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arXiv:1108.0100 · IEEE Transactions on Signal Processing

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

Jiangyuan Li, Athina P. Petropulu

Published Apr 11, 2012• 23 citations
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Abstract

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.

DOI
10.1109/tsp.2012.2192111

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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.
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.
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.
A Gaussian multiple-input single-output (MISO) secrecy channel is considered, where a transmitter is equipped with multiple antennas, and an intended receiver and an eavesdropper each equipped with a single antenna. This paper studies the robust beamforming design in the presence of uncertainty of channel state information (CSI) on the eavesdropper channel. Under the assumption that all possible states of the eavesdropper channel are in a given set, the problem of optimizing the transmit covariance for the worst-case secrecy capacity which is the maximum transmission rate at which the eavesdropper is unable to decode under any channel realization in the set, is cast as a max-min optimization problem. We propose to transfer the max-min problem into a convex optimization problem that can be solved efficiently. The optimal secrecy rate and transmit covariance are expressed in the form of the generalized eigenvalue and eigenvector, the same form as the conventional case of the perfect eavesdropper's CSI, which indicates our results is the generalization of the conventional case.
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 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.
In this paper, we consider the achievable sum secrecy rate in MISO (multiple-input-single-output) full-duplex wiretap channel in the presence of a passive eavesdropper and imperfect channel state information (CSI). We assume that the users participating in full-duplex communication have multiple transmit antennas, and that the users and the eavesdropper have single receive antenna each. The users have individual transmit power constraints. They also transmit jamming signals to improve the secrecy rates. We obtain the achievable perfect secrecy rate region by maximizing the worst case sum secrecy rate. We also obtain the corresponding transmit covariance matrices associated with the message signals and the jamming signals. Numerical results that show the impact of imperfect CSI on the achievable secrecy rate region are presented.