Smart Jammer and LTE Network Strategies in An Infinite-Horizon Zero-Sum Repeated Game with Asymmetric and Incomplete Information

TL;DR

This paper models the interaction between a smart jammer and LTE networks as an infinite-horizon zero-sum game with asymmetric information, proposing efficient suboptimal strategies for both players and analyzing their effectiveness through simulations.

Contribution

It introduces a novel game-theoretic framework for LTE network security against smart jammers, developing approximated and expected strategies to handle asymmetric and incomplete information.

Findings

Smart jammer employs non-revealing, misleading strategies.

Proposed strategies are computationally feasible with fixed-sized statistics.

Simulation confirms effectiveness of the strategies against smart jammers.

Abstract

LTE/LTE-Advanced networks are known to be vulnerable to denial-of-service and loss-of-service attacks from smart jammers. In this article, the interaction between a smart jammer and LTE network is modeled as an infinite-horizon, zero-sum, asymmetric repeated game. The smart jammer and eNode B are modeled as the informed and the uninformed player, respectively. The main purpose of this article is to construct efficient suboptimal strategies for both players that can be used to solve the above-mentioned infinite-horizon repeated game with asymmetric and incomplete information. It has been shown in game-theoretic literature that security strategies provide optimal solution in zero-sum games. It is also shown that both players' security strategies in an infinite-horizon asymmetric game depend only on the history of the informed player's actions. However, fixed-sized sufficient statistics are needed for both players to solve the above-mentioned game efficiently. The smart jammer uses its evolving belief state as the fixed-sized sufficient statistics for the repeated game. Whereas, the LTE network (uninformed player) uses worst-case regret of its security strategy and its anti-discounted update as the fixed-sized sufficient statistics. Although fixed-sized sufficient statistics are employed by both players, optimal security strategy computation in {\lambda}-discounted asymmetric games is still hard to perform because of non-convexity. Hence, the problem is convexified in this article by devising `approximated' security strategies for both players that are based on approximated optimal game value. However, `approximated' strategies require full monitoring. Therefore, a simplistic yet effective `expected' strategy is also constructed for the LTE network that does not require full monitoring. The simulation results show that the smart jammer plays non-revealing and misleading strategies.