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International Conference on Communications

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

Qiang Li, Wing‐Kin Ma

Published Jun 1, 2011• 34 citations
Publisher

Abstract

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.

DOI
10.1109/icc.2011.5963115

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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 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.
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 a two-user multiple-input single-output Gaussian broadcast channel model with two sorts of information transfer, i.e., multicasting and confidential broadcasting. Specifically, three service messages are combined at the transmitter. The transmitter sends a multicast message to both users, and a confidential message to each user which is kept perfectly secret from the other user. Our goal is to jointly design the optimal input covariances for the multicast message and the two confidential messages, such that the secrecy capacity region is maximized. This problem can be formulated as a secrecy rate maximization (SRM) problem with the quality of multicast service constraint and the quality of confidential service constraint. This SRM problem is nonconvex by nature. To solve it, we reveal its hidden convexity and transform the original SRM problem into a semidefinite programming problem. Furthermore, we prove that the optimal input covariance matrices of the multicast message and the two confidential messages are always with rank one, which implies the optimality of beamforming. Besides, we show that the arithmetic complexity of our proposed method is polynomial with regard to the dimension of the optimization variables. Numerical results are finally presented to show the efficacy of our proposed method.
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 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.