Linear Precoding for MIMO Channels with QAM Constellations and Reduced Complexity

In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-output mutual information for QAM systems with relatively moderate MIMO channel sizes. The proposed methodology is next applied in conjunction with the complexity-reducing per-group processing (PGP) technique, which is semi-optimal, to both perfect channel state information at the transmitter (CSIT) as well as statistical channel state information (SCSI) scenarios, with high transmitting and receiving antenna size, and for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder, and the maximum diversity precoder for QAM with constellation sizes $M=16,~32$, and $~64$ and for MIMO channel size $100\times100$

Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches

Uncertainty quantification in aerodynamic simulations calls for efficient numerical methods since it is computationally expensive, especially for the uncertainties caused by random geometry variations which involve a large number of variables. This paper compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and gradient-enhanced version of Kriging, radial basis functions and point collocation polynomial chaos, in their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry which is parameterized by 9 independent Gaussian variables. The results show that gradient-enhanced surrogate methods achieve better accuracy than direct integration methods with the same computational cost

Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations

The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate convergence in MCMC and EM algorithms but are still not well studied for variational Bayes (VB) methods. As a fast deterministic approach to posterior approximation, VB is attracting increasing interest due to its suitability for large high-dimensional data. Use of different parametrizations for VB has not only computational but also statistical implications, as different parametrizations are associated with different factorized posterior approximations. We examine the use of partially noncentered parametrizations in VB for generalized linear mixed models (GLMMs). Our paper makes four contributions. First, we show how to implement an algorithm called nonconjugate variational message passing for GLMMs. Second, we show that the partially noncentered parametrization can adapt to the quantity of information in the data and determine a parametrization close to optimal. Third, we show that partial noncentering can accelerate convergence and produce more accurate posterior approximations than centering or noncentering. Finally, we demonstrate how the variational lower bound, produced as part of the computation, can be useful for model selection.Comment: Published in at http://dx.doi.org/10.1214/13-STS418 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Linear quantile mixed models

Dependent data arise in many studies. For example, children with the same parents or living in neighbouring geographic areas tend to be more alike in many characteristics than individuals chosen at random from the population at large; observations taken repeatedly on the same individual are likely to be more similar than observations from different individuals. Frequently adopted sampling designs, such as cluster, multilevel, spatial, and repeated measures (or longitudinal or panel), may induce this dependence, which the analysis of the data needs to take into due account. In a previous publication (Geraci and Bottai, Biostatistics 2007), we proposed a conditional quantile regression model for continuous responses where a random intercept was included along with fixed-coefficient predictors to account for between-subjects dependence in the context of longitudinal data analysis. Conditional on the random intercept, the response was assumed to follow an asymmetric Laplace distribution. The approach hinged upon the link existing between the minimization of weighted least absolute deviations, typically used in quantile regression, and the maximization of Laplace likelihood. As a follow up to that study, here we consider an extension of those models to more complex dependence structures in the data, which are modelled by including multiple random effects in the linear conditional quantile functions. Differently from the Gibbs sampling expectation-maximization approach proposed previously, the estimation of the fixed regression coefficients and of the random effects covariance matrix is based on a combination of Gaussian quadrature approximations and optimization algorithms. The former include Gauss-Hermite and Gauss-Laguerre quadratures for, respectively, normal and double exponential (i.e., symmetric Laplace) random effects; the latter include a gradient search algorithm and general purpose optimizers. As a result, some of the computational burden associated with large Gibbs sample sizes is avoided. We also discuss briefly an estimation approach based on generalized Clarke derivatives. Finally, a simulation study is presented and some preliminary results are shown