Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Communications Letters

A Closed-Form Power Allocation for Minimizing Secrecy Outage Probability for MISO Wiretap Channels via Masked Beamforming

Jun Xiong, Kai‐Kit Wong, Dongtang Ma, Jibo Wei

Published Aug 3, 2012• 59 citations
Publisher

Abstract

In this letter, we aim to achieve secure communication for a multiple-input single-output (MISO) wiretap channel in the presence of multiple non-colluding eavesdroppers. It is assumed that the eavesdroppers' channels are unavailable to the transmitter, and artificial noise (AN) is used to provide masked beamforming for degrading the eavesdroppers' channels. First, we derive the secrecy rate outage probability for the masked beamforming system and then the optimal power allocation between data and AN is obtained in closed form for minimizing the secrecy rate outage probability under a total power constraint. The effects of the number of transmit antennas, the transmit power, and the target secrecy rate on the optimal power allocation parameter are characterized. Numerical results are presented to show the performance of our proposed power allocation scheme.

DOI
10.1109/lcomm.2012.073112.121254

Related papers

Minimization of Secrecy Outage Probability With Artificial-Noise-Aided Beamforming for MISO Wiretap Channels

Darui Hu, Pengcheng Mu, Weile Zhang +1 more

The problem of optimal power allocation between the information-bearing signal and the artificial noise (AN) signal is addressed in this letter to enhance the physical layer security of the multiple-input-single-output wiretap channel. Differing from the existing works concerning the secrecy rate maximization, this letter studies the problem of minimizing the secrecy outage probability given the secrecy rate, where the channel state information concerning the eavesdropper is modeled as quasi-static Rayleigh fading and only known statistically. After formulating the problem as an optimization problem of power allocation, we prove that the optimal solution can be conveniently obtained by using the method of bi-section search. Simulation results show that the proposed power allocation method is efficient and can enhance the physical layer security by reducing the secrecy outage probability.

IEEE Communications Letters•Dec 2, 2019•22 citations

Power Allocation for AN-Aided Beamforming Design in MISO Wiretap Channels with Finite-Alphabet Signaling

Xiaoran Liu, Dongtang Ma, Jun Xiong +2 more

In this paper, we address physical layer security in multiple-input single-output (MISO) wiretap channels in the presence of a passive eavesdropper. Artificial noise (AN) is used to provide masked beamforming for degrading the eavesdropper's channel. Existing works based on Gaussian input assumption may lead to substantial secrecy rate loss when considering practical finite-alphabet input. In order to maximize ergodic secrecy rate, a power allocation scheme between the information-bearing signal and AN is proposed. Despite the fact that there is no closed- form expression of mutual information under the constraint of finite-alphabet input, we exploit the relationship between mutual information and minimum mean square error (MMSE) to transform the original problem into a zero-searching problem, which can be solved via gradient search algorithm. Numerical simulations demonstrate that the proposed scheme offers a very good approximation to the optimal performance.

IEEE Vehicular Technology Conference•Sep 1, 2016•2 citations

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

Bo Wang, Pengcheng Mu, Zongze Li

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.

IEEE Transactions on Wireless Communications•Aug 25, 2017•32 citations

Switched power allocation for MISOME wiretap channels

Thang Van Nguyen, Tony Q. S. Quek, Hyundong Shin

In this paper, we consider secure communication over a multiple-input single-output Rayleigh-fading channel in the presence of a multiple-antenna eavesdropper - referred to as a multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, secure beamforming with artificial noise is treated when the transmitter has access to full channel state information (CSI) of a legitimate channel but only partial statistical CSI of an eavesdropper channel. We first derive the optimal power allocation between the information-bearing signal and artificial noise (or simulated interference) to maximize the achievable secrecy rate in the presence of a weak or strong eavesdropper. We then develop a near-optimal power allocation strategy in a switched fashion for a general case and derive a closed-form expression for the ergodic secrecy rate achieved by secure beamforming with this switched power allocation in the MISOME wiretap channel.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•4 citations

Power allocation for secrecy diversity in MISOME wiretap channels

Thang Van Nguyen, Youngmin Jeong, Hyundong Shin

We consider secure beamforming with artificial noise in a multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel, where a transmitter has access to full channel state information (CSI) of a legitimate channel but only partial CSI of eavesdropper channels. In this paper, we first put forth a notion of symbol error probability (SEP) for confidential information—called the δ-secrecy SEP—to connect the reliability and confidentiality of the legitimate communication in MISOME wiretap channels. For single-antenna colluding and non-colluding eavesdroppers, we determine the optimal power allocation between the information-bearing signal and artificial noise to minimize the δ-secrecy SEP in the presence of weak or strong eavesdroppers, and further develop the switched power allocation for general eavesdropping attacks.

International Conference on Information and Communication Technology Convergence (ICTC)•Oct 1, 2013•0 citations

Artificial-noise-aided beamforming design against a multi-antenna eavesdropper under secrecy outage constraint

Bo Wang, Pengcheng Mu, Zongze Li +3 more

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.

International Conference on Communications•May 1, 2017•3 citations
In this letter, we aim to achieve secure communication for a multiple-input single-output (MISO) wiretap channel in the presence of multiple non-colluding eavesdroppers. It is assumed that the eavesdroppers' channels are unavailable to the transmitter, and artificial noise (AN) is used to provide masked beamforming for degrading the eavesdroppers' channels. First, we derive the secrecy rate outage probability for the masked beamforming system and then the optimal power allocation between data and AN is obtained in closed form for minimizing the secrecy rate outage probability under a total power constraint. The effects of the number of transmit antennas, the transmit power, and the target secrecy rate on the optimal power allocation parameter are characterized. Numerical results are presented to show the performance of our proposed power allocation scheme.
The problem of optimal power allocation between the information-bearing signal and the artificial noise (AN) signal is addressed in this letter to enhance the physical layer security of the multiple-input-single-output wiretap channel. Differing from the existing works concerning the secrecy rate maximization, this letter studies the problem of minimizing the secrecy outage probability given the secrecy rate, where the channel state information concerning the eavesdropper is modeled as quasi-static Rayleigh fading and only known statistically. After formulating the problem as an optimization problem of power allocation, we prove that the optimal solution can be conveniently obtained by using the method of bi-section search. Simulation results show that the proposed power allocation method is efficient and can enhance the physical layer security by reducing the secrecy outage probability.
In this paper, we address physical layer security in multiple-input single-output (MISO) wiretap channels in the presence of a passive eavesdropper. Artificial noise (AN) is used to provide masked beamforming for degrading the eavesdropper's channel. Existing works based on Gaussian input assumption may lead to substantial secrecy rate loss when considering practical finite-alphabet input. In order to maximize ergodic secrecy rate, a power allocation scheme between the information-bearing signal and AN is proposed. Despite the fact that there is no closed- form expression of mutual information under the constraint of finite-alphabet input, we exploit the relationship between mutual information and minimum mean square error (MMSE) to transform the original problem into a zero-searching problem, which can be solved via gradient search algorithm. Numerical simulations demonstrate that the proposed scheme offers a very good approximation to the optimal performance.
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.
In this paper, we consider secure communication over a multiple-input single-output Rayleigh-fading channel in the presence of a multiple-antenna eavesdropper - referred to as a multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, secure beamforming with artificial noise is treated when the transmitter has access to full channel state information (CSI) of a legitimate channel but only partial statistical CSI of an eavesdropper channel. We first derive the optimal power allocation between the information-bearing signal and artificial noise (or simulated interference) to maximize the achievable secrecy rate in the presence of a weak or strong eavesdropper. We then develop a near-optimal power allocation strategy in a switched fashion for a general case and derive a closed-form expression for the ergodic secrecy rate achieved by secure beamforming with this switched power allocation in the MISOME wiretap channel.
We consider secure beamforming with artificial noise in a multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel, where a transmitter has access to full channel state information (CSI) of a legitimate channel but only partial CSI of eavesdropper channels. In this paper, we first put forth a notion of symbol error probability (SEP) for confidential information—called the δ-secrecy SEP—to connect the reliability and confidentiality of the legitimate communication in MISOME wiretap channels. For single-antenna colluding and non-colluding eavesdroppers, we determine the optimal power allocation between the information-bearing signal and artificial noise to minimize the δ-secrecy SEP in the presence of weak or strong eavesdroppers, and further develop the switched power allocation for general eavesdropping attacks.
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.