Covert Multi-Hop Communications for Heterogeneous Networks With Multiple Wardens

This paper investigates covert multi-hop communications in heterogeneous wireless networks monitored by multiple passive wardens. To maximize network-wide covertness while satisfying a strict end-to-end rate requirement, we jointly optimize routing, modality selection, and transmit power. Under a simultaneous multi-hop transmission scheme, we analyze the detection capabilities of two distinct warden models: colluding wardens employing a central fusion center, and non-colluding wardens operating independently. For both models, we derive optimal detectors and exact expressions for the detection error probability (DEP). In addition, to reduce the complexity of evaluating the DEP, we develop highly accurate closed-form approximations based on gamma moment matching and establish rigorous DEP lower bounds using Kullback-Leibler (KL) divergence. Building on this theoretical foundation, we propose an efficient two-stage optimization algorithm that decouples link-level resource allocation from network-level path selection. By translating the KL divergence bounds into a novel, low-complexity routing metric, which universally simplifies to a linear summation of signal-to-noise ratios, we substantially reduce the computational overhead compared to conventional per-hop detection-based metrics. Finally, numerical simulations validate the theoretical analysis and demonstrate the near-optimal performance of the proposed framework.

Simultaneous Multi-Modal Covert Communications: Analysis and Optimization

This paper investigates the problem of covert communications in a heterogeneous wireless network where multiple communication modalities are used simultaneously. In this setup, a legitimate transmitter sends confidential data to its receiver by selecting multiple modalities with the goal of maximizing communication covertness against a passive adversary (Willie) while satisfying a transmission rate requirement. We analyze two distinct scenarios for a given observation time by Willie. The two scenarios are: (i) Willie knows the modalities selected by the friendly transmitter, and (ii) Willie is unaware of the selected modalities. We first derive the optimal detector for Willie that minimizes the detection error probability (DEP) in both cases. For the first scenario, we derive an exact expression for the DEP and provide a computationally efficient approximation. For the second scenario, we introduce the DEP expressions in the low-signal-to-noise ratio (SNR) regime at Willie. Building on this analysis, we propose a novel low-complexity modality set selection technique designed to maximize the DEP subject to a rate constraint. Numerical simulations validate the derived analytical expressions and demonstrate that the proposed modality set selection technique achieves near-optimal performance, outperforming benchmark schemes.

Deep Reinforcement Learning Based Routing for Heterogeneous Multi-Hop Wireless Networks

Routing in multi-hop wireless networks is a complex problem, especially in heterogeneous networks where multiple wireless communication technologies coexist. Reinforcement learning (RL) methods, such as Q-learning, have been introduced for decentralized routing by allowing nodes to make decisions based on local observations. However, Q-learning suffers from scalability issues and poor generalization due to the difficulty in managing the Q-table in large or dynamic network topologies, especially in heterogeneous networks (HetNets) with diverse channel characteristics. Thus, in this paper, we propose a novel deep Q-network (DQN)-based routing framework for heterogeneous multi-hop wireless networks to maximize the end-to-end rate of the route by improving scalability and adaptability, where each node uses a deep neural network (DNN) to estimate the Q-values and jointly select the next-hop relay and a communication technology for transmission. To achieve better performance with the DNN, selecting which nodes to exchange information is critical, as it not only defines the state and action spaces but also determines the input to the DNN. To this end, we propose neighbor node selection strategies based on channel gain and rate between nodes rather than a simple distance-based approach for an improved set of states and actions for DQN-based routing. During training, the model experiences diverse network topologies to ensure generalization and robustness, and simulation results show that the proposed neighbor node selection outperforms simple distance-based selection. Further, we observe that the DQN-based approach outperforms various benchmark schemes and performs comparably to the optimal approach.