• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.4C
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• pp.413-423
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• 2003

The CMA algorithmis most widely investigated blind algorithm and the most widely used one in practice. But, since nonlinear CM cost function have not closed form solution about the optimum weight. There have been difficultiesto analyze the CMA equalizer's theoretical performance. Recently, Zeng presents the notable theoretical resultabout the MSE of CM-minimizing estimators for the FIR linear channel in the presence of AWGN. Through this method, It wouldbe possible to campare the theoretical performance between CMA and Wiener equalizer in terms of MSE. In this paper, based on Zeng's method, we first calculate the theoretical MSE bound of CMA equalizer in partial response channel which is widely used in HDD, digital VCR such as high-density digital recording.playback systems. We confirmedthis result withthe computer simulation. Except this, we also performedthe theoretical and simulation analysis about the modified CMA equalizer, which was proposed to improve the performance of CMA equalizer in partial response channel. Finally, we compare and evaluate the performance analysis results between CMA and Modified CMA equalizer.

• The Journal of the Acoustical Society of Korea
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• v.34 no.5
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• pp.394-402
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• 2015

CMA (Constant Modulus Algorithm) is one of the well-known algorithms in blind acoustic channel equalization. Generally, CMA converges slowly and the speed of convergence is dependent on a step-size in the CMA procedure. Many researches have tried to speed up the convergence speed by applying a variable step-size to CMA, e.g. the orthogonal projection CMA and algebraic optimal step-size CMA. In this paper, we summarize these two algorithms, and we propose a new CMA with improved convergence performance. The improvement comes from the switching between the orthogonal projection CMA and algebraic optimal step-size CMA. In simulation results, we show the performance improvement in the time invariant channels as well as in time varying channel.

• The Journal of the Acoustical Society of Korea
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• v.28 no.7
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• pp.640-645
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• 2009

CMA (Constant Modulus Algorithm) is one of the famous algorithms in blind channel equalization. Generally, CMA converges slowly and the speed of convergence is dependent on a step-size in the CMA procedure. Many researches have tried to speed up the convergence speed by applying a variable step-size to CMA. In this paper, we propose a new CMA algorithm with improved convergence performance. The improvement comes from an orthogonal projection of an average error gradient. We show the improvement in simulation results.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.2
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• pp.477-480
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• 2005

CMA-DD is proposed to improve the steady-state performance of CMA and its performance is depending on switching time between two modes of operation. Castro et al. who proposed a concurrent equalizer for solving problem of CMA-DD, which reduced the sensibility of switching time. However, concurrent algorithm has a problem that it keeps working after convergence. In this paper, we propose concurrent MCMA-DD equalizer combined modified CMA(MCMA) and DD mode for making better concurrent algorithm. The proposed equalizer is better than previous algorithm in convergence speed and steady-state performance. Also, the proposed algorithm decides optimum switching time using residual ISI of the equalizer output.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.3C
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• pp.157-162
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• 2011

For blind equalization of communication channels, concurrent equalization is useful to improve convergence characteristics. However, the concurrent equalization will result in limited performance enhancement by continuing concurrent adaptation with two algorithms after the equalizer converges to steady-state. In this paper, to improve the convergence characteristics and steady-state performance of the concurrent equalization, proposed is a new concurrent equalization technique with variable step-size parameter and weight-based tap coefficients update. The proposed concurrent vsCMA+DD equalization calculates weight factors using error signals of the variable step-size CMA (vsCMA) and DD (decision-directed) algorithm, and then updates the two equalizers based on the weights respectively. The proposed method, first, improves the error performance of the CMA by the vsCMA, and enhances the steady-state performance as well as the convergence speed further by the weight-based tap coefficients update. The performance improvement by the proposed scheme is verified through simulations.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.3
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• pp.63-68
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• 2014

This paper related with the I-CMA (Improved-CMA) algorithm that is possible to compensates of phase in CMA adatpve equalizer which is used for the elemination of intersymbol interference in the multipath fading and band limit characteristics of channel. The new cost function is proposed for the eliminate the amplitude and phase simulataneous by modifying the cost fuction for get the error signal in present CMA algorithm. It has a merit to the algorithm simplicities and eliminats the PLL device for phase compensation after equalization. For proving this, the recovered signal constellation that is the output of equalizer output signal and the residual isi and Maximum Distortion charateristic learning curve that are presents the convergence performance in the equalizer and the overall frequency transfer function of channel and equalizer were used. As a result of computer simulation, the I-CMA has more good compensation capability of amplitude and phas in the recovered constellation. But the convergence time is slow due to the simultaneously phase compensation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.3
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• pp.107-113
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• 2011

This paper is concerned with the CR-CMA (Coordinate Reduction-Constant Modulus Algorithm) adaptive equalization algorithm using the coordinate reduction in order to improve the convergence characteristic and residual intersymbol interference which are used as the performance index for an adaptive equalizer. The equalizer is used to reduce the distortion caused by the intersymbol interference on the wireless and the wired band-limited channel that connect the transmitting system and receiving system. The CMA is widely known as the representative algorithm for equalization. In order to transmitting the mass information with a high speed through the channels, a fast convergence speed in the equalizer performance that is able to minimize overhead needed for equalization is acquired. In this paper, we introduce the new cost function to reduce the constellation of received signal at the input stage of a equalizer. It reduce the error at the steady equalization state. By the computer simulation, we confirmed that the proposed CR-CMA algorithm has the faster convergence speed and the smaller residual intersymbole interference than the conventional CMA.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.1
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• pp.133-143
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• 1996

The constant modulus algorithm (CMA), one of the widely used blind equalization algorithms, equalizes channels using the second-order statistic of equalizer outputs. The performance of the CMA for multi-level signals such as the quadrature amplitude modulation (QAM) signal degrades because the CMA maps all signal power onto a single modulus. in this paper, to improve the equalization performance of a QAM system, we propose a shell partitioning method based on error magnitude. We assume the probability distribution of an equalizer output as Gaussian, and obtain decision boundaries by maximum likelihood estimation based on the fact that the distribution of the equalizer output power is noncentral $x^2$. The proposed CMA constructs a multi-moduli equlization system based on the fact that each shell separated by decision boundaries employs a single modulus. Computer simulation results for 32-QAM and 64-QAM show the effectiveness of the proposed algorithm.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.3
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• pp.115-120
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• 2011

This paper is concerned with the performance comparison of CR-CMA (Coordinate Reduction-CMA) and CM-CMA (Constellation Matching-Constant Modulus Algorithm) that is used for improving the convergence characteristic and residual intersymbol interference which are used as the performance index for an adaptive equalizer. The equalizer is used to reduce the distortion caused by the intersymbol interference on the wireless and the wired band-limited channel, and the blind method which does not need for extra bandwidth by the training sequence of digital code are researched. Recently, by using the merit of simple operation in the CMA, the performance improvement is obtained by the modifying the cost function of it. In this paper, the new algorithm, CR-CMA and CM-CMA, the performance analysis are performed and compared by computer simulation. The CR-CMA has a superior equalization characteristics in the recovered constellation, convergence speed and residual intersymbol interference than the CM-CMA by computer simulation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.1
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• pp.121-127
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• 2010

This paper relates with the improved CMA blind adaptive equalization algorithm which uses the constellation matching method that improve the inverse modelling efficiency of a communication channel compared to the present CMA blind adaptive equalizer. The amplitude distortion can be compensated in the present CMA blind adaptive equalizer which is used for the reduction of intersymbol interference by distortion that generate such as a band limited wireless mobile channel, but in the improved adaptive alogorithm operates with the minimize the amplitude phase distortion in the output of equalizer by applying the cost function that is composition of additional signal constellation matching error terms. In order to evaluation of the inverse modeling efficiency of improved algorithm, the residual intersymbol interference and recovered signal constellation were compared by computer simulation. As a result of comparion of computer simulation, the improved algorithm has a good stability in the residual intersymbol interference in the steady state, but it has a slow convergence rate in the adaptation state in initial state.