An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> D. Statistical MCSI and 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> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> D. Statistical MCSI and ECSI <s> Wireless security has become an important issue for modern wireless networks. Due to the broadcast nature of wireless channels possibility of eavesdropping the transmission is provided for non-legitimate receivers. In the present paper, we consider a multi-antenna wiretap channel in a fast-fading environment with only statistical channel state information available at the receiver. The overall performance of such channel is characterized by the ergodic secrecy capacity, which, in general, cannot be characterized explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation for the achievable ergodic secrecy rate under arbitrary channel inputs. The obtained large-system approximation matches well with the actual simulated secrecy rates, revealing some interesting behavior of the secrecy rates in the given scenario. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> D. Statistical MCSI and ECSI <s> We propose transmit optimization techniques for multi-input multi-output (MIMO) wiretap channels with statistical channel state information (CSI) at the transmitter. We consider doubly correlated channels towards the legitimate receiver and the eavesdropper. The aim is to maximize the secrecy rates using the knowledge of the channel correlation matrices. We develop gradient-descent based optimization algorithms for obtaining the optimal transmit signals for both Gaussian and finite-alphabet inputs. Furthermore, we introduce a joint precoder and artificial noise (AN) design scheme. We demonstrate the efficacy of the proposed schemes via numerical examples. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> D. Statistical MCSI and 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> BIB004
While most of the existing physical layer security solutions rely on the assumption that the transmitter is capable of estimating at least the instantaneous main CSI, in some scenarios (e.g., for fast fading channels), it may be difficult for the transmitter to track the rapidly varying channel coefficients. For these cases, the impact of the discrete inputs on the achievable secrecy rates is analyzed in BIB002 . Under the assumption that both channels are doubly correlated, using the knowledge of transmit and receive correlation matrices, transmit signal design algorithms are proposed in BIB003 to maximize the resulting achievable secrecy rates. The results in BIB003 reveal that jointly optimizing the precoder matrix and artificial noise results in increased achievable secrecy rates with respect to precoding without artificial noise injection. The existing studies on MIMO wiretap channels with statistical CSI are summarized in Table V . We now compare the secrecy rates achieved by different transmit signal design approaches under different CSIT assumptions. In particular, we overview the results for the scenarios with perfect or statistical CSI at the transmitter. When perfect CSI is available, each element of H B and H E are modeled as independent and identically distributed (i.i.d.) with CN (0, σ 2 B ) and CN (0, σ 2 E ), respectively. When considering the statistical CSI corresponding to the main channel or the eavesdropper's channel, a commonly adopted model in the literature employs doubly correlated channels with where the elements ofĤ B andĤ E are i.i.d., and the transmitter is capable of acquiring the transmit and receive correlation matrices, i.e., Ψ tb , Ψ te , Ψ rb and Ψ re , from the long-term statistics of the channel. Perfect instantaneous CSI is available at both receivers. Fig. 6 demonstrates the achievable secrecy rates by different transmission schemes over a MIMOME wiretap channel with N t = 4 and N B = N E = 2. Correlation matrices are assumed to have exponentially decaying entries as It is demonstrated that the precoder design using a gradient descent optimization approach BIB001 , BIB004 is a promising strategy for maximizing the secrecy rates. Fig. 6 also reveals the importance of CSIT. When perfect CSI corresponding to the eavesdropper is available at the transmitter, it is possible to construct precoders, which are aligned with the null-space of the eavesdropper's channel. By this means, the achievable rate of the eavesdropper can be suppressed to zero. Furthermore, even when only the statistical CSI of the eavesdropper along with perfect CSI of the main user is available, high secrecy rates are still achievable with the aid of appropriately designed artificial noise injection strategies. However, in the absence of instantaneous CSI, the precoder matrices designed with the knowledge of correlation matrices are not capable of preventing the ergodic secrecy rates from dropping to zero at high SNRs. In other words, since statistical CSI does not provide sufficient degrees of freedom to take advantage of fading for improving secrecy, the behavior is similar to that in AWGN channels described in Section III.