An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IV. FADING AND MULTI-ANTENNA WIRETAP CHANNELS DRIVEN BY FINITE-ALPHABET INPUTS <s> The broadcast nature of the wireless medium makes the communication over this medium vulnerable to eavesdropping. This paper considers the problem of secret communication between two nodes, over a fading wireless medium, in the presence of a passive eavesdropper. The assumption used is that the transmitter and its helpers (amplifying relays) have more antennas than the eavesdropper. The transmitter ensures secrecy of communication by utilizing some of the available power to produce 'artificial noise', such that only the eavesdropper's channel is degraded. Two scenarios are considered, one where the transmitter has multiple transmit antennas, and the other where amplifying relays simulate the effect of multiple antennas. The channel state information (CSI) is assumed to be publicly known, and hence, the secrecy of communication is independent of the secrecy of CSI. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IV. FADING AND MULTI-ANTENNA WIRETAP CHANNELS DRIVEN BY FINITE-ALPHABET INPUTS <s> We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Amplitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IV. FADING AND MULTI-ANTENNA WIRETAP CHANNELS DRIVEN BY FINITE-ALPHABET INPUTS <s> This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical layer message authentication is also briefly introduced. The survey concludes with observations on potential research directions in this area. <s> BIB003
Fading introduces new potentials for securing communications at the physical layer. Specifically, randomness due to channel fluctuations can be exploited opportunistically by a transmitter to guarantee secrecy even in the scenarios where the eavesdropper possesses a higher SNR (on average) than the legitimate receiver. Dissimilar to the Gaussian wiretap channel where Gaussian inputs are secrecy capacity achieving, in the presence of fading, discrete signaling may achieve higher secrecy rates. For instance, it is shown in BIB002 that, when Bob's channel gain is on average worse than that of Eve's, QAM inputs achieve higher secrecy rates at low and moderate SNR regimes. This is because the discrete nature of QAM inputs limits the leakage at the eavesdropper whose channel is unusually good. At sufficiently high SNRs, however, the secrecy rate with QAM inputs drops to zero similar to what is observed for the case of Gaussian wiretap channels. Taking advantage of the spatial degrees of freedom introduced by multi-antenna transmission can serve as an efficient solution to prevent secrecy rate of standard constellations from dropping to zero at high SNRs. In the remainder of this section, we focus on a system model where Alice, Bob and Eve are equipped with N t , N B and N E antennas, as depicted in Fig. 4 . The received signals are given by where H B and H E are the channel matrices corresponding to the legitimate receiver and the eavesdropper, respectively, while n y and n z denote circularly symmetric complex AWGN vectors, elements of which are independent and follow CN (0, σ 2 ny ) and CN (0, σ 2 nz ), respectively. Transmit precoding and artificial noise injection serve as important approaches for enhancing secrecy BIB003 . Via precoding, it is possible to strengthen (or weaken) the transmitted signals in certain directions. Accordingly, it can be used as an effective tool to increase the quality difference between the signals received at the legitimate receiver and the eavesdropper. Beamforming is a special case of precoding where the transmitter is restricted to using rank-one signals. It has a lower complexity with respect to the general transmit precoding solutions, achieved at the price of some performance loss. Furthermore, injection of artificial noise BIB001 can degrade the reception at the eavesdropper effectively while having no (or minimal) effect on the signal received at the legitimate receiver. We also note that, to take advantage of the potentials offered by channel fading, the transmitter needs a certain level of knowledge on the CSI of both channels. In what follows, we review the existing solutions for secure transmission over MIMO wiretap channels with finite-alphabet inputs under different CSIT assumptions.