Adaptive Blind Channel Equalization (original) (raw)
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On-line blind multichannel equalization based on mutually referenced filters
IEEE Transactions on Signal Processing, 1997
This paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and timevarying communication channels. In the context of channel diversity, we introduce the concept of mutually referenced equalizers (MRE's) in which several filters are considered, the outputs of which act as training signals for each other. A corresponding (constrained) multidimensional mean-square error (MSE) cost function is derived, the minimization of which is shown to be a necessary and sufficient condition for equalization. The links with a standard linear prediction problem are demonstrated. The proposed technique exhibits properties of important practical concern: 1) The proposed algorithm is globally convergent. 2) Simple closed-form solutions exist for the MRE's, but the MRE's also lend themselves readily to adaptive implementation. In particular, the recursive least-squares (RLS) algorithm can be used to offer optimal convergence rate. 3) The MRE method provides a solution for all equalization delays, which results in robustness properties with respect to SNR and ill-defined channel lengths. I. INTRODUCTION T RANSMISSION over high-speed digital communication channels is subject to inter-symbol interference (ISI) inducing channel distortion, which has to be compensated for by an equalization device. In the context of digital radiocommunications, the problem is very challenging due to the length of the ISI that stems from the data transmission at high rates in a multipath propagation environment. Traditional equalization schemes rely on the periodic transmission of training sequences, which are known from the receiver and are used to acquire and update either the channel or the equalizer coefficients. This strategy, however, results in a significant reduction of the effective communication rate. The need for very high bit rates that arises in the field of digital communications makes very attractive the methods that do not resort to such training sequences (blind equalization).
Blind Channel Equalization Using Adaptive Signal Processing Algorithms
IOSR Journals , 2019
The objective of this paper is to investigate the blind channel equalization using least mean square (LMS) algorithm and its variants. Digital transmission systems impose the application of channel equalizers with short training time, high tracking rate, high data rate and quality. Thus, it is necessary to define new and robust algorithms to equalize channels and reduce noise in communications. In this paper LMS algorithm and its variants normalized LMS (NLMS) and sign LMS (SLMS) algorithms are used for implementation of blind channel equalization. The performance of each algorithm is studied separately and results are compared. It is found that the convergence rate and error performance of NLMS and SLMS equalizers are better than LMS equalizer.
Adaptive Equalization for Fast Varying Digital Communication Systems
2013
— The recent digital transmission systems impose the application of channel equalizers with bandwidth efficiency, which mitigates the bottleneck of intersymbol interference for high-speed data transmission-over communication channels. This leads to the exploration of blind equalization techniques that do not require the use of a training sequence. Blind equalization techniques however suffer from computational complexity and slow convergence rate. The Constant Modulus Algorithm (CMA) is a better technique for blind channel equalization. This paper examined three different error functions for fast convergence and proposed an adaptive blind equalization algorithm with variable step size based on CMA criterion. A comparison of the existing and proposed algorithms ’ speed of convergence shows that the proposed algorithm outperforms the other algorithms. The proposed algorithm can suitably be employed in blind equalization for rapidly changing channels as well as for high data rate appli...
An efficient blind decision feedback equalizer
IEEE Communications Letters, 2000
Efficient and fully blind Decision Feedback Equalizer (DFE) remains an open issue, mainly because of the potential errors in the decision loop. Based on the Weighted Decision Feedback Equalizer (WDFE), our previous work aiming at decreasing the error propagation phenomena, we propose a new blind DFE called Blind Weighted Decision Feedback Equalizer. The main idea of the WDFE was to commute between Linear Recursive Equalizer (LRE) and DFE for the error computation at the decision device. In this paper, we extend this idea in order to commute also both the algorithms and the filtering structure. This commutation is performed softly and blindly. I. INTRODUCTION At first sight, the drawbacks of the DFE, for example error propagation, make it a poor candidate for blind equalization, although its performance when optimal is particularly attractive. Extending our previous work Weighted Decision Feedback Equalizer [1] we propose here a new fully blind DFE: the Blind-Weigthed Decision Feedback Equalizer (B-WDFE). The main idea is to commute softly and blindly the algorithms, the filtering structure and the decision device between the two extremes cases: the LRE and the DFE. This should be performed under the following constraints, in order to achieve our objective: • No structure change-i.e. all the parts of the equalizer are used equally for the convergence of the algorithm and for the equalization of the channel once converged. This avoids having one equalizer that opens the eye in the first stage and then another that derives from it once the decisions are sufficiently certain, as in [3]. • No sudden change in the cost functions-i.e. the equalizer must adapt itself to achieve the best possible correspondence between the convergence phase and the channel variation tracking phase, without changing the cost functions to be optimized. • The equalizer must be as simple as possible in its architecture. Thus sample-by-sample algorithms and structures based on filtering are considered positively. In Section II we first describe the filtering structure of our equalizer then in Section III we explain the proposed algorithm, which softly commutes between a blind algorithm and the Decision Directed (DD) algorithm. We prove the efficiency of our B-WDFE thanks to simulation presented in Section IV and finally we conclude the paper.
PERFORMANCE COMPARISONS OF ADAPTIVE ALGORITHMS FOR BLIND EQUALIZATION
In this paper, we compare several algorithms for blind channel equalization. The analysis includes the joint order detection and blind channel estimation by least squares smoothing (J-LSS), the adaptive version of the J-LSS algorithm, and the prediction error algorithm. Analysis are performed with respect to the computa-tional complexity and convergence speeds of the algo-rithms.
International Journal of Advanced Computer Science and Applications, 2012
The recent digital transmission systems impose the application of channel equalizers with bandwidth efficiency, which mitigates the bottleneck of intersymbol interference for high-speed data transmission-over communication channels. This leads to the exploration of blind equalization techniques that do not require the use of a training sequence. Blind equalization techniques however suffer from computational complexity and slow convergence rate. The Constant Modulus Algorithm (CMA) is a better technique for blind channel equalization. This paper examined three different error functions for fast convergence and proposed an adaptive blind equalization algorithm with variable step size based on CMA criterion. A comparison of the existing and proposed algorithms' speed of convergence shows that the proposed algorithm outperforms the other algorithms. The proposed algorithm can suitably be employed in blind equalization for rapidly changing channels as well as for high data rate applications.
Adaptive blind equalizers with automatically controlled parameters
IEEE Transactions on Communications, 1995
Signals when pass through a channel undergo various forms of distortion, most common of which is Inter-symbol-interference, so called ISI. Inter-symbol interference induced errors can cause the receiver to misinterpret the received samples. Equalizers are important parts of receivers, which minimizes the linear distortion produced by the channel. If channel characteristics are known a priori, then optimum setting for equalizers can be computed. But in practical systems the channel characteristics are not known a priori, so adaptive equalizers are used. Adaptive equalizers adapt or change the value of its taps as time progresses. There are two main types of adaptive equalizers, trained equalizers and blind equalizers. In trained equalizers there is a pseudo-random pattern of bits called training sequence known both to receiver and transmitter. But equalizers for which such a initial training period can be avoided are called BLIND EQUALIZERS. Blind equalizer as opposed to data trained equalizer, is able to compensate amplitude and delay distortion of a communication channel using only channel output sample and knowledge of basic statistical properties of the data symbol. Among some algorithms of blind equalizers like CMA, Stop and Go, GSA, SGA, SRCA etc., Stop and Go is one of the most important algorithms. Unfortunately all blind equalizers converge very slowly. So there is a proposed method for automatic control of step size and filter length for a blind equalizer which is driven by stop and go directed algorithm. This idea was presented by Krzysztof Wesolowski in his paper "Adaptive Blind Equalizers With Automatically Controlled Parameters". This proposed method for varying the step size results substantial shortening of the convergence time.
Convergence analysis of finite length blind adaptive equalizers
IEEE Transactions on Signal Processing, 1995
Abstracf-l'his paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers, namely, the Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one correspondence in I d " a is shown to exist between Godard and Shalvi-Weinstein equalizers, hence establishing the equivalent relationship between the two algorithms. Convergence behaviors of finite length Godard and Shalvi-Weinstein equalizers are analyzed, and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition. It is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufliciently many parameters and adequate initialization. The convergence analysis of the equalizers in PAM communication system can be easily extended to the equalizers in QAM communication systems.
A Review on Training and Blind Equalization Algorithms for Wireless Communications
Wireless Personal Communications, 2019
Every wireless communication system comes with an innate problem of multipath propagation, which results in spreading the resultant symbols on a time scale and thus causes the symbols to overlap and end up in Inter-symbol Interference (ISI). The overall signal is distorted and the receiver is unable to recover the original signal. ISI from the signal must be removed and the signal must be brought back to its original form as it was sent or as close to it as possible; and process of equalization is used in all wireless communication system for this purpose. Two types of equalization processes are common in modern wireless communication systems. Training based equalization requires the sender block of communication system to constantly send a pilot/training signal in order to update the receiver about the original signal. The receiver removes the ISI and extracts the unadulterated signal. The second equalization process is called blind equalization and it does not require any pilot signal. The receiver only needs to know the type of constellation scheme used in modulation and then the original signal is extracted based on that information. In this paper we have thoroughly reviewed four equalization algorithms, two from each type of equalization for 16-QAM constellation and 64-QAM constellation. We came up with constellation diagrams for each equalization algorithm and comparison of BER, residual ISI and MSE for 16-QAM and 64-QAM is done through simulations. In case of LMS and RLS algorithm for 16 QAM, the performance of RLS gets slightly better than LMS at 6 dB, however, at around 12-14 dB and onwards the BER of RLS leads and there is a significantly better BER than LMS. In future, we will compare these algorithms in order to figure out the best algorithms for the current and upcoming 5G and 6G communication technologies.