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.
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.
We in this paper introduce an advanced eavesdropper that aims to paralyze the artificial-noise-aided secure communications. We consider the M-1-2 Gaussian MISO wiretap channel, which consists of a M-antenna transmitter, a single-antenna receiver, and a two-antenna eavesdropper. This type of eavesdropper, by adopting an optimal Grassmann manifold (OGM) filtering structure, can reduce the maximum achievable secrecy rate (MASR) to be zero by using only two receive antennas, regardless of the number of antennas at the transmitter. Specifically, the eavesdropper exploits linear filters to serially recover the legitimate information symbols and intends to find the optimal filter that minimizes the mean-square error (MSE) in estimating the symbols. During the process, a convex semidefinite programming (SDP) problem with constraints on the filter matrix can be formulated and solved. Interestingly, the resulted optimal filters constitute a complex Grassmann manifold on the matrix space. Based on the filters, a novel expression of MASR is derived and further verified to be zero under the noiseless environment. Besides this, an achievable variable region (AVR) that induces zero MASR is presented analytically in the noisy case. Numerical results are provided to illustrate the huge disaster in the respect of secrecy rate.
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.
In this paper, we consider the problem of secure communication in multiuser downlink wiretap networks where there exist a base-station (BS) equipped with multiple antennas, multiple legitimate receivers and a passive eavesdropper. The transmitter simultaneously transmits an information signal and artificial noise (AN) separately to the intended receivers and the eavesdropper, in which way, the secrecy rate at the eavesdropper can be seriously degraded without thinking about it location. Different schemes are studied about the power allocation of the multiple antennas in the BS, namely the average power allocation scheme and the Water-filling scheme. And in the average power allocation scheme, Zero-forcing (ZF) pre-coding scheme is used at the BS to eliminate the internal interference of all the security users. We obtain an analytical closed form expression of an achievable ergodic secrecy rate and use it as the objective function to optimize the power allocation rate between the information signal and the AN in the two schemes.
The artificial noise (AN) scheme is an efficient strategy for enhancing the secrecy rate of a multiple-input-single-output channel in the presence of a passive eavesdropper, whose channel state information is unavailable. Recently, a randomized beamforming scheme has been proposed for deteriorating the eavesdropper's bit-error-rate performance via corrupting its receiving signal by time-varying multiplicative noise. However, the secrecy rate of such a scheme has not been well addressed yet. In this paper, we name it the artificial fast fading (AFF) scheme and provide a comprehensive secrecy rate analysis for it. We show that with this scheme, the eavesdropper will face a noncoherent Ricean fading single-input-multiple-output channel. Although the closed-form secrecy rate is difficult to obtain, we derive an exact expression for the single-antenna-eavesdropper case and a lower bound for the multiantenna-eavesdropper case, both of which can be numerically calculated conveniently. Furthermore, we compare the AFF scheme with the AN scheme and show that their respective superiorities to each other depend on the number of antennas that the transmitter and the eavesdropper possessed, i.e., when the eavesdropper has more antennas than the transmitter does, the AFF scheme achieves a larger secrecy rate; otherwise, the AN scheme outperforms. Motivated by this observation, we propose a hybrid AN-AFF scheme and investigate the power allocation problem, which achieves better secrecy performance further.
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.
We investigate the physical layer security of a multiple-input single-output (MISO) channel in the presence of a multi-antenna passive eavesdropper. Traditionally, artificial noise (AN) scheme is an efficient security strategy without the channel state information (CSI) of the eavesdropper. In this paper, we propose and analyze an efficient security scheme called the artificial fast fading (AFF) scheme. The basic idea is to randomly weight the information symbols at different transmit antennas in a special manner so that the channel of the intended receiver is an AWGN channel while that of the eavesdropper is a fast fading channel. This prevents the eavesdropper obtaining the CSI using the blind channel estimation techniques so that it can only detect the information symbols in a non-coherent way, which greatly reduces the amount of information intercepted. More importantly, we derive the achievable secrecy rate of the sheme and provide a low bound of it, which can be numerically calculated. Compared with the exact secrecy rate of the AN scheme, even the low bound of the AFF scheme is larger, when the eavesdropper has more antennas than the transmitter.