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It is well-known that the traditional transmit beamforming at a base station (BS) to manage interference in serving multiple users is effective only when the number of users is less than the number of transmit antennas at the BS. Non-orthogonal multiple access (NOMA) can improve the throughput of users with poorer channel conditions by compromising their own privacy because other users with better channel conditions can decode the information of users in poorer channel state. NOMA still prefers that the number of users is less than the number of antennas at the BS transmitter. This paper resolves such issues by allocating separate fractional time slots for serving the users with similar channel conditions. This enables the BS to serve more users within the time unit while the privacy of each user is preserved. The fractional times and beamforming vectors are jointly optimized to maximize the system's throughput. An efficient path-following algorithm, which invokes a simple convex quadratic program at each iteration, is proposed for the solution of this challenging optimization problem. Numerical results confirm its versatility., Comment: IEEE Communications Letters (To Appear)

This paper considers the joint design of user power allocation and relay beamforming in relaying communications, in which multiple pairs of single-antenna users exchange information with each other via multiple-antenna relays in two time slots. All users transmit their signals to the relays in the first time slot while the relays broadcast the beamformed signals to all users in the second time slot. The aim is to maximize the system's energy efficiency (EE) subject to quality-of-service (QoS) constraints in terms of exchange throughput requirements. The QoS constraints are nonconvex with many nonlinear cross-terms, so finding a feasible point is already computationally challenging. The sum throughput appears in the numerator while the total consumption power appears in the denominator of the EE objective function. The former is a nonconcave function and the latter is a nonconvex function, making fractional programming useless for EE optimization. Nevertheless, efficient iterations of low complexity to obtain its optimized solutions are developed. The performances of the multiple-user and multiple-relay networks under various scenarios are evaluated to show the merit of the paper development., Comment: 26 pages, 9 figures

Considering a multiple-user multiple-input multiple-output (MIMO) channel with an eavesdropper, this letter develops a beamformer design to optimize the energy efficiency in terms of secrecy bits per Joule under secrecy quality-of-service constraints. This is a very difficult design problem with no available exact solution techniques. A path-following procedure, which iteratively improves its feasible points by using a simple quadratic program of moderate dimension, is proposed. Under any fixed computational tolerance the procedure terminates after finitely many iterations, yielding at least a locally optimal solution. Simulation results show the superior performance of the obtained algorithm over other existing methods., Comment: 12 pages, 2 figures

Next-generation communication networks will likely involve the energy-efficient transfer of information and energy over the same wireless channel, for which the physical layer will become more vulnerable to cyber attacks by potential multi-antenna eavesdroppers. To address this issue, this paper considers transmit time-switching (TS) mode, in which energy and information signals are transmitted separately in time by the BS. This protocol is not only easy to implement but also delivers the opportunity of multi-purpose beamforming, in which energy beamformers during wireless power transfer are useful in jamming the eavesdropper. In the presence of imperfect channel estimation and multi-antenna eavesdroppers, the energy and information beamformers and the transmit TS ratio are jointly optimized to maximize the worst-case user secrecy rate subject to UEs' harvested energy thresholds and a BS transmit power budget. New robust path-following algorithms, which involve one simple convex quadratic program at each iteration are proposed for computational solutions of this difficult optimization problem and also the problem of secure energy efficiency maximization. The latter is further complex due to additional optimization variables appearing in the denominator of the secrecy rate function. Numerical results confirm that the performance of the proposed computational solutions is robust against the channel uncertainties.

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and compression quality. Regardless of tensor order, MPS compresses tensors to matrices of moderate dimension which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement and arrives at the global optimal matrix, bypassing local alternating optimization, which is not only computationally expensive but cannot yield the global solution. Benchmark results show that MPS can achieve better classification performance with favorable computation cost compared to other tensor compression methods., Comment: 12 pages, 4 figures

This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor, applying a dimensionality augmentation technique to the tensor, utilizing a tensor completion algorithm for recovering its missing entries, and finally extracting the recovered image from the tensor. The solution relies on two key components that have been recently proposed to take advantage of the tensor train (TT) rank: A tensor augmentation tool called ket augmentation (KA) that represents a low-order tensor by a higher-order tensor, and the algorithm tensor completion by parallel matrix factorization via tensor train (TMac-TT), which has been demonstrated to outperform state-of-the-art tensor completion algorithms. Simulation results for color image recovery show the clear advantage of our framework against current state-of-the-art tensor completion algorithms., Comment: 7 pages, 6 figures, submitted to ICSPCS 2016

We consider the joint design of transmit beamforming and receive signal-splitting ratios in the downlink of a wireless network with simultaneous radio-frequency (RF) information and energy transfer. Under constraints on the signal-to-interference-plus-noise ratio (SINR) at each user and the total transmit power at the base station, the design objective is to maximize either the sum harvested energy or the minimum harvested energy. We develop a computationally efficient path-following method to solve these challenging nonconvex optimization problems. We mathematically show that the proposed algorithms iteratively progress and converge to locally optimal solutions. Simulation results further show that these locally optimal solutions are the same as the globally optimal solutions for the considered practical network settings., Comment: accepted for publication in IEEE Communication Letters

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via tensor train (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher-orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods., Comment: Submitted to the IEEE Transactions on Image Processing. arXiv admin note: substantial text overlap with arXiv:1601.01083

Our aim in this paper is to establish stable manifolds near hyperbolic equilibria of fractional differential equations in arbitrary finite dimensional spaces.

This paper presents two-hop relay gain-scheduling control in a Wireless Sensor Network to estimate a static target prior characterized by Gaussian probability distribution. The target is observed by a network of linear sensors, whose observations are transmitted to a fusion center for carrying out final estimation via a amplify-and-forward relay node. We are concerned with the joint transmission power allocation for sensors and relay to optimize the minimum mean square error (MMSE) estimator, which is deployed at the fusion center. Particularly, such highly nonlinear optimization problems are solved by an iterative procedure of very low computational complexity. Simulations are provided to support the efficiency of our proposed power allocation., Comment: Submitted to IEEE ICCE 2016

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global information of tensors thanks to its construction by a well-balanced matricization scheme. Two algorithms are proposed to solve the corresponding tensor completion problem. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing the TT nuclear norm. The second one is based on a multilinear matrix factorization model to approximate the TT rank of the tensor and called tensor completion by parallel matrix factorization via tensor train (TMac-TT). These algorithms are applied to complete both synthetic and real world data tensors. Simulation results of synthetic data show that the proposed algorithms are efficient in estimating missing entries for tensors with either low Tucker rank or TT rank while Tucker-based algorithms are only comparable in the case of low Tucker rank tensors. When applied to recover color images represented by ninth-order tensors augmented from third-order ones, the proposed algorithms outperforms the Tucker-based algorithms., Comment: 11 pages, 9 figures

Using synchrotron powder diffraction the structure of a co-crystal between benzene and ethane has been determined. The structure is remarkable, a lattice of benzene molecules playing host to ethane molecules. This is demonstrated by the similarity between the interactions found in the co-crystal structure and those in the pure structure, showing that the C-H...{\pi} network of benzene is maintained as a 'host' but expands to allow the ethane 'guest' to situate within the channels that result from this network. The co-crystal is determined to be a 3:1 benzene:ethane co-crystal and its structure is described by the trigonal space group $R\bar{3}$ with a = 15.977(1) {\AA} and c = 5.581(1) {\AA} at 90 K, resulting in a density of 1.067 g$\cdot$cm$^{-3}$. Conditions under which this co-crystal forms indicate that it could readily be present on the surface of Saturn's moon Titan as an evaporite deposit following the evaporation of hydrocarbon fluids., Comment: 12 pages, 7 figures, submitted to IuCrJ

The infinite Projected Entangled Pair States (iPEPS) algorithm [J. Jordan et al, PRL 101, 250602 (2008)] has become a useful tool in the calculation of ground state properties of 2d quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly-entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings, and (ii) improved overall stability. Besides, we extend the application of the \emph{local gauge fixing}, successfully implemented for finite-size PEPS [M. Lubasch, J. Ignacio Cirac, M.-C. Ba\~{n}uls, PRB 90, 064425 (2014)], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method, but also accelerates the convergence of the alternating least squares sweeping in the (either "full" or "fast full") tensor update scheme. The improvement in terms of computational cost and stability of the resulting "improved" iPEPS algorithm is benchmarked by studying the ground state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice., Comment: 13 pages, 13 figures, 1 table, Revised version

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to the so-called core tensor of maximum order three which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement without any recursive procedure needed for optimizing local tensors. Thus, it leads to substantial computational savings compared to other tensor feature extraction methods such as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition (TD). Benchmark results show that MPS can reduce significantly the feature space of data while achieving better classification performance compared to HOOI., Comment: 10 pages, 3 figures, updated introduction, submitted to IEEE Transactions on Signal Processing