Jiangyuan Li

On Cooperative Relaying Schemes for Wireless Physical Layer Security

We consider a cooperative wireless network in the presence of one or more eavesdroppers, and exploit node cooperation for achieving physical (PHY) layer based security. Two different cooperation schemes are considered. In the first scheme, cooperating nodes retransmit a weighted version of the source signal in a decode-and-forward (DF) fashion. In the second scheme, referred to as cooperative jamming (CJ), while the source is transmitting, cooperating nodes transmit weighted noise to confound the eavesdropper. We investigate two objectives: i) maximization of the achievable secrecy rate subject to a total power constraint and ii) minimization of the total power transmit power under a secrecy rate constraint. For the first design objective, we obtain the exact solution for the DF scheme for the case of a single or multiple eavasdroppers, while for the CJ scheme with a single eavesdropper we reduce the multivariate problem to a problem of one variable. For the second design objective, existing work introduces additional constraints in order to reduce the degree of difficulty, thus resulting in suboptimal solutions. Our work raises those constraints, and obtains either an analytical solution for the DF scheme with a single eavesdropper, or reduces the multivariate problem to a problem of one variable for the CJ scheme with a single eavesdropper. Numerical results are presented to illustrate the proposed results and compare them to existing work.

Improving Physical Layer Secrecy Using Full-Duplex Jamming Receivers

This paper studies secrecy rate optimization in a wireless network with a single-antenna source, a multi-antenna destination and a multi-antenna eavesdropper. This is an unfavorable scenario for secrecy performance as the system is interference-limited. In the literature, assuming that the receiver operates in half duplex (HD) mode, the aforementioned problem has been addressed via use of cooperating nodes who act as jammers to confound the eavesdropper. This paper investigates an alternative solution, which assumes the availability of a full duplex (FD) receiver. In particular, while receiving data, the receiver transmits jamming noise to degrade the eavesdropper channel. The proposed self-protection scheme eliminates the need for external helpers and provides system robustness. For the case in which global channel state information is available, we aim to design the optimal jamming covariance matrix that maximizes the secrecy rate and mitigates loop interference associated with the FD operation. We consider both fixed and optimal linear receiver design at the destination, and show that the optimal jamming covariance matrix is rank-1, and can be found via an efficient 1-D search. For the case in which only statistical information on the eavesdropper channel is available, the optimal power allocation is studied in terms of ergodic and outage secrecy rates. Simulation results verify the analysis and demonstrate substantial performance gain over conventional HD operation at the destination.

Destination assisted cooperative jamming for wireless physical layer security

A wireless network with one source, one destination, one eavesdropper, and multiple decode-and-forward relays is considered. A two-slot cooperative relaying scheme is proposed that targets at maximizing the secrecy rate. In the first slot, the source transmits the information bearing signal, and at the same time, it cooperates with the destination in jamming the eavesdropper without creating interference at the relay. In the second slot, one optimally selected relay retransmits the decoded source signal, and at the same time, that particular relay cooperates with the source to jam the eavesdropper without creating interference at the destination. Optimal relay selection and also optimal power allocation among the first/second slot data signal and jamming noise are proposed. It is shown that the secrecy rate of the proposed scheme scales with the total system power P0 and the number of available relays K according to 1/2log2(1 + P0 /8logK) - 1.6 bits/channel use . Although the proposed power allocation and relay selection assume global CSI available, the performance under imperfect relay CSI is also investigated. Also, the performance under distributed relay selection with limited feedback is demonstrated.

On Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper, each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero mean and unit variance, i.e., the channels have trivial covariances. This paper addresses the general case in which the eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framework, it is shown that when full information on the legitimate channel is available to the transmitter, the optimal input covariance has always rank one. It is also shown that when only statistical information on the legitimate channel is available to the transmitter, the legitimate channel has some general non-trivial covariance and the eavesdropper channel has trivial covariance, the optimal input covariance has the same eigenvectors as the legitimate channel covariance.

Cooperative Transmission for Relay Networks Based on Second-Order Statistics of Channel State Information

Cooperative transmission in relay networks is considered, in which a source transmits to its destination with the help of a set of cooperating nodes. The source first transmits locally. The cooperating nodes that receive the source signal retransmit a weighted version of it in an amplify-and-forward (AF) fashion. Assuming knowledge of the second-order statistics of the channel state information, beamforming weights are determined so that the signal-to-noise ratio (SNR) at the destination is maximized subject to two different power constraints, i.e., a total (source and relay) power constraint, and individual relay power constraints. For the former constraint, the original problem is transformed into a problem of one variable, which can be solved via Newtons method. For the latter constraint, this problem is solved completely. It is shown that the semidefinite programming (SDP) relaxation of the original problem always has a rank one solution, and hence the original problem is equivalent to finding the rank one solution of the SDP problem. An explicit construction of such a rank one solution is also provided. Numerical results are presented to illustrate the proposed theoretical findings.

Uncoordinated Cooperative Jamming for Secret Communications

We consider a Gaussian wiretap channel model with a single-antenna source, destination and eavesdropper. The communication is assisted by multiple multiantenna helpers that transmit noise to confound the eavesdropper. First, we consider a nulling scheme, in which each helper independently transmits noise, designed to maximize the system secrecy rate while creating no interference to the destination. In this scheme, each helper requires only local relay-destination channel state information (CSI). When global CSI is available at the relays, the nulling scheme is not optimal. The optimal jamming noise structure is also provided under global CSI. Interestingly, it is shown both analytically and via simulations that, despite its reduced CSI requirements, the nulling scheme may have secrecy rate performance that is very close to the optimal one. The probability of outage of the nulling scheme is provided in closed form based on the statistics of the eavesdropper CSI.

Ergodic Secrecy Rate for Multiple-Antenna Wiretap Channels With Rician Fading

A Gaussian multiple-antenna wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver equipped with a single antenna, and an eavesdropper equipped with multiple antennas. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, assuming that full information on the legitimate channel is available to the transmitter, but only statistical information on the eavesdropper channel is known. More specifically, we investigate the case of MIMO Rician fading for the eavesdropper channel. We show that the optimal input covariance has rank one, which allows us to reduce the original optimization problem to a smooth one variable optimization problem. We propose a Newton-type method for a local maximizer, and Piyavskiis algorithm for the global maximizer. Numerical results are presented to illustrate the proposed algorithms.

Explicit Solution of Worst-Case Secrecy Rate for MISO Wiretap Channels With Spherical Uncertainty

A multiple-input single-output (MISO) wiretap channel model is considered, in which a multi-antenna source communicates with a single-antenna destination in the presence of one single-antenna eavesdropper. It is assumed that both the channel to the destination and the channel to the eavesdropper contain spherical uncertainty. The problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a sum power constraint is studied, and an explicit expression for the maximum worst-case secrecy rate is provided.

Outage constrained secrecy rate maximization using cooperative jamming

We consider a Gaussian MISO wiretap channel, where a multi-antenna source communicates with a single-antenna destination in the presence of a single-antenna eavesdropper. The communication is assisted by multi-antenna helpers that act as jammers to the eavesdropper. Each helper independently transmits noise, which lies in the null space of the helper-destination channel, thus creating no interference to the destination. Under source-eavesdropper channel uncertainty, we derive the optimal source covariance matrix that maximizes the secrecy rate subject to probability of outage and power constraints. Further, for the case in which the helper-eavesdropper channels follow a zero-mean Gaussian model with known covariances, we derive the outage probability in a closed form. Simulation results in support of the analysis are provided.

Physical layer security with uncoordinated helpers implementing cooperative jamming

A wireless communication network is considered, consisting of a source, a destination and an eavesdropper, each equipped with a single antenna. The communication is assisted by multiple multi-antenna helpers, which independently transmit jamming noise to confound the eavesdropper. The optimal structure of the jamming noise that maximizes the secrecy rate is derived. A suboptimal solution that results in nulling at the legitimate receiver is also considered. Unlike the optimal solution, which requires global channel information, the suboptimal solution requires local channel information only, i.e., each helper needs to know only its own channel to the destination. Although the nulling solution results in lower secrecy rate as compared to the optimal solution, simulations show that the difference is rather small, with the inexpensive and easy to implement nulling scheme performing near optimal.