The effectiveness and the simple implementation of physical layer jammers make them an essential threat for wireless networks. In a multihop wireless network, where jammers can interfere with the transmission of user messages at intermediate nodes along the path, one can employ jamming oblivious routing and then employ physical-layer techniques (e.g., spread spectrum) to suppress jamming. However, whereas these approaches can provide significant gains, the residual jamming can still severely limit system performance. This motivates the consideration of routing approaches that account for the differences in the jamming environment between different paths. First, we take a straightforward approach where an equal outage probability is allocated to each link along a path and develop a minimum energy routing solution. Next, we demonstrate the shortcomings of this approach and then consider the joint problem of outage allocation and routing by employing an approximation to the link outage probability. This yields an efficient and effective routing algorithm that only requires knowledge of the measured jamming at each node. Numerical results demonstrate that the amount of energy saved by the proposed methods with respect to a standard minimum energy routing algorithm, especially for parameters appropriate for terrestrial wireless networks, is substantial.
The security issue in collaborative sensing in cognitive radio networks can be modeled as attackers and secondary users in a jamming and anti-jamming scenario. In this paper, we introduce a stochastic zero-sum game model to study the strategies. Primary users, secondary users and jammers are the three types of agents in the system. The primary users dictate the system states and their transitions while the secondary users and jammers behave non-cooperatively to achieve their goals independently under different system environment. Our Markovian game model captures not only the zero-sum interactions between secondary users and the jammers but also the dynamics of the system. Our results indicate that the secondary users can enhance their security level or increase their long-term payoff by either improving their sensing capabilities to confuse the jammer with the choice or choosing to communicate under states where the available channels are less prone to jamming. In the numerical experiments, we point out that the payoff of the secondary users increases with the number of available jamming-free channels and is eventually limited by the behavior of primary users. We consider a scenario where a sophisticated jammer jams an area in a single-channel wireless sensor network. The jammer controls the probability of jamming and transmission range to cause maximal damage to the network in terms of corrupted communication links. The jammer action ceases when it is detected by a monitoring node in the network, and a notification message is transferred out of the jamming region. The jammer is detected at a monitor node by employing an optimal detection test based on the percentage of incurred collisions. On the other hand, the network computes channel access probability in an effort to minimize the jamming detection plus notification time. In order for the jammer to optimize its benefit, it needs to know the network channel access probability and number of neighbors of the monitor node. Accordingly, the network needs to know the jamming probability of the jammer. We study the idealized case of perfect knowledge by both the jammer and the network about the strategy of one another, and the case where the jammer or the network lack this knowledge. The latter is captured by formulating and solving optimization problems, the solutions of which constitute best responses of the attacker or the network to the worst-case strategy of each other. We also take into account potential energy constraints of the jammer and the network. We extend the problem to the case of multiple observers and adaptable jamming transmission range and propose a intuitive heuristic jamming strategy for that case. The process of communication jamming can be modeled as a two-person zero-sum noncooperative dynamic game played between a communicator (a transmitter-receiver pair) and a jammer. We consider a one-way time-slotted packet radio communication link in the presence of a jammer, where the data rate is fixed and (1) in each slot, the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value; (2) both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating. The payoff function is the time average of the mean payoff per slot. The game is solved for certain ranges of the players' transmitter parameters. Structures of steady-state solutions to the game are also investigated. The general behavior of the players' strategies and payoff increment is found to depend on a parameter related to the payoff matrix, which me call the payoff parameter, and the transmitters' parameters. When the payoff parameter is lower than a threshold, the optimal steady-state strategies are mixed and the payoff increment constant over time, whereas when it is greater than the threshold, the strategies are pure, and the payoff increment exhibits oscillatory behavior. In this work, we study the problem of power allocation and adaptive modulation in teams of decision makers. We consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE).