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International Conference on Signal Processing and Communications (SPCOM)

Artificial noise revisited: When Eve has more antennas than Alice

Shuiyin Liu, Yi Hong, Emanuele Viterbo

Published Jul 1, 2014• 11 citations
Publisher

Abstract

We consider secure communications over MIMO wiretap channels, in the presence of a passive eavesdropper with an unlimited number of antennas. In this scenario, we characterize the performance of the artificial noise scheme proposed by Goel et al., and show that non-zero secrecy capacity is available even when the eavesdropper has more antennas than the transmitter. Our results are derived based on the fraction of the transmission power used for artificial noise and the ratio of the channel noise variances of the eavesdropper and the intended receiver. Finally, we investigate the attack option for the eavesdropper to drive the secrecy rate to zero by increasing the number of antennas.

DOI
10.1109/spcom.2014.6983970

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We consider secure communications over MIMO wiretap channels, in the presence of a passive eavesdropper with an unlimited number of antennas. In this scenario, we characterize the performance of the artificial noise scheme proposed by Goel et al., and show that non-zero secrecy capacity is available even when the eavesdropper has more antennas than the transmitter. Our results are derived based on the fraction of the transmission power used for artificial noise and the ratio of the channel noise variances of the eavesdropper and the intended receiver. Finally, we investigate the attack option for the eavesdropper to drive the secrecy rate to zero by increasing the number of antennas.
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.
We consider secure communications over MISO wiretap channels, in the presence of a passive eavesdropper with multiple antennas. In this scenario, an artificial-noise-resistant (ANR) eavesdropping behavior is introduced to invalidate the artificial noise (AN) scheme proposed by Goel et al. This novel eavesdropper, by exploiting the statistical filter derived from the collected signals, can completely eliminate the influence of AN by using only two receive antennas. In particular, the received signals are firstly syphered to eliminate the power influence of AN by a linear weight which is generated from the statistical estimation for the signal covariance matrix. In comparison with the original legitimate signals, the weighted signals are however imposed by a phase difference which can be then erased by a weight vector inferred from the available information at the eavesdropper. Based on the two filtering processes, we derive a novel expression of achievable secrecy rate and give an analytical expression for the zero-secrecy-rate distance of eavesdropper to the transmitter. Finally, we characterize the expression of maximum achievable secrecy rate (MASR) and show that the optimal power allocation strategy under an ANR eavesdropping behavior is transformed into no allocation of transmission power to AN. Numerical results are presented to illustrate the damage caused by the investigated eavesdropping behavior. Interestingly, the consequence of AN elimination is not influenced even under large number of transmit antennas.
Physical layer security in wireless networks has received increasing attention in recent years. In this paper, we consider multiple-input single-output (MISO) fading wiretap channels, where the transmitter utilizes artificial noise-aided precoding (ANaP) transmission strategy to maximize the secrecy capacity of the channel. When the channel state information (CSI) of Eavesdropper's (Eve's) channel is known at Alice, we prove that the optimal ANaP strategy reduces to the conventional precoding strategy, i.e., all the transmit power should be allocated to the precoding of information signal. When the CSI of Eve's channel is unknown at Alice, we find that there exists an optimal power allocation ratio between the information signal and the artificial noise and that this power ratio depends on the number of antennas as well as the available transmit power at Alice. In particular, when the available transmit power at Alice increases or the number of antennas at Alice decreases, more power should be allocated to the artificial noise.
In wireless communication, the transmitter (Alice) can send artificial noise (AN) to interfere with the eavesdropper (Eve). This letter considers the AN MIMO scenario, i.e., both Alice and the legitimate receiver (Bob) are equipped with multiple antennas. A closed-form expression for the lower bound of secrecy capacity is obtained. It is proved that water-filling is the optimal power allocation scheme. An efficient iterative algorithm is proposed to find the optimal power distribution ratio between information and AN so that maximum secrecy capacity can be achieved. Simulation results show that the proposed algorithm converges fast, and multiple antennas can improve the secrecy capacity to some extent compared to the AN MISO case.
Security is one of the major issues in wireless communication system. In a wireless communication system as the transmission of information signal is over the air, eavesdroppers may have easy access to the transmitted data. The conventional network security mainly depends on cryptographic schemes. But as the security level increases, computational complexity will be high and cause complex key management problems. In this paper, the problem of secret communication between two nodes in the presence of a passive eavesdropper is considered. In general, nodes with multiple transmit antenna elements can ensure secure communication using directional antenna. In this paper, MIMO channel with multiple transmit antenna elements utilize fraction of the available power to produce „artificial noise‟ for the improvement of secure communication. The artificial noise is generated by the transmitter in such away that it degrades only the eavesdropper‟s channel. The various performance metrics such as bit error rate, channel capacity, optimal power allocation and secrecy rate were analyzed in the presence of non-colluding and colluding eavesdroppers. The obtained simulation results are compared with the existing work that does not use artificial noise. It is inferred from the results that the proposed work achieves improved secrecy rate than the existing work.
The role of multiple antennas for secure communication is investigated within the framework of Wyner's wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacity-achieving. In addition, we show that in the high signal-to-noise (SNR) ratio regime the penalty for not knowing eavesdropper's channel is small--a simple ``secure space-time code'' that can be thought of as masked beamforming and radiates power isotropically attains near-optimal performance. In the limit of large number of antennas, we obtain a realization-independent characterization of the secrecy capacity as a function of the number βββ: the number of eavesdropper antennas per sender antenna. We show that the eavesdropper is comparatively ineffective when β<1β<1β<1, but that for β≥2β\ge2β≥2 the eavesdropper can drive the secrecy capacity to zero, thereby blocking secure communication to the intended receiver. Extensions to ergodic fading channels are also provided.