Orthogonal Estimation Research Articles

Iterative Channel Estimation for the Chinese Digital Television Terrestrial Broadcasting Systems with the Multiple-Antenna Receivers

Orthogonal frequency division multiplexing is an effective against multipath fading and high data throughput wireless channel transmission technology. Assistance with the inverse fast Fourier transform and fast Fourier transform operation, orthogonal frequency division multiplexing modulation and demodulation operations of the system convenient and convenient hardware implementation, orthogonal frequency division multiplexing, so in the modern digital television terrestrial broadcasting the system is widely used to support high performance bandwidth-efficient multimedia services. Broadband multi-carrier orthogonal frequency division multiplexing with multi-antenna and multi-antenna receiving system, to increase the diversity gain and improve the capacity of the system in different multipath fading channel. Accurate channel estimation in a simple channel equalization and decoding of broadband multi-carrier orthogonal frequency division multiple-antenna receiver and channel estimation accuracy and multiplexing system is very important, is the key to the performance of the overall broadband multi-carrier orthogonal frequency division multiplexing system in the multi-antenna receiver bit error rate. In this paper, iterative channel estimation to plan for digital terrestrial television broadcasting broadband multi-carrier orthogonal frequency division multiple antenna receiver multiplexing system proposal.

Novel semi-blind channel estimation schemes for Rician fading MIMO channel

In this paper, we propose two novel semi-blind channel estimation techniques based on QR decomposition for Rician fading Multiple Input Multiple Output (MIMO) channel. In the first technique, the MIMO channel matrix H can be decomposed as an upper triangular matrix R and unitary rotation matrix Q as H = RQ. The matrix R is estimated blindly from only received data by using the orthogonal matrix triangularization based Householder QR decomposition, while the optimum rotation matrix Q is estimated exclusively from the algorithm of Orthogonal Pilot Maximum Likelihood Estimator (OPML) based on pilot information. In the second technique, the joint semi-blind channel and data estimation is performed by using the Least Square (LS) algorithm based on QR decomposition. The simulation results obtained for 4-PSK data modulation scheme using two transmitters and six receiver antennas for different Rice factor (K) have shown that the BER performance increases with an increase in the Rice factor. Finally, we compare these two new techniques with the conventional semi-blind channel estimation technique based on Whitening Rotation (WR), and the results show that the first proposed technique outperforms and the second technique achieves a very nearby performance as compared to the technique based on whitening rotation.

Evaluating Covariance Forecasts Via Mean-Variance Portfolio Decisions

This paper presents an empirical comparative study of di fferent covariance estimators. The Engle-Colacito test is used for an indirect evaluation of alternative out-of-sample covariance forecasts in a portfolio setting for varying sample sizes, short selling constraints and market conditions. Errors in the estimation of variances have a higher impact on realized portfolio variance than errors in the estimation of covariances. Bayesian shrinkage estimators and the orthogonal GARCH estimator of covariance matrices lead to signi ficantly lower realized portfolio volatility compared to benchmark estimators.

Coherent estimates of genetic effects with missing information

Genetic effect estimates for loci detected in quantitative trait locus (QTL) mapping experiments depend upon two factors. First, they are parameterizations of the genotypic values determined by the model of genetic effects. Second, they are consequently also affected by the regression method used to estimate the genotypic values from the observed marker genotypes and phenotypes. There are two common causes for marker-genotype data to be incomplete in those experiments—missing marker-genotypes and within-interval mapping. Different regression methods tend to differ in how this missing information is represented and handled. In this communication we explain why the estimates of genetic effects of QTL obtained using standard regression methods are not coherent with the model of genetic effects and indeed show intrinsic inconsistencies when there is incomeplete genotype information. We then describe the interval mapping by imputations (IMI) regression method and prove that it overcomes those problems. A numerical example is used to illustrate the use of IMI and the consequences of using current methods of choice. IMI enables researchers to obtain estimates of genetic effects that are coherent with the model of genetic effects used, despite incomplete genotype information. Furthermore, because IMI allows orthogonal estimation of genetic effects, it shows potential performance advantages for being implemented in QTL mapping tools.

Improved orthogonal polynomial density estimates

Density estimates that are expressible as the product of a base density function and a linear combination of orthogonal polynomials are considered in this paper. More specifically, two criteria are proposed for determining the number of terms to be included in the polynomial adjustment component and guidelines are suggested for the selection of a suitable base density function. A simulation study reveals that these stopping rules produce density estimates that are generally more accurate than kernel density estimates or those resulting from the application of the Kronmal–Tarter criterion. Additionally, it is explained that the same approach can be utilized to obtain multivariate density estimates. The proposed orthogonal polynomial density estimation methodology is applied to several univariate and bivariate data sets, some of which have served as benchmarks in the statistical literature on density estimation.

Online wavelet-based density estimation for non-stationary streaming data

There has been an important emergence of applications in which data arrives in an online time-varying fashion (e.g. computer network traffic, sensor data, web searches, ATM transactions) and it is not feasible to exchange or to store all the arriving data in traditional database systems to operate on it. For this kind of applications, as it is for traditional static database schemes, density estimation is a fundamental block for data analysis. A novel online approach for probability density estimation based on wavelet bases suitable for applications involving rapidly changing streaming data is presented. The proposed approach is based on a recursive formulation of the wavelet-based orthogonal estimator using a sliding window and includes an optimised procedure for reevaluating only relevant scaling and wavelet functions each time new data items arrive. The algorithm is tested and compared using both simulated and real world data.

Nonparametric Regression With Predictors Missing at Random

Nonparametric regression with predictors missing at random (MAR), where the probability of missing depends only on observed variables, is considered. Univariate predictor is the primary case of interest. A new adaptive orthogonal series estimator is developed. Large sample theory shows that the estimator is rate-minimax and it is also sharp-minimax whenever predictors are missing completely at random (MCAR). Furthermore, confidence bands, estimation of nuisance functions, including conditional probability of observing the predictor, design density and scale, and multiple regression are also considered. Numerical study and a real example show feasibility of the proposed methodology for small samples. Supplementary materials, containing results of the numerical study, are available online.

Novel Semi-blind Channel Estimation Schemes for Rayleigh Flat Fading MIMO Channels

In this paper, we propose two novel semi-blind channel estimation techniques based on QR decomposition for Rayleigh flat fading Multiple Input Multiple output (MIMO) channel using various pilot symbols. In the first technique, the flat-fading MIMO channel matrix H can be decomposed as an upper triangular matrix R and a unitary rotation matrix Q as H = RQ. The matrix R is estimated blindly from only received data by using orthogonal matrix triangularization based house holder QR decomposition, while the optimum rotation matrix Q is estimated exclusively from pilot based Orthogonal Pilot Maximum Likelihood Estimator (OPML) algorithm. In the second technique, joint semi-blind channel and data estimation is performed using QR decomposition based Least Square (LS) algorithm. Simulations have taken under 4-PSK data modulation scheme for two transmitters and six receiver antennas using various training symbols. Finally, these two new techniques compare with Whitening Rotation (WR) based semi-blind channel estimation technique and results shows that those new techniques achieve very nearby performance with low complexity compare to Whitening rotation based technique. Also first technique with perfect R outperforms Whitening Rotation based technique.

Blocking Response Surface Designs Incorporating Neigh-bour Effects

In this paper, blocking in response surface for fitting first order model incorporating neighbour effects has been investigated. The conditions for orthogonal estimation of the parameters of the model have been obtained. A method of constructing designs which ensures the constancy of variance of the parameter estimates of the model has also been given.

A Signal-Perturbation-Free Transmit Scheme for MIMO-OFDM Channel Estimation

In this paper, a novel signal-perturbation-free (SPF) approach is presented for frequency-selective multiple-input-multiple-output orthogonal frequency division multiplexing channel estimation. First, an efficient transmit scheme, which bears partial information of the correlation matrix of the transmitted signal called SPF data, is proposed for the cancellation of signal-perturbation error at the receiver. A detailed transmit structure is designed to implement the SPF scheme, which is then employed along with linear prediction (LP) to derive a new semiblind channel-estimation algorithm. It is shown that the new transmit scheme can completely cancel the signal-perturbation error in the noise-free case while being able to sufficiently suppress the perturbation error in noisy conditions. It is also shown that the SPF data needs only to be transmitted over a small number of subcarriers, and its overhead to the overall transmission is negligible as compared with regular pilot signals. Computer simulations show that the proposed SPF solution significantly outperforms the LP semiblind method without using the proposed transmit scheme as well as the least square method in terms of the mean-square error of the channel estimate.

Dimension Reduction and Adaptation in Conditional Density Estimation

An orthogonal series estimator of the conditional density of a response given a vector of continuous and ordinal/nominal categorical predictors is suggested. The estimator is based on writing a conditional density as a sum of orthogonal projections on all possible subspaces of reduced dimensionality and then estimating each projection via a shrinkage procedure. The shrinkage procedure uses a universal thresholding and a dyadic-blockwise shrinkage for low and high frequencies, respectively. The estimator is data-driven, is adaptive to underlying smoothness of a conditional density, and attains a minimax rate of the mean integrated squared error convergence. Furthermore, if a conditional density depends only on a subgroup of predictors, then the estimator seizes the opportunity and attains a corresponding minimax rate of convergence. The latter property relaxes the notorious “curse of dimensionality.” Moreover, the estimator is fast, because neither projections nor shrinkages are computation-intensive. A numerical study for finite samples and a real example are presented. Our results indicate that the proposed estimation procedure is practical and has a rigorous theoretical justification.

Two-level fractional factorial designs in blocks of size two for the orthogonal estimation of all main effects and two-factor interactions

In this paper we consider the problem of constructing two-level fractional factorial designs in blocks of size two that allow for the orthogonal estimation of all main effects and two-factor interactions (after adjusting for blocks). This problem has been considered in the literature, e.g., see Yang and Draper (2003), Wang (2004) and Kerr (2006). In this paper we give two systematic methods for the construction of such designs. The first construction method gives in many situations designs requiring fewer runs than those designs previously given whereas the second method gives a systematic method for constructing designs analogous to those illustrated in Yang and Draper (2003) by example.

Optimal training design and placement for MIMO orthogonal frequency division multiplexing channel estimation

This paper deals with optimal training design and placement over multiple orthogonal frequency division multiplexing (OFDM) symbols for the least squares (LS) channel estimation in multiple-input multipleoutput (MIMO) OFDM systems. First, the optimal pilot sequences over multiple OFDM symbols are derived by co-cyclic Jacket matrices based on the minimum mean square error (MSE) of the LS channel estimation. Then, an enhanced channel estimation method using sliding window is proposed to improve further the performance for the optimal pilot sequences in fast-varying channels. Simulation results show that the enhanced method can efficiently improve the performances for the optimal pilot sequences over two and four OFDM symbols, especially in fast-varying channels.

Orthogonal tests and precipitation estimates for the outside signal fluidic sprinkler

A new outside signal fluidic sprinkler is proposed in this paper. Its main structural parameters include offset length (A), working area length (B), plate cover diameter (C), and lead-flow length (D). An orthogonal array with four factors and three levels was selected to carry out the experiments. The factors influencing the coefficient of uniformity (CU) and range, in decreasing order of importance, were BADC and CDBA, respectively. The optimal values for the structural parameters were confirmed. The radial water distribution data for the sprinkler were obtained by experimentation. Water distribution figure for single sprinkler was drawn using Matrix Laboratory (MATLAB), which allowed for three-dimensional visualization of the data. The combined CU of the outside signal fluidic sprinkler was simulated for different combined spacing patterns. The CU was much larger in the rectangular configuration than in the triangular configuration. When the combined spacing coefficient was 1.2 to 1.3, the CU was found to exceed 75% in both the rectangular and triangular configurations.

A non-linear ARMAX for short term load forecasting

This paper presents a methodology for forecasting the hourly load demand of the power provider enterprise using a non-linear autoregressive moving average model with exogenous variable (NARMAX). The NARMAX method can use fewer order terms and more combination terms to capture the dynamic characteristics of highly non-linear system with orthogonal parameter estimation. And the NARMAX method is expected to be improved the model identification and fewer orders in the short term load forecasting. In this paper, the proposed NARMAX method is used to test on a practice power provider enterprise (Taiwan power supply networks) for short term load forecasting to illustrate its performance.

Effect of column combinations on two-dimensional separation in comprehensive two-dimensional gas chromatography: Estimation of orthogonality and exploring of mechanism

With the analysis of Chinese liquor Moutai as an example, the effect of different column combinations was studied on two-dimensional separation in comprehensive two-dimensional gas chromatography (GC × GC). A method to optimize column combinations was developed for achieving maximum orthogonality. Using a geometric approach to factor analysis, the degree of separation orthogonality was quantitatively estimated. The parameters evaluated include peak spreading angle, retention correlation, and practical peak capacity. When using the “reversed-type” column combinations (a polar column as the first dimension and a non- or less polar one as the second dimension), correlation coefficient was lower than or equal to 0.221, the spreading angle was higher than or equal to 77°, and more than 92% of the theoretical peak capacity was reasonably used. For Moutai liquor mainly consisting of some polar compounds, the HP-Innowax + DB1701 column combination was optimal. In addition, through the test of Grob mixture and McReynolds constant, the mechanism of solute-stationary phase interactions was disclosed in details, which validated the estimation of GC × GC orthogonality in a molecular level.

Periodic performance of the chaotic spreadspectrum sequence on finite precision

It is well known that the periodic performance of spread spectrum sequence heavily affects the cor-relative and secure characteristics of communication systems. The chaotic binary sequence is paid more and moreattention since it is one kind of applicable spread spectrum sequences. However, there are unavoidable short cyclicproblems for chaotic binary sequences in finite precision. The chaotic binary sequence generating methods arestudied first. Then the short cyclic behavior of the chaotic sequences is analyzed in detail, which are generatedby quantification approaches with finite word-length. At the same time, a chaotic similar function is defined forpresenting the cyclic characteristics of the sequences. Based on these efforts, an improved method with scramblingcontrol for generating chaotic binary sequences is proposed. To quantitatively describe the improvement of periodicperformance of the sequences, an orthogonal estimator is also defined. Some simulating results are provided. Fromthe theoretical deduction and the experimental results, it is concluded that the proposed method can effectivelyincrease the period and raise the complexity of the chaotic sequences to some extent.

Relevant statistics for models with commutative orthogonal block structure and unbiased estimator for variance components

A model has orthogonal block structure, OBS, when it’s covariance matrix is a linear combination of pairwise orthogonal projection matrices P 1, … , Pl . If one of this models has mean vector μ n = ΔT v and the P 1, … , P l commute with the orthogonal projection matrix on the range space of ΔT, the model will have commutative orthogonal block structure, COBS. We obtain relevant statistics for these models as well as BLUE for estimable vectors and unbiased estimators for variance components. When we assume the normality, we show that these statistics will be sufficient and completes. These statistics will be used to get confidence regions and tests of hypotheses for variance components and estimable vectors. We will also show how to induce probabilities measures in parametric spaces and how to adjust confidence ellipsoids for estimable vectors. Lastly we characterize mixed models with COBS.

How To Perform Meaningful Estimates of Genetic Effects

Although the genotype-phenotype map plays a central role both in Quantitative and Evolutionary Genetics, the formalization of a completely general and satisfactory model of genetic effects, particularly accounting for epistasis, remains a theoretical challenge. Here, we use a two-locus genetic system in simulated populations with epistasis to show the convenience of using a recently developed model, NOIA, to perform estimates of genetic effects and the decomposition of the genetic variance that are orthogonal even under deviations from the Hardy-Weinberg proportions. We develop the theory for how to use this model in interval mapping of quantitative trait loci using Halley-Knott regressions, and we analyze a real data set to illustrate the advantage of using this approach in practice. In this example, we show that departures from the Hardy-Weinberg proportions that are expected by sampling alone substantially alter the orthogonal estimates of genetic effects when other statistical models, like F2 or G2A, are used instead of NOIA. Finally, for the first time from real data, we provide estimates of functional genetic effects as sets of effects of natural allele substitutions in a particular genotype, which enriches the debate on the interpretation of genetic effects as implemented both in functional and in statistical models. We also discuss further implementations leading to a completely general genotype-phenotype map.

Unsupervised Bayesian image segmentation using orthogonal series

This paper deals with the problem of unsupervised image segmentation which consists in first mixture identification phase and second a Bayesian decision phase. During the mixture identification phase, the conditional probability density function (pdf) and the a priori class probabilities must be estimated. The most difficult part is the estimation of the number of pixel classes or in other words the estimation of the number of density mixture components. To resolve this problem, we propose here a Stochastic and Nonparametric Expectation-Maximization (SNEM) algorithm. The algorithm finds the most likely number of classes, their associated model parameters and generates a segmentation of the image by classifying the pixels into these classes. The non-parametric aspect comes from the use of the orthogonal series estimator. Experimental results are promising, we have obtained accurate results on a variety of real images.