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IEEE Transactions on Wireless Communications

Achieving Secret Communication for Fast Rayleigh Fading Channels

Zang Li, Roy D. Yates, Wade K. Trappe

Published Aug 24, 2010• 60 citations
Publisher

Abstract

We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Amplitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good.

DOI
10.1109/twc.2010.080210.090948

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We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Amplitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good.
We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Am- plitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good.
We investigate the achievable secrecy rate with Gaussian random codes when the main channel is an AWGN channel, while the eavesdropper's channel is Rayleigh fading with additive Gaussian noise. Several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. We show that even if the main channel channel gain is arbitrarily worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved with artificial noise injection and a burst signaling strategy.
This thesis examines the challenges of information-theoretic secret communication that exploits the temporal and spatial variations of the wireless medium to improve secret communication rates. We first examine the secrecy capacity of a system consisting of independent parallel channels with one transmitter, one intended receiver and one eavesdropper. We show that the secrecy capacity of the system is the sum of the secrecy capacities of the individual subchannels. We further derive the optimal power allocation strategy for a system of parallel AWGN channels subject to a total power constraint, and also extend the results to random fading channels with additive Gaussian noise. We then study the achievable secrecy rate with Gaussian random codes for the situation where the channel of the intended receiver is a constant AWGN channel, while the eavesdropper's channel is fast Rayleigh fading with unknown realizations but known statistics to the transmitter. The proposed method with artificial noise and bursting provides ways to achieve positive secrecy rate even when Bob's channel is worse than Eve's channel on average. We also examine the achievable secrecy rate for a multiple antenna system, and the optimal input structure needed to achieve this rate. For the multiple input single output case, an analytical solution is derived. Multiple antenna systems provide extra degrees of freedom to the transmitter so that a beamforming-like approach can be used to provide advantage to the intended receiver against the eavesdropper. Next we derive a secrecy capacity outer bound region for a class of one-sided interference channels. The outer bound is shown to be tight for a class of binary deterministic one-sided interference channels, and can be achieved within one bit for some Gaussian one-sided interference channels.Finally, as Gaussian random codes are impractical, we evaluate achievable secrecy rates with discrete signaling. We observe that with discrete signaling, there exists an optimal power that maximizes the achievable secrecy rate. For the AWGN channel, larger constellation is always better. While for fading channel, the optimal constellation size varies with the power constraint, and discrete signaling can perform better than random Gaussian coding.
Consider a wireless transmission from Alice to Bob in the presence of an eavesdropper, Eve. We propose a technique to allow Alice to send a message such that Bob can decode it but Eve can get little information about the message. This scenario is a classic example of the wiretap channel, for which several researchers have begun to develop practical schemes. However, we consider a challenging version in which the channel from Alice to Eve may be as good or better than the channel from Alice to Bob. There have been no practical secrecy coding techniques that have been developed for this scenario. The key to allow secret communication in such a scenario is feedback from Bob to Alice (which Eve can also observe). The scheme we develop uses reliability-based hybrid automatic-repeat-request (RB-HARQ) over a fast fading channel to provide a decoding advantage at Bob. Bob requests information about received symbols that suffer from deep fades. The retransmitted symbols improve Bobpsilas ability to decode the message faster than at Eve, who sees retransmission of bits with random reliabilities. We evaluate the proposed scheme by performance measures such as the probability of successful decoding and the equivocation rate at Eve.
A transmission between two agents, Alice and Bob, over a set of parallel sub-channels is overheard by a third agent Eve, through a second set of parallel sub-channels. All subchannels are flat with random and independent gains and additive white Gaussian noise (AWGN). Alice splits the total amount of available power among the sub-channels, with the purpose of maximizing the communication rate to Bob, under reliability and secrecy constraints. To this end, two schemes are considered. In one case the secret message is encoded with a single wiretap code and then split among the sub-channels. In the latter case the secret message is first split into a number of sub-messages, each separately encoded and transmitted on a different sub-channel. The achievable secrecy rates under a constraint on the secrecy outage probability (SOP) are derived and closed form expressions for Rayleigh fading sub-channels are obtained. In order to limit the complexity of resources optimization (power and rates) we also consider suboptimal solutions based on the selection of active sub-channels over which power is split either equally or according to a waterfilling algorithm with respect to the Alice-Bob channel.
For a communication where agent Alice aims at transmitting to agent Bob a message which must be kept secret to a third agent Eve, we consider terminals equipped with multiple antennas, obtaining the multiple-input multiple-output multiple-output-eavesdropper (MIMOME) channel. In this scenario, we assume that Alice knows the instantaneous channel conditions of the Alice-Bob channel before transmission, while knowing only the statistics of the Alice-Eve channel. For Rayleigh fading channels there is a non-zero probability that Eve gets a better channel than Bob, thus obtaining some information on the secret message (secrecy outage probability). We derive a closed form expression of the secrecy outage probability and then we consider the problem of allocating the power among the space streams, in order to maximize the total rate of the secret message under a constraint on the secrecy outage probability.