An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. Multiuser and Multi-Eve Networks 1) Broadcast Channel With Confidential Messages: <s> The secrecy capacity of a discrete memoryless Gaussian Wire-Tap Channel when the input is from a finite complex constellation is studied. It is shown that the secrecy capacity curves of a finite constellation plotted against the SNR, for a fixed noise variance of the eavesdropper's channel has a global maximum at an internal point. This is in contrast to what is known in the case of Gaussian codebook input where the secrecy capacity curve is a bounded, monotonically increasing function of SNR. Secrecy capacity curves for some well known constellations like BPSK, 4-QAM, 16-QAM and 8-PSK are plotted and the SNR at which the maximum occurs is found through simulation. It is conjectured that the secrecy capacity curves for finite constellations have a single maximum. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. Multiuser and Multi-Eve Networks 1) Broadcast Channel With Confidential Messages: <s> This paper investigates the secrecy capacity of the Gaussian wiretap channel with M-PAM inputs, by capitalizing on the relationship between mutual information and minimum mean squared error (MMSE). In particular, we establish optimality conditions for both the M-PAM input power and the M-PAM input distribution, which we specialize to the asymptotic low-power and high-power regimes. By using the properties of the MMSE to establish sufficient conditions for the uniqueness of the solution of some of the underlying non-convex optimization problems, we also propose efficient algorithms to compute the optimal solutions. Interestingly, we show that with M-PAM inputs it is sub-optimal to use all the available power for some range of parameters — this is in sharp contrast to standard Gaussian channels. We also extend the results to the parallel Gaussian wiretap channel with M-PAM inputs. We put forth a mercury-waterfilling interpretation of the optimal power allocation procedure for parallel Gaussian wiretap channels which generalizes the conventional mercury-waterfilling interpretation for parallel Gaussian channels, with the mercury level amending the base level to account for both the non-Gaussianess of the input and the secrecy constraint. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. Multiuser and Multi-Eve Networks 1) Broadcast Channel With Confidential Messages: <s> This paper considers the Broadcast Channel with Confidential Message (BCCM) where the sender attempts to send altogether a common message to two receivers and a confidential message to one of them. The achievable rate regions are derived for the power-constrained Gaussian BCCM with finite input alphabet using various transmission strategies. Namely, time sharing, superposition modulation and superposition coding are used as broadcast strategies. For superposition modulation and superposition coding, the maximal achievable rate regions are obtained by maximizing over both constellation symbol positions and the joint probability distribution. The maximization of the secrecy rate for wiretap channels is also studied as a particular case of the BCCM problem. We compare the considered transmission strategies in terms of percentage gains in achievable rates. We concentrate on the impact of the finite alphabet constraint on achievable rates, and show that this constraint may change well known results obtained in the Gaussian case. We show also that the secrecy constraint can change the shape of the achievable rate region in superposition modulation used in some standards when symbols are equiprobable. On a more practical side, it is shown that a performance close to the optimum can be obtained by strategies with reduced complexity. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. Multiuser and Multi-Eve Networks 1) Broadcast Channel With Confidential Messages: <s> This paper investigates the linear precoder design for cognitive multiple-access wiretap channel (CMAC-WT), where two secondary-user transmitters (STs) communicate with one secondary-user receiver (SR) in the presence of an eavesdropper and subject to interference threshold constraints at primary-user receivers (PRs). It designs linear precoders to maximize the ergodic secrecy sum rate for multiple-input multiple-output (MIMO) CMAC-WT under finite-alphabet inputs and statistical channel state information (CSI). For this non-convex problem, a two-layer algorithm is proposed by embedding the convex-concave procedure into an outer approximation framework. The key idea of this algorithm is to reformulate the approximated ergodic secrecy sum rate as a difference of convex (DC) functions, and then generate a sequence of simpler relaxed sets to approach the non-convex feasible set. In this way, near optimal precoding matrices are obtained by maximizing the approximated ergodic secrecy sum rate over a sequence of relaxed sets. Numerical results show that the proposed precoder design provides a significant performance gain over the Gaussian precoding method in the medium and high SNR regimes. <s> BIB004 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. Multiuser and Multi-Eve Networks 1) Broadcast Channel With Confidential Messages: <s> This paper considers the precoder design for multiantenna secure cognitive radio networks. We use finite-alphabet inputs as the signaling and exploit statistical channel state information (CSI) at the transmitter. We maximize the secrecy rate of the secondary user and control the transmit power and the power leakage to the primary receivers that share the same frequency spectrum. The secrecy rate maximization is important for practical systems, but challenging to solve, mainly due to two reasons. First, the secrecy rate with statistical CSI is computationally prohibitive to evaluate. Second, the optimization over the precoder is a nondeterministic polynomial-time hard (NP-hard) problem. We utilize an accurate approximation of the secrecy rate to reduce the computational effort and then propose a global optimization approach based on branch-and-bound method. The idea is to define a simplex and transform the secrecy rate into a concave function. The derived concave function converges to the secrecy rate when the defined simplex shrinks down. Using this feature, we solve a sequence of concave maximization problems over iteratively shrinking simplices and eventually attain the globally optimal solution that maximizes the approximation of the secrecy rate. When the complexity is concerned, a low-complexity variant with limited number of iterations can be used in practice. We demonstrate the performance gains when compared with others through numerical examples. <s> BIB005 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. Multiuser and Multi-Eve Networks 1) Broadcast Channel With Confidential Messages: <s> We investigate the physical layer security of synchronous multiple access transmissions using the Alamouti space-time block code in fading channels where multiple users communicate with a single intended receiver in the presence of an eavesdropper. We propose an artificial-noise-aided technique to secure the transmissions by having the Alamouti users collaborate with each other, without exchanging information, to degrade the eavesdropper’s channel. Unlike previous work, which assumes that the transmitters have complete knowledge of the legitimate as well as the eavesdropper’s channels, our proposed technique requires no communications between the users, minimal knowledge of the legitimate channel, and no channel knowledge regarding the eavesdropper. <s> BIB006
The achievable rate region for a Gaussian broadcast channel with confidential messages is characterized for discrete inputs in BIB003 . In this scenario, the transmitter's objective is to send a common message to two receivers as well as to deliver a confidential message to one of them. Dissimilar to BIB001 and BIB002 where standard constellations are considered, in BIB003 , the symbols are allowed to be arbitrary, and the achievable secrecy rate region is enlarged by optimizing the symbol positions and the probability distribution of the symbols. The shrinkage of the rate region due to employing PAM inputs is quantified with respect to the optimal Gaussian inputs, and a number of important behavioral differences between these cases are highlighted. 2) Multiple Access Channels: Allen et al. BIB006 focus their attention on multiple access wiretap channels (as depicted in Fig. 9 ) under the assumption that the users employ the Alamouti STBC scheme. Specifically, they consider a case where multiple transmitters communicate with one legitimate receiver in the presence of an eavesdropper. Under the assumption that the transmitter has the knowledge of the legitimate user's channel and does not know the eavesdropper's channel gain, an artificial noise injection is proposed along the null-space of the main channel, which is shown to provide considerable improvements in the secrecy sum-rate. 3) Cognitive Radio Networks: The linear precoder design for the cognitive multiple-access wiretap and the cognitive multi-antenna wiretap channels with finite-alphabet inputs are studied in BIB004 and BIB005 , respectively. Jin et al. BIB004 consider a setup in which two secondary-user transmitters are communicating with a secondary-user receiver in the presence of an eavesdropper and under interference threshold constraints at the primary users. A two-layer precoding algorithm is proposed using statistical CSI at the transmitters to maximize the ergodic secrecy sum rate. In BIB005 , on the other hand, the authors study a scenario where a multi-antenna secondary-user transmitter communicates with a multi-antenna secondary-user receiver, and the communication is wiretapped by a multiantenna eavesdropper (Fig. 10 ). In this work, the precoder matrix is optimized using an iterative algorithm (assuming statistical CSI of all the channels) so that the secrecy rate of the secondary user is maximized while power leakage to the primary user sharing the same frequency spectrum is controlled.