This paper considers an energy-efficient transmit design in a general multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from several external multi-antenna eavesdroppers. Assuming imperfect channel state information (CSI) at the transmitter, our goal is to design the input transmit covariance, such that the worst-case secrecy energy efficiency (WC-SEE) is maximized, subject to the quality of service (QoS) and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum WC-SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the optimality of transmit beamforming to achieve the maximum WC-SEE. Numerical results are presented to verify the efficacy of our proposed method.
This paper considers an energy-efficient transmit design in a general multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from several external multi-antenna eavesdroppers. Assuming imperfect channel state information (CSI) at the transmitter, our goal is to design the input transmit covariance, such that the worst-case secrecy energy efficiency (WC-SEE) is maximized, subject to the quality of service (QoS) and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum WC-SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the optimality of transmit beamforming to achieve the maximum WC-SEE. Numerical results are presented to verify the efficacy of our proposed method.
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 single-antenna eavesdroppers. Assuming statistical 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, subject to the outage-constrained secrecy rate and transmit power constraints. The resultant problem is intractable to solve even after introducing a semidefinite relaxation (SDR) reformulation. To handle it, an equivalent parametric reformulation, based on the fractional programming and difference-of-concave programming theories, is proposed to recast this problem as a convex problem. By this means, the maximum outage SEE can be found in an iterative fashion. Moreover, we also give an approach to constructing a rank-one covariance matrix from our proposed method, implying the feasibility of transmit beamforming to achieve the obtained SEE performance. Numerical results are presented to show the effectiveness of our proposed method.
This paper considers an energy-efficient transmit design in a three-node MISO wiretap channel in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for both receivers and one confidential message intended for only one authorized receiver. The confidential message must be kept perfectly secure from the unauthorized receiver. Our goal is to jointly design the input covariance matrices of the multicast message and confidential message such that the secrecy energy efficiency (SEE) is maximized, subject to the multicast rate, secrecy rate and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the feasibility of transmit beamforming to achieve the maximum SEE. Numerical results are finally presented to verify the efficacy of our proposed method.
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 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.
This paper studies secure wireless transmission from a multi-antenna transmitter to a single-antenna intended receiver overheard by multiple eavesdroppers with considering the imperfect channel state information (CSI) of wiretap channel.To enhance security of communication link, the artificial noise (AN) is generated at transmitter.We first design the robust joint optimal beamforming of secret signal and AN to minimize transmit power with constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers.The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs).The semidefinite relaxation (SDR) technique is used and the approximated method is proved to solve the original problem exactly.To verify the robustness and tightness of proposed beamforming, we also provide a method to calculate the worst-case SINR at eavesdroppers for a designed transmit scheme using semidefinite programming (SDP).Additionally, the secrecy rate maximization is explored for fixed total transmit power.To tackle the nonconvexity of original formulation, we develop an iterative approach employing sequential parametric convex approximation (SPCA).The simulation results illustrate that the proposed robust transmit schemes can effectively improve the transmit performance.
This paper studies the secure transmission issue for simultaneous wireless information and power transfer in a multiuser multiple-input-multiple-output system with multiple external eavesdroppers, where the transmitter broadcasts independent confidential messages to different legitimate receivers. Each receiver can be seen as an internal eavesdropper intended by other receivers. Our objective is to achieve the robust beamforming design under imperfect channel state information, in which the total transmission power is minimized with constraints on the achievable secrecy rate and the energy harvesting. Since the problem is nonconvex, we propose a two-level optimization scheme. For the inner problem, we investigate two conservative relaxation approaches, large-deviation inequality and Bernstein-type inequality (BTI), to reformulate the outage secrecy rate constraints into some convex ones, yielding a convex optimization by semidefinite programming (SDP) relaxation. For the outer problem, it is a K-variable optimization problem, which can be solved via the novel line-dimensional-like search method. Moreover, we characterize the rank profile of SDP relaxed solution for these two approaches. Specifically, the optimal solution is proved to be rank-one. Numerical results are provided to verify the performance of the proposed algorithms, where the LDI-based scheme outperforms the BTI-based scheme in terms of energy efficiency.