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arXiv:1012.3875 · IEEE Transactions on Signal Processing

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

Qiang Li, Wing‐Kin Ma

Published Apr 26, 2011• 246 citations
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Abstract

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.

DOI
10.1109/tsp.2011.2146775

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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.
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.
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.
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.
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.
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.
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.