Mean Square Error Matrix Research Articles

Sequential Linear MIMO Precoder Optimization for Hybrid ARQ Retransmission of QAM Signals

Our investigation centers on the issue of linear precoding for hybrid-ARQ retransmissions in linear multi-input-multi-output (MIMO) channels driven by non-Gaussian inputs. Leveraging recent works on single transmission MIMO precoding , we derive the gradient of input-output mutual information with respect to precoder matrix for optimization. We further establish that the right eigenvectors of optimum precoder are determined by the associated minimum mean-square error (MMSE) matrix. We then propose a gradient algorithm for maximizing the mutual information. Compared with precoders designed for Gaussian input, our new precoders can significantly improve the input-output mutual information, especially at low signal-to-noise ratio (SNR) and for lower dimensional constellations.

Optimum Linear Design of Two-Hop MIMO Relay Networks With QoS Requirements

This paper investigates the optimal design issue of general two-hop amplify-and-forward (AF) MIMO relay networks with one source, one destination and multiple relays, each having multiple antennas. Beginning with the study of the mean-square error (MSE) matrix of the system and the use of Wiener filter for the destination processing, a constrained optimization problem with respect to the unknown relay precoder matrix is formulated with a goal of minimizing the total relay transmit power subject to the MSE-based quality of service (QoS) requirement on each data stream. As the original optimization problem is very difficult to solve, a lower bound of the cost function is pursued to achieve an approximate optimization problem. The modified problem is then solved under the perfect channel state information (CSI) condition using the diagonalization method along with the majorization theory to obtain optimal relay precoder with either nonoptimal or optimal source precoding. It is shown that a convex relay precoding solution is available in the case of nonoptimal source precoding whereas a joint optimal source and relay precoder can be obtained through a multilevel waterfilling algorithm. The optimal design of the relay network under imperfect CSI condition is also considered by modifying the optimization problem with the channel mean and covariance matrix, leading to a robust optimization design of the relay precoder. The proposed technique is validated by Monto Carlo simulations and is also compared with one existing method.

A Stochastic Restricted Two-Parameter Estimator in Linear Regression Model

Özkale and Kaciranlar (2007) proposed a two-parameter estimator (TPE) for the unknown parameter vector in linear regression when exact restrictions are assumed to hold. In this article, under the assumption that the errors are not independent and identically distributed, we introduce a new estimator by combining the ideas underlying the mixed estimator (ME) and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The new estimator is called the stochastic restricted two-parameter estimator (SRTPE) and necessary and sufficient conditions for the superiority of the SRTPE over the ME and TPE are derived by the mean squared error matrix (MSEM) criterion. Furthermore, selection of the biasing parameters is discussed and a numerical example is given to illustrate some of the theoretical results.

Combining two-parameter and principal component regression estimators

This paper is concerned with the parameter estimation in linear regression model. To overcome the multicollinearity problem, a new class of estimator, namely principal component two-parameter (PCTP) estimator is proposed. The superiority of the new estimator over the principal component regression (PCR) estimator, the r − k class estimator, the r − d class estimator and the two-parameter estimator proposed by Yang and Chang (Commun Stat Theory Methods 39:923–934 2010) are discussed with respect to the mean squared error matrix (MSEM) criterion. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.

State estimation with quantised sensor information in wireless sensor networks

The problem of state estimation with quantised measurements is considered for general vector state-vector observation model in wireless sensor networks (WSNs), which broadens the scope of sign of innovations Kalman filtering (SOI-KF) and multiple-level quantised innovations Kalman filter (MLQIKF). Adhering to the limited power and bandwidth resources WSNs must operate with, this paper introduces a novel decentralised unscented Kalman filtering (UKF) estimators based on quantised measurement innovations. In the quantisation approach, the region of a measurement innovation is partitioned into L contiguous, non-overlapping intervals. After quantised, the measurement information is broadcasted by using a variable number of bytes coding method. A filtering algorithm for general vector state-vector observation case is developed based on the quantised measurement information. Performance analysis and Monte Carlo simulations reveal that under the same bandwidth constraint condition, the performance of novel quantised UKF tracker, indeed better than those of SOI-KF and MLQIKF in error covariance matrix (ECM) and root mean-square error (RMSE) and almost identical to these of an UKF based on analogue-amplitude observations.

A New Two-Parameter Estimator in Linear Regression

This article is concerned with the parameter estimation in linear regression model. To overcome the multicollinearity problem, a new two-parameter estimator is proposed. This new estimator is a general estimator which includes the ordinary least squares (OLS) estimator, the ridge regression (RR) estimator, and the Liu estimator as special cases. Necessary and sufficient conditions for the superiority of the new estimator over the OLS, RR, Liu estimators, and the two-parameter estimator proposed by Ozkale and Kaciranlar (2007) in the mean squared error matrix (MSEM) sense are derived. Furthermore, we obtain the estimators of the biasing parameters and give a numerical example to illustrate some of the theoretical results.

Linear MMSE Transceiver Design in Amplify-and-Forward MIMO Relay Systems

We consider the precoding problem in an amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay system in which multiple antennas are equipped at the source, the relay, and the destination. Most existing methods for this problem only consider the design of the relay precoder, and some even ignore the direct link. In this paper, we consider a joint source/relay precoder design problem, taking both the direct and the relay links into account. Using a minimum-mean-square-error (MMSE) criterion, we first formulate the problem as a constrained optimization problem. However, it is found that the mean square error (MSE) is a highly nonlinear function of the precoders, and a direct optimization is difficult to conduct. We then design the precoders to diagonalize the MSE matrix in the cost function. To do that, we pose certain structural constraints on the precoders and derive an MSE upper bound. It turns out that minimization with respect to this bound becomes simple and straightforward. Using the standard Lagrange technique, we can finally obtain the solution with an iterative water-filling method. Simulation results show that the proposed method, with an additional precoder, outperforms the existing methods, in terms of either the MSE or the bit error rate (BER).

Mean Squared Error Matrix Comparisons of Some Restricted Almost Unbiased Estimators

In this article, we introduce two almost unbiased estimators for the vector of unknown parameters in a linear regression model when additional linear restrictions on the parameter vector are assumed to hold. Superiority of the two estimators under the mean squared error matrix (MSEM) is discussed. Furthermore, a numerical example and simulation study are given to illustrate some of the theoretical results.

Linear processing and sum throughput in the multiuser MIMO downlink

We consider linear precoding and decoding in the downlink of a multiuser multiple-input, multiple-output (MIMO) system, wherein each user may receive more than one data stream. We propose several mean squared error (MSE) based criteria for joint transmit-receive optimization and establish a series of relationships linking these criteria to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. In particular, we show that achieving the maximum sum throughput is equivalent to minimizing the product of MSE matrix determinants (PDetMSE). Since the PDetMSE minimization problem does not admit a computationally efficient solution, a simplified scalar version of the problem is considered that minimizes the product of mean squared errors (PMSE). An iterative algorithm is proposed to solve the PMSE problem, and is shown to provide near-optimal performance with greatly reduced computational complexity. Our simulations compare the achievable sum rates under linear precoding strategies to the sum capacity for the broadcast channel.

Linear regression with nonstationary variables and constraints on its parameters

The problem of estimating parameters of a linear regression with allowance for inequality constraints on the parameters is considered in the special case when its variables have a trend. A parameter estimation algorithm is described. The consistency of parameter estimates is proved and their asymptotic distribution is found. Consistent estimates are proposed for the mean-square error matrix of estimates of regression parameters and noise dispersion under rather general assumptions on the law of noise distribution.

Optimal designs for linear MIMO transceivers using directional derivative

Optimal designs for minimising the combination of symbol estimation errors subject to lp-norm constraint are investigated. Instead of considering each constraint in a separate way, the authors develop a unifying framework to obtain the optimal solution by employing a directional derivative method. The sum or peak power constraint turns out to be the case of p=1 or p→∞. Simulation results demonstrate the effectiveness of the proposed algorithm. Moreover, based on directional derivative, the authors show that the minimisation of the determinant of the minimum mean-square error (MMSE) matrix and the maximisation of mutual information are equivalent criteria.

An Intercell Interference Cancellation Method for Eigen-Beamforming Transmission

Eigen-beamforming (EB) transmission for multiple-input multiple-output (MIMO) systems is an effective means to maximize the receiver signal-to-noise ratio (SNR) in a noise-limited environment, but suffers a performance degradation when strong interference signals exist. In this letter, we propose an interference cancellation method for EB signals by constructing a new receive beamforming vector which jointly utilizes the EB matrix and minimum mean-square error (MMSE) spatial demultiplexing. The proposed method is shown to outperform the conventional EB receiver in the entire cell range, with a significant increase in the effective signal-to-interference plus noise ratio (SINR) near the cell boundary.

The superiority of empirical bayes estimation of parameters in partitioned normal linear model

In this article, the empirical Bayes (EB) estimators are constructed for the estimable functions of the parameters in partitioned normal linear model. The superiorities of the EB estimators over ordinary least-squares (LS) estimator are investigated under mean square error matrix (MSEM) criterion.

An alternative stochastic restricted Liu estimator in linear regression

In this paper, we introduce an alternative stochastic restricted Liu estimator for the vector of parameters in a linear regression model when additional stochastic linear restrictions on the parameter vector are assumed to hold. The new estimator is a generalization of the ordinary mixed estimator (OME) (Durbin in J Am Stat Assoc 48:799–808, 1953; Theil and Goldberger in Int Econ Rev 2:65–78, 1961; Theil in J Am Stat Assoc 58:401–414, 1963) and Liu estimator proposed by Liu (Commun Stat Theory Methods 22:393–402, 1993). Necessary and sufficient conditions for the superiority of the new stochastic restricted Liu estimator over the OME, the Liu estimator and the estimator proposed by Hubert and Wijekoon (Stat Pap 47:471–479, 2006) in the mean squared error matrix (MSEM) sense are derived. Furthermore, a numerical example based on the widely analysed dataset on Portland cement (Woods et al. in Ind Eng Chem 24:1207–1241, 1932) and a Monte Carlo evaluation of the estimators are also given to illustrate some of the theoretical results.

The Superiorities of Bayes Linear Minimum Risk Estimation in Linear Model

In this article, the Bayes linear minimum risk estimator (BLMRE) of parameters is derived in linear model. The superiorities of the BLMRE over ordinary least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Pitman closeness (PC) criterion.

Estimation of Constrained Parameters With Guaranteed MSE Improvement

We address the problem of estimating an unknown parameter vector x in a linear model y=Cx+v subject to the a priori information that the true parameter vector x belongs to a known convex polytope X. The proposed estimator has the parametrized structure of the maximum a posteriori probability (MAP) estimator with prior Gaussian distribution, whose mean and covariance parameters are suitably designed via a linear matrix inequality approach so as to guarantee, for any xisinX, an improvement of the mean-squared error (MSE) matrix over the least-squares (LS) estimator. It is shown that this approach outperforms existing superefficient estimators for constrained parameters based on different parametrized structures and/or shapes of the parameter membership region X

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

In the presence of multicollinearity, ordinary least squares (OLS) estimation is inadequate. Alternative estimation techniques were proposed. One of which is unbiased ridge regression (URR) estimator given by Crouse et al. (1995). In this article, we introduced the URR estimator in two different ways by following Farebrother (1984) and Troskie et al. (1994). We discuss its properties in some detail, comparing URR estimator to the OLS, the ordinary ridge regression (ORR), and the r − k class estimators in the sense of matrix mean square error (MMSE) and residuals. We also illustrate our findings with a numerical example based on the data generated by Hoerl and Kennard (1981) which is commonly used in literature to study the effect of multicollinearity.

Curvature‐adjusted optimal design of sampling times for the inference of pharmacokinetic compartment models

In pharmacokinetics, compartment models are often used to describe the time course of blood concentration after the administration of a drug. In this article, we propose an optimal design criterion for precise estimation of parameters included in the compartment model and illustrate the non-sequential design of sampling times of blood drug concentration data in individual pharmacokinetics. The proposed optimal design criterion minimizes the determinant of the mean-squared error matrix of the parameter estimator that is quadratically approximated by the curvature array. Therefore, the proposed criterion considers the intrinsic and parameter-effects nonlinearity underlying the compartment model, and so is applicable in a pharmacokinetic experiment where the sample size of the blood drug concentration data is quite small.

Single epoch algorithm based on Tikhonov regularization for deformation monitoring using single frequency GPS receivers

A new single epoch algorithm for deformation monitoring using single frequency GPS receivers, based on Tikhonov Regularization, is proposed in this paper. At first, the characteristic of the normal matrix for carrier phase measurements is analyzed. Since the normal matrix is rank-deficient, Tikhonov regularization theorem is applied to the least squares problem, and a regulariser is chosen to transform the matrix from the rank-deficient to the full rank. Then, the float ambiguity solutions and their Mean Squared Error Matrix (MSEM) are obtained. MSEM can be used to determine the search space for the integer ambiguities, combined with other integer ambiguity fixers such as LAMBDA. The proposed single epoch algorithm is tested using carrier phase measurements of two single frequency GPS receivers with a baseline over 3km and the results show that the success rate of the integer ambiguity fix is greater than 90%.

SINGLE EPOCH ALGORITHM BASED ON TIKHONOV REGULARIZATION FOR DEFORMATION MONITORING USING SINGLE FREQUENCY GPS RECEIVERS

A new single epoch algorithm for deformation monitoring using single frequency GPS receivers, based on Tikhonov Regularization, is proposed in this paper. At first, the characteristic of the normal matrix for carrier phase measurements is analyzed. Since the normal matrix is rank-deficient, Tikhonov regularization theorem is applied to the least squares problem, and a regulariser is chosen to transform the matrix from the rank-deficient to the full rank. Then, the float ambiguity solutions and their Mean Squared Error Matrix (MSEM) are obtained. MSEM can be used to determine the search space for the integer ambiguities, combined with other integer ambiguity fixers such as LAMBDA. The proposed single epoch algorithm is tested using carrier phase measurements of two single frequency GPS receivers with a baseline over 3km and the results show that the success rate of the integer ambiguity fix is greater than 90%.