• 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.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.11-18
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• 2006

Let f : (X, A) ${\rightarrow}$ (Y, B) be a map of pairs of compact polyhedra. A surplus Nielsen root number $SN(f;X\;{\backslash}\;A,\;c)$ is defined which is lower bound for the number of roots on X \ A for all maps in the homotopy class of f. It is shown that for many pairs this lower bound is the best possible one, as $SN(f;X\;{\backslash}\;A,\;c)$ can be realized without by-passing condition.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.143-150
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• 2004

In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound of tr$(X'G^{-1}X)^{-1}$ is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9B
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• pp.1697-1703
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• 1999

In this paper, we propose the fast block matching algorithm with half pel accuracy using the lower bound of mean absolute difference (MAD) at search point of half pel accuracy motion estimation. The proposed method uses the lower bound of MAD at search point of half pel accuracy which calculated from MAD's at search points of integer pel accuracy. We can reduce the computational complexity by executing the block matching operation only at the necessary search point. The points are selected when the lower bound of MAD at that point is smaller than reference MAD of integer pel motion estimation. Experimental results show that the proposed method can reduce the computational complexity considerably and keeping the same performance with conventional method.

• Journal of Satellite, Information and Communications
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• v.7 no.1
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• pp.53-58
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• 2012

In this paper, we evaluate and analyze representative estimation methods for the sparse channel. In order to evaluate error performance of matching pursuit(MP) and minimum mean square error(MMSE) algorithm, lower bound of MMSE is determined by Cramer-Rao bound and compared with upper bound of MP. Based on analysis of those bounds, mean square error of MP which is effective in the estimation of sparse channel can be larger than that of MMSE according to the number of estimated tap and signal-to-noise ratio. Simulation results show that the performances of both algorithm are reversed on the sparse channel with Rayleigh fading according to signal-to-noise ratio.

• The Journal of the Acoustical Society of Korea
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• v.16 no.5
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• pp.83-91
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• 1997

A reactor vibration monitoring has been performed using neutron noise obtained from excore detectors for the safety operation, Traditionally, the spectral estimator based on Fourier analysis has been widely used in the noise analysis of the reactor system. If the bias is too severe, the resolution would not be adequate for a given application. One major motivation for the current interests in the parametric approach to spectral estimation is the apparent higher resolution achievable with these modern techniques. In considering an unbias, a consistency, an efficency, and a minimum lower bound of the statictic estimation, an AR model is appropriate for noise spectral estimation with sharp peaks but not deep valley. In order to select an appropriate model order, the lag value of autocorrleaton function is applied. Burg method to trace the vibration mode of RPV internal is the most sucuessful.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.372-377
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• 1993

In this paper, we investigate a set-membership identification approach to the quantification of an upper bound of model uncertainty in frequency domain, which is required in the H$_{\infty}$ robust control system design. First we formulate this problem as a set-membership identification of a nominal model error in the presence f unknown noise input with unknown bound, while the ordinary set-membership approaches assume that an upper bound of the uncertain input is known. For this purpose, the proposed algorithm includes the estimation of the bound of the uncertain input. thus the proposed method can obtain the hard bound of the model error in frequency domain as well as a parametric lower-order nominal model. Finally numerical simulation results are shown to confirm the validity of the presented algorithm..

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.30 no.5
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• pp.373-379
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• 2019

If two signals with the same single-tone frequency and differing phases impinge simultaneously on an antenna at slightly differing angles, then a large error in the angle estimation might occur if the phase difference is either $0^{\circ}$ or $180^{\circ}$. This phenomenon might arise with an airborne fire-control radar, which has a relatively small bandwidth, for a low-flying target over the sea or terrain surface. In this paper, we show that the $Cram{\acute{e}}r$-Rao lower bound for such a target can be significantly lowered with the use of two frequencies.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.443-456
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• 1999

The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure are examined when the distribution s of lifetimes are exponential. it is assumed that due to physical restrictions and/or economic constraints the number of failures is investigated only at several inspection times during the lifetime test; thus there is interval censoring. Comparisons of mixed replacement designs are made with those with and without replacement The maximum likelihood estimator is found in an implicit form. The Cramer-Rao lower bound which is the asymptotic variance of the estimator is derived. The test conditions for minimizing the Cramer-Rao lower bound and minimizing the test costs within a desired width of the Cramer-Rao bound have been studied.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.6
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• pp.2074-2093
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• 2022

RSA is known as one of the best techniques for securing secret information across an unsecured network. The private key which is one of private parameters is the aim for attackers. However, it is exceedingly impossible to derive this value without disclosing all unknown parameters. In fact, many methods to recover the private key were proposed, the performance of each algorithm is acceptable for the different cases. For example, Wiener's attack is extremely efficient when the private key is very small. On the other hand, Fermat's factoring can quickly break RSA when the difference between two large prime factors of the modulus is relatively small. In general, if all private parameters are not disclosed, attackers will be able to confirm that the private key is unquestionably inside the scope [3, n - 2], where n is the modulus. However, this scope has already been reduced by increasing the greatest lower bound to [d_il, n - 2], where d_il ≥ 3. The aim of this paper is to decrease the least upper bound to narrow the scope that the private key will remain within this boundary. After finishing the proposed method, the new scope of the private key can be allocated as [d_il, d_ir], where d_ir ≤ n - 2. In fact, if the private key is extremely close to the new greatest lower bound, it can be retrieved quickly by performing a brute force attack, in which d_ir is decreased until it is equal to the private key. The experimental results indicate that the proposed method is extremely effective when the difference between prime factors is close to each other and one of two following requirement holds: the first condition is that the multiplier of Euler totient function is very close to the public key's small value whereas the second condition is that the public key should be large whenever the multiplier is far enough.