• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.5C
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• pp.521-526
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• 2009

In this paper, a complex-valued recursive least squares escalator filter algorithm with reduced computational complexity for complex-valued signal processing applications is presented. The local tap weight of RLS-ESC algorithm is updated by incrementing its old value by an amount equal to the local estimation error times the local gain scalar, and for the gain scalar, the local input autocorrelation is calculated at the previous time. By deriving a new gain scalar that can be calculated by using the current local input autocorrelation, reduced computational complexity is accomplished. Compared with the computational complexity of the complex-valued version of RLS-ESC algorithm, the computational complexity of the proposed method can be reduced by 50% without performance degradation. The reduced computational complexity of the proposed algorithm is even less than that of the LMS-ESC. Simulation results for complex channel equalization in 64QAM modulation schemes demonstrate that the proposed algorithm has superior convergence and constellation performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2554-2580
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• 2018

Lenstra-Lenstra-$Lov{\acute{a}}sz$ (LLL) is an effective receiving algorithm for Multiple-Input-Multiple-Output (MIMO) systems, which is believed can achieve full diversity in MIMO detection of fading channels. However, the LLL algorithm features polynomial complexity and shows poor performance in terms of convergence. The reduction of algorithmic complexity and the acceleration of convergence are key problems in optimizing the LLL algorithm. In this paper, a variant of the LLL algorithm, the Hybrid-Fix-and-Round LLL algorithm, which combines both fix and round measurements in the size reduction procedure, is proposed. By utilizing fix operation, the algorithmic procedure is altered and the size reduction procedure is skipped by the hybrid algorithm with significantly higher probability. As a consequence, the simulation results reveal that the Hybrid-Fix-and-Round-LLL algorithm carries a faster rate of convergence compared to the original LLL algorithm, and its algorithmic complexity is at most one order lower than original LLL algorithm in real field. Comparing to other families of LLL algorithm, Hybrid-Fix-and-Round-LLL algorithm can make a better compromise in performance and algorithmic complexity.

• The Journal of the Acoustical Society of Korea
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• v.17 no.3E
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• pp.53-57
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• 1998

Spectral information at a speech coder should be quantized with sufficient accuracy to keep perceptually transparent output speech. Spectral information at a low bit rate speech coder is usually transformed into corresponding line spectrum pair parameters and is often quantized with a vector quantization algorithm. As the vector quantization algorithm generally has high complexity in the optimal code vector searching routine, the complexity reduction in that routine is investigated using the ordering property of the line spectrum pair. When the proposed complexity reduction algorithm is applied to the well-known split vector quantization algorithm, the 46% complexity reduction is achieved in the distortion measure compu-tation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4C
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• pp.217-225
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• 2011

In this paper, we propose an adaptive de-interlacing algorithm that is based on the degree of local complexity. The conventional intra field de-interlacing algorithms show the different performance according to the ways which find the edge direction. Furthermore, FDD (Fine Directional De-interlacing) algorithm has the better performance than other algorithms but the computational complexity of FDD algorithm is too high. In order to alleviate these problems, the proposed algorithm selects the most efficient de-interacing algorithm among LA (Line Average), MELA (Modified Edge-based Line Average), and LCID (Low-Complexity Interpolation Method for De-interlacing) algorithms which have low complexity and good performance. The proposed algorithm is trained by the DoLC (Degree of Local Complexity) for selection of the algorithms mentioned above. Simulation results show that the proposed algorithm not only has the low complexity but also performs better objective and subjective image quality performances compared with the conventional intra-field methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.2
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• pp.485-499
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• 2021

Although non-binary low-density parity-check (NB-LDPC) codes have better error-correction capability than that of binary LDPC codes, their decoding complexity is significantly higher. Therefore, it is crucial to reduce the decoding complexity of NB-LDPC while maintaining their error-correction capability to adopt them for various applications. The extended min-sum (EMS) algorithm is widely used for decoding NB-LDPC codes, and it reduces the complexity of check node (CN) operations via message truncation. Herein, we propose a low-cost CN processing method to reduce the complexity of CN operations, which take most of the decoding time. Unlike existing studies on low complexity CN operations, the proposed method employs quick selection algorithm, thereby reducing the hardware complexity and CN operation time. The experimental results show that the proposed selection-based CN operation is more than three times faster and achieves better error-correction performance than the conventional EMS algorithm.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.959-973
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• 2001

We shall discuss one of some techniques needed to analyze algorithms. It is called a big-O function technique. The measures of efficiency of an algorithm have two cases. One is the time used by a computer to solve the problem using this algorithm when the input values are of a specified size. The other one is the amount of computer memory required to implement the algorithm when the input values are of a specified size. Mainly, we will restrict our attention to time complexity. To figure out the Time Complexity in nonlinear problems of Numerical Analysis seems to be almost impossible.

• IEMEK Journal of Embedded Systems and Applications
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• v.13 no.1
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• pp.1-8
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• 2018

This paper proposes a low complexity super resolution algorithm for frequency modulated continuous wave (FMCW) radar systems for foreign object debris (FOD) detection. FOD radar has a requirement to detect foreign object in small units in a large area. However, The fast Fourier transform (FFT) method, which is most widely used in FMCW radar, has a disadvantage in that it can not distinguish between adjacent targets. Super resolution algorithms have a significantly higher resolution compared with the detection algorithm based on FFT. However, in the case of the large number of samples, the computational complexity of the super resolution algorithms is drastically high and thus super resolution algorithms are difficult to apply to real time systems. In order to overcome this disadvantage of super resolution algorithm, first, the proposed algorithm coarsely obtains the frequency of the beat signal by employing FFT. Instead of using all the samples of the beat signal, the number of samples is adjusted according to the frequency of the beat signal. By doing so, the proposed algorithm significantly reduces the computational complexity of multiple signal classifier (MUSIC) algorithm. Simulation results show that the proposed method achieves accurate location even though it has considerably lower complexity than the conventional super resolution algorithms.

• Journal of Positioning, Navigation, and Timing
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• v.11 no.2
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• pp.91-98
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• 2022

In the next generation wireless communication system, the beamforming technique based on a massive antenna is one of core technologies for transmitting and receiving huge amounts of data, efficiently and accurately. For highly performed and highly reliable beamforming, it is required to accurately estimate the Angle of Arrival (AOA) for the desired signal incident to an antenna. Employing the massive antenna with a large number of elements, although the accuracy of the AOA estimation is enhanced, its computational complexity is dramatically increased so much that real-time communication is difficult. In order to improve this problem, AOA estimation algorithms based on the massive antenna with the low computational complexity have been actively studied. In this paper, we compute and analyze the computational complexity of the cascade AOA estimation algorithm based on the Flexible Massive Concentric Circular Array (FMCCA). In addition, its computational complexity is compared to conventional AOA estimation techniques such as the Multiple Signal Classification (MUSIC) algorithm with the high resolution and the Only Beamspace MUSIC (OBM) algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.11A
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• pp.1027-1037
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• 2010

In this paper, we propose the linear interpolation-based BD (Block Diagonalization) precoding approximation algorithm for low complexity in downlink multiuser MIMO-OFDM (Multiple-input Multiple-output Orthogonal Frequency Division Multiplexing) systems. In the case of applying the general BD precoding algorithm to multiuser MIMO-OFDM systems, the computational complexity increases in proportional to the number of subcarriers. The proposed interpolation-based BD precoding approximation algorithm can be achieved similar SER performance with general BD algorithm and can decrease the computational complexity. It is proved that proposed algorithm can achieve the significantly decreased computational complexity by computer simulation.