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IEEE Transactions on Wireless Communications

A Robust Beamforming Approach to Guarantee Instantaneous Secrecy Rate

Jinho Choi

Published Sep 25, 2015• 11 citations
Publisher

Abstract

We consider a well-known beamforming approach that induces jamming signals to avoid eavesdropping from a transmitter equipped with an antenna array in this paper. With this beamforming, which is called masked beamforming, in order to guarantee a certain instantaneous secrecy rate, we formulate robust beamforming problems with a constraint that deals with the eavesdropper channel's uncertainty and find the solutions. Unlike a guaranteed ergodic secrecy rate, this guaranteed instantaneous secrecy rate allows us to use codes of short codewords for secure communications with masked beamforming over slow-fading channels. In addition, since the optimal solutions are found in closed form, we do not need to resort to any convex optimization solvers.

DOI
10.1109/twc.2015.2482494

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We consider a well-known beamforming approach that induces jamming signals to avoid eavesdropping from a transmitter equipped with an antenna array in this paper. With this beamforming, which is called masked beamforming, in order to guarantee a certain instantaneous secrecy rate, we formulate robust beamforming problems with a constraint that deals with the eavesdropper channel's uncertainty and find the solutions. Unlike a guaranteed ergodic secrecy rate, this guaranteed instantaneous secrecy rate allows us to use codes of short codewords for secure communications with masked beamforming over slow-fading channels. In addition, since the optimal solutions are found in closed form, we do not need to resort to any convex optimization solvers.
In order to avoid eavesdropping, beamforming can be used not only to induce artificial noise or jamming signal to an eavesdropper, but also transmit desired signals to a legitimate user (or sensor) from an access point (AP) equipped with an antenna array. In this paper, with proper power allocation, we show that beamforming under a rich scattering environment can guarantee a certain secrecy rate with an overwhelming probability. This approach becomes attractive for slow fading channels where the ergodic secrecy rate cannot be used to decide a target secrecy rate.
For physical layer security with multiple antennas over wireless channels, we consider an artificial noise-aided secure beamforming system. A transmitter can send the confidential information to the legitimate user more securely without eavesdropping when an artificial jamming signal interfering eavesdroppers is transmitted with the confidential information signal. The transmitter splits its transmit power for both the information and jamming signals with a power splitting factor. Under such a system model, we investigate the impacts on secrecy performance of a power splitting factor, the numbers of antennas and eavesdroppers, and noise variance at the legitimate receivers and eavesdroppers by analyzing the expected secrecy rate. The optimal power splitting factor and limiting secrecy rate with large number of antennas are also derived. Moreover, we examine the expected secrecy rate loss caused by channel variation over time. It is shown that the secrecy rate loss is independent of system parameters like a power splitting factor, the numbers of antennas and eavesdroppers in a high signal to interference plus noise ratio (SINR) region. In a low SINR region, on the other hand, the secrecy rate loss changes with system parameters. Simulation results verify these observations on ergodic secrecy rate and its loss due to time-varying channels.
This paper studies masked beamforming schemes for secure communication in broadcast multiple-input multiple-output (MIMO) systems with a passive multiple-antenna eavesdropper. Assuming no information about the eavesdropper is available at the transmitter, we aim to maximize the transmit power of the artificial noise while meeting mean square error (MSE) constraints at the legitimate receivers and the total power constraint at the transmitter. Based on imperfect channel state information (CSI) of the legitimate receivers at the transmitter, we present a worst-case robust masked beamforming algorithm. By exploiting alternating iterative optimization, the proposed algorithm recasts the non-convex optimization problem as two semidefinite program (SDP) based subproblems, which are solvable with interior-point methods. Simulation results are provided to illustrate the secrecy performance of the proposed algorithm.
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.
This paper considers the secure communication via combining the artificial noise with the masked beamforming scheme. In this scenario, the transmitter is equipped with multi-antenna while each of the eavesdroppers is equipped with only one antenna, and the legitimate receiver has a receiving antenna and a transmitting antenna, respectively. The transmitter simultaneously transmits a beamformed secret information-bearing signal to a legitimate receiver and artificial noise (AN) to the eavesdroppers. The legitimate receiver sends the AN to confuse the eavesdropper while receiving the desired signal from the transmitter. We compare the proposed scheme that combining the AN with masked beamforming with no beamforming vector scheme, and derive that the combined strategy obviously improved the secrecy rate.
In this paper, we investigate the physical layer security of a full-duplex base station (BS)-aided system in the worst case, where an uplink transmitter (UT) and a downlink receiver (DR) are equipped with a single antenna, while a powerful eavesdropper is equipped with multiple antennas. For securing the confidentiality of signals transmitted from the BS and UT, an artificial noise (AN)-aided secrecy beamforming scheme is proposed, which is robust to the realistic imperfect state information of both the eavesdropping channel and the residual self-interference channel. Our objective function is that of maximizing the worst-case sum secrecy rate achieved by the BS and UT, through jointly optimizing the beamforming vector of the confidential signals and the transmit covariance matrix of the AN. However, the resulting optimization problem is non-convex and non-linear. In order to efficiently obtain the solution, we transform the non-convex problem into a sequence of convex problems by adopting the block coordinate descent algorithm. We invoke a linear matrix inequality for finding its Karush-Kuhn-Tucker (KKT) solution. In order to evaluate the achievable performance, the worst-case secrecy rate is analytically derived. Furthermore, we construct another secrecy transmission scheme using the projection matrix theory for performance comparison. Our simulation results show that the proposed robust secrecy transmission scheme achieves substantial secrecy performance gains, which verifies the efficiency of the proposed method.