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

Wireless Communications and Mobile Computing

Secrecy‐Capacity‐Optimization‐Artificial‐Noise in Large‐Scale MIMO: Ergodic Lower Bound on Secrecy Capacity and Optimal Power Allocation

Yebo Gu, Zhilu Wu, Zhendong Yin

Published Jan 1, 2021• 0 citations
Publisher

Abstract

The security of wireless information transmission in large‐scale multi‐input and multioutput (MIMO) is the focus of research in wireless communication. Recently, a new artificial noise—SCO‐AN which shows no orthogonality to the channel, is proposed to overcome the shortcomings of traditional artificial noise. In the previous research, the optimization function of SCO‐AN is not convex, and its extremum cannot be obtained. Usually, nonconvex optimization algorithms or iterative relaxation algorithms are used to get the maximum value of the optimization objective function. Nonconvex optimization algorithms or iterative relaxation algorithms are greatly affected by the initial value, and the extremum cannot be obtained by a nonconvex optimization algorithm or iterative relaxation algorithm. In this paper, we creatively apply the strong law of large numbers to obtain the optimal value of the optimization function of SCO‐AN under the condition of large‐scale MIMO: the strong law of large numbers is applied to obtain the ergodic lower bound (ELB) expression of SC for SCO‐AN. The power allocation (PA) problem of the SCO‐AN system is discussed. We use a statistical method to get the formula for calculating the optimal power distribution coefficient of the SCO‐AN system. The transmitter can use the optimal power ratio of PA to distribute the transmitted power without using the PA algorithm. The effect of imperfect channel state information is discussed. Through simulation, we found that more power should be generated for SCO‐AN if the channel estimation is imperfect and the proposed method can achieve better security performance in the large‐scale MIMO system.

DOI
10.1155/2021/9420982

Related papers

Secrecy capacity optimization artificial noise: the ergodic secrecy capacity lower bound and optimal power allocation

Yebo Gu, Zhilu Wu, Zhendong Yin +1 more

Abstract The secure transmission problem of MIMO wireless system in fading channels is studied in this paper. We add a secrecy capacity optimization artificial noise(SCO-AN) to the transported signal for improving the security performance of the system. The closed-form expression of secrecy capacity's lower bound is obtained. Base on the closed-form expression of secrecy capacity's lower bound, We optimize the power allocation between the information-bearing signal and the SCO-AN. By calculating, the optimal ratio of power alloation betwenn the information-bearing signal and the SCO-AN is obtained. Through simulation, the results shows the secrecy capacity increases with more receiving antennas and less eavesdropping antennas.And more power should be allocated to the SCO-AN with the increase of the colluding eavedroppers.More over, we study the effect of channel estimation error on power allocation between information-bearing signal and SCO-AN and find that more power should be allocated to decrease eavesdroppers capacity if the channel estimation is not perfect.

•Jul 27, 2020•0 citations

Power Allocation for Secrecy-Capacity-Optimization-Artificial-Noise Secure MIMO Precoding Systems under Perfect and Imperfect Channel State Information

Yebo Gu, Bowen Huang, Zhilu Wu

In this paper, we consider the physical layer security problem of the wireless communication system. For the multiple-input, multiple-output (MIMO) wireless communication system, secrecy capacity optimization artificial noise (SCO−AN) is introduced and studied. Unlike its traditional counterpart, SCO−AN is an artificial noise located in the range space of the channel state information space and thus results in a significant increase in the secrecy capacity. Due to the limitation of transmission power, making rational use of this power is crucial to effectively increase the secrecy capacity. Hence, in this paper, the objective function of transmission power allocation is constructed. We also consider the imperfect channel estimation in the power allocation problems. In traditional AN research conducted in the past, the expression of the imperfect channel estimation effect was left unknown. Still, the extent to which the channel estimation error impacts the accuracy of secrecy capacity computation is not negligible. We derive the expression of channel estimation error for least square (LS) and minimum mean squared error (MMSE) channel estimation. The objective function for transmission power allocation is non-convex. That is, the traditional gradient method cannot be used to solve this non-convex optimization problem of power allocation. An improved sequence quadratic program (ISQP) is therefore applied to solve this optimization problem. The numerical result shows that the ISQP is better than other algorithms, and the power allocation as derived from ISQP significantly increases secrecy capacity.

Applied Sciences•May 17, 2021•4 citations

SCO-AN:Improve Secrecy Capacity for Secure Transmission Using Power Allocation

Yebo Gu, Zhilu Wu, Zhendong Yin +1 more

Abstract Artificial noise(AN) is a core technique in physical layer security field which has been widely studied.AN reduces the channel capacity of eavesdroppers without affecting the channel capacity of the communicator so that AN can increase secrecy capacity.Secrecy capacity is defined as channel capacity of the communicator minus channel capacity of eavesdroppers.The AN is prohibited from affecting the channel capacity of the legal receiving channel. This condition brings good performance to AN as well as limitations.Recently, the secrecy capacity optimization artificial noise (SCO-AN) is proposed to increase the secrecy capacity more effectively.SCO-AN can reduce the channel capacity of the communicator to a small extent while greatly reducing the channel capacity of the eavesdropper. So, SCO-AN can further expand the secrecy capacity on the basis of AN. Due to the limitation of transmit power, SCO-AN cannot be added indefinitely, so it is an important issue to increase the secrecy capacity as much as possible under a certain power limit.In this paper, a secrecy capacity function with SCO-AN added under certain power constraints is established.Because this function is non-convex, the traditional convex optimization algorithm cannot be applied. A sequence quadratic program(SQP) is adopted to solve this power allocation problem.Simulation results show that SQP can effectively improve the secrecy capacity under a certain power limit.

•Mar 16, 2020•0 citations

Artificial Noise Generated in MIMO Scenario: Optimal Power Design

Yan Mei Zhu, Yongkai Zhou, Sulaiman Saleem Patel +3 more

In wireless communication, the transmitter (Alice) can send artificial noise (AN) to interfere with the eavesdropper (Eve). This letter considers the AN MIMO scenario, i.e., both Alice and the legitimate receiver (Bob) are equipped with multiple antennas. A closed-form expression for the lower bound of secrecy capacity is obtained. It is proved that water-filling is the optimal power allocation scheme. An efficient iterative algorithm is proposed to find the optimal power distribution ratio between information and AN so that maximum secrecy capacity can be achieved. Simulation results show that the proposed algorithm converges fast, and multiple antennas can improve the secrecy capacity to some extent compared to the AN MISO case.

IEEE Signal Processing Letters•Jul 31, 2013•30 citations

Artificial Noise Assisted Secure Massive MIMO Transmission Exploiting Statistical CSI

Wenjin Wang, Chen Xu, Li You +2 more

For the single-cell massive multiple-input multiple-output (MIMO) downlink transmission, we investigate an artificial noise (AN) assisted secure transmission strategy where the base station has only access to statistical channel state information (CSI) of the legitimate user terminals and the eavesdropper. By maximizing a lower bound of the ergodic secrecy sum rate, we figure out the eigenvectors of the optimal secrecy signal and AN transmit covariance matrices in the closed-form. Notably, such a solution reveals that it is more favorable to transmit both the secrecy signals and the AN in the beam domain, by which we translate the original problem into a simpler power allocation problem in the beam domain. Building on the approaches of sequential optimization and the deterministic equivalent, we further propose an iterative algorithm for power allocation with guaranteed convergence to a local optimum. Numerical results show the superior performance of the proposed approach compared with the traditional one without AN.

IEEE Communications Letters•Oct 15, 2019•27 citations

Secure Transmission with Artificial Noise of MIMO Systems: Secrecy Rate and BER Performance

Zhiyue Zhao, Fuyuan Liu, Xin Gou +2 more

At present, there has been a large amount of research on secrecy rate optimization. However, the reliability analysis of secure transmission is equally important although relatively less attention has been dedicated to. Therefore, this paper proposes a secure transmission method with artificial noise for the physical layer security issues in the transmission process of Multiple Input Multiple Output (MIMO) wireless communication systems. Firstly, we establish an artificial noise assisted MIMO systems model. Then, the channel state information (CSI) matrix is subjected to singular value decomposition to obtain the reasonable precoding and artificial noise matrices. Finally, the impact of artificial noise on the bit error rate performance of potential eavesdropper is analyzed, and based on the analysis, the problem of maximizing the system secrecy rate is established. The concave-convex procedure (CCCP) method is used to obtain the optimal power allocation, which significantly improves the security of MIMO systems. The simulation results show that using the null space of CSI matrix and artificial noise for signal encryption effectively improves the bit error rate of potential eavesdropping nodes. In addition, the secrecy rate obtained by the CCCP algorithm is consistent with the performance obtained by the particle swarm optimization algorithm, which verifies the effectiveness of the proposed algorithm.

International Conference on Communication and Network Security (ICCNS)•Dec 6, 2024•0 citations
The security of wireless information transmission in large‐scale multi‐input and multioutput (MIMO) is the focus of research in wireless communication. Recently, a new artificial noise—SCO‐AN which shows no orthogonality to the channel, is proposed to overcome the shortcomings of traditional artificial noise. In the previous research, the optimization function of SCO‐AN is not convex, and its extremum cannot be obtained. Usually, nonconvex optimization algorithms or iterative relaxation algorithms are used to get the maximum value of the optimization objective function. Nonconvex optimization algorithms or iterative relaxation algorithms are greatly affected by the initial value, and the extremum cannot be obtained by a nonconvex optimization algorithm or iterative relaxation algorithm. In this paper, we creatively apply the strong law of large numbers to obtain the optimal value of the optimization function of SCO‐AN under the condition of large‐scale MIMO: the strong law of large numbers is applied to obtain the ergodic lower bound (ELB) expression of SC for SCO‐AN. The power allocation (PA) problem of the SCO‐AN system is discussed. We use a statistical method to get the formula for calculating the optimal power distribution coefficient of the SCO‐AN system. The transmitter can use the optimal power ratio of PA to distribute the transmitted power without using the PA algorithm. The effect of imperfect channel state information is discussed. Through simulation, we found that more power should be generated for SCO‐AN if the channel estimation is imperfect and the proposed method can achieve better security performance in the large‐scale MIMO system.
Abstract The secure transmission problem of MIMO wireless system in fading channels is studied in this paper. We add a secrecy capacity optimization artificial noise(SCO-AN) to the transported signal for improving the security performance of the system. The closed-form expression of secrecy capacity's lower bound is obtained. Base on the closed-form expression of secrecy capacity's lower bound, We optimize the power allocation between the information-bearing signal and the SCO-AN. By calculating, the optimal ratio of power alloation betwenn the information-bearing signal and the SCO-AN is obtained. Through simulation, the results shows the secrecy capacity increases with more receiving antennas and less eavesdropping antennas.And more power should be allocated to the SCO-AN with the increase of the colluding eavedroppers.More over, we study the effect of channel estimation error on power allocation between information-bearing signal and SCO-AN and find that more power should be allocated to decrease eavesdroppers capacity if the channel estimation is not perfect.
In this paper, we consider the physical layer security problem of the wireless communication system. For the multiple-input, multiple-output (MIMO) wireless communication system, secrecy capacity optimization artificial noise (SCO−AN) is introduced and studied. Unlike its traditional counterpart, SCO−AN is an artificial noise located in the range space of the channel state information space and thus results in a significant increase in the secrecy capacity. Due to the limitation of transmission power, making rational use of this power is crucial to effectively increase the secrecy capacity. Hence, in this paper, the objective function of transmission power allocation is constructed. We also consider the imperfect channel estimation in the power allocation problems. In traditional AN research conducted in the past, the expression of the imperfect channel estimation effect was left unknown. Still, the extent to which the channel estimation error impacts the accuracy of secrecy capacity computation is not negligible. We derive the expression of channel estimation error for least square (LS) and minimum mean squared error (MMSE) channel estimation. The objective function for transmission power allocation is non-convex. That is, the traditional gradient method cannot be used to solve this non-convex optimization problem of power allocation. An improved sequence quadratic program (ISQP) is therefore applied to solve this optimization problem. The numerical result shows that the ISQP is better than other algorithms, and the power allocation as derived from ISQP significantly increases secrecy capacity.
Abstract Artificial noise(AN) is a core technique in physical layer security field which has been widely studied.AN reduces the channel capacity of eavesdroppers without affecting the channel capacity of the communicator so that AN can increase secrecy capacity.Secrecy capacity is defined as channel capacity of the communicator minus channel capacity of eavesdroppers.The AN is prohibited from affecting the channel capacity of the legal receiving channel. This condition brings good performance to AN as well as limitations.Recently, the secrecy capacity optimization artificial noise (SCO-AN) is proposed to increase the secrecy capacity more effectively.SCO-AN can reduce the channel capacity of the communicator to a small extent while greatly reducing the channel capacity of the eavesdropper. So, SCO-AN can further expand the secrecy capacity on the basis of AN. Due to the limitation of transmit power, SCO-AN cannot be added indefinitely, so it is an important issue to increase the secrecy capacity as much as possible under a certain power limit.In this paper, a secrecy capacity function with SCO-AN added under certain power constraints is established.Because this function is non-convex, the traditional convex optimization algorithm cannot be applied. A sequence quadratic program(SQP) is adopted to solve this power allocation problem.Simulation results show that SQP can effectively improve the secrecy capacity under a certain power limit.
In wireless communication, the transmitter (Alice) can send artificial noise (AN) to interfere with the eavesdropper (Eve). This letter considers the AN MIMO scenario, i.e., both Alice and the legitimate receiver (Bob) are equipped with multiple antennas. A closed-form expression for the lower bound of secrecy capacity is obtained. It is proved that water-filling is the optimal power allocation scheme. An efficient iterative algorithm is proposed to find the optimal power distribution ratio between information and AN so that maximum secrecy capacity can be achieved. Simulation results show that the proposed algorithm converges fast, and multiple antennas can improve the secrecy capacity to some extent compared to the AN MISO case.
For the single-cell massive multiple-input multiple-output (MIMO) downlink transmission, we investigate an artificial noise (AN) assisted secure transmission strategy where the base station has only access to statistical channel state information (CSI) of the legitimate user terminals and the eavesdropper. By maximizing a lower bound of the ergodic secrecy sum rate, we figure out the eigenvectors of the optimal secrecy signal and AN transmit covariance matrices in the closed-form. Notably, such a solution reveals that it is more favorable to transmit both the secrecy signals and the AN in the beam domain, by which we translate the original problem into a simpler power allocation problem in the beam domain. Building on the approaches of sequential optimization and the deterministic equivalent, we further propose an iterative algorithm for power allocation with guaranteed convergence to a local optimum. Numerical results show the superior performance of the proposed approach compared with the traditional one without AN.
At present, there has been a large amount of research on secrecy rate optimization. However, the reliability analysis of secure transmission is equally important although relatively less attention has been dedicated to. Therefore, this paper proposes a secure transmission method with artificial noise for the physical layer security issues in the transmission process of Multiple Input Multiple Output (MIMO) wireless communication systems. Firstly, we establish an artificial noise assisted MIMO systems model. Then, the channel state information (CSI) matrix is subjected to singular value decomposition to obtain the reasonable precoding and artificial noise matrices. Finally, the impact of artificial noise on the bit error rate performance of potential eavesdropper is analyzed, and based on the analysis, the problem of maximizing the system secrecy rate is established. The concave-convex procedure (CCCP) method is used to obtain the optimal power allocation, which significantly improves the security of MIMO systems. The simulation results show that using the null space of CSI matrix and artificial noise for signal encryption effectively improves the bit error rate of potential eavesdropping nodes. In addition, the secrecy rate obtained by the CCCP algorithm is consistent with the performance obtained by the particle swarm optimization algorithm, which verifies the effectiveness of the proposed algorithm.