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IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Energy efficiency optimization for MISO wiretap channels with statistical and imperfect CSI

Weidong Mei, Zhi Chen, Jun Fang, Boyu Ning

Published Jul 1, 2017• 4 citations
Publisher

Abstract

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.

DOI
10.1109/spawc.2017.8227734

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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.
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 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.
In this paper, we investigate the robust secure transmit beamformming design for multiple-input single-output wiretap channels overheard by multiple non-collaborating single-antenna eavesdroppers. Assuming that at the transmitter, the instantaneous legitimate receiver's channel state information (CSI) is imperfect and only the statistical eavesdroppers' CSI is known, we seek to maximize the target secrecy rate R with the total transmit power constraint and the secrecy outage probability constraint. The resulting outage-constrained secrecy rate maximization (O-SRM) is non-convex and difficult to solve. Thus, we develop an efficient algorithm to solve it and determine the robust secure beamforming design. Specifically speaking, we first prove that the original O-SRM problem can be solved by an equivalent outage-constrained power minimization problem (O-PMP), which is easy to perform semi-definite relaxation (SDR) and can be solved by semi-definite program (SDP) consequently. Second, we transform the non-convex secrecy rate outage constraints into deterministic ones by resorting to Bernstein-type inequality II. Finally, by solving the convex approximation of the O-PMP with different Rs and bisection search over R, we convert the original O-SRM problem into a sequence of solvable SDPs. Simulation results are provided to verify the secrecy-rate performance improvement of the proposed robust beamforming compared with the existing worst-case design proposed by Li and Ma and the simple non-robust maximum-ratio transmission.
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 investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.
A Gaussian multiple-input single-output (MISO) secrecy channel is considered, where a transmitter is equipped with multiple antennas, and an intended receiver and an eavesdropper each equipped with a single antenna. This paper studies the robust beamforming design in the presence of uncertainty of channel state information (CSI) on the eavesdropper channel. Under the assumption that all possible states of the eavesdropper channel are in a given set, the problem of optimizing the transmit covariance for the worst-case secrecy capacity which is the maximum transmission rate at which the eavesdropper is unable to decode under any channel realization in the set, is cast as a max-min optimization problem. We propose to transfer the max-min problem into a convex optimization problem that can be solved efficiently. The optimal secrecy rate and transmit covariance are expressed in the form of the generalized eigenvalue and eigenvector, the same form as the conventional case of the perfect eavesdropper's CSI, which indicates our results is the generalization of the conventional case.