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 International Conference on Acoustics Speech and Signal Processing

Secrecy rate maximization of a miso channelwith multiple multi-antenna eavesdroppers via semidefinite programming

Qiang Li, Wing‐Kin Ma

Published Mar 1, 2010• 9 citations
Publisher

Abstract

The advances of multi-antenna techniques has recently led to renewed interest in physical-layer secrecy, a meaningful topic that enables us to prevent eavesdroppers from retrieving information intended for a legitimate user through physical layer designs. This paper address a secrecy-rate maximization problem for the scenario of a multi-input single-output channel listened by multiple multi-antenna eavesdroppers; e.g., in downlink. This problem is nonconvex and has no analytical solution. Through a careful analysis and reformulation, we show that the secrecy-rate maximization problem has a convex equivalent in form of a semidefinite program (SDP). We also prove that the respective optimal transmit covariance generally can yield a rank-one structure, implying that transmit beamforming is secrecy-rate optimal in the considered scenario. Simulation results are also provided to illustrate that the optimal transmit design solved by our SDP approach can yield significantly improved secrecy rates than an existing closed-form design.

DOI
10.1109/icassp.2010.5496122

Related papers

Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming

Qiang Li, Wing‐Kin Ma

In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.

arXiv:1012.3875•IEEE Transactions on Signal Processing•Apr 26, 2011•246 citations

Multicast Secrecy Rate Maximization for MISO Channels with Multiple Multi-Antenna Eavesdroppers

Qiang Li, Wing‐Kin Ma

Recently, there has been growing interest in secure communication via multi-antenna physical-layer designs. In this paper, we consider a transmit covariance design for a secrecy rate maximization problem under a multicast scenario, where a multi-antenna transmitter delivers a common confidential message to multiple single-antenna receivers in the presence of multiple multi-antenna eavesdroppers. This multicast secrecy rate maximization (SRM) problem is nonconvex by nature. By resorting to a convex approximation, we provide an upper bound and lower bounds of the multicast secrecy rate by solving a semidefinite program. In particular, for the case of either i) no more than three legitimate receivers and one eavesdropper, or ii) one legitimate receiver and arbitrary number of eavesdroppers, these bounds are shown to be tight and transmit beamforming is an optimal transmit strategy. We also demonstrate by simulations that the multicast SRM problem can be accurately approximated by the proposed method.

International Conference on Communications•Jun 1, 2011•34 citations

Optimal transmit design for miso secrecy-rate maximization with general covariance constraints

Qiang Li, Wing‐Kin Ma

The notion of providing secure communication via physical-layer designs has gained much attention in recent studies. This paper considers the transmit covariance design for a generalized secrecy rate maximization (SRM) problem under the scenario of a multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. This generalized SRM design encompasses various existing SRM designs, e.g., the per-antenna power constrained design and the interference temperature constrained design. While the considered generalized SRM problem is nonconvex by nature, this paper shows that the problem can actually be solved in a convex fashion, by recasting the generalized SRM problem as a semidefinite program (SDP). The development of the solution to the generalized SRM shows that transmit beamforming is generally an optimal transmit strategy. Simulation results are also provided to demonstrate the secrecy-rate performance gains of the proposed algorithm over some closed-form, but suboptimal algorithms.

International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)•Dec 1, 2010•6 citations

A robust artificial noise aided transmit design for MISO secrecy

Qiang Li, Wing‐Kin Ma

This paper considers an artificial noise (AN) aided secrecy rate maximization (SRM) problem for a multi-input single-output (MISO) channel overheard by multiple single-antenna eavesdroppers. We assume that the transmitter has perfect knowledge about the channel to the desired user but imperfect knowledge about the channels to the eavesdroppers. Therefore, the resultant SRM problem is formulated in the way that we maximize the worst-case secrecy rate by jointly designing the signal covariance W and the AN covariance Σ. However, such a worst-case SRM problem turns out to be hard to optimize, since it is nonconvex in W and Σ jointly. Moreover, it falls into the class of semi-infinite optimization problems. Through a careful reformulation, we show that the worst-case SRM problem can be handled by performing a one-dimensional line search in which a sequence of semidefinite programs (SDPs) are involved. Moreover, we also show that the optimal W admits a rank-one structure, implying that transmit beamforming is secrecy rate optimal under the considered scenario. Simulation results are provided to demonstrate the robustness and effectiveness of the proposed design compared to a non-robust AN design.

arXiv:1104.4260•IEEE International Conference on Acoustics Speech and Signal Processing•May 1, 2011•20 citations

Secrecy Rate Optimizations for a MISO Secrecy Channel with Multiple Multiantenna Eavesdroppers

Zheng Chu, Hong Xing, Martin Johnston +1 more

This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.

IEEE Transactions on Wireless Communications•Aug 24, 2015•115 citations

Optimal MISO secrecy beamforming via quasi-convex programming with rank-one transmit covariance guarantee

Ling Tang, Hao Liu, Jianhui Wu

This paper studies the secrecy capacity of the multiple input single output (MISO) secrecy channel where a transmitter is communicating to a receiver in the presence of K eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each has a single antenna. The transmitter maximizes the communication rate, while concealing the message from all the eavesdroppers. It is known that the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the mutual information of the secrecy user channel and those of the eavesdroppers channels. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently. This paper proposes an efficient algorithm based on quasi-convex programming, which not only leads to the optimal transmit covariance matrix, but also guarantees that it is always rank-one at any search step with finite accuracy. Such a guaranteed rank-one covariance matrix is critical to practical implementations of MISO secrecy transmission beam-forming.

International Wireless Communications and Mobile Computing Conference (IWCMC)•Jun 28, 2010•4 citations
The advances of multi-antenna techniques has recently led to renewed interest in physical-layer secrecy, a meaningful topic that enables us to prevent eavesdroppers from retrieving information intended for a legitimate user through physical layer designs. This paper address a secrecy-rate maximization problem for the scenario of a multi-input single-output channel listened by multiple multi-antenna eavesdroppers; e.g., in downlink. This problem is nonconvex and has no analytical solution. Through a careful analysis and reformulation, we show that the secrecy-rate maximization problem has a convex equivalent in form of a semidefinite program (SDP). We also prove that the respective optimal transmit covariance generally can yield a rank-one structure, implying that transmit beamforming is secrecy-rate optimal in the considered scenario. Simulation results are also provided to illustrate that the optimal transmit design solved by our SDP approach can yield significantly improved secrecy rates than an existing closed-form design.
In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.
Recently, there has been growing interest in secure communication via multi-antenna physical-layer designs. In this paper, we consider a transmit covariance design for a secrecy rate maximization problem under a multicast scenario, where a multi-antenna transmitter delivers a common confidential message to multiple single-antenna receivers in the presence of multiple multi-antenna eavesdroppers. This multicast secrecy rate maximization (SRM) problem is nonconvex by nature. By resorting to a convex approximation, we provide an upper bound and lower bounds of the multicast secrecy rate by solving a semidefinite program. In particular, for the case of either i) no more than three legitimate receivers and one eavesdropper, or ii) one legitimate receiver and arbitrary number of eavesdroppers, these bounds are shown to be tight and transmit beamforming is an optimal transmit strategy. We also demonstrate by simulations that the multicast SRM problem can be accurately approximated by the proposed method.
The notion of providing secure communication via physical-layer designs has gained much attention in recent studies. This paper considers the transmit covariance design for a generalized secrecy rate maximization (SRM) problem under the scenario of a multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. This generalized SRM design encompasses various existing SRM designs, e.g., the per-antenna power constrained design and the interference temperature constrained design. While the considered generalized SRM problem is nonconvex by nature, this paper shows that the problem can actually be solved in a convex fashion, by recasting the generalized SRM problem as a semidefinite program (SDP). The development of the solution to the generalized SRM shows that transmit beamforming is generally an optimal transmit strategy. Simulation results are also provided to demonstrate the secrecy-rate performance gains of the proposed algorithm over some closed-form, but suboptimal algorithms.
This paper considers an artificial noise (AN) aided secrecy rate maximization (SRM) problem for a multi-input single-output (MISO) channel overheard by multiple single-antenna eavesdroppers. We assume that the transmitter has perfect knowledge about the channel to the desired user but imperfect knowledge about the channels to the eavesdroppers. Therefore, the resultant SRM problem is formulated in the way that we maximize the worst-case secrecy rate by jointly designing the signal covariance W and the AN covariance Σ. However, such a worst-case SRM problem turns out to be hard to optimize, since it is nonconvex in W and Σ jointly. Moreover, it falls into the class of semi-infinite optimization problems. Through a careful reformulation, we show that the worst-case SRM problem can be handled by performing a one-dimensional line search in which a sequence of semidefinite programs (SDPs) are involved. Moreover, we also show that the optimal W admits a rank-one structure, implying that transmit beamforming is secrecy rate optimal under the considered scenario. Simulation results are provided to demonstrate the robustness and effectiveness of the proposed design compared to a non-robust AN design.
This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.
This paper studies the secrecy capacity of the multiple input single output (MISO) secrecy channel where a transmitter is communicating to a receiver in the presence of K eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each has a single antenna. The transmitter maximizes the communication rate, while concealing the message from all the eavesdroppers. It is known that the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the mutual information of the secrecy user channel and those of the eavesdroppers channels. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently. This paper proposes an efficient algorithm based on quasi-convex programming, which not only leads to the optimal transmit covariance matrix, but also guarantees that it is always rank-one at any search step with finite accuracy. Such a guaranteed rank-one covariance matrix is critical to practical implementations of MISO secrecy transmission beam-forming.