Power Control in Relay-Assisted Anti-Jamming Systems: A Bayesian Three-Layer Stackelberg Game Approach

Abstract

This paper investigates the multiuser power control problem in relay-assisted anti-jamming systems. Because of the hierarchical confrontation characteristics between users and jammer, we take the incomplete information and observation error into consideration and formulate an anti-jamming Bayesian three-layer Stackelberg game, in which primary users act as leaders, relay users act as vice-leaders, and jammer acts as a follower. Both users and jammer have the ability to sense others' transmission power and choose optimal power to realize the maximum of utility. Based on the backward induction method, we propose a multiuser hierarchical iterative algorithm to obtain the Stackelberg equilibrium (SE) and prove the existence and uniqueness of SE. Finally, simulation results are compared with the Nash equilibrium to verify the effectiveness of the proposed game. Moreover, both the influence of incomplete information and the observation error on utility are analyzed. INDEX TERMS Power control, anti-jamming, three-layer Stackelberg game, Stackelberg equilibrium.

An Anti-Jamming Hierarchical Optimization Approach in Relay Communication System via Stackelberg Game

“…The main differences from our previous work [36] are summarized as: (i) There exist multiple relays in the anti-jamming system which needs to realize the optimization of relay selection and power control simultaneously. (ii) The feedback error and eavesdropping error are introduced because it is hard for the the user and jammer to get accurate feedback information.…”

“…In the domain of relay communication [26][27][28][29][30][31][32][33][34][35][36][37][38][39], the anti-jamming problem has also been widely investigated. In [27], the authors studied communication frequency selection optimization problem in unpredictable jamming environment.…”

“…With the increasing complexity of communication scenarios and jamming modes, in [34,35], the authors studied the optimal power allocation problem in friendly jamming and Gaussian noise jamming environments to increase secrecy sum rate in untrusted relay communication networks. In [36], the authors studied anti-jamming power optimization problem in multi-user relay communication system, a three-layer Stackelberg game was proposed and Stackelberg equilibrium (SE) was also obtained based on duality optimization theory. In [37], the authors studied the problem of resource assigning in a single carrier communication system in the presence of a jammer, a Bayesian jamming game framework was proposed and the Nash strategy was also compared to the Stackelberg strategy to verify its sensibility.…”

“…In [39], considering the idealized case and potential energy constraint, the authors investigated the jamming attacks optimization problem that the jammer could control the probability of jamming and transmission range to cause maximal damage to wireless network. The existing works [34][35][36][37][38][39] investigated the anti-jamming problems from the perspectives of adaptive defense strategies, potential energy constraint, jamming modes, ideal and non-ideal cases in different communication scenarios to perfect the study. Game theoretical approaches, such as stochastic game and Stackelberg game, are just methods which can help us analyze the anti-jamming problems effectively.…”

“…The main difference between this paper and the above anti-jamming works [29][30][31][32][33][34][35][36][37][38][39] is that, in the presence of an intelligent jammer, we investigate the relay selection problem under a power-energy constraint with imperfect information. Moreover, considering the existing power optimization methods in anti-jamming domain, there are still some problems needing to be solved.…”