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Telecommunications Forum (TELFOR)

Comparison of the secrecy rates of two suboptimal transmission methods for the fading MIMO wiretap channel

Sanja Angelova, Venceslav Kafedziski

Published Nov 1, 2014• 0 citations
Publisher

Abstract

Secure transmission in Multiple Input Multiple Output Multiple Eavesdropper (MIMOME) wiretap channels under quasi static Rayleigh fading is considered. Closed-form expression for the secrecy capacity of this type of channel is known only for some special cases. Therefore, we investigate the performance of two different suboptimal transmission methods under the assumption that the transmitter has full Channel State Information (CSI). In the first method the transmitter performs beamforming based on the Generalized Singular Value Decomposition (GSVD). In the second method the transmitter sends information along directions where there is gain to the legitimate receiver and artificial noise in all other directions. We determine the SNR regions where each of the methods outperforms the other.

DOI
10.1109/telfor.2014.7034393

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Secure transmission in Multiple Input Multiple Output Multiple Eavesdropper (MIMOME) wiretap channels under quasi static Rayleigh fading is considered. Closed-form expression for the secrecy capacity of this type of channel is known only for some special cases. Therefore, we investigate the performance of two different suboptimal transmission methods under the assumption that the transmitter has full Channel State Information (CSI). In the first method the transmitter performs beamforming based on the Generalized Singular Value Decomposition (GSVD). In the second method the transmitter sends information along directions where there is gain to the legitimate receiver and artificial noise in all other directions. We determine the SNR regions where each of the methods outperforms the other.
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.
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.
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. The input covariance matrix that achieves the secrecy capacity is determined. In particular, it is shown that the secrecy capacity of this channel can be achieved by linear precoding. Precoding and power allocation schemes that maximize the achievable secrecy rate, and thus achieve the secrecy capacity, are developed. The secrecy capacity is then compared with the achievable secrecy rate of generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed technique for this problem. Numerical results demonstrate that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.
In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.
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 rate of the multiple antenna MIMO wiretap channel is maximized for arbitrary 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 maximizes the achievable secrecy rate is derived. Numerical results are presented to illustrate that the achievable secrecy rate of the GSVD-based precoding approach is nearly identical to that of the optimal scheme.
This paper studies the secrecy performance of multiple-input multiple-output (MIMO) wiretap channels, also termed as multiple-input multiple-output multiple-eavesdropper (MIMOME) channels, under transmit antenna selection (TAS) and BPSK/QPSK modulations. In the main channel between the transmitter and the legitimate receiver, a single transmit antenna is selected to maximize the instantaneous Signal to Noise Ratio (SNR) at the receiver. At the receiver and the eavesdropper, selection combining (SC) is utilized. Additionally, suppose that the transmitted message is modulated by BPSK/QPSK modes. We first derive the closed-form approximated expression for the ergodic secrecy rate under Rayleigh fading, assuming that the channel state information of the eavesdropper (CSIE) is available at the transmitter. Next, analytical formulas for the approximated and asymptotic secrecy outage probability are also developed when CSIE is unavailable (NCSIE). Simulation results are provided to demonstrate the approximation precision of the derived results above. Furthermore, the asymptotic results reveal that the secrecy diversity order degrades into 0 due to the finite-alphabet inputs, which is totally different from that driven by the Gaussian inputs.