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arXiv:1202.5830 · IEEE Journal on Selected Areas in Communications

On Secrecy Rate of the Generalized Artificial-Noise Assisted Secure Beamforming for Wiretap Channels

Pin-Hsun Lin, Szu-Hsiang Lai, Shih‐Chun Lin, Hsuan-Jung Su

Published Aug 30, 2013• 188 citations
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Abstract

In this paper we consider the secure transmission with multiple-input, single-output, single-antenna eavesdropper (MISOSE) in fast fading channels where the transmitter knows perfect legitimate channel state information but only the statistics of the eavesdropper's channel. For the MISOSE channels, the artificial noise assisted beamforming proposed by Goel and Negi is a promising technique, where the artificial noise is imposed on the null space of the legitimate channel to disrupt the eavesdropper's reception. Here we propose a generalized artificial noise scheme which allows the injection of the artificial noise to the legitimate channel. Although the generalized artificial noise may cause the leakage of artificial noise at the legitimate receiver, the secrecy rate can still be improved since the covariance matrix of it is more flexible than the heuristic one selected by Goel and Negi. To fully characterize the proposed scheme, we investigate the optimization of its secrecy rate. We first derive the conditions under which the beamformers of the message bearing signal and the generalized artificial noise being the same is optimal. Based on this choice, the complicated secrecy rate optimization problem over the covariance matrices of the message-bearing signal and the generalized artificial noise can be reduced to a much simpler power allocation problem. We also develop an efficient algorithm to solve this non-convex power allocation problem. Numerical results show that our generalized artificial noise scheme outperforms Goel and Negi's heuristic selection, especially in the near eavesdropper settings. In particular, with the aid of the proposed scheme, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the network.

DOI
10.1109/jsac.2013.130907

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In this paper we consider the secure transmission with multiple-input, single-output, single-antenna eavesdropper (MISOSE) in fast fading channels where the transmitter knows perfect legitimate channel state information but only the statistics of the eavesdropper's channel. For the MISOSE channels, the artificial noise assisted beamforming proposed by Goel and Negi is a promising technique, where the artificial noise is imposed on the null space of the legitimate channel to disrupt the eavesdropper's reception. Here we propose a generalized artificial noise scheme which allows the injection of the artificial noise to the legitimate channel. Although the generalized artificial noise may cause the leakage of artificial noise at the legitimate receiver, the secrecy rate can still be improved since the covariance matrix of it is more flexible than the heuristic one selected by Goel and Negi. To fully characterize the proposed scheme, we investigate the optimization of its secrecy rate. We first derive the conditions under which the beamformers of the message bearing signal and the generalized artificial noise being the same is optimal. Based on this choice, the complicated secrecy rate optimization problem over the covariance matrices of the message-bearing signal and the generalized artificial noise can be reduced to a much simpler power allocation problem. We also develop an efficient algorithm to solve this non-convex power allocation problem. Numerical results show that our generalized artificial noise scheme outperforms Goel and Negi's heuristic selection, especially in the near eavesdropper settings. In particular, with the aid of the proposed scheme, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the network.
We consider secure transmission in fading channels with only the statistics of the eavesdropper's channel state information known at the transmitter. We optimize the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi using heuristically selected AN and beamforming directions. We find that Goel and Negi's AN selection is strictly sub-optimal. On the contrary, one may inject AN to the beam direction of the message to improve the secrecy rate performance. We prove that for a multiple-input, single-output, single-antenna-eavesdropper system, the optimal transmission scheme is a beamformer which is aligned to the direction of the legitimate channel. We then prove that, for the part of the AN in the null space of the legitimate channel, uniform power allocation is optimal. We also provide the necessary condition for the proposed AN selection to be optimal. Simulation results show that our AN selection outperforms Goel and Negi's, especially when the legitimate user's channel quality is poor. In particular, when AN assisted beamforming is applied, the region with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of secure networks.
In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.
In this paper we consider secure transmission for the multiple-input, multiple-output, single-antenna-eavesdropper systems with perfect information of the main channel and only the statistics of the eavesdropper's channel state information known at the transmitter. We adopt the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi with the limitation that the AN must be allocated in the null space of the main channel. By removing this limitation, we study the rate optimization problems over the covariance matrices of the signal and the AN. After exploring the structure of the optimal solutions, we show that the original optimization problem can be simplified as a much simpler power allocation problem. Our results show that to improve the rate performance, one may allocate the power of the AN in the directions of the right singular vectors of the main channel. Thus Goel and Negi's AN selection is strictly sub-optimal. Moreover, our simulations show that when the main channel has no null space, the rate performance of our optimized signaling outperforms that of Goel and Negi's significantly.
This paper studies the design of artificial-noise-aided (AN-aided) secure transmission in slow-fading multiple-input–single-output (MISO) channels. We consider the scenario where a multiantenna transmitter sends messages to a single-antenna legitimate receiver in the presence of multiple noncolluding single-antenna eavesdroppers. It is assumed that the transmitter possesses instantaneous channel state information (CSI) of the legitimate channel but only the statistics of the eavesdropper's channels. Instead of adopting the well-known adaptive and nonadaptive transmission schemes, we consider the newly proposed semiadaptive scheme, in which the communication rate is fixed, and the secrecy rate is adaptively adjusted according to the legitimate channel's CSI. Compared with the adaptive scheme, a major advantage of fixing the communication rate is that the codebook can be fixed, and thus, the encoder and decoder designs are both simplified. We consider a generalized AN-aided beamforming structure, which allows arbitrary beamforming direction. Specifically, we focus on the problem of maximizing the secrecy throughput on the premise of reliable and secure transmission. By solving this problem, the optimal beamforming direction, power-allocation parameters, and secrecy rate are derived in closed form, and the optimal communication rate is obtained numerically. Finally, simulation results are presented to show the performance of the semiadaptive scheme.
This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.
New insights into the role of artificial noise in securing communication in a Gaussian multi-antenna fading wiretap channel are presented. An appropriate secrecy-outage-based optimization framework is developed for the Multiple-Input Single-Output Single-Eavesdropper (MISOSE) case to measure the performance of artificial noise. It is assumed that only the legitimate receiver's instantaneous channel state information and the average statistics of the eavesdropper's channel are available at the transmitter. The optimization is based on maximizing the effective secret-message rate constrained by a given maximum secrecy outage criterion. Under this framework, a fundamental investigation is conducted into whether it is worthwhile for the transmitter to allocate any of its available power for artificial noise. By numerically solving the optimization problem, it is demonstrated that there are: (i) scenarios where artificial noise does indeed give significant gains in the secret-message rate, and (ii) scenarios where any amount of power allocation to artificial noise is wasteful in view of the overall performance.