Modeling, Control and Industry
In this article is presented a genetic programming (GP) with a local search heuristic (LSHS) to emulate the Radio Frequency (RF) Power Amplifier(PA) Doherty 7W @2.11 GHz conversion curves.The full data package related to the conversion curves that describe the PA behavior has a length of 122,880 data. The basic RF-PA modeling techniques involves special truncations of the Volterra Series[1-3],but for very complex nonlinear model swith wide data range is required the use of the whole Volterra Series[4-5], Fuzzy Neural Network [6-7] or GP[8-9]. By other hand, GP performs an evolutionary search within the space of possible program syntaxes, achieving the expression that best solves a given model.
GP can be viewed as a biologic evolutionary inspired algorithm where a pool of symbolic expressions are built in a synergy fashion upon a target. Each expression competes for survival at each iteration by measuring its fitness value. This is usually expressed by an error metric toward the objective. In general, each symbolic expression consist of a mathematical equation that represent a potential candidate model in the imposed problem. Standard GP can solve complex problems by searching in the syntax space, however accuracy on the solutions can be stagnated through the evolution and expressions might grow in size.
In this work we propose a similar approach as performed in other population based algorithms: a combination of explorative search by using genetic operators and an exploitative search by numerical optimization means is designed. This synergy produces better quality solutions in faster times. The numerical optimization is performed by an iterative algorithm called Trust Region which minimizes the error for a parameterized non-linear function. This deterministic optimization is usually called Local Search (LS), since the optimum usually locates closer to the actual model by searching only in the parameter space given by thecurrent symbolic expression. A set of small candidates models are picked up to be optimized during evolution. We call this approach LSHS[10-11].The Fig. 1 shows the LSHS flowchart.
Experimental results shows that LSHS’s best models accuracy outperforms Canonical GP ones. The selected model including 17 parameters shows that produced model by GP for the AM/PM conversion curve has a MSE of 0.26033 during the implementation. The implementation stage for the AM/AM conversion curve is done in DSP Development Board Cyclone III-ALTERA.The test performed on the development board in the laboratoyy indicate that the GP model accuracy is very high.
The authors wish to thank the Dr. José Raúl Loo Yauof the CINVESTAV for the support provided during the RF-PA Doherty 7W @2.11 GHz measurement. In addition, the authors would like to express their gratitude to the Dr. J. Apolinar Reynoso Hernández of the CICESE for provide the RF-PA as device under test.
 L. Ping-hui and W. Peng. Wiener-Saleh modeling of nonlinear RF power amplifiers considering memory effects.International Conference on Microwave and Milimeter Wave Technology, Chengdu, China, 1447-1449, May 2010.
M. Junghwan, O. Saad, S. Jungwan, C. Fager and K. Bumman. 2-D enhanced hammerstein behavior model for concurrent dual-band power amplifiers. European Microwave Conference,Amsterdam, 1249-1252, November 2012
J. Misic, V. Markovic and Z. Marinkovic. Volterra kernels extraction from neural networks for amplifier behavioral modeling. International Symposium on Telecommunications,Sarajevo, Bosnia-Herzegovina, 1-6, October 2014.
J. Staudinger,J. Nanan and J. Wood. Memory Fading Volterra series model for high power infrastructure amplifiers.IEEE Radio and Wireless Symposium, New Orleans,184-187.January 2010
Z. Anding and T. J. Brazil. Behavioral modeling of RF power amplifiers based on pruned Volterra series.IEEE Microwave and Wireless Components Letters,14(12):563-565, December 2014
 J. Zhai, J. Zhou, L. Zhang and W. Hong. Behavioral Modelling of Power Amplifiers With Dynamic Fuzzy Neural Network.IEEE Microwave and Wireless Components Letters, 20(9):528-530, 2010.
 F. Mkadem, M. Ben Ayed, S. Boumaiza, J. Wood and P. Aean. Behavioral modeling and digital predistortion of power amplifiers with memory using two hidden layers artificial neural networks,IEEE International Microwave Symposium, Anaheim, USA,1,May 2010.
Z. Sheng, S. Xiuyuand W. Wei. An ANN model of optimizing activation functions based on constructive algorithmand GP. International Conference on Computer Application and System Modeling, 1:420-424, October 2010.
A. Patelli and L. Ferariu. A regressive schema theory based tool for GP evolved nonlinear models. 201-206, September 2011.
E. Z-Flores, L. Trujillo, O. Schütze, and P. Legrand. Evaluating the effects of local search ingenetic programming. In EVOLVE of Advances in Intelligent Systems and Computing, Springer International Publishing, 288:213–228, 2014.
 E. Z.-Flores, L. Trujillo, O. Schütze, and P. Legrand. A local search approach to genetic programming for binary classification. In Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2015, Madrid, Spain, 1151–1158, July 2015.
- Jose Ricardo Cardenas