An Overview of Physical Layer Security with Finite-Alphabet Signaling

Providing secure communications over the physical layer with the objective of achieving perfect secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step towards a practical implementation of physical layer security. With this motivation, this article reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and we discuss some open problems and directions for future research.Comment: Submitted to IEEE Communications Surveys & Tutorials (1st Revision

On the Transmit Beamforming for MIMO Wiretap Channels: Large-System Analysis

With the growth of wireless networks, security has become a fundamental issue in wireless communications due to the broadcast nature of these networks. In this work, we consider MIMO wiretap channels in a fast fading environment, for which the overall performance is characterized by the ergodic MIMO secrecy rate. Unfortunately, the direct solution to finding ergodic secrecy rates is prohibitive due to the expectations in the rates expressions in this setting. To overcome this difficulty, we invoke the large-system assumption, which allows a deterministic approximation to the ergodic mutual information. Leveraging results from random matrix theory, we are able to characterize the achievable ergodic secrecy rates. Based on this characterization, we address the problem of covariance optimization at the transmitter. Our numerical results demonstrate a good match between the large-system approximation and the actual simulated secrecy rates, as well as some interesting features of the precoder optimization.Comment: Published in Lecture Notes in Computer Science 8317, pp. 90-102, 2014. (Proceedings of International Conference on Information-Theoretic Security (ICITS), Singapore, November 2013

SECURITY UNDER IMPERFECT CHANNEL KNOWLEDGE IN WIRELESS NETWORKS

This dissertation studies physical layer security in wireless networks using an information theoretic framework. The central theme of this work is exploring the effect of delayed or no channel state information (CSI) on physical layer security in various wireless channel models. We begin with the fast Rayleigh fading wiretap channel, over which a legitimate transmitter wishes to have secure communication with a legitimate receiver in the presence of an eavesdropper. Subject to an average power constraint on the input, and with no CSI at any user, we show that the input distribution that achieves the secrecy capacity for this wiretap channel is discrete with a finite number of mass points. This enables us to evaluate the exact secrecy capacity of this channel numerically. Next, we consider multi-user models, specifically, the wiretap channel with M helpers, the K-user multiple access wiretap channel, and the K-user interference channel with an external eavesdropper, when no eavesdropper's CSI is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSI at the transmitter (CSIT) does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the K-user multiple access wiretap channel reduces to a wiretap channel with (K-1) helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from K(K-1)/(K(K-1)+1) to (K-1)/K. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from K(K-1)/(2K-1) to (K-1)/2 in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. We, then, study multiple-input multiple-output (MIMO) multi-user channels. We begin with the case when full CSIT is available. We consider a two-user MIMO multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum s.d.o.f. for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel. In line with the theme of this dissertation, we next consider the MIMO wiretap channel with one helper and the two-user MIMO multiple access channel when no eavesdropper CSIT is available. In each case, the eavesdropper has K antennas while the remaining terminals have N antennas. We determine the optimal sum s.d.o.f. for each channel model for the regime K= N. Finally, we explore the effect of delayed CSIT on physical layer security. In particular, we consider the two user multiple-input single-output (MISO) broadcast channel with confidential messages, in which the nature of CSIT from each user can be of the form I_{i}, i=1,2 where I_{i} belongs to {P, D,N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can be any of nine possible states corresponding to all possible values of (I_{1},I_{2}). While the optimal sum s.d.o.f. in the homogeneous settings corresponding to I_1=I_2 are already known in the literature, we focus on the heterogeneous settings where I_1 is not equal to I_2 and establish the optimal s.d.o.f. region in each case. We further consider the case where the CSIT state varies with time. Each state (I_1,I_2) can then occur for \lambda_{I_{1}I_{2}} fraction of the total duration. We determine the s.d.o.f. region of the MISO broadcast channel with confidential messages under such an alternating CSIT setting, with a mild symmetry assumption, where \lambda_{I_{1} I_{2}}=\lambda_{I_{2}I_{1}}

Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT

We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SDoF) region. We show that, in presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed CSIT. This result shows that, upon availability of asymmetric output feedback and delayed CSIT, there is no performance loss in terms of sum SDoF due to the distributed nature of the transmitters. Next, we show that this result also holds if only output feedback is conveyed to the transmitters, but in a symmetric manner, i.e., each receiver feeds back its output to both transmitters and no CSIT. We also study the case in which only asymmetric output feedback is provided to the transmitters, i.e., without CSIT, and derive a lower bound on the sum SDoF for this model. Furthermore, we specialize our results to the case in which there are no security constraints. In particular, similar to the setting with security constraints, we show that the optimal sum DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.Comment: To Appear in IEEE Transactions on Information Forensics and Securit