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arXiv:2004.06644 · IEEE Transactions on Communications

Bounds on the Secrecy Outage Probability for Dependent Fading Channels

Karl-Ludwig Besser, Eduard Axel Jorswieck

Published Sep 25, 2020• 24 citations
arXivHTMLPDF

Abstract

The amount of sensitive data, which is transmitted wirelessly will increase with future technologies. This raises many questions about secure data transmission. Besides cryptography, information-theoretic security gained increasing attention over the recent years. Among others, it deals with the problem of secure data transmission on the physical layer to a legitimate receiver (Bob) in the presence of an eavesdropper (Eve). In this work, we investigate upper and lower bounds on the secrecy outage probability for slowly-fading wiretap channels with an arbitrary dependency structure between the fading channels to Bob and Eve. Both cases of absence of channel-state information at the transmitter (CSI-T) and availability of CSI-T of only the main channel to the legitimate receiver are considered. Furthermore, we derive explicit expressions for the upper and lower bounds for Rayleigh fading and compare them to the case of independent channels. The joint distribution of the legitimate and eavesdropper channels has a tremendous impact on the achievable secrecy outage probability. The bounds enable developing guaranteed secrecy schemes by only measuring the marginal channel distributions.

DOI
10.1109/tcomm.2020.3026654

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This paper considers the transmission of confidential data over a quasi-static fading wiretap channel where the main and eavesdropper channels are correlated. Assuming that before transmission the transmitter knows the channel state information (CSI) of the main channel, we derive the secrecy outage probability in a closed-form expression based on a new secrecy outage probability formula, which gives a more explicit measure on the level of security compared with the previous one. Remarkably, our results, which cover the corresponding results when the main channel and eavesdropper channels are independent as special cases, reveal that channel correlation has a significant impact on secrecy outage probability and such impact can be helpful or harmful depending on the relative channel conditions and transmission SNR threshold.
We study the secrecy capacity of fast fading channels under imperfect main channel (between the transmitter and the legitimate receiver) estimation at the transmitter. Lower and upper bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate follows from a standard wiretap code in which a simple on-off power control is employed along with a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and eavesdropper channels and is the best known upper bound so far. The upper and lower bounds coincide with recently derived ones in case of perfect main CSI. Furthermore, the upper bound is tight in case of no main CSI, where the secrecy capacity is equal to zero. Asymptotic analysis at high and low signal-to-noise ratio (SNR) is also given. At high SNR, we show that the capacity is bounded by providing upper and lower bounds that depend on the channel estimation error. At low SNR, however, we prove that the secrecy capacity is asymptotically equal to the capacity of the main channel as if there were no secrecy constraint. Numerical results are provided for i.i.d. Rayleigh fading channels.
The ergodic secrecy capacity of the wiretap channel is known when the main channel (between the transmitter and the legitimate receiver) state information (CSI) is perfect at the transmitter and the coherence period is sufficiently large to enable random coding arguments in each block. In a fast fading scenario, when the codeword length spans many coherence periods, the secrecy capacity is still not known. In this paper, we present a framework that characterizes this secrecy capacity under imperfect main channel estimation at the transmitter. Inner and outer bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate is a simple on-off scheme using a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels. The upper and the lower bounds coincide with recently derived ones in the perfect main CSI extreme. Furthermore, the lower bound matches the upper bound in no main CSI extreme, where the secrecy capacity is equal to zero. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels.
In this paper, we consider secure broadcasting over fast fading channels. Assuming imperfect main channel state information (CSI) at the transmitter, we first provide an upper and a lower bounds on the ergodic secrecy capacity when a common message is broadcasted to multiple legitimate receivers in the presence of one eavesdropper. For this case, we show that the secrecy rate is limited by the legitimate receiver having, on average, the worst main channel link. Then, we present an expression for the achievable secrecy sum-rate when each legitimate receiver is interested in an independent message. The special cases of high SNR, perfect and no-main CSI are also analyzed. Numerical results are presented to illustrate the obtained results for the case of independent but not necessarily identically distributed Rayleigh fading channels.
In this two-part paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through another independent quasi-static fading channel. We define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for Gaussian wiretap channels (without feedback), our contribution shows that in the presence of fading information-theoretic security is achievable even when the eavesdropper has a better average signal-to-noise ratio (SNR) than the legitimate receiver - fading thus turns out to be a friend and not a foe. The issue of imperfect channel state information is also addressed. Practical schemes for wireless information-theoretic security are presented in Part II, which in some cases comes close to the secrecy capacity limits given in this paper.
In this paper, we consider the problem of secret communication through Rayleigh fading single-input multiple-output (SIMO) broadcast channel in the presence of an eavesdropper. At first, we define the ergodic secrecy capacity and find the optimal power allocation at the transmitter that achieves the secrecy capacity for the full channel state information (CSI) case, where transmitter has access to both the main channel and eavesdropper's channel gains, and for the case of only main channel CSI at the transmitter. Then, we define the secrecy capacity in case of open-loop transmission scheme and present the analytical expression for the lower bound of ergodic secrecy capacity. We also find the analytical expression for secure outage probability to study the secure outage performance of the proposed model.