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IEEE Wireless Communications Letters

Robust Coordinated Beamforming for Secure MISO Interference Channels with Bounded Ellipsoidal Uncertainties

Jiqing Ni, Zesong Fei, Kai‐Kit Wong, Chengwen Xing, Jingming Kuang, Kin‐Fai Tong

Published Aug 1, 2013• 15 citations
Publisher

Abstract

This letter addresses the robust optimization problem of downlink coordinated beamforming over the multiple-input single-output (MISO) interference channel with confidential messages (IFC-CM) exploiting imperfect channel state information (CSI) at the transmitters. Our aim is to minimize the total transmitted power subject to the worst-case individual signal-to-interference-plus-noise-ratio (SINR) and equivocation rates. To model the imperfect CSI, bounded ellipsoidal uncertainties for channel vector and covariance are both considered. By deriving the equivalent forms for the SINR and secrecy constraints, the worst-case robust problem can be reformulated as a semi-definite programming (SDP) with the help of rank relaxation. Simulation results show the effectiveness of the proposed algorithm.

DOI
10.1109/wcl.2013.050613.130177

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This letter addresses the robust optimization problem of downlink coordinated beamforming over the multiple-input single-output (MISO) interference channel with confidential messages (IFC-CM) exploiting imperfect channel state information (CSI) at the transmitters. Our aim is to minimize the total transmitted power subject to the worst-case individual signal-to-interference-plus-noise-ratio (SINR) and equivocation rates. To model the imperfect CSI, bounded ellipsoidal uncertainties for channel vector and covariance are both considered. By deriving the equivalent forms for the SINR and secrecy constraints, the worst-case robust problem can be reformulated as a semi-definite programming (SDP) with the help of rank relaxation. Simulation results show the effectiveness of the proposed algorithm.
ABSTRACT In this paper, we address the optimization problems of downlink coordinated beamforming over theK‐user multiple‐input single‐output interference channel with confidential messages. Our design objective is to minimise the total transmit power subject to the constraints of individual signal‐to‐interference plus noise ratio and equivocation rates. For the case with perfect channel state information (CSI), by deriving the equivalent forms for the signal‐to‐interference plus noise ratio and the secrecy constraints, the optimization problem is reformulated as a second‐order cone programme problem. Then, an optimal distributed algorithm using the partial Lagrangian duality is discussed. In addition we extend the analysis to the imperfect CSI scenario with bounded ellipsoidal errors, the centralised algorithm has been proposed by solving a semi‐definite programme with the help of rank relaxation, whereas the distributed robust algorithm is devised by using ADMM. Finally, the simulation results have shown that with perfect CSI, the centralised and distributed algorithms have nearly the same performance, but in the case of imperfect CSI, the centralised algorithm shows a slightly better performance. Copyright © 2014 John Wiley & Sons, Ltd.
This paper investigates robust beamforming techniques for a multiple-input-single-output (MISO) secrecy transmission with a cooperative jammer by incorporating two different types of channel uncertainties. We solve the worst-case signal-to-interference-plus-noise ratio (SINR) maximization of the legitimate user with the worst-case SINR constraint of the eavesdropper and the transmit power constraint. The original problems are not convex in terms of transmit covariance matrices, and cannot be solved directly. Thus, we present two approaches to convert these problems into semidefinite programmings (SDPs) by exploiting S-Procedure and deriving the corresponding Lagrangian dual problem. Numerical results are provided to validate the performance of the proposed robust schemes.
In this letter, we investigate the secure beamforming design for multiuser multiple-input single-output interference channel with an eavesdropper. The robust secrecy rate optimization problem is studied with the imperfect channel state information. We consider the beamforming design to maximize the minimum worst case secrecy rate subject to the transmit power constraints with norm-bounded channel uncertainty. The problem is non-convex and hard to solve. We propose an effective method to reformulate this non-convex problem as a series of tractable convex program problems with linear matrix inequality and second-order cone constraints by exploiting the conservative approximation and the sequential convex approximation methods. The simulation results demonstrate the effectiveness of the proposed algorithm.
In this paper, we investigate multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) broadcast channels with confidential messages (BCC) scenario, in which a multiple-antenna transmitter simultaneously transmits confidential messages and power to multiple single-antenna receivers. Considering the imperfect channel state information (CSI), we study the joint optimization of transmit beamforming vectors, covariance of artificial noise, and power splitting ratios so as to minimize the total transmit power while satisfying the worst-case conservative secrecy rate and energy harvesting constraints. The original optimization is non-convex and intractable in general. To handle this challenge, in this paper, we first derive the exact upper or lower bounds of the constraints in original optimization problem by using the Lagrangian approach, and then convert the corresponding non-convex problem into a convex one with the aid of the rank relaxation technique. Finally, we provide simulation results to illustrate the robustness of the proposed design.
In this paper, we study beamforming techniques for secrecy with worst case signal-to-interference-plus-noise ratio (SINR) guarantees in cooperative communications with imperfect channel state information (CSI). The worst case SINRs are the minimum SINR at the intended destination and the maximum SINR at the eavesdroppers. We consider a norm bounded CSI error model. With the available imperfect channel estimates, we design beamformers such that the minimum SINR receivable by the intended destination is above a certain threshold, while the maximum value of SINRs receivable at the eavesdroppers are below another lower threshold. We consider amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes. The relays do the worst case transmit beamforming and injection of artificial noise (AN). We jointly optimize the beamformers and the AN for the AF and DF schemes subject to the worst case SINR constraints at the destination and the eavesdroppers. We solve the corresponding optimization problems as semi-definite programming (SDP) problems by rank relaxation and S-procedure. Numerical results show that AN injection at the relays significantly reduces the average total transmit power required to meet the worst case SINR constraints, and improves the solution feasibility of the optimization problems.
This paper addresses robust designs of secure simultaneous wireless information and power transfer for multiple-input single-output (MISO) multiuser systems. By using a bounded uncertainty model for the channel state information (CSI) from transmitters to legitimate receivers and under the assumption of only available statistic knowledge of the CSI to eavesdroppers, we consider the robust designs with both worst-case and chance-constrained optimizations. To jointly optimize transmit beamforming vectors and power splitting factors, we formulate three problems aiming at minimizing the system power, maximizing the sum secrecy rate, and maximizing the minimal secrecy rate, respectively, subject to both energy harvesting and secrecy outage constraints. These problems are intractable in their original forms due to the CSI models and their non-convexity. To reach computationally efficient solutions, we first rewrite the original problems by semi-definite relaxation, then transform the CSI uncertainty related constraints by S-procedure, and finally approximate the non-convex constraints by the first-order Taylor expansion. By the reformulations, we present iterative successive convex approximation algorithm for approaching the optimized solutions. Simulation results under various setups of system parameters are provided to examine the system performance and validate the effectiveness of the proposed schemes.