book

Blind Equalization in Neural Networks

Name: Blind Equalization in Neural Networks
ISBN: 9783110449679

by Liyi Zhang, Tsinghua University Tsinghua University Press

December 2017

Intermediate to advanced

268 pages

7h 59m

English

De Gruyter

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Cover
Title Page
Copyright
Preface
Contents
1 Introduction
1.1 The research significance of the BE technology1.2 The application of BE technology1.2.1 The application in digital television1.2.2 The application in CATV system1.2.3 The application in smart antenna1.2.4 The application in software radio1.2.5 The application in blind image restoration1.2.6 The application in radiofrequency identification1.3 The research progress of neural network BE algorithm1.3.1 The FFNN BE algorithm1.3.2 The BE algorithm based on FBNN1.3.3 The FNN BE algorithm1.3.4 The ENN BE algorithm1.3.5 BE algorithm based on WNN1.4 The research background and structure1.4.1 The research background1.4.2 The structure of the book
2 The Fundamental Theory of Neural Network Blind Equalization Algorithm
2.1 The fundamental principle of blind equalization2.1.1 The concept of blind equalization2.1.2 The structure of blind equalizer2.1.3 The basic algorithm of blind equalization2.1.4 The equalization criteria of blind equalization
2.2 The fundamental theory of neural network
2.2.1 The concept of artificial neural network2.2.2 The development of ANN2.2.3 The characteristics of ANN2.2.4 Structure and classification of ANN2.3 The fundamental principle of neural network blind equalization algorithm2.3.1 The principle of blind equalization algorithm based on neural network filter2.3.2 The principle of blind equalization algorithm based on neural network controller2.3.3 The principle of blind equalization algorithm based on neural network controller classifier2.4 The learning method of neural network blind equalization algorithm2.4.1 The BP algorithm
2.4.2 The improved BP algorithm
2.5 The evaluation index of the neural network blind equalization algorithm2.5.1 Convergence speed2.5.2 The computational complexity2.5.3 The bit error characteristics2.5.4 The ability of tracking the time-varying channel2.5.5 The ability of anti interference2.5.6 The convexity of the cost function2.5.7 The steady-state residual error
2.6 Summary

3 Research of Blind Equalization Algorithms Based on FFNN
3.1 Basic principles of FFNN3.1.1 Concept of FFNN3.1.2 Structure of FFNN3.1.3 Characteristics of FFNN3.2 Blind equalization algorithm based on the three-layer FFNN3.2.1 Model of the three-layer FFNN3.2.2 Real blind equalization algorithm based on the three-layer FFNN3.2.3 Complex blind equalization algorithm based on the three-layer FFNN3.3 Blind equalization algorithm based on the multilayer FFNN3.3.1 Concept of the multilayer FFNN3.3.2 Blind equalization algorithm based on the four-layer FFNN
3.3.3 Blind equalization algorithm based on the five-layer FFNN
3.4 Blind equalization algorithm based on the momentum term FFNN
3.4.1 Basic principles of algorithm3.4.2 Derivation of algorithm3.4.3 Computer simulation results3.5 Blind equalization algorithm based on the time-varying momentum term FFNN3.5.1 Basic principles of algorithm
3.5.2 Derivation of algorithm
3.5.3 Computer simulation results3.6 Blind equalization algorithm based on variable step-size FFNN3.6.1 Basic principles of algorithm3.6.2 Derivation of algorithm3.6.3 Computer simulation results3.7 Summary
4 Research of Blind Equalization Algorithms Based on the FBNN
4.1 Basic principles of FBNN4.1.1 Concept of FBNN4.1.2 Structure of FBNN4.1.3 Characteristics of FBNN4.2 Blind equalization algorithm based on the bilinear recurrent NN4.2.1 Basic principles of algorithm4.2.2 Real blind equalization algorithm based on BLRNN4.2.3 Complex blind equalization algorithm based on BLRNN4.3 Blind equalization algorithm based on the diagonal recurrent NN4.3.1 Model of diagonal recurrent NN4.3.2 Derivation of algorithm
4.3.3 Computer simulation results
4.4 Blind equalization algorithm based on the quasi-DRNN4.4.1 Model of quasi-DRNN4.4.2 Derivation of algorithm
4.4.3 Computer simulation results
4.5 Blind equalization algorithm based on the variable step-size DRNN4.5.1 Basic principles of algorithm4.5.2 Derivation of algorithm4.5.3 Computer simulation results4.6 Blind equalization algorithm based on the variable step-size QDRNN4.6.1 Basic principles of algorithm4.6.2 Derivation of algorithm4.6.3 Computer simulation results4.7 Summary
5 Research of Blind Equalization Algorithms Based on FNN
5.1 Basic principles of FNN5.1.1 Concept of FNN5.1.2 Structure of FNN5.1.3 The choice of fuzzy membership function5.1.4 Learning algorithm of FNN5.1.5 Characteristics of FNN5.2 Blind equalization algorithm based on the FNN filter5.2.1 Basic principles of algorithm5.2.2 Derivation of algorithm5.2.3 Computer simulation results5.3 Blind equalization algorithm based on the FNN controller5.3.1 Basic principles of the algorithm5.3.2 Derivation of algorithm
5.3.3 Computer simulation results
5.4 Blind equalization algorithm based on the FNN classifier5.4.1 Basic principles of algorithm5.4.2 Derivation of algorithm
5.4.3 Computer simulation results
5.5 Summary
6 Blind Equalization Algorithm Based on Evolutionary Neural Network
6.1 Basic principles of evolutionary neural networks6.1.1 The concept of GA6.1.2 Development of GA6.1.3 GA parameters6.1.4 The basic process of GA6.1.5 Characteristics of GA6.1.6 The integration mechanism of GAand neural network6.2 Blind equalization algorithm based on neural network weights optimized byGA6.2.1 The basic algorithm principle6.2.2 Feed-forward neural network weights optimized by GA blind equalization algorithm (GA-FFNNW) in binary encoding6.2.3 Real encoding GA-FFNNW blind equalization algorithm6.3 GA optimization neural network structure blind equalization algorithm (GA-FFNNS)6.3.1 The basic algorithm principle6.3.2 Algorithm derivation6.3.3 Computer simulation6.4 Summary
7 Blind equalization Algorithm Based on Wavelet Neural Network
7.1 Basic principle of wavelet neural network7.1.1 The concept of wavelet neural network7.1.2 The structure of wavelet neural network7.1.3 The characteristics of wavelet neural network7.2 Blind equalization algorithm based on feed-forward wavelet neural network7.2.1 Algorithm principle7.2.2 Blind equalization algorithm based on feed-forward wavelet neural network in real number system7.2.3 Blind equalization algorithm based on FFWNN in complex number system
7.3 Blind equalization algorithm based on recurrent wavelet neural network
7.3.1 Principle of algorithm7.3.2 Blind equalization algorithm based on BLRWNN in real number system
7.3.3 Blind equalization algorithm based on BLRWNN in complex system
7.4 Summary
8 Application of Neural Network Blind Equalization Algorithm in Medical Image Processing
8.1 Concept of image blind equalization8.1.1 Imaging mechanism and degradation process of medical CT image8.1.2 The basic principle of medical CT images blind equalization8.1.3 Quantitative measurements8.2 Medical CT image neural network blind equalization algorithm based on Zigzag8.2.1 Basic principle of algorithm8.2.2 Iterative formula derivation8.2.3 Analysis of algorithm convergence performance
8.2.4 Experimental simulation
8.3 Medical CT image neural network blind equalization algorithm based on double zigzag encoding8.3.1 The basic principle of algorithm8.3.2 Formula derivation of iterative algorithm
8.3.3 Experimental simulation
8.4 Summary
Appendix A: Derivation of the Hidden Layer Weight Iterative Formula in the Blind Equalization Algorithm Based on the Complex Three-Layer FFNN
Appendix B: Iterative Formulas Derivation of Complex Blind Equalization Algorithm Based on BRNN
Appendix C: Types of Fuzzy Membership Function
Appendix D: Iterative Formula Derivation of Blind Equalization Algorithm Based on DRFNN
References
Index

Content preview from Blind Equalization in Neural Networks

where μ_k is the step between output layer and hidden layer.

8.3.2.2Weights iterative formula of the hidden layer

The weight between the kth node in the hidden layer and the lth node in the input layer is w_lk(n) in the complex feed-forward neural network. The iteration formula is

$w_{l k} (n + 1) = w_{l k} (n) - μ_{l k} \frac{\partial J (n)}{\partial w_{l k} (n)} (8.58)$

$\frac{\partial J (n)}{\partial w_{l k} (n)} = 2 [{| \tilde{f} (n) |}^{2} - R_{2}] | \tilde{f} (n) | [\frac{\partial | \tilde{f} (n) |}{\partial w_{l k, R} (n)} + \frac{\partial | \tilde{f} (n) |}{\partial w_{l k, I} (n)}] (8.59)$

According to eqs. (8.47) and (8.53),

$\begin{aligned} \frac{\partial | \tilde{f} (n) |}{\partial w_{l k, R} (n)} = \frac{\partial \sqrt{\tilde{f} (n) {\tilde{f}}^{*} (n)}}{\partial w l l k, R} = \frac{1}{2 | \tilde{f} (n) |} \frac{\partial | \tilde{f} (n) {\tilde{f}}^{*} (n) |}{\partial w_{l k, R} (n)} \\ = \frac{1}{2 | \tilde{f} (n) |} \frac{d^{2} {q^{2} [v_{R} (n)] + q^{2} [v_{I} (n)]}}{\partial w_{l k, R} (n)} \\ = \frac{1}{| \tilde{f} (n) |} q [v_{R} (n)] q' [v_{R} (n)] \frac{\partial v_{R} (n)}{\partial w_{l k, R}} + \frac{1}{| \tilde{f} (n) |} q [v_{I} (n)] q' [v_{I} (n)] \frac{\partial v_{I} (n)}{\partial w_{l k, R} (n)} \\ (8.60) \end{aligned}$

$\begin{array}{l} \frac{\partial v_{R} (n)}{\partial w_{l k, R} (n)} = w_{k, R} (n) q' [u \end{array}$

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Blind Equalization in Neural Networks

by Liyi Zhang, Tsinghua University Tsinghua University Press

8.3.2.2Weights iterative formula of the hidden layer

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