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IEEE Transactions on Vehicular Technology

On the Secrecy Rate and Optimal Power Allocation for Artificial Noise Assisted MIMOME Channels

Sangseok Yun, Sanghun Im, Il‐Min Kim, Jeongseok Ha

Published Nov 22, 2017• 31 citations
Publisher

Abstract

This paper considers the artificial noise (AN) scheme, proposed by Goel and Negi for securing wireless communications over multiple-input multiple-output multiantenna eavesdropper (MIMOME) channels. In this paper, we develop a lower bound on the ergodic secrecy rate of the AN scheme and derive an analytic expression of the bound without assuming any asymptotes for system parameters. Thus, the derived bound explicitly elucidates how the system parameters exert influence on the secrecy rate in various cases to some of which the previous work cannot be applied. It will also be shown that the bound is tight over wide combinations of system parameters, and a normalized difference between the bound and secrecy rate vanishes with a growing number of antennas at the transmitter. The derived bound is analytically so amenable that it enables one to not only extend the results of the previous work but also explore untouched aspects of the AN scheme. The bound answers an intriguing question: When is the AN signal beneficial? Besides, it makes possible to study a new important system parameter called the minimum required transmit power for a certain target secrecy rate, which has never been touched before.

DOI
10.1109/tvt.2017.2776338

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IEICE Transactions on Communications•Nov 7, 2024•4 citations
This paper considers the artificial noise (AN) scheme, proposed by Goel and Negi for securing wireless communications over multiple-input multiple-output multiantenna eavesdropper (MIMOME) channels. In this paper, we develop a lower bound on the ergodic secrecy rate of the AN scheme and derive an analytic expression of the bound without assuming any asymptotes for system parameters. Thus, the derived bound explicitly elucidates how the system parameters exert influence on the secrecy rate in various cases to some of which the previous work cannot be applied. It will also be shown that the bound is tight over wide combinations of system parameters, and a normalized difference between the bound and secrecy rate vanishes with a growing number of antennas at the transmitter. The derived bound is analytically so amenable that it enables one to not only extend the results of the previous work but also explore untouched aspects of the AN scheme. The bound answers an intriguing question: When is the AN signal beneficial? Besides, it makes possible to study a new important system parameter called the minimum required transmit power for a certain target secrecy rate, which has never been touched before.
This paper studies a secure communication over multiple-input multiple-output multi-antenna eavesdropper (MIMOME) channels which consist of legitimate parities, namely a transmitter and receiver, equipped with multi-antennas and a passive eavesdropper with multi-antennas. For securing the communication between the legitimate parties, we consider an artificial noise (AN) scheme in which the legitimate transmitter sends its secret messages and AN signal together. Meanwhile, it is assumed that the legitimate receiver has a full-duplex capability which enables it to capture the secret message from the transmitter and simultaneously generate a jamming signal to strengthen security. While there have been studies on similar setups, most of them focus on the design of the jamming signal with the assumption of full channel-state information (CSI) and/or system parameter optimization based on numerical evaluations. On the contrary, in this work, we instead introduce a tight lower bound on an achievable ergodic secrecy rate as a versatile analytic tool and derive a closed-form expressions for the bound. To confirm the analytic results, we carry out numerical evaluations of the ergodic secrecy rate which are compared with the proposed lower bound.
The artificial noise (AN) scheme, proposed by Goel and Negi, is being considered as one of the key enabling technology for secure communications over multiple-output multiple-input wiretap channels. However, the decrease in secrecy rate due to the increase in the number of Eve's antennas is not well understood. In this paper, we develop an analytical framework to characterize the secrecy rate of the AN scheme as a function of Eve's SNR, Bob's SNR, the number of antennas in each terminal, and the power allocation scheme. We first derive a closed-form expression for the average secrecy rate. We then derive a closed-form expression for the asymptotic instantaneous secrecy rate with large number of antennas at all terminals. Finally, we derive simple lower and upper bounds on the average/instantaneous secrecy rate that provide a tool for the system design.
This paper investigates the power allocation problem for artificial noise (AN) secure precoding systems, and proposes closed-form solutions for maximizing the achievable secrecy rate. It is assumed that the transmitter knows the full channel information at the legitimate receiver, and knows only the statistics of the channel information at the eavesdropper. Lower bounds are derived for the secrecy rates in multiple-input single-output channels with single or multiple eavesdroppers and multiple-input multiple-output channels with multiple eavesdroppers. When the number of transmit antennas is sufficiently large, the bounds are tight, and closed-form solutions can be derived from these bounds. The analytical results suggest simple and yet informative solutions as follows: Let the numbers of receive antennas at the legitimate receiver and at the eavesdropper beNrN_{r}Nr​andNr,eN_{r,e}Nr,e​, respectively. The system should distributeNr,e/(Nr+Nr,e)N_{r,e}/(N_{r}+N_{r,e})Nr,e​/(Nr​+Nr,e​)of the power to AN in the high SNR regime, and distribute zero power to AN in the low SNR regime; the rate loss due to the eavesdropper is−Nrlog⁡(Nr/(Nr+Nr,e))−Nr,elog⁡(Nr,e/(Nr+Nr,e))-N_{r}\log(N_{r}/(N_{r}+N_{r,e}))-N_{r,e}\log(N_{r,e}/(N_{r}+N_{r,e}))−Nr​log(Nr​/(Nr​+Nr,e​))−Nr,e​log(Nr,e​/(Nr​+Nr,e​))bits/sec/Hz in the high SNR regime and nearly negligible in the low SNR regime. The derived results also show that equal power and water-filling power allocations lead to similar solutions and rate loss. Simulation results corroborate the theoretical results.
This correspondence paper studies how correlation of the wiretap channel affects the secrecy rate of the artificial noise (AN) scheme. To this end, we first develop a simple but tight lower bound on the ergodic secrecy rate of the AN scheme on correlated multiple-input single-output wiretap channels. Then, utilizing the derived bound, we investigate the influence of correlation on the secrecy rate, which explicitly manifests how the channel correlation affects the optimal power allocation. Ultimately, this paper answers two fundamental questions: when is the AN signal beneficial? and how much power should be allocated for the AN signal to achieve a higher ergodic secrecy rate? in terms of channel correlation.
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.
Multiple antennas aided wireless communications under dense urban environments often suffer from keyhole effect, which leads to rank deficiency. Secrecy performance of artificial noise (AN) aided multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) keyhole channels is investigated in this paper. Expressions of the asymptotic lines of some vital secrecy metrics are obtained in terms of secrecy outage probability (SOP) and average secrecy rate (ASR) in the high signal-to-noise ratio (SNR) regime, and are verified by Monte-Carlo simulations. It is shown that the secrecy performance is influenced by the antenna numbers at the transceiver and the eavesdropper. Most importantly, by comparing the scheme aided with AN to that without AN, it is found that AN plays a great role in enhancing security of MIMOME keyhole channels.