An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Relay Channels and Cooperative Communications <s> In this letter, we compute the secrecy rate of decode-and-forward (DF) relay beamforming with finite input alphabet of size M. Source and relays operate under a total power constraint. First, we observe that the secrecy rate with finite-alphabet input can go to zero as the total power increases, when we use the source power and the relay weights obtained assuming Gaussian input. This is because the capacity of an eavesdropper can approach the finite-alphabet capacity of \frac{1}{2}\log_2 M with increasing total power, due to the inability to completely null in the direction of the eavesdropper. We then propose a transmit power control scheme where the optimum source power and relay weights are obtained by carrying out transmit power (source power plus relay power) control on DF with Gaussian input using semi-definite programming, and then obtaining the corresponding source power and relay weights which maximize the secrecy rate for DF with finite-alphabet input. The proposed power control scheme is shown to achieve increasing secrecy rates with increasing total power with a saturation behavior at high total powers. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Relay Channels and Cooperative Communications <s> This letter considers cooperative jamming to secure communication in the presence of multiple eavesdroppers with finite alphabet inputs. Considering the global constraint, the joint design of artificial noise covariance matrices and power allocation between the source and the relays is studied. Specifically, we transformed the problem of artificial noise design into a semi-definite programming problem, which is efficiently solved by standard optimization method. Besides, the power allocation between the source and relays is derived by utilizing the relationship between mutual information and minimum mean square error. Furthermore, a two-step algorithm is developed to enhance the achievable secrecy rate of cooperative jamming wireless network. Numerical examples demonstrate the proposed algorithm achieves a significant gain over the conventional counterparts in terms of secrecy rate. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Relay Channels and Cooperative Communications <s> This paper considers secure transmission with the aid of a helper for finite alphabet signals in multiple-input–multiple-output multiple antenna eavesdropper networks, where the helper transmits a jamming signal along with the confidential message sent by the source node to confuse the eavesdropper. For the scenario in which the only statistical channel-state-information (CSI) of the eavesdropper links is available at the transmitter, the ergodic secrecy rate lacks closed-form expression, and the evaluation of the ergodic secrecy rate is computationally prohibitive. To address this problem, an accurate approximation of the ergodic secrecy rate is proposed to reduce the computational complexity. Utilizing this approximation of the ergodic secrecy rate, the joint optimization of precoding design and power allocation between the source and the helper is investigated to improve the ergodic secrecy rate. Furthermore, to achieve a tradeoff between computational complexity and performance, low-complexity schemes without iteration are proposed based on the analysis at extreme signal-to-noise ratio (SNR). In the low SNR regime, we prove that it is optimal to transmit confidential messages with full power, and the beamforming design is the first-order optimal precoder. At high SNR, we transform the problem of precoding design into a semi-definite programming problem, which can be efficiently solved by the interior-point method. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> B. Relay Channels and Cooperative Communications <s> In this paper, a practical power efficient technique is proposed for an untrusted decode-and-forward (DAF) based cooperative communication system to provide secure communication between the source and the destination. More specifically, a DAF relay, called switchable DAF (sDAF), is designed in such a way that it can be switched to amplify-and-forward (AAF) in certain predefined situations. The algorithm is based on destination-assisted jamming and comprised of two phases. The first phase securely shares the random manipulating sequence (RMS) through an untrusted relay, while the second phase uses this RMS for secure communication through untrusted relay. This algorithm not only provides secrecy, but also enhances the power efficiency as compared to other destination-assisted jamming techniques. <s> BIB004
Cooperation serves as an efficient method for enhancing secrecy in wireless networks. In this context, along with the studies conducted on secrecy capacity in various cooperative scenarios, a number of recent studies focus on finite-alphabet inputs. In this context, the secrecy rates achieved with decodeand-forward (DF) relay beamforming under the finite-alphabet input constraints are characterized in BIB001 . It is shown that by optimizing the source power and also the relay weights using the global CSI, it is possible to prevent the secrecy rates from dropping to zero. Cao et al. BIB002 consider a cooperative jamming network in presence of multiple eavesdroppers, and develop a secure transmission scheme with finite-alphabet inputs, which relies on a joint optimization of the artificial noise (injected in the null-space of the relay to destination links), and power allocation among the source and the relays. The study in BIB003 considers secure transmission over a MIMOME setup with the aid of a multi-antenna helper, which transmits a jamming signal to degrade the signal received by BIB002 , a framework is provided for joint optimization of the precoder matrix and power allocation between the transmitter and the helper. Furthermore, low-complexity transmit signal design schemes are developed for both low and high SNR regimes. Furqan et al. BIB004 focus on the problem of secure transmission with cooperative jamming via an untrusted relay. They propose a power efficient secure DF-based cooperative communication technique and demonstrate the efficacy of their scheme via simulations using practical constellation-constrained inputs. Table VIII summarizes the recent research results of secure transmission over finite-input multi-user, multi-eavesdropper and cooperative channels.