Power and Efficiency Enhancement of 3G Multicarrier ... - IEEE Xplore

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Power and Efficiency Enhancement of 3G Multicarrier Amplifiers Using Digital Signal Processing With Experimental Validation Mohamed Helaoui, Student Member, IEEE, Slim Boumaiza, Member, IEEE, Adel Ghazel, Senior Member, IEEE, and Fadhel M. Ghannouchi, Senior Member, IEEE

Abstract—This paper proposes a digital signal-processing-based approach suitable for the performance optimization of third-generation (3G) amplifiers in terms of spectrum and power. A peak-to-average power ratio (PAPR) reduction method, which is coding and modulation independent, based on peak clipping and digital filtering techniques, is proposed. Moreover, the multibranch memory polynomial pre-distorter identified with an optimized recursive least square technique was efficiently implemented in a digital signal processor. The cascade of the proposed PAPR reduction technique with the memory pre-distorter results in a substantial enhancement of the power amplifier (PA) output linear power and efficiency, while still meeting the 3G partnership project standard requirements. An experimental validation carried out on a 90-W laterally diffused metal–oxide–semiconductor PA, which was fed with a wide-band code-division multiple-access signal, led to a 4-dB rise in output mean linear power accompanied with 60% increase in its power-added efficiency. Index Terms—Digital signal processing, multicarrier clipping, nonlinear power amplifier (PA), peak-to-average power ratio (PAPR) reduction, predistortion.

I. INTRODUCTION

T

HE proliferation of video and real-time applications in communication systems implies an inordinate increase of transmission data rates in a relatively limited spectral resource. Accordingly, complex modulations schemes and multiple access techniques, such as 64-point quadrature amplitude modulation (64-QAM), orthogonal frequency division multiplex (OFDM), and code division multiple access (CDMA), were proposed to optimize the spectral efficiency. These advanced modulation and access techniques result in highly varying envelope signals that have high peak-to-average power ratio (PAPR) values. This imposes stringent constraints on the linearity of the transmitter’s power amplifier (PA). Thus, the PA should operate

Manuscript received June 22, 2005; revised October 27, 2005. This work was supported by the Informatics Circle of Research Excellence, by the National Sciences and Engineering Research Council of Canada, and by the Canada Research Chairs. M. Helaoui, S. Boumaiza, and F. M. Ghannouchi are with the Intelligent RF Radio Laboratory, Electrical and Computer Engineering Department, University of Calgary, Calgary, AB, Canada T3N 1N4 (e-mail: [email protected]; [email protected]; [email protected]). A. Ghazel is with the MEDIATRON Research Laboratory, Physics, Electronics, and Propagation Department, École Supérieure des Communications de Tunis, Ariana 2083, Tunisia (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.871238

in its linear region to avoid distortion and quality degradation of the RF signal as a rise in the error vector magnitude (EVM) value; and, a large backoff should be considered to guarantee linear operation of the PA. However, this domino effect leads to power-efficiency degradation and a significant increase in cooling and running costs. Consequently, the reduction of the required backoff allows for an advantageous increase in the effective linear power of a given PA. In the literature, one can distinguish several approaches for moving the operation region of the PA toward the high efficient area while keeping an acceptable linearity. Among these approaches, PA linearization techniques such as feed forward, feedback, and predistortion have been the research focus of numerous academic and industrial laboratories [1]–[3] in the last decade. Baseband digital predistortion (DPD) linearizers [4]–[7] are particularly currently of interest since they benefit from the high-speed digital signal-processing implementation in field programmable gate arrays (FPGAs) and digital signal processors (DSPs). The DPD function, which consists of the inverse response of the PA, compensates for its nonlinearity so that the overall response of the cascade (DPD-PA) is linear. Furthermore, given that peaks in CDMA and OFDM signals rarely appear, the PAPR reduction approach represents an interesting way for enhancing the efficiency of the PA [8]–[14]. The fundamental idea behind PAPR reduction methods is clipping or reducing the signal magnitude when it exceeds a certain threshold. This operation unavoidably causes an undesirable spectrum regrowth and signal leakage into adjacent channels. For the multicarrier case, this leads to inter-carrier interference, resulting in unrecoverable signal quality degradation in each carrier. This paper proposes a concurrent application of the peak power clipping method, which is appropriate for multicarrier applications, and DPD on the baseband signal to substantially increase the effective linear power range of third-generation (3G) PAs/transmitters. Section II presents a PAPR reduction algorithm based on a clipping and filter shaping technique suitable for multicarrier applications. Subsequently, the structure of the DPD with memory, along with its parameter identification, is explained. The implementation details of the two preprocessing functions are revealed, and the experimental results in terms of adjacent channel power ratio (ACPR), EVM, and peak code domain error (PCDE) are presented in Section IV.

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II. PAPR REDUCTION A. Single-Carrier Signal Case In the literature, one can distinguish numerous PAPR reduction techniques. Coding [11], tone reservation [12], selective mapping [13], and active constellation extension [14] require access and modification of the modulation and coding and, consequently, are standard dependant. Clipping [8] and clipping and filtering [9], [10] techniques are simpler and more general since they can be applied to each standard and for different modulation types. However, the PAPR reduction for these methods is achieved at a cost of in-band and out-of-band noise. This can be tolerated when the signal quality continues to meet the standard requirement in terms of EVM and ACPR. For the clipping method [8], the magnitude of the signal is compared to the threshold value in order to calculate a scaling factor. This scaling factor is then used to clip the in-phase (I) and quadrature (Q) components of the baseband signal. An LPF reduces the out-of-band radiation caused by the clipping operation. Clipping and filtering [9], [10] eliminates the signal peaks by adding canceling pulses. In this study, a hard clipping algorithm followed by a waveshaper, which consists of a pre-synthesized finite impulse response (FIR) filter, are implemented as stated in [15]. The following equation expresses the hard clipping function:

Fig. 1. Measured spectrum of the input, clipped, and clipped and filtered signals.

Fig. 2. Clipping multicarrier signals.

(1) and denote the signal magnitude at the clipper where represents the desired input and output, respectively. threshold value. The clipping factor is defined as the ratio of the maximum output voltage over the maximum clipper input voltage

(2) A clipping factor fixed at 55% results in an increase of the EVM to 7% and a reduction in the PAPR value from 8.03 to 3 dB for wide-band code-division multiple-access (WCDMA) signals. The ACPR value decreases drastically, as shown in Fig. 1; therefore, a 128-tap FIR low-pass filter (LPF) was included in order to reduce the level of the out-of-band emission and to consequently enhance the ACPR, as shown in Fig. 1. The LPF has passband and cutoff frequencies equal to 1.93 and 2.5 MHz, respectively. Its in-band and out-of-band rejection are 0.01 and 100 dB, respectively. The resulting signal admits a PAPR of 5.77 dB, while the EVM is limited to 7.5%. Thus, one can shift the operation point of the PA by almost 2.3 dB toward its power efficient and saturation region. B. Multicarrier Signal Case Reducing the PAPR of a multicarrier signal is more complicated, since out-of-band distortion located between the different carriers cannot be filtered out by a simple FIR filter. In the literature, different solutions based on the phase shift between carriers [16], [17] were proposed to overcome the problem of

the noise introduced by clipping. These methods are based on shifting each carrier by a phase value to reduce the PAPR of the composite signal. The carriers’ phase values can be set randomly, and the optimal values are determined iteratively [16] or directly calculated [17]. These techniques require access to the baseband information of each carrier, which is not always available from the modulating circuits. Alternatively, a PAPR reduction method based on hard clipping and a multistage filtering, which needs the composite baseband multicarrier signal as an input, is proposed. It is well known that signal clipping introduces out-of-band distortions, as well as in-band noise. As shown in Section II-A, out-of-band distortion can be eliminated by applying an LPF. In the case of WCDMA, the ACPR requirements are more stringent than those related to the EVM metric and dominated by in-band distortion; therefore, PAPR reduction is considered as a simple and efficient solution to reduce the backoff in single-carrier WCDMA signals. However, the generalization of this concept to multicarrier WCDMA signals is not straightforward due to the difficulty in eliminating the out-of-band distortion, which causes interference between adjacent carriers. To overcome this problem, a more elaborate PAPR reduction scheme is proposed, as shown in Fig. 2. The composite complex envelope of a multicarrier signal is clipped to the specified threshold. The signal is then down-converted to the baseband frequency of each carrier. For each carrier, the corresponding down-converted signal is filtered using an LPF, which eliminates the adjacent carriers and out-of-band distortion. The LPF that is used is identical to the one used in the single-carrier case. Thus, after combining the different filtered carriers, the resulting signal has a lower PAPR value than the unclipped one. This technique guarantees PAPR

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TABLE I DIFFERENT CLIPPING-TYPE PERFORMANCES FOR A WCDMA THREE-CARRIER SIGNAL

Fig. 3. Measured clipped spectrum of multicarrier signal.

Fig. 4. CCDF function of the original and clipped two-carrier signals.

the clipping level is set at 45%, and the baseband filter used in Section II-A is kept the same. It can be seen that the PAPR of the two-carrier signal is reduced from 10.8 to 8 dB. For the three-carrier signal, the PAPR is reduced from 11 to 7.7 dB after clipping and filtering operations. In order to demonstrate the superiority of the enhanced PAPR reduction algorithm, the EVM of a three-carrier WCDMA signal is calculated with the clipping threshold fixed at 45% for both cases, as shown in Table I. It is found that the PAPR value obtained after clipping and filtering each carrier (Case 2) is higher than the one obtained with the enhanced PAPR algorithm (Case 1). In addition, the latter offers better signal quality (EVM) in comparison to the previous one, as shown in Table I. This is predictable since unnecessary clipping is achieved in Case 2, when the carriers’ peaks do not correspond to the composite signal peak. III. BASEBAND DPD A. Memoryless DPD As mentioned above, the predistortion technique is based on synthesizing a nonlinear function, which is complementary to that of the PA. Two methods are used for the implementation of such a technique, namely the lookup table (LUT) and polynomial function. In the latter method, complex envelopes of the pre-distorter input and output signals can be related as follows:

Fig. 5. CCDF function of the original and clipped three-carrier signals.

(3) reduction, while keeping good ACPR performance and acceptable signal quality. Fig. 3 shows the spectrum of the PAPR reduced signals for the following two cases. Case 1) The clipping is applied for the composite multicarrier signal, and then each carrier is filtered separately and summed at the end. Case 2) The clipping function followed by filtering is applied to each carrier separately, and then all carriers are summed. In the second case, the distortion between the carriers is increased by approximately 30 dB relative to the first case. Figs. 4 and 5 show the complementary cumulative distribution functions (CCDFs) of the original and clipped signal for the two- and three-carrier signals, respectively. In both cases,

is the polynomial order of the pre-distorter nonlinearity. Both polynomial function coefficients and correction parameters, used for the LUT implementation, have to be determined based on the PA characterization results. Given the nonmonotonic AM/AM characteristic of the highly nonlinear class-AB amplifier, which is currently employed in 3G base stations, a LUT-based configuration was chosen to avoid the high-order and complex polynomial function that would be needed in such a context. Accurate characterization of the PA is, therefore, needed for the deduction of the LUT entries. A test bench was developed to record the baseband components (I and Q) at the input and the output of the amplifier fed with 3G signals. The path delay between both signals is estimated and compensated

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Fig. 6. Synthesized AM/AM and AM/PM of the pre-distorter.

for according to equations given in [18]. The AM/AM and AM/PM LUT of the PA are then deduced and inverted to obtain the AM/AM and AM/PM LUT of the pre-distorter. A 90-W peak-envelop-power three-stage PA (2110–2170 MHz) was used in this study. The AM/AM and AM/PM measured characteristics of the device-under-test were used to deduce those of the corresponding pre-distorter, as shown in Fig. 6. B. DPD With Memory When dealing with wide-band signals, the PA power response is no longer constant over time. The power gain for a given instant power value depends on previous signal values. It can be seen as a nonlinear system with memory. Such behavior can be attributed to: 1) the frequency response variation of the PA over the whole bandwidth; 2) the frequency response of the biasing circuits [19], [20]; 3) trap effects; and 4) thermal effects. Neither the polynomial model, nor the LUT model described above can compensate for the memory effects. Thus, a memory model should be involved. Much research is related to this topic, and it reports upon different models to compensate for the memory effect. In [21], a model using the Volterra series is presented to describe the PA response. The Volterra model is suitable to model the nonlinear power response and the memory effects in the PA. Its only constraint is complexity since all the interactions between products are taken into account, given as follows by (4):

Fig. 7. Multibranch pre-distorter block diagram.

presents a considerable memory effect. The multibranch model, introduced by Kim et al. [24] and revisited by Raich et al. [25], is another particular case of the Volterra model that neglects the hybrid products in the Volterra-model equation. It can be seen as a filter, where each tap is a polynomial function of the input signal (Fig. 7). In this study, this model will be used to compensate for the dynamic nonlinear PA’s response since it offers a good compromise between precision and complexity. The pre-distorter function can be written as

(5) where and are the digital complex envelope signal at the pre-distorter input and output, respectively. designate the polynomial coefficients of the th filter tap. and are the maximum polynomial order and memory depth, respectively. C. Identification of the Memory Polynomial Model The multibranch model allows for the reduction of the number of unknown coefficients, from co. efficients in the Volterra series model to This reduces the complexity for the coefficient extraction algorithms. Generally, the least square (LS) method is applied for the model’s identification of coefficients. This algorithm is based on inverting a complex matrix using singular value decomposition (SVD), and has a calculation complexity proportional to . Equation (5) could be rewritten in matrix format as follows:

(4) where represents the model’s memory depth. Consequently, its implementation needs many resources and the coefficients’ identification is not straightforward. A Hammerstein model is introduced in [22] and [23] as a simpler solution than the Volterra model, and is considered as a particular case of the Volterra model. However, this solution is shown to be inefficient in describing the PA behavior when it

(6) where , , and are shown in the equation at the bottom of the following page and

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TABLE II RECURSIVE ALGORITHMS PERFORMANCES FOR IDENTIFYING THE PRE-DISTORTER COEFFICIENTS

algorithms. In addition, it has the fastest convergence, as shown in Table II. While the RLS algorithm needs 200 iterations to converge, its required convergence time is not greater than the LS nonrecursive algorithm. In fact, the LS algorithm waits for approximately 8000 data samples before starting their one iteration process. The RLS algorithm processes recursively these data by a block of for each iteration. This training is achieved once when the PA is turned on. Moreover, the RLS algorithm allows for the reduction of calculation complexity that becomes proportional to without loss of the convergence time and error performance.

The coefficients of are determined using a least squared optimization procedure and are calculated as follows:

IV. IMPLEMENTATION AND RESULTS A. Implementation Platform

(7) where is the pseudoinverse matrix of calculated by means of the SVD algorithm implemented into the DSP. To reduce the calculation complexity induced by the SVD algorithm, a recursive algorithm is applied to extract the pre-distorter coefficients. Table II summarizes the simulation results for different recursive algorithms: least mean squared (LMS), normalized least mean squared (nLMS) and recursive least square (RLS). A comparison is made between these algorithms and the LS. The residual mean error is calculated by the following formula: (8) where represents the difference between the instantaneous pre-distorter output and the desired output . Indeed, to extract the pre-distorter parameter, the recursive algorithm is fed with the stored baseband envelope of the PA output . Therefore, the desired algorithm output should be the stored baseband PA input , and is given by

(9)

It is shown that the residual error for the RLS algorithm gives the smallest error value when compared to the LMS and nLMS

The PAPR reduction algorithm and the pre-distorter algoand fixed at 3 rithm are implemented with parameters and 12, respectively. These values are chosen large enough to get acceptable ACPR performance. The hybrid platform used for implementation is composed of an FPGA board and a DSP. It also contains two digital-to-analog converters (DACs) operating at 165 Ms/s and a fast analog-to-digital converter (ADC) operating at 210 Ms/s. The capture of the feedback signal (PA output) is performed by means of a low-IF receiver architecture in order to reduce the loop distortions and, consequently, enhance the predistortion quality; therefore, a down-converter is used to translate the feedback signal around 30.720 MHz. The down-converter is composed of a cascade of a mixer, a bandpass filter for image-rejection purposes, and a variable gain amplifier (VGA) that is used to adjust the signal power to the ADC dynamic range. The IF signal is then digitized by the high-speed ADC. The I/Q demodulation is performed inside the FPGA side to avoid imbalance and leakage distortions introduced by the analog demodulator. The amplification stage is composed of a cascade of three amplifiers from Freescale Inc., Austin, TX. The dB, dB dBm). first driver is MHPA21010 (gain The second driver is MRF21045 (14.9 dB, 47 dBm). The PA is MRF21085 (13.6 dB, 50 dBm). As shown in Fig. 8, the PAPR reduction algorithm is implemented on the FPGA device. The clipped and filtered signal feeds the multibranch memory pre-distorter, which is implemented on the FPGA board and controlled by the DSP. In fact, the predistortion function is synthesized by the DSP board, which collects the data from the FPGA memory and extracts the pre-distorter parameters and then updates the predistortion block on the FPGA. This block adjusts the I and Q signals at

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Fig. 8. Implementation schematic of the PAPR reduction and predistortion algorithms cascade.

Fig. 10. Measured output spectrum of the transmitter with and without predis. tortion when driven with the clipped and filtered signal Cl

Fig. 9. Imbalance in IMD3 products caused by memory effect.

Fig. 11. Measured ACPR enhancement performances for clipping and predistortion techniques.

( = 55%)

the output of the PAPR reduction block, and then feeds the processed envelope to the two DACs. B. Memory Effect Detection To demonstrate that the utilized amplifier exhibits memory effects, a varying spacing two-tone test is carried out. The frequency spacing between the two tones is varied and both left and right third-order intermodulation distortion (IMD3) products are measured. Fig. 9 shows IMD3 products imbalance and their level variation with frequency spacing, which become significant at 2 MHz. A difference of 14 dB is registered at a frequency spacing of 10 MHz. This is attributed to the nonconstant frequency response at the envelope and second harmonic frequencies since the variation of the carrier frequency response does not exceed 0.5 dB for a 20-MHz bandwidth. C. Single-Carrier Results Fig. 10 shows the output spectrum of the transmitter for three cases, which are: 1) without predistortion; 2) with memoryless LUT predistortion; and 3) with multibranch predistortion with memory when driven with the clipped and pre-equalized signal. These spectrums are measured for an output power equal to 42.5 dBm. Based on Fig. 11, it can be seen that the combination of the peak power clipping, waveform shaping, and predistortion techniques leads to an increase in the linear output power of approximately 4 dB when compared to the maximum linear power obtained with the original WCDMA signal. A maximum output mean power equal to 44.5 dBm is reached while keeping the

Fig. 12. Measured PA efficiency versus mean output power.

ACPR level lower than 45 dBc. For larger backoff values, the ACPR is kept around 61 dBc, up to an output power value equal to 42 dBm. At this operating point, the impact of the PAPR reduction technique on the linearized PA is the reduction of the ACPR by 9 dB. Moreover, from Fig. 12, one can distinguish that the amplifier power efficiency rises up to 24% for the maximum output mean power in the case of clipped, filtered, and linearized signal (44.5 dBm). This power efficiency is 19% for an operation point corresponding to the maximum output mean power for the nonclipped and linearized case (42.5 dBm). Only 15% power efficiency can be achieved in the nonlinearized and nonclipped case when operating at the maximum output mean power (40.5 dBm). The digital circuit’s contribution to the dc power consumption (10 W) is minor when compared to the PA’s dc power consumption (105 W), and it leads to a slight reduction of the power-added efficiency (PAE) by 2% (from 24% to 22%). Fig. 13 shows that the clipping operation introduces in-band signal degradation that is not eliminated by filtering. This can

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Fig. 13. Measured EVM enhancement performances for clipping and predistortion techniques. Fig. 14. Measured output spectrum of the transmitter with and without predistortion for a two-carrier signal.

be seen in the EVM increase from 1% to 7% in the cases of linearly amplified nonclipped and clipped signals, respectively. The PA nonlinearity introduces additional in-band signal degradation that is compensated by applying predistortion. This linearization technique allows for a reduction of the EVM from 5% to 2% for a nonclipped signal for an output mean power equal to 42.5 dBm, and from 11.5% to 8.2% for the case of clipped signal for an output mean power equal to 44.5 dBm. These values of EVM still meet the standard requirements. The overall performance obtained with the combination of peak clipping, waveform shaping, and predistortion is superior to what has been reported in the available literature using techniques based on similar concepts [3]. In fact, the improvement in the measured ACPR ( 51 dBc) when increasing the effective linear power by 4 dB for class-AB LDMOS with a WCDMA signal is a significant achievement compared to the ACPR performance in [3] ( 45 dBc) when increasing the effective linear power by 3.7 dB. D. Multicarrier Results In order to illustrate the impact of memory effects on signal quality and the importance of the multibranch pre-distorter, twoand three-carrier signals are used. The PAPR reduction method, described in Section II, is applied to each type of signal with a clipping factor equal to 45%. The PAPR values of the clipped signals are 8 and 7.7 dB for two- and three-carrier signals, respectively. At the output of the clipper, a predistortion function is applied. In both cases, memoryless LUT predistortion and multibranch predistortion with memory are considered. Fig. 14 shows the spectrum of the PA output signal when applying LUT predistortion (memoryless), multibranch predistortion with memory, and no predistortion to a two-carrier signal. Fig. 15 shows the same three cases for three-carrier signals. It is important to highlight the considerable residual out-of-band noise when applying a memoryless predistortion. This residual noise increases with the signal bandwidth since it is mainly caused by memory effects. Table III shows the performances in terms of signal quality and channel leakage. The signal quality is measured using two metrics: the EVM and PCDE. The ACPR values of adjacent and alternate channels are used for quantifying the channel leakage performance. When using a memoryless LUT pre-distorter, the EVM values are enhanced from 10.1% to 9.4% for the two-carrier signal and from 8.6% to 7.8% for the three-carrier signal.

Fig. 15. Measured output spectrum of the transmitter with and without predistortion for a three-carrier signal.

TABLE III SIGNAL QUALITY ENHANCEMENT BY CASCADING CLIPPING AND PREDISTORTION FOR MULTICARRIER SIGNALS

The PCDE is also enhanced by predistortion and its value passes from 34.4 to 36.1 dB for the two-carrier signal and from 36.5 to 38.1 dB for the three-carrier signal. The residual

HELAOUI et al.: POWER AND EFFICIENCY ENHANCEMENT OF 3G MULTICARRIER AMPLIFIERS

in-band error is caused by the clipping operation and cannot be corrected. The memory pre-distorter keeps the same values of EVM and PCDE as the LUT. The memory effects are observed more in the out-of-band region. In fact, the ACPR performance obtained with a multibranch predistortion is better than the one obtained with a memoryless model. For example, the ACPR for adjacent channel is reduced from 37.1 to 52.1 dB when applying the LUT predistortion and to 58.9 dB when using a multibranch linearizer. V. CONCLUSION This paper has proposed that DSP algorithms be used to boost the 3G PA’s output power and efficiency performances. A modulation and coding independent PAPR reduction method, based on clipping the composite signal and filtering each carrier, has been proposed, and it was found to be more suitable for multicarrier signals. It allowed for PAPR reductions by more than 3 dB for two- and three-carrier WCDMA signals. The cascade of the latter to a memory multibranch pre-distorter permits the compensation for the PA nonlinearity and memory effects. The experimental validation of the proposed approach led to a significant increase (equal to 4 dB) in the maximum output mean power, while meeting the 3GPP standard requirements in terms of ACPR, EVM, and PCDE. This was also accompanied by power-efficiency enhancement equal to 60%. ACKNOWLEDGMENT The authors would like to acknowledge O. Hammi and T. Liu, both with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada, for providing technical and software support during measurements and C. Heys, Calgary, AB, Canada, for proofreading this paper’s manuscript. REFERENCES [1] S. P. Stapleton and F. C. Costescu, “An adaptive predistorter for power amplifier based on adjacent channel emissions,” IEEE Trans. Veh. Technol., vol. 41, no. 2, pp. 49–56, Feb. 1992. [2] E. G. Jeckeln, F. Beauregard, M. A. Sawan, and F. M. Ghannouchi, “Adaptive baseband/RF predistorter for power amplifiers through instantaneous AM-AM and AM-PM characterization using digital receivers,” in IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 2000, vol. 1, pp. 489–492. [3] R. Sperlich, Y. Park, G. Copeland, and J. S. Kenney, “Power amplifier linearization with digital pre-distortion and crest factor reduction,” in IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, Jun. 2004, vol. 2, pp. 669–672. [4] J. K. Cavers, “Amplifier linearization using a digital predistorter with fast adaptation and low memory requirements,” IEEE Trans. Veh. Technol., vol. 39, no. 4, pp. 374–382, Nov. 1990. [5] D. S. Hilborn, S. P. Stapleton, and J. K. Cavers, “An adaptative direct conversion transmitter,” IEEE Trans. Veh. Technol., vol. 43, no. 2, pp. 223–233, May 1994. [6] M. Faulkner and M. Johansson, “Adaptative linearization using predistortion: Experimental results,” IEEE Trans. Veh. Technol., vol. 43, no. 2, pp. 323–332, May 1994. [7] J. De Mingo and A. Valdovinos, “Performance of a new digital baseband predistorter using calibration memory,” IEEE Trans. Veh. Technol., vol. 50, no. 4, pp. 1169–1176, Jul. 2001. [8] G. Hill and M. Faulkner, “Comparison of low complexity clipping algorithms for OFDM,” in 13th IEEE Int. Pers. Indoor Mobile Radio Commun. Symp, Lisbon, Sep. 2002, vol. 1, pp. 227–231.

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[9] R. van Nee and A. de Wild, “Reducing the peak-to-average power ratio of OFDM,” in 48th IEEE Veh. Technol. Conf., Ottawa, ON, Canada, May 1998, vol. 3, pp. 2072–2076. [10] M. Pauli and P. Kuchenbecker, “On the reduction of the out-of-band radiation of OFDM-signals,” in IEEE Int. Commun. Conf., Atlanta, GA, Jun. 1998, vol. 3, pp. 1304–1308. [11] K. G. Paterson and V. Tarokh, “On the existence and construction of good codes with low peak-to-average power ratios,” IEEE Trans. Inf. Theory, vol. 46, no. 6, pp. 1974–1987, Sep. 2000. [12] J. Tellado, “Peak to average power reduction for multicarrier modulation,” Ph.D. dissertation, Dept. Elect. Eng., Stanford Univ., Stanford, CA, 2000. [13] H. Breiling, S. H. Müller-Weinfurtner, and J. B. Huber, “SLM peakpower reduction without explicit side information,” IEEE Commun. Lett., vol. 5, no. 6, pp. 239–241, Jun. 2001. [14] B. S. Krongold and D. L. Jones, “PAR reduction in OFDM via active constellation extension,” IEEE Trans. Broadcast., vol. 49, no. 3, pp. 258–268, Sep. 2003. [15] M. Helaoui, S. Boumaiza, A. Ghazel, and F. M. Ghannouchi, “On the RF/DSP design-for-efficiency of OFDM transmitters,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 7, pp. 2355–2361, Jul. 2005. [16] H. Nikookar and K. S. Lidsheim, “Random phase updating algorithm for OFDM transmission with low PAPR,” IEEE Trans. Broadcast., vol. 48, no. 2, pp. 123–128, Jun. 2002. [17] V. Tarokh and H. Jafrakhani, “On the computation and reduction of the peak-to-average power ratio in multicarrier communications,” IEEE Trans. Commun., vol. 48, no. 1, pp. 37–44, Jan. 2000. [18] T. Liu, S. Boumaiza, and F. M. Ghannouchi, “De-embedding static nonlinearities and accurately identifying and modeling memory effects in wide-band RF transmitters,” IEEE Trans. Microw. Theory Tech., to be published. [19] W. Bosch and G. Gatti, “Measurement and simulation of memory effects in predistortion linearizers,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 12, pp. 1885–1890, Dec. 1989. [20] J. H. K. Vuolevi, T. Rahkonen, and J. P. A. Mannien, “Measurement technique for characterizing memory effects in RF power amplifier,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 8, pp. 1383–1389, Aug. 2001. [21] C. Eun and E. J. Powers, “A new Volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Process., vol. 45, no. 1, pp. 223–227, Jan. 1997. [22] C. J. Clark, G. Chrisikos, M. S. Muha, A. A. Moulthrop, and C. P. Silva, “Time-domain envelope measurement technique with application to wide-band power amplifier modeling,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2531–2540, Dec. 1998. [23] L. Ding, R. Raich, and G. T. Zhou, “A Hammerstein predistortion linearization design based on the indirect learning architecture,” in IEEE Int. Acoust., Speech, Signal Process. Conf., Orlando, FL, May 2002, vol. 3, pp. 2689–2692. [24] J. Kim and K. Konstantinou, “Digital predistortion of wide-band signals based on power amplifier model with memory,” Electron. Lett., vol. 37, no. 23, pp. 1417–1418, Nov. 2001. [25] R. Raich, H. Qian, and G. Tong Zhou, “Orthogonal polynomials for power amplifier modeling and predistorter design,” IEEE Trans. Veh. Technol., vol. 53, no. 5, pp. 1468–1479, Sep. 2004.

Mohamed Helaoui (S’06) received his B.Eng. degree in communications and M.Sc.A. degree from the École Supérieure des Communications de Tunis, Tunis, Tunisia, in 2002 and 2003, respectively, and is currently working toward the Ph.D. degree at the University of Calgary, Calgary, AB, Canada. In 2002, he was a student member with the MEDIATRON Research Laboratory, École Supérieure des Communications de Tunis, and a Visiting Student with the System Design Group Research Laboratory, École Nationale Supérieure des Telecommunications de Paris. From 2003 to 2004, he was with the Polygrames Research Center, École Polytechnique de Montreal. In 2005, he joined the Intelligent RF Radio Laboratory, University of Calgary. His current research interests are DSP, PA predistortion, power efficiency enhancement for wireless transmitters, and 3G/fourth-generation (4G) transmitter optimization.

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Slim Boumaiza (S’00–M’04) 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. In May 2005, he joined the Electrical Engineering Department, University of Calgary, Calgary, AB, Canada, as an Assistant Professor and faculty member of the Intelligent RF Radio Laboratory. His research interests are in the general areas of RF/microwave and millimeter components and systems for broad-band wireless and satellite communications. His specific current interests include RF/DSP mixed design of intelligent RF transmitters, design, characterization, modeling and linearization of high-power RF amplifiers, and adaptive DSP.

Adel Ghazel (M’97–SM’01) received the E.E. and M.S. degrees in systems analysis and digital processing and Ph.D. degree in electrical engineering from the Ecole Nationale d’Ingénieurs de Tunis (ENIT), Tunis, Tunisia, in 1990, 1990, and 1996, respectively, and the Habilitation degree in communication and information technologies from Ecole Supérieure des Communications (SUP’COM) de Tunis, Ariana, Tunisia, in 2002. From 1990 to 1992, he was a Specialist Engineer with the Tunisia Engineering and Industrial Construction Company, where he was involved with design and field supervision of industrial instrumentation installation. In 1993, he joined the Ecole Supérieure des Postes et des Télécommunications de Tunis, where he was an Assistant Professor and then an Associate Professor of telecommunications. In 1999, he became the Head of the Department of Electronics and Propagation, and in 2002, a Professor with the Ecole Supérieure des Communications (SUP’COM). Since 1998, he has been working with the Software and Systems Technology Division, Analog Devices Inc., Boston, MA, where he is involved with research and development projects related to power line communication circuits and networks. He is also a founder and Technical Manager of the Research and Development Center for Embedded Systems Technology since September 2001. His current research interests include very large scale integration (VLSI)

and DSP circuits, algorithms, and architectures for telecommunications. He has authored or coauthored several journal papers and numerous conference contributions and technical reports. He is a reviewer for several international journals and transactions. Dr. Ghazel has been session chairman and member of Technical and Steering Committees of national and international conferences and symposia. He is a committee member and referee for evaluating new startup projects to be supported. He was the recipient (along with his research team) of the 2002 Tunisian President Award of Research in Telecommunications presented by the Ecole Supérieure des Communications (SUP’COM) de Tunis.

Fadhel M. Ghannouchi (S’84–M’88–SM’93) 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 an iCORE Professor with the Intelligent RF Radio Laboratory, Electrical and Computer Engineering Department, University of Calgary, Calgary, AB, Canada, and Tier-I Canada Research Chair in Intelligent RF Radio Technology. From 1984 to 2005, he was a Professor with the Department of Electrical Engineering, École Polytechnique de Montréal. He has taught microwave theory and techniques and RF communications systems. He held several invited positions at several academic and research institutions in Europe, North America, Japan, and North Africa. He has provided consulting services to numerous microwave and wireless communications companies. He is also the founder of AmpliX Inc., Montréal, QC, Canada, 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 communications systems, design of power- and spectrum-efficient microwave amplification systems, and design of intelligent RF transceivers for wireless communications. He has authored or coauthored approximately 300 publications. He holds seven patents. Dr. Ghannouchi is a Registered Professional Engineer in the Province of Quebec, Canada. He has served on the Technical Committees of several international conferences and symposiums.