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Blind source separation: The location of local minima in the case of finitely many samples

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第9期56卷 4340-4353页

作者： Leshem, Amir van der Veen, Alle-Jan Bar Ilan Univ Sch Engn IL-52900 Ramat Gan Israel Delft Univ Technol Dept Elect Engn NL-2628 CD Delft Netherlands

Cost functions used in blind source separation are often defined in terms of expectations, i.e., an infinite number of samples is assumed. An open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case. To answer this question, we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions. In particular, we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix. The method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function. This shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function. We also answer a long-standing problem of the mean-squared error (MSE) behavior of the (finite sample) least squares constant modulus algorithm (LS-CMA), namely whether there exist LS-CMA receivers with good MSE performance. We demonstrate how the proposed techniques can be used to determine the required number of samples' for LS-CMA to exceed a specified performance. The paper concludes with simulations that validate the results.

关键词： blind source separation constant modulus algorithm finite sample analysis

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Blind CMA-based asynchronous multiuser detection using generalized sidelobe canceller with decision feedback

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IEICE TRANSACTIONS ON COMMUNICATIONS 2008年第1期E91B卷 376-380页

作者： Chang, Ann-Chen Jen, Chih-Wei Ling Tung Univ Dept Informat Technol Taichung 408 Taiwan Minist Natl Defense Taipei 100 Taiwan

This letter deals with blind multiuser detection based on the multi-channel linearly constrained constant modulus algorithm (MLCCMA) for asynchronous code division multiple access (CDMA) systems over frequency-selective Rayleigh fading channels. In conjunction with the decision-feedback generalized sidelobe canceller (DFGSC), we present an efficient approach to combat multiple access interference and intersymbol interference. Computer simulations confirm that the proposed MLCCMA-based DFGSC can significantly speed up convergence and improve the output performance.

关键词： CDMA asynchronous constant modulus algorithm decision-feedback generalized sidelobe canceller

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A Variable Step-Size Dual-Mode Blind Equalization algorithm Based on Cadzow Theorem

A Variable Step-Size Dual-Mode Blind Equalization Algorithm ...

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4th International Conference on Wireless Communications, Networking and Mobile Computing

作者： Zhu Tingting Wang Yinming NW Polytech Univ Coll Marine Xian Peoples R China

ISBN: (纸本)9781424421077

To overcome the shortcomings that slow convergence rate and big steady-state error of the constant modulus algorithm, a variable step-size dual mode blind equalization based on Cadzow theorem is brought forward. Utilizing the normalized cumulant of order (4,2) and under the direction of Cadzow theorem, the new algorithm will speed up the convergence rate and decrease the steady-state error under the help of step-size. It will turn to the DD algorithm to get better effect of convergence. The algorithm's better equalization property is proved by the computer simulation results.

关键词： constant modulus algorithm variable step-size blind equalization cadzow theorem

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Decision Feedback Blind Equalization algorithm Based on Equal Gain Combining Time Diversity

Decision Feedback Blind Equalization Algorithm Based on Equa...

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2nd International Symposium on Test Automation and Instrumentation

作者： Guo Yecai He Long-qing Zhu Jie Anhui Univ Sci & Technol Huainan 232001 Peoples R China

Inter-Symbol Interference (ISI), caused by the multi-path and fading channels at the receiver, affects communication quality seriously. In order to improve the communication system performance and to decrease Bit Error Rate(BER), modified constant modulus algorithm and Decision Feedback blind Equalization based on Equal Gain Combining time diversity is proposed in order to analyse the performances of time diversity and decision feedback equalizer. The proposed algorithm employs the time diversity for reducing the effect of fading channel on communication quality and utilizes decision feedback equalizer to eliminate ISI, uses Modified constant modulus algorithm (MCMA) to overcome phase rotations. Accordingly, the proposed algorithm has faster convergence speed and smaller mean square error, and its validity is verified by computer simulation with multi-path underwater acoustic channel.

关键词： Decision feedback blind equalization equal gain combining time diversity constant modulus algorithm multi-path underwater acoustic channel

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Minimum Kurtosis CMA Deconvolution for Blind Image Restoration

Minimum Kurtosis CMA Deconvolution for Blind Image Restorati...

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4th International Conference on Information and Automation for Sustainability

作者： Samarasinghe, Pradeepa D. Kennedy, Rodney A. Australian Natl Univ Res Sch Informat Sci & Engn ANU Coll Engn & Comp Sci Canberra ACT 0200 Australia

ISBN: (纸本)9781424428991

A critical assumption in applying Godard CMA algorithm for blind deconvolution and equalization is the assumption of an independently distributed source. Almost all the applications in the literature have based their implementations on this assumption. To our knowledge, no research has been done on the effect of source correlation on adaptive blind deblurring of images through CMA, and this paper addresses that gap, coming up with a novel model of addressing the source correlation problem in the image deblurring through CMA.

关键词： blind equalization blind deconvolution image processing blind image restoration constant modulus algorithm CMA Godard algorithm kurtosis

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A Blind Adaptive Step-Size Time-Domain Receiver for MC-CDMA Systems

A Blind Adaptive Step-Size Time-Domain Receiver for MC-CDMA ...

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5th International Conference on Electrical Engineering/Electronics, Computer Telecommunications and Information Technology

作者： Yuvapoositanon, Peerapol Suwannajan, Sutat Mahanakorn Univ Technol Dept Elect Engn Ctr Elect Syst Design & Signal Proc Bangkok 10530 Thailand Mahanakorn Univ Technol Bangkok 10530 Thailand

ISBN: (纸本)9781424421015

A blind adaptive step-size time-domain receiver for multi-carrier code-division multiple access (MC-CDMA) systems is presented. Adjustment rules for the receiver tap-weight as well as its step-size are based upon the stochastic approximation of the constant modulus (CM) criterion. The ability of the proposed receiver to detect the desired user in multipath fading channels at full load is assessed. Sensitivity to the various initial values of the step-size and the adaptation rates of the algorithm is also investigated.

关键词： Multi-carrier CDMA Adaptive step-size constant modulus algorithm

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Blind Equalization for Single Carrier Frequency Domain Equalization with Low Complexity

Blind Equalization for Single Carrier Frequency Domain Equal...

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China-Japan Joint Microwave Conference

作者： Wang, Xin Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing Peoples R China

ISBN: (纸本)9781424438211

A novel approach of blind constant modulus algorithm (CMA) for single carrier frequency domain equalization is proposed to solve the application of CMA implemented in frequency domain, based on the constant modulus property from frequency domain to time domain. It is illustrated that this method has lower complexity than time-domain subspace algorithm has in broad wireless systems. And compared with the frequency-domain algorithm in (5), the complexity of the new idea is greatly reduced as well. In this research, the transformation of constant modulus algorithm from time domain to frequency domain is obtained under the assumption that the source signal amplitude remains 1. Therefore, the validity of equation (8) results in the conclusion that the performance of symbol error of the method would not be influenced by the transformation from time domain to frequency domain. Simulation results demonstrate it.

关键词： Single carrier frequency domain equalization constant modulus algorithm complexity discrete Fourier transform

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Orthogonal Wavelet Transform Based Sign Decision Dual-mode Blind Equalization algorithm

Orthogonal Wavelet Transform Based Sign Decision Dual-mode B...

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9th International Conference on Signal Processing

作者： Guo, Ye-cai Han, Ying-ge Yang, Chao Nanjing Univ Informat Sci & Technol Nanjing 210044 Peoples R China Anhui Univ Sci & Technol Huainan 232001 Peoples R China

ISBN: (纸本)9781424421787

Aiming at the slow convergence rate and the high mean square error of constant modulus algorithm(CMA), a new orthogonal Wavelet Transform based Sign Decision Dual-mode blind equalization algorithm(WT-SDDA) is proposed. In the proposed algorithm, orthogonal Wavelet Transform based constant modulus algorithm (WT-CMA) is integrated with orthogonal Wavelet Transform based Stop-and-Go Changeable modulus blind equalization algorithm (WT-SG-CMA), and the switch process is decided by the sign decision. Simulation tests with underwater acoustic channel shows that the proposed WT-SDDA algorithm outperforms the CMA and the WT-CMA in the convergence rates and residual mean square error and that it has the faster convergence rate than the WT-SG-CMA under condition of the same residual error.

关键词： constant modulus algorithm wavelet transform dual-mode under-water acoustic channel convergence rate

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A batch processing constant modulus algorithm

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IEEE COMMUNICATIONS LETTERS 2004年第9期8卷 582-584页

作者： Xu, CJ Li, J Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Nanjing Univ Posts & Telecommun Dept Telecommun Engn Nanjing 210003 Peoples R China

We present a batch processing constant modulus algorithm (BP-CMA) derived by a nonlinear optimization approach to minimizing the constant modulus (CM) criterion. BP-CMA is a line search iteration algorithm. The search direction may be taken as deepest descent direction or Newton direction. The exact step size is obtained from the roots of a cubic equation. The initial value is calculated by using the eigenvectors of the signal subspace. The BP-CMA with the Newton direction has a fast convergence rate and can converge to the minima of the CM criterion after a few iterations.

关键词： batch processing algorithm constant modulus algorithm signal-subspace

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Orthogonal Wavelet Transform Based Sign Decision Dual-mode Blind Equalization algorithm

Orthogonal Wavelet Transform Based Sign Decision Dual-mode B...

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9th International Conference on Signal Processing(第九届国际信号处理学术会议)(ICSP'08)

作者： Ye-cai Guo Chao Yang Ying-ge Han Nanjing University of Information Science &Technology Nanjing 210044P.R.China Anhui University of S Anhui University of Science and Technology Huainan 232001P.R.China

Aiming at the slow convergence rate and the high mean square error of constant modulus algorithm(CMA) ,a new orthogonal Wavelet Transform based Sign Decision Dual-mode blind equalization algorithm(WT-SDDA) is *** the proposed algorithm,orthogonal Wavelet Transform based constant modulus algorithm (WT-CMA) is integrated with orthogonal Wavelet Transform based Stop-and-Go Changeable modulus blind equalization algorithm (WT-SG-CMA),and the switch process is decided by the sign *** tests with underwater acoustic channel shows that the proposed WT-SDDA algorithm outperforms the CMA and the WT-CMA in the convergence rates and residual mean square error and that it has the faster convergence rate than the WT-SG-CMA under condition of the same residual error.

关键词： constant modulus algorithm wavelet transform dual-mode underwater acoustic channel convergence rate

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