arXiv subjects

Xiaodong Wang

Publications and source records attributed to Xiaodong Wang.

At least 199 records · Page 11Linked to original sources

arXiv2017

Adaptive Interference Removal for Un-coordinated Radar/Communication Co-existence

Most existing approaches to co-existing communication/radar systems assume that the radar and communication systems are coordinated, i.e., they share information, such as relative position, transmitted waveforms and channel state. In this paper, we consider an un-coordinated scenario where a communication receiver is to operate in the presence of a number of radars, of which only a sub-set may be active, which poses the problem of estimating the active waveforms and the relevant parameters thereof, so as to cancel them prior to demodulation. Two algorithms are proposed for such a joint waveform estimation/data demodulation problem, both exploiting sparsity of a proper representation of the interference and of the vector containing the errors of the data block, so as to implement an iterative joint interference removal/data demodulation process. The former algorithm is based on classical on-grid compressed sensing (CS), while the latter forces an atomic norm (AN) constraint: in both cases the radar parameters and the communication demodulation errors can be estimated by solving a convex problem. We also propose a way to improve the efficiency of the AN-based algorithm. The performance of these algorithms are demonstrated through extensive simulations, taking into account a variety of conditions concerning both the interferers and the respective channel states.

eess.SY↗

arXiv2017

On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion

In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling patterns in the absence of noise based on the geometric analysis on the Grassmannian manifold. A special case where each column has a certain number of noisy entries is considered, where our probabilistic analysis performs very efficiently. Furthermore, assuming that the rank of the original matrix is not given, we provide an analysis to determine if the rank of a valid completion is indeed the actual rank of the data corrupted with sparse noise by verifying some conditions.

cs.IT↗

arXiv2017

Hyperbolicity versus weak periodic orbits inside homoclinic classes

We prove that, for $C^1$-generic diffeomorphisms, if the periodic orbits contained in a homoclinic class $H(p)$ have all their Lyapunov exponents bounded away from 0, then $H(p)$ must be (uniformly) hyperbolic. This is in sprit of the works of the stability conjecture, but with a significant difference that the homoclinic class $H(p)$ is not known isolated in advance, hence the "weak" periodic orbits created by perturbations near the homoclinic class have to be guaranteed strictly inside the homoclinic class. In this sense the problem is of an "intrinsic" nature, and the classical proof of the stability conjecture does not pass through. In particular, we construct in the proof several perturbations which are not simple applications of the connecting lemmas.

math.DS↗

arXiv2017

Joint Design of Overlaid Communication Systems and Pulsed Radars

The focus of this paper is on co-existence between a communication system and a pulsed radar sharing the same bandwidth. Based on the fact that the interference generated by the radar onto the communication receiver is intermittent and depends on the density of scattering objects (such as, e.g., targets), we first show that the communication system is equivalent to a set of independent parallel channels, whereby pre-coding on each channel can be introduced as a new degree of freedom. We introduce a new figure of merit, named the {\em compound rate}, which is a convex combination of rates with and without interference, to be optimized under constraints concerning the signal-to-interference-plus-noise ratio (including {\em signal-dependent} interference due to clutter) experienced by the radar and obviously the powers emitted by the two systems: the degrees of freedom are the radar waveform and the afore-mentioned encoding matrix for the communication symbols. We provide closed-form solutions for the optimum transmit policies for both systems under two basic models for the scattering produced by the radar onto the communication receiver, and account for possible correlation of the signal-independent fraction of the interference impinging on the radar. We also discuss the region of the achievable communication rates with and without interference. A thorough performance assessment shows the potentials and the limitations of the proposed co-existing architecture.

cs.IT↗

arXiv2017

Millimeter-Wave Beamformed Full-dimensional MIMO Channel Estimation Based on Atomic Norm Minimization

The millimeter-wave (mmWave) full-dimensional (FD) MIMO system employs planar arrays at both the base station and user equipment and can simultaneously support both azimuth and elevation beamforming. In this paper, we propose atomic-norm-based methods for mmWave FD-MIMO channel estimation under both uniform planar arrays (UPA) and non-uniform planar arrays (NUPA). Unlike existing algorithms such as compressive sensing (CS) or subspace methods, the atomic-norm-based algorithms do not require to discretize the angle spaces of the angle of arrival (AoA) and angle of departure (AoD) into grids, thus provide much better accuracy in estimation. In the UPA case, to reduce the computational complexity, the original large-scale 4D atomic norm minimization problem is approximately reformulated as a semi-definite program (SDP) containing two decoupled two-level Toeplitz matrices. The SDP is then solved via the alternating direction method of multipliers (ADMM) where each iteration involves only closed-form computations. In the NUPA case, the atomic-norm-based formulation for channel estimation becomes nonconvex and a gradient-decent-based algorithm is proposed to solve the problem. Simulation results show that the proposed algorithms achieve better performance than the CS-based and subspace-based algorithms.

eess.SY↗

arXiv2017

Reliable Beamspace Channel Estimation for Millimeter-Wave Massive MIMO Systems with Lens Antenna Array

Millimeter-wave massive MIMO with lens antenna array can considerably reduce the number of required radio-frequency (RF) chains by beam selection. However, beam selection requires the base station to acquire the accurate information of beamspace channel. This is a challenging task, as the size of beamspace channel is large while the number of RF chains is limited. In this paper, we investigate the beamspace channel estimation problem in mmWave massive MIMO systems with lens antenna array. Specifically, we first design an adaptive selecting network for mmWave massive MIMO systems with lens antenna array, and based on this network, we further formulate the beamspace channel estimation problem as a sparse signal recovery problem. Then, by fully utilizing the structural characteristics of mmWave beamspace channel, we propose a support detection (SD)-based channel estimation scheme with reliable performance and low pilot overhead. Finally, the performance and complexity analyses are provided to prove that the proposed SD-based channel estimation scheme can estimate the support of sparse beamspace channel with comparable or higher accuracy than conventional schemes. Simulation results verify that the proposed SD-based channel estimation scheme outperforms conventional schemes and enjoys satisfying accuracy, even in the low SNR region as the structural characteristics of beamspace channel can be exploited.

cs.IT↗

arXiv2017

Scaled Nuclear Norm Minimization for Low-Rank Tensor Completion

Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover a low-TT-rank sampled tensor by minimizing a weighted sum of nuclear norms of unfoldings of the tensor. We provide numerical results to show that our proposed method requires significantly less number of samples to recover to the original tensor in comparison with simply minimizing the sum of nuclear norms since the structure of the unfoldings in the TT tensor model is fundamentally different from that of matricizations in the Tucker tensor model.

stat.ML↗

arXiv2017

Rank Determination for Low-Rank Data Completion

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries and some given completion. We consider a number of data models, including single-view matrix, multi-view matrix, CP tensor, tensor-train tensor and Tucker tensor. For each of these data models, we provide an upper bound on the rank when an arbitrary low-rank completion is given. We characterize these bounds both deterministically, i.e., with probability one given that the sampling pattern satisfies certain combinatorial properties, and probabilistically, i.e., with high probability given that the sampling probability is above some threshold. Moreover, for both single-view matrix and CP tensor, we are able to show that the obtained upper bound is exactly equal to the unknown rank if the lowest-rank completion is given. Furthermore, we provide numerical experiments for the case of single-view matrix, where we use nuclear norm minimization to find a low-rank completion of the sampled data and we observe that in most of the cases the proposed upper bound on the rank is equal to the true rank.

cs.LG↗

arXiv2017

Joint Energy-Bandwidth Allocation for Multi-User Channels with Cooperating Hybrid Energy Nodes

In this paper, we consider the energy-bandwidth allocation for a network of multiple users, where the transmitters each powered by both an energy harvester and conventional grid, access the network orthogonally on the assigned frequency band. We assume that the energy harvesting state and channel gain of each transmitter can be predicted for $K$ time slots a priori. The different transmitters can cooperate by donating energy to each other. The tradeoff among the weighted sum throughput, the use of grid energy, and the amount of energy cooperation is studied through an optimization objective which is a linear combination of these quantities. This leads to an optimization problem with O($N^2K$) constraints, where $N$ is the total number of transmitter-receiver pairs, and the optimization is over seven sets of variables that denote energy and bandwidth allocation, grid energy utilization, and energy cooperation. To solve the problem efficiently, an iterative algorithm is proposed using the Proximal Jacobian ADMM. The optimization sub-problems corresponding to Proximal Jacobian ADMM steps are solved in closed form. We show that this algorithm converges to the optimal solution with an overall complexity of O($N^2K^2$). Numerical results show that the proposed algorithms can make efficient use of the harvested energy, grid energy, energy cooperation, and the available bandwidth.

cs.IT↗

arXiv2017

Attack Detection in Sensor Network Target Localization Systems with Quantized Data

We consider a sensor network focused on target localization, where sensors measure the signal strength emitted from the target. Each measurement is quantized to one bit and sent to the fusion center. A general attack is considered at some sensors that attempts to cause the fusion center to produce an inaccurate estimation of the target location with a large mean-square-error. The attack is a combination of man-in-the-middle, hacking, and spoofing attacks that can effectively change both signals going into and coming out of the sensor nodes in a realistic manner. We show that the essential effect of attacks is to alter the estimated distance between the target and each attacked sensor to a different extent, giving rise to a geometric inconsistency among the attacked and unattacked sensors. Hence, with the help of two secure sensors, a class of detectors are proposed to detect the attacked sensors by scrutinizing the existence of the geometric inconsistency. We show that the false alarm and miss probabilities of the proposed detectors decrease exponentially as the number of measurement samples increases, which implies that for sufficiently large number of samples, the proposed detectors can identify the attacked and unattacked sensors with any required accuracy.

cs.IT↗

arXiv2017

Fourth-order Tensors with Multidimensional Discrete Transforms

The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to the development of multilinear modeling tools and efficient algorithms. In this paper, we build a novel multilinear tensor space that supports useful algorithms such as SVD and QR, while generalizing the matrix space to fourth-order tensors was believed to be challenging. Specifically, given any multidimensional discrete transform, we show that fourth-order tensors are bilinear operators on a space of matrices. First, we take a transform-based approach to construct a new tensor space by defining a new multiplication operation and tensor products, and accordingly the analogous concepts: identity, inverse, transpose, linear combinations, and orthogonality. Secondly, we define the $\mathcal{L}$-SVD for fourth-order tensors and present an efficient algorithm, where the tensor case requires a stronger condition for unique decomposition than the matrix case. Thirdly, we define the tensor $\mathcal{L}$-QR decomposition and propose a Householder QR algorithm to avoid the catastrophic cancellation problem associated with the conventional Gram-Schmidt process. Finally, we validate our schemes on video compression and one-shot face recognition. For video compression, compared with the existing tSVD, the proposed $\mathcal{L}$-SVD achieves $3\sim 10$dB gains in RSE, while the running time is reduced by about $50\%$ and $87.5\%$, respectively. For one-shot face recognition, the recognition rate is increased by about $10\% \sim 20\%$.

math.NA↗

arXiv2017

Deterministic and Probabilistic Conditions for Finite Completability of Low-rank Multi-View Data

We consider the multi-view data completion problem, i.e., to complete a matrix $\mathbf{U}=[\mathbf{U}_1|\mathbf{U}_2]$ where the ranks of $\mathbf{U},\mathbf{U}_1$, and $\mathbf{U}_2$ are given. In particular, we investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries for finite completability of such a multi-view data given the corresponding rank constraints. In contrast with the existing analysis on Grassmannian manifold for a single-view matrix, i.e., conventional matrix completion, we propose a geometric analysis on the manifold structure for multi-view data to incorporate more than one rank constraint. We provide a deterministic necessary and sufficient condition on the sampling pattern for finite completability. We also give a probabilistic condition in terms of the number of samples per column that guarantees finite completability with high probability. Finally, using the developed tools, we derive the deterministic and probabilistic guarantees for unique completability.

cs.IT↗

arXiv2017

Fundamental Conditions for Low-CP-Rank Tensor Completion

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to the tensors with the given rank and define a set of polynomials based on the sampling pattern and CP decomposition. Then, we show that finite completability of the sampled tensor is equivalent to having a certain number of algebraically independent polynomials among the defined polynomials. Our proposed approach results in characterizing the maximum number of algebraically independent polynomials in terms of a simple geometric structure of the sampling pattern, and therefore we obtain the deterministic necessary and sufficient condition on the sampling pattern for finite completability of the sampled tensor. Moreover, assuming that the entries of the tensor are sampled independently with probability $p$ and using the mentioned deterministic analysis, we propose a combinatorial method to derive a lower bound on the sampling probability $p$, or equivalently, the number of sampled entries that guarantees finite completability with high probability. We also show that the existing result for the matrix completion problem can be used to obtain a loose lower bound on the sampling probability $p$. In addition, we obtain deterministic and probabilistic conditions for unique completability. It is seen that the number of samples required for finite or unique completability obtained by the proposed analysis on the CP manifold is orders-of-magnitude lower than that is obtained by the existing analysis on the Grassmannian manifold.

cs.LG↗

arXiv2017

Improved NN-JPDAF for Joint Multiple Target Tracking and Feature Extraction

Feature aided tracking can often yield improved tracking performance over the standard multiple target tracking (MTT) algorithms with only kinematic measurements. However, in many applications, the feature signal of the targets consists of sparse Fourier-domain signals. It changes quickly and nonlinearly in the time domain, and the feature measurements are corrupted by missed detections and mis-associations. These two factors make it hard to extract the feature information to be used in MTT. In this paper, we develop a feature-aided nearest neighbour joint probabilistic data association filter (NN-JPDAF) for joint MTT and feature extraction in dense target environments. To estimate the rapidly varying feature signal from incomplete and corrupted measurements, we use the atomic norm constraint to formulate the sparsity of feature signal and use the $\ell_1$-norm to formulate the sparsity of the corruption induced by mis-associations. Based on the sparse representation, the feature signal are estimated by solving a semidefinite program (SDP) which is convex. We also provide an iterative method for solving this SDP via the alternating direction method of multipliers (ADMM) where each iteration involves closed-form computation. With the estimated feature signal, re-filtering is performed to estimate the kinematic states of the targets, where the association makes use of both kinematic and feature information. Simulation results are presented to illustrate the performance of the proposed algorithm in a radar application.

eess.SY↗

arXiv2017

Characterization of Deterministic and Probabilistic Sampling Patterns for Finite Completability of Low Tensor-Train Rank Tensor

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ensure finite completability. Specifically, we propose an algebraic geometric analysis on the TT manifold that can incorporate the whole rank vector simultaneously in contrast to the existing approach based on the Grassmannian manifold that can only incorporate one rank component. Our proposed technique characterizes the algebraic independence of a set of polynomials defined based on the sampling pattern and the TT decomposition, which is instrumental to obtaining the deterministic condition on the sampling pattern for finite completability. In addition, based on the proposed analysis, assuming that the entries of the tensor are sampled independently with probability $p$, we derive a lower bound on the sampling probability $p$, or equivalently, the number of sampled entries that ensures finite completability with high probability. Moreover, we also provide the deterministic and probabilistic conditions for unique completability.

cs.LG↗

arXiv2017

Demixing Sines and Spikes: Robust Spectral Super-resolution in the Presence of Outliers

We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a sinusoidal and a sparse component. We propose to demix the two components and super-resolve the spectrum of the multisinusoidal signal by solving a convex program. Our main theoretical result is that-- up to logarithmic factors-- this approach is guaranteed to be successful with high probability for a number of spectral lines that is linear in the number of measurements, even if a constant fraction of the data are outliers. The result holds under the assumption that the phases of the sinusoidal and sparse components are random and the line spectrum satisfies a minimum-separation condition. We show that the method can be implemented via semidefinite programming and explain how to adapt it in the presence of dense perturbations, as well as exploring its connection to atomic-norm denoising. In addition, we propose a fast greedy demixing method which provides good empirical results when coupled with a local nonconvex-optimization step.

math.OC↗

arXiv2017

Asymptotically Optimal Stochastic Encryption for Quantized Sequential Detection in the Presence of Eavesdroppers

We consider sequential detection based on quantized data in the presence of eavesdropper. Stochastic encryption is employed as a counter measure that flips the quantization bits at each sensor according to certain probabilities, and the flipping probabilities are only known to the legitimate fusion center (LFC) but not the eavesdropping fusion center (EFC). As a result, the LFC employs the optimal sequential probability ratio test (SPRT) for sequential detection whereas the EFC employs a mismatched SPRT (MSPRT). We characterize the asymptotic performance of the MSPRT in terms of the expected sample size as a function of the vanishing error probabilities. We show that when the detection error probabilities are set to be the same at the LFC and EFC, every symmetric stochastic encryption is ineffective in the sense that it leads to the same expected sample size at the LFC and EFC. Next, in the asymptotic regime of small detection error probabilities, we show that every stochastic encryption degrades the performance of the quantized sequential detection at the LFC by increasing the expected sample size, and the expected sample size required at the EFC is no fewer than that is required at the LFC. Then the optimal stochastic encryption is investigated in the sense of maximizing the difference between the expected sample sizes required at the EFC and LFC. Although this optimization problem is nonconvex, we show that if the acceptable tolerance of the increase in the expected sample size at the LFC induced by the stochastic encryption is small enough, then the globally optimal stochastic encryption can be analytically obtained; and moreover, the optimal scheme only flips one type of quantized bits (i.e., 1 or 0) and keeps the other type unchanged.

cs.IT↗

arXiv2017

Qualitative Action Recognition by Wireless Radio Signals in Human-Machine Systems

Human-machine systems required a deep understanding of human behaviors. Most existing research on action recognition has focused on discriminating between different actions, however, the quality of executing an action has received little attention thus far. In this paper, we study the quality assessment of driving behaviors and present WiQ, a system to assess the quality of actions based on radio signals. This system includes three key components, a deep neural network based learning engine to extract the quality information from the changes of signal strength, a gradient based method to detect the signal boundary for an individual action, and an activitybased fusion policy to improve the recognition performance in a noisy environment. By using the quality information, WiQ can differentiate a triple body status with an accuracy of 97%, while for identification among 15 drivers, the average accuracy is 88%. Our results show that, via dedicated analysis of radio signals, a fine-grained action characterization can be achieved, which can facilitate a large variety of applications, such as smart driving assistants.

cs.HC↗