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Asia-Pacific Conference on Communications (APCC)

Secrecy capacity of correlated rayleigh fading channels

Jinxiao Zhu, Xiaohong Jiang, Osamu Takahashi, Norio Shiratori

Published Oct 1, 2012• 5 citations
Publisher

Abstract

We consider the secure transmission of information over Rayleigh fading wiretap channel when the main and eavesdropper channels are correlated there. Assuming that before transmission the transmitter knows the full channel state information (CSI) of both the main and eavesdropper channels, we analyze the average secrecy capacity with limited signal-to-noise ratio (SNR), for which a simple closed-form expression is derived based on the typical Marcum Q function. This is achieved by exploring the symmetry property between the main channel and eavesdropper channel to avoid a complicated integration involved in the secrecy capacity analysis, such that the secrecy capacity derivation can be significantly simplified. Numerical results are also provided to confirm our analytical ones.

DOI
10.1109/apcc.2012.6388157

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We consider the secure transmission of information over Rayleigh fading wiretap channel when the main and eavesdropper channels are correlated there. Assuming that before transmission the transmitter knows the full channel state information (CSI) of both the main and eavesdropper channels, we analyze the average secrecy capacity with limited signal-to-noise ratio (SNR), for which a simple closed-form expression is derived based on the typical Marcum Q function. This is achieved by exploring the symmetry property between the main channel and eavesdropper channel to avoid a complicated integration involved in the secrecy capacity analysis, such that the secrecy capacity derivation can be significantly simplified. Numerical results are also provided to confirm our analytical ones.
We investigate the secrecy capacity of an ergodic fading wiretap channel in which the main channel is correlated with the eavesdropper channel. In this study, the full Channel State Information (CSI) is assumed, and thus the transmitter knows the channel gains of the legitimate receiver and the eavesdropper. By analyzing the resulting secrecy capacity we quantify the loss of the secrecy capacity due to the correlation. In addition, we study the asymptotic behavior of the secrecy capacity as Signal-to-Noise Ratio (SNR) tends to infinity. The capacity of an ordinary fading channel logarithmically increases with SNR. On the contrary, the secrecy capacity converges to a limit which can be an upper bound on the secrecy capacity over the fading wiretap channel. We find a closed form of the upper bound for the correlated Rayleigh wiretap channel which also includes the independent case as a special one. Our work shows that the upper bound is determined by only two channel parameters; the correlation coefficient and the ratio of the main to the eavesdropper channel gains that will be called the average Channel Gain Ratio (CGR). The analysis of the upper bound tells how the two channel parameters affect the secrecy capacity and leads to the conclusion that the excessively large signal power does not provide any advantage in the secrecy capacity and the loss due to the correlation is especially serious in low CGR regime.
We investigate the secrecy capacity of an ergodic fading wiretap channel when the main and eavesdropper channels are correlated. Assuming that the transmitter knows the full channel state information (CSI) (i.e., the channel gains from the transmitter to the legitimate receiver and eavesdropper), we quantify the loss of the secrecy capacity due to the correlation and investigate the asymptotic behavior of the secrecy capacity in the high signal-to-noise ratio (SNR) regime. While the ergodic capacity of fading channels grows logarithmically with SNR in general, we have found that the secrecy capacity converges to an upper-bound (a closed-form expression is derived) that will be shown to be a function of two channel parameters; the correlation coefficient and the ratio of the main to eavesdropper channel gains. From this, we are able to see how the two channel parameters affect the secrecy capacity and conclude that the excessively large signal power does not help to improve the secrecy capacity and the loss due to the correlation could be significant especially when the ratio of the main to eavesdropper channel gains is low.
This paper is concerned with the study of confidential communication through independent and identically distributed (i.i.d.) and evenly correlated Rayleigh fading channels, where a single antenna transmitter communicates with the corresponding receiver in the presence of an eavesdropper. Both the receiver and eavesdropper are equipped with multiple antennas and employ diversity combining receptions such as maximal ratio combining (MRC) and selection combining (SC) diversities. In the presence of channel diversity, we derive the upper and lower bounds on the secrecy capacity with full channel state information (CSI) at the transmitter. The closed-form expression for the upper bound is also derived at high signal-to-noise ratio (SNR) regime. The analysis of upper bound with the diversity combining techniques tells how the channel diversity enhances secrecy capacity. Moreover, as a result of deriving the expression in a closed-form, it is insightful to see, how the channel parameters such as correlation coefficient and the ratio of main and eavesdropper channel gains that will be called average channel gain ratio (CGR) affect the secrecy capacity.
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.
This paper studies performance analysis of physical layer security in a Rayleigh fading wiretap channel, where, the main (transmitter-to-legitimate receiver) and eavesdropper (transmitter-to-eavesdropper) channel coefficients are correlated. By exploiting the novel approach called Copula theory, we derive closed-form expressions for average secrecy capacity (ASC), secrecy outage probability (SOP), and secrecy coverage region (SCR). Moreover, to more evaluate the impact of channel correlation, the asymptotic behavior of SOP in high signal-to-noise ratio (SNR) regime and other scenarios is studied, and finally, the analytical results are illustrated numerically under the positive dependence, independence, and negative dependence structures. Based on the insights from this analysis, we found that the effect of correlated fading on the performance of physical layer security can be helpful or harmful in different scenarios, depending on the structure of dependency between the main and eavesdropper channels.