systematic and adaptive characterization approach for behavior modeling and correction of dynamic...

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 6, DECEMBER 2007 2203

Systematic and Adaptive Characterization Approachfor Behavior Modeling and Correction of

Dynamic Nonlinear TransmittersSlim Boumaiza, Senior Member, IEEE, Mohamed Helaoui, Student Member, IEEE,

Oualid Hammi, Student Member, IEEE, Taijun Liu, Member, IEEE, and Fadhel M. Ghannouchi, Fellow, IEEE

Abstract—This paper proposes a comprehensive and systematiccharacterization methodology that is suitable for the forward andreverse behavior modeling of wireless transmitters (Txs) driven bywideband-modulated signals. This characterization approach canbe implemented in adaptive radio systems since it does not requireparticular signal or training sequences. The importance of thenature of the driving signal and its average power on the behaviorof radio-frequency Txs are experimentally investigated. Criticalissues related to the proposed characterization approach are an-alytically studied. This includes a new delay-estimation methodthat achieves good accuracy with low computational complexity.In addition, the receiver linear calibration and its noise budget areinvestigated. To demonstrate the accuracy and robustness of theproposed method, a full characterization (including the memory-less nonlinearity and the memory effects) of a 100-W Tx drivenby a multicarrier wideband code-division multiple-access signalis carried out, and its forward and reverse models are identified.Cascading the identified reverse model derived using the proposedmethodology and the Tx prototype leads to excellent compensationof the static nonlinearities and the memory effects exhibited bythe latter. Critical issues in implementing this approach are alsodiscussed.

Index Terms—Behavioral modeling, memory effects, nonlinearcharacterization, power amplifiers (PAs), wideband transmitters(Txs).

I. INTRODUCTION

B EHAVIORAL modeling of radio-frequency (RF) poweramplifiers (PAs) and transmitters (Txs), in the context of

the third-generation (3G) and beyond (3G+) wireless standards,has become increasingly important and, to some extent, un-

Manuscript received January 31, 2007; revised August 16, 2007. This workwas supported in part by the Natural Sciences and Engineering ResearchCouncil of Canada (NSERC) and in part by the Informatics Circle of ResearchExcellence (iCORE).

S. Boumaiza was with the iRadio Laboratory, Electrical and ComputerEngineering Department, The Schulich School of Engineering, University ofCalgary, Calgary, AB T2N 1N4, Canada. He is now with the Department ofElectrical and Computer Engineering, University of Waterloo, Waterloo, ONN2L 3G1, Canada (e-mail: [email protected]).

M. Helaoui, O. Hammi, and F. M. Ghannouchi are with the iRadio Labora-tory, Electrical and Computer Engineering Department, The Schulich Schoolof Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada (e-mail:[email protected]; [email protected]; [email protected]).

T. Liu is with the Communication Technology Institute, College of Infor-mation Science and Engineering, Ningbo University, Ningbo 315211, China(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2007.908600

avoidable in RF/digital-signal-processor (DSP) cosimulationsand linearization. In fact, behavioral modeling is needed in theprocess of design and performance optimization of these Txs.This challenging task relies first and foremost on an accuratecharacterization of these Txs.

Over the past decades, the PA/Tx behavior measurementhas been the subject of the numerous studies that reportedseveral techniques aiming at an accurate characterization oftheir nonlinear large-signal behavior. These reported techniquescan be classified in two distinguished categories: The first oneis based on the use of specific test signals such as continuouswave (CW), two tones [1]–[3], and multitones [4]–[6], whereasthe second one [7] exploits realistic test signals which aresimilar to those that will be applied to the Tx once installedin the field. The long-established and simplest characterizationmethod employs a vector network analyzer (VNA) with aCW power sweep to measure the A.M./A.M. and A.M./P.M.characteristics of the PA. However, as demonstrated in [1] and[7], there is a significant discrepancy between the measuredmemoryless characteristics of the PA using the aforementionedVNA-based method and those obtained while driving the PAwith varying envelope signals.

To take into account the frequency response of the am-plifier, Launay et al. [8] proposed to extract the behavioral-model parameters by fitting the static A.M./A.M. and A.M./P.M.characteristics at several carrier frequencies that fall withinthe signal bandwidth. These static A.M./A.M. and A.M./P.M.characteristics are obtained by using the CW measurements atthe designated carrier frequency. Even though this approach issimple and easy to implement, it suffers from the lack of accu-racy since the static PA characterization technique is separatelyperformed at each nonmodulated carrier frequency. Conversely,the two-tone excitation signal was used to achieve a moreaccurate characterization by including mixing frequency prod-ucts resulting from the intermodulation distortions. However,in such two-tone-based tests, accurate A.M./P.M. characteristicmeasurement requires complicated setups using two spectrumanalyzers: a VNA and a power meter [3]. This method alsorequires a reference intermodulation generator, the precisionof which determines the measurement accuracy. Ku et al. [9]applied the two-tone test to extract the PA’s model parametersby concurrently fitting the measured amplitudes and phases ofthe output-spectrum components. Indeed, the fundamental, thethird-order, and the fifth-order intermodulations were measured

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2204 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 6, DECEMBER 2007

Fig. 1. Functional block diagram of the proposed characterization solution.

by performing a sweep over both the input power and thefrequency spacing. In order to better emulate the PA under morerealistic test conditions, multitone (also known as multisine)signals have been employed. A careful choice of the signal sta-tistics is required in order to obtain an accurate characterization[4], [6]. In addition, the conventional multitone excitation mightlead to an overestimation of the PA’s nonlinearity [5] and is notsuitable for online characterization.

The characterization of the PA/Tx is often perceived as astep in a more comprehensive procedure that aims to model thebehavior of the amplifier or Tx and to linearize its response.The identification of the different PA/Tx models’ parametersrequires generally specific characterization procedures that arefeasible only in a laboratory or factory environment and thatcould not be used in operating base stations [8]–[12]. Never-theless, the PA/Tx measurement results obtained using any ofthe aforementioned characterizations will depend on the exci-tation signal. As a consequence, an accurate characterizationof the PA requires the use of realistic test signals. In [7], arealistic, accurate, and versatile test bed was proposed for thePA/Tx characterization purposes. This approach uses the PA/Txinstantaneous input and output complex waveforms to extractthe A.M./A.M. and A.M./P.M. characteristics of the amplifierunder realistic test conditions. Such approach is convenientfor characterizing memoryless PAs as well as those exhibitingmemory effects. Several behavioral methods can be used alongwith the aforementioned characterization technique to providea complete characterization and modeling solution appropriatefor the implementation in adaptive communication systems[13], [14].

Besides the forward behavior-modeling aspect of the Tx, thecompensation of its nonlinearity requires the identification ofits reverse model, which relies on the accuracy of the character-ization procedure. The inverse model could be designed eitherdirectly from the measured characteristics of the PA [7] or byinverting its model [15]. In both cases, the performance of thelinearized amplifier depends on the characterization accuracy.

The remainder of this paper is organized as follows.Section II describes the principles of the PA/Tx’s characteri-zation technique and its main advantages (systematic, accurate,and comprehensive) when compared with the state of the art.An analytical study of the critical issues related to the useof the proposed technique is also presented in this section.Section III will cover the modeling procedure and the parameteridentification of the Tx forward model built herein using the

augmented Wiener model. In Section IV, the reverse-modelingmethodology is explained, and it is shown that its accuracy isintimately tied and dependent on the accuracy of the character-ization step.

II. REAL-TIME ADAPTIVE PA/TX

CHARACTERIZATION TECHNIQUE

A. Proposed Instantaneous Characterization Scheme

To overcome the relatively limited characterization perfor-mances of the previously mentioned methods, an instantaneouscharacterization procedure is proposed. This technique exploitsthe signal’s waveform at the input and output of the Tx inorder to derive its nonlinear characteristics. Fig. 1 shows ageneric functional block diagram of the proposed characteri-zation scheme. First, a sample of the RF signal at the output ofthe amplifier is attenuated, down-converted to an intermediatefrequency (IF), and then digitized. The resulting digital signalis fed to a digital demodulator to recover the correspondingIout and Qout components. Finally, these measured data arecompared with the input data (Iin and Qin) in order to determinethe instantaneous A.M./A.M. and A.M./P.M. characteristics ofthe device under test (DUT).

The proposed method makes possible of the Tx character-ization on the fly without interrupting the service and doesnot require any specific training sequence or signal. This is acrucial concern since the PA/Tx behavior is sensitive to severaloperation factors, namely, temperature, aging, network load,etc. In a laboratory-test environment, the DUT can accuratelybe characterized according to this approach using only an arbi-trary waveform generator and a vector signal analyzer (VSA)[7]. The arbitrary waveform generator is then used to feed theamplifier with the modulated RF or IF signal. The attenuatedPA’s output signal is captured and demodulated by the VSA.For an operating base-station environment, the proposed ap-proach is not only feasible but also cost effective. Indeed, itneeds just a feedback path, including a down-converter and ananalog-to-digital converter. The digital-signal-processing algo-rithms required for the characterization can be implementedin a commercial DSP and/or a field-programmable gate array.Inherently, this characterization scheme is real time and adap-tive. Indeed, a performance decisive factor, e.g., the adjacent-channel power-ratio (ACPR) level at the output of the PA, canbe used to decide whether a new characterization is needed or

BOUMAIZA et al.: SYSTEMATIC AND ADAPTIVE CHARACTERIZATION APPROACH FOR BEHAVIOR MODELING 2205

not. Moreover, a single measurement run using the proposedmethod is sufficient to capture the memoryless behavior of thePA as well as the memory effects it exhibits. The critical issuesrelated to the use of the proposed technique, including the delayestimation and alignment, the receiver calibration, and the noiseanalysis, are developed in the next section.

In this paper, the digital input waveforms are generated usingAgilent’s Advanced Design System (ADS) software and thendownloaded into a signal generator (ESG4438C) through ageneral-purpose interface bus. The signal generator feeds theamplifier with the corresponding RF signal. The PA’s outputsignal is first attenuated and then fed into a VSA (E4440A)having an 80-MHz bandwidth that performs the signal down-conversion, digitization, and demodulation. The resulting Iout

and Qout components are then downloaded into the computerwhere the Matlab (Mathworks Inc.) software is used alongwith the Agilent’s ADS software to perform the requiredPA characterization and signal processing associated with themodeling.

B. Critical Issues for Using Input- andOutput-Waveform-Based Characterization

1) Delay Estimation and Alignment: The proposed charac-terization method uses the input and output waveforms of theDUT to deduce its complex gain compression curve. Thus,a perfect time alignment between the digital input data (Iin

and Qin) and the digital output data (Iout and Qout) is nec-essary to take into account the delay caused by the DUTand to ensure an accurate behavior prediction. Indeed, thisdelay introduces a significant dispersion in the A.M./A.M. andA.M./P.M. characteristics of the PA which may be interpretedas memory effects. Delay misalignment leads to an inaccu-rate PA behavior estimation and, consequently, to a degrada-tion in the correction capability of the predistortion function.Liu et al. [14] used the maximum cross correlation betweenthe input and output signals to estimate the DUT delay. Forthat, two steps were proposed: a coarse delay tuning and a finedelay tuning. A Lagrange interpolation of the input and outputsignals was applied in the fine-tuning step to improve the delay-tuning resolution. Indeed, a precise delay estimation requireslarge interpolation factor and results in a high computationalcomplexity. To alleviate this problem, a new single-step fine-tuning method, which eliminates the need for the interpolationand allows for accurate delay estimation independent of thesampling frequency, is proposed. This method is based onthe computation of the complex ratio between the Fouriertransforms of both the input and output signals. Hence, if sin(t)and sout(t) represent the complex input and output signals, adelay between the two signals can be expressed as

sout(t) = sin(t − to) (1)

where to represents the delay offset between both signals.Then, the resulting Sin(f) and Sout(f), which designate their

corresponding Fourier transforms, can be related by

Sout(f) = Sin(f) exp(ϕ). (2)

Fig. 2. Measured phase variation of the ratio of the input and output spectraas a function of frequency.

Based on (2), the phase ϕ = −2jπtof of the ratio betweenSin(f) and Sout(f) linearly varies with the frequency. Itsderivative versus frequency is constant and only depends on thedelay-offset value. The value of the delay offset is then given by

to = − 12π

dϕ

df. (3)

To demonstrate its good accuracy, the proposed delay-estimation method was used to compute the delay of theDUT when excited with the two-carrier wideband code-division multiple-access (WCDMA) signal. For that, the DUTinput- and output-signal waveforms were sampled at fs =92.16 MHz. Fig. 2 shows the resulting variation of the phaseϕ as a function of the normalized frequency. Based on Fig. 2and (2), the delay of the DUT was found to be 8.96 ns. Thesame waveforms were also used to calculate the DUT delayusing the method presented in [14] with an oversampling factorof 25, which leads to almost the same result than the new one(9.18 ns). However, this oversampling-based technique involvesmuch more computational complexity.2) Receiver Calibration: The receiver calibration is another

critical issue that affects the accuracy of the characterizationresults. Indeed, the measured Iout and Qout data, which areobtained at the demodulator output, have to be deembedded tothe output of the PA. Thus, a precise knowledge of the receiverresponse is required in order to design its equivalent function.The receiver preequalization enhances the measurement accu-racy, particularly for the wideband signals. It also ensures aflat response of the feedback path. This operation is performedoffline.

The receiver calibration should be done in two steps. The firststep ensures its linearity, and the second one compensates forits linear frequency response. To minimize the nonlinear effectsintroduced by the receiver, its input-signal power should be keptbelow the maximum distortion-free signal (MDFS) which isgiven by the following equation:

MDFS = BNL + 10 log10(BW) + NFreceiver + SFDRreceiver

(4)

where BNL is the background noise level and is equal to−174 dBm/Hz at the reference temperature (T0 = 290 K).


BW is the signal bandwidth expressed in hertz, and NFreceiver

is the noise figure of the receiver. SFDRreceiver designates thereceiver spurious-free dynamic range that is given by

SFDR=23

(IIP3receiver − BNL −10 log10(BW) − NFreceiver)(5)

where IIP3receiver represents the receiver input third-orderintercept point.

By combining (4) and (5), the receiver MDFS can bewritten as

MDFS=13

(BNL+10 log10(BW)+NFreceiver)+23

IIP3receiver.

(6)

Moreover, the IIP3receiver can be expressed as a function ofthe VSA’s input third-order intercept point (IIP3VSA) and thegain of the attenuator (Gattenuator) based on

IIP3receiver =IIP3VSA

Gattenuator. (7)

Hence, for a fixed IIP3VSA, one can modify the attenuationvalue to vary the IIP3receiver and consequently adjust the valueof the MDFS and avoid the nonlinearity due to the receiver. Asit will be demonstrated in the following section, the value of theattenuation does not have an important impact on the signal-to-noise ratio (SNR) of the DUT output signal.

Once the nonlinearity of the receiver is minimized, themain remaining concern in its calibration process would bethe extraction of the receiver’s frequency response. For that, ifxout and xf are the equivalent time-domain complex envelopesof the signals at the input and the output of the receiver,respectively, and Xout and Xf are their corresponding Fouriertransforms, then the frequency response of the receiver can bewritten as

H(f) =Xf (f)

Xout(f). (8)

If xout = δ(t), then (9) becomes

H(f) = Xf (f). (9)

Since it is difficult to achieve a perfect delta function in prac-tice, a more accurate way consists in sweeping the frequencyof a constant amplitude sine wave at the input of the receiverand capturing the receiver output signal. One can then deducethe frequency response H(f) of the receiver over the desiredbandwidth around the carrier frequency.

The receiver frequency response is then used during the char-acterization process to deembed the captured envelope signal atthe receiver output to its input which represents the actual Txoutput. This can be done by applying a digital filter having afrequency response equal to H−1(f) to the captured signal atthe receiver output.3) Noise Analysis of the Proposed Scheme: The noise analy-

sis of the characterization setup is crucial since it directlyaffects the SNR of the measured output signal and, thus, thecharacterization accuracy. Herein, a noise analysis is provided

for the case where the configuration corresponding to thelaboratory-test environment is used. For this purpose, the noisefloor level at the output of the signal generator was measuredunder the two-carrier WCDMA excitation signal presented inthe previous section. Then, the equivalent noise temperature ofthe signal generator was derived using

Teq,ESG =1k· 10

NESG10 (10)

where k is the Boltzmann constant, and NESG is the noisepower density at the output of the ESG expressed in decibelsper hertz. The measured NESG is −171 dB/Hz. Accordingly,Teq,ESG is 575 600 K.

The equivalent noise temperatures of the PA lineup (Teq,PA)and the output attenuator (Teq,Att) are

Teq,PA =T0 ·(10

NFPA10 − 1

)(11)

Teq,Att =T0 ·(10

NFAtt10 − 1

)= T0 ·

(10

LAtt,dB10 − 1

)(12)

where NFPA and NFAtt are the noise figures of the PA lineupand the attenuator, respectively, T0 is the reference noisetemperature (T0 = 290 K), and LAtt,dB is the attenuator lossexpressed in decibels.

At the generator’s output reference plan, the equivalent noisetemperature of the considered Tx, including the signal gener-ator, the power-amplifier lineup, and the output attenuator, isthen given by

Teq = Teq,ESG + Teq,PA +Teq,Att

GPA

+Teq,Down−converter.LAtt

GPA. (13)

GPA designates the gain of the PA lineup. The first two termscontributing to the overall noise equivalent temperature are partof the system to characterize and cannot be minimized in thecharacterization step. However, the noise components gener-ated by the output attenuator are related to the experimentalsetup, and thus, its effects on the measurement accuracy needto be quantified. The contribution of the output attenuator to thesystem’s equivalent noise temperature is

Teq,Att

GPA=

T0(LAtt − 1)GPA

. (14)

Since the output attenuation is generally chosen to cancel thegain of the PA lineup in the feedback path, its value is equalto the gain of the PA lineup. In addition, it is worthy to notethat GPA � 1. Consequently, the contribution of the outputattenuator to the system’s equivalent noise temperature will be

Teq,Att

GPA= T0 ·

(1 − 1

GPA

)≈ T0. (15)

Accordingly, it is clear that the attenuator contribution to theequivalent noise temperature of the Tx is very limited since


Fig. 3. DUT used for experimental validation.

Teq,ESG is very high compared with the attenuator contributionin the overall equivalent noise temperature.

C. PA’s Behavior Sensitivity to the Excitation Signal

A key feature of the proposed characterization technique isthat it is done under the realistic test conditions in the sensethat it does not use any particular test signal. This is even morecritical knowing the sensitivity of the amplifier’s behavior to thetest signal. Indeed, the accuracy of the behavior characterizationis greatly dependent on the signal applied to the amplifier andits characteristics in such a manner that almost no other signalcould precisely reproduce the same PA behavior. To furtherinvestigate this issue, a 3G high PA was characterized using thetraditional VNA-based CW measurements, the multitone-basedcharacterization, and the proposed characterization method.Fig. 3 shows the DUT used for these experiments. It consistsof a three-stage 100-W peak LDMOS PA operating around2140 MHz.

The multitone test signal that was applied to the DUTconsists of eight tones centered on the carrier frequency(2140 MHz) with a 500-kHz spacing between each successivetones resulting in a total bandwidth of 3.5 MHz comparablewith that of the WCDMA signal. The phases of the tones werealigned to get a peak-to-average-power ratio (PAPR) compa-rable with that of the WCDMA signal used. This latter signalwas synthesized using the WCDMA 3G partnership project testmodel 1 with 64 dedicated physical channels. This WCDMAsignal has a 3.84-MHz bandwidth and a PAPR of 10.2 dB. Themeasured A.M./A.M. and A.M./P.M. curves obtained under thethree types of excitation are shown in Fig. 4.

The characterization results obtained with various excitationsignals confirm the sensitivity of the PA’s behavior to the typeof the input signal. In fact, one can observe the significantdiscrepancy between the A.M./A.M. and A.M./P.M. curves mea-sured using a CW signal and those obtained using either amultisine or a WCDMA signal. Indeed, for a high-power levelCW input signal, the PA is driven into its nonlinear region fora large time sweep compared with the case of the multisines orthe WCDMA signals [7]. This results in an extra self-heatingeffect that takes place for high input-power levels and decreasesthe gain of the PA. As a consequence, the 1-dB compressionpoint measured with the CW is approximately 3 dB below thatmeasured with the modulated test signal, although, in the caseof the multisines and the WCDMA signals, the behavior of theamplifier will be free of the aforementioned self-heating effect.Furthermore, in the case of the multisines and the WCDMAsignals, the behavior disparity is small due to the similaritybetween the bandwidth and the PAPR of these two signals.However, this small variation will have important repercussionson the modeling accuracy and, particularly, the linearizationcapability.

Fig. 4. Measured Tx’s characteristics for various excitation signals.(a) A.M./A.M. curves. (b) A.M./P.M. curves.

In addition to the PA’s behavior dependence on the input-signal type, the proposed characterization system was used toinvestigate the influence of the average power variation on theA.M./A.M. and A.M./P.M. characteristics of the DUT. This is acommon situation for the PAs used in the base stations wherethe output average power can vary over a wide range dependingon the network load. For this purpose, a two-carrier WCDMAsignal having a PAPR of 10.2 dB was used to characterizethe DUT for an average power at the input of the PA of−7.7 and −10.8 dBm, respectively. The smoothed dynamicA.M./A.M. and A.M./P.M. curves are shown in Fig. 5. Theseresults demonstrate the sensitivity of the PA behavior to theaverage power even for the same input signal. This emphasizesthe need for a real-time and adaptive characterization techniquein order to maintain accurate measurement results and goodlinearization capability.

D. Adaptive Characterization Procedure

The major difference between the laboratory or the fac-tory environment and that of an operating base station is theneed for an adaptive characterization procedure that is ableto track the PA/Tx behavior changes and maintain the systemperformances. This is required following either the short- orlong-term variations. The flowchart of the adaptive charac-terization procedure is shown in Fig. 6. At the beginning, afirst characterization step is performed. This step includes theacquisition of the Tx’s input and output baseband data, theequalization of the feedback path, and the delay estimation andcompensation. The captured data are then used to extract theA.M./A.M. and A.M./P.M. characteristics of the Tx that willbe used in the forward- and reverse-model identification steps.


Fig. 5. Measured Tx’s characteristics for various mean power levels.(a) A.M./A.M. curves. (b) A.M./P.M. curves.

Fig. 6. Flowchart of the adaptive characterization procedure.

The Tx’s model is determined by successively identifying itsstatic and dynamic behaviors. The accuracy of the model is thenvalidated using a new set of measured data. The determinationof the reverse model, which stands for the digital predistortionfunction, is analogous to that of the forward one. Indeed, atfirst, the static predistorter is derived and then the dynamicone. The linearization performances are assessed by measuringthe ACPR levels at the output of the PA. This could easily bedone using the measured Iout and Qout data. As long as themodel accuracy and linearized Tx’s ACPR are satisfactory, thecharacterization process will be set to the idle mode; otherwise,a new characterization will be performed.

Fig. 7. Measured and fitted Tx’s characteristics. (a) A.M./A.M. curve.(b) A.M./P.M. curve.

III. STEP-BY-STEP CHARACTERIZATION-RESULT

POSTPROCESSING FOR NONLINEAR MODELING

A. Forward Static Model Identification

The trace of the A.M./A.M. and A.M./P.M. characteristicsof the Tx drawn using the waveforms recorded at its inputand output, after the delay compensation, shows a significantdispersion. This dispersion is attributed in part to the noise mea-surement but mainly to the dynamic response of the Tx. Thismemory effect is introduced by the frequency response of thePA’s biasing and matching circuits at the envelope frequenciesaround the carrier and its harmonics. Several methods aim toconstruct the memoryless model of the PA. As an example, thecoefficients of a polynomial function can be determined usingthe least square error (LSE) criteria in order to fit the measureddata. However, in the case of highly nonlinear behavior, suchas that of class AB amplifiers, having nonregular A.M./A.M.and A.M./P.M. curves, high-order polynomial functions mightbe required, and good fitting all along the input-signal dynamicrange may be too difficult to achieve [16].

In [14], the deduction of the memoryless characteristics isperformed using a dynamic moving-average (MA) algorithmwhich is separately applied to the A.M./A.M. and A.M./P.M.curves. Better fitting results all over the input-signal dynamicrange are obtained. The main advantage of this method is itsrobustness to the A.M./A.M. and A.M./P.M. curve shapes, andconsequently, it is independent from the device technology andthe class of operation of the PA. Fig. 7 shows the A.M./A.M.and A.M./P.M. curves for the measured and fitted data using the


Fig. 8. Predicted and measured Tx’s output spectra.

MA method. The test signal used in this measurement is thepreviously employed two-carrier WCDMA signal.

B. Forward Dynamic Model Identification

The Tx’s measured A.M./A.M. and A.M./P.M. characteristicsshown in the previous section undergo a significant scattering.This is attributed to the dynamic behavior of the Tx. Thus,the model cannot be limited to a memoryless or a quasi-memoryless one. Indeed, the Tx’s instantaneous output signalis not only dependent on the present input signal but is alsosignificantly influenced by the preceding input samples. In theliterature, this phenomenon is called memory effects [7], [17],[18]. Several methods were proposed in the literature to detectthese effects and/or model them. For example, the augmentedWiener model in [14] was proposed to take into account thefrequency response of the biasing and matching circuits at theenvelope frequencies and around the even-order harmonics.

To evaluate the accuracy and robustness of the differentWiener models, a novel validation method has been proposed[14]. This method is based on annulling the spectrum re-growth that is caused by the static nonlinearity with the helpof cascading the inverse of the complex memoryless model.The measured spectrum was compared to that of the signal atthe augmented Wiener-model output after compensating for thememoryless nonlinearity. As shown in Fig. 8, a good agreementwas obtained between both power spectral densities under thetwo-carrier WCDMA excitation.

IV. TX REVERSE MODELING AND LINEARIZATION BASED

ON THE ADAPTIVE CHARACTERIZATION

To better point out the importance of the online adaptivecharacterization using a real signal waveform, the basebandreverse model of the characterized Tx is first synthesized basedon the measurement results and then cascaded to the basebandpart of the Tx. The model is based on Hammerstein structure[14], which is composed of the cascade of a memory-effectmodel and a memoryless nonlinear one. The model filters’coefficients are extracted using the LSE algorithm in such a waythat the memory effects of the Tx are canceled. Similarly, thestatic nonlinear model of the Hammerstein structure is set tocancel out the effect of the memoryless nonlinear behavior ofthe Tx.

Fig. 9. Linearized Tx output spectrum for different input powers.

Fig. 10. Linearized Tx output spectrum obtained using two different predis-tortion functions.

Figs. 9 and 10 show the spectra of the signal at the output ofthe linearized Tx using the identified augmented Hammersteinmodel. In Fig. 9, this reverse model is obtained using the two-carrier WCDMA signal with an average power of −7.7 dBmat the Tx input. As one can observe in this figure, adding thereverse model upstream the Tx that operates at the same inputaverage power leads to almost a complete distortion cancella-tion. This testifies the accuracy and precision of the character-ization procedure. To the best of the authors’ knowledge, nosuch performances were obtained by a characterization methodother than the proposed online characterization using the re-alistic test signals. However, when the previously identifiedreverse model is applied to the Tx operating at different inputaverage powers (−10.8 or −13.8 dBm), a linearity degradationis observed, as shown in Fig. 9. Accordingly, as the averagepower-operation point is shifted from the characterization aver-age power point (−7.7 dBm), the accuracy and quality of thereverse model increasingly deteriorates. As an example, a 3-dBback off of the average power-operation point (from −7.7 to−10.8 dBm) induces a 4-dB degradation on the ACPR perfor-mances of the linearized Tx. To further investigate this fact, anew characterization is carried out at an average input power of−10.8 dBm, and the corresponding augmented Hammersteinreverse model is synthesized. By using this newly identifiedreverse model, the linearization capability of the predistortionscheme was recovered. Fig. 10 shows the linearized Tx outputspectra obtained according to the two previous scenarios. Itdemonstrates that an enhancement of 6 dB in the ACPR isachieved by using the new characterization data. These results


confirm the dependence of the nonlinear behavior of the Tx onthe average power.

V. CONCLUSION

In this paper, a comprehensive and adaptive characterizationmethodology using the input and output time-domain wave-forms under the realistic test conditions was presented. Thestudy of the main critical issues related to this technique showedthe importance of a proper DUT delay estimation and receiversetting and calibration to ensure its anticipated good accuracy.For that, a low computation complexity and precise new delayestimation and receiver calibration were also proposed. Fur-thermore, the accuracy of this characterization method and itsapplication to the forward and reverse modeling were assessedthrough experimental validation carried on a 100-W 3G Tx.Contrary to the other characterization techniques, the proposedapproach takes into account the sensitivity of the Tx behaviorto the signal characteristics and is suitable for laboratory testingas well as on the field implementation environments. In addi-tion, this characterization technique simultaneously allows thedetection of the static memoryless nonlinearity as well as thememory effects around the carrier frequency.

The worth of the characterization method is first testifiedvia the good agreement observed between the Tx-prototypeoutput spectrum and the predicted one using the augmentedWiener model. The good agreement between the measuredand predicted output spectra gives evidence of the ability andaccuracy of the characterization method in capturing all theseeffects.

Similarly, the output-spectrum linearity metric was usedto evaluate the performances of the characterization-methodaccuracy through the deduction of a reverse model. The cascadeof such reverse model with a Tx operating at a given averagepower led to almost a complete distortion cancellation. How-ever, the application of the previously identified reverse modelto the same Tx which operates at different average powersintroduced significant linearity degradation. This degradationwas successfully eliminated through the substitution of the firstreverse model with a new one that is synthesized using the Txcharacterization data obtained at the same average power eachtime. These results confirmed the dependence of the nonlinearbehavior of the Tx on its average power operation.

REFERENCES

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Slim Boumaiza (S’00–M’04–SM’07) receivedthe B.Eng. degree in electrical engineering fromthe École Nationale d’Ingénieurs de Tunis, Tunis,Tunisia, in 1997 and the M.S. and Ph.D. degreesfrom the École Polytechnique de Montréal,Montréal, QC, Canada, in 1999 and 2004,respectively.

From May 2005 to August 2007, he was withthe Electrical Engineering Department, Universityof Calgary, Calgary, AB, Canada, as an AssistantProfessor and a Faculty Member with the iRadio

Laboratory. He is currently with the Department of Electrical and ComputerEngineering, University of Waterloo, Waterloo, ON, Canada, where he isleading the Emerging Radio System Research Group that is conducting multi-disciplinary research activities in the general areas of design of RF/microwaveand millimeter components and systems for wireless communications. He hasauthored or coauthored over 70 refereed journal and international conferencepapers. His specific current research interests include RF/DSP mixed design ofintelligent RF transmitters, design, characterization, modeling and linearizationof high-power RF amplifiers, reconfigurable and multiband transceivers, andadaptive DSP.


Mohamed Helaoui (S’06) received the B.Eng. andM.Sc.A. degrees in communications from the ÉcoleSupérieure des Communications de Tunis, Tunis,Tunisia, in 2002 and 2003, respectively. He is cur-rently working toward the Ph.D. degree at the Uni-versity of Calgary, Calgary, AB, Canada.

In 2002, he was a student member of the MEDIA-TRON Laboratory, École Supérieure des Communi-cations de Tunis. From 2003 to 2004, he was with thePolygrames Research Center, École Polytechniquede Montréal, Montréal, QC, Canada. Since 2005, he

has been with the iRadio Laboratory, Electrical and Computer EngineeringDepartment, The Schulich School of Engineering, University of Calgary.His current research interests are digital signal processing, power-amplifierpredistortion, power-efficiency enhancement for wireless transmitters (Tx), and3G/4G Tx optimization.

Oualid Hammi (S’03) received the B.Eng. degreein electrical engineering from the École Nationaled’Ingénieurs de Tunis, Tunis, Tunisia, in 2001, andthe M.Sc. degree from the École Polytechnique deMontréal, Montréal, QC, Canada, in 2004. He iscurrently working toward the Ph.D. degree with theiRadio Laboratory, Electrical and Computer Engi-neering Department, The Schulich School of Engi-neering, University of Calgary, Calgary, AB, Canada.

His current research interest is in the area of mi-crowave and millimeter-wave engineering. His par-

ticular research activities are related to the design of intelligent and highlyefficient linear transmitters for wireless communications and the developmentof DSP techniques for power-amplifier linearization purposes.

Taijun Liu (S’05–M’06) received the B.S. degreein applied physics from the China University ofPetroleum, Dongying, China, in 1986, the M. Eng.degree in electrical engineering from the Universityof Electronic Science and Technology of China,Chengdu, China, in 1989, and the Ph.D. degree fromthe École Polytechnique de Montréal, Montréal, QC,Canada, in 2005.

From 1989 to 1992, he was a Lecturer with theChongqing University of Posts and Telecommunica-tions, Chongqing, China. From 1992 to 1998, he was

a Senior Engineer with the Information Technology Company, DianqianguiPetroleum Exploration Bureau, Kunming, China. From 1999 to 2000, he wasa Software Engineer with the ElectromagneticWorks Inc., Montréal. He wasa Postdoctoral Fellow with the University of Calgary, Calgary, AB, Canada,from October 2005 to December 2006. He is currently a Professor with theCommunication Technology Institute, College of Information Science andEngineering, Ningbo University, Ningbo, China. His research interests are DSP,neural networks, nonlinear modeling and linearization of wideband transmitters(Tx)/power amplifiers, and the design of ultralinear high-efficiency intelligentdigital Txs for broadband wireless and satellite communication systems.

Dr. Liu was the recipient of the 1990 Second-Class Award from the Scienceand Technology Progress Prize of the Ministry of Machine-Building and Elec-tronics Industry of China and the 1991 Third-Class Award from the NationalScience and Technology Progress Prize of China.

Fadhel M. Ghannouchi (S’84–M’88–SM’93–F’07)received the B.Eng. degree in engineering physicsand the M.S. and Ph.D. degrees in electrical engi-neering from the École Polytechnique de Montréal,Montréal, QC, Canada, in 1983, 1984, and 1987,respectively.

He is currently a Professor with the Electrical andComputer Engineering Department, The SchulichSchool of Engineering, University of Calgary,Calgary, AB, Canada, and the Director of the iRadioLaboratory. He presently holds an iCORE Professor-

ship and a Tier 1 Canada Research Chair with RF Radio Technology. He hasheld several invited positions at several academic and research institutions inEurope, North America, and Japan. He has provided consulting services toa number of microwave and wireless communication companies. He is alsothe Founder of AmpliX Inc., Montréal, QC, which is a company that offerslinearization products and services to wireless- and satellite-communicationequipment manufacturers. His research interests are in the areas of microwaveinstrumentation and measurements, nonlinear modeling of microwave devicesand communication systems, the design of power and spectrum efficientmicrowave amplification systems, and the design of intelligent RF transceiversfor wireless and satellite communications. His research activities have led toover 350 publications and seven U.S. patents, and he has supervised more than60 M.S. and Ph.D. students.

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