An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> 4) Multi-Eavesdropper Scenarios: <s> In this paper, we consider the problem of power allocation in MIMO wiretap channel for secrecy in the presence of multiple eavesdroppers. Perfect knowledge of the destination channel state information (CSI) and only the statistical knowledge of the eavesdroppers CSI are assumed. We first consider the MIMO wiretap channel with Gaussian input. Using Jensen's inequality, we transform the secrecy rate max-min optimization problem to a single maximization problem. We use generalized singular value decomposition and transform the problem to a concave maximization problem which maximizes the sum secrecy rate of scalar wiretap channels subject to linear constraints on the transmit covariance matrix. We then consider the MIMO wiretap channel with finite-alphabet input. We show that the transmit covariance matrix obtained for the case of Gaussian input, when used in the MIMO wiretap channel with finite-alphabet input, can lead to zero secrecy rate at high transmit powers. We then propose a power allocation scheme with an additional power constraint which alleviates this secrecy rate loss problem, and gives non-zero secrecy rates at high transmit powers. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> 4) Multi-Eavesdropper Scenarios: <s> This paper considers secure transmission design for multiple-input-single-output multiple multi-antenna eavesdroppers networks with finite alphabet inputs. To improve the achievable secrecy rate, the joint optimization of beamforming vector and transmitting power is studied. We transform the multi-variable problem into a single-variable problem, and then derive the beamforming vector and the transmitting power using one-dimensional search method. Specially, the secure transmission designs in the extremely signal-to-noise ratio (SNR) regime are investigated. In the low SNR regime, the problem of beamforming design is transformed into a semi-definite programming problem, which can be handled by interior-point-based methods, and the optimal transmitting power is obtained. Besides, two different secure schemes, which are zero-force beamforming scheme and joint beamforming and jamming scheme, are proposed to increase the achievable secrecy rate at high SNR. Numerical results demonstrate that the proposed schemes significantly improve the secrecy performance of the system. <s> BIB002
Cao et al. BIB002 study a setup comprised of a source, a legitimate receiver and multiple multi-antenna eavesdroppers. They first obtain an expression for an achievable secrecy rate, and then, under the full CSI assumption, they optimize the transmit power and the beamforming vector. The problem of power allocation for secrecy over MIMO wiretap channels with multiple eavesdroppers is studied in BIB001 . Under the assumption that the transmitter has perfect MCSI and statistical ECSI, the proposed power allocation strategy gives non-zero secrecy rates at high transmit powers. This is important because in the absence of this power control strategy, secrecy rate decreases with increasing transmit power, and it drops to zero when the eavesdroppers' SNRs become higher than a certain value.