Diguele, Daniel · RIT Scholar Works (Rochester Institute of Technology) · 1994
An equalizer is an adaptive filter that compensates for the non-ideal characteristics of a communication channel by processing the received signal. The adaptive algorithm searches for the inverse impulse response of the channel, and it requires knowledge of a training sequence, in order to generate an error signal necessary for the adaptive process. There are practical situations where it would be highly desirable to achieve complete adaptation without the use of a training sequence, hence the the term "blind". Examples of these situations are multipoint data networks, high-capacity line-of-sight digital radio, and reflection seismology. A blind adaptive algorithm has been developed, based on simplified equalization criteria. These criteria are that the second- and fourth-order moments of the input and output sequences are equalized. The algorithm is entirely driven by statistics, only requiring knowledge of the variance of the input signal. Because of the insensitivity of higher-order statistics to Gaussian processes, the algorithm performs well when additive white Gaussian noise is present in the channel. Simulations are presented in which the new blind equalizer developed is compared to other equalization algorithms.
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Diguele, Daniel · RIT Scholar Works (Rochester Institute of Technology) · 1994
An equalizer is an adaptive filter that compensates for the non-ideal characteristics of a communication channel by processing the received signal. The adaptive algorithm searches for the inverse impulse response of the channel, and it requires knowledge of a training sequence, in order to generate an error signal necessary for the adaptive process. There are practical situations where it would be highly desirable to achieve complete adaptation without the use of a training sequence, hence the the term "blind". Examples of these situations are multipoint data networks, high-capacity line-of-sight digital radio, and reflection seismology. A blind adaptive algorithm has been developed, based on simplified equalization criteria. These criteria are that the second- and fourth-order moments of the input and output sequences are equalized. The algorithm is entirely driven by statistics, only requiring knowledge of the variance of the input signal. Because of the insensitivity of higher-order statistics to Gaussian processes, the algorithm performs well when additive white Gaussian noise is present in the channel. Simulations are presented in which the new blind equalizer developed is compared to other equalization algorithms.
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E.B. Olasz · PRISM (University of Calgary) · 1996
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Rueywen Liu · Kluwer Academic Publishers eBooks · 2006
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L. Litwin · IEEE Potentials · 1999
Signals that pass through a channel undergo various forms of distortion. One very common type of distortion is intersymbol interference, or ISI. ISI is caused by interference from the symbols that were transmitted before and after the given symbol. ISI-induced errors can cause the receiver to misinterpret the received samples. The equalizer is an important part of a modern digital communications receiver. It filters the received data to minimize the linear distortion induced during the transmission of the signal. (There is no nonlinear distortion.) This distortion occurs when the signal is transmitted through a channel. The channel is the physical medium that connects the transmitter and receiver. For example, the Earth's atmosphere is the medium in a wireless communications system. By sending the signal through the equalizer, the effects of ISI are counteracted; i.e. the receiver can make accurate symbol decisions based on the equalizer output. This article discusses the constant modulus algorithm, or CMA. This is the most popular algorithm used to blindly update equalizer coefficients.
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Pierre Duhamel · 2002
This paper gives an overview of several algorithms which have been proposed in the context of blind (i.e. without training sequence) multivariable (i.e. oversampled or multichannel) equalization. We focus first on the compatibility of previously known blind equalization (BE) algorithms with this relatively new framework. Then, two basic approaches are presented, explicitly dealing with the multivariable context. These two approaches are the subspace and the linear prediction methods. Finally, we emphasize on the validity of the underlying hypotheses (absence of common zeroes, given degree of the channel) in practical situations. These considerations serve as guidelines for discussing further research on blind multivariable equalization.
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Monisha Ghosh · Optical Engineering · 1992
A new approach to blind equalization is investigated in which the receiver performs joint data and channel estimation in an iterative manner. Instead of estimating the channel inverse, the receiver computes the maximum-likelihood estimate of the channel itself. The iterative algorithm that is developed involves maximum-likelihood sequence estimation (Viterbi decoding) for the data estimation part, and least-squares estimation for the channel estimation part. A suboptimal algorithm is also proposed that uses a reduced-state trellis instead of the Viterbi algorithm. Simulation results show that the performance obtained by these algorithms is comparable to that of a receiver operating with complete knowledge of the channel.
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Peter Purdue, Peter Purdue Professor, Y. Chen et al. · 1992
FOR THE OFFICE OF NAVAL RESEARCH Reproduction in whole or in part is permitted for any purpose of the United States Government. Approved for public release; distribution unlimited
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2006
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D. R. Brown, Brown Schniter, C. R. Johnson · 1997
: Adaptive blind equalization has gained wide-spread use in communication receivers that operate without training signals. In particular, the Constant Modulus Algorithm (CMA) [6, 10] has become a favorite of practitioners due to its LMS-like complexity and desirable robustness properties [4, 5, 14]. This paper presents a signed-error version of CMA (SE-CMA) which is motivated by a further reduction in the computation complexity of the equalizer coefficient update. The authors investigate the performance of SE-CMA and establish connections to previously proposed signed blind algorithms. A novel dithered signed blind algorithm (DSE-CMA) is proposed which overcomes significant SE-CMA convergence issues and possesses similar robustness properties to the standard (i.e. unsigned) CMA. 1 Introduction Digital communication through band-limited or multipath channels results in intersymbol interference (ISI) which, if left uncompensated, can cause unnecessarily high symbol error rates (SER) at ...
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K. Itoh, Tetsuya Shimamura, Jouji Suzuki · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract A major problem with blind equalization algorithms based on the distribution matching principle is that they need a long time to accomplish their convergence. What affects convergence has not been discovered to date. the similarity between the least mean‐square (LMS) algorithm (widely used for adaptive equalization) and the blind algorithms is considered here. It is expected that the convergence of the blind algorithms is dependent on the condition number of the correlation matrix of the input sequence. Prefiltering methods, including coefficient‐fixed type and coefficient‐adaptive type, are derived for blind equalization. In these methods, the prefilters are realized by a prediction error filter, which has the ability to compensate for amplitude distortion induced by a channel. Since the prefilters have such ability, the blind equalizers to be cascaded with them are required only to compensate for phase distortion. As a result, the burden imposed on the blind equalizers is reduced. the prefilters output a near‐white sequence and lead to an improvement in the convergence of the blind algorithms, being degraded as the condition number is increased. the effective ness of the proposed methods is validated by computer simulations.
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Xiangyang Zhuang, A. Lee Swindlehurst · 2007
This paper addresses the application of blind source separation (BSS) algorithms to the problem of blind equalization (BE) in a frequency selective multi-user environment. Compared with other algorithms that exploit the structural properties of the channel or data matrix, our approaches are insensitive to channel order estimation, robust to ill-conditioned channels and able to choose the "best" equalizer delay(s). Many batch and adaptive BSS algorithms are briefly discussed for the application to BE, but we mainly focus on the application of two particular well-known batch approaches, i.e., JADE (Joint Approximate Diagonalization of Eigenmatrices) and ACM (Analytical Constant Modulus). Their respective underlying principles, assumptions, methodologies, computational complexity and performance are analyzed respectively. The relation between output noise power and the delay at which the equalizer recovers the signal is studied, from which an MMSE criterion is introduced to the JADE algor...
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Björn Jelonnek, K.-D. Kammeyer · 2002
The authors introduce a new algorithm for blind equalization which uses a set of cost functions. Each of them guarantees a closed form solution of the equalization problem and approximates the ideal MSE (mean square error) solution. On the basis of an iterative process the best approximation is selected. Application of this algorithm is not limited to linear equalizers operating at symbol rate. As a possible generalization to include other areas (such as system identification, decision-feedback equalization or fractionally spaced equalization), an extension to fractional tap space equalizers is outlined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Marcelino Lázaro, Ignacio Santamarı́a, C. Pantaleón et al. · 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). · 2004
In this paper, a new blind equalization algorithm for multilevel modulations is proposed. It is based on maximizing the correlation between the probability density function (pdf) of the signal at the output of the equalizer and the desired pdf. The algorithm employs the Parzen window method to estimate the pdf of the squared modulus of the equalizer output. A stochastic gradient-based algorithm is used to maximize the correlation between this pdf and the pdf of the corresponding modulation. The proposed algorithm shows an excellent performance when compared with conventional adaptive blind algorithms, such as CMA, in quadrature amplitude modulation (QAM) schemes.
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João Batista Destro Filho, Gérard Favier, João Marcos Travassos Romano · 2002
This paper presents general guidelines for applying neural networks (NNs) to blind equalization. Firstly, basic concepts and practical issues related to NNs and traditional equalization techniques are discussed. Then, the main neural-network-based solutions for equalization are reviewed and classified in four groups, depending on the type of equalization (supervised or blind) and the use of NNs (nonlinear filter or classifier). Finally, based on conclusions drawn from the analysis of the considered papers, a new effective neural solution is proposed for blind equalization.
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Koen Blom · 2014
Underwater wireless (sensor) networks would vastly improve man's ability to explore and exploit remote aquatic environments. Despite underwater sensor and vehicle technology being relatively mature, underwater communications is still a major challenge. The most challenging characteristics of the underwater acoustic communication channel are its low and variable propagation speed, frequency-dependent attenuation and time-varying multipath propagation. Spatial and spectral signal processing techniques can be employed to mitigate the effects of the distortion caused by the underwater acoustic channel. In general, the underwater channel capacity is scarce and underwater transmitters have limited energy resources. To reduce energy consumption and to make more efficient use of the available capacity, this thesis elaborates on compensation of underwater channel distortion without employing training sequences. The latter is known as blind (adaptive) equalization. As a substitute for the missing training sequences, the constant modulus property of the transmitted signals is exploited. Deviations of the equalizer output from a constant modulus act as a reference for equalizer updates. Two blind spatial equalization methods, which both exploit structural properties of the signal-of-interest, are presented in this thesis. The first method, the extended CMA (E-CMA), is an algorithm capable of updating the directionality of the array to improve signal reception, while simultaneously correcting for phase offsets. Initial results from our underwater experiments demonstrate the E-CMA's promising performance. The second method for blind spatial equalization discussed in this thesis, is the angular CMA (A-CMA). In contrast to conventional adaptive methods, the A-CMA calculates steering angle updates instead of updates for the entire equalizer weight vector. Compared to the conventional CMA, the A-CMA provides faster convergence to a low mean square error level. Since the propagation speed of underwater acoustic pressure waves is variable, a direct-path acoustic wave can arrive later than a reflected/refracted wave. This phenomenon, which is known as nonminimum-phase behavior, complicates blind extraction of a channel's phase response. A method to improve and accelerate blind equalization of a channel's nonminimum-phase response, known as the all-pass CMA (AP-CMA) is presented. No standard synthetic underwater acoustic channel model exists. Therefore, real-life experiments are performed for true testing. Current commercially available systems for underwater acoustic signal processing make use of dedicated hardware. To implement other physical layer processing techniques (often) changes in hardware and/or proprietary firmware are required. Therefore, a flexible multi-channel underwater testbed has been developed and used in experiments, to evaluate the performance of (novel) blind equalizers. Overall, based on simulated and empirical data, this thesis indicates that blind spectral and blind spatial equalization are appealing means for mitigation of distortion experienced in the underwater channel.
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Colonnese S., Panci G., Scarano G. · IRIS Research product catalog (Sapienza University of Rome) · 2006
This paper addresses the problem of semi-blind equalization following a Bussgang approach. An equalization scheme that integrates the training information into the iterative Bussgang algorithm is analyzed. The semi-blind equalization scheme allows flexible introduction of redundancy in the transmission scheme. The accuracy is assessed in the reference case of the Global System for Mobile communication (GSM), i.e. GMSK modulated signals received through typical mobile radio channels. Numerical simulations show that the semi-blind Bussgang equalization algorithm achieves performance comparable with the Maximum Likelihood Sequence Estimator (MLSE) implemented by Viterbi algorithm. Its flexibility allows to consider different amounts of training information as well as higher order constellations.
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Yang, Jian · cIRcle (University of British Columbia) · 1997
In bandwidth-efficient digital transmission, the training of a receiver requires a start-up procedure. This start-up includes the three steps of setting the automatic gain control, recovering timing, and converging the adaptive filters. For many applications, start-up is facilitated by using a known training sequence, which can be used as an ideal reference by the receiver. However, sometimes the use of a training sequence is not feasible or not desirable. In this case, start-up has to be done blindly. The most challenging aspect of blind start-up is the convergence of the adaptive equalizer. This function is called blind equalization. Without ideal reference, the receiver has to make decisions about what data have been transmitted. Normally we use a decision device to make the assumptions on the input signals. This decision device is also called a slicer. These decisions are highly unreliable because the received data are corrupted by intersymbol interference due to distortion introduced by the communication link. As a result, the equalizer does not converge with the conventional least mean square (LMS) algorithm because the probability of wrong decisions is too high. The requirement for reducing wrong decisions leads to the development of blind algorithms. Several algorithms were developed in the past for blind equalization. The two most common ones are the constant modulus algorithm (CMA) and the reduced constellation algorithm (RCA). Both algorithms have been successfully used in many practical applications in data communications. However, improved blind algorithms are still in demand in order to meet the requirements of high data rate communications, where the implementation of blind equalization is required to be simple and reliable. RCA is simple to implement but is not very reliable. CMA is very reliable but has a high complexity., In this thesis, an improved blind algorithm, called multimodulus algorithm (MMA), is proposed. This new algorithm is more reliable than RCA and less complex than CMA. Blind algorithms, such as RCA or CMA, do not take full advantage of the knowledge of the statistics of the data signal, because they only use one statistical quantity, called modulus, during blind convergence. In contrast, MMA makes better usage of the knowledge of the statistics of the data signal and employs multiple moduli to achieve initial convergence. The use of multiple moduli makes MMA very flexible and easily adaptable to applications using two-dimensional transmission schemes with nonsquare or very dense signal constellations. Both RCA and CMA are not very effective for these types of applications. Most blind equalization algorithms minimize a cost function. Our investigation has shown that the minimum (residual) value of this cost function has a great influence on the reliability and speed of convergence of the corresponding blind algorithm. For example, for CMA, RCA and MMA, this residual value increases when the bandwidth efficiency of the transmission system increases, and the blind algorithms suffer a corresponding decrease in performance. Two generalized versions of MMA are proposed to circumvent the above problem. One is called generalized MMA (GMMA). The basic version of MMA uses multiple moduli primarily for nonsquare constellations when nonuniform symbol distributions are utilized. Multiple moduli are also used with GMMA but the additional purpose there is to decrease the residual value of the cost function. A similar effect is achieved by using another blind algorithm, called windowed MMA (WMMA). With WMMA, only one modulus is used, but the tap coefficients of the filter are only updated with some of the data, which leads to a reduction of the residual value of the cost function. The new MMA algorithm has been extensively tested with computer simulations. Most simulation results presented here were obtained with the 155 Mb/s 64-CAP transceiver specified in the ATM LAN standard for category 3 unshielded-twisted-pair office wiring. However, our results are equally applicable to other applications, such as the 52 Mb/s 16-CAP transceiver defined in DAVIC's specification for fiber-to-the-curb networks. Some preliminary experimental results obtained in the laboratory with such a 16-CAP transceiver are presented in this thesis. The computer simulations and laboratory experiments have confirmed that the basic MMA and its generalized algorithms show improved blind convergence performance or complexity savings when compared to previously available algorithms. MMA will likely be incorporated in future broadband access systems from Lucent Technologies, and will replace RCA and CMA, which were previously used, or eliminate the need for a training sequence.
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Xue Jiang, Wenjun Zeng, Jiayi Chen et al. · 2020
A polynomial optimization based blind equalizer (POBE) is proposed. Different from the popular constant modulus algorithm and its variants, the POBE adopts an eighth-order multivariate polynomial as the loss function. Since the loss function is sensitive to phase rotation, the POBE can achieve automatic carrier phase recovery. A gradient descent method with optimal step size is developed for solving the optimization problem. We reveal that this optimal step size is one root of a seventh-order univariate polynomial and hence, can be computed easily. Compared with the blind equalizers based on stochastic gradient descent with empirical step size, which suffers from slow convergence or even divergence, the POBE significantly accelerates the convergence rate. Moreover, it attains a much lower inter-symbol interference (ISI), resulting in a noticeable improvement of equalization performance. Simulation results demonstrate the superiority of POBE over several representative blind equalizers.
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Jian Yang, Jean-Jacques Werner, Guy A. Dumont · 2002
This paper presents a new blind equalization algorithm called the multimodulus algorithm (MMA). This algorithm is particularly well suited to applications using two-dimensional transmission schemes such as carrierless AM/PM (CAP) and quadrature amplitude modulation (QAM). The paper also discusses some of the advantages provided by MMA when compared to traditional blind equalization algorithms, such as the reduced constellation algorithm (RCA) and the constant modulus algorithm (CMA).
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