• ETRI Journal
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• v.34 no.4
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• pp.511-517
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• 2012

The best linear unbiased estimator (BLUE) is most suitable for practical application and can be determined with knowledge of only the first and second moments of the probability density function. Although the BLUE is an existing algorithm, it is still largely unexplored and has not yet been applied to channel estimation in amplify and forward (AF)-based wireless relay networks (WRNs). In this paper, a BLUE-based algorithm is proposed to estimate the overall channel impulse response between the source and destination of AF strategy-based WRNs. Theoretical mean square error (MSE) performance for the BLUE is derived to show the accuracy of the proposed channel estimation algorithm. In addition, the Cram$\acute{e}$r-Rao lower bound (CRLB) is derived to validate the MSE performance. The proposed BLUE channel estimation algorithm approaches the CRLB as the length of the training sequence and number of relays increases. Further, the BLUE performs better than the linear minimum MSE estimator due to the minimum variance characteristic exhibited by the BLUE, which happens to be a function of signal-to-noise ratio.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.502-507
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• 2003

Toward the development of practical methods for observed data oriented bispectral estimation, an automatic means for determining the smoothing bandwidth of bispectral windows is proposed, that can also provide an associated optimum bispectral estimate of stationary non-Gaussian signals, systematically only from an observed time series datum of finite length. For the conventional non-parametric bispectral estimation, the MSE (mean squared error) of the normalized estimate is reviewed under a certain mixing condition and sufficient data length, mainly from the viewpoint of the inverse relation between its bias and variance with respect to the smoothing bandwidth. Based on the fundamental relation, a systematic method not only for determining the bandwidth, but also for obtaining the optimum bispectral estimate is presented by newly introducing a MSE evaluation index of the estimate only from an observed time series datum of finite length. The effectiveness and fundamental features of the proposed method are illustrated by the basic results of numerical experiments.

• Journal of Communications and Networks
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• v.16 no.4
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• pp.447-457
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• 2014

In this paper, we investigate the frequency domain channel estimation for multiple-input multiple-output (MIMO) single-carrier frequency-division multiple-access (SC-FDMA) systems. In MIMO SC-FDMA, code-division multiplexed (CDM) pilots such as cyclic-shifted Zadoff-Chu sequences have been adopted for channel estimation. However, most frequency domain channel estimation schemes were developed based on frequency-division multiplexing of pilots. We first develop a channel estimation error model by using CDM pilots, and then analyze the mean-square error (MSE) of various minimum MSE (MMSE) frequency domain channel estimation techniques. We show that the cascaded one-dimensional robust MMSE (C1D-RMMSE) technique is complexity-efficient, but it suffers from performance degradation due to the channel correlation mismatch when compared to the two-dimensional MMSE (2D-MMSE) technique. To improve the performance of C1D-RMMSE, we design a robust iterative channel estimation (RITCE) with a frequency replacement (FR) algorithm. After deriving the MSE of iterative channel estimation, we optimize the FR algorithm in terms of the MSE. Then, a low-complexity adaptation method is proposed for practical MIMO SC-FDMA systems, wherein FR is performed according to the reliability of the data estimates. Simulation results show that the proposed RITCE technique effectively improves the performance of C1D-RMMSE, thus providing a better performance-complexity tradeoff than 2D-MMSE.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.2
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• pp.566-578
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• 2018

In this paper, we design a segment training based individual channel estimation (STICE) scheme for the classical two-way relay network (TWRN) with multi-pair sources (MPS) and amplify-and-forward (AF). We adopt the linear minimum mean square error (LMMSE) channel estimator to minimize the mean square error (MSE) without channel estimation error, where the optimal power allocation strategy from the relay for different sources is obtained. Then the MSE gains are given with different source pairs among the proposed power allocation scheme and the existing power allocation schemes. Numerical results show that the proposed method outperforms the existing ones.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.625-636
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• 2011

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

• Journal of Korean Society of Transportation
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• v.35 no.1
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• pp.63-78
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• 2017

The purpose of this study is to determine the optimal aggregation interval to increase the reliability when estimating representative value of individual vehicle travel time collected by DSRC equipment in interrupted traffic flow section in National Highway. For this, we use the bimodal asymmetric distribution data, which is the distribution of the most representative individual vehicle travel time collected in the interrupted traffic flow section, and estimate the MSE(Mean Square Error) according to the variation of the aggregation interval of individual vehicle travel time, and determine the optimal aggregation interval. The estimation equation for the MSE estimation utilizes the maximum estimation error equation of t-distribution that can be used in asymmetric distribution. For the analysis of optimal aggregation interval size, the aggregation interval size of individual vehicle travel time was only 3 minutes or more apart from the aggregation interval size of 1-2 minutes in which the collection of data was normally lost due to the signal stop in the interrupted traffic flow section. The aggregation interval that causes the missing part in the data collection causes another error in the missing data correction process and is excluded. As a result, the optimal aggregation interval for the minimum MSE was 3~5 minutes. Considering both the efficiency of the system operation and the improvement of the reliability of calculation of the travel time, it is effective to operate the basic aggregation interval as 5 minutes as usual and to reduce the aggregation interval to 3 minutes in case of congestion.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.5
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• pp.3434-3439
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• 2015

As a criterion of information theoretic learning, the Euclidean distance (ED) of two error probability distribution functions (minimum ED of error, MEDE) has been adopted in nonlinear (decision feedback, DF) supervised equalizer algorithms and has shown significantly improved performance in severe channel distortion and impulsive noise environments. However, the MEDE-DF algorithm has the problem of heavy computational complexity. In this paper, the recursive ED for MEDE-DF algorithm is derived first, and then the feed-forward and feedback section gradients for weight update are estimated recursively. To prove the effectiveness of the recursive gradient estimation for the MEDE-DF algorithm, the number of multiplications are compared and MSE performance in impulsive noise and underwater communication environments is compared through computer simulation. The ratio of the number of multiplications between the proposed DF and the conventional MEDE-DF algorithm is revealed to be $2(9N+4):2(3N^2+3N)$ for the sample size N with the same MSE learning performance in the impulsive noise and underwater channel environment.

• Journal of electromagnetic engineering and science
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• v.4 no.1
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• pp.23-29
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• 2004

In this paper we analyze convergence constraints and time constant of IT-LMS algorithm and derive a method of making it's time constant independent of signal power by using input variance estimation. The method for estimating the input variance is to use a single-pole low-pass filter(LPF) with common smoothing parameter value, θ. The estimator is with narrow bandwidth for large θ but with wide bandwidth for small θ. This small θ gives long term average estimation(low frequency) of the fluctuating input variance well as short term variations (high frequency) of the input power. In our simulations of multipath communication channel equalization environments, the method with large θ has shown not as much improved convergence speed as the speed of the original IT-LMS algorithm. The proposed method with small θ=0.01 reach its minimum MSE in 100 samples whereas the IT-LMS converges in 200 samples. This shows the proposed, tap-power normalized IT-LMS algorithm can be applied more effectively to digital wireless communication systems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.3C
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• pp.141-146
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• 2005

The authors investigate the convergence speed problem of nonlinear adaptive equalization. Convergence constraints and time constant of radial basis function network using stochastic gradient (RBF-SG) algorithm is analyzed and a method of making time constant independent of hidden-node output power by using sample-by-sample node output power estimation is derived. The method for estimating the node power is to use a single-pole low-pass filter. It is shown by simulation that the proposed algorithm gives faster convergence and lower minimum MSE than the RBF-SG algorithm.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.285-292
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• 1999

In this paper we propose the several estimators of the Lorenz curve in the Pareto distribution and obtain the bias and the mean squared error for each estimator. We compare the proposed estimators with the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) in terms of the mean squared error (MSE) through Monte Carlo methods and discuss the results.