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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Safe convex approximation to outage-based MISO secrecy rate optimization under imperfect CSI and with artificial noise

Qiang Li, Wing‐Kin Ma, Anthony Man–Cho So

Published Nov 1, 2011• 42 citations
Publisher

Abstract

Consider a scenario in which an MISO channel is overheard by multiple single-antenna eavesdroppers. The transmitter has perfect channel state information (CSI) with the legitimate channel, but has imperfect CSI with the eavesdroppers' channels. The CSI uncertainties are assumed stochastic. We formulate an artificial-noise (AN)-aided secrecy-rate maximization problem where the CSI uncertainties are handled using an outage-based formulation. Our aim is to find, for this problem, tractable designs for the transmit and AN covariances. Unfortunately, outage-based optimization problems are generally difficult to solve. The main contribution here is to derive a safe, convex optimization-based, approximation to the considered problem. The advantages of the method are shown by simulations.

DOI
10.1109/acssc.2011.6189986

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Consider a scenario in which an MISO channel is overheard by multiple single-antenna eavesdroppers. The transmitter has perfect channel state information (CSI) with the legitimate channel, but has imperfect CSI with the eavesdroppers' channels. The CSI uncertainties are assumed stochastic. We formulate an artificial-noise (AN)-aided secrecy-rate maximization problem where the CSI uncertainties are handled using an outage-based formulation. Our aim is to find, for this problem, tractable designs for the transmit and AN covariances. Unfortunately, outage-based optimization problems are generally difficult to solve. The main contribution here is to derive a safe, convex optimization-based, approximation to the considered problem. The advantages of the method are shown by simulations.
Consider an MISO channel overheard by multiple eavesdroppers. Our goal is to design an artificial noise (AN)-aided transmit strategy, such that the achievable secrecy rate is maximized subject to the sum power constraint. AN-aided secure transmission has recently been found to be a promising approach for blocking eavesdropping attempts. In many existing studies, the confidential information transmit covariance and the AN covariance are not simultaneously optimized. In particular, for design convenience, it is common to prefix the AN covariance as a specific kind of spatially isotropic covariance. This paper considers joint optimization of the transmit and AN covariances for secrecy rate maximization (SRM), with a design flexibility that the AN can take any spatial pattern. Hence, the proposed design has potential in jamming the eavesdroppers more effectively, based upon the channel state information (CSI). We derive an optimization approach to the SRM problem through both analysis and convex conic optimization machinery. We show that the SRM problem can be recast as a single-variable optimization problem, and that resultant problem can be efficiently handled by solving a sequence of semidefinite programs. Our framework deals with a general setup of multiple multi-antenna eavesdroppers, and can cater for additional constraints arising from specific application scenarios, such as interference temperature constraints in interference networks. We also generalize the framework to an imperfect CSI case where a worst-case robust SRM formulation is considered. A suboptimal but safe solution to the outage-constrained robust SRM design is also investigated. Simulation results show that the proposed AN-aided SRM design yields significant secrecy rate gains over an optimal no-AN design and the isotropic AN design, especially when there are more eavesdroppers.
This paper proposes a physical-layer secrecy transmission based on artificial noise (AN) for a multi-input single-output (MISO) channel overheard by one single-antenna eavesdropper. Legitimate receiver transmits AN using beamforming to improve the secret capacity. The AN is designed for two cases assuming that legitimate receiver has perfect or imperfect knowledge of eavesdropper's channel state information (CSI). The optimization problem of AN design in both cases are not convex. A one-dimensional line search on a sequence of semidefinite programs (SDP) is proposed to solve the problem in perfect CSI case through reformulation. In the case with imperfect CSI, the beamforming and AN vectors are designed for achieving quality of service discrimination. The problem is approximated to be a convex SDP problem by relaxing some restrictions. Furthermore, the optimal covariance is shown to be of rank one. Simulation results verify that our methods precede the existed AN aided scheme.
Consider a multi-input multi-output (MIMO) channel wiretapped by multiple multi-antenna eavesdroppers. Assuming imperfect eavesdroppers' channel state information (CSI) at the transmitter, an outage-constrained secrecy rate maximization (OC-SRM) problem is considered. Specifically, we aim to design the transmit covariance matrix such that the outage secrecy rate is maximized for a given outage probability. The OC-SRM problem is challenging, and as a compromise, we resort to a recently developed Bernstein-type inequality approach to obtain a safe (conservative) approximate solution for OC-SRM. The merit of the proposed safe design lies in its tractability. In particular, a safe solution can be efficiently computed by alternately solving two convex conic optimization problems. The efficacy of the proposed design is demonstrated by simulations.
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 considers an energy-efficient transmit design in a multiple-input single-output (MISO) wiretap channel. In particular, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from multiple external eavesdroppers. Assuming partial eavesdroppers' channel state information (ECSI) at the transmitter, we aim to design the transmit beamformer such that the outage secrecy energy efficiency (SEE) is maximized. Two ECSI uncertainty scenarios are studied, i.e., statistical ECSI and imperfect ECSI. For the statistical ECSI case, only the distribution of ECSI is available at the transmitter. The SEE outage constraint admits a closed-form expression in this case, and an approximate solution can be obtained by solving a sequence of convex optimization problems. However, this does not apply to the imperfect ECSI case, where the channel lies in some uncertainty set centered at the true channel. We show that a conservative transmit scheme can be derived by invoking the Bernstein-type inequality. It is proved that our proposed methods always yield a solution of rank one, with either statistical or imperfect CSI. Numerical results are finally presented to confirm the efficacy of our proposed methods.
In this work, a robust artificial noise (AN) aided transmit method is proposed for a multicast multiple-input single-output (MISO) system in the presence of multiple single-antenna eavesdroppers. With the imperfect covariance-based channel state information (CSI), we aim to minimize the transmit power at the transmitter under the multicast secrecy rate constraint and the maximum transmit power constraint. The resulting optimization problem involves the joint optimization of the beamforming vector and AN covariance matrix. After using the semidefinite relaxation (SDR) technique, we derive the exact reformulation of the original optimization through the Lagrange duality. Then this non-convex problem is transformed into a one-variable optimization problem, which can be handled by solving a series of semidefinite programs (SDPs). Simulation results demonstrate the effectiveness of the proposed robust transmit method.