On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly ($P$) or with delay ($D$) to the transmitter. Denoting by $S_1$, $S_2$, and $S_3$ the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., $(S_1,S_2,S_3) \in \{P,D\}^3$. We denote by $\lambda_{S_1 S_2 S_3}$ the fraction of time during which the state $S_1S_2S_3$ occurs. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we consider the general multi-receiver setup and characterize the SDoF region of fixed hybrid states $PPD$, $PDP$, and $DDP$. We then focus our attention on the symmetric case in which $\lambda_{PDD}=\lambda_{DPD}$. For this case, we establish bounds on SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates. Furthermore, we specialize our results for the two receivers channel with an external eavesdropper to the two-user broadcast channel. We show that, the synergistic gains in terms of SDoF by alternating CSIT is not restricted to multi-receiver wiretap channels; and, can also be harnessed under broadcast setting.Comment: To Appear in IEEE Transactions on Information Forensics and Securit

Sum-Rate Maximization for Linearly Precoded Downlink Multiuser MISO Systems with Partial CSIT: A Rate-Splitting Approach

This paper considers the Sum-Rate (SR) maximization problem in downlink MU-MISO systems under imperfect Channel State Information at the Transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This Rate-Splitting (RS) approach was shown to boost the achievable Degrees of Freedom (DoF) when CSIT errors decay with increased SNR. In this work, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized Ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of Sample Average Approximation (SAA) coupled with the Weighted Minimum Mean Square Error (WMMSE) approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared to conventional transmission with NoRS.Comment: accepted to IEEE Transactions on Communication

Secrecy Wireless Information and Power Transfer in Fading Wiretap Channel

Simultaneous wireless information and power transfer (SWIPT) has recently drawn significant interests for its dual use of radio signals to provide wireless data and energy access at the same time. However, a challenging secrecy communication issue arises as the messages sent to the information receivers (IRs) may be eavesdropped by the energy receivers (ERs), which are presumed to harvest energy only from the received signals. To tackle this problem, we propose in this paper an artificial noise (AN) aided transmission scheme to facilitate the secrecy information transmission to IRs and yet meet the energy harvesting requirement for ERs, under the assumption that the AN can be cancelled at IRs but not at ERs. Specifically, the proposed scheme splits the transmit power into two parts, to send the confidential message to the IR and an AN to interfere with the ER, respectively. Under a simplified three-node wiretap channel setup, the transmit power allocations and power splitting ratios over fading channels are jointly optimized to minimize the outage probability for delay-limited secrecy information transmission, or to maximize the average rate for no-delay-limited secrecy information transmission, subject to a combination of average and peak power constraints at the transmitter as well as an average energy harvesting constraint at the ER. Both the secrecy outage probability minimization and average rate maximization problems are shown to be non-convex, for each of which we propose the optimal solution based on the dual decomposition as well as suboptimal solution based on the alternating optimization. Furthermore, two benchmark schemes are introduced for comparison. Finally, the performances of proposed schemes are evaluated by simulations in terms of various trade-offs for wireless (secrecy) information versus energy transmissions.Comment: to appear in IEEE Transactions on Vehicular Technolog

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

Joint Optimization for Secure and Reliable Communications in Finite Blocklength Regime

To realize ultra-reliable low latency communications with high spectral efficiency and security, we investigate a joint optimization problem for downlink communications with multiple users and eavesdroppers in the finite blocklength (FBL) regime. We formulate a multi-objective optimization problem to maximize a sum secrecy rate by developing a secure precoder and to minimize a maximum error probability and information leakage rate. The main challenges arise from the complicated multi-objective problem, non-tractable back-off factors from the FBL assumption, non-convexity and non-smoothness of the secrecy rate, and the intertwined optimization variables. To address these challenges, we adopt an alternating optimization approach by decomposing the problem into two phases: secure precoding design, and maximum error probability and information leakage rate minimization. In the first phase, we obtain a lower bound of the secrecy rate and derive a first-order Karush-Kuhn-Tucker (KKT) condition to identify local optimal solutions with respect to the precoders. Interpreting the condition as a generalized eigenvalue problem, we solve the problem by using a power iteration-based method. In the second phase, we adopt a weighted-sum approach and derive KKT conditions in terms of the error probabilities and leakage rates for given precoders. Simulations validate the proposed algorithm.Comment: 30 pages, 8 figure

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 Precoding for Future Wireless Communication Systems

Department of Electrical EngineeringPhysical layer security has emerged a flourishing strategy to protect confidential information from eavesdroppers with lower computational complexity compared to cryptography. Secure precoding is a promising transmission method of physical layer security to improve security by exploiting an intrinsic attribute of wireless communications. The main goal of the secure precoding is to maximize secrecy rate in multi-input and multi-output (MIMO) systems with the presence of eavesdroppers. Unfortunately, there exists no optimal solution, and also solving the secrecy rate maximization problem becomes more challenging as networks involve a multi-user (MU) and multi-eavesdropper (ME) scenario because of its non-smoothness and non-convexity. In this thesis, I proposed a novel secure precoding algorithm for downlink MU-MIMO systems under ME threat to enhance the secrecy rate, and provide subsequent analyses for realizing ultra-reliable low latency communications (URLLC). By incorporating strong security, communication reliability, and latency, a multi-objective optimization problem is investigated in the finite blocklength (FBL) regime. The derived optimization problem aims to maximize the secrecy rate by designing a secure precoder, while simultaneously minimizing both the maximum error probability and the rate of information leakage. The proposed FBL-based optimization algorithm provides the significantly improved tradeoff among the security, the error probability, and information leakage rate. Therefore, the proposed algorithms can offer significantly improved security for future wireless communication systems.clos