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

Asilomar Conference on Signals, Systems and Computers (ACSSC)

Explicit solution of worst-case secrecy rate for MISO wiretap channels with spherical uncertainty

Jiangyuan Li, Athina P. Petropulu

Published Nov 1, 2011• 2 citations
Publisher

Abstract

A multiple-input single-output (MISO) wiretap channel model is considered, that includes a multi-antenna transmitter, a single-antenna legitimate receiver and a single-antenna eavesdropper. Assuming a spherical uncertainty model for for both the legitimate and the eavesdropper channels, the problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a power constraint is considered, and an explicit expression for the maximum worst-case secrecy rate is provided.

DOI
10.1109/acssc.2011.6189984

Related papers

Explicit Solution of Worst-Case Secrecy Rate for MISO Wiretap Channels With Spherical Uncertainty

Jiangyuan Li, Athina P. Petropulu

A multiple-input single-output (MISO) wiretap channel model is considered, in which a multi-antenna source communicates with a single-antenna destination in the presence of one single-antenna eavesdropper. It is assumed that both the channel to the destination and the channel to the eavesdropper contain spherical uncertainty. The problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a sum power constraint is studied, and an explicit expression for the maximum worst-case secrecy rate is provided.

arXiv:1108.0100•IEEE Transactions on Signal Processing•Apr 11, 2012•23 citations

The achievable secrecy rate of MISO wiretap channels

Zhang Haiyang, Baoyun Wang

In this paper, we study the achievable secrecy rate of the multiple input single output (MISO) wiretap channel, which consists of a transmitter, a legitimate receiver and multiple eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each have a single antenna. We assume that the transmitter has perfect channel state information (CSI) for their links to legitimate receiver, but it has only imperfect CSI for their channels to eavesdroppers. Optimal transmit covariance matrix is obtained based on worst-case secrecy rate maximization, under power constraints. The maximum secrecy rate computation can be formulated as a non-convex optimal problem, which cannot be solved directly. In this paper, we transform non-convex optimal problem into a quasi-convex optimal problem which can be efficiently solved with the bisection method. The simulation result and analysis demonstrate the effectiveness of our methods.

International Conference on Wireless Communications and Signal Processing (WCSP)•Nov 1, 2011•3 citations

Optimal input covariance for achieving secrecy capacity in Gaussian MIMO wiretap channels

Jiangyuan Li, Athina P. Petropulu

We consider a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each node equipped with multiple antennas. We study the problem of finding the optimal input covariance that achieves secrecy capacity subject to a power constraint, which in general leads to a difficult non-convex optimization problem. For the Gaussian multiple-input single-output (MISO) wiretap channel where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with one antenna, the optimal input covariance is obtained in closed form. For the general case, we derive the necessary conditions for the optimal input covariance in the form of a set of equations. We show that for MISO case, the derived conditions guarantee the optimal input covariance. Numerical results are presented to illustrate the proposed theoretical findings.

IEEE International Conference on Acoustics Speech and Signal Processing•Jan 1, 2010•33 citations

On Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels

Jiangyuan Li, Athina P. Petropulu

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper, each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero mean and unit variance, i.e., the channels have trivial covariances. This paper addresses the general case in which the eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framework, it is shown that when full information on the legitimate channel is available to the transmitter, the optimal input covariance has always rank one. It is also shown that when only statistical information on the legitimate channel is available to the transmitter, the legitimate channel has some general non-trivial covariance and the eavesdropper channel has trivial covariance, the optimal input covariance has the same eigenvectors as the legitimate channel covariance.

IEEE Transactions on Wireless Communications•Jan 21, 2011•145 citations

Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels with Non-Trivial Covariance

Jiangyuan Li, Athina P. Petropulu

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that achieves ergodic secrecy rate subject to a power constraint where the full information on the legitimate channel is known to the transmitter, but only statistical information on the eavesdropper channel is available at the transmitter. Existing results address the case in which the eavesdropper channel has independent and identically distributed Gaussian entries with zero-mean, i.e., the channel has trivial covariance. This paper addresses the general case where eavesdropper channel has nontrivial covariance. A set of equations describing the optimal input covariance matrix are proposed. Based on this framework, we show that the optimal input covariance has always rank one. Numerical results are presented to illustrate the algorithm.

Globecom•Dec 1, 2010•1 citation

Ergodic secrecy rate for Gaussian MISO wiretap channels with Rician fading

Jiangyuan Li, Shuangyu Luo, Athina P. Petropulu

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where the full information on the legitimate channel is known to the transmitter, but only statistical information on the eavesdropper channel is available at the transmitter. Existing results address the case in which the eavesdropper channel has independent and identically distributed Gaussian entries with zero-mean, i.e., the channel has trivial covariance. This paper addresses the general case where eavesdropper channel has non-zero mean and nontrivial covariance. We show that the optimal input covariance has always rank one. Based on this, for the non-zero mean but trivial covariance, we reduce the original problem to an one variable optimization problem and propose Newton's method to solve the resulting optimization problem. Numerical results are presented to illustrate the algorithm.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Nov 1, 2010•1 citation
A multiple-input single-output (MISO) wiretap channel model is considered, that includes a multi-antenna transmitter, a single-antenna legitimate receiver and a single-antenna eavesdropper. Assuming a spherical uncertainty model for for both the legitimate and the eavesdropper channels, the problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a power constraint is considered, and an explicit expression for the maximum worst-case secrecy rate is provided.
A multiple-input single-output (MISO) wiretap channel model is considered, in which a multi-antenna source communicates with a single-antenna destination in the presence of one single-antenna eavesdropper. It is assumed that both the channel to the destination and the channel to the eavesdropper contain spherical uncertainty. The problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a sum power constraint is studied, and an explicit expression for the maximum worst-case secrecy rate is provided.
In this paper, we study the achievable secrecy rate of the multiple input single output (MISO) wiretap channel, which consists of a transmitter, a legitimate receiver and multiple eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each have a single antenna. We assume that the transmitter has perfect channel state information (CSI) for their links to legitimate receiver, but it has only imperfect CSI for their channels to eavesdroppers. Optimal transmit covariance matrix is obtained based on worst-case secrecy rate maximization, under power constraints. The maximum secrecy rate computation can be formulated as a non-convex optimal problem, which cannot be solved directly. In this paper, we transform non-convex optimal problem into a quasi-convex optimal problem which can be efficiently solved with the bisection method. The simulation result and analysis demonstrate the effectiveness of our methods.
We consider a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each node equipped with multiple antennas. We study the problem of finding the optimal input covariance that achieves secrecy capacity subject to a power constraint, which in general leads to a difficult non-convex optimization problem. For the Gaussian multiple-input single-output (MISO) wiretap channel where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with one antenna, the optimal input covariance is obtained in closed form. For the general case, we derive the necessary conditions for the optimal input covariance in the form of a set of equations. We show that for MISO case, the derived conditions guarantee the optimal input covariance. Numerical results are presented to illustrate the proposed theoretical findings.
A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper, each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero mean and unit variance, i.e., the channels have trivial covariances. This paper addresses the general case in which the eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framework, it is shown that when full information on the legitimate channel is available to the transmitter, the optimal input covariance has always rank one. It is also shown that when only statistical information on the legitimate channel is available to the transmitter, the legitimate channel has some general non-trivial covariance and the eavesdropper channel has trivial covariance, the optimal input covariance has the same eigenvectors as the legitimate channel covariance.
A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that achieves ergodic secrecy rate subject to a power constraint where the full information on the legitimate channel is known to the transmitter, but only statistical information on the eavesdropper channel is available at the transmitter. Existing results address the case in which the eavesdropper channel has independent and identically distributed Gaussian entries with zero-mean, i.e., the channel has trivial covariance. This paper addresses the general case where eavesdropper channel has nontrivial covariance. A set of equations describing the optimal input covariance matrix are proposed. Based on this framework, we show that the optimal input covariance has always rank one. Numerical results are presented to illustrate the algorithm.
A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where the full information on the legitimate channel is known to the transmitter, but only statistical information on the eavesdropper channel is available at the transmitter. Existing results address the case in which the eavesdropper channel has independent and identically distributed Gaussian entries with zero-mean, i.e., the channel has trivial covariance. This paper addresses the general case where eavesdropper channel has non-zero mean and nontrivial covariance. We show that the optimal input covariance has always rank one. Based on this, for the non-zero mean but trivial covariance, we reduce the original problem to an one variable optimization problem and propose Newton's method to solve the resulting optimization problem. Numerical results are presented to illustrate the algorithm.