Computation of Two-Dimensional Fourier Transforms for Noisy Band-Limited Signals

The computation of the two-dimensional Fourier transform by the sampling points creates an ill-posed problem. In this chapter, we will cover this problem for the band-limited signals in the noisy case. We will present a regularized algorithm based on the two-dimensional Shannon Sampling Theorem, the two-dimensional Fourier series, and the regularization method. First, we prove the convergence property of the regularized solution according to the maximum norm. Then an error estimation is given according to the L2-norm. The convergence property of the regularized Fourier series is given in theory, and some examples are given to compare the numerical results of the regularized Fourier series with the numerical results of the Fourier series

Transmit design for MIMO wiretap channel with a malicious jammer

In this paper, we consider the transmit design for multi-input multi-output (MIMO) wiretap channel including a malicious jammer. We first transform the system model into the traditional three-node wiretap channel by whitening the interference at the legitimate user. Additionally, the eavesdropper channel state information (ECSI) may be fully or statistically known, even unknown to the transmitter. Hence, some strategies are proposed in terms of different levels of ECSI available to the transmitter in our paper. For the case of unknown ECSI, a target rate for the legitimate user is first specified. And then an inverse water-filling algorithm is put forward to find the optimal power allocation for each information symbol, with a stepwise search being used to adjust the spatial dimension allocated to artificial noise (AN) such that the target rate is achievable. As for the case of statistical ECSI, several simulated channels are randomly generated according to the distribution of ECSI. We show that the ergodic secrecy capacity can be approximated as the average secrecy capacity of these simulated channels. Through maximizing this average secrecy capacity, we can obtain a feasible power and spatial dimension allocation scheme by using one dimension search. Finally, numerical results reveal the effectiveness and computational efficiency of our algorithms.Comment: 2015 IEEE 81st Vehicular Technology Conference (VTC Spring

Physical Layer Service Integration in 5G: Potentials and Challenges

High transmission rate and secure communication have been identified as the key targets that need to be effectively addressed by fifth generation (5G) wireless systems. In this context, the concept of physical-layer security becomes attractive, as it can establish perfect security using only the characteristics of wireless medium. Nonetheless, to further increase the spectral efficiency, an emerging concept, termed physical-layer service integration (PHY-SI), has been recognized as an effective means. Its basic idea is to combine multiple coexisting services, i.e., multicast/broadcast service and confidential service, into one integral service for one-time transmission at the transmitter side. This article first provides a tutorial on typical PHY-SI models. Furthermore, we propose some state-of-the-art solutions to improve the overall performance of PHY-SI in certain important communication scenarios. In particular, we highlight the extension of several concepts borrowed from conventional single-service communications, such as artificial noise (AN), eigenmode transmission etc., to the scenario of PHY-SI. These techniques are shown to be effective in the design of reliable and robust PHY-SI schemes. Finally, several potential research directions are identified for future work.Comment: 12 pages, 7 figure

Artificial Noise-Aided Biobjective Transmitter Optimization for Service Integration in Multi-User MIMO Gaussian Broadcast Channel

This paper considers an artificial noise (AN)-aided transmit design for multi-user MIMO systems with integrated services. Specifically, two sorts of service messages are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver and required to be perfectly secure from other unauthorized receivers. Our interest lies in the joint design of input covariances of the multicast message, confidential message and artificial noise (AN), such that the achievable secrecy rate and multicast rate are simultaneously maximized. This problem is identified as a secrecy rate region maximization (SRRM) problem in the context of physical-layer service integration. Since this bi-objective optimization problem is inherently complex to solve, we put forward two different scalarization methods to convert it into a scalar optimization problem. First, we propose to prefix the multicast rate as a constant, and accordingly, the primal biobjective problem is converted into a secrecy rate maximization (SRM) problem with quality of multicast service (QoMS) constraint. By varying the constant, we can obtain different Pareto optimal points. The resulting SRM problem can be iteratively solved via a provably convergent difference-of-concave (DC) algorithm. In the second method, we aim to maximize the weighted sum of the secrecy rate and the multicast rate. Through varying the weighted vector, one can also obtain different Pareto optimal points. We show that this weighted sum rate maximization (WSRM) problem can be recast into a primal decomposable form, which is amenable to alternating optimization (AO). Then we compare these two scalarization methods in terms of their overall performance and computational complexity via theoretical analysis as well as numerical simulation, based on which new insights can be drawn.Comment: 14 pages, 5 figure