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International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)

Precoding Schemes for the Gaussian Wire-Tap Channels

Jun H. Cheng

Published Sep 1, 2015• 0 citations
Publisher

Abstract

This paper presents an investigation of channel capacity for the MIMO wire-tap channel. Instantaneous channel state information of the intended receiver and the eavesdropper are assumed to be available at the transmitter. We consider that the eavesdropper employs optimum combining, and investigate the two cases the intended receiver employs. We derive analytical expressions of the average secrecy capacities for these two cases in the high-SNR regime. We compare the performance of the proposed antenna selection scheme to a precoding scheme based on generalized singular value decomposition. Our investigations show that the average secrecy capacities increase with the number of antennas when the eavesdropper is at high SNR.

DOI
10.1109/cyberc.2015.60

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This paper presents an investigation of channel capacity for the MIMO wire-tap channel. Instantaneous channel state information of the intended receiver and the eavesdropper are assumed to be available at the transmitter. We consider that the eavesdropper employs optimum combining, and investigate the two cases the intended receiver employs. We derive analytical expressions of the average secrecy capacities for these two cases in the high-SNR regime. We compare the performance of the proposed antenna selection scheme to a precoding scheme based on generalized singular value decomposition. Our investigations show that the average secrecy capacities increase with the number of antennas when the eavesdropper is at high SNR.
This paper presents an investigation of employing transmit antenna selection for the MIMO wiretap channel. Instantaneous channel state information of the intended receiver and the eavesdropper are assumed to be available at the transmitter. We consider that the eavesdropper employs optimum combining, and investigate the two cases the intended receiver employs (a) optimum combining, (b) sub-optimal combining. We derive analytical expressions of the average secrecy capacities for these two cases in the high-SNR regime. We compare the performance of the proposed antenna selection scheme to a precoding scheme based on generalized singular value decomposition. Our investigations show that the average secrecy capacities increase with the number of antennas when the eavesdropper is at low SNR, but decrease when the eavesdropper is at high SNR.
This paper presents an investigation of employing transmit antenna selection under secrecy constraints. The transmitter is equipped with multiple antennas while the intended receiver and the eavesdropper have a single antenna each. Instantaneous channel state information of the intended receiver and the eavesdropper are assumed to be available at the transmitter. We derive an analytical expression for the average secrecy rate, in terms of the number of available transmit antennas and the average signal-to-noise ratios at the intended receiver and the eavesdropper. We compare the performance of the antenna selection scheme, as revealed by our analysis, to a precoding scheme based on Generalized Singular Value Decomposition (GSVD) and characterize the loss in the secrecy capacity. In addition, we also derive an expression for the average secrecy capacity for the high SNR regime. From our investigation of the proposed system, we find that the increase of the average secrecy rate with the number of transmit antennas is sub-logarithmic.
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation schemes achieving the secrecy capacity are developed subsequently, and the secrecy capacity is compared with the generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed precoding for this problem. Numerical results show that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, the perfect secrecy capacity of the multiple antenna MIMO wiretap channel is found for aribtrary numbers of antennas under the assumption that the transmitter performs beamforming based on the generalized singular value decomposition (GSVD). More precisely, the optimal allocation of power for the GSVD-based precoder that achieves the secrecy capacity is derived. This solution is shown to have several advantages over prior work that considered secrecy capacity for the general MIMO Gaussian wiretap channel under a high SNR assumption. Numerical results are presented to illustrate the proposed theoretical findings.
We consider the optimal precoding design under power constraint for the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, and an eavesdropper, each equipped with arbitrary number of antennas. The transmitter has access to full channel state information (CSI) of the legitimate link and eavesdropper link. Such an optimization problem is non-convex and an analytical optimal solution is difficult to obtain. In this paper, by resorting to the majorization theory, we develop a theoretical upper bound on the secrecy capacity which is proved useful in evaluating existing sub-optimal methods. Our analysis shows that, given that the number of antennas at the eavesdropper is no less than that of the transmitter, the generalized singular value decomposition (GSVD)-based method proposed in [1], albeit generally non-optimal, provides a near-optimal solution to the MIMO wiretap precoding design in the high signal-to-noise ratio (SNR) regime. Numerical results are provided to corroborate our theoretical results.
Wyner's wiretap channel is generalized to the case when the sender, the receiver and the eavesdropper have multiple antennas. We consider two cases: the deterministic case and the fading case. In the deterministic case, the channel matrices of the intended receiver and the eavesdropper are fixed and known to all the nodes. In the fading case, the channel matrices experience block fading and the sender has only the intended receiver's channel state information (CSI) and statistical knowledge of the eavesdropper's channel. For the deterministic case, a scheme based on the generalized-singular-value-decomposition (GSVD) of the channel matrices is proposed and shown to achieve the secrecy capacity in the high signal-to-noise-ratio (SNR) limit. When the intended receiver has only one antenna (MISO case) the secrecy-capacity is characterized for any SNR. Next, a suboptimal "artificial noise" based scheme is considered. Its performance is characterized and observed to be nearly optimal in the high SNR regime for the MISO case. This scheme extends naturally to the fading case and results are reported for the MISO case. For the independent Rayleigh fading distribution as we simultaneously increase the number of antennas at the sender and the eavesdropper, the secrecy capacity approaches zero if and only if the ratio of the number of eavesdropper antennas to transmitter antennas is at least two.