Systematic and Adaptive Characterization Approach for Behavior ...

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

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Systematic and Adaptive Characterization Approach for Behavior Modeling and Correction of Dynamic Nonlinear Transmitters Slim 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 systematic characterization methodology that is suitable for the forward and reverse behavior modeling of wireless transmitters (Txs) driven by wideband-modulated signals. This characterization approach can be implemented in adaptive radio systems since it does not require particular signal or training sequences. The importance of the nature of the driving signal and its average power on the behavior of radio-frequency Txs are experimentally investigated. Critical issues related to the proposed characterization approach are analytically studied. This includes a new delay-estimation method that achieves good accuracy with low computational complexity. In addition, the receiver linear calibration and its noise budget are investigated. To demonstrate the accuracy and robustness of the proposed method, a full characterization (including the memoryless nonlinearity and the memory effects) of a 100-W Tx driven by a multicarrier wideband code-division multiple-access signal is carried out, and its forward and reverse models are identified. Cascading the identified reverse model derived using the proposed methodology and the Tx prototype leads to excellent compensation of the static nonlinearities and the memory effects exhibited by the latter. Critical issues in implementing this approach are also discussed. Index Terms—Behavioral modeling, memory effects, nonlinear characterization, power amplifiers (PAs), wideband transmitters (Txs).

I. I NTRODUCTION

B

EHAVIORAL modeling of radio-frequency (RF) power amplifiers (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, unManuscript received January 31, 2007; revised August 16, 2007. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and in part by the Informatics Circle of Research Excellence (iCORE). S. Boumaiza was with the iRadio Laboratory, Electrical and Computer Engineering Department, The Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada. He is now with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: [email protected]). M. Helaoui, O. Hammi, and F. M. Ghannouchi are with the iRadio Laboratory, Electrical and Computer Engineering Department, The Schulich School of 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 Information 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 online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2007.908600

avoidable in RF/digital-signal-processor (DSP) cosimulations and linearization. In fact, behavioral modeling is needed in the process of design and performance optimization of these Txs. This challenging task relies first and foremost on an accurate characterization of these Txs. Over the past decades, the PA/Tx behavior measurement has been the subject of the numerous studies that reported several techniques aiming at an accurate characterization of their nonlinear large-signal behavior. These reported techniques can be classified in two distinguished categories: The first one is based on the use of specific test signals such as continuous wave (CW), two tones [1]–[3], and multitones [4]–[6], whereas the second one [7] exploits realistic test signals which are similar to those that will be applied to the Tx once installed in the field. The long-established and simplest characterization method employs a vector network analyzer (VNA) with a CW 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 measured memoryless characteristics of the PA using the aforementioned VNA-based method and those obtained while driving the PA with varying envelope signals. To take into account the frequency response of the amplifier, Launay et al. [8] proposed to extract the behavioralmodel parameters by fitting the static A . M ./A . M . and A . M ./P. M . characteristics at several carrier frequencies that fall within the signal bandwidth. These static A . M ./A . M . and A . M ./P. M . characteristics are obtained by using the CW measurements at the designated carrier frequency. Even though this approach is simple and easy to implement, it suffers from the lack of accuracy since the static PA characterization technique is separately performed at each nonmodulated carrier frequency. Conversely, the two-tone excitation signal was used to achieve a more accurate characterization by including mixing frequency products resulting from the intermodulation distortions. However, in such two-tone-based tests, accurate A . M ./P. M . characteristic measurement requires complicated setups using two spectrum analyzers: a VNA and a power meter [3]. This method also requires a reference intermodulation generator, the precision of which determines the measurement accuracy. Ku et al. [9] applied the two-tone test to extract the PA’s model parameters by concurrently fitting the measured amplitudes and phases of the output-spectrum components. Indeed, the fundamental, the third-order, and the fifth-order intermodulations were measured

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

by performing a sweep over both the input power and the frequency spacing. In order to better emulate the PA under more realistic test conditions, multitone (also known as multisine) signals have been employed. A careful choice of the signal statistics is required in order to obtain an accurate characterization [4], [6]. In addition, the conventional multitone excitation might lead to an overestimation of the PA’s nonlinearity [5] and is not suitable for online characterization. The characterization of the PA/Tx is often perceived as a step in a more comprehensive procedure that aims to model the behavior of the amplifier or Tx and to linearize its response. The identification of the different PA/Tx models’ parameters requires generally specific characterization procedures that are feasible only in a laboratory or factory environment and that could not be used in operating base stations [8]–[12]. Nevertheless, the PA/Tx measurement results obtained using any of the aforementioned characterizations will depend on the excitation signal. As a consequence, an accurate characterization of the PA requires the use of realistic test signals. In [7], a realistic, accurate, and versatile test bed was proposed for the PA/Tx characterization purposes. This approach uses the PA/Tx instantaneous input and output complex waveforms to extract the A . M ./A . M . and A . M ./P. M . characteristics of the amplifier under realistic test conditions. Such approach is convenient for characterizing memoryless PAs as well as those exhibiting memory effects. Several behavioral methods can be used along with the aforementioned characterization technique to provide a complete characterization and modeling solution appropriate for the implementation in adaptive communication systems [13], [14]. Besides the forward behavior-modeling aspect of the Tx, the compensation of its nonlinearity requires the identification of its reverse model, which relies on the accuracy of the characterization procedure. The inverse model could be designed either directly from the measured characteristics of the PA [7] or by inverting its model [15]. In both cases, the performance of the linearized 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 characterization 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 use of the proposed technique is also presented in this section. Section III will cover the modeling procedure and the parameter identification of the Tx forward model built herein using the

augmented Wiener model. In Section IV, the reverse-modeling methodology is explained, and it is shown that its accuracy is intimately tied and dependent on the accuracy of the characterization step.

II. R EAL -T IME A DAPTIVE PA/T X C HARACTERIZATION T ECHNIQUE A. Proposed Instantaneous Characterization Scheme To overcome the relatively limited characterization performances of the previously mentioned methods, an instantaneous characterization procedure is proposed. This technique exploits the signal’s waveform at the input and output of the Tx in order to derive its nonlinear characteristics. Fig. 1 shows a generic functional block diagram of the proposed characterization scheme. First, a sample of the RF signal at the output of the amplifier is attenuated, down-converted to an intermediate frequency (IF), and then digitized. The resulting digital signal is fed to a digital demodulator to recover the corresponding Iout and Qout components. Finally, these measured data are compared with the input data (Iin and Qin ) in order to determine the instantaneous A . M ./A . M . and A . M ./P. M . characteristics of the device under test (DUT). The proposed method makes possible of the Tx characterization on the fly without interrupting the service and does not require any specific training sequence or signal. This is a crucial concern since the PA/Tx behavior is sensitive to several operation factors, namely, temperature, aging, network load, etc. In a laboratory-test environment, the DUT can accurately be characterized according to this approach using only an arbitrary waveform generator and a vector signal analyzer (VSA) [7]. The arbitrary waveform generator is then used to feed the amplifier with the modulated RF or IF signal. The attenuated PA’s output signal is captured and demodulated by the VSA. For an operating base-station environment, the proposed approach is not only feasible but also cost effective. Indeed, it needs just a feedback path, including a down-converter and an analog-to-digital converter. The digital-signal-processing algorithms required for the characterization can be implemented in a commercial DSP and/or a field-programmable gate array. Inherently, this characterization scheme is real time and adaptive. Indeed, a performance decisive factor, e.g., the adjacentchannel power-ratio (ACPR) level at the output of the PA, can be used to decide whether a new characterization is needed or

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

not. Moreover, a single measurement run using the proposed method is sufficient to capture the memoryless behavior of the PA as well as the memory effects it exhibits. The critical issues related to the use of the proposed technique, including the delay estimation and alignment, the receiver calibration, and the noise analysis, are developed in the next section. In this paper, the digital input waveforms are generated using Agilent’s Advanced Design System (ADS) software and then downloaded into a signal generator (ESG4438C) through a general-purpose interface bus. The signal generator feeds the amplifier with the corresponding RF signal. The PA’s output signal is first attenuated and then fed into a VSA (E4440A) having an 80-MHz bandwidth that performs the signal downconversion, digitization, and demodulation. The resulting Iout and Qout components are then downloaded into the computer where the Matlab (Mathworks Inc.) software is used along with the Agilent’s ADS software to perform the required PA characterization and signal processing associated with the modeling. B. Critical Issues for Using Input- and Output-Waveform-Based Characterization

(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).

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

Based on (2), the phase ϕ = −2jπto f of the ratio between Sin (f ) and Sout (f ) linearly varies with the frequency. Its derivative versus frequency is constant and only depends on the delay-offset value. The value of the delay offset is then given by to = −

1) Delay Estimation and Alignment: The proposed characterization method uses the input and output waveforms of the DUT 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 necessary to take into account the delay caused by the DUT and to ensure an accurate behavior prediction. Indeed, this delay introduces a significant dispersion in the A . M ./A . M . and A . M ./ P. M . characteristics of the PA which may be interpreted as memory effects. Delay misalignment leads to an inaccurate PA behavior estimation and, consequently, to a degradation in the correction capability of the predistortion function. Liu et al. [14] used the maximum cross correlation between the input and output signals to estimate the DUT delay. For that, two steps were proposed: a coarse delay tuning and a fine delay tuning. A Lagrange interpolation of the input and output signals was applied in the fine-tuning step to improve the delaytuning resolution. Indeed, a precise delay estimation requires large interpolation factor and results in a high computational complexity. To alleviate this problem, a new single-step finetuning method, which eliminates the need for the interpolation and allows for accurate delay estimation independent of the sampling frequency, is proposed. This method is based on the computation of the complex ratio between the Fourier transforms of both the input and output signals. Hence, if sin (t) and sout (t) represent the complex input and output signals, a delay between the two signals can be expressed as sout (t) = sin (t − to )

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(2)

1 dϕ . 2π df

(3)

To demonstrate its good accuracy, the proposed delayestimation method was used to compute the delay of the DUT when excited with the two-carrier wideband codedivision multiple-access (WCDMA) signal. For that, the DUT input- and output-signal waveforms were sampled at fs = 92.16 MHz. Fig. 2 shows the resulting variation of the phase ϕ as a function of the normalized frequency. Based on Fig. 2 and (2), the delay of the DUT was found to be 8.96 ns. The same waveforms were also used to calculate the DUT delay using the method presented in [14] with an oversampling factor of 25, which leads to almost the same result than the new one (9.18 ns). However, this oversampling-based technique involves much more computational complexity. 2) Receiver Calibration: The receiver calibration is another critical issue that affects the accuracy of the characterization results. Indeed, the measured Iout and Qout data, which are obtained at the demodulator output, have to be deembedded to the output of the PA. Thus, a precise knowledge of the receiver response is required in order to design its equivalent function. The receiver preequalization enhances the measurement accuracy, particularly for the wideband signals. It also ensures a flat response of the feedback path. This operation is performed offline. The receiver calibration should be done in two steps. The first step ensures its linearity, and the second one compensates for its linear frequency response. To minimize the nonlinear effects introduced by the receiver, its input-signal power should be kept below the maximum distortion-free signal (MDFS) which is given 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).

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BW is the signal bandwidth expressed in hertz, and NFreceiver is the noise figure of the receiver. SFDRreceiver designates the receiver spurious-free dynamic range that is given by SFDR =

2 (IIP3receiver − BNL −10 log10 (BW) − NFreceiver ) 3 (5)

where IIP3receiver represents the receiver input third-order intercept point. By combining (4) and (5), the receiver MDFS can be written as MDFS =

2 1 (BNL+10 log10 (BW)+NFreceiver )+ IIP3receiver . 3 3 (6)

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

IIP3VSA . Gattenuator

(7)

Hence, for a fixed IIP3VSA , one can modify the attenuation value to vary the IIP3receiver and consequently adjust the value of the MDFS and avoid the nonlinearity due to the receiver. As it will be demonstrated in the following section, the value of the attenuation does not have an important impact on the signal-tonoise ratio (SNR) of the DUT output signal. Once the nonlinearity of the receiver is minimized, the main remaining concern in its calibration process would be the extraction of the receiver’s frequency response. For that, if xout and xf are the equivalent time-domain complex envelopes of the signals at the input and the output of the receiver, respectively, and Xout and Xf are their corresponding Fourier transforms, then the frequency response of the receiver can be written 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 practice, a more accurate way consists in sweeping the frequency of a constant amplitude sine wave at the input of the receiver and capturing the receiver output signal. One can then deduce the frequency response H(f ) of the receiver over the desired bandwidth around the carrier frequency. The receiver frequency response is then used during the characterization process to deembed the captured envelope signal at the receiver output to its input which represents the actual Tx output. This can be done by applying a digital filter having a frequency response equal to H −1 (f ) to the captured signal at the receiver output. 3) Noise Analysis of the Proposed Scheme: The noise analysis of the characterization setup is crucial since it directly affects the SNR of the measured output signal and, thus, the characterization accuracy. Herein, a noise analysis is provided

for the case where the configuration corresponding to the laboratory-test environment is used. For this purpose, the noise floor level at the output of the signal generator was measured under the two-carrier WCDMA excitation signal presented in the previous section. Then, the equivalent noise temperature of the signal generator was derived using Teq,ESG =

NESG 1 · 10 10 k

(10)

where k is the Boltzmann constant, and NESG is the noise power density at the output of the ESG expressed in decibels per 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
NFPA  Teq,PA = T0 · 10 10 − 1
NFAtt Teq,Att = T0 · 10 10

(11)    LAtt,dB − 1 = T0 · 10 10 − 1 (12)

where NFPA and NFAtt are the noise figures of the PA lineup and the attenuator, respectively, T0 is the reference noise temperature (T0 = 290 K), and LAtt,dB is the attenuator loss expressed in decibels. At the generator’s output reference plan, the equivalent noise temperature of the considered Tx, including the signal generator, the power-amplifier lineup, and the output attenuator, is then given by Teq = Teq,ESG + Teq,PA +

Teq,Att GPA +

Teq,Down−converter .LAtt . (13) GPA

GPA designates the gain of the PA lineup. The first two terms contributing to the overall noise equivalent temperature are part of the system to characterize and cannot be minimized in the characterization step. However, the noise components generated by the output attenuator are related to the experimental setup, and thus, its effects on the measurement accuracy need to be quantified. The contribution of the output attenuator to the system’s equivalent noise temperature is T0 (LAtt − 1) Teq,Att = . GPA GPA

(14)

Since the output attenuation is generally chosen to cancel the gain of the PA lineup in the feedback path, its value is equal to the gain of the PA lineup. In addition, it is worthy to note that GPA  1. Consequently, the contribution of the output attenuator to the system’s equivalent noise temperature will be   Teq,Att 1 = T0 · 1 − (15) ≈ T0 . GPA GPA Accordingly, it is clear that the attenuator contribution to the equivalent noise temperature of the Tx is very limited since

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Fig. 3.

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DUT used for experimental validation.

Teq,ESG is very high compared with the attenuator contribution in the overall equivalent noise temperature. C. PA’s Behavior Sensitivity to the Excitation Signal A key feature of the proposed characterization technique is that it is done under the realistic test conditions in the sense that it does not use any particular test signal. This is even more critical knowing the sensitivity of the amplifier’s behavior to the test signal. Indeed, the accuracy of the behavior characterization is greatly dependent on the signal applied to the amplifier and its characteristics in such a manner that almost no other signal could precisely reproduce the same PA behavior. To further investigate this issue, a 3G high PA was characterized using the traditional VNA-based CW measurements, the multitone-based characterization, and the proposed characterization method. Fig. 3 shows the DUT used for these experiments. It consists of a three-stage 100-W peak LDMOS PA operating around 2140 MHz. The multitone test signal that was applied to the DUT consists of eight tones centered on the carrier frequency (2140 MHz) with a 500-kHz spacing between each successive tones resulting in a total bandwidth of 3.5 MHz comparable with that of the WCDMA signal. The phases of the tones were aligned to get a peak-to-average-power ratio (PAPR) comparable with that of the WCDMA signal used. This latter signal was synthesized using the WCDMA 3G partnership project test model 1 with 64 dedicated physical channels. This WCDMA signal has a 3.84-MHz bandwidth and a PAPR of 10.2 dB. The measured A . M ./A . M . and A . M ./P. M . curves obtained under the three types of excitation are shown in Fig. 4. The characterization results obtained with various excitation signals confirm the sensitivity of the PA’s behavior to the type of the input signal. In fact, one can observe the significant discrepancy between the A . M ./A . M . and A . M ./P. M . curves measured using a CW signal and those obtained using either a multisine or a WCDMA signal. Indeed, for a high-power level CW input signal, the PA is driven into its nonlinear region for a large time sweep compared with the case of the multisines or the WCDMA signals [7]. This results in an extra self-heating effect that takes place for high input-power levels and decreases the gain of the PA. As a consequence, the 1-dB compression point measured with the CW is approximately 3 dB below that measured with the modulated test signal, although, in the case of the multisines and the WCDMA signals, the behavior of the amplifier will be free of the aforementioned self-heating effect. Furthermore, in the case of the multisines and the WCDMA signals, the behavior disparity is small due to the similarity between the bandwidth and the PAPR of these two signals. However, this small variation will have important repercussions on the modeling accuracy and, particularly, the linearization capability.

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 inputsignal type, the proposed characterization system was used to investigate the influence of the average power variation on the A . M ./ A . M . and A . M ./ P. M . characteristics of the DUT. This is a common situation for the PAs used in the base stations where the output average power can vary over a wide range depending on the network load. For this purpose, a two-carrier WCDMA signal having a PAPR of 10.2 dB was used to characterize the DUT for an average power at the input of the PA of −7.7 and −10.8 dBm, respectively. The smoothed dynamic A . M ./ A . M . and A . M ./ P. M . curves are shown in Fig. 5. These results demonstrate the sensitivity of the PA behavior to the average power even for the same input signal. This emphasizes the need for a real-time and adaptive characterization technique in order to maintain accurate measurement results and good linearization capability. D. Adaptive Characterization Procedure The major difference between the laboratory or the factory environment and that of an operating base station is the need for an adaptive characterization procedure that is able to track the PA/Tx behavior changes and maintain the system performances. This is required following either the short- or long-term variations. The flowchart of the adaptive characterization procedure is shown in Fig. 6. At the beginning, a first characterization step is performed. This step includes the acquisition of the Tx’s input and output baseband data, the equalization of the feedback path, and the delay estimation and compensation. The captured data are then used to extract the A . M ./ A . M . and A . M ./ P. M . characteristics of the Tx that will be used in the forward- and reverse-model identification steps.

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Fig. 5. Measured Tx’s characteristics for various mean power levels. (a) A . M ./A . M . curves. (b) A . M ./P. M . curves. Fig. 7. Measured and fitted Tx’s characteristics. (a) A . M ./A . M . curve. (b) A . M ./P. M . curve.

III. S TEP - BY -S TEP C HARACTERIZATION -R ESULT P OSTPROCESSING FOR N ONLINEAR M ODELING A. Forward Static Model Identification

Fig. 6. Flowchart of the adaptive characterization procedure.

The Tx’s model is determined by successively identifying its static and dynamic behaviors. The accuracy of the model is then validated using a new set of measured data. The determination of the reverse model, which stands for the digital predistortion function, is analogous to that of the forward one. Indeed, at first, the static predistorter is derived and then the dynamic one. The linearization performances are assessed by measuring the ACPR levels at the output of the PA. This could easily be done using the measured Iout and Qout data. As long as the model accuracy and linearized Tx’s ACPR are satisfactory, the characterization process will be set to the idle mode; otherwise, a new characterization will be performed.

The trace of the A . M ./A . M . and A . M ./P. M . characteristics of the Tx drawn using the waveforms recorded at its input and output, after the delay compensation, shows a significant dispersion. This dispersion is attributed in part to the noise measurement but mainly to the dynamic response of the Tx. This memory effect is introduced by the frequency response of the PA’s biasing and matching circuits at the envelope frequencies around the carrier and its harmonics. Several methods aim to construct the memoryless model of the PA. As an example, the coefficients of a polynomial function can be determined using the least square error (LSE) criteria in order to fit the measured data. However, in the case of highly nonlinear behavior, such as that of class AB amplifiers, having nonregular A . M ./A . M . and A . M ./P. M . curves, high-order polynomial functions might be required, and good fitting all along the input-signal dynamic range may be too difficult to achieve [16]. In [14], the deduction of the memoryless characteristics is performed using a dynamic moving-average (MA) algorithm which is separately applied to the A . M ./A . M . and A . M ./P. M . curves. Better fitting results all over the input-signal dynamic range are obtained. The main advantage of this method is its robustness to the A . M ./A . M . and A . M ./P. M . curve shapes, and consequently, it is independent from the device technology and the 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

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Fig. 9. Linearized Tx output spectrum for different input powers. Fig. 8.

Predicted and measured Tx’s output spectra.

MA method. The test signal used in this measurement is the previously employed two-carrier WCDMA signal. B. Forward Dynamic Model Identification The Tx’s measured A . M ./A . M . and A . M ./P. M . characteristics shown 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 quasimemoryless one. Indeed, the Tx’s instantaneous output signal is not only dependent on the present input signal but is also significantly influenced by the preceding input samples. In the literature, this phenomenon is called memory effects [7], [17], [18]. Several methods were proposed in the literature to detect these effects and/or model them. For example, the augmented Wiener model in [14] was proposed to take into account the frequency response of the biasing and matching circuits at the envelope frequencies and around the even-order harmonics. To evaluate the accuracy and robustness of the different Wiener models, a novel validation method has been proposed [14]. This method is based on annulling the spectrum regrowth that is caused by the static nonlinearity with the help of cascading the inverse of the complex memoryless model. The measured spectrum was compared to that of the signal at the augmented Wiener-model output after compensating for the memoryless nonlinearity. As shown in Fig. 8, a good agreement was obtained between both power spectral densities under the two-carrier WCDMA excitation. IV. T X R EVERSE M ODELING AND L INEARIZATION B ASED ON THE A DAPTIVE C HARACTERIZATION To better point out the importance of the online adaptive characterization using a real signal waveform, the baseband reverse model of the characterized Tx is first synthesized based on the measurement results and then cascaded to the baseband part of the Tx. The model is based on Hammerstein structure [14], which is composed of the cascade of a memory-effect model and a memoryless nonlinear one. The model filters’ coefficients are extracted using the LSE algorithm in such a way that the memory effects of the Tx are canceled. Similarly, the static nonlinear model of the Hammerstein structure is set to cancel out the effect of the memoryless nonlinear behavior of the Tx.

Fig. 10. Linearized Tx output spectrum obtained using two different predistortion functions.

Figs. 9 and 10 show the spectra of the signal at the output of the linearized Tx using the identified augmented Hammerstein model. In Fig. 9, this reverse model is obtained using the twocarrier WCDMA signal with an average power of −7.7 dBm at the Tx input. As one can observe in this figure, adding the reverse model upstream the Tx that operates at the same input average power leads to almost a complete distortion cancellation. This testifies the accuracy and precision of the characterization procedure. To the best of the authors’ knowledge, no such performances were obtained by a characterization method other than the proposed online characterization using the realistic test signals. However, when the previously identified reverse model is applied to the Tx operating at different input average powers (−10.8 or −13.8 dBm), a linearity degradation is observed, as shown in Fig. 9. Accordingly, as the average power-operation point is shifted from the characterization average power point (−7.7 dBm), the accuracy and quality of the reverse model increasingly deteriorates. As an example, a 3-dB back off of the average power-operation point (from −7.7 to −10.8 dBm) induces a 4-dB degradation on the ACPR performances of the linearized Tx. To further investigate this fact, a new characterization is carried out at an average input power of −10.8 dBm, and the corresponding augmented Hammerstein reverse model is synthesized. By using this newly identified reverse model, the linearization capability of the predistortion scheme was recovered. Fig. 10 shows the linearized Tx output spectra obtained according to the two previous scenarios. It demonstrates that an enhancement of 6 dB in the ACPR is achieved by using the new characterization data. These results

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confirm the dependence of the nonlinear behavior of the Tx on the average power. V. C ONCLUSION In this paper, a comprehensive and adaptive characterization methodology using the input and output time-domain waveforms under the realistic test conditions was presented. The study of the main critical issues related to this technique showed the importance of a proper DUT delay estimation and receiver setting and calibration to ensure its anticipated good accuracy. For that, a low computation complexity and precise new delay estimation and receiver calibration were also proposed. Furthermore, the accuracy of this characterization method and its application to the forward and reverse modeling were assessed through experimental validation carried on a 100-W 3G Tx. Contrary to the other characterization techniques, the proposed approach takes into account the sensitivity of the Tx behavior to the signal characteristics and is suitable for laboratory testing as well as on the field implementation environments. In addition, this characterization technique simultaneously allows the detection of the static memoryless nonlinearity as well as the memory effects around the carrier frequency. The worth of the characterization method is first testified via the good agreement observed between the Tx-prototype output spectrum and the predicted one using the augmented Wiener model. The good agreement between the measured and predicted output spectra gives evidence of the ability and accuracy of the characterization method in capturing all these effects. Similarly, the output-spectrum linearity metric was used to evaluate the performances of the characterization-method accuracy through the deduction of a reverse model. The cascade of such reverse model with a Tx operating at a given average power led to almost a complete distortion cancellation. However, the application of the previously identified reverse model to the same Tx which operates at different average powers introduced significant linearity degradation. This degradation was successfully eliminated through the substitution of the first reverse model with a new one that is synthesized using the Tx characterization data obtained at the same average power each time. These results confirmed the dependence of the nonlinear behavior of the Tx on its average power operation. R EFERENCES [1] A. A. Moulthrop, C. J. Clark, C. P. Silva, and M. S. Muha, “A dynamic AM/AM and AM/PM measurement technique,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Denver, CO, Jun. 8–13, 1997, vol. 3, pp. 1455–1458. [2] H. Ku, M. D. Mckinley, and J. S. Kenney, “Extraction of accurate behavioral models for power amplifiers with memory effects using two-tone measurements,” in IEEE MTT-S Int. Microw. Symp. Dig., Seattle, WA, Jun. 2–7, 2002, pp. 139–142. [3] Y. Yang, J. Yi, J. Nam, B. Kim, and M. Park, “Measurement of twotransfer characteristics of high-power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 3, pp. 568–571, Mar. 2001. [4] D. Schreurs, M. Myslinski, and K. Remley, “RF behavioral modeling from multisine measurements: Influence of excitation type,” in Proc. 33rd Eur. Microw. Conf., Munich, Germany, Oct. 7–9, 2003, pp. 1011–1014. [5] K. Remley, “Multisine excitation for ACPR measurements,” in IEEE MTT-S Int. Microw. Symp. Dig., Philadelphia, PA, Jun. 8–13, 2003, pp. 2141–2144.

[6] J. C. Pedro and N. B. Carvalho, “Designing multisine excitations for nonlinear model testing,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 45–54, Jan. 2005. [7] S. Boumaiza and F. M. Ghannouchi, “Realistic power-amplifiers characterization with application to baseband digital predistortion for 3G base stations,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 3016– 3021, Dec. 2002. [8] F. Launay, Y. Wang, S. Toutain, S. T. D. Barataud, J. M. Nebus, and R. Quere, “Nonlinear amplifier modeling taking into account HF memory frequency,” in IEEE MTT-S Int. Microw. Symp. Dig., Seattle, WA, Jun. 2–7, 2002, pp. 865–868. [9] H. Ku, M. D. McKinley, and J. S. Kenney, “Quantifying memory effects in RF power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2843–2849, Dec. 2002. [10] P. Crama and Y. Rolain, “Broadband measurement and identification of a Wiener–Hammerstein model for an RF amplifier,” in 60th ARFTG Conf. Dig., Washington, DC, Dec. 5–6, 2002, pp. 49–57. [11] C. J. Clark, G. Chrisikos, M. S. Muha, A. A. Moulthrop, and C. P. Silva, “Time-domain envelope measurement technique with application to wideband power amplifier modeling,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2531–2540, Dec. 1998. [12] P. Jantunen, G. Gamez, and T. Laakso, “Measurements and modeling of nonlinear power amplifiers,” in Proc. 6th Nordic Signal Process. Symp., Espoo, Finland, Jun. 9–11, 2004, pp. 328–331. [13] T. Liu, S. Boumaiza, and F. M. Ghannouchi, “Dynamic behavioral modeling of 3G power amplifiers using real-valued time-delay neural networks,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 1025–1033, Mar. 2004. [14] T. Liu, S. Boumaiza, and F. M. Ghannouchi, “Deembedding static nonlinearities and accurately identifying and modeling memory effects in wideband RF transmitters,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3578–3587, Nov. 2005. [15] S. Chang and E. J. Powers, “A simplified predistorter for compensation of nonlinear distortion in OFDM systems,” in Proc. IEEE Global Telecommun. Conf., San Antonio, TX, Nov. 2001, vol. 5, pp. 3080–3084. [16] O. Hammi, S. Boumaiza, and F. M. Ghannouchi, “On the robustness of the predistortion function synthesis for highly nonlinear RF power amplifiers linearization,” in Proc. 36th IEEE Eur. Microw. Conf., Sep. 2006, pp. 145–148. [17] J. H. K. Vuolevi, T. Rahkonen, and J. P. A. Manninen, “Measurement technique for characterizing memory effects in RF power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 1383–1389, Dec. 2001. [18] L. Ding and G. T. Zhou, “Effects of even-order nonlinear terms on power amplifier modeling and predistortion linearization,” IEEE Trans. Veh. Technol., vol. 53, no. 1, pp. 156–162, Jan. 2004.

Slim Boumaiza (S’00–M’04–SM’07) received the B.Eng. degree in electrical engineering from the École Nationale d’Ingénieurs de Tunis, Tunis, Tunisia, in 1997 and the M.S. and Ph.D. degrees from the École Polytechnique de Montréal, Montréal, QC, Canada, in 1999 and 2004, respectively. From May 2005 to August 2007, he was with the Electrical Engineering Department, University of Calgary, Calgary, AB, Canada, as an Assistant Professor and a Faculty Member with the iRadio Laboratory. He is currently with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada, where he is leading the Emerging Radio System Research Group that is conducting multidisciplinary research activities in the general areas of design of RF/microwave and millimeter components and systems for wireless communications. He has authored or coauthored over 70 refereed journal and international conference papers. His specific current research interests include RF/DSP mixed design of intelligent RF transmitters, design, characterization, modeling and linearization of high-power RF amplifiers, reconfigurable and multiband transceivers, and adaptive DSP.

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

Mohamed Helaoui (S’06) received the B.Eng. and M.Sc.A. degrees in communications from the École Supérieure des Communications de Tunis, Tunis, Tunisia, in 2002 and 2003, respectively. He is currently working toward the Ph.D. degree at the University of Calgary, Calgary, AB, Canada. In 2002, he was a student member of the MEDIATRON Laboratory, École Supérieure des Communications de Tunis. From 2003 to 2004, he was with the Polygrames Research Center, École Polytechnique de Montréal, Montréal, QC, Canada. Since 2005, he has been with the iRadio Laboratory, Electrical and Computer Engineering Department, The Schulich School of Engineering, University of Calgary. His current research interests are digital signal processing, power-amplifier predistortion, power-efficiency enhancement for wireless transmitters (Tx), and 3G/4G Tx optimization.

Oualid Hammi (S’03) received the B.Eng. degree in electrical engineering from the École Nationale d’Ingénieurs de Tunis, Tunis, Tunisia, in 2001, and the M.Sc. degree from the École Polytechnique de Montréal, Montréal, QC, Canada, in 2004. He is currently working toward the Ph.D. degree with the iRadio Laboratory, Electrical and Computer Engineering Department, The Schulich School of Engineering, University of Calgary, Calgary, AB, Canada. His current research interest is in the area of microwave and millimeter-wave engineering. His particular research activities are related to the design of intelligent and highly efficient linear transmitters for wireless communications and the development of DSP techniques for power-amplifier linearization purposes.

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Taijun Liu (S’05–M’06) received the B.S. degree in applied physics from the China University of Petroleum, Dongying, China, in 1986, the M. Eng. degree in electrical engineering from the University of Electronic Science and Technology of China, Chengdu, China, in 1989, and the Ph.D. degree from the École Polytechnique de Montréal, Montréal, QC, Canada, in 2005. From 1989 to 1992, he was a Lecturer with the Chongqing University of Posts and Telecommunications, Chongqing, China. From 1992 to 1998, he was a Senior Engineer with the Information Technology Company, Dianqiangui Petroleum Exploration Bureau, Kunming, China. From 1999 to 2000, he was a Software Engineer with the ElectromagneticWorks Inc., Montréal. He was a Postdoctoral Fellow with the University of Calgary, Calgary, AB, Canada, from October 2005 to December 2006. He is currently a Professor with the Communication Technology Institute, College of Information Science and Engineering, 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 intelligent digital Txs for broadband wireless and satellite communication systems. Dr. Liu was the recipient of the 1990 Second-Class Award from the Science and Technology Progress Prize of the Ministry of Machine-Building and Electronics Industry of China and the 1991 Third-Class Award from the National Science and Technology Progress Prize of China.

Fadhel M. Ghannouchi (S’84–M’88–SM’93–F’07) received the B.Eng. degree in engineering physics and the M.S. and Ph.D. degrees in electrical engineering from the École Polytechnique de Montréal, Montréal, QC, Canada, in 1983, 1984, and 1987, respectively. He is currently a Professor with the Electrical and Computer Engineering Department, The Schulich School of Engineering, University of Calgary, Calgary, AB, Canada, and the Director of the iRadio Laboratory. He presently holds an iCORE Professorship and a Tier 1 Canada Research Chair with RF Radio Technology. He has held several invited positions at several academic and research institutions in Europe, North America, and Japan. He has provided consulting services to a number of microwave and wireless communication companies. He is also the Founder of AmpliX Inc., Montréal, QC, which is a company that offers linearization products and services to wireless- and satellite-communication equipment manufacturers. His research interests are in the areas of microwave instrumentation and measurements, nonlinear modeling of microwave devices and communication systems, the design of power and spectrum efficient microwave amplification systems, and the design of intelligent RF transceivers for wireless and satellite communications. His research activities have led to over 350 publications and seven U.S. patents, and he has supervised more than 60 M.S. and Ph.D. students.