AM  Vol.5 No.20 , November 2014
Legendre Wavelet Neural Networks for Power Amplifier Linearization
ABSTRACT
In this paper, a novel technique for power amplifier (PA) linearization is presented. The Legendre wavelet neural networks (LWNN) is first utilized to model PA and inverse structure of the PA by applying practical transmission signals and the gradient descent algorithm is applied to estimate the coefficients of the LWNN. Secondly, this technique is implemented to identify and optimize the coefficient parameters of the proposed pre-distorter (PD), i.e., the inversion model of the PA. The proposed method is most efficient and the pre-distorter shows stability and effectiveness because of the rich properties of the LWNN. A quite significant improvement in linearity is achieved based on the measured data of the PA characteristics and out power spectrum has been compared.

Cite this paper
Zheng, X. , Wei, Z. and Xu, X. (2014) Legendre Wavelet Neural Networks for Power Amplifier Linearization. Applied Mathematics, 5, 3249-3255. doi: 10.4236/am.2014.520302.
References
[1]   Dallinger, R., Ruotsalainen, H., Wichman, R. and Rupp, M. (2010) Adaptive Pre-Distortion Techniques Based on Orthogonal Polynomials. Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[2]   Raich, R., Qian, H. and Zhou, G.T. (2004) Orthogonal Polynomials for Power Amplifier Modeling and Predistorter Design. IEEE Transactions on Vehicular Technology, 53, 1468-1479.

[3]   Liu, T., Boumaiza, S. and Ghannouchi, F.M. (2006) Augmented Hammerstein Predistorter for Linearization of Broad-Band Wireless Transmitters. IEEE Transactions on Microwave Theory and Techniques, 54, 1340-1349.
http://dx.doi.org/10.1109/TMTT.2006.871230

[4]   Alpert, B., Beylkin, G., Gines, D. and Vozovoi, L. (2002) Adaptive Solution Partial Differential Equations in Multiwavelet Bases. Journal of Computational Physics, 182, 149-190.
http://dx.doi.org/10.1006/jcph.2002.7160

[5]   Zheng, X.Y. and Yang, X.F. (2009) Techniques for Solving Integral and Differential Equations by Legendre Wavelets. International Journal of Systems Science, 40, 1127-1137.
http://dx.doi.org/10.1080/00207720902974710

[6]   Razzaghi, M. and Yousefi, S. (2001) The Legendre Wavelets Operational Matrix of Integration. International Journal of Systems Science, 32, 500-502.
http://dx.doi.org/10.1080/00207720120227

[7]   Bachir, S. and Duvanaud, C. (2011) Linearization of Radio Frequency Amplifiers Using Nonlinear Internal Model Control Method. International Journal of Electronics and Communications (AEü), 65, 495-501.
http://dx.doi.org/10.1016/j.aeue.2010.07.004

[8]   Zhou, G.T. and Kenney, J.S. (2002) Predicting Spectral Regrowth of Nonlinear Power Amplifiers. IEEE Transactions on Communications, 50, 718-722.
http://dx.doi.org/10.1109/TCOMM.2002.1006553

[9]   Hammi, O., Ghannouchi, F.M. and Vassilakis, B. (2008) Acompact Envelope-Memory Polynomial for RF Transmitters Modeling with Application to Baseband and RF-Digital Predistortion. IEEE Microwave and Wireless Components Letters, 18, 359-361.

[10]   Figueroa, J., Cousseau, J. and de Figueiredo, R. (2004) A Simplicial Canonical Piecewise Linear Adaptive Filter. Circuits, Systems, and Signal Processing, 5, 365-386.
http://dx.doi.org/10.1007/s00034-004-0808-6

[11]   Zhou, D. and De Brunner, V.E. (2007) Novel Adaptive Nonlinear Predistorters Based on the Direct Learning Algorithm. IEEE Transactions on Signal Process, 55, 120-130.
http://dx.doi.org/10.1109/TSP.2006.882058

[12]   Dallinger, R., Ruotsalainen, H., Wichman, R. and Rupp, M. (2010) Adaptive Pre-Distortion Techniques Based on Orthogonal Polynomials. Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[13]   Raich, R., Qian, H. and Zhou, G.T. (2004) Orthogonal Polynomials for Power Amplifier Modeling and Predistorter Design. IEEE Transactions on Vehicular Technology, 53, 1468-1479.

[14]   Liu, T., Boumaiza, S. and Ghannouchi, F.M. (2006) Augmented Hammerstein Predistorter for Linearization of Broad-Band Wireless Transmitters. IEEE Transactions on Microwave Theory and Techniques, 54, 1340-1349.
http://dx.doi.org/10.1109/TMTT.2006.871230

[15]   Alpert, B., Beylkin, G., Gines, D. and Vozovoi, L. (2002) Adaptive Solution Partial Differential Equations in Multiwavelet Bases. Journal of Computational Physics, 182, 149-190.
http://dx.doi.org/10.1006/jcph.2002.7160

[16]   Zheng, X.Y. and Yang, X.F. (2009) Techniques for Solving Integral and Differential Equations by Legendre Wavelets. International Journal of Systems Science, 40, 1127-1137.
http://dx.doi.org/10.1080/00207720902974710

[17]   Razzaghi, M. and Yousefi, S. (2001) The Legendre Wavelets Operational Matrix of Integration. International Journal of Systems Science, 32, 500-502.
http://dx.doi.org/10.1080/00207720120227

[18]   Bachir, S. and Duvanaud, C. (2011) Linearization of Radio Frequency Amplifiers Using Nonlinear Internal Model Control Method. International Journal of Electronics and Communications (AEü), 65, 495-501.
http://dx.doi.org/10.1016/j.aeue.2010.07.004

[19]   Zhou, G.T. and Kenney, J.S. (2002) Predicting Spectral Regrowth of Nonlinear Power Amplifiers. IEEE Transactions on Communications, 50, 718-722.
http://dx.doi.org/10.1109/TCOMM.2002.1006553

[20]   Hammi, O., Ghannouchi, F.M. and Vassilakis, B. (2008) Acompact Envelope-Memory Polynomial for RF Transmitters Modeling with Application to Baseband and RF-Digital Predistortion. IEEE Microwave and Wireless Components Letters, 18, 359-361.

[21]   Figueroa, J., Cousseau, J. and de Figueiredo, R. (2004) A Simplicial Canonical Piecewise Linear Adaptive Filter. Circuits, Systems, and Signal Processing, 5, 365-386.
http://dx.doi.org/10.1007/s00034-004-0808-6

[22]   Zhou, D. and De Brunner, V.E. (2007) Novel Adaptive Nonlinear Predistorters Based on the Direct Learning Algorithm. IEEE Transactions on Signal Process, 55, 120-130.
http://dx.doi.org/10.1109/TSP.2006.882058

 
 
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