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arXiv:1006.5938 · IEEE Transactions on Vehicular Technology

Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation

Xiangyun Zhou, Matthew R. McKay

Published Jul 29, 2010• 544 citations
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Abstract

We consider the problem of secure communication with multiantenna transmission in fading channels. The transmitter simultaneously transmits an information-bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near-optimal strategy for the case of noncolluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the SNR, above which, the achievable secrecy rate is positive and shows that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.

DOI
10.1109/tvt.2010.2059057

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We consider the problem of secure communication with multiantenna transmission in fading channels. The transmitter simultaneously transmits an information-bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near-optimal strategy for the case of noncolluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the SNR, above which, the achievable secrecy rate is positive and shows that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.
We consider the problem of secure communication in wireless fading channels in the presence of non-colluding passive eavesdroppers. The transmitter has multiple antennas and is able to simultaneously transmit an information bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form lower bound for secrecy capacity, which is used as the objective function to optimize transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple and generic strategy which achieves near optimal capacity performance. We also find that adaptive power allocation based on each channel realization provides no or insignificant capacity improvement over equal power allocation.
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.
We consider the problem of secure communication in the multiuser downlink with an external eavesdropper. The transmitter simultaneously transmits concurrent information signals to the users and an artificial noise (AN) to the eavesdropper. We derive a closed-form expression for the secrecy sum-rate in the large system limit and use it as the objective function to optimize the power allocation between the information signals and the AN to maximize the secrecy sum-rate. We obtain a simple approximation for the optimal power allocation in the high signal-to-noise ratio regime, which proves to be a generic and near-optimal strategy. Analytical and simulation results show that more power needs to be allocated to AN if the system serves fewer users and the eavesdropper has more antennas.
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average signal-to-noise ratio (SNR) goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Overall, channel fading has a positive impact on the secrecy capacity and rate adaptation, based on the main channel CSI, is critical in facilitating secure communications over slow fading channels.
We study secure multi-antenna transmission with limited feedback from the intended receiver and no feedback from the malicious eavesdropper. Our system uses the artificial-noise-aided beamforming approach to enhance secrecy, considering slow fading channels with outage constraints on the reliability performance of legitimate communication and the secrecy performance against eavesdropping. Our analytical results provide conditions on the minimum number of feedback bits and the minimum strength of the intended channel for making secure transmission possible. We observe that strengthening the secrecy outage constraint puts higher requirements on the number of feedback bits and the strength of the intended channel. To maximize the achievable secrecy rate, the optimal transmit power allocation between the information signal and the artificial noise is also derived in closed form.
Utilizing artificial noise (AN) is a good means to guarantee security against eavesdropping in a multi-input multi-output system, where the AN is designed to lie in the null space of the legitimate receiver's channel direction information (CDI). However, imperfect CDI will lead to noise leakage at the legitimate receiver and cause significant loss in the achievable secrecy rate. In this paper, we consider a delayed feedback system, and investigate the impact of delayed CDI on security by using a transmit beamforming and AN scheme. By exploiting the Gauss-Markov fading spectrum to model the feedback delay, we derive a closed-form expression of the upper bound on the secrecy rate loss, where Nt= 2. For a moderate number of antennas where Nt>; 2, two special cases, based on the first-order statistics of the noise leakage and large number theory, are explored to approximate the respective upper bounds. In addition, to maintain a constant signal-to-interference-plus-noise ratio degradation, we analyze the corresponding delay constraint. Furthermore, based on the obtained closed-form expression of the lower bound on the achievable secrecy rate, we investigate an optimal power allocation strategy between the information signal and the AN. The analytical and numerical results obtained based on first-order statistics can be regarded as a good approximation of the capacity that can be achieved at the legitimate receiver with a certain number of antennas, Nt. In addition, for a given delay, we show that optimal power allocation is not sensitive to the number of antennas in a high signal-to-noise ratio regime. The simulation results further indicate that the achievable secrecy rate with optimal power allocation can be improved significantly as compared to that with fixed power allocation. In addition, as the delay increases, the ratio of power allocated to the AN should be decreased to reduce the secrecy rate degradation.