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International Conference on Communications and Networking in China (ChinaCom)

Secrecy capacity of wireless links subject to log-normal fading

Xian Liu

Published Aug 1, 2012• 17 citations
Publisher

Abstract

In this paper, we investigate the information-theoretic secrecy for the log-normal fading channel. In particular, we derive the closed-form expressions of the probability of strictly positive secrecy capacity for two wireless communication systems, with single eavesdropper and double eavesdroppers, respectively.
DOI
10.1109/chinacom.2012.6417469

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This paper is concerned with the study of secrecy capacity for the log-normal fading channel in which the main channel is correlated with the eavesdropper channel. Perfect secrecy is achieved when the transmitter and legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. We consider the full channel state information (CSI) case, where the transmitter has access to both the main channel and eavesdropper channel gains. Under this assumption, we define the secrecy capacity of single-input single-output (SISO) log-normal fading channel and find the optimal power allocation at the transmitter that achieves the secrecy capacity. By analyzing the resulting secrecy capacity, we quantify the loss of secrecy capacity due to the correlation. We also find the closed-form analytical expression for the upper bound of secrecy capacity in terms of correlation coefficient which includes the independent case as a special one. The analysis of upper bound tells how the correlation coefficient and the ratio of main and eavesdropper channel gains affect the secrecy capacity.
We consider a confidential communication through log-normal fading channel in which a single antenna transmitter communicates with a legitimate receiver in the presence of an eavesdropper. Employing maximal ratio combining (MRC) and equal gain combining (EGC) reception schemes at the legitimate receiver and eavesdropper, we find the closed-form expressions for the secrecy parameters, namely, the probability of non-zero secrecy capacity and the asymptotic secrecy capacity in terms of channel parameters such as correlation coefficient and the diversity order. We quantify the effect of diversity and antenna correlation and investigate, how the logarithmic standard deviation influences these effects of diversity and antenna correlation on the secrecy parameters. Moreover, as a result of obtaining closed-form expressions for the secrecy parameters, it is insightful to see how the channel parameters affect the security of lognormal fading channels.
We present a general and compact framework for the analysis of the wireless information-theoretic security of arbitrarily-distributed fading channels. We show that performance metrics such as the outage probability of the secrecy capacity, the probability of strictly positive secrecy capacity and the e-outage secrecy capacity can be compactly expressed in terms of the moment generating function (MGF) of the fading models. Using this approach, we can study the effect of considering different propagation conditions for the legitimate and eavesdropper's fading links, which accommodate to many practical scenarios.