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### 增强型Hammerstein预失真器在宽带无线发射机线性化中的应用 #### 摘要及背景介绍随着现代高速无线通信系统的发展，如WiMAX（Worldwide Interoperability for Microwave Access）、第三代（3G）及后续系统等，设计高效率的宽带发射机变得愈发复杂且具有挑战性。这类系统需要同时实现高线性和高功率效率，以有效利用宝贵的有限频谱资源。为了达成这一目标，复杂的调制技术被广泛应用到现代宽带无线通信系统中，而这些调制技术对放大器提出了更为严格的要求，尤其是在非线性放大过程中产生的信号失真问题。为了解决这一问题，本文提出了一种增强型的基于查找表（Lookup Table, LUT）的Hammerstein预失真器，旨在进一步提升传统Hammerstein预失真器在宽带高功率无线发射机中的预校正能力。该预失真器由两个独立模块组成，并通过两步法确定其参数：首先是静态预失真器的识别，其次是动态部分的识别。 #### 主要内容概述 ##### 预失真器设计方案增强型Hammerstein预失真器的设计主要包括两个模块：静态预失真模块和动态预失真模块。其中，静态预失真模块主要负责消除信号中的非线性失真，而动态预失真模块则用于补偿记忆效应带来的影响。这两个模块的设计与实现对于提高整个系统的性能至关重要。 ##### 测试与评估为了验证该新型预失真器在不同带宽信号下的鲁棒性，研究团队采用了单载波和三载波的第三代合作伙伴计划（3GPP）频率分集时分双工（FDD）宽带码分多址（WCDMA）信号作为测试信号。实验平台包括了一个宽带推挽式GaAs场效应晶体管（Field-Effect Transistor, FET），峰值包络功率放大器（Power Amplifier, PA）达到45 dBm。测试结果表明，与传统的Hammerstein预失真器相比，增强型预失真器能够显著抑制因记忆效应导致的频谱再生长现象，从而显著提升了线性化的宽带无线发射机原型的输出信号质量。 ##### 讨论与结论 1. **记忆效应的影响**：记忆效应是指非线性放大器中信号输出不仅取决于当前输入信号的幅度，还受到过去输入信号的影响。这种现象会导致输出信号产生额外的非线性失真，进而影响整个系统的性能。增强型Hammerstein预失真器能够有效补偿记忆效应，减少信号失真。 2. **预失真器的两步法设计**：通过将预失真器的设计过程分为静态预失真识别和动态部分识别两个步骤，可以更精确地调整预失真器的参数，从而提高其补偿效果。 3. **实测数据分析**：通过对实测数据的分析可以看出，无论是单载波还是多载波信号场景下，增强型预失真器均能表现出良好的性能。特别是在多载波环境下，其对于抑制频谱再生长、提高信号质量的效果更为明显。 4. **未来发展方向**：尽管本文提出的增强型Hammerstein预失真器已经取得了一定的成果，但随着未来无线通信技术的发展，如5G甚至6G系统，对预失真器的要求会越来越高。因此，进一步的研究方向可能包括但不限于：开发更加高效且适应性强的预失真算法、探索新的硬件架构以降低功耗和提高处理速度等。本文提出的增强型Hammerstein预失真器为宽带无线发射机的线性化提供了一种有效的解决方案。通过优化预失真器的设计并采用两步法确定其参数，不仅可以显著提高系统的线性度，还能有效应对复杂的调制技术和记忆效应所带来的挑战。

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1340 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006

Augmented Hammerstein Predistorter for

Linearization of Broad-Band Wireless Transmitters

Taijun Liu, Member, IEEE,

Slim Boumaiza, Member, IEEE

, and

Fadhel M. Ghannouchi, Senior Member, IEEE

Abstract—In this paper, an augmented lookup-table-based

Hammerstein predistorter is proposed for the ﬁrst time in order

to further improve the pre-correction capability of the tradi-

tional Hammerstein predistorter in the context of broad-band

high-power wireless transmitters. The predistorter scheme con-

sists of two separate modules, and its parameters are determined

in two steps, which are: 1) static predistorter identiﬁcation and

then 2) dynamic part identiﬁcation. The performance assessment

of the newly proposed predistorter is carried out on a wireless

transmitter prototype, which includes an

-band push–pull GaAs

ﬁeld-effect transistor 45-dBm peak-envelope power ampliﬁer.

Moreover, one- and three-carrier Third-Generation Partnership

Projects frequency-division duplex wide-band code-division mul-

tiple-access signals are used as test signals to verify the robustness

of this novel predistorter under different bandwidth signals. The

linearized transmitter prototype output spectrum demonstrates

noticeable superiority of the proposed augmented predistorter in

suppressing the spectrum regrowth caused by the memory effects

in comparison to the traditional Hammerstein predistorter.

Index Terms—Augmented Hammerstein predistorter, broad-

band wireless transmitters, Hammerstein predistorter, lookup

table (LUT), memory effects.

I. INTRODUCTION

IGH-EFFICIENCY wide-band transmitter design for

modern high-speed wireless communication systems,

such as worldwide interoperability for microwave access

(WiMAX), third-generation (3G) and beyond systems, etc., is

a complex task since it involves numerous inconsistent require-

ments. In such contexts, simultaneously accomplishing high

linearity and high-power efﬁciency is particularly a great chal-

lenge. In fact, to efﬁciently utilize the precious limited spectrum

resources, several complicated modulation schemes have been

widely used in the modern wide-band wireless communica-

tion systems. These modulated signals lead to a nonconstant

envelope with large peak-to-average power ratios (PAPRs),

which can be as high as 12 dB in some cases. Consequently,

the power ampliﬁer (PA) in the transmitter has to be designed

either to operate near its saturated area, so as to provide higher

system power efﬁciency, or at large backoff from its nonlinear

region, in order to meet the required linearity. Accordingly,

the PA ends up with either high efﬁciency, but bad linearity, or

Manuscript received May 23, 2005; revised October 4, 2005. This work was

supported by the Natural Sciences and Engineering Research Council of Canada

(NSERC), by the Informatics Circle of Research Excellence (iCORE), by TR-

Labs, and by Canada Research Chairs (CRC).

The authors are with the Intelligent RF Radio Laboratory, Electrical

and Computer Engineering Department, University of Calgary, Calgary,

AB, Canada T2N 1N4 (e-mail: liut@ucalgary.ca; sboumaiz@ucalgary.ca;

fghannou@ucalgary.ca).

Digital Object Identiﬁer 10.1109/TMTT.2006.871230

vice versa. Therefore, to satisfy the linearity requirement while

operating the PA at its nonlinear area, one has to correct for the

different sources of distortion all along the entire transmitter

chain. For this reason, different linearization techniques, such

as feedback [1], feed-forward [2], and predistortion [3], [4]

have been proposed to improve the linearity of the transmitter.

Among the various linearization techniques, digital baseband

predistortion is one of the most promising and cost-effective

linearization techniques due to its digital implementation that

offers signiﬁcant accuracy and ﬂexibility. Considering its sim-

plicity and relative ease of implementation, the lookup table

(LUT) is by far the most widely used means for the construction

of the inverse of the amplitude-modulation /amplitude-modu-

lation (AM/AM) and amplitude-modulation /phase-modulation

(AM/PM) characteristic curves of the transmitter or PA [5]–[8].

However, this type of predistorter is only valid for memory-

less nonlinear cases such as the traditional narrow-band wire-

less communication systems.

In the wide-band transmitter/PA context, the memory effects

exhibited by the transmitter/PA signiﬁcantly limit the ability of

the memoryless predistorter to suppress the spectrum regrowth

[9]. These memory effects can generally be categorized as elec-

trothermal memory effects and electrical memory effects. The

electrothermal memory effects are mainly caused by the thermal

capacitance and resistance that form a low-pass thermal ﬁlter.

The electrical memory effects can be mainly attributed to the

nonconstant frequency response of the transmitter around the

carrier frequency, the impedance variation of bias circuits at

baseband, and the harmonic loading in the PA power stage [10],

[11]. In the context of a broad-band wireless transmitter, the

electrical memory effects are the dominant sources of the spec-

trum regrowth since the thermal ﬁlter time constant is too large

compared to the inverse of the signal bandwidth [12]. Therefore,

the memory effects in the remainder of this paper are limited to

the electrical memory effects.

Different predistorter architectures, which are intended

to compensate for the nonlinearity, as well as the memory

effects, have been reported in the literature. For example, a

memory polynomial model was proposed in [13] and utilized in

[14]–[16] to address these effects. However, a memory polyno-

mial-based predistorter suffers from numerical instability when

higher order polynomial terms are included because a matrix

inversion is needed for the determination of the polynomial

coefﬁcients [17]. Alternatively, Raich

et al. [17] employed

orthogonal polynomials to alleviate the numerical instability

problem associated with the traditional polynomials.

Two-box-based predistorters, which are called either a Ham-

merstein predistortor or a Wiener predistorter, depending on

the cascading order of the nonlinear block and linear block,

LIU et al.: AUGMENTED HAMMERSTEIN PREDISTORTER FOR LINEARIZATION OF BROAD-BAND WIRELESS TRANSMITTERS 1341

are another type of common predistorter architecture in the

literature. For example, a Hammerstein predistorter, which is a

cascade of a memoryless nonlinear block followed by a linear

ﬁlter, was utilized to compensate for the nonlinearity, as well

as the memory effects of a PA [18], [19]. Recently, Wang and

Ilow [20] demonstrated the compensation performance using a

Wiener predistorter to linearize the high power ampliﬁer (HPA)

with memory effects in an orthogonal frequency-division

multiplexing (OFDM) transmitter while considering the HPA

as a Hammerstein nonlinear system. In these two examples,

the memoryless nonlinearity is represented by a complex

high-order memoryless polynomial. In addition, the identiﬁca-

tion of the coefﬁcients of the memoryless nonlinear block and

the taps of the linear ﬁlter are concurrently resolved by means of

complicated algorithms that are applied either in a time domain

[18], [19] or frequency domain [20]. Moreover, Sano and Sun

[21] proposed a new three-box efﬁcient Wiener–Hammerstein

predistortion scheme for pre-compensating the nonlinear dis-

tortion of an HPA. The identiﬁcation algorithm of this scheme

is implemented in a frequency domain.

In this paper, a LUT-based Hammerstein predistorter is

initially developed to compensate for the nonlinearity and the

memory effects that occur in a broad-band wireless transmitter.

To further improve the compensation performance of the

predistorter, an augmented Hammerstein predistorter is then

proposed.

The remainder of this paper is organized as follows. Sec-

tion II elucidates the details of the LUT-based Hammerstein

predistorter and its corresponding identiﬁcation procedure.

In Section III, a new augmented Hammerstein predistorter is

proposed in order to improve the correction performance for

the nonlinearity and the memory effects in the context of the

broad-band wireless transmitter. Section IV describes the test

bed used in the experimental validation of different predistorters

involved in this paper. In Section V, the validation results of the

Hammerstein predistorter and augmented Hammerstein predis-

torter with different conﬁgurations under one- and three-carrier

third-generation partnership projects frequency-division-

duplex (3GPP-FDD) wide-band code-division multiple-access

(WCDMA) signals are illustrated and discussed using an

-band 45-dBm GaAs ﬁeld-effect transistor (FET) push–pull

PA-based transmitter. Section VI presents the conclusion.

II. LUT-B

ASED HAMMERSTEIN PREDISTORTER

AND

IDENTIFICATION

A. LUT-Based Hammerstein Predistorter

A Hammerstein predistorter, as illustrated in Fig. 1, is uti-

lized to build a predistortion function for a broad-band wire-

less transmitter. Accordingly, the predistorter is decomposed

into a nonlinear static memoryless subsystem and a linear dy-

namic one. The static memoryless subsystem is intended to pre-

compensate for the static nonlinearity of the transmitter, while

the linear dynamic ﬁlter is focused on suppressing the spectrum

regrowth caused by the memory effects. The memoryless pre-

distortion can be implemented using the traditional LUT. This

LUT is constructed based on the AM/AM and AM/PM char-

acteristics of the transmitter that are extracted directly from the

Fig. 1. Hammerstein predistorter diagram.

Fig. 2. Ofﬂine training scheme for Hammerstein predistorter identiﬁcation.

baseband measurement data by means of a moving average pro-

cedure, as explained in [22]. Consequently, the complex dy-

namic predistortion problem is simpliﬁed to a relatively easy

linear dynamic problem. In this way, resolving the Hammerstein

predistortion becomes more convenient than the traditional so-

lutions [18]–[20], where all of the linear and nonlinear param-

eters of the Hammerstein model are resolved concurrently by

means of elaborate algorithms.

The identiﬁcation of the static memoryless predistorter on the

basis of raw measured baseband data

and permits the

extraction of the nonmeasurable variable

, shown in Fig. 1,

which is required in the identiﬁcation of the linear ﬁlter sub-

system. For this reason, the input signal

of the predistorter

is applied to the memoryless predistorter subsystem so as to get

the dynamic linear ﬁlter input signal

The input and output signals of the two blocks in Fig. 1 can

be related as follows:

(1)

(2)

where

refers to the

memoryless complex gain of the predistorter that depends only

on the instantaneous magnitude of

; is a linear transfer

function of the linear ﬁlter.

B. Hammerstein Predistorter Identiﬁcation

Hammerstein parameter identiﬁcation is performed using an

ofﬂine training scheme, as shown in Fig. 2. To identify the pa-

rameters of the predistorter, the output

of the transmitter

is normalized by the designated linear gain

of the trans-

mitter and taken as the input training sequence

of the pre-

distorter, i.e.,

(3)

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jiaowodd

2014-11-16

是一篇论文，网上可以查到，不是代码内容，放错地方了。论文本身有参考价值。

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