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IEEE Vehicular Technology Conference

Asymptotic Analysis of Average Secrecy Capacity under Transmit Antenna Selection for the MIMO Wiretap Channel

Nayeema Sadeque, Ingmar Land, Ramanan Subramanian

Published Sep 1, 2014• 2 citations
Publisher

Abstract

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.

DOI
10.1109/vtcfall.2014.6965886

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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 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 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.
We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with multiple antennas at the transmitter, the receiver, and the eavesdropper. We consider the practical scenario of passive eavesdropping, where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. In the main channel between the transmitter and the receiver, we select a single antenna at the transmitter that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. At the receiver and the eavesdropper, we consider two combining techniques: 1) maximal-ratio combining (MRC) and 2) selection combining (SC). For non-identical Rayleigh fading between the main channel and the eavesdropper's channel, we first derive new closed-form expressions for the exact and asymptotic secrecy outage probabilities. The asymptotic results accurately reveal the secrecy diversity order and the secrecy array gain. Next, we derive new closed-form expressions for the probability of positive secrecy and characterize the ε-outage secrecy capacity. We show that, under TAS/MRC and TAS/SC protocols, the secrecy outage probability approaches zero and the ε-outage secrecy capacity increases with increasing number of transmitter antennas.
In this paper, a novel transmit antenna selection scheme for multiple input multiple output (MIMO) wiretap channels is proposed. This new scheme achieves higher secrecy performance by exploiting eavesdropper's channel state information. The key idea behind our proposal is to perform the antenna selection aiming to maximize the overall secrecy rate instead of maximizing the instantaneous signal-to-noise ratio of the main channel. In our analysis, we assume that the legitimate receiver and the eavesdropper employ a maximal-ratio combining technique to combine the received signals from the transmitter. Considering Nakagami-m fading channels, a closed-form expression for the secrecy outage probability is derived, which can be used as a quality of service metric. Further, an asymptotic analysis is carried out and the diversity/array gains are obtained. The ergodic secrecy rate is also investigated for the case of multiple input single output wiretap channels. Representative numerical examples are plotted and validated through Monte Carlo simulations. Insightful discussions are drawn from the proposed analysis.
We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with NAantennas at the transmitter, NBantennas at the receiver, and NEantennas at the eavesdropper. We focus on the practical scenario where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. The transmitter selects a single antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. The receiver and the eavesdropper employ either maximal-ratio combining (MRC) or selection combining (SC) to combine the received signals. For the proposed protocols, we derive new closed-form expressions for the probability of non-zero secrecy capacity. We consider Nakagami-m fading with non-identical fading parameters of the main channel, mB, and of the eavesdropper's channel, mE. Next, we derive new closed-form expressions for the exact secrecy outage probability, based on which the ε-outage secrecy capacity is characterized. Based on the exact expressions, we derive the asymptotic secrecy outage probability which accurately reveals the secrecy diversity order and the secrecy array gain. We confirm that the proposed protocols achieve identical secrecy diversity orders of NANBmB. An interesting conclusion is reached that this diversity order is independent of NEand mE. Furthermore, we prove that under the proposed protocols, the secrecy outage probability and the ε-outage secrecy capacity improve with increasing NA.
This paper presents a general analytical framework to evaluate the secrecy performance of transmit antenna selection (TAS) systems without requiring the identical average signal-to-noise ratios (SNRs) from different transmit antennas. Closed-form expressions of secrecy outage probability are derived in a multiple-input multiple-output (MIMO) wiretap channel. Moreover, a novel TAS scheme based on the limited feedback from both the receiver and the eavesdropper is proposed and analysed. With the additional consideration of the eavesdropper's channel, security is shown to be enhanced although the instantaneous channel state information (CSI) keeps unknown to the transmitter. Finally, numerical results substantiate the aforementioned analysis.