ngxiang Li

A Full-Duplex Bob in the MIMO Gaussian Wiretap Channel: Scheme and Performance

This letter considers secrecy communication from an information-theoretic perspective, and studies the secrecy capacity of a multi-input multi-output (MIMO) Gaussian wiretap channel with a source (Alice), an eavesdropper (Eve) and a Full-Duplex (FD) legitimate receiver (Bob). Bob can allocate part of his antennas to transmit jamming signals to impair Eves channel. Our goal is to identify the secrecy capacity behavior in the high signal-to-noise ratio (SNR) regimes, i.e., the maximal achievable secure degrees of freedom (S.D.o.F). Such S.D.o.F maximization is generally difficult to solve since it requires to face a nonlinear fractional problem. To deal with this issue, we first propose a cooperative secrecy transmission scheme, and prove its optimality in the sense of achieving the maximal S.D.o.F.. By studying this proposed transmission scheme, we obtain the maximal achievable S.D.o.F. in closed form for any given antenna allocation at Bob. Based on this closed-form result, we further analytically derive the optimal antenna allocation at Bob. To the best of our knowledge, this is the first time that the benefit brought by using the FD jamming Bob has been quantified.

On Secrecy Capacity of Gaussian Wiretap Channel Aided by A Cooperative Jammer

We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped with M and N antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rate R_N. The relationship between the average secrecy capacity C̅_N of Gaussian wiretap channel and the average secrecy rate R̅_N achieved by the null-space jamming scheme is investigated, and we prove that R̅_N ≤ C̅_N ≤ R̅_N+1. Based on this inequality and the derived lower and upper bounds on R_N, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that when N > M, the average secrecy capacity increases linearly with the total transmit power; while when N ≤ M - 1, there exists a performance ceiling on it.

Improving Wireless Physical Layer Security via Exploiting Co-Channel Interference

This paper considers a scenario in which a source-destination pair needs to establish a confidential connection against an external eavesdropper, aided by the interference generated by another source-destination pair that exchanges public messages. The goal is to compute the maximum achievable secrecy degrees of freedom (S.D.o.F) region of a MIMO two-user wiretap network. First, a cooperative secrecy transmission scheme is proposed, whose feasible set is shown to achieve all S.D.o.F. pairs on the S.D.o.F. region boundary. In this way, the determination of the S.D.o.F. region is reduced to a problem of maximizing the S.D.o.F. pair over the proposed transmission scheme. The maximum achievable S.D.o.F. region boundary points are obtained in closed form, and the construction of the precoding matrices achieving the maximum S.D.o.F. region boundary is provided. The proposed expressions are functions of the number of antennas at each terminal, and apply to any number of antennas, thus constituting an advancement over prior works that have considered only fixed antenna configurations.

Robust artificial-noise aided transmit design for multi-user MISO systems with integrated services

This paper considers an optimal artificial noise (AN)-aided transmit design for multi-user MISO systems in the eyes of service integration. Specifically, two sorts of services are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. This paper considers a general case of imperfect channel state information (CSI), aiming at a joint and robust design of the input covariances for the multicast message, confidential message and AN, such that the worst-case secrecy rate region is maximized subject to the sum power constraint. To this end, we reveal its hidden convexity and transform the original worst-case robust secrecy rate maximization (SRM) problem into a sequence of semidefinite programming. Numerical results are presented to show the efficacy of our proposed method.

Robust Transmit Design for Secure AF Relay Networks Based on Worst-Case Optimization

This paper studies robust transmit design to maximize the worst-case secrecy rate in AF networks under both total and individual relay power constraints. Channel state information (CSI) in the network is assumed to be perfectly known except for that associated with the eavesdroppers whose imperfection is modeled as deterministic bounded errors. To use the power at the relay nodes more efficiently, a joint cooperative relaying and jamming scheme is considered. Through some matrix manipulations, we recast the original nonconvex optimization problem as a sequence of semidefinite programs (SDPs), which enables us to obtain the optimal relay weights and the optimal covariance matrix of the jamming signal. Numerical results are presented to show the efficacy of the proposed scheme.

Secrecy degrees of freedom of a MIMO Gaussian wiretap channel with a cooperative jammer

This paper considers secrecy communication from a signal processing point of view, and studies the maximal achievable secrecy degrees of freedoms (S.D.o.F.) of a helper-assisted Gaussian wiretap channel, consisting of a source, a legitimate receiver, an eavesdropper and an external helper. Each terminal is equipped with multiple antennas. We first propose a cooperative secrecy transmission scheme, and show that it achieves the maximal secrecy degrees of freedom. We then propose a heuristic method, through which, we solve analytically the optimization problem associated with the proposed cooperative secrecy transmission scheme. By this way, we obtain the maximal achievable S.D.o.F. and also the precoding matrices which achieve the maximal S.D.o.F. in closed-form.

On Artificial-Noise-Aided Transmit Design for Multiuser MISO Systems With Integrated Services

This paper considers an optimal artificial noise (AN)-aided transmit design for multi-user MISO systems in the eyes of service integration. Specifically, two sorts of services are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. This paper considers a general case of imperfect channel state information (CSI), aiming at a joint and robust design of the input covariances for the multicast message, confidential message and AN, such that the worst-case secrecy rate region is maximized subject to the sum power constraint. To this end, we reveal its hidden convexity and transform the original worst-case robust secrecy rate maximization (SRM) problem into a sequence of semidefinite programming. Numerical results are presented to show the efficacy of our proposed method.

Non-asymptotic analysis of secrecy capacity in massive MIMO system

In this paper, we consider a massive MIMO wiretap system where the transmitter, the receiver and the eavesdropper are equipped with a large number of antennas. Being different from the previous works using asymptotic random matrix theory, our analysis relies on the concentration measure of non-asymptotic random matrix theory which allows us to obtain tight bounds for secrecy capacity of massive MIMO system with finite antenna number. The analytical and simulation results reveal the following, in the massive MIMO system employing equal power allocation at each transmit antenna: 1) the secrecy capacity falls within a bounds with a probability growing exponentially with the number of transmit antenna, while the ergodic secrecy capacity falls within a deterministic bounds; 2) the gap between the upper and the lower bound on secrecy rate is proportional to the square root of the SNR at legitimate receiver and the SNR at eavesdropper, respectively; 3) when the entry of legitimate channel matrix and eavesdropping channel matrix satisfies Gaussian distribution, the gap between the upper and the lower bound on secrecy rate is a linear reciprocal function of the number of transmit antennas.

On Secrecy Capacity of Helper-Assisted Wiretap Channel with an Out-of-Band Link

We consider a physical layer security problem where there is a source, an external helper, a legitimate receiver, and an eavesdropper, each equipped with one antenna. We assume that an additional out-of-band link from the source to the helper is available to improve the transmission security rate. A two-stage cooperative scheme is proposed. The proposed scheme consists of an information sharing stage and a cooperative transmission stage. Specifically, in the information sharing stage the source informs the helper of the signal to be transmitted, while in the cooperative transmission stage the source and the helper cooperate to transmit the signal to the legitimate receiver. Under this framework, we determine the optimal weights associated with this scheme and examine the secrecy capacity of the helper-assisted wiretap channel. The optimal weight design problem is generally nonconvex. To deal with this issue, an algorithm involving a one-dimensional search is developed. On the other hand, an analytical lower bound on the secrecy capacity is derived. Based on this lower bound, we further analyze the sufficient and necessary condition to ensure a positive secrecy capacity and derive the maximal achievable secure degrees of freedom, which are shown to be exactly the same as those of the multi-input single-output (MISO) wiretap channel.

Distributed interference alignment and power allocation with QoS requirements

We study interference alignment (IA) with quality of service (QoS) requirements in a K-user multiple input multiple output interference channel (K-user MIMO IFC). Specifically, we establish design formulations: i) that maximize the minimum signal-to-interference-noise ratio (SINR) at receivers, and that ii) minimize the sum mean squared error (Sum-MSE). The uplink-downlink (UL-DL) SINR duality is firstly established for the K-user MIMO IFC. With this result, we develop iterative IA algorithms which design the transmit/receive filters and optimizes power allocation among users jointly. The convergence of the proposed algorithms is proved based on the established UL-DL SINR duality. Numerical results show that, compared with the classic distributed IA algorithm and Max-SINR algorithm, the proposed algorithms achieve significant gain under mild signal-to-noise ratios (SNRs), and exhibits similar performance at high SNRs.