Abstract
This paper shows and compares three techniques based on the least squared error for the estimation of the constant coefficients of the memory polynomial model used for the modeling of power amplifiers for radio-frequency and for the construction of a pre-distorter. The first technique is the conventional linear regression using the least square error method. The second technique is the order recursive least squares which can be used for exploring the most adequate nonlinearity order and memory depth of the memory polynomial model by comparing subsequent errors. The sequential least squares method is useful when the measurements of a system are coming sample by sample and the parameters of the model should be adjusted on-line. The mathematical background of the three methods is shown; as an experimental validation of this methods they were simulated in Matlab for the measurements of a 10W NPX Power Amplifier based on the transistor CLF1G0060 GaN HEMTs. An NMSE of \(-19.83\) dB was reached for the best model. Also in order to linearize the power amplifier a pre-distorter was constructed through indirect learning architecture achieving a 50 dBm spurious free dynamic range and a 25 dBc reduction in the adjacent power ratio.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Katz, A., Wood, J., Chokola, D.: The evolution of PA linearization: from classic feedforward and feedback through analog and digital predistortion. IEEE Microw. Mag. 17(2), 32–40 (2016)
Roblin, P., Quindroit, C., Naraharisetti, N., Gheitanchi, S., Fitton, M.: Concurrent linearization: the state of the art for modeling and linearization of multiband power amplifiers. IEEE Microw. Mag. 14(7), 75–91 (2013)
Liu, Y., Huang, C., Quan, X., Roblin, P., Pan, W., Tang, Y.: Novel linearization architecture with limited ADC dynamic range for green power amplifiers. IEEE J. Sel. Areas Commun. 34(12), 3902–3914 (2016)
Nuñez-Pérez, J.C., Cárdenas-Valdez, J.R., Gontrand, C., Reynoso-Hernandez, J.A., Hirata-Flores, F.I., Jauregui-Duran, R., Perez-Pinal, F.J.: Flexible test bed for the behavioural modelling of power amplifiers. COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 33(1/2), 355–375 (2013)
Rahati Belabad, A., Motamedi, S.A., Sharifian, S.: An adaptive digital predistortion for compensating nonlinear distortions in \(\{{\rm RF}\}\) power amplifier with memory effects. Integr. \(\{{\rm VLSI}\}\) J. 57, 184–191 (2017)
Roblin, P., Myoung, S.K., Chaillot, D., Kim, Y.G., Fathimulla, A., Strahler, J., Bibyk, S.: Frequency-selective predistortion linearization of RF power amplifiers. IEEE Trans. Microw. Theory Tech. 56(1), 65–76 (2008)
Li, H., Kwon, D.H., Chen, D., Chiu, Y.: A fast digital predistortion algorithm for radio-frequency power amplifier linearization with loop delay compensation. IEEE J. Sel. Top. Signal Process. 3(3), 374–383 (2009)
Nuñez-Pérez, J.C., Cárdenas-Valdez, J.R., Montoya-Villegas, K., Reynoso-Hernandez, J.A., Loo-Yau, J.R., Gontrand, C., Tlelo-Cuautle, E.: FPGA-based test bed for measurement of AM/AM and AM/PM distortion and modeling memory effects in \(\{{\rm RF}\}\) \(\{{\rm PAs}\}\). Integr. \(\{{\rm VLSI}\}\) J. 52, 291–300 (2016)
Naraharisetti, N., Roblin, P., Quindroit, C., Rawat, M., Gheitanchi, S.: Quasi-exact inverse PA model for digital predistorter linearization. In: 82nd ARFTG Microwave Measurement Conference, pp. 1–4 (2013)
Wu, X., Shi, J., Chen, H.: On the numerical stability of RF power amplifier’s digital predistortion. In: 2009 15th Asia-Pacific Conference on Communications, pp. 430–433 (2009)
Dvorak, J., Marsalek, R., Blumenstein, J.: Adaptive-order polynomial methods for power amplifier model estimation. In: 2013 23rd International Conference Radioelektronika (RADIOELEKTRONIKA), pp. 389–392 (2013)
Ntoun, R.S.N., Bahoura, M., Park, C.W.: Power amplifier behavioral modeling by neural networks and their implementation on FPGA. In: 2012 IEEE Vehicular Technology Conference (VTC Fall), pp. 1–5 (2012)
Zhu, A., Brazil, T.J.: Behavioral modeling of RF power amplifiers based on pruned volterra series. IEEE Microw. Wirel. Compon. Lett. 14(12), 563–565 (2004)
Ku, H., Kenney, J.S.: Behavioral modeling of nonlinear RF power amplifiers considering memory effects. IEEE Trans. Microw. Theory Tech. 51(12), 2495–2504 (2003)
Cárdenas Valdez, J.R., Z-Flores, E., Núñez Pérez, J.C., Trujillo, L.: Local Search Approach to Genetic Programming for RF-PAs Modeling Implemented in FPGA, pp. 67–88. Springer International Publishing, Cham (2017)
Golovins, E., Ventura, N.: Modified order-recursive least squares estimator for the noisy OFDM channels. In: Fifth Annual Conference on Communication Networks and Services Research (CNSR’07), pp. 93–100 (2007)
Wang, Y., Ikeda, K., Nakayama, K.: A numerically stable fast newton-type adaptive filter based on order recursive least squares algorithm. IEEE Trans. Signal Process. 51(9), 2357–2368 (2003)
HongWei, Z., Qiang, S., Wang, G., You, H.: System errors estimation of DOA and TDOA jointed locating system using sequential least squares. In: Proceedings of 2011 IEEE CIE International Conference on Radar, vol. 2, pp. 1025–1028 (2011)
Chen, Y., Zhang, D., Lin, Z., Lai, X.: A sequential weighted least squares procedure for design of IIR filters and two-channel IIR filter banks. In: 2014 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1195–1198 (2014)
Diniz, P.S.R.: Conventional RLS Adaptive Filter, pp. 209–247. Springer, Boston (2013)
Chani-Cahuana, J., Fager, C., Eriksson, T.: A new variant of the indirect learning architecture for the linearization of power amplifiers. In: 2015 10th European Microwave Integrated Circuits Conference (EuMIC), pp. 444–447 (2015)
Amin, S., Zenteno, E., Landin, P.N., Rnnow, D., Isaksson, M., Hndel, P.: Noise impact on the identification of digital predistorter parameters in the indirect learning architecture. In: 2012 Swedish Communication Technologies Workshop (Swe-CTW), pp. 36–39 (2012)
Dwivedi, N., Bohara, V.A., Hussein, M.A., Venard, O.: Fixed point digital predistortion system based on indirect learning architecture. In: 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI), pp. 1376–1380 (2014)
Chani-Cahuana, J., Landin, P.N., Fager, C., Eriksson, T.: Iterative learning control for RF power amplifier linearization. IEEE Trans. Microw. Theory Tech. 64(9), 2778–2789 (2016)
Paaso, H., Mammela, A.: Comparison of direct learning and indirect learning predistortion architectures. In: 2008 IEEE International Symposium on Wireless Communication Systems, pp. 309–313 (2008)
Abd-Elrady, E., Gan, L., Kubin, G.: Direct and indirect learning methods for adaptive predistortion of IIR hammerstein systems. e & i Elektrotechnik und Informationstechnik 125(4), 126–131 (2008)
Halstead, M.H.: Elements of Software Science. Operating and Programming Systems Series. Elsevier Science Inc., New York (1977)
Acknowledgements
The authors wish to thank PhD. Patrick Roblin, Professor at Ohio State University, for its support provided through the measuring data. In addition, the authors would like to express their gratitude to the IPN for its financial support by the project SIP-20170588.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Allende-Chávez, E. et al. (2018). Coefficients Estimation of MPM Through LSE, ORLS and SLS for RF-PA Modeling and DPD. In: Maldonado, Y., Trujillo, L., Schütze, O., Riccardi, A., Vasile, M. (eds) NEO 2016. Studies in Computational Intelligence, vol 731. Springer, Cham. https://doi.org/10.1007/978-3-319-64063-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-64063-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64062-4
Online ISBN: 978-3-319-64063-1
eBook Packages: EngineeringEngineering (R0)