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 Transactions on Information Forensics and Security

Artificial-Noise-Aided Secure Multi-User Multi-Antenna Transmission With Quantized CSIT: A Comprehensive Design and Analysis

Liang Sun, Lu Cao, Zhiyao Tang, Yong Feng

Published Jan 1, 2020• 16 citations
Publisher

Abstract

We present a secure multi-user multi-antenna transmission framework based on artificial-noise-aided linear zero-forcing beamforming, with limited channel state information feedback from multiple distributed legitimate users (LUs). The secrecy performance of the proposed scheme is analytically investigated and optimized. We develop a new accurate closed-form expression of a lower bound on the ergodic secrecy rate (ESR) of each LU without assuming asymptotes for any system parameter. To make system design tractable, we develop another lower bound on ESR which is so analytically amenable that it enables one to not only extend the results of the previous related works but also explore some untouched aspects of the well known artificial-noise-aided scheme. We derive the optimized power allocation coefficient to message-bearing signals which maximizes the latter ESR lower bound. Furthermore, we theoretically study respectively the impacts of the two main parameters, i.e., transmit power P and the number of feedback bits of each LU B, on the power allocation coefficient, and show the asymptotic results for the high-power and high-quantization-resolution systems. We also develop a sufficient condition on P and B under which a positive ESR of each LU can be achieved. We study some important parameters called the minimum required transmit power (MRTP) and the minimum required number of feedback bits (MRFBs) for each LU to achieve a positive ESR or to achieve a target ESR, which have rarely been touched before. Besides, we propose the algorithms to obtain the MRTP and MRFBs. Numerical results are also provided to verify our theoretical results.

DOI
10.1109/tifs.2020.2998942

Related papers

Artificial-Noise-Aided Coordinated Secure Transmission Design in Multi-Cell Multi-Antenna Networks With Limited Feedback

Zhiyao Tang, Liang Sun, Xinyu Tian +2 more

In this paper, we consider secure communications in a multi-cell downlink multi-antenna system, where each multi-antenna base station (BS) sends confidential messages to one intended legitimate user (LU) with a passive multi-antenna eavesdropper trying to intercept the messages in this cell. To enhance the secure communications of the cell-edge users, the multiple BSs employ coordinated beamforming with the aid of artificial-noise (AN) beamforming. We conduct a mathematically rigorous secrecy performance analysis of the considered system and obtain new accurate closed-form expressions of a lower bound on the ergodic rate of each LU and an upper bound of the ergodic rate of each eavesdropper without assuming asymptotes for any system parameter (except for the “worst-case” scenario with zero noise power). Then, a lower bound on the ergodic secrecy rate (ESR) of each LU follows. Based on the derived analytical results, we propose a low-complexity algorithm to optimize the channel sate information (CSI) feedback bits allocation for the channels of target signal link and inter-cell interference links. Furthermore, we develop explicit sufficient conditions on the set of system parameters under which there are at least two BSs to coordinated secure transmission. Through both theoretical analysis and numerical results, we can verify that the obtained analytical lower bound on ESR of each LU as a function of the set of power allocation coefficients is generallyneither convex nor concave. Thus, we propose to employ some numerical method to find a sub-optimal power allocation solution. Finally, numerical results are also provided to validate our theoretical results and the proposed feedback bits and power allocation methods.

IEEE Transactions on Vehicular Technology•Dec 13, 2021•13 citations

Secrecy Performance Analysis for An-Aided Linear ZFBF in MU-MIMO Systems with Limited Feedback

Lu Cao, Zhiyao Tang, Liang Sun +3 more

Although there have been extensive works on artificial-noise-aided (AN-aided) secure transmission schemes for multi-antenna systems, there is still lack of study on the AN-aided scheme employing the widely used linear zero-forcing beamforming (ZFBF) for systems with multiple distributed users. Particularly, there is no analytical secrecy performance for general system settings with neither perfect nor imperfect channel state information of the legitimate users at the transmitter (CSIT). This paper considers the AN-aided ZFBF based on the quantized CSIT for secure communication in the downlink multiuser multi-antenna systems with an external multi-antenna eavesdropper. We develop an approximated closed-form lower bound on the ergodic rate of each legitimate user (LU), and also a closed-form upper bound on the maximum achievable ergodic rate for each LU's messages over the eavesdropper's channel without assuming any asymptotes for system parameters. Then, an approximated closed-form lower bound on the ergodic secrecy rate of each LU follows. Simulation results validate our analytical secrecy performance results and also the effectiveness of AN in enhancing the secrecy performance of linear ZFBF.

Globecom•Dec 1, 2019•0 citations

Physical Layer Security in Multi-Antenna Cellular Systems: Joint Optimization of Feedback Rate and Power Allocation

Liang Sun, Xinyu Tian

This paper comprehensively studies the physical layer security in frequency division duplex multi-antenna cellular systems, where the multi-antenna base stations (BSs), legitimate users (LUs), and eavesdroppers are all randomly located. Each BS employs artificial-noise (AN)-aided multi-user linear beamforming with limited channel state information feedback. Based on the stochastic geometry theory, we first derive an analytical expression of a lower bound on the ergodic secrecy rate (ESR) of the typical LU without assuming asymptotes for any system parameter. We then develop a tight closed-form approximation on the optimal number of feedback bits to maximize a lower bound on the per-user net ESR, which takes into consideration the cost of uplink spectral efficiency for limited feedback. Moreover, the power allocation coefficient between message-bearing signals and AN can be optimized by using a bisection search method. Our main finding is that, the optimum number of feedback bits scales linearly with the path-loss exponent and the number of antennas, and scales logarithmically with the channel coherence time. The derived analytical results can also provide system-level insights into the ESR performance of the multi-antenna random cellular networks with limited feedback and the optimal system design. Numerical results are also presented to verify the obtained results.

IEEE Transactions on Wireless Communications•Mar 8, 2022•26 citations

Artificial-Noise-Aided Nonlinear Secure Transmission for Multiuser Multi-Antenna Systems With Finite-Rate Feedback

Liang Sun, Rui Wang, Zhiyao Tang +1 more

We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.

IEEE Transactions on Communications•Nov 22, 2018•15 citations

Artificial-noise-aided nonlinear secure transmission for MU-MISO wiretap channel with quantized CSIT

Liang Sun, Rui Wang, Hai Wang +1 more

We consider nonlinear transceiver design for downlink multiuser multi-antenna secure communications with an external multi-antenna eavesdropper. The multi-antenna transmitter simultaneously transmits confidential-message-bearing signals and artificial noise (AN) using nonlinear Tomlinson Harashima precoding based on the limited channel state information feedback. For the proposed nonlinear secure transceiver, we reveal the mechanism behind which makes this nonlinear precoding superior than the linear precoding methods in guaranteeing secrecy of wireless multiuser multi-antenna systems. We also obtain analytical bounds of the ergodic secrecy rate of each legitimate receiver and the ergodic secrecy sum rate of the system. Based on the analytical result, the near optimal power allocation to the information signals and AN can be obtained using numerical method. Numerical results are shown to verify the advantage of the proposed nonlinear method over the linear zero-forcing precoding.

International Conference on Communications•May 1, 2017•2 citations

Artificial-Noise-Aided Secure Multi-Antenna Transmission With Limited Feedback

Xi Zhang, Matthew R. McKay, Xiangyun Zhou +1 more

We present an optimized secure multi-antenna transmission approach based on artificial-noise-aided beamforming, with limited feedback from a desired single-antenna receiver. To deal with beamformer quantization errors as well as unknown eavesdropper channel characteristics, our approach is aimed at maximizing throughput under dual performance constraints-a connection outage constraint on the desired communication channel and a secrecy outage constraint to guard against eavesdropping. We propose an adaptive transmission strategy that judiciously selects the wiretap coding parameters, as well as the power allocation between the artificial noise and the information signal. This optimized solution reveals several important differences with respect to solutions designed previously under the assumption of perfect feedback. We also investigate the problem of how to most efficiently utilize the feedback bits. The simulation results indicate that a good design strategy is to use approximately 20% of these bits to quantize the channel gain information, with the remainder to quantize the channel direction, and this allocation is largely insensitive to the secrecy outage constraint imposed. In addition, we find that 8 feedback bits per transmit antenna is sufficient to achieve approximately 90% of the throughput attainable with perfect feedback.

arXiv:1501.05186•IEEE Transactions on Wireless Communications•Jan 13, 2015•94 citations
We present a secure multi-user multi-antenna transmission framework based on artificial-noise-aided linear zero-forcing beamforming, with limited channel state information feedback from multiple distributed legitimate users (LUs). The secrecy performance of the proposed scheme is analytically investigated and optimized. We develop a new accurate closed-form expression of a lower bound on the ergodic secrecy rate (ESR) of each LU without assuming asymptotes for any system parameter. To make system design tractable, we develop another lower bound on ESR which is so analytically amenable that it enables one to not only extend the results of the previous related works but also explore some untouched aspects of the well known artificial-noise-aided scheme. We derive the optimized power allocation coefficient to message-bearing signals which maximizes the latter ESR lower bound. Furthermore, we theoretically study respectively the impacts of the two main parameters, i.e., transmit power P and the number of feedback bits of each LU B, on the power allocation coefficient, and show the asymptotic results for the high-power and high-quantization-resolution systems. We also develop a sufficient condition on P and B under which a positive ESR of each LU can be achieved. We study some important parameters called the minimum required transmit power (MRTP) and the minimum required number of feedback bits (MRFBs) for each LU to achieve a positive ESR or to achieve a target ESR, which have rarely been touched before. Besides, we propose the algorithms to obtain the MRTP and MRFBs. Numerical results are also provided to verify our theoretical results.
In this paper, we consider secure communications in a multi-cell downlink multi-antenna system, where each multi-antenna base station (BS) sends confidential messages to one intended legitimate user (LU) with a passive multi-antenna eavesdropper trying to intercept the messages in this cell. To enhance the secure communications of the cell-edge users, the multiple BSs employ coordinated beamforming with the aid of artificial-noise (AN) beamforming. We conduct a mathematically rigorous secrecy performance analysis of the considered system and obtain new accurate closed-form expressions of a lower bound on the ergodic rate of each LU and an upper bound of the ergodic rate of each eavesdropper without assuming asymptotes for any system parameter (except for the “worst-case” scenario with zero noise power). Then, a lower bound on the ergodic secrecy rate (ESR) of each LU follows. Based on the derived analytical results, we propose a low-complexity algorithm to optimize the channel sate information (CSI) feedback bits allocation for the channels of target signal link and inter-cell interference links. Furthermore, we develop explicit sufficient conditions on the set of system parameters under which there are at least two BSs to coordinated secure transmission. Through both theoretical analysis and numerical results, we can verify that the obtained analytical lower bound on ESR of each LU as a function of the set of power allocation coefficients is generallyneither convex nor concave. Thus, we propose to employ some numerical method to find a sub-optimal power allocation solution. Finally, numerical results are also provided to validate our theoretical results and the proposed feedback bits and power allocation methods.
Although there have been extensive works on artificial-noise-aided (AN-aided) secure transmission schemes for multi-antenna systems, there is still lack of study on the AN-aided scheme employing the widely used linear zero-forcing beamforming (ZFBF) for systems with multiple distributed users. Particularly, there is no analytical secrecy performance for general system settings with neither perfect nor imperfect channel state information of the legitimate users at the transmitter (CSIT). This paper considers the AN-aided ZFBF based on the quantized CSIT for secure communication in the downlink multiuser multi-antenna systems with an external multi-antenna eavesdropper. We develop an approximated closed-form lower bound on the ergodic rate of each legitimate user (LU), and also a closed-form upper bound on the maximum achievable ergodic rate for each LU's messages over the eavesdropper's channel without assuming any asymptotes for system parameters. Then, an approximated closed-form lower bound on the ergodic secrecy rate of each LU follows. Simulation results validate our analytical secrecy performance results and also the effectiveness of AN in enhancing the secrecy performance of linear ZFBF.
This paper comprehensively studies the physical layer security in frequency division duplex multi-antenna cellular systems, where the multi-antenna base stations (BSs), legitimate users (LUs), and eavesdroppers are all randomly located. Each BS employs artificial-noise (AN)-aided multi-user linear beamforming with limited channel state information feedback. Based on the stochastic geometry theory, we first derive an analytical expression of a lower bound on the ergodic secrecy rate (ESR) of the typical LU without assuming asymptotes for any system parameter. We then develop a tight closed-form approximation on the optimal number of feedback bits to maximize a lower bound on the per-user net ESR, which takes into consideration the cost of uplink spectral efficiency for limited feedback. Moreover, the power allocation coefficient between message-bearing signals and AN can be optimized by using a bisection search method. Our main finding is that, the optimum number of feedback bits scales linearly with the path-loss exponent and the number of antennas, and scales logarithmically with the channel coherence time. The derived analytical results can also provide system-level insights into the ESR performance of the multi-antenna random cellular networks with limited feedback and the optimal system design. Numerical results are also presented to verify the obtained results.
We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.
We consider nonlinear transceiver design for downlink multiuser multi-antenna secure communications with an external multi-antenna eavesdropper. The multi-antenna transmitter simultaneously transmits confidential-message-bearing signals and artificial noise (AN) using nonlinear Tomlinson Harashima precoding based on the limited channel state information feedback. For the proposed nonlinear secure transceiver, we reveal the mechanism behind which makes this nonlinear precoding superior than the linear precoding methods in guaranteeing secrecy of wireless multiuser multi-antenna systems. We also obtain analytical bounds of the ergodic secrecy rate of each legitimate receiver and the ergodic secrecy sum rate of the system. Based on the analytical result, the near optimal power allocation to the information signals and AN can be obtained using numerical method. Numerical results are shown to verify the advantage of the proposed nonlinear method over the linear zero-forcing precoding.
We present an optimized secure multi-antenna transmission approach based on artificial-noise-aided beamforming, with limited feedback from a desired single-antenna receiver. To deal with beamformer quantization errors as well as unknown eavesdropper channel characteristics, our approach is aimed at maximizing throughput under dual performance constraints-a connection outage constraint on the desired communication channel and a secrecy outage constraint to guard against eavesdropping. We propose an adaptive transmission strategy that judiciously selects the wiretap coding parameters, as well as the power allocation between the artificial noise and the information signal. This optimized solution reveals several important differences with respect to solutions designed previously under the assumption of perfect feedback. We also investigate the problem of how to most efficiently utilize the feedback bits. The simulation results indicate that a good design strategy is to use approximately 20% of these bits to quantize the channel gain information, with the remainder to quantize the channel direction, and this allocation is largely insensitive to the secrecy outage constraint imposed. In addition, we find that 8 feedback bits per transmit antenna is sufficient to achieve approximately 90% of the throughput attainable with perfect feedback.