Elsevier

Neurocomputing

Volume 154, 22 April 2015, Pages 24-32
Neurocomputing

Short Communication
Behavioral modeling of nonlinear RF power amplifiers using ensemble SDBCC network

https://doi.org/10.1016/j.neucom.2014.12.027Get rights and content

Abstract

A new behavioral model of nonlinear RF power amplifiers (PA) is presented to treat memory effects. The key issue here is considering the phenomenon that uplink quadrature modulation signals are influenced not only by the current uplink signals, but also by previous terms. The variation of AM/AM and AM/PM, and the asymmetries in lower and upper intermodulation terms are frequently observed in high-power PAs. To treat these phenomena, this paper proposes a model based on artificial neural network. The contribution made of this model is to solve the order determination issue (determining the order of the previous output and input signals that have influence on the current output signal). In addition, the recognized difficulty of long training process is overcome by using SDBCC algorithm, a novel neural network design method combining structure decomposition and the Cascade-Correlation neural network algorithm. The required maximum delay is established by examining the autocorrelation coefficient of the residual error. Ensemble system is finally used to improve the performance further. This proposed method is successfully validated in nonlinear modeling of the RF PAs from HuaWei Company, including 8000 samples.

Introduction

RF power amplifiers (PAs) [14,15] are important part of wireless transceiver which has been always focusing on wireless broadband communication field for many years [1], [2], [13]. With the development of newer communication systems such as W-CDMA, wider PA bandwidths have become imperative and the memory effects of the PA are becoming increasingly important to performance. The most critical first step and also the key issue in analyzing a PA system and designing a linearizer is to model the PA nonlinearity accurately [4], [5], [17]. In recent years increasing attention has been given to behavioral modeling which is often used in PA nonlinearity modeling [16,20,28]. It has been shown that behavioral modeling provides an effective computation method by relating input and output signals, eliminating the need of physical analysis of a device or system. We model the nonlinear behavioral of a PA and then extract model parameters based on the observed data. After obtaining the behavioral model, we can use it as a mathematical description of the PA nonlinearity in predistortion linearizer design and the analysis of wireless broadband communication systems.

In the last decades, much deep and productive research [9], [10], [11] in memoryless nonlinear behavioral modeling of PAs has been carried out. AM/AM and AM/PM functions are usually adopted. These are static functions at a given temperature and dc bias. However, memory effects in real PAs often arise due to thermal effects and longtime constants in dc-bias circuits. It is now well understood that the PA is affected by two types of memory: the short-term memory, primarily caused by matching networks and transit time within the transistors, and long-term memory, due to biasing circuits, automatic gain control circuits, transistor self-heating and trapping effects [12]. With the development of newer communication systems, the memory effects can never be ignored any more. Several studies have been conducted to deal with the memory effects in PA recently [3], [6], [7], [8]. In [8], the use of continuous wave and pulsed RF large-signal measurements was investigated to quantify the impact of thermal and electrical memory effects upon the large-signal RF performance of transistors. Liu et al. [3] used a complexity-reduced generalized memory polynomial (MP) (GMP) (CR-GMP) connected with a nonlinear memory effect (NME) subblock in parallel to construct a robust model for the accurate behavioral modeling. In [7], noise contributions are considered for a better modeling based on a memory polynomial model. The model extracts the input noise contribution and subtracts it from the output, using determined modeling coefficients. In [6], Morgan et al. employed digital baseband predistortion ahead of the amplifier to compensate for the nonlinearity effects, hence allowing it to run closer to its maximum output power while maintaining low spectral regrowth. Whatever reason causes the asymmetric effects and variation of AM/AM and AM/PM, a model to treat these phenomena is needed.

In this paper, to treat the memory effects, artificial neural network [24], [25] is adopted. It has been shown that feedforward neural networks with sufficient neurons are “universal approximators” [26], [27] and can model any linear or nonlinear system. The lengthy training time required to reach an acceptable performance is solved by using Cascade-Correlation network. Combining it with structure decomposition theory, we propose a novel neural network, called SDBCC algorithm. The required maximum delay is established by examining the autocorrelation coefficient of the residual error. Then we use ensemble system to finally improve the performance. The data of the RF PAs from HuaWei Company show the promising performance of our proposed method. The overall system can be seen in Fig. 1.

This paper is organized as follows. In Section 2, we introduce the behavioral model of nonlinear RF PAs using artificial neural networks. Cascade-Correlation algorithm, decomposable system and ensemble system are adopted. The key issue of order determination is solved. More details can be seen in Section 3. In Section 4, we demonstrate the validation of our proposed method. Finally, conclusions are presented in Section 5.

Section snippets

Cascade-correlation neural network

The Cascade-Correlation (CC) [19] neural networks are also referred to as self-organizing networks. They were proposed by Fahlman et al. [18]. A CC network is made up of input, hidden and output layers. As a constructive neural network, the CC network adds hidden neurons as they are needed. As shown in Fig. 2, in the initial state, a CC network only consists of an input and output layers, and they are connected to each other. The “+1” sign denotes the bias. In the training process, the neuron

Ensemble SDBCC model

Our proposed method, ensemble SDBCC model, consists of several steps: structure decomposition is the first step, CC network is adopted to model it. And then we integrate the output values of all the subnets to final decision. Finally, we train 10 same SDBCC network to ensemble the system. A better performance can be obtained.

Model validation

In this section, practical measured data are studied to validate the proposed model. These data came from the RF PAs of one base station in HuaWei Company, including two input signals and two output signals, sampling at 61.44 MHz (Fig. 7). A total of 8000 samples are obtained. We assume that the input values I(k), Q(k) are the downlink signals, and the output values I(k), Q(k) are the uplink signals. The performance requirement from HuaWei Company isEVM<3%whereEVM=PerrorPsignalPerror=(ErrorI2+

Conclusions and discussions

RF power amplifiers are important part of wireless transceiver which has been always focusing on wireless broadband communication field for many years. The proposed method for behavioral modeling considers the memory effects based on artificial neural network. One key contribution of this model is to solve the order determination issue (determining the order of the previous output and input signals that have influence on the current output signal) automatically. In addition, the recognized

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61374006, and by the Major Program of National Natural Science Foundation of China under Grant 11190015.

Liping Xie received the B.S. degree from the Department of Automation, Southeast University, China, in 2011. After that, she has been working toward the Ph.D. degree in the School of Automation, Southeast University, China. Her main research interest is neural networks and video-based facial expression recognition.

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    Liping Xie received the B.S. degree from the Department of Automation, Southeast University, China, in 2011. After that, she has been working toward the Ph.D. degree in the School of Automation, Southeast University, China. Her main research interest is neural networks and video-based facial expression recognition.

    Haikun Wei received the B.S. degree from the Department of Automation, North China University of Technology, China, in 1994, and the M.S. and Ph.D. degrees from the Research Institute of Automation, Southeast University, China, in 1997 and 2000, respectively. He was a visiting scholar in RIKEN Brain Science Institute, Japan, from 2005 to 2007. He is currently a professor in the School of Automation, Southeast University. His research interest is real and artificial in neural networks and industry automation.

    Kanjian Zhang received the B.S. degree in Mathematics from Nankai University, China, in 1994, and the M.S. and Ph.D. degrees in Control Theory and Control Engineering from Southeast University, China, in 1997 and 2000, respectively. He is currently a professor in the School of Automation, Southeast University. His research is in nonlinear control theory and its applications, with particular interest in robust output feedback design and optimization control.

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