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A Class of Channels Resulting in Ill-Convergence for CMA in Decision Feedback Equalizers

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第11期58卷 5736-5743页

作者： Neves, Aline Panazio, Cristiano Univ Fed ABC Ctr Engn Modelagem & Ciencias Sociais Aplicadas BR-09210170 Sao Paulo Brazil Univ Sao Paulo Escola Politecn BR-05508900 Sao Paulo Brazil

This paper analyzes the convergence of the constant modulus algorithm (CMA) in a decision feedback equalizer using only a feedback filter. Several works had already observed that the CMA presented a better performance than decision directed algorithm in the adaptation of the decision feedback equalizer, but theoretical analysis always showed to be difficult specially due to the analytical difficulties presented by the constant modulus criterion. In this paper, we surmount such obstacle by using a recent result concerning the CM analysis, first obtained in a linear finite impulse response context with the objective of comparing its solutions to the ones obtained through the Wiener criterion. The theoretical analysis presented here confirms the robustness of the CMA when applied to the adaptation of the decision feedback equalizer and also defines a class of channels for which the algorithm will suffer from ill-convergence when initialized at the origin.

关键词： Blind equalization constant modulus algorithm decision directed algorithm decision feedback equalization ill-convergence

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The unsupervised optimum linear finite length filter for fourth order wide sense stationary single output systems

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DIGITAL SIGNAL PROCESSING 2019年 85卷 99-112页

作者： Jamali, Hamadi Sequoia Appl Technol Thiruvananthapuram Kerala India Santa Clara Univ Elect Dept Santa Clara CA 95053 USA Santa Clara Univ Comp Sci Dept Santa Clara CA 95053 USA

The finite length absolute minimum vectors of the constant modulus (CM) criterion with an arbitrary source and a single output linear regression model are shown to equal the Wiener filter or one of its phase shifted versions. The exact equations for these vectors are also provided and depend on the second and the fourth order statistical moments of the sample sequence only. These expressions describe the behavior of the constant modulus algorithm (CMA) when it operates at the desired global minimum and expose key characteristics of the CM minimization approach. These characteristics include the existence conditions, the persistency of excitation, the computational complexity, the excess CM cost, the robustness to an additive noise, and the tolerance to the length variations. Moreover, several computer simulation experiments are included to validate our findings. (C) 2018 Published by Elsevier Inc.

关键词： Blind optimum algorithms constant modulus criterion constant modulus algorithm NP-hard Unsupervised optimization

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Implementation of enhanced fractionally spaced algorithm for blind equalization technology in WSNs

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AD HOC NETWORKS 2014年第0期14卷 26-34页

作者： Sung, Wen-Tsai Hsiao, Sung-Jung Natl Chin Yi Univ Technol Dept Elect Engn Taichung 41170 Taiwan Natl Taipei Univ Technol Dept Elect Engn Taipei 106 Taiwan

This study proposed a fractionally spaced equalizer constant modulus algorithm (CMA) for improving wireless sensor network (WSN) transmission, which could suppress noise amplification, reduce the sensibility to time phase errors and converge to the expected global minimum point, so as to reach the effectiveness of a global equalization communication channel. Based on the multi-channel equalization model in the WSN transmission system, various experimental analyses and performance comparisons proved that the convergence rate of the method proposed in this study was higher than that of general existing algorithms. The final experimental analysis proved that the higher the sampling rate was, the higher the convergence rate and the smaller the mean square error would be. The sampling rate had an important effect on the blind equalization, and it was proved that the method proposed in this study had an improved blind equalization algorithm to some extent. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Enhanced fractionally spaced Wireless sensor network Transmission system constant modulus algorithm 4QAM

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Interference Gaussianization: Time-Domain Inter-Symbol Spreading for Blind Adaptive Array Signal Source Identification

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IEEE ACCESS 2021年 9卷 89539-89553页

作者： Maruta, Kazuki Senoo, Katsuya Hisano, Daisuke Nakayama, Yu Nishimori, Kentaro Tokyo Inst Technol Acad Super Smart Soc Tokyo 1528552 Japan Chiba Univ Grad Sch Engn Chiba 2638522 Japan Osaka Univ Grad Sch Engn Osaka 5650871 Japan Tokyo Univ Agr & Technol Inst Engn Tokyo 1848588 Japan Niigata Univ Fac Engn Niigata 9502181 Japan

This paper proposes a novel blind adaptive array (BAA) interference suppression scheme incorporated with a time-domain symbol spreading (TISS). It can expand an operational region of BAA irrespective of input signal-to-interference power ratio (SIR) conditions. Independent component analysis (ICA) and constant modulus algorithm (CMA) are expected as the promising BAA approaches to suppress unknown interference which is extensively caused due to the small cell densification and spectrum superposing between a plurality of wireless communication systems. These BAA algorithms basically require an input SIR to be larger than 0 dB to suppress interference by capturing the desired signal appropriately. The proposed scheme applies TISS to the transmission signal for the desired user and then de-spreads it at the receiver side. It Gaussianizes statistical inherence of the interference signals and can bring beneficial effects;reducing the kurtosis for ICA as well as collapsing the constant envelope properties for CMA. Such intentional modification to the interference signals can improve the capture performance of the desired signal and realize its effective identification even at SIR < 0 dB. Its fundamental effectiveness is presented through various perspectives such as input SIR, symbol amount, and modulation orders.

关键词： Interference suppression Adaptive arrays Time-domain analysis Wireless sensor networks Quadrature amplitude modulation Proposals Independent component analysis Adaptive arrays blind source separation independent component analysis constant modulus algorithm Gaussianization time-domain inter-symbol spreading

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Blind image deconvolution via dispersion minimization

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DIGITAL SIGNAL PROCESSING 2006年第2期16卷 137-148页

作者： Vural, C Sethares, WA Sakarya Univ TR-54187 Sakarya Turkey Univ Wisconsin Elect & Comp Engn Dept Madison WI 53706 USA

In linear image restoration, the point spread function of the degrading system is assumed known even though this information is usually not available in real applications. As a result, both blur identification and image restoration must be performed from the observed noisy blurred image. This paper presents a computationally simple iterative blind image deconvolution method which is based on non-linear adaptive filtering. The new method is applicable to minimum as well as mixed phase blurs. The noisy blurred image is assumed to be the output of a two-dimensional linear shift-invariant system with an unknown point spread function contaminated by an additive noise. The method passes the noisy blurred image through a two-dimensional finite impulse response adaptive filter whose parameters are updated by minimizing the dispersion. When convergence occurs, the adaptive filter provides an approximate inverse of the point spread function. Moreover, its output is an estimate of the unobserved true image. Experimental results are provided. (c) 2005 Elsevier Inc. All rights reserved.

关键词： blur identification blind image deconvolution image restoration non-linear adaptive filtering constant modulus algorithm image and multimedia processing general methods

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CMA-based channel estimation for space-time block coding transmission systems

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WIRELESS PERSONAL COMMUNICATIONS 2004年第4期28卷 241-258页

作者： Xu, CJ Le-Ngoc, T McGill Univ Dept ECE Montreal PQ H3A 2A7 Canada

In this paper, we present channel estimation methods for space-time block coding (STBC) transmissions using constant modulus algorithm (CMA). The channel estimates are directly calculated from the convergence value of the CMA. Two algorithms using the channel-vector-based and channel-gain-based constant modulus ( CM) criteria are proposed. An approximation of the CM cost function is introduced to allow the use of the recursive least-square (RLS) technique in designing fast RLS-CMA's. Performance of the proposed schemes is evaluated and compared with others using simulation. Illustrative results show that the proposed scheme outperforms the cross-correlated method and can approach the performance of the training-based method.

关键词： transmit diversity space-time block coding constant modulus algorithm channel estimation wireless communications

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Recursive blind image deconvolution via dispersion minimization

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2005年第8期19卷 601-622页

作者： Vural, C Sethares, WA Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA Sakarya Univ Dept Elect & Elect Engn TR-54173 Sakarya Turkey

This paper presents an adaptive autoregressive (AR) approach to the blind image deconvolution problem which has several advantages over standard adaptive FIR filters. There is no need to figure out the optimum filter support when using an AR deconvolution filter because it is the same as the support of the blur. Thus there is no distortion introduced by the finite support of the FIR filter. While an FIR filter provides an approximate inverse to the blur at convergence, the AR filter converges to an approximation of the blur itself. Hence, the method can be used for blur identification. Simulations suggest that convergence of the adaptive AR filter coefficients occur rapidly and the improvement in signal-to-noise ratios are higher than in the FIR case for a given blur (and with the same step-size for the adaptive algorithms). When the adaptive AR method is derived naively to minimize the dispersion, it requires a recursion within a recursion which is computationally complex. We propose a simplification that removes the inner recursion, and prove conditions under which this simplification is valid when dealing with binary images. Simulations are used to show that the method may also be applied to certain multi-valued images as well. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： image restoration blind image deconvolution blur identification constant modulus algorithm recursive adaptive filtering local stability analysis

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Capture Properties of the Generalized CMA in Alpha-Stable Noise Environment

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WIRELESS PERSONAL COMMUNICATIONS 2009年第1期49卷 107-122页

作者： Tang, Hong Qiu, Tianshuang Li, Ting Dalian Univ Technol Sch Elect & Informat Engn Dalian 116024 Peoples R China Dalian Natl Univ Coll Electromech & Informat Engn Dalian 116600 Peoples R China

constant modulus algorithm (CMA) is an adaptive technique for correcting multipath and interference-induced degradations in constant envelope waveforms. The algorithm exploits the fact that both multipath and additive interference can disrupt the constant envelope of the received signal. By detecting the received envelope variations, the adaptive algorithm has the ability to reset the coefficients vector so as to remove the variations, and in the process, reject the various interference components from the desired signal. If both the interferer and the signal of interest have constant envelope and are spectrally non-overlapped, it is possible to find two different solutions for the coefficient vector, in which one suppresses the interferer and the other "captures" the interferer. The problem of how "capture" can occur and how it may be prevented in Gaussian noise environment has been perfectly developed in the previous work (Treichler, Larimore, IEEE Trans Acoust Speech Signal Process, 33:946-958, 1985). However, recent investigation on the physical channels in wireless communication shows that there is aggregate noise component exhibiting high amplitudes for small duration time interval. This paper proposes a GCMA (Generalized CMA) which generalizes the CMA by introducing the alpha-stable distribution as the noise model. Here the original CMA is only a special case of the GCMA. In order to describe the average behavior of the GCMA, a simple model consisting of only two sinusoids is presented. As assuming slow adaptation, the adaptive weight recursion is shown to compress into a two-by-two recursion in the tone output amplitudes. The simplified recursion is analyzed to determine what combination of signals power and initialization on coefficient vectors leads to "lock" and what leads to the capture of the interferer. The method to determine lock and capture zone boundaries is analyzed. These convergence properties of the GCMA are studied by computer simulations.

关键词： Impulsive interference alpha-stable process Fractional lower-order statistics constant modulus algorithm Adaptive blind beam forming

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Dithered signed-error CMA: Robust, computationally efficient blind adaptive equalization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1999年第6期47卷 1592-1603页

作者： Schniter, P Johnson, CR Cornell Univ Sch Elect Engn Ithaca NY 14853 USA

Adaptive blind equalization has gained widespread use in communication systems that operate without training signals. In particular, the constant modulus algorithm (CMA) has become a favorite of practitioners due to its LMS-like complexity and desirable robustness properties. The desire for further reduction in computational complexity has motivated signed-error versions of CMA, which have been found to lack the robustness properties of CMA. This paper presents a simple modification of signed-error CMA, based on the judicious use of dither, that results in an algorithm with robustness properties closely resembling those of CMA. In this paper, we establish the fundamental transient and steady-state properties of dithered signed-error CMA and compare them with those of CMA.

关键词： adaptive equalizers adaptive signal processing blind equalization constant modulus algorithm deconvolution dither techniques HDTV

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Blind algorithm for decision feedback equalizer

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IEICE TRANSACTIONS ON COMMUNICATIONS 1997年第1期E80B卷 200-204页

作者： Seo, BS Lee, JH Woong, C Department of Electronics Engineering Seoul National University Seoul 151-742 South Korea

In this letter, we propose a blind adaptation method for the decision feedback equalizer (DFE). In the proposed scheme, a DFE is divided into two parts: a front-end linear equalizer (LE), and a prediction error filter (PEF) followed by a feedback part. The coefficients of the filters in each part are updated using constant modulus algorithm and decision feedback prediction algorithm, respectively. The front-end LE removes intersymbol interference ISI, and the PEF with feedback part whitens the noise to reduce noise power enhanced by the LE. Pre-processing by the LE enables the DFE to equalize nonminimum phase channels. Simulation results show that the proposed scheme provides reliable convergence, and the resulting symbol error rate is much less than that of the conventional LE and very close to that of the DFE using a training sequence.

关键词： blind equalization decision feedback equalizer constant modulus algorithm decision feedback prediction algorithm

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