arXiv subjects

Xiaodong Wang

Publications and source records attributed to Xiaodong Wang.

At least 235 records · Page 13Linked to original sources

arXiv2015

On the dominated splitting of Lyapunov stable aperiodic classes

Recent works related to Palis conjecture of J. Yang, S. Crovisier, M. Sambarino and D. Yang showed that any aperiodic class of a $C^1$-generic diffeomorphism far away from homoclinic bifurcations (or homoclinic tangencies) is partially hyperbolic. We show in this paper that, generically, a non-trivial dominated splitting implies partial hyperbolicity for an aperiodic class if it is Lyapunov stable. More precisely, for $C^1$-generic diffeomorphisms, if a Lyapunov stable aperiodic class has a non-trivial dominated splitting $E\oplus F$, then one of the two bundles is hyperbolic (either $E$ is contracted or $F$ is expanded).

math.DS↗

arXiv2015

Information and Energy Cooperation in OFDM Relaying: Protocols and Optimization

Integrating power transfer into wireless communications for supporting simultaneous wireless information and power transfer (SWIPT) is a promising technique in energy-constrained wireless networks. While most existing work on SWIPT focuses on capacity-energy characterization, the benefits of cooperative transmission for SWIPT are much less investigated. In this paper, we consider SWIPT in an orthogonal frequency-division multiplexing (OFDM) relaying system, where a source node transfers information and a fraction of power simultaneously to a relay node, and the relay node uses the harvested power from the source node to forward the source information to the destination. To support the simultaneous information and energy cooperation, we first propose a transmission protocol assuming that the direct link between the source and destination does not exist, namely power splitting (PS) relaying protocol, where the relay node splits the received signal power in the first hop into two separate parts, one for information decoding and the other for energy harvesting. Then, we consider the case that the direct link between the source and destination is available, and the transmission mode adaptation (TMA) protocol is proposed, where the transmission can be completed by cooperative mode and direct mode simultaneously (over different subcarriers). In direct mode, when the source transmits signal to the destination, the destination receives the signal as information and the relay node concurrently receives the signal for energy harvesting. Joint resource allocation problems are formulated to maximize the system throughput. By using the Lagrangian dual method, we develop efficient algorithms to solve the nonconvex optimization problems.

cs.IT↗

arXiv2015

An Efficient Dynamic Programming Algorithm for STR-IC-SEQ-EC-LCS Problem

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length $s$ must be included as a substring and the other constraining sequence of length $t$ must be excluded as a subsequence of two main sequences and the length of the result must be maximal. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and the given two constraining sequences of length $s$ and $t$, we present an $O(nmst)$ time dynamic programming algorithm for solving the new generalized longest common subsequence problem. The time complexity can be reduced further to cubic time in a more detailed analysis. The correctness of the new algorithm is proved.

cs.DS↗

arXiv2015

An efficient dynamic programming algorithm for the generalized LCS problem with multiple substring inclusive constraints

In this paper, we consider a generalized longest common subsequence problem with multiple substring inclusive constraints. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints $P=\{P_1,\cdots,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ including each of constraint string in $P$ as a substring and the length of $Z$ is maximized. A new dynamic programming solution to this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(d2^dnmr)$. In the case of the number of constraint strings is fixed, our new algorithm for the generalized longest common subsequence problem with multiple substring inclusive constraints requires $O(nmr)$ time and space.

cs.DS↗

arXiv2015

Decentralized Sequential Composite Hypothesis Test Based on One-Bit Communication

This paper considers the sequential composite hypothesis test with multiple sensors. The sensors observe random samples in parallel and communicate with a fusion center, who makes the global decision based on the sensor inputs. On one hand, in the centralized scenario, where local samples are precisely transmitted to the fusion center, the generalized sequential likelihood ratio test (GSPRT) is shown to be asymptotically optimal in terms of the expected sample size as error rates tend to zero. On the other hand, for systems with limited power and bandwidth resources, decentralized solutions that only send a summary of local samples (we particularly focus on a one-bit communication protocol) to the fusion center is of great importance. To this end, we first consider a decentralized scheme where sensors send their one-bit quantized statistics every fixed period of time to the fusion center. We show that such a uniform sampling and quantization scheme is strictly suboptimal and its suboptimality can be quantified by the KL divergence of the distributions of the quantized statistics under both hypotheses. We then propose a decentralized GSPRT based on level-triggered sampling. That is, each sensor runs its own GSPRT repeatedly and reports its local decision to the fusion center asynchronously. We show that this scheme is asymptotically optimal as the local thresholds and global thresholds grow large at different rates. Lastly, two particular models and their associated applications are studied to compare the centralized and decentralized approaches. Numerical results are provided to demonstrate that the proposed level-triggered sampling based decentralized scheme aligns closely with the centralized scheme with substantially lower communication overhead, and significantly outperforms the uniform sampling and quantization based decentralized scheme.

stat.AP↗

arXiv2014

Sequential and Decentralized Estimation of Linear Regression Parameters in Wireless Sensor Networks

Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed samples, hence is random, as opposed to fixed-sample-size estimation. Specifically, after receiving a new sample, if a target accuracy level is reached, we stop and estimate using the samples collected so far; otherwise we continue to receive another sample. It is known that finding an optimum sequential estimator, which minimizes the average sample number for a given target accuracy level, is an intractable problem with a general stopping rule that depends on the complete observation history. By properly restricting the search space to stopping rules that depend on a specific subset of the complete observation history, we derive the optimum sequential estimator in the centralized case via optimal stopping theory. However, finding the optimum stopping rule in this case requires numerical computations that {\em quadratically} scales with the number of parameters to be estimated. For the decentralized setup with stringent energy constraints, under an alternative problem formulation that is conditional on the observed regressors, we first derive a simple optimum scheme whose computational complexity is {\em constant} with respect to the number of parameters. Then, following this simple optimum scheme we propose a decentralized sequential estimator whose computational complexity and energy consumption scales {\em linearly} with the number of parameters. Specifically, in the proposed decentralized scheme a close-to-optimum average stopping time performance is achieved by infrequently transmitting a single pulse with very short duration.

stat.AP↗

arXiv2014

On the hyperbolicity of $C^1$-generic homoclinic classes

Works of Liao, Mañé, Franks, Aoki and Hayashi characterized lack of hyperbolicity for diffeomorphisms by the existence of weak periodic orbits. In this note we announce a result which can be seen as a local version of these works: for C$^1$-generic diffeomorphism, a homoclinic class either is hyperbolic or contains a sequence of periodic orbits that have a Lyapunov exponent arbitrarily close to 0. Des travaux de Liao, Mañé, Franks, Aoki et Hayashi ont caractérisé le manque d'hyperbolicité des difféomorphismes par l'existence d'orbites périodiques faibles. Dans cette note, nous annonçons un résultat qui peut être considéré comme une version locale de ces travaux: pour les difféomorphismes C$^1$-génériques, une classe homocline ou bien est hyperbolique, ou bien contient une suite d'orbites périodiques qui ont un exposant de Lyapunov arbitrairement proche de 0.

math.DS↗

arXiv2014

Cooperative Change Detection for Online Power Quality Monitoring

This paper considers the real-time power quality monitoring in power grid systems. The goal is to detect the occurrence of disturbances in the nominal sinusoidal voltage/current signal as quickly as possible such that protection measures can be taken in time. Based on an autoregressive (AR) model for the disturbance, we propose a generalized local likelihood ratio (GLLR) detector which processes meter readings sequentially and alarms as soon as the test statistic exceeds a prescribed threshold. The proposed detector not only reacts to a wide range of disturbances, but also achieves lower detection delay compared to the conventional block processing method. Then we further propose to deploy multiple meters to monitor the power signal cooperatively. The distributed meters communicate wirelessly to a central meter, where the data fusion and detection are performed. In light of the limited bandwidth of wireless channels, we develop a level-triggered sampling scheme, where each meter transmits only one-bit each time asynchronously. The proposed multi-meter scheme features substantially low communication overhead, while its performance is close to that of the ideal case where distributed meter readings are perfectly available at the central meter.

eess.SY↗

arXiv2014

Energy Management and Cross Layer Optimization for Wireless Sensor Network Powered by Heterogeneous Energy Sources

Recently, utilizing renewable energy for wireless system has attracted extensive attention. However, due to the instable energy supply and the limited battery capacity, renewable energy cannot guarantee to provide the perpetual operation for wireless sensor networks (WSN). The coexistence of renewable energy and electricity grid is expected as a promising energy supply manner to remain function for a potentially infinite lifetime. In this paper, we propose a new system model suitable for WSN, taking into account multiple energy consumptions due to sensing, transmission and reception, heterogeneous energy supplies from renewable energy, electricity grid and mixed energy, and multidimension stochastic natures due to energy harvesting profile, electricity price and channel condition. A discrete-time stochastic cross-layer optimization problem is formulated to achieve the optimal trade-off between the time-average rate utility and electricity cost subject to the data and energy queuing stability constraints. The Lyapunov drift-plus-penalty with perturbation technique and block coordinate descent method is applied to obtain a fully distributed and low-complexity cross-layer algorithm only requiring knowledge of the instantaneous system state. The explicit trade-off between the optimization objective and queue backlog is theoretically proven. Finally, the extensive simulations verify the theoretic claims.

cs.NI↗

arXiv2014

Sequential Joint Detection and Estimation: Optimum Tests and Applications

We treat the statistical inference problems in which one needs to detect and estimate simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the intrinsic coupling between them. However, a joint detection and estimation problem should be solved to maximize the overall performance. We address the sample size concern through a sequential and Bayesian setup. Specifically, we seek the optimum triplet of stopping time, detector, and estimator(s) that minimizes the number of samples subject to a constraint on the combined detection and estimation cost. A general framework for optimum sequential joint detection and estimation is developed. The resulting optimum detector and estimator(s) are strongly coupled with each other, proving that the separate treatment is strictly sub-optimum. The theoretical results derived for a quite general model are then applied to several problems with linear quadratic Gaussian (LQG) models, including dynamic spectrum access in cognitive radio, and state estimation in smart grid with topological uncertainty. Numerical results corroborate the superior overall detection and estimation performance of the proposed schemes over the conventional methods that handle the subproblems separately.

stat.AP↗

arXiv2014

Dynamic Optimization For Heterogeneous Powered Wireless Multimedia Sensor Networks With Correlated Sources and Network Coding

The energy consumption in wireless multimedia sensor networks (WMSN) is much greater than that in traditional wireless sensor networks. Thus, it is a huge challenge to remain the perpetual operation for WMSN. In this paper, we propose a new heterogeneous energy supply model for WMSN through the coexistence of renewable energy and electricity grid. We address to cross-layer optimization for the multiple multicast with distributed source coding and intra-session network coding in heterogeneous powered wireless multimedia sensor networks (HPWMSN) with correlated sources. The aim is to achieve the optimal reconstruct distortion at sinks and the minimal cost of purchasing electricity from electricity grid. Based on the Lyapunov drift-plus-penalty with perturbation technique and dual decomposition technique, we propose a fully distributed dynamic cross-layer algorithm, including multicast routing, source rate control, network coding, session scheduling and energy management, only requiring knowledge of the instantaneous system state. The explicit trade-off between the optimization objective and queue backlog is theoretically proven. Finally, the simulation results verify the theoretic claims.

cs.NI↗

arXiv2014

On the Capacity Regions of Two-Way Diamond Channels

In this paper, we study the capacity regions of two-way diamond channels. We show that for a linear deterministic model the capacity of the diamond channel in each direction can be simultaneously achieved for all values of channel parameters, where the forward and backward channel parameters are not necessarily the same. We divide the achievability scheme into three cases, depending on the forward and backward channel parameters. For the first case, we use a reverse amplify-and-forward strategy in the relays. For the second case, we use four relay strategies based on the reverse amplify-and-forward with some modifications in terms of replacement and repetition of some stream levels. For the third case, we use two relay strategies based on performing two rounds of repetitions in a relay. The proposed schemes for deterministic channels are used to find the capacity regions within constant gaps for two special cases of the Gaussian two-way diamond channel. First, for the general Gaussian two-way relay channel with a simple coding scheme the smallest gap is achieved compared to the prior works. Then, a special symmetric Gaussian two-way diamond model is considered and the capacity region is achieved within four bits.

cs.IT↗

arXiv2014

Stochastic Optimal Linear Control of Wireless Networked Control Systems with Delays and Packet Losses

In this paper, the design of the optimal decentralized state-feedback controllers is considered for a wireless sensor and actuator network (WSAN) with stochastic network-induced delays and packet losses. In particular, taking advantage of multiple controllers, we model the WSAN as a wireless networked control system (NCS) with decentralized controllers, and then formulate the stochastic optimal state-feedback control problem as a non-cooperative linear quadratic (LQ) game. The optimal control law of each controller is obtained that is a function of the current plant state and all past control signals. The performance of the proposed stochastic optimal control algorithm is investigated using both a genetic control system and a load frequency control (LFC) system in power grid.

eess.SY↗

arXiv2014

Multiuser Joint Energy-Bandwidth Allocation with Energy Harvesting - Part I: Optimum Algorithm & Multiple Point-to-Point Channels

In this paper, we develop optimal energy-bandwidth allocation algorithms in fading channels for multiple energy harvesting transmitters, each may communicate with multiple receivers via orthogonal channels. We first assume that the side information of both the channel states and the energy harvesting states is known for $K$ time slots {\em a priori}, and the battery capacity and the maximum transmission power in each time slot are bounded. The objective is to maximize the weighted sum-rate of all transmitters over the $K$ time slots by assigning the transmission power and bandwidth for each transmitter in each slot. The problem is formulated as a convex optimization problem with ${\cal O}(MK)$ constraints, where $M$ is the number of the receivers, making it hard to solve with a generic convex solver. An iterative algorithm is proposed that alternatively solves two subproblems in each iteration. The convergence and the optimality of this algorithm are also shown. We then consider the special case that each transmitter only communicates with one receiver and the objective is to maximize the total throughput. We develop efficient algorithms for solving the two subproblems and the optimal energy-bandwidth allocation can be obtained with an overall complexity of ${\cal O}(MK^2)$. Moreover, a heuristic algorithm is also proposed for energy-bandwidth allocation based on causal information of channel and energy harvesting states.

cs.IT↗

arXiv2014

Multiuser Joint Energy-Bandwidth Allocation with Energy Harvesting - Part II: Multiple Broadcast Channels & Proportional Fairness

In this paper, we consider the energy-bandwidth allocation for a network with multiple broadcast channels, where the transmitters access the network orthogonally on the assigned frequency band and each transmitter communicates with multiple receivers orthogonally or non-orthogonally. We assume that the energy harvesting state and channel gain of each transmitter can be predicted for $K$ slots {\em a priori}. To maximize the weighted throughput, we formulate an optimization problem with $O(MK)$ constraints, where $M$ is the number of the receivers, and decompose it into the energy and bandwidth allocation subproblems. In order to use the iterative algorithm proposed in [1] to solve the problem, we propose efficient algorithms to solve the two subproblems, so that the optimal energy-bandwidth allocation can be obtained with an overall complexity of ${\cal O}(MK^2)$, even though the problem is non-convex when the broadcast channel is non-orthogonal. For the orthogonal broadcast channel, we further formulate a proportionally-fair (PF) throughput maximization problem and derive the equivalence conditions such that the optimal solution can be obtained by solving a weighted throughput maximization problem. Further, the algorithm to obtain the proper weights is proposed. Simulation results show that the proposed algorithm can make efficient use of the harvested energy and the available bandwidth, and achieve significantly better performance than some heuristic policies for energy and bandwidth allocation. Moreover, it is seen that with energy-harvesting transmitters, non-orthogonal broadcast offers limited gain over orthogonal broadcast.

cs.IT↗

arXiv2014

Distributed Energy Efficient Cross-layer Optimization for Multihop MIMO Cognitive Radio Networks with Primary User Rate Protection

Due to the unique physical-layer characteristics associated with MIMO and cognitive radio (CR), the network performance is tightly coupled with mechanisms at the physical, link, network, and transport layers. In this paper, we consider an energy-efficient cross-layer optimization problem in multihop MIMO CR networks. The objective is to balance the weighted network utility and weighted power consumption of SU sessions, with a minimum PU transmission rate constraint and SU power consumption constraints. However, this problem is highly challenging due to the nonconvex PU rate constraint. We propose a solution that features linearization-based alternative optimization method and a heuristic primal recovery method. We further develop a distributed algorithm to jointly optimize covariance matrix at each transmitting SU node, bandwidth allocation at each SU link, rate control at each session source and multihop/multi-path routing. Extensive simulation results demonstrate that the performance of the proposed distributed algorithm is close to that of the centralized algorithm, and the proposed framework provides an efficient way to significantly save power consumption, while achieving the network utility very close to that achieved with full power consumption.

cs.NI↗

arXiv2014

An integral formula in Kahler geometry with applications

We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski type formula on the complex hyperbolic space we prove that any closed, embedded hypersurface of constant mean curvature must be a geodesic sphere, provided the hypersurface is Hopf. A similar result is established on the complex projective space.

math.DG↗

arXiv2014

Boundary Effect of Ricci Curvature

On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature. Then we discuss related rigidity questions and prove Ricci curvature rigidity results for manifolds with boundary.

math.DG↗