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IEEE Transactions on Wireless Communications

Artificial-Noise-Aided Beamforming Design in the MISOME Wiretap Channel Under the Secrecy Outage Probability Constraint

Bo Wang, Pengcheng Mu, Zongze Li

Published Aug 25, 2017• 32 citations
Publisher

Abstract

This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.

DOI
10.1109/twc.2017.2742954

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IEEE Transactions on Communications•Apr 3, 2015•143 citations
This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.
The artificial noise (AN) aided beamforming design in the MISOME (multiple-input, single-output, multiple-eavesdropper) wiretap channel is studied from the perspective of secrecy outage. Unlike many existing works which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper's antennas from the perspective of secrecy outage. The power allocation problem is also studied and the closed-form optimal solution is obtained. It is found that the increase in the eavesdropper's antenna number is equivalent to requiring a smaller SOP.
The secrecy rate maximization with the artificial noise (AN) aided beamforming for the multipel-input-single-output (MISO) wiretap channel is addressed in this paper under the constraint of secrecy outage probability. The channel state information (CSI) of the main channel is assumed to be perfectly known while the CSI of the eavesdropper is modeled as a complex Gaussian random vector. The generalized AN scheme where the AN is not constrained to be orthogonal to the information-bearing signal is considered. The complete solution to the maximum achievable secrecy rate and the corresponding optimal power allocation between the information-bearing signal and the AN is obtained without making any approximation of the secrecy outage probability constraint. The result shows that the optimal AN is always orthogonal to the information-bearing signal.
This paper studies the artificial noise (AN) aided secure transmission design in a multiple-input- single-output multicast channel where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. In this scenario, there may be no valid null space which allows the AN not to affect the legitimate receivers, and the traditional null-space AN scheme may not be applicable. To find the optimal design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem which applies to an arbitrary number of the receivers. We adopt a novel approximation of the intractable SOP constraint and establish an efficient algorithm which solves the approximated problem to global optimality. The effectiveness of AN as well as the proposed solution is confirmed by simulation results. It is shown that the AN aided approach performs much better than pure beamforming even when there is no valid null space.
An artificial-noise (AN)-aided beamformer specific to correlated main and wiretap channels is designed in this paper. We consider slow-fading multiple-input-single-output (MISO) wiretap channels with a passive single-antenna eavesdropper, in which independent transmitter-side and correlated receiver-side are assumed. Additionally, the source has accurate main channel information and statistical wiretap channel information. To reduce the secrecy loss due to receiver-side correlation, this paper proposes the scheme of channel-correlation-enabled transmit optimization. Particularly, the correlation is viewed as a resource to acquire more knowledge about wiretap channel. Based on this, the statistical distribution of wiretap channel is described more precisely. Then, the power of AN in the null space of main channel is placed more reasonably instead of simple uniform distribution and an elaborate beamformer for the information-bearing signal is designed. Finally, an efficient algorithm for power allocation between the information-bearing signal and the AN is developed. Simulation results show that the secrecy rate under transmit power and secrecy outage constraint is improved.
An artificial-noise (AN)-aided beamformer for reducing secrecy loss due to the correlation between the main and wiretap channels is designed in this letter. We consider slow-fading multiple-input-single-output wiretap channels with a passive single-antenna eavesdropper, where the source has accurate main channel information and statistical wiretap channel information. By exploiting the channel correlation, the power of the AN in the null space of the main channel can be placed more reasonably instead of using a simple uniform distribution. Then, an efficient algorithm for power allocation between the information-bearing signal and the AN is developed. The simulation results show that the secrecy rate under the transmit power and secrecy outage constraint is improved.
We analyze and optimize the secrecy performance of artificial noise (AN) in multi-input single-output wiretap channels with multiple antennas at the transmitter and a single antenna at the receiver and the eavesdropper. We consider two transmission schemes: 1) an on-off transmission scheme with a constant secrecy rate for all transmission periods, and 2) an adaptive transmission scheme with a varying secrecy rate during each transmission period. For the on-off transmission scheme, an easy-to-compute expression is derived for the hybrid outage probability, which allows us to evaluate the transmission outage probability and the secrecy outage probability. For the adaptive transmission scheme where transmission outage does not occur, we derive a closed-form expression for the secrecy outage probability. Using these expressions, we determine the optimal power allocation between the information signal and the AN signal and also determine the optimal secrecy rate such that the effective secrecy throughput is maximized for both transmission schemes. We show that the maximum effective secrecy throughput requires more power to be allocated to the AN signal when the quality of the transmitter-receiver channel or the transmitter-eavesdropper channel improves. We also show that both transmission schemes achieve a higher maximum effective secrecy throughput while incurring a lower secrecy outage probability than existing schemes.