A Wideband Digital Predistortion Based on Adaptive Subband Decomposition Technique

Transcription

1 A Wideband Digital Pedistotion Based on Adaptive Subband Decomposition Technique Xiaofang Wu,Miao Xiong Abstact In wideband communication systems, conventional pedistotion techniques suffe fom coection bandwidth limitation, which implies that the lineaization pefomance will deteioate when the signal bandwidth expands. In this pape, a subband pedistotion stuctue is poposed, aiming at coecting the dynamic nonlinea distotion of wideband powe amplifies. The pedistotion is composed of an adaptive memoyless lookup table followed by an adaptive subband linea filtebank. The fome is used to compensate fo the nonlineaity of powe amplifies, and the latte is used to compensate fo the memoy effects of powe amplifies. In addition, the identification algoithm of the subband pedistotion is descibed, taking account of coodinating the two adaptive modules. Simulation esults show that the poposed pedistotion can emakably suppess the nonlinea distotion with about db s ACPR eduction. The compaative esults of a fou-subband-filte case and a full-band-filte case show that the subband pedistotion has bette lineaization pefomance, as well as faste convegence speed due to the smalle coelation of each subband signals. Keywods digital pedistotion, adaptive filteing, subband decomposition, identification, powe amplifie I. INTRODUCTION n ecent yeas, new standads enhancing high data ates by Imeans of spectally-efficient complex modulation schemes ae tending to be applied in moden communication systems, which esults in powe amplifies (PAs) in the RF tansmitte chains handling signals that pesent high peak-to-aveage powe atios (PAPRs). Howeve, these high PAPR modulation fomats ae vey sensitive to the intemodulation distotion of the PAs. In ode to satisfy the mandatoy lineaity equiements in communication standads, significant backoff (BO) levels of opeation ae equied, thus penalizing powe efficiency in the PAs. Theefoe, thee exists contadiction between high efficiency and good lineaity. A popula solution to avoid the powe inefficient BO opeation (incease powe efficiency while keeping good lineaity) is the use of PA lineaizes. Besides the efficiency poblem, when the signal bandwidth inceases, memoy effects will appea due to the PA s intinsic This wok was suppoted in pat by the Natual Science Foundation of China unde Gant Xiaofang Wu is with the School of Infomation Science and Technology, Xiamen Univesity, Xiamen, China (coesponding autho to povide xfwu@ xmu.edu.cn). Miao Xiong is with the School of Infomation Science and Technology, Xiamen Univesity, Xiamen, China ( @qq.com). dynamics, which implies that the amplified signal not only depends on the input signal at the same time instant, but also on the histoy of the input signals as well. In the liteatue [1]-[3], two categoies of memoy effects have been identified, which ae electical and electo-themal memoy effects. The main facto that causes electical memoy effects is the vaiation of teminal impedances (biasing and matching cicuit s impedances) ove the input signal bandwidth aound the caie fequency and its hamonics, as well as at the baseband fequency. On the othe hand, tempeatue effects, taps and aging lead to electothemal memoy effects. With the bandwidth inceases, the memoy effects will incease too, and the pefomance of PA lineaizes will degade. Theefoe memoy effects have to be moved away by the lineaizes especially in wideband applications. Among lineaizes, digital pedistotion (DPD) is becoming one of the mainsteam lineaization techniques due to the apid development of digital signal pocessing (DSP) techniques [4]-[8]. Diffeent pedistotion techniques, which ae intended to compensate fo the nonlineaity as well as the memoy effects, have been epoted in the liteatue. Fo example, box-oiented models, such as Hammestein o Wiene, ae widely used fo thei explicit stuctues to descibe the cascaded nonlineaity and memoy effects [9]-[11]. Besides, the lookup table (LUT) based method has been anothe impotant banch of DPD techniques fo its low cost of hadwae ealization [1][13]. Although these conventional techniques ae poweful, they suffe fom a coection bandwidth limitation poblem due to the equied computation complexity, which implies that the lineaization pefomance will deteioate when the signal bandwidth expands [14]. In [14], a subband pedistote was poposed to solve this poblem by dividing the wideband signal into seveal naow-band signals. The pedistote can be seen as a hybid stuctue of LUT and Hammestein. Concetely, it consists of a cascade of a static LUT-based pedistote followed by an adaptive subband filtebank. The subband technique bings two majo benefits, the eduction of the length of linea subband filtes and the impovement of the adaptive convegence speed. Howeve, due to the use of a static LUT, this stuctue can only compensate fo tempeatue dift in a long peiod, i.e. electothemal memoy effect. But as mentioned above, in wideband communication systems, electical memoy effect plays a pedominant ole and beeds shot-time dynamic dift of nonlinea chaacteistic of PA. Theefoe, in this pape, we will ISSN:

2 intoduce an impoved subband based pedistotion, devoting to coecting the dynamic nonlinea behavio of powe amplifies. The pape is oganized as follows. In Section Ⅱ, the subband filteing technology is biefly pesented. The poposed subband pedistote and its adaptive algoithm ae descibed in Section Ⅲ. The Matlab simulation esults of the poposed pedistotion ae demonstated in Section Ⅳ. Finally, conclusions ae dawn in Section Ⅴ. II. SUBBAND FILTERING TECHNOLOGY A stuctue of L-channel filte bank is shown in Fig. 1, it is composed of two stages, which ae the analysis stage and the synthesis stage. In Fig. 1, x( k) is the input signal and xˆ( k) is the output signal, while h ( k), l,1,, L1} is the analysis l filte bank and fl ( k), l,1,, L1} is the synthesis filte bank. D and D espectively epesent decimato and intepolato whee D ( D L ) is the facto of decimato (intepolato). D L efes to the citically sampling case, and D L efes to the ovesampling case. Since citically sampled filte banks have contadiction between stop-band attenuation and aliasing inhibition, wheeas ove-sampled filte banks which intoduce edundancy can solve this poblem vey well, so we use ove-sampling in the following simulations. In Fig. 1, the analysis filte bank divides the input signal x( k ) into L subband signals unifomly, and then the signals ae extacted with the atio D. On the othe side, the subband signals ae intepolated by the same atio D to ecove sampling ate and the synthesis filte bank is used to emove mio components poduced by intepolating. Finally, by adding all of the subband signals we can get the full-band output x ^ ( k ). When x ^ ( k ) is equivalent to the input signal x( k ) with a pue time delay, i.e., x( k) cx( k d), whee c and d ae constants, we call x( k) x( k) is the pefect econstuction (PR) of x( k ). ^ x ( k ) Fig. 1 L-channel filte bank In the system shown in Fig. 1, the main distotion of vesus x( k ) usually divides into thee kinds: aliasing distotion, amplitude distotion and phase distotion. Theefoe, in ode to ensue the pefect econstuction of the filte bank, the key to design filte bank is to eliminate these distotions. We uses the cosine-modulated filte bank (CMFB) which is modulated by a low-pass pototype filte, thus the optimization poblem of the filte bank can be simplified to a low-pass pototype filte s optimization poblem. We suppose the L-channel cosine-modulated filte bank is built on a low-pass pototype filte function hn ( ) with the cut-off fequencies L and the length N. So the functions of analysis filte bank and synthesizing filte bank ae as follows: N 1 k hk ( n) h( n)cos[( k.5)( n ) ( 1) 4] (1) L N 1 k gk ( n) h( n)cos[( k.5)( n ) ( 1) 4] () L i.e., hk ( n) and gk ( n ) ae modulated by hn ( ) with shift k, whee k,1,,, L 1. The filte bank got fom L L (1) and () can achieve linea phase, so we only need to eliminate amplitude distotion and aliasing distotion. We use linea iteative optimization method [15] to design the pototype low-pass filte, whose advantage is tansfoming the nonlinea optimization poblem into an optimization poblem of linea equation, thus the computational complexity can be educed. III. SUBBAND DIGITAL PREDISTORTION The poposed stuctue of the subband digital pedistotion is shown in Fig.. The pedistote consists of a memoyless adaptive lookup table (LUT) module and a subband adaptive filte bank module. The latte is fomed by inteposing a pocessing stage to the L-channel filte bank descibed in Section Ⅱ, i.e., it is a cascade of the analysis stage, the pocessing stage and the synthesis stage. The LUT is used to compensate fo the nonlineaity of powe amplifie, and the subband adaptive filte bank is designed to compensate fo the memoy effects of powe amplifie, whee Fl ( z), l,1,, L1 is the linea finite impulse esponse (FIR) filte. The DPD-PA system has un ( ) as its input and zn ( ) as its output. When the adaptive algoithm conveges, ideally, we will get zn ( ) Gun ( ) Gdn ( ), whee G is the gain of the lineaized PA, and is the delay of the fowad pedistote-pa path. Compaed with the subband pedistotion stuctue in [14], the poposed stuctue has two advantages: Fist, since the LUT in [14] always keeps stationay and only the subband pocessing stage adaptively updates to mitigate the slow tempeatue dift of a PA, the subband pedistotion in [14] can only be used to compensate fo electo-themal memoy effects of the PA. Howeve, in the context of a wideband wieless PA, the electic memoy effects ae the dominant souces of the memoy effects since the themal filte time constant is too lage compaed to the invese of the signal bandwidth [3]. In this pape, the LUT is adaptive, so the pedistote can effectively compensate fo the PA s dynamic nonlinea vaiation, especially the electical memoy effects. Second, in [14], the analysis and synthesis filte banks have a tee stuctue cascaded by two-channel othogonal mio filte bank (QMFB). Since the aliasing components caied by each subband signals have to be eliminated by suitable filtes, it is a tough job to ISSN:

3 design the QMFB filtes. On the contay, the advantage of using nealy econstucted CMFB in ou pape is that by modulating a pototype low-pass filte to get the filte coefficients in L channels, it can educe the difficulty of filte bank design. whee H R () and H () epesent the amplitude signal and the phase signal of LUT espectively, and and ae the step sizes of iteations. un ( ) ( n) φ( n) H R () n ( ) x ( n ) ( n) 1 G () H Rn ( ) zn ( ) Fig. Stuctue of the subband digital pedistotion A. Adaptive Pola Lookup Table Module In this pape, the LUT method uses pola lookup table algoithm and contains two one-dimensional pedistotion tables. The tables stoe amplitude compensation infomation and phase compensation infomation as shown in Fig. 3. Fist the input signal un ( ) goes though a ectangle/pola (/p) tansfomation to get its amplitude ( n) and phase ( n), and adds to the pedistote. Then the LUT index addess is obtained fom unifom quantization of the input powe: ( n) X Int Lx ( n) Pmax Pmax (3) X Lx -1 ( n) Pmax whee ( n) is the powe of input signal, P max epesents the ideal powe uppe value and L x is the size of the lookup table. Thus, the addess X is an intege among,1,, Lx 1. By addessing, the LUT pedistote obtains amplitude and phase compensation signals. At last the coected amplitude signal n ( ) and phase signal ( n) ae tansfomed by pola/ectangle (p/) and we get the LUT pedistote s output signal x( n ). In Fig. 3, zn ( ) is the output signal of the PA, whose amplitude and phase ae R( n ) and ( n) espectively. The LUT lineaization goal is: G( n) ( n) Pmax Rn ( ) Asat ( n) P (4) max ( n) ( n) whee G is the expected linea gain, and P max is the uppe limit of the input powe. The LMS adaptive algoithm [16] is used to update LUT: H ( ) R( ( n)) n ( R( n) G( n)) n Pmax HR( ( n)) n1 Asat / ( n) ( n) Pmax H( ( n)) n1 H( ( n)) n ( ( n) ( n)) (5) ( n) Fig. 3 Stuctue of the pola lookup table B. Subband Adaptive Linea Filte Bank Module The subband adaptive filte bank uses open-loop adaptive stuctue. As shown in Fig., in the fowad path, the output of LUT, x( n ), is decomposed into L subband signals x( n),, xl 1( n) by an analysis stage as (1), then the subband signals go though a linea filte bank Fl ( z), l,1,, L1, which has the fomat of FIR as: L l 1 k F( z) w z (6) l k whee Ll is the length of the lth subband filte, and wk is the kth tap s weight needed to be estimate. The output of the FIR filtes ae synthesized by a synthesizing filte bank as (), and then the whole-band signal is sent to the PA. Also shown as in Fig., in the feedback path, the delay signal dn ( ) xn ( ) is decomposed into L subband signals d( n),, dl 1( n) afte going though the same analysis stage as in the fowad path. The feedback signal zn ( )/ G is also decomposed into L subband feedback signals z( n),, zl 1( n) afte going though the same analysis stage. The eo of each subband channel is el( n) dl( n) zl( n). The subband LMS adaptive algoithm is as follows: * Wl( i1) Wl( i) l Xl( i) el ( i) (7) l l T whee Wl() i [ w,, wl 1] l is the weight vecto of the l th subband FIR filte Fl ( z ), Xl( i) [ xl( i), xl( i1),, xl( i Ll 1)] and l is the step size. C. Adaptive Algoithm of the Subband Pedistotion Because the subband pedistote consists of two adaptive modules, it becomes an impotant issue to coodinate the two adaptive modules. Taking into account of the pedistote stuctue which can be egaded as an extended Hammestein stuctue, we use Naenda-Gallman (NG) [9] iteative algoithm, a geneal leaning algoithm fo Hammestein stuctue, as the adaptive algoithm of the whole pedistote. It has the advantage of low computational complexity. When k ISSN:

4 calculating the nonlinea module, the linea module is assumed to be still. Likewise, when calculating the linea module, the nonlinea module is assumed to be still. The LMS algoithms of the two modules wok altenately until the two modules convege. The steps of the NG adaptive algoithm ae descibed below: a. Initialize the amplitude table and the phase table of the LUT module. The amplitude values ae set to be 1 and the phase values ae set to be, which means that the LUT is an all-pass system. Initialize the weight vecto of each subband FIR filtes W() l to be [1,, ], which means that the subband filte bank is an all-pass system too. b. As shown in Fig., thee ae two switches to contol the on/off of the subband filte bank adaptive path and the LUT adaptive path espectively. Tun off the subband filte bank adaptive path to emain the filte bank still and tun on the LUT adaptive path simultaneously to update the LUT module by (5) until the table conveges. c. Altenately, tun off the LUT adaptive path and tun on the subband filte bank adaptive path at the same time, then updates the subband module by (7) until the filtes conveges. d. Judge whethe the system eo etotal ( n ) zn ( ) Gdn ( ) eaches convegence theshold. If yes, stop the iteation; else, etun to () and go on. IV. SIMULATION RESULTS In the following simulations, the econstuction pefomance of the CMFB filte bank is given, and the lineaization pefomance of the poposed subband pedistote is assessed using a two-caie WCDMA signal in Matlab envionment. Futhemoe, we compae and analyze the lineaization and convegence pefomance of the subband pedistote and the conventional Hammestein pedistote ( which is also called full-band pedistote in this pape). A. Reconstuction Pefomance of the CMFB Filte Bank The channel numbe of the CMFB filte bank (L) is set to be 4. We use the linea iteative optimization method [15] to design the low-pass pototype filte, and the tap numbe of the filte is set to be 64, and the enegy atio of pass-band and 4 stop-band is set to be 1. Fig. 4 and Fig. 5 show the fequency esponse and amplitude distotion function of the CMFB analysis filte bank espectively. All of the esults ae measued afte 5 iteations. As we can see in Fig. 4 and Fig. 5, the design esults show that the pass-band of analysis filte bank is vey flat and it can each -1dB stop-band attenuation, and the amplitude distotion is below Fig. 4 also illustates that thee ae no ovelaps between nonadjacent channels, that is to say, aliasing distotion doesn't exist. So we get the conclusion that the CMFB obtained by the linea iteation method is close to pefect econstuction. B. Lineaization Pefomance of the Subband Pedistotion In the following simulations, we compae the lineaization pefomance of the poposed subband pedistotion model with the model in [14]. We choose the augmented Wiene PA model [17] fo the sake that it descibes the dynamic nonlinea behavio accuately. Fig. 6 is the block diagam of the augmented Wiene model, which is a cascade system with a dynamic memoy module followed by a static nonlinea module. The dynamic memoy module paallelizes two banches of FIR filtes. The fist banch is a FIR filte, which contibutes the memoy effects aound the caie fequency. The second banch multiplies the input signal s amplitude by the input signal and then the poduct goes though the second FIR filte, which contibutes to the memoy effects intoduced by the non-ideal biasing and matching cicuits. Theefoe, the two-paallel-banch model epesents the electonic memoy effects accuately [17]. Amplitude Response(dB) Nomalized Fequency(/) Fig. 4 Amplitude fequency esponse of the fou-channel analysis filte bank Fig. 5 Amplitude distotion function of the fou-channel analysis filte bank ISSN:

5 vn ( ) yn ( ) zn ( ) vn ( ) vn ( ) Fig. 6 Block diagam of the augmented Wiene model Both of the tansfe functions of the two FIR filtes ae as follows: 1 3 H( z) z.344z.41z (8) z.118z The static nonlinea model uses Saleh model [18], whose AM/AM esponse function A () and AM/PM esponse function () ae as follows: f A () () (9) 1 1f whee is the input signal s amplitude.,, f, f ae model coefficients, and.1587, , f 4.33, f Two-caie WCDMA signal is used as the test signal, the size of LUT is 51, and the tap of each subband FIR filtes is 3. The channel numbe L is 4, and the decimato facto D is, which means two times ovesampling. The powe spectal density (PSD) of PA output in diffeent cases is shown in Fig. 7 fo a compaison. In Fig. 7(a), a static Saleh PA and a memoyless LUT pedistote ae used, we can see fom the figue that the memoyless LUT pedistote can almost completely compensate fo the PA s memoyless nonlinea distotion. In Fig. 7(b), the PA model changes to the augmented Wienne model, we can see that the memoyless LUT almost fail to compensate fo amplifie s distotion. If keeping LUT unchanging while update subband FIR filtes dynamically as the method used in [14], Fig. 7(c) shows that the outcome is almost same as Fig. 7(b). Howeve, if the poposed subband pedistote model and the NG iteative adaptive method ae used, Fig. 7(d) shows that the PA s nonlinea distotion is emakably cubed and the adjacent channel powe atio (ACPR) is educed by nealy db in the fist adjacent channel. In a summay, the compaison esults show that the pedistotion in [14] is not suitable to compensate fo PA s dynamic shot-time memoy effect, on the contay, the subband pedistotion we poposed in this pape achieves an outstand lineaization pefomance (a) (c) (b) (d) Fig. 7 Powe spectal density of PA output(blue line epesents signal souce, geen line epesents oiginal PA s Output, ed line epesents PA s output with pedistote ) (a)memoyless Saleh PA+Memoyless LUT pedistote; (b)augmented Wienne PA+Memoyless LUT pedistote ; (c) Augmented Wienne PA+Subband pedistote in [14] ; (d) Augmented Wienne PA+Poposed subband pedistote C. Compaison of the Subband Pedistotion and the Full-band Pedistotion The subband pedistote stuctue can be egaded as an extension of Hammestein pedistote stuctue. When the L-channel subband FIR filtes mege into a FIR filte, the suband pedistote is equivalent to a conventional Hammestein full-band pedistote. In this section, we compae the lineaization pefomance and the convegence speed of the subband pedistotion and the full-band pedistotion. Fo a fai compaison, the length of the full-band filte is set to be L times of the length of the subband filtes. The simulation uses two-caie WCDMA signal and the augmented Wienne PA model too. The pedistote coefficients ae set as follows: to the subband pedistote, 4-channel CMFB and two times ovesampling ae used, the size of LUT is 51, and the tap of each FIR is 5; to the full-band pedistote, the size of LUT is 51, and the tap of FIR is. Fig. 8 shows the PSD of the PA output. We can see that the ACPR pefomance of the subband pedistotion outpefoms the full-band pedistotion, and it indicates that the subband stuctue can emove memoy effects bette due to the fact that the deceased bandwidth mitigates the memoy effects. In othe wods, the subband stuctue can shoten the length of FIR filtes effectively. ISSN:

6 Signal Souce PA Output Subband DPD Full-band DPD Fig. 8 PSD of the PA with the full-band and the subband pedistotion Anothe advantage of subband pedistotion is that because the subband bandwidth becomes naowe, the subband signals have lowe coelation, and the subband adaptive filtes have faste convegence speed consequently. The signal coelation can be evaluated by condition numbe of the input signal s autocoelation matix, which is defined as atio of the maximum eigenvalue of the autocoelation matix to the minimum eigenvalue, i.e., max / min. When the condition numbe is smalle, the convegence speed of LMS algoithm is faste [19]. Table 1 compaes the condition numbes of full-band signals with the subband signals unde diffeent filte taps. Table 1 Condition numbes of full-band and subband signals Filte Type Filte Condition Numbe Tap ( max / min ) Full-band 1 7.5e+3 4-Channel Channel Subband Channel Channel Channel Full-band 5.86e+6 4-Channel Subband 4-Channel Subband Channel e+4 Channel Channel Channel Full-band e+7 Channel e+5 Channel Channel e+3 Channel The compaison esults of Table 1 show that with the filte tap inceasing, the condition numbe becomes bigge. As a esult, unde the same iteation step size, the convegence speed of LMS algoithm becomes slowe. Futhemoe, the condition numbes of the subband decomposed signals ae much smalle than the coesponding full-band signal; theefoe the convegence popety of the subband pedistotion is bette than the full-band one. Fig. 9 shows the convegence pefomance of the full-band pedistotion and the subband pedistotion. The taps ae set to be 5 fo the subband filtes and fo the full-band filte espectively. The iteation step sizes ae set to be.. It is obvious that the convegence speed of the subband pedistotion is faste than the full-band pedistotion. Once convegence, the nomalization mean squae eo (NMSE) of the subband pedistotion is about db while the full-band is about -3.6 db. NMSE(dB) Leaning Cuve Fou Subband Full Band Iteations Fig. 9 Convegence cuve of the full-band pedistotion and the subband pedistotion V. CONCLUSION A digital pedistote based on subband decomposition has been intoduced in this pape, which consists of an adaptive LUT and an adaptive subband linea filte bank. The Naenda-Gallman iteative algoithm is used to identify the pedistote coefficients of the two modules coodinately. The simulation esults show a good lineaization pefomance of the poposed pedistote. Futhemoe, compaed to a conventional full-band pedistotion, the subband achitectue acceleates the convegence speed by deceasing signal coelation. REFERENCES [1] J. H. K. Vuolevi, T. Rahkonen and J. P. A. Manninen, Measuement technique fo chaacteizing memoy effects in RF powe amplifies, IEEE Tans. Micow. Theoy Tech., vol. 49, no. 8, pp , 1. [] J. P. Matins, P. M. Cabal, N. B. Gavalho, and J. C. A. Pedo, Metic fo the quantification of memoy effects in powe amplifies, IEEE Tans. Micow. Theoy Tech., vol. 54, no. 1, pp , 6. [3] P. Roblin, S. K. Myoung, D. Chaillot, Y. G. Kim, A. Fathimulla, J. Stahle and S. Bibyk, Fequency-selective pedistotion lineaization of RF powe amplifies, IEEE Tans. Micow. Theoy Tech., vol. 56, no. 1, pp , 8. [4] Y. Ma, Y. Yamao, Y. Akaiwa, Wideband digital pedistotion using spectal extapolation of band-limited feedback signal, IEEE Tans. Cicuits and Systems I: Regula Papes, vol. 61, no. 7, pp. 8897, 14. [5] H. Cao, H. M. Nemati, A. S. Tehani, T. Eiksson and C. Fage, Digital pedistotion fo high efficiency powe amplifie achitectues using a dual-input modeling appoach, IEEE Tans. Micow. Theoy Tech., vol. 6, no., pp , 1. ISSN:

7 [6] C. D. Pesti, D. F. Kimball and P. M. Asbeck, Close-loop digital pedistotion system with fast eal-time adaptation applied to a handset WCDMA PA module, IEEE Tans. Micow. Theoy Tech., vol. 6, no. 3, pp , 1. [7] M. Rawat, K. Rawat, F. M. Ghannouchi, Genealized ational functions fo educed-complexity behavioal modeling and digital pedistotion of boadband wieless tansmittes, IEEE Tans. Instum. Meas., vol. 63, no., pp , 14. [8] D. R. Mogan, Z. Ma, J. Kim, M. G. Ziedt, J. Pastalan, A genealized memoy polynomial model fo digital pedistotion of RF powe amplifies, IEEE Tans. Signal Pocess., vol. 54, no. 1, pp , 6. [9] L. Ding, R. Raich and G. T. Zhou, A Hammestein pedistotion lineaization design based on the indiect leaning achitectue, IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocess., Olando, USA, pp. Ⅲ689-Ⅲ 69,. [1] X. Wu and J. Shi, Adaptive pedistotion using cubic spline nonlineaity based Hammestein modeling, IEICE Tans. Fundamentals, vol. E95. A, no., pp , 1. [11] J. Moon and B. Kim, Enhanced Hammestein behavioal model fo boadband wieless tansmittes, IEEE Tans. Micow. Theoy Tech., vol. 59, no. 4, pp , 11. [1] P. Jadin and G. Baudoin, Filte lookup table method fo powe amplifie lineaization, IEEE Tans. Vehicula Tech., vol. 56, no. 3, pp , 7. [13] H. Li, D. H. Kwon, D. Chen and Y. Chiu, A fast digital pedistotion algoithm fo adio-fequency powe amplifie lineaization with loop delay compensation, IEEE Jounal of Selected Topics in Signal Pocess., vol. 3, no. 3, pp , 9. [14] O. Hammi, S. Boumaiza, M. Jaidance-Saidane and F. M. Ghannouchi, Digital subband filteing pedistote achitectue fo wieless tansmittes, IEEE Tans. Micow. Theoy Tech., vol. 53, no. 5, pp , 5. [15] C. K. Chen and J. H. Lee, Design of quadatue mio filtes with linea phase in the fequency Domain, IEEE Tans. Cicuits and Systems Ⅱ, vol. 39, no. 9, pp , 199. [16] D. Zenobio, G. Santella and F. Mazzenga, Adaptive lineaization of powe amplifie in othogonal multicaie schemes, IEEE Int. Wieless Communication System Symposium, NY USA, pp. 5-3, Nov [17] T. Liu, S. Boumaiza and F. M. Ghannouchi, Augmented Hammestein pedistote fo lineaization of boad-band wieless tansmittes, IEEE Tans. Micow. Theoy Tech., vol. 54, no. 4, pp , 6. [18] A. Saleh, Fequency-independent and fequency-dependent nonlinea model models of TWT amplifies, IEEE Tans. Commun., vol. 9, no. 11, pp , [19] S. Hakin, Adaptive filte Theoy, 3d ed., Pentice-Hall: Englewood Cliffs, N. J., Xiaofang Wu eceived the B.S. and the M.S. degees in electonic engineeing fom Xiamen Univesity, China, in 1993 and 1997 espectively, and the Ph. D. degee in communication and infomation systems fom Xiamen Univesity in 11. She is cuently an associate pofesso with the School of Infomation Science and Technology, Xiamen Univesity, China. He eseach inteests ae in the pedistotion lineaization of nonlinea powe amplifies fo wieless applications, analog cicuits design, and wieless communication signal pocessing. Miao Xiong eceived the B.S. degee in electonic infomation engineeing fom Nanjing Agicultual Univesity, 13. He is a maste degee candidate at Xiamen Univesity, China. His eseach inteest is digital pedistotion fo powe amplifies. ISSN: