61,660 research outputs found
A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels
In this paper, we establish a general framework on the reduced dimensional
channel state information (CSI) estimation and pre-beamformer design for
frequency-selective massive multiple-input multiple-output MIMO systems
employing single-carrier (SC) modulation in time division duplex (TDD) mode by
exploiting the joint angle-delay domain channel sparsity in millimeter (mm)
wave frequencies. First, based on a generic subspace projection taking the
joint angle-delay power profile and user-grouping into account, the reduced
rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived
for spatially correlated wideband MIMO channels. Second, the statistical
pre-beamformer design is considered for frequency-selective SC massive MIMO
channels. We examine the dimension reduction problem and subspace (beamspace)
construction on which the RR-MMSE estimation can be realized as accurately as
possible. Finally, a spatio-temporal domain correlator type reduced rank
channel estimator, as an approximation of the RR-MMSE estimate, is obtained by
carrying out least square (LS) estimation in a proper reduced dimensional
beamspace. It is observed that the proposed techniques show remarkable
robustness to the pilot interference (or contamination) with a significant
reduction in pilot overhead
Three-Valued Spatio-Temporal Logic: a further analysis on spatio-temporal properties of stochastic systems
In this paper we present Three-Valued Spatio-Temporal Logic (TSTL), which enriches the available spatio-temporal analysis of properties expressed in Signal Spatio-Temporal Logic (SSTL), to give further insight into the dynamic behaviour of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and a specific extended monitoring algorithm to check the validity of TSTL formulas. We conclude with two case studies that demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and control programmes based on spatial stochastic population models
Computationally efficient estimation of high-dimension autoregressive models : with application to air pollution in Malta
The modelling and analysis of spatiotemporal behaviour is receiving wide-spread attention due to its applicability to various scientific fields such as the mapping of the electrical activity in the human brain, the spatial spread of pandemics and the diffusion of hazardous pollutants. Nevertheless, due to the complexity of the dynamics describing these systems and the vast datasets of the measurements involved, efficient computational methods are required to obtain representative mathematical descriptions
of such behaviour. In this work, a computationally efficient method for the estimation of heterogeneous spatio-temporal autoregressive models is proposed and tested on a dataset of air pollutants measured over the Maltese islands. Results will highlight the
computation advantages of the proposed methodology and the accuracy of the predictions obtained through the estimated model.peer-reviewe
Big Data and Reliability Applications: The Complexity Dimension
Big data features not only large volumes of data but also data with
complicated structures. Complexity imposes unique challenges in big data
analytics. Meeker and Hong (2014, Quality Engineering, pp. 102-116) provided an
extensive discussion of the opportunities and challenges in big data and
reliability, and described engineering systems that can generate big data that
can be used in reliability analysis. Meeker and Hong (2014) focused on large
scale system operating and environment data (i.e., high-frequency multivariate
time series data), and provided examples on how to link such data as covariates
to traditional reliability responses such as time to failure, time to
recurrence of events, and degradation measurements. This paper intends to
extend that discussion by focusing on how to use data with complicated
structures to do reliability analysis. Such data types include high-dimensional
sensor data, functional curve data, and image streams. We first provide a
review of recent development in those directions, and then we provide a
discussion on how analytical methods can be developed to tackle the challenging
aspects that arise from the complexity feature of big data in reliability
applications. The use of modern statistical methods such as variable selection,
functional data analysis, scalar-on-image regression, spatio-temporal data
models, and machine learning techniques will also be discussed.Comment: 28 pages, 7 figure
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used
in the machine learning and dynamical systems literature to represent complex
dynamical or sequential relationships between variables. More recently, as deep
learning models have become more common, RNNs have been used to forecast
increasingly complicated systems. Dynamical spatio-temporal processes represent
a class of complex systems that can potentially benefit from these types of
models. Although the RNN literature is expansive and highly developed,
uncertainty quantification is often ignored. Even when considered, the
uncertainty is generally quantified without the use of a rigorous framework,
such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a
more formal framework while maintaining the forecast accuracy that makes these
models appealing, by presenting a Bayesian RNN model for nonlinear
spatio-temporal forecasting. Additionally, we make simple modifications to the
basic RNN to help accommodate the unique nature of nonlinear spatio-temporal
data. The proposed model is applied to a Lorenz simulation and two real-world
nonlinear spatio-temporal forecasting applications
Benefits of spatio-temporal modelling for short term wind power forecasting at both individual and aggregated levels
The share of wind energy in total installed power capacity has grown rapidly
in recent years around the world. Producing accurate and reliable forecasts of
wind power production, together with a quantification of the uncertainty, is
essential to optimally integrate wind energy into power systems. We build
spatio-temporal models for wind power generation and obtain full probabilistic
forecasts from 15 minutes to 5 hours ahead. Detailed analysis of the forecast
performances on the individual wind farms and aggregated wind power are
provided. We show that it is possible to improve the results of forecasting
aggregated wind power by utilizing spatio-temporal correlations among
individual wind farms. Furthermore, spatio-temporal models have the advantage
of being able to produce spatially out-of-sample forecasts. We evaluate the
predictions on a data set from wind farms in western Denmark and compare the
spatio-temporal model with an autoregressive model containing a common
autoregressive parameter for all wind farms, identifying the specific cases
when it is important to have a spatio-temporal model instead of a temporal one.
This case study demonstrates that it is possible to obtain fast and accurate
forecasts of wind power generation at wind farms where data is available, but
also at a larger portfolio including wind farms at new locations. The results
and the methodologies are relevant for wind power forecasts across the globe as
well as for spatial-temporal modelling in general
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