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arXiv:1601.01183 · IEEE Transactions on Vehicular Technology

Optimal Power Allocation for Artificial Noise Under Imperfect CSI Against Spatially Random Eavesdroppers

Tong-Xing Zheng, Hui-Ming Wang

Published Dec 29, 2015• 88 citations
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Abstract

In this paper, we study the secure multiantenna transmission with artificial noise (AN) under imperfect channel state information (CSI) in the presence of spatially randomly distributed eavesdroppers. We derive the optimal solutions of the power allocation between the information signal and the AN for minimizing the secrecy outage probability (SOP) under a target secrecy rate and for maximizing the secrecy rate under an SOP constraint, respectively. Moreover, we provide an interesting insight that channel estimation error affects the optimal power allocation strategy in opposite ways for the two given objectives. When the estimation error increases, more power should be allocated to the information signal if we aim to decrease the rate-constrained SOP, whereas more power should be allocated to the AN if we aim to increase the SOP-constrained secrecy rate.

DOI
10.1109/tvt.2015.2513003

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In this paper, we study the secure multi-antenna transmission with artificial noise (AN) under slow fading channels coexisting with randomly located eavesdroppers. We provide a comprehensive secrecy performance analysis and system design/optimization under a stochastic geometry framework. Specifically, we first evaluate the secrecy outage performance, and derive a closed-form expression for the optimal power allocation ratio of the information signal power to the total transmit power that minimizes the secrecy outage probability (SOP). Subject to a SOP constraint, we then propose a dynamic parameter transmission scheme (DPTS) and a static parameter transmission scheme (SPTS) to maximize secrecy throughput, and provide explicit solutions on the optimal transmission parameters, including the wiretap code rates, the on-off transmission threshold and the power allocation ratio. Our results give new insight into secure transmission designs. For example, secrecy rate is a concave function of the power allocation ratio in DPTS, and AN plays a significant role under SOP constraints and in dense eavesdropper scenarios. In SPTS, transmission probability is a concave function of the power allocation ratio, and secrecy throughput is a quasi-concave function of the secrecy rate. Numerical results are demonstrated to validate our theoretical analysis.
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.
This paper investigates the power allocation problem for secure multiple-input single-output transmission with the injection of artificial noise (AN), in the presence of an unknown eavesdropper (Eve). Two power allocation schemes, the optimal adaptive power allocation (OAPA) and suboptimal fixed power allocation (SFPA) schemes, are proposed to enhance the physical layer security of the considered system. Since the noise power at Eve is unknown, both power allocation schemes are designed for the worst-case scenario in which the noise power at Eve is assumed to be zero, aiming to minimize the secrecy outage probability (SOP). To characterize the performance of the proposed power allocation schemes, approximate closed-form expressions for average SOP under a preset noise power level are derived by applying Gauss-Chebyshev quadrature. We also address the worst-case secrecy outage performance for the proposed OAPA and SFPA schemes. Our analytical and numerical results show that, compared with the exhaustive search method that requires Eve’s prior information, the proposed OAPA scheme exhibits comparable secrecy outage performance without Eve’s prior information. Additionally, the SFPA scheme, also without Eve’s prior information, is capable of achieving almost the same worst-case SOP as the OAPA scheme, with a much lower implementation complexity.
This paper investigates power allocation problem for secure multiple-input single-output transmission with artificial noise (AN). With an unknown eavesdropper, we propose an optimal adaptive power allocation scheme, which adaptively adjust the power allocation factor (PAF) according to the instantaneous channel state information of the legitimate channel. On this basis, we derive a closed-form expression for the optimal PAF aiming to minimize the secrecy outage probability (SOP). A suboptimal fixed power allocation scheme is also proposed to reduce system complexity. Moreover, exact closed-form expressions of SOP for both schemes are also obtained.
We analyze and optimize the use of artificial noise (AN) for a predefined secrecy rate in wiretap channels with a multi-antenna transmitter, a single-antenna receiver, and a single-antenna eavesdropper. We derive a new closed-form expression for the secrecy outage probability that is independent of the channel realization. Based on this expression, we first optimize the power allocation between the information signal and the AN signal such that the secrecy outage probability is minimized. We then optimize jointly the power allocation and secrecy rate such that the secrecy throughput is maximized. As demonstrated by our analysis, the minimum secrecy outage probability requires more power to be allocated to the AN signal when the quality of the main channel quality or the eavesdropper's channel improves.
The secrecy rate maximization with the artificial noise (AN) aided beamforming for the multipel-input-single-output (MISO) wiretap channel is addressed in this paper under the constraint of secrecy outage probability. The channel state information (CSI) of the main channel is assumed to be perfectly known while the CSI of the eavesdropper is modeled as a complex Gaussian random vector. The generalized AN scheme where the AN is not constrained to be orthogonal to the information-bearing signal is considered. The complete solution to the maximum achievable secrecy rate and the corresponding optimal power allocation between the information-bearing signal and the AN is obtained without making any approximation of the secrecy outage probability constraint. The result shows that the optimal AN is always orthogonal to the information-bearing signal.