EVR算法驱动的PA行为建模与数字预失真记忆多项式模型高效修剪

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本文是一篇发表在2014年10月《IEEE Transactions on Microwave Theory and Techniques》上的研究论文，标题为“适用于PA行为建模和数字预失真的记忆多项式模型的有效修剪技术”。作者们，Wenhua Chen（IEEE资深会员）、Siling Zhang（IEEE学生会员）、You-Jiang Liu（IEEE成员）、Fadhel M. Ghannouchi（IEEE院士）以及Zhenghe Feng（IEEE院士）和Yuanan Liu（IEEE成员），针对功率放大器(Power Amplifier, PA)行为建模中的记忆多项式模型(Memory Polynomial Models, MPs)复杂度降低问题提出了一个创新的解决方案。该研究关注的主要问题是记忆多项式模型在PA行为建模中的精度与效率平衡。传统的MP模型可能包含大量的项，这些项对于预测PA的行为至关重要。然而，过多的项会增加模型的计算复杂度，特别是在数字预失真(Digital Predistortion, DSP)应用中，这可能导致系统性能下降和资源浪费。为了优化模型，论文提出了一种基于误差变化排名(Energy Variation Ranking, EVR)的修剪方法。 EVR方法的核心思想是通过量化每个多项式项去除后对预测误差的影响来评估其重要性。具体步骤是，逐个移除每个项，并计算其删除导致的预测误差变化，然后根据这个变化量为所有项排序。排序结果反映了各个项对于整体预测性能的影响程度。根据排序，研究人员选择那些对误差影响最小、排名靠后的项进行剪枝。这种方法旨在在保持模型准确性的同时，显著减少模型的复杂度。实验结果显示，当将EVR修剪技术应用于数字预失真器时，可以有效地去除大约74%的MP模型中的项，以及高达78%的二维数字预失真模型中的项，而这些剪枝几乎不会对预测性能造成明显负面影响。这种有效的修剪策略对于设计高效且实时性强的PA控制系统具有重要意义，因为它允许设计师在满足系统性能需求的同时，降低硬件资源的占用，提高系统整体的能源效率和可靠性。因此，这项工作为PA建模和数字预失真领域的工程实践提供了有力的理论支持和实用工具。

2290 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 62, NO. 10, OCTOBER 2014

Efﬁcient Pruning Technique of Memory Polynomial

Models Suitable for PA Behavioral Modeling

and D igital Predistortion

Wenhua Chen, Senior Member, IEEE, Silong Zhang, Student Member, IEEE, You-Jiang Liu, Member, IEEE,

Fadhel M. Ghannouchi, Fellow, IEEE, Zhenghe Feng, Fellow, IEEE, and Yuanan Liu, Member, IEEE

Abstract—This paper proposes an error variation ranking

(EVR)-based pruning method to reduce the c

omplexity of memory

polynomials (MPs) for power ampliﬁer behavioral modeling.

During the EVR pruning, the variation of prediction error caused

by removing each term is calculated and r

anked as a quantiﬁcation

factor to show the term’s importance. The dominant terms are

then s ele cte d based on their ranking positions among all terms.

This method is veriﬁed by comparin

g its results with all other

possible selections under the same conditions. When it is used to

prune digital predistorters, approximately 74% of the terms in the

MP model and 78% of the terms in th

e 2-D digital-predistortion

model can be removed with negligible deterioration of the predic-

tion and linearization performance. Moreover, further discussion

is presented to strategize th

econﬁguration of MP models based on

the EVR pruning results.

Index Terms—Basis selection, digital predistortion (DPD), error

variation, nonlinear model, power ampliﬁer (PA).

I. INTRODUCTION

OLYNOMIAL-BASED models have greatly contributed

to solving the problem o f describ ing the behav ior of power

ampliﬁers (PAs), including nonlinearities and memory effects.

They are also widely used as digital predistort e rs to linearize

Manuscript received April 01, 2014; revised June 14, 2014 and July 28, 2014;

accepted August 10, 2014. Date of publication S eptember 05, 2014; date of cur-

rent version October 02, 2014. This work was supported in part by the National

Basic Research Program of China under Grant 2014CB339900, the National

Science and Technology Major Project of the M inistry of Science and Tech-

nology of China under Grant 2014ZX03003007-008, the National Natural Sci-

ence Foundation of China under Grant 61201043, and the New Century Excel-

lent Talents in University (NCET).

W. Chen and Z . Feng are wi th the Departme nt of Electronic E ngineering,

Tsinghu a University, B eijing 100084, China (e-mail: chenwh@ tsin gh u a .edu.cn;

fzh-dee@ tsinghua.edu.cn ).

S. Zhang was with the Department of Electronic E ngineering, Tsinghua Uni-

versity, Beijing 100084, China. He is now with Smarter Micro In c., S h an gh ai

201203, China (e-mail: szhang@smartermicro.com).

Y.-J. Liu is wit h the Department of Electrical and Com puter Engineering,

University of California at San Diego, La Jolla, CA 92093 USA (e-mail:

yol006@ucsd.edu).

F. M. Ghannouchi is with the Intelligent RF Radio L ab or ato ry (iRadio Lab),

Department of Electrical and Com pute r Engineering, Schulish School of Engi-

neering, Un iv ersity of Calgary, Calgary, AB, Canada T2N 1N4 (e- mail: fadhel.

ghannouchi@ucalgary.ca).

Y. Liu is with the Scho ol of Electronic Engineering, Beijin g Universi ty of

Posts and Telecommunications, 1 00 876 Beijing, China.

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TMTT.2014.2351779

PAs, due to their potential for est imation or implementation i n

real-time systems [1]–[12]. However, the tradeoff between im -

plementation complexity and modeling capacity is still a chal-

lenge.

In recent years, several types of modern PA structures (e.g.,

supply modulated PAs [12],[13] and concurrent dual-band PAs

[20],[21]) have been developed and are considered promising

for next-gen eration comm un ication systems. These new PA

structures have two or more input ports w ith nonlinear interfer-

ences betw een each other. Correspondingly, several two-to-one

mapping models have been proposed. However, they further

exacerbate the difference between complexity and perform ance

[10]–[21].

In fact, m uch research has been published on the simpliﬁca-

tion of the Volterra series, which is the origin of most polyno-

mial-based models. Most of the methods have been based on the

analysis of the physical characteristics of PAs and/or modiﬁca-

tion of the structure of the original polynomials. Several com-

pact and useful PA models have been obtained, such as memory

polynomials (MPs), dynamic deviation reduction (DDR)-based

Volterra series, and 2-D digital predistortion ( 2-D-DPD) model.

Although these models have led, in most cases, to good perfor-

mance, they encom pass a relatively high number of coefﬁcients.

This has triggered the need and provided the motivation f or fur-

ther reduction in the dimensions of such models without sacri-

ﬁcing performance.

Recently, some efforts have been made to prune the models

adaptively with captured input and output PA signals. In [22]

and [23], terms with small kernels were considered negligible

and removed, which effectively pruned the Wiener G-function.

However, the Wiener G-functio n is im practical for ﬁeld-pro-

grammable gate-array (FPGA ) implementation, due to the com-

plexity in constructing and im pl ementing its basis fu ncti ons. I n

[24]–[26], an adaptive pruning method was used to p run e the

MP model online. However, since sig niﬁcant multicollinearity

effects exist in the MP model (i.e., some basis functions in the

model can be approximated by a linear combination of the other

basis functions), a stab le resu lt u sing this me th od cannot be

achieved, especially w hen the num ber of coefﬁcients in the orig-

inal m odel is large.

We have presented an iterative pruning method where only

the term with the minimum kernel was removed in each iteration

[27]. Although it outperformed the previous pruning techniques,

it still suffers fr om inherent instability.

See http://www.ieee.org/publications_standards/publications/rights/index.html for more inform ation.

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