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IEEE Wireless Communications and Networking Conference

Bounds on the secrecy capacity with diversity combining techniques

Md. Zahurul I. Sarkar, Tharmalingam Ratnarajah

Published Apr 1, 2012• 8 citations
Publisher

Abstract

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.

DOI
10.1109/wcnc.2012.6214287

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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.
In this correspondence, we consider a confidential communication through slow non-selective correlated Rayleigh fading channel, where a single antenna transmitter communicates at a pre-decided constant rate with a legitimate receiver in the presence of an eavesdropper. Both the legitimate receiver and eavesdropper are equipped with multiple antennas and employ maximal ratio combining (MRC) reception scheme. With the presence of channel diversity, we find the closed-form expressions for the probability of non-zero secrecy capacity and the outage probability of secrecy capacity in terms of channel parameters such as correlation coefficient and the ratio of main and eavesdropper channel gains that will be called average channel gain ratio (CGR). The analysis of secure outage performance with the MRC diversity scheme tells how the channel diversity enhances the secrecy capacity. We quantify the effect of antenna correlation on the probability of positive secrecy capacity and the secure outage probability. We also investigate how the target secrecy rate influences the effect of antenna correlation on the secure outage probability. Moreover, as a result of obtaining the closed-form expressions for the probability of positive secrecy capacity and the outage probability, it is insightful to see how the channel parameters affect the secure outage performance of the correlated channels.
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 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.
In the perspective of information-theoretical security, inspired by the heterogeneity between legal and illegal channels, we consider the physical layer secrecy performance of a novel system model with a single antenna employed for both the transmitter and legal receiver, in the presence of a multiple antennas passive eavesdropper over dissimilar fading channels, where the legal/illegal channels are subject to Rayleigh/Nakagami-m and Nakagami-m/Rayleigh fading, respectively. We assume that the eavesdropper employs either maximal-ratio combining or selection combining reception in order to benefit from space diversity. Specifically, the exact closed-form expressions of the probability of existence of secrecy capacity and the secrecy outage probability are derived by utilizing statistical characteristics of the signal-to-noise ratio. Moreover, the delightful results reveal that the secrecy performance achieves a greater level when the Nakagami-m fading is supposed on the main link due to the line of sight component. In final, the analytical results are verified by Monte-Carlo simulation.
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 investigates the secrecy performance of maximal ratio combining (MRC) and selection combining (SC) with imperfect channel state information (CSI) in the physical layer. In a single-input multipleoutput (SIMO) wiretap channel, a source transmits confidential messages to the destination equipped with M antennas using the MRC/SC scheme to process the received multiple signals. An eavesdropper equipped with N antennas also adopts the MRC/SC scheme to promote successful eavesdropping. We derive the exact and asymptotic closed-form expressions for the ergodic secrecy capacity (ESC) in two cases: (1) MRC with weighting errors, and (2) SC with outdated CSI. Moreover, two important indicators, namely high signal-to-noise ratio (SNR) slope and high SNR power offset, which govern ESC at the high SNR region, are derived. Finally, simulations are conducted to validate the accuracy of our proposed analytical models. Results indicate that ESC rises with the increase of the number of antennas and the received SNR at the destination, and fades with the increase of those at the eavesdropper. Another finding is that the high SNR slope is constant, while the high SNR power offset is correlated with the number of antennas at both the destination and the eavesdropper.