior under relatively mild conditions. Simulation results show that the proposed PWNTI-MH has better inference accuracy under various communication modes and network scales, outperforming most baseline algorithms as well as the active interaction framework on small-scale networks.