An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Perfect MCSI and Statistical ECSI <s> This work investigates the effect of limiting source signals to finite-alphabet on the secrecy rate of a multi-antenna wiretap system. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single- and multi-antenna systems based on Gaussian source signals and secrecy code. Despite the impracticality of Gaussian source, its compact closed-form expression of mutual information motivated broad use of Gaussian input assumption. For practical consideration, we study the effect of finite discrete-constellation on instantaneous and ergodic secrecy rate of multiple-antenna wire-tap channels. Our results demonstrate substantial difference between systems involving finite-alphabet inputs and systems with Gaussian inputs. Results from Gaussian inputs serve as upper-bound of secrecy rate for practical systems with finite alphabet inputs. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Perfect MCSI and Statistical ECSI <s> The use of multiple-antenna arrays can leverage the physical-layer security of wireless systems. It is therefore important to characterize such systems in a realistic situation where we can apply the so-called artificial-noise solution in multiple-antenna systems to enhance the communication confidentiality by only exploiting a fading nature of wireless environments. In this paper, we consider secure communication over a multiple-input single-output Rayleigh-fading channel in the presence of a multiple-antenna eavesdropper—referred to as a multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, secure beamforming with artificial noise is treated when the transmitter has access to full channel state information (CSI) of a legitimate channel but only channel distribution information of an eavesdropper channel. We first put forth a new notion of the symbol error probability (SEP) of confidential information—called the δ-secrecy SEP—to connect the reliability and confidentiality of the legitimate communication. We then quantify the diversity impact of secure beamforming with artificial noise on the δ-secrecy SEP in the MISOME wiretap channel and show that the artificial-noise strategy preserves the secrecy diversity of order n t - n e for n t transmit and n e eavesdropper antennas. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Perfect MCSI and Statistical ECSI <s> In this paper, we investigate the secrecy rate of finite-alphabet communications over multiple-input-multiple-output-multiple-antenna eavesdropper (MIMOME) channels. Traditional precoding designs based on Gaussian input assumption may lead to substantial secrecy rate loss when the Gaussian input is replaced by practical finite-alphabet input. To address this issue, we investigate linear precoding designs to directly maximize the secrecy rate for MIMOME systems under the constraint of finite-alphabet input. By exploiting the theory of Karush-Kuhn-Tucker (KKT) analysis and matrix calculus, we first present necessary conditions of the optimal precoding design when instantaneous channel-state information (CSI) of the eavesdropper is known at the transmitter. In this light, an iterative algorithm for finding the optimal precoding matrix is developed, utilizing a gradient decent method with backtracking line search. Moreover, we find that the beamforming design in MIMONE systems, which is a secrecy-capacity-achieving approach for Gaussian signaling, no longer provides the maximum secrecy rate for finite-alphabet input data. This case is substantially different from the Gaussian input case. In addition, we derive the closed-form results on the precoding matrix, which maximizes the secrecy rate in the low signal-to-noise ratio (SNR) region, and reveal the optimal precoding structure in the high-SNR region. A novel jamming signal generation method that draws on the CSI of the eavesdropper to additionally increase the secrecy rate is further proposed. The precoding design with only statistical CSI of the eavesdropper available at the transmitter is also considered. Numerical results show that the proposed designs provide significant gains over recent precoding designs through a power control policy and the precoding design with the Gaussian input assumption in various scenarios. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Perfect MCSI and Statistical ECSI <s> In this paper we consider the secure transmission in fast Rayleigh fading channels with full knowledge of the main channel and only the statistics of the eavesdropper's channel state information at the transmitter. For the multiple-input, single-output, single-antenna eavesdropper systems, we generalize Goel and Negi's celebrated artificial-noise (AN) assisted beamforming, which just selects the directions to transmit AN heuristically. Our scheme may inject AN to the direction of the message, which outperforms Goel and Negi's scheme where AN is only injected in the directions orthogonal to the main channel. The ergodic secrecy rate of the proposed AN scheme can be represented by a highly simplified power allocation problem. To attain it, we prove that the optimal transmission scheme for the message bearing signal is a beamformer, which is aligned to the direction of the legitimate channel. After characterizing the optimal eigenvectors of the covariance matrices of signal and AN, we also provide the necessary condition for transmitting AN in the main channel to be optimal. Since the resulting secrecy rate is a non-convex power allocation problem, we develop an algorithm to efficiently solve it. Simulation results show that our generalized AN scheme outperforms Goel and Negi's, especially when the quality of legitimate channel is much worse than that of eavesdropper's. In particular, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the secure network when the proposed AN assisted beamforming is applied. <s> BIB004 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Perfect MCSI and Statistical ECSI <s> We propose a low complexity transmit signal design scheme for achieving information-theoretic secrecy over a MIMO wiretap channel driven by finite-alphabet inputs. We assume that the transmitter has perfect channel state information (CSI) of the main channel and also knows the statistics of the eavesdropper's channel. The proposed transmission scheme relies on jointly optimizing the precoder matrix and the artificial noise so as to maximize the achievable secrecy rates. In order to lower the computational complexity associated with the transmit signal design, we employ a design metric using the cut-off rate instead of the mutual information. We formulate a gradient-descent based optimization algorithm and demonstrate via extensive numerical examples that the proposed signal design scheme can yield an enhanced secrecy performance compared with the existing solutions in spite of its relatively lower computational complexity. The impacts of the modulation order as well as the number of antennas at the transmitter and receiver ends on the achievable secrecy rates are also investigated. <s> BIB005 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Perfect MCSI and Statistical ECSI <s> We consider precoder and artificial noise (AN) design for multi-antenna wiretap channels under the finite-alphabet input assumption. We assume that the transmitter has access to the channel coefficients of the legitimate receiver and knows the statistics of the eavesdropper’s channel. Accordingly, we propose a secrecy rate maximization algorithm using a gradient descent-based optimization of the precoder matrix and an exhaustive search over the power levels allocated to the AN. We also propose algorithms to reduce the complexities of direct ergodic secrecy rate maximization by: 1) maximizing a cut-off rate-based approximation for the ergodic secrecy rate, simplifying the mutual information expression, which lacks a closed-form and 2) diagonalizing the channels toward the legitimate receiver and the eavesdropper, which allows for employing a per-group precoding-based technique. Our numerical results reveal that jointly optimizing the precoder and the AN outperforms the existing solutions in the literature, which rely on the precoder optimization only. We also demonstrate that the proposed low complexity alternatives result in a small loss in performance while offering a significant reduction in computational complexity. <s> BIB006
While availability of perfect ECSI at the transmitter may be practical in some limited scenarios, in general, it is highly challenging to obtain it instantaneously. A more practical assumption regarding CSIT is availability of perfect MCSI along with the statistical ECSI at the transmitter. On the other hand, the precoder design in this scenario is not as effective as those carried out with the perfect knowledge of both channels. In other words, with the absence of the instantaneous ECSI, precoding is not as forceful in suppressing the reception at the eavesdropper. For instance, transmission along the null-space of the eavesdropper's channel is not even possible in this scenario. An example of secure transmission schemes under perfect MCSI and statistical ECSI is given in BIB002 where the authors consider a MISOME channel and define a practical secrecy metric (instead of an information theoretic one), which quantifies the symbol error probability of the confidential data, and show that in the absence of artificial noise, secrecy diversity (i.e., the high-SNR slope of their defined metric) vanishes. This result underlines the importance of artificial noise injection in these scenarios. Artificial noise-aided transmit precoding strategies with the objective of maximizing the secrecy rate are proposed in BIB001 - BIB006 . Bashar et al. BIB001 employ naive beamforming along with the artificial noise injection while considering single-antenna receivers. The strategy proposed in BIB003 , on the other hand, relies on an iterative maximization of an approximation to the instantaneous secrecy rate. In both of these studies, it is shown that the optimal schemes allocate only a fraction of the total power for signal transmission at high SNRs. Hence, the remaining power is employed for artificial noise injection. It is shown in BIB005 that jointly optimizing the precoder matrix and portion of the power allocated to the artificial noise outperforms the solutions which rely on optimizing the precoder only. Moreover, inspired by the idea proposed in BIB004 , a generalized artificial noise aided transmission is introduced in BIB006 , which guarantees high secrecy rates for the scenarios with N t < N E for which injection of artificial noise along the null-space of the main channel is not possible. A summary of the existing solutions for the scenarios with perfect MCSI and statistical ECSI at the transmitter is given in Table III .