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Mathematical Problems in Engineering

Outage Constraint Robust Cooperative Beamforming and Jamming Design for Secure AF Relay Networks

Jinxin Zhu, Jun Shao

Published Nov 5, 2021• 1 citation
Publisher

Abstract

This paper investigates a joint robust scheme in a secrecy relay network where distributed relays perform cooperative beamforming and a friendly jammer transmits jamming signal to enhance the information security. Specifically, we consider the outage constraint secrecy rate maximization design with imperfect channel state information. Through semidefinite relaxation and one-dimensional search, we propose a two-layer optimization method to solve the nonconvex problem. In addition, the Bernstein-type inequality and large deviation inequality are utilized to convert the probabilistic constraint. Simulation results demonstrate the performance of the proposed design.

DOI
10.1155/2021/5919617

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This paper investigates the physical-layer security issue of an amplify-and-forward (AF) relay network. We propose a joint cooperative beamforming (CB) and cooperative jamming (CJ) design that is robust to the imperfect channel state information (CSI) of the multiple multiantenna eavesdroppers. The objective is the worst-case secrecy rate maximization (WCSRM). Based on the inner convex approximation and semidefinite relaxation (SDR) technique, the original nonconvex problem is transformed into a sequence of approximate convex problems, which can be solved conveniently. The proposed robust design guarantees to converge to a Karush-Kuhn-Tucker (KKT) solution and is efficient in computational complexity. Furthermore, we prove that SDR always has a rank-1 solution, which identifies that SDR is tight. Simulations demonstrate the validity of the proposed strategy.
This paper studies robust transmit design to maximize the worst-case secrecy rate in AF networks under both total and individual relay power constraints. Channel state information (CSI) in the network is assumed to be perfectly known except for that associated with the eavesdroppers whose imperfection is modeled as deterministic bounded errors. To use the power at the relay nodes more efficiently, a joint cooperative relaying and jamming scheme is considered. Through some matrix manipulations, we recast the original nonconvex optimization problem as a sequence of semidefinite programs (SDPs), which enables us to obtain the optimal relay weights and the optimal covariance matrix of the jamming signal. Numerical results are presented to show the efficacy of the proposed scheme.
This letter studies the secure cooperative transmission for an amplify-and-forward (AF) relay network in the presence of multiple multi-antenna eavesdroppers. Since the perfect channel state information (CSI) of the eavesdroppers are not available, we propose a robust joint distributed beamforming and artificial noise scheme to maximize the worst-case secrecy rate of the network, under the total power constraint of all the relay nodes. With the semidefinite relaxation (SDR) technique, the design can be solved by a one-dimension search which involves a sequence of semidefinite programming (SDP). Simulation results demonstrate the validity of the proposed strategy.
In this paper, we study robust joint beamforming and cooperative jamming (CJ) in a secure decode-and-forward (DF) relay system in the presence of multiple eavesdroppers, in which a multi-antenna DF relay employs transmit beamforming to help the source deliver information to the destination and simultaneously generates Gaussian artificial noise to confuse these eavesdroppers. We assume that all the channel state information (CSI) is imperfectly known at the relay subject to norm-bounded CSI errors. Our objective is to maximize the achievable secrecy rate at the destination by jointly optimizing the transmit beamforming vector of information signals and the covariance matrix of jamming signals at the relay subject to its total transmit power constraint. Although this problem is non-convex and in general difficult to be solved, we obtain its optimal solution via the technique of semi-definite relaxation (SDR) together with a one-dimensional (1-D) search. Specifically, we prove that the SDR is tight for the problem of our interest. Finally, numerical results are provided to validate our proposed scheme.
This paper investigates the secure transmit design of a cooperative hybrid satellite-terrestrial relay network (HSTRN). Assuming that amplify-and-forward (AF) protocol is adapted at terrestrial relays, and global channel state information (CSI) is known, we propose two schemes through jointly optimizing the relay beamforming vector and the covariance matrix of artificial noise (AN) to maximize the secrecy rate. In the first scheme, our design is based on secrecy rate maximization and optimal solution is obtained by following the idea of two-level optimization which is composed of one-dimensional search technique and semidefinite relaxation (SDR) technique. In the second scheme, to reduce the computation, we assume that there is no information leakage to all eavesdroppers, and the solution of this problem is obtained by solving one semidefinite programing (SDP) only with SDR. Numerical results are provided to demonstrate the performance of different designs and the benefit of AN.