Adaptive equalization of finite non-linear channels using multilayer perceptrons

Chen, Sheng; Gibson, Gavin J.; Cowan, C.F.N.; Grant, Peter

doi:10.1016/0165-1684(90)90122-f

Cited by 264 publications

(116 citation statements)

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“…Otherwise, nonlinear filtering is required in order to achieve an adequate performance. Examples of such nonlinear filtering include nonlinear single-user channel equalisation [89][90][91][92][93][94][95][96][97][98][99][100][101], nonlinear CDMA multiuser detection [102], nonlinear beamforming assisted detection [103][104][105][106], and nonlinear space-time equalisation [107]. Let us consider the generic nonlinear filter of the form y R ðkÞ ¼ f ðxðkÞ; wÞ,…”

Section: Extension To Nonlinear Filteringmentioning

confidence: 99%

Adaptive minimum error-rate filtering design: A review

Chen

Tan

et al. 2008

Signal Processing

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Adaptive filtering has been an enabling technology and has found ever-increasing applications in various state-of-the-art communication systems. Traditionally, adaptive filtering has been developed based on the Wiener or minimum mean square error (MMSE) approach, and the famous least mean square algorithm with its low computational complexity readily meets the fast real-time computational constraint of modern high-speed communication systems. For a communication system, however, it is the system's bit error rate (BER), not the mean square error (MSE), that really matters. It has been recognised that minimising the MSE criterion does not necessarily produce the minimum BER (MBER) performance. The introduction of the novel MBER design has opened up a whole new chapter in the optimisation of communication systems, and its design trade-offs have to be documented in contrast to those of the classic but actually still unexhausted MMSE and other often-used optimisation criteria. This contribution continues this theme, and we provide a generic framework for adaptive minimum error-probability filter design suitable for the employment in a variety of communication systems. Advantages and disadvantages of the adaptive minimum error-probability filter design are analysed extensively, in comparison with the classic Wiener filter design. r

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Section: Extension To Nonlinear Filteringmentioning

confidence: 99%

Adaptive minimum error-rate filtering design: A review

Chen

Tan

et al. 2008

Signal Processing

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“…In fact, the approach discussed in the present study can directly be applied to the case of nonlinear channel model and additive non-Gaussian correlated noise without any modification [3]. It does not really matter whether x(t) takes value 1 with a higher probability, or vice versa.…”

Section: Channel Equalisationmentioning

confidence: 96%

Adaptive channel equalisation using a polynomial-perceptron structure

Chen

Gibson

Cowan

1990

IEE Proc. I Commun. Speech Vis.

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Abstract:The paper investigates the application of a simple nonlinear structure to the problem of adaptive channel equalisation. Based on the Bayes decision rule, it is shown that the optimal equalisation solution is an inherently nonlinear problem and, therefore, it is desired to incorporate some degree of nonlinearity in the design of equaliser structure. The approximate realisation of the optimal equalisation solution is implemented using a polynomial-perceptron architecture and simulation results are included to support the theoretical analysis. IntroductionCommunications channel equalisation is concerned with the reconstruction of digital signals that have been passed through a dispersive channel and then corrupted with additive noise. Traditional techniques for solving this equalisation problem are based on linear finite filters. Adaptive linear equalisers are robust and can easily be implemented. The operation of an equaliser at each sample instant is typically based on a finite number of channel observations and decisions are usually made on a symbol-by-symbol base. Even under this classical information constraint, it has been shown that channel equalisation is an inherently nonlinear problem [4] regardless of whether a channel is minimum or nonminimum phase. Nonlinear structures are therefore required to achieve fully or near optimal performance. Gibson et al.[4] proposed a nonlinear equaliser structure based on the multilayer perceptron and demonstrated its superior performance over the linear equaliser. The multilayer perceptron has a very general ability of nonlinear decision making and, theoretically, a multilayer perceptron equaliser with sufficient size can realise the optimal performance. There are, however, some practical difficulties associated with this highly nonlinear structure that require further investigation. The selection of architecture and parameter values for the multilayer perceptron equaliser is mainly by experiment. The training [7], and training times are typically very long. Although the use of recursive Gauss-Newton algorithms [2, 91 can significantly improve the convergence properties of the multilayer perceptron equaliser, these algorithms require more computation at each recursion and will have difficulties in meeting the real-time requirements of high-speed data transmission where adaptive equalisation is mostly needed.In this paper an alternative nonlinear equaliser structure is examined. Using the Bayes decision rule, it is shown that the optimal equalisation solution is highly nonlinear, a result identical to that derived in [4] by a different approach. An old technique, namely polynomial approximation, is then employed as a means of approximately realising the optimal solution. This leads to a polynomial-perceptron equaliser that is theoretically more tractable compared with the multilayer perceptron equaliser as the filter parameters are almost linear with respect to the output error. Simple simulation examples are included to compare the performance of this polynomia...

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“…The geometric formulation of the MAP equalizer is shown in (Chen, S., 1990) and (Chen, S., 1991). We are using the same notation as in those studies and we define:…”

Section: Geometric Formulation For Map Equalizermentioning

confidence: 99%

Extended Kalman Filter Based Fuzzy Adaptive Filter

Wong¹,

Lim²

2009

Kalman Filter Recent Advances and Applications

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A fuzzy logic system is composed of four principal components: a fuzzifier, a fuzzy rule base, a fuzzy inference engine and a defuzzifier (Mendel, J. M., 1995). It is an information processing system. Fig. 2 depicts a fuzzy logic system that is widely used in fuzzy logic controllers and signal processing applications. The crisp inputs s, are first converted into fuzzy quantities u. This process is known as fuzzification, where a fuzzifier transforms crisp input values into linguistic values. Input values are translated into linguistic concepts, which are represented by fuzzy sets. Rules may be provided by experts or can be extracted from numerical data. In either case, engineering rules are expressed as a collection of IF-THEN statements. The inference engine Open Access Database www.intechweb.org temperature regulator that uses a fan. Fig. 3 shows the fuzzy sets and the membership functions for the input temperature. Fig. 3. Fuzzy sets of a simple temperature regulator that use a fanA membership function x , for x∈ X, quantifies the grade of membership of the elements x to the fundamental set Χ. An element mapping to the value 0 means that the member is not included in the given set, 1 describes a fully included member. Values strictly between 0 and 1 characterize the fuzzy members. Membership functions are applied to the measurement and the degree of truth in each determined premise. According to Fig.3, if the input temperature s is 33ºC, after fuzzification, the membership value that s belongs to warm and hot temperature are The fuzzy rules may be provided by a human expert, or can be extracted from numerical input-output data pairs. In either case, engineering rules are expressed as a collection of IF-THEN statements, i.e., "IF temperature is very hot THEN speed maximum fan." "IF temperature is hot THEN speed medium high fan." "IF temperature is warm THEN maintain medium fan." "IF temperature is cold THEN turn down medium low fan." "IF temperature is very cold THEN stop fan." These rules reveal that we will need an understanding of (Mendel, J.M., 1995): 1. Linguistic variables versus numerical values of the variable, e.g., very hot versus 45ºC. 2. Quantifying linguistic variables. E.g., u may have a finite number of linguistic terms associated with it, ranging from very hot to very cold, which is fuzzifying using fuzzy membership functions. There is no unique membership function in a situation and it is primarily subjective in nature. But this does not mean that membership function can be assigned arbitrarily, it is rather on the basis of application-specific criteria. Some of the commonly used membership functions are shown in Fig. 1 (Chen, S., 1990). 3. Implications, which is the relationship between two statements where the truth of one suggests the truth of the other, e.g., "IF temperature is warm THEN maintain medium www.intechopen.comKalman Filter: Recent Advances and Applications 90 fan." Here, the truth of temperature is warm suggests the fan to maintain in medium speed. 4. Logical connections for li...

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Adaptive equalization of finite non-linear channels using multilayer perceptrons

Cited by 264 publications

References 5 publications

Adaptive minimum error-rate filtering design: A review

Adaptive minimum error-rate filtering design: A review

Adaptive channel equalisation using a polynomial-perceptron structure

Extended Kalman Filter Based Fuzzy Adaptive Filter

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