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IEEE Military Communications Conference (MILCOM)

Secure rates in multiband broadcast channels with combating jammers

Karim Banawan, Şennur Ulukuş, Peng Wang, Brian J. Henz

Published Nov 1, 2016• 4 citations
Publisher

Abstract

We consider the broadcast channel with confidential messages (BCCM) over N parallel Gaussian channels. The transmitter aims at maximizing the sum-rate. The system has two combating jammers, each aiming to enhance the secure rate to one receiver only, while hurting the other receiver by sending Gaussian jamming signals. We cast the problem as an extensive-form game and derive the optimal jamming policy. We show that the jamming strategy is a form of generalized water-filling, and provide theoretical insights on the optimal solution. We provide simulation results to show the convergence of the rate and power allocations, and study the effect of increasing the available power of the transmitter and/or the jammers.

DOI
10.1109/milcom.2016.7795358

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IEEE Transactions on Communications•Jan 1, 2014•10 citations
We consider the broadcast channel with confidential messages (BCCM) over N parallel Gaussian channels. The transmitter aims at maximizing the sum-rate. The system has two combating jammers, each aiming to enhance the secure rate to one receiver only, while hurting the other receiver by sending Gaussian jamming signals. We cast the problem as an extensive-form game and derive the optimal jamming policy. We show that the jamming strategy is a form of generalized water-filling, and provide theoretical insights on the optimal solution. We provide simulation results to show the convergence of the rate and power allocations, and study the effect of increasing the available power of the transmitter and/or the jammers.
This paper investigates optimal power allocation strategies over a bank of independent parallel Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and an unfriendly jammer. 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. Our scenario, which is applicable to current OFDM communications systems, demonstrates that transmitters that adapt to jammer experience much higher secrecy rates than non-adaptive transmitters.
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.
A friendly eavesdropper assists communication in a broadcast scenario in which one transmitter wishes to send a common message to two receivers in the presence of a malicious jammer. The jammer attempts to disrupt communication by transmitting a high power Gaussian signal, whereas the friendly eavesdropper `hears' the jammer's transmission and sends an assisting signal to the destinations over an orthogonal channel in order to help them alleviate the jammer's impact. We derive an expression for capacity, i.e., the maximum data rate that can be reliably communicated from the transmitter to the receivers and we show that it is optimal for the friendly eavesdropper to send a Gaussian description of the jamming signal with the help of a scheme based on a modified compress-and-forward relaying that uses a list decoding procedure.
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.
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 considers the Broadcast Channel with Confidential Message (BCCM) where the sender attempts to send altogether a common message to two receivers and a confidential message to one of them. The achievable rate regions are derived for the power-constrained Gaussian BCCM with finite input alphabet using various transmission strategies. Namely, time sharing, superposition modulation and superposition coding are used as broadcast strategies. For superposition modulation and superposition coding, the maximal achievable rate regions are obtained by maximizing over both constellation symbol positions and the joint probability distribution. The maximization of the secrecy rate for wiretap channels is also studied as a particular case of the BCCM problem. We compare the considered transmission strategies in terms of percentage gains in achievable rates. We concentrate on the impact of the finite alphabet constraint on achievable rates, and show that this constraint may change well known results obtained in the Gaussian case. We show also that the secrecy constraint can change the shape of the achievable rate region in superposition modulation used in some standards when symbols are equiprobable. On a more practical side, it is shown that a performance close to the optimum can be obtained by strategies with reduced complexity.