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IEEE Communications Letters

Guaranteed Payoffs Resource Allocation Problem With Application to Countering Reinforced Eavesdropping

Andrey Garnaev, Wade K. Trappe

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Wireless communication between a transmitter (e.g., an operator) and agents (e.g., drones) may be vulnerable to eavesdropping attacks on some or all agents. A drawback of the traditional communication approach that aims to maximize the total secrecy capacity is that it may neglect communication with specific agents, thereby leading to mission failure for those agents. To address this drawback, we develop and solve a novel guaranteed-payoffs problem that generalizes max-min optimization in a resource-restricted setting and prove that its solution combines egalitarian and water-filling properties. The developed generalization is a convenient tool for researchers to apply across different research areas. Based on this, we design an anti-eavesdropping strategy that maximizes the minimal secrecy capacity of communication with agents facing an adversary capable of reinforcing eavesdropping devices in a game-theoretic framework. Robustness of the derived anti-eavesdropping strategy is proven, and strategies are illustrated.

DOI
10.1109/lcomm.2026.3685008

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As the technology and computing power advance day by day, physical layer security in wireless communications gains more importance. It allows the security of wireless communications based on information theoretical guarantees without the need for cryptography. One important practical challenge for physical layer security arises from the fact that no information about the passive eavesdroppers is available to the legitimate nodes. Without such information, optimizing the transmission parameters has always been a difficult task. In this study we aim to address various challenging aspects about this issue and propose a new perspective into the analysis of secrecy with a focus on jamming. We start from the case of eavesdropper's channel state information (CSI) known to users in a three-node single-antenna multi-subcarrier network and present an improved optimization algorithm compared to previous methods. Then we expand our horizon to the case of multiple-antenna nodes with eavesdropper's CSI unknown to users. We investigate a secure wireless communication scheme which combines two of the most effective strategies to combat eavesdropping, namely mixing information with artificial noise at the transmitter and jamming from a full-duplex receiver. While such setup has been investigated in related works, new and important insights are revealed in this study. We investigate the design of optimal jamming parameters to achieve higher secrecy.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme, makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme, makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.

•Jan 1, 2018•0 citations
Wireless communication between a transmitter (e.g., an operator) and agents (e.g., drones) may be vulnerable to eavesdropping attacks on some or all agents. A drawback of the traditional communication approach that aims to maximize the total secrecy capacity is that it may neglect communication with specific agents, thereby leading to mission failure for those agents. To address this drawback, we develop and solve a novel guaranteed-payoffs problem that generalizes max-min optimization in a resource-restricted setting and prove that its solution combines egalitarian and water-filling properties. The developed generalization is a convenient tool for researchers to apply across different research areas. Based on this, we design an anti-eavesdropping strategy that maximizes the minimal secrecy capacity of communication with agents facing an adversary capable of reinforcing eavesdropping devices in a game-theoretic framework. Robustness of the derived anti-eavesdropping strategy is proven, and strategies are illustrated.
This dissertation investigates the physical layer security of wireless communication networks using game-theoretic and optimization models. Considered is a wireless network of parallel channels that may be under eavesdropping attack. Game models are played between a friendly interferer (he) who can broadcast artificial noise and a strategic eavesdropper (she). The friendly interferer wants to maximize the secrecy level of the wireless communication network by decreasing the eavesdropper's listening capability with intentionally generated noise signals, while the eavesdropper wants to maximize her own capability and avoid interference. The game-theoretic models reflect the strategic confrontation between the friendly interferer and the eavesdropper in different communication environments. These models address some of the limitations in literature. Most existing resource allocation strategies for friendly interference adopt the conservative assumption that all parallel channels are under attack. Game-theoretic approaches provide more efficient strategies to the friendly interferer by anticipating the channels to be attacked by the eavesdropper. The first model considers the case in which the friendly interferer can flexibly allocate cooperative jamming power to all communication channels in the network under a total power constraint. When all channels used for secret communication are under the threat of eavesdropping attacks, the optimal power allocation policy results from solving a convex optimization problem. In this case, the optimal policy is unique and can be obtained via a water-filling scheme. When the eavesdropper can not attack all channels, the eavesdropper should behave strategically and may select the targets probabilistically. In this case, a non-zero-sum game helps the friendly interferer predict and concentrate on the targets selected by the eavesdropper. When the eavesdropper can only attack a single channel, an analytical form of the NE strategies is presented; while an iterative numerical method that guarantees the convergence to NE strategies is proposed if the eavesdropper can attack multiple channels. Compared to naive power allocation strategies, such as splitting the power equally to each channel, the game-theoretic power allocation strategy always delivers better expected total secrecy capacity. Next, an extension of the power allocation game for cooperative jamming models the case in which the state information of the eavesdropping channels may not be known completely. New utility functions for the friendly interferer and the eavesdropper are designed to include the distributional information of eavesdropping channels' state information. A non-zero sum game using the new utility functions is analyzed between the friendly interferer and the strategic eavesdropper who can only attack a limited number of channels. Note that the friendly interferer may not have the capability to send cooperative jamming signals to multiple channels simultaneously. For such a friendly interferer, a probabilistic cooperative jamming scheme is devised such that the defender focuses on protecting randomly selected channels. In the mean time, the eavesdropper selects the most vulnerable channels to attack. A linearly constrained non-zero-sum bimatrix game models the competition between the defender and the eavesdropper. The Nash equilibrium is shown to be equivalent to the solution of a quadratic programming problem. A closed form solution is derived for the special case in which the eavesdropper can only attack a single channel. We show that there exists a cut-off index determining the set of channels that will be covered in the equilibrium strategies. Furthermore, the adverse effect of the interference signal plays an important role in the value of the cut-off index and it represents the vulnerability of wireless communication networks against eavesdroppers Wireless communication networks of parallel channels actually share a lot of similarities with general cyber networks. Thus, the final model in this dissertation is a cost-efficient network security game for defensive resource allocation in a heterogeneous cyber network of N nodes. A defender, by allocating defensive resources to a networked node, can decrease the node's vulnerabilities. At the same time, the cost of using defensive resources is taken into consideration. Two non-zero-sum Nash games model the competition between the defender and two types of attackers, respectively. The first type tries to maximize damage based on the value of security assets related to networked nodes, while the second type aims at infiltrating the network. Consideration of the case that the defender does not know the attacker's type leads to a Bayesian game. For all three games, we derive conditions for the existence of a unique Nash equilibrium (NE), and obtain the equilibria and the value functions in closed form.
Wireless network communication of a transmitter with a group of receivers (nodes) is susceptible to malicious eavesdropping attacks. In this paper, motivated by the observation that maximizing the secrecy rate protocol might lead to neglecting communication with some nodes, we suggest designing a protocol to maximize fairness of the secrecy rates, specifically, α− fairness, in the transmitter’s communication with all the nodes. The problem is modeled in a non-zero-sum game-theoretical framework between a transmitter and an adversary (eavesdropper). Equilibrium strategies are derived in closed form and their uniqueness is proven which reflects the stability of the suggested transmission protocol. Moreover, although an equilibrium is established as unique for each fixed fairness coefficient, all together it results in a continuum of transmission protocols, one protocol per fairness coefficient. To deal with this issue, in this paper, we suggest using a trade-off fairness coefficient between the expected secrecy rate of the whole nodes’ group and the expected secrecy rate of the worst-off secrecy rate node, reflecting "a weak link" in the communication, as the best protocol among all such fair protocols in its application. The derived equilibria and trade-off fairness coefficient are numerically illustrated.
Wireless communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy issues have become increasingly critical for wireless networks. This paper considers the problem of secret communication in the multiuser downlink eavesdropped by a passive eavesdropper (EVE). The well-known zero-forcing preceding is adopted at the transmitter to produce concurrent data streams to the users, and at the same time an artificial noise (AN) is generated to prevent EVE from intercepting the information. We first derive an analytical closed-form expression for the secrecy sum-rate in the large system limit. We then use it as the objective function to optimize the power allocation (PA) between the information signals and the AN to maximize the secrecy sum-rate. A simple analytical expression of the optimal PA is derived in the high transmit power regime, which proves to be a near-optimal and generic strategy. The large system results are quite accurate for finite-size systems and thus can provide useful insights into system analysis and design. Our analytical and simulation results show that the AN assisted strategy achieves the same multiplexing gain as in the multiuser downlink without eavesdropping. Moreover, more power should be allocated to AN when the system serves fewer users and EVE has more antennas.
The broadcast nature of wireless channels introduces significant security vulnerabilities in information transmission, particularly when the eavesdropper is close to the legitimate destination. In such scenarios, the eavesdropping channel often exhibits high spatial correlation with, or even superior quality to, the legitimate channel. This makes it challenging for traditional power optimization methods to effectively suppress the eavesdropping rate. To address this challenge, this paper proposes an optimization method for the secrecy capacity of unmanned aerial vehicle (UAV) relaying based on the dynamic adjustment of the power allocation factor. By injecting artificial noise (AN) during signal forwarding and combining it with real-time channel state information, the power allocation factor can be dynamically adjusted to achieve precise jamming of the eavesdropping link. We consider a four-node communication model consisting of a source, a UAV, a legitimate destination, and a passive eavesdropper, and formulate a joint optimization problem to maximize the secrecy rate. Due to the non-convexity of the original problem, we introduce relaxation variables and apply successive convex approximation (SCA) to reformulate it into an equivalent convex optimization problem. An analytical solution for the power allocation factor is derived using the water-filling (WF) algorithm. Furthermore, an alternating iterative optimization algorithm with AN assistance is proposed to achieve global optimization of the system parameters. Simulation results demonstrate that, compared to traditional power optimization schemes, the proposed algorithm substantially suppresses the eavesdropping channel capacity while enhancing transmission efficiency, thereby significantly improving both secrecy performance and overall communication reliability.
Security issue is of paramount importance yet significant challenge for wireless communications, and this problem can be even more intricate when facing with a full-duplex adversary. In this paper, we investigate the physical layer security of a legitimate transmission link in the presence of a full-duplex active eavesdropper, who is capable to perform eavesdropping and jamming simultaneously. The legitimate user aims at a target secrecy rate while the eavesdropper intends to maximize its wiretap rate. To this end, the eavesdropper imposes a jamming signal at the legitimate receiver to stimulate higher-power legitimate transmissions and thus facilitates its eavesdropping. This, however, generates residual self-interference at the eavesdropper itself and is subject to a linear price for the jamming power. The problem is then formulated within a game-theoretic framework, where the closed-form strategies of both the legitimate user and active eavesdropper are obtained. Moreover, we analyze the performance in terms of secrecy outage probability for the legitimate link in such a hostile situation. Also provided are the simulation results which validate our theoretical analysis.
As the technology and computing power advance day by day, physical layer security in wireless communications gains more importance. It allows the security of wireless communications based on information theoretical guarantees without the need for cryptography. One important practical challenge for physical layer security arises from the fact that no information about the passive eavesdroppers is available to the legitimate nodes. Without such information, optimizing the transmission parameters has always been a difficult task. In this study we aim to address various challenging aspects about this issue and propose a new perspective into the analysis of secrecy with a focus on jamming. We start from the case of eavesdropper's channel state information (CSI) known to users in a three-node single-antenna multi-subcarrier network and present an improved optimization algorithm compared to previous methods. Then we expand our horizon to the case of multiple-antenna nodes with eavesdropper's CSI unknown to users. We investigate a secure wireless communication scheme which combines two of the most effective strategies to combat eavesdropping, namely mixing information with artificial noise at the transmitter and jamming from a full-duplex receiver. While such setup has been investigated in related works, new and important insights are revealed in this study. We investigate the design of optimal jamming parameters to achieve higher secrecy.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme, makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme, makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.