The mismatched communication channel with an infinite-dimensional real separable Hilbert space as input and output spaces is considered. To study communication in the presence of jamming, a two person zero sum game with mutual information of input source and output source as the payoff function can be formulated. The coder’s goal is to make mutual information as large as possible, and the jammer’s goal is to make mutual information as small as possible. The optimal mutual information under appropriate constraints of coders and jammers is obtained.
The mismatched communication channel with an infinite-dimensional real separable Hilbert space as input and output spaces is considered. To study communication in the presence of jamming, a two person zero sum game with mutual information of input source and output source as the payoff function can be formulated. The coder’s goal is to make mutual information as large as possible, and the jammer’s goal is to make mutual information as small as possible. The optimal mutual information under appropriate constraints of coders and jammers is obtained.
Abstract : The additive infinite-dimensional Gaussian channel subject to jamming is modeled as a two-person zero-sum game with mutual information as the payoff function. The jammer's noise is added to the ambient Gaussian noise. The coder's signal energy is subject to a constraint is necessary in order that the capacity without feedback be finite. It is shown that use of this same RKHS constraint on the jammer's process is too strong; the jammer would then not be able to reduce capacity, regardless of the amount of jamming energy available. The constraint on the jammer is thus on the total jamming energy, without regard to its distribution relative to that of the ambient noise energy. The existence of a saddle value for the problem does not follow from the von Neuman minimax theorem in the original problem formulation. However, a solution is shown to exist. A saddle point, saddle value, and the jammer's minimax strategy are determined. The solution is a function of the problem parameters: the constraint on the coder, the constraint on the jammer, and the covariance of the ambient Gaussian noise.
We investigate the behavior of two users and one jammer in an additive white Gaussian noise (AWGN) channel with and without fading when they participate in a noncooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop on the channel and can use the information obtained to perform correlated jamming. We also differentiate between the availability of perfect and noisy information about the user signals at the jammer. Under various assumptions on the channel characteristics, and the extent of information available at the users and the jammer, we show the existence, or otherwise nonexistence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist.
Gaussian wireless channels are studied under two forms of security attacks: (i) the jamming attack, where the adversary is active and transmits corruptive signal, but is not interested in the content of the communication, (ii) the eavesdropping attack, where the adversary is passive and overhears the communication and tries to obtain the message that has been transmitted. The active attack is studied in a multi-user setting. The behavior of two users and one jammer in an additive white Gaussian channel (AWGN) with and without fading is investigated, when they participate in a non-cooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop the channel and can use the information obtained to perform correlated jamming. We also differentiate between the availability of perfect and noisy information about the user signals at the jammer. Under various assumptions on the channel characteristics, and the extent of channel state information available at the users and the jammer, we show the existence, or otherwise non-existence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist. For the passive eavesdropping attack, we study multiple-input multiple-output (MIMO) AWGN channels. We first consider a multiple-input single-output (MISO) channel, where the transmitter has multiple antennas, while the receiver and the eavesdropper have single antennas each. We find achievable rates for this channel. With the channel input restricted to Gaussian signalling with no pre-processing of information, optimal transmission strategies that maximize the achievable secrecy rates are found, in terms of the input covariance matrices. It is shown that, under the optimal communication strategy, the system reduces to a single-input single-output (SISO) channel. We then extend the achievability results to fading Gaussian MISO channels. Finally, as a step toward generalizing the problem to one with multiple antennas at the receiver, we discuss the Gaussian 2-2-1 channel with a transmitter and a receiver with two antennas each, and a single antenna eavesdropper. We develop an achievability scheme similar to those of the SISO and MISO channels, and further show that in fact, it achieves the secrecy capacity of this 2-2-1 channel.
Worst-case jamming of legitimate communications over multiple-input multiple-output Gaussian channels is studied in this paper. A worst-case scenario with a `smart' jammer that knows all channels and the transmitter's strategy and is only power limited is considered. It is shown that the simplification of the system model by neglecting the properties of the jamming channel leads to a loss of important insights regarding the effects of the jamming power and jamming channel on optimal jamming strategies of the jammer. Without neglecting the jamming channel, a lower-bound on the rate of legitimate communication subject to jamming is derived, and conditions for this bound to be positive are given. The lower-bound rate can be achieved regardless of the quality of the jamming channel, the power limit of the jammer, and the transmit strategy of the jammer. Moreover, general forms of an optimal jamming strategy, on the basis of which insights into the effect of jamming power and jamming channel are exposed, are given. It is shown that the general forms can lead to closed-form optimal jamming solutions when the power limit of the jammer is larger than a threshold. Subsequently, the scenario in which the effect of jamming dominates the effect of noise (the case of practical interest) is considered, and an optimal jamming strategy is derived in closed-form. Simulation examples demonstrate lower-bound rates, performance of the derived jamming strategy, and an effect of inaccurate channel information on the jamming strategy.
This paper investigates reliable and covert transmission strategies in a multiple-input multiple-output (MIMO) wiretap channel with a transmitter, receiver and an adversarial wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper possesses a novel capability to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data, or broadcasting artificial interference along with the information signal in an attempt to jam the eavesdropper (assuming its instantaneous channel state is unknown). To examine the resulting trade-offs for the legitimate transmitter and the adversary, we model their interactions as a two-person zero-sum game with the ergodic MIMO secrecy rate as the payoff function. We first examine conditions for the existence of pure-strategy Nash equilibria (NE) and the structure of mixed-strategy NE for the strategic form of the game. We then derive equilibrium strategies for the extensive form of the game where players move sequentially under scenarios of perfect and imperfect information. Finally, numerical simulations are presented to examine the equilibrium outcomes of the various scenarios considered.
We investigate optimal power allocation strategies over a OFDM Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and a jammer-who acts as unfriendly to both the legitimate parties and the eavesdropper. In particular, we formulate a zero-sum power allocation game between the transmitter and the jammer where the payoff function is the secrecy rate. We characterize the optimal power allocation strategies as well as the Nash equilibrium in some asymptotic regimes. We also provide a set of results that cast further insight into the problem.