This paper considers a cellular multiple-input single- output (MISO) system overheard by multiple eavesdroppers, in the presence of one pair of device- to-device (D2D) nodes working as an underlay to the cellular network. A novel eavesdropping scenario is studied in this paper, where the eavesdroppers intend to simultaneously overhear the cellular communication as well as the D2D communication. Assuming imperfect channel state information (CSI) at the transmitter, our goal is to design the input covariance matrix of confidential message such that the worst-case sum secrecy rate is maximized, while satisfying the quality of service (QoS) requirement in the D2D communication. Although this worst-case sum secrecy rate maximization (SSRM) problem is non-convex, we show that it can be handled by solving a sequence of semidefinite programming (SDP) problems. Moreover, we give complexity analysis of our proposed optimization method and prove that transmit beamforming is an optimal strategy for the confidential message transmission. Numerical results are presented to verify the efficacy of our proposed method.
This paper considers a cellular multiple-input single- output (MISO) system overheard by multiple eavesdroppers, in the presence of one pair of device- to-device (D2D) nodes working as an underlay to the cellular network. A novel eavesdropping scenario is studied in this paper, where the eavesdroppers intend to simultaneously overhear the cellular communication as well as the D2D communication. Assuming imperfect channel state information (CSI) at the transmitter, our goal is to design the input covariance matrix of confidential message such that the worst-case sum secrecy rate is maximized, while satisfying the quality of service (QoS) requirement in the D2D communication. Although this worst-case sum secrecy rate maximization (SSRM) problem is non-convex, we show that it can be handled by solving a sequence of semidefinite programming (SDP) problems. Moreover, we give complexity analysis of our proposed optimization method and prove that transmit beamforming is an optimal strategy for the confidential message transmission. Numerical results are presented to verify the efficacy of our proposed method.
This study considers a cellular multiple‐input single‐output system overheard by multiple eavesdroppers, in the presence of multiple pairs of single‐antenna device‐to‐device (D2D) nodes working as an underlay. All D2D nodes are permitted to access the cellular channel for their own communications. A novel eavesdropping scenario, termed as simultaneous eavesdropping, is studied, where the eavesdroppers intend to simultaneously overhear the cellular communication as well as D2D communications. Assuming imperfect channel state information (CSI) at the transmitter, the authors goal is to design the robust transmit covariance of confidential message and artificial noise, such that the worst‐case sum secrecy rate is maximised. This worst‐case sum secrecy rate maximisation problem is challenging to solve due to its non‐convexity and semi‐infiniteness incurred by the imperfect CSI. As a compromise, the authors develop a tractable approximation to its objective secrecy rate function for deriving a computationally efficient lower bound. Then a successive convex approximation (SCA) algorithm is proposed to solve the approximated problem in an iterative manner with provable convergence guarantee. Then it is proved that the SCA algorithm always yields a beam‐forming solution to the confidential message transmission. Numerical results illustrate that the proposed scheme outperforms the traditional one.
This paper considers a cellular multiple-input multiple-output multiple-eavesdropper (MIMOME) channel, with a pair of single-antenna device-to-device (D2D) nodes working as an underlay. A novel eavesdropping scenario is studied in this paper, where the eavesdroppers intend to simultaneously overhear the cellular communication and the D2D communication. Our goal is to jointly optimize the covariance of confidential message and artificial noise, as well as the transmit power at the D2D transmitter, such that the sum secrecy rate is maximized, while satisfying the quality of service constraint on the D2D communication. This sum secrecy rate maximization (SSRM) problem is non-convex by nature. To handle it, an equivalent reformulation of this SSRM problem is introduced, wherein the resulting problem becomes primal decomposable and thus can be iteratively solved using an alternating optimization (AO) algorithm. Also, we prove that the AO algorithm is bound to converge to a stationary point of the primal SSRM problem. Furthermore, we extend the SSRM problem to a more general case with multiple pairs of D2D nodes. Again, the resulting problem is shown to be solvable by the AO algorithm, with provable convergence to the stationary point. Finally, numerical results are presented to verify the efficacy of our proposed method.
Consider a cellular multiple-input single-output (MISO) channel, in the presence of multiple eavesdroppers (Eves) and one pair of single-antenna device-to-device (D2D) nodes working as an underlay. A novel eavesdropping scenario, termed as selective eavesdropping, is studied in this paper, where Eves arbitrarily select one target from the cellular receiver and the D2D receiver to overhear, but their selection is unknown to any other nodes. Since Eves' two sorts of selection would lead to two different secrecy rates, we define the achievable secrecy rate as the smaller one of the two rates. With imperfect channel state information on all links, our interest lies in the robust design of transmit covariances at the cellular transmitter, such that the worst-case achievable secrecy rate is maximized. This worst-case secrecy rate maximization problem is nonconvex by nature. To deal with it, we develop a convex approximation to seek a computationally efficient lower bound. In particular, the solution can be efficiently computed by successively solving a sequence of convex optimization problems. Then it is proved that the obtained lower bound is attainable by simply utilizing single-stream beamforming. Numerical results are finally presented to demonstrate the efficacy of our proposed methods.
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.
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.
Robust quality-of-service (QoS)-based and secrecy rate-based secure transmission designs are investigated for a multiple-input single-output system with multiple eavesdroppers and a cooperative jammer. Two scenarios are considered: (a) eavesdroppers' channel state information (ECSI) is available and (b) ECSI is unavailable. In scenario (a), a QoS-based design is considered to minimize the worst case signal-to-interference-and-noise ratio at the eavesdroppers and to guarantee the QoS of the legitimate receiver. A secrecy rate-based design is also studied where the worst case secrecy rate is maximized. In scenario (b), a QoS-based design is considered to maximize the power of jamming signals under the QoS constraint of the legitimate receiver, and the secrecy rate-based design is not applicable. In all these designs, we jointly optimize the transmit beamforming vector and the covariance matrix of jamming signals under individual power constraints. As the optimization problems are non-convex, we propose an algorithm for each problem through semidefinite relaxation. Our analysis and simulation results show that, even though the linear precoding scheme in our designs is transmit beamforming rather than the general rank transmit covariance, this does not cause any loss of optimality.