We consider secure transmission in fading channels with only the statistics of the eavesdropper's channel state information known at the transmitter. We optimize the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi using heuristically selected AN and beamforming directions. We find that Goel and Negi's AN selection is strictly sub-optimal. On the contrary, one may inject AN to the beam direction of the message to improve the secrecy rate performance. We prove that for a multiple-input, single-output, single-antenna-eavesdropper system, the optimal transmission scheme is a beamformer which is aligned to the direction of the legitimate channel. We then prove that, for the part of the AN in the null space of the legitimate channel, uniform power allocation is optimal. We also provide the necessary condition for the proposed AN selection to be optimal. Simulation results show that our AN selection outperforms Goel and Negi's, especially when the legitimate user's channel quality is poor. In particular, when AN assisted beamforming is applied, the region with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of secure networks.
We consider secure transmission in fading channels with only the statistics of the eavesdropper's channel state information known at the transmitter. We optimize the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi using heuristically selected AN and beamforming directions. We find that Goel and Negi's AN selection is strictly sub-optimal. On the contrary, one may inject AN to the beam direction of the message to improve the secrecy rate performance. We prove that for a multiple-input, single-output, single-antenna-eavesdropper system, the optimal transmission scheme is a beamformer which is aligned to the direction of the legitimate channel. We then prove that, for the part of the AN in the null space of the legitimate channel, uniform power allocation is optimal. We also provide the necessary condition for the proposed AN selection to be optimal. Simulation results show that our AN selection outperforms Goel and Negi's, especially when the legitimate user's channel quality is poor. In particular, when AN assisted beamforming is applied, the region with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of secure networks.
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.
In this paper we consider the secure transmission with multiple-input, single-output, single-antenna eavesdropper (MISOSE) in fast fading channels where the transmitter knows perfect legitimate channel state information but only the statistics of the eavesdropper's channel. For the MISOSE channels, the artificial noise assisted beamforming proposed by Goel and Negi is a promising technique, where the artificial noise is imposed on the null space of the legitimate channel to disrupt the eavesdropper's reception. Here we propose a generalized artificial noise scheme which allows the injection of the artificial noise to the legitimate channel. Although the generalized artificial noise may cause the leakage of artificial noise at the legitimate receiver, the secrecy rate can still be improved since the covariance matrix of it is more flexible than the heuristic one selected by Goel and Negi. To fully characterize the proposed scheme, we investigate the optimization of its secrecy rate. We first derive the conditions under which the beamformers of the message bearing signal and the generalized artificial noise being the same is optimal. Based on this choice, the complicated secrecy rate optimization problem over the covariance matrices of the message-bearing signal and the generalized artificial noise can be reduced to a much simpler power allocation problem. We also develop an efficient algorithm to solve this non-convex power allocation problem. Numerical results show that our generalized artificial noise scheme outperforms Goel and Negi's heuristic selection, especially in the near eavesdropper settings. In particular, with the aid of the proposed scheme, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the network.
This paper studies the design of artificial-noise-aided (AN-aided) secure transmission in slow-fading multiple-input–single-output (MISO) channels. We consider the scenario where a multiantenna transmitter sends messages to a single-antenna legitimate receiver in the presence of multiple noncolluding single-antenna eavesdroppers. It is assumed that the transmitter possesses instantaneous channel state information (CSI) of the legitimate channel but only the statistics of the eavesdropper's channels. Instead of adopting the well-known adaptive and nonadaptive transmission schemes, we consider the newly proposed semiadaptive scheme, in which the communication rate is fixed, and the secrecy rate is adaptively adjusted according to the legitimate channel's CSI. Compared with the adaptive scheme, a major advantage of fixing the communication rate is that the codebook can be fixed, and thus, the encoder and decoder designs are both simplified. We consider a generalized AN-aided beamforming structure, which allows arbitrary beamforming direction. Specifically, we focus on the problem of maximizing the secrecy throughput on the premise of reliable and secure transmission. By solving this problem, the optimal beamforming direction, power-allocation parameters, and secrecy rate are derived in closed form, and the optimal communication rate is obtained numerically. Finally, simulation results are presented to show the performance of the semiadaptive scheme.
In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.
In this paper, we consider multiple-input single-output multi-eavesdropper cognitive radio networks (MISOME-CRNs), where a secondary user (SU) aims to transmit confidential information to a legitimate SU receiver in the presence of a primary user (PU) and a multi-antenna passive eavesdropper in fast fading environments. For this system setting, we study beamforming with artificial noise (AN) for the SU to achieve confidential communications. We consider designing an AN-assisted optimal beamforming scheme, denoted cognitive beamforming (CB), which maximizes the ergodic secrecy rate. Moreover, we propose two suboptimal beamforming schemes, namely, scaled beamforming (SB) and projected beamforming (PB). We develop an analytical framework to assess the performance of the proposed schemes in a unified manner. First, we analyze the achievable ergodic secrecy rate of the three schemes. Second, we derive the optimal power allocation for the information and AN signals that maximizes the achievable ergodic secrecy rate in the large-antenna regime. Third, we study the performance of the three schemes in terms of the secrecy outage probability. Using numerical simulations, we validate our analytical results and show that CB achieves the best performance among the three proposed schemes. In addition, we provide insights into the effect of various system parameters on the secrecy performance. In particular, we show that the interference threshold at the PU plays an important role in the beamforming design.
Secrecy on the physical layer receives increased research interest. Especially in the wireless communication scenarios, the interest in confidentiality of messages increases. In this paper, we discuss the effectiveness of the beamforming strategies maximum ratio transmission (MRT), zero forcing (ZF), and an optimized beamforming (BF) strategy for the transmission under secrecy constraints. The applied channel model is the flat-fading MISO (multiple-input single-output) wiretap channel, where the channel to the eavesdropper is only partly known at the transmitter. The scenario with perfect and no channel information to the eavesdropper are included as special cases. We show that under certain conditions the achievable secrecy rates for the transmission with optimized beam-forming can be increased by transmitting artificial noise (AN) in the null space of the channel to the intended receiver, which produces additional interference only at the eavesdropper. We provide a characterization of the optimal beamforming and artificial noise beamforming and analyze the optimal power allocation for asymptotic cases (low and high SNR as well as no and perfect channel information). Numerical simulations illustrate the results.