Cancellation of Power Amplifier Induced Nonlinear Self-Interference in Full-Duplex Transceivers

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1 Cacellatio o Power Ampliier Iduced Noliear Sel-Itererece i Full-Duplex Trasceivers Lauri Attila, Dai Korpi, Ville Syrjälä, ad Mikko Valkama Departmet o Electroics ad Commuicatios Egieerig, Tampere Uiversity o Techology, Filad lauri.attila@tut.i, dai.korpi@tut.i, ville.syrjala@tut.i, mikko.e.valkama@tut.i arxiv: v1 [cs.it] 14 Ja 214 Abstract Recetly, ull-duplex (FD) commuicatios with simultaeous trasmissio ad receptio o the same chael has bee proposed. The FD receiver, however, suers rom ievitable sel-itererece (SI) rom the much more powerul trasmit sigal. Aalogue radio-requecy (RF) ad basebad, as well as digital basebad, cacellatio techiques have bee proposed or suppressig the SI, but so ar most o the studies have ailed to take ito accout the iheret oliearities o the trasmitter ad receiver rot-eds. To ill this gap, this article proposes a ovel digital oliear itererece cacellatio techique to mitigate the power ampliier (PA) iduced oliear SI i a FD trasceiver. The techique is based o modelig the oliear SI chael, which is comprised o the oliear PA, the liear multipath SI chael, ad the RF SI caceller, with a parallel Hammerstei oliearity. Stemmig rom the modelig, ad appropriate parameter estimatio, the kow trasmit data is the processed with the developed oliear parallel Hammerstei structure ad suppressed rom the receiver path at digital basebad. The results illustrate that with a give IIP3 igure or the PA, the proposed techique eables higher trasmit power to be used compared to existig liear SI cacellatio methods. Alteratively, or a give maximum trasmit power level, a lower-quality PA (i.e., lower IIP3) ca be used. I. INTRODUCTION FULL-DUPLEX commuicatios usig the same carrier or simultaeous trasmissio ad receptio has log bee cosidered impossible due to the high sel-itererece (SI) rom the trasmitter to the receiver path. Recetly, several research groups have experimetally demostrated that, by utilizig various radio-requecy ad digital basebad SI cacellatio techiques, FD commuicatios may ideed be possible with trasmit powers i the local area commuicatios (e.g. WiFi) rage ( 2 dbm) [1] [7]. I [8], it was oud that the oliear sel-itererece due to power ampliier (PA) oliearity may become a bottleeck i FD commuicatios with higher trasmit powers. Eve though the trasmit-receive atea isolatio ad may RF SI cacellatio techiques atteuate the PA-iduced itermodulatio distortio, such oliear SI ca still be higher tha The research work leadig to these results was uded by the Academy o Filad (uder the projects #259915, # I-bad Full-Duplex MIMO Trasmissio: A Breakthrough to High-Speed Low-Latecy Mobile Networks ), the Fiish Fudig Agecy or Techology ad Iovatio (Tekes, uder the project Full-Duplex Cogitive Radio ), the Liz Ceter o Mechatroics (LCM) i the ramework o the Austria COMET-K2 programme, ad Emil Aaltoe Foudatio. the weak received sigal ad prevet successul detectio [8]. So ar, oly oe o the digital SI cacellatio techiques i the literature has cosidered these oliear eects explicitly [6]. 1 The purpose o this article is to study the eects o PA oliearity o received sigal quality, i ull duplex trasceiver cotext, with various amouts o RF cacellatio (passive+active) ad liear digital SI cacellatio, ad to propose a ovel oliear SI cacellatio techique to mitigate such oliear eects. The proposed techique ca be utilized i digital basebad or digitally-assisted aalog SI cacellatio. We demostrate the perormace improvemets with ull waveorm simulatios, showig that with typical RF rot-ed ad sigal parameters, up to 1 db higher trasmit power ca be used without degradig the receiver sigal-toitererece-plus-oise ratio (SINR) by usig the proposed oliear SI cacellatio techique istead o traditioal liear SI cacellatio. Alteratively, assumig some maximum trasmit power level, utilizig the proposed techique eables usig a PA with a lower IIP3 igure. The rest o this paper is orgaized as ollows. I Sectio II, the challeges preseted by a oliear PA i the cotext o ull-duplex trasceivers are discussed. I Sectio III, the proposed oliear digital SI cacellatio algorithm is preseted. The, i Sectio IV, the perormace o the proposed algorithm is evaluated with waveorm simulatios. Fially, the coclusios are draw i Sectio V. II. PA NONLINEARITY CHALLENGE IN FD TRANSCEIVER The assumed FD trasceiver model is show i Fig. 1. I this device, separate trasmit ad receive ateas provide atural isolatio betwee the trasmitter ad receiver paths, ad it is the basic FD trasceiver model assumed i most o the existig literature [4], [5]. A otable exceptio is [1], where a sigle-atea device is assumed alog with a circulator based isolatio structure to provide passive cacellatio o up to 4 45 db over a 8 MHz bad. However, the chose FD model with separate trasmit ad receive ateas does ot limit the applicability o the proposed techiques to this structure oly, but the techiques ca be applied i circulator based sigleatea FD devices as well. 1 I [6], a similar model as the oe proposed i this article, was used to model the cascade o the PA ad the multipath SI chael. This work was uavailable at the time o submissio o our origial mauscript.

2 Tx Trasmit RF chai Sel-itererece Atteuator - 3 db PA VGA IQ Mixer LPF DAC Selitererece chael model Coder Tx bits i Rx Amplitude & phase matchig RF cacellatio sigal LO Receive RF chai Digital cacellatio samples Rx bits out RF cacellatio BPF LNA IQ Mixer LPF VGA ADC Digital cacellatio Detector Fig. 1. A block diagram o the assumed ull-duplex direct-coversio trasceiver. I geeral, there ca be our levels o SI cacellatio i a FD device: 1) Passive SI mitigatio; the atea isolatio betwee trasmit ad receive ateas i a separate-atea FD device, or the circulator isolatio i a shared-atea FD device 2) Active spatial SI mitigatio, i.e., beamormig i multiatea FD devices 3) Active aalog cacellatio; SI cacellatio i aalog RF or basebad usig the trasmit sigal as a reerece 4) Active digital cacellatio; suppressio o the residual SI with digital sigal processig The state-o-the-art passive cacellatio techiques, utilizig atea desig ad placemet techiques [2] [5], or circulator desig [1], ca yield up to 4 45 db o cacellatio. Active RF cacellatio ca give a extra db o SI cacellatio, depedig o the implemetatio [1] [6], thus brigig the maximum achievable aalog cacellatio to the rage o 65 9 db. Up to this poit the atteuatio is the same or the liear ad the oliear SI term. The, digital basebad cacellatio has bee show to brig aother 2 3 db o atteuatio, at best [2], [3], [5]. However, the digital cacellatio techiques reported up to ow have oly cosidered liear SI, thus relyig o ully liear sigal processig. I the ollowig, we irst show with simple system power calculatios that uder realistic radio rot-ed ad sigal parameters rom LTE user equipmet, these cacellatio levels are ot eough to atteuate the power ampliier iduced oliearities below the oise loor at higher trasmit power levels. Motivated by this, we the propose ovel oliear digital sel-itererece cacellatio methods to suppress such distortio below the oise loor i Sectio III. Table I shows the baselie parameters o the trasceiver used or the motivatig system calculatios, ad also or the simulatios. For the system calculatios example, we assume 4 db o passive cacellatio, 3 db o active aalog cacellatio, ad a variable amout o liear digital cacellatio to keep the liear SI term below the thermal oise loor at all power levels. These are somewhat optimistic assumptios, because or example the amout o achievable digital liear cacellatio depeds very much o the quality o the SI chael estimates, which i tur are aected greatly by the levels o oliear SI as well as thermal ad quatizatio oise. The power level o the actual received sigal o iterest is assumed to be 5 db above the sesitivity level i the ollowig calculatios. I additio, a automatic gai cotrol algorithm is assumed to be tuig the gai o the VGA to match the dyamic rage o the sigal to the dyamic rage o the aalog-to-digital coverter (ADC). Fig. 2 shows the powers o the dieret sigal ad itererece terms at the detector iput o the receiver. Despite the somewhat optimistic assumptios, the oliear SI, stemmig rom the PA oliearity, becomes the most powerul itererece term already with trasmit power o 14 dbm. With more realistic passive isolatio ad RF cacellatio igures, the PAiduced oliear sel-itererece would be emphasized eve urther. Details o the aalysis techique ca be oud rom [8]. III. NONLINEAR SELF-INTERFERENCE CHANNEL MODELING, ESTIMATION AND CANCELLATION A. Basebad oliear sel-itererece chael model We deote the origial digital basebad trasmit sigal by x. For discrete-time basebad modelig o the oliear PA, we assume the widely-deployed parallel Hammerstei (PH) model, give as x PA = P M 1 k= p,k ψ p (x k ), (1) where the basis uctios are deied as ψ p (x ) = x p 1 x, p, are FIR ilter impulse resposes o the PH braches, M

3 Power o dieret sigal compoets (dbm) Atea separatio: 4 db, RF cacellatio: 3 db PA gai = 2 db, = 15 dbm 7 PA oliearity 8 Sel itererece Sigal o iterest 9 Quatizatio oise Thermal oise Trasmit power (dbm) Fig. 2. A example plot o the power levels o the dieret sigal compoets at receiver chai detector iput with respect to trasmit power. x PA a Noliear SI chael y1() y 3 () yp c () SI chael h RF SI cac. ˆ 1, ˆ 3, Estimated oliear SI chael ˆ P, c SI x ˆSI x s w Digital SI cacellatio Fig. 3. A block diagram illustratig the trasceiver modelig ad the proposed caceller structure. sˆ TABLE I THE PARAMETERS OF THE FULL-DUPLEX TRANSCEIVER. Parameter SNR requiremet Badwidth Receiver oise igure Sesitivity Received sigal power Atea separatio RF cacellatio Value 1 db 12.5 MHz 4.1 db dbm dbm 3/4/5 db 3 db ADC bits 12 ADC voltage rage PAPR o the TX/RX waveorm PA gai PA IIP3 PA 1 db compressio poit 4.5 V 1 db 2 db 15 dbm 24.5 dbm deotes the memory legth, ad P deotes the oliearity order o the PH model [9] [11]. The PH model has bee show to be a versatile tool or direct as well as iverse modelig o power ampliiers [9] [12]. The multipath SI chael betwee TX ad RX ateas is modeled with a FIR ilter h. RF cacellatio aims to mitigate the mai compoet o the multipath SI chael. To model possible requecy-depedecy i the RF caceller path, due to or example delay mismatch or usig a actual multitap RF caceller [6], [13], we model the RF SI caceller respose also with a FIR ilter a operatig o x PA. The received sel-itererece sigal ater the RF SI caceller ca the be writte as (with the omial propagatio delay removed) x SI = h x PA P M 1 = = P k= M 2 a x PA ((h k a k ) p,k ) ψ p (x k ) k= M 1 p,k ψ p (x k ). (2) Here, p,k deote the eective model coeiciets o the overall oliear SI chael, ad M 1 ad M 2 are the o-causal ad causal memory depths o the model, respectively. Thereore, the overall SI sigal model, comprisig o the oliear PA, the multipath SI chael, ad the RF caceller, ca also be expressed as a parallel Hammerstei model. Despite the oliear ature o the model, it is liear i the parameters p,k, thus acilitatig eiciet estimatio with, or example, liear least-squares methods. Notice also that the PH oliearity ca model perectly a variety o other PAplus-chael models as well, or example the cascade o a polyomial oliearity ad a LTI system, or the cascade o a Hammerstei oliearity ad a LTI system, i additio to modelig the cascade o a PH oliearity ad a LTI system. Thereore, choosig the PH oliearity as the cascade model is well justiied i this sese also. B. Digital SI caceller parameter estimatio The objective is ow to estimate the parameters p,k based o the above SI sigal model, ad the to regeerate the SI sigal ad subtract it rom the overall received sigal at digital basebad. A block diagram o the overall oliear SI chael, its modellig, regeeratio, ad digital cacellatio is show i Fig. 3. There, the dieret braches, correspodig to oliear terms o dieret order, ca be see, alogside

4 with the coeiciets p,. The total received sigal beore digital cacellatio is ow give as x RF = s + w + x SI, (3) where s is the actual received sigal o iterest, w is the additive oise compoet, ad x SI is the received selitererece sigal whose model was give i (2). Stemmig rom the previous modelig, the output o the digital SI caceller is give as ŝ = x RF with the sel-itererece estimate ˆx SI ˆx SI = P c M c2 ˆx SI, (4) give as k= M c1 ˆ p,k ψ p (x k ). (5) Here, P c is the oliearity order, ad M c1 ad M c2 are the o-causal ad causal memory depths o the digital SI caceller. To derive the estimator or p,k, we irst write vector represetatios o the relevat ormulae with L observed samples o x RF : Ψ p = x RF = Ψ + s + w, with RF de x = [ x RF x RF +1 x RF +L 1 de = [ 1, Mc1 1,Mc2 3, Mc1 Pc, Mc1 Pc,Mc2 ] T Ψ de = [ Ψ 1 Ψ 3 Ψ Pc ] ] T ψ p(+m c1) ψ p(+m c1 1) ψ p( M c2) ψ p(+m c1+1) ψ p(+m c1) ψ p( M c2+1) ψ p(+m c1+l 1) ψ p(+m c1+l 2) ψ p( M c2+l 1) The least-squares estimator is the derived as the vector which miimizes the power o the digital SI caceller output ŝ, treatig the received sigal o iterest s as oise, as ˆ LS = arg mi x RF ˆx SI 2 = arg mi x RF Ψˆ 2. Assumig ull colum rak i Ψ, we obtai the well-kow solutio ˆ LS = (Ψ H Ψ) 1 Ψ H x RF. The basis matrix Ψ is kow iside the device, so the estimatio ca be perormed durig actual data trasmissio, or by usig embedded pilot sigals withi the data rame. I the latter case the calculatio o the pseudoiverse (Ψ H Ψ) 1 Ψ H ca be perormed a priori ad stored, thereore reducig the real-time computatioal load. Adaptive estimatio techiques, or example usig the recursive LS (RLS) algorithm, usually avoid the matrix iversio, ad are thereore practically more appealig compared to the above block LS solutio whe actual trasmit data is used or estimatio. These are straightorward to derive based o adaptive ilter theory literature (e.g., [14]) ad are let to the reader. TABLE II ADDITIONAL PARAMETERS FOR THE WAVEFORM SIMULATOR. Parameter Costellatio Value 16-QAM Number o subcarriers 64 Number o data subcarriers 48 Guard iterval Sample legth 16 samples s Symbol legth 4 µs Sigal badwidth 12.5 MHz Oversamplig actor 4 PA memory legth 6 K-actor o the SI chael 35.8 db SI chael legth 5 IV. NUMERICAL RESULTS AND ANALYSIS I this Sectio, we perorm ull waveorm simulatios o the whole ull-duplex trasceiver with Matlab/Simulik to test ad aalyze the proposed oliearity model ad its estimatio ad cacellatio. The trasceiver parameters are the same as i the system calculatio example i Sectio II. The simulated trasmit ad receive waveorms are OFDM sigals with the parameters give i Table II. The SI couplig chael betwee TX ad RX ateas is modeled as a FIR ilter, icludig the mai path plus our multipath compoets. The power dierece betwee the mai compoet ad the multipath compoets (K-actor) is approximately 36 db [15]. I the simulatios, RF cacellatio is implemeted by subtractig the trasmitted sigal rom the received sigal with a small amplitude ad phase mismatch such that the speciied amout o total SI power reductio is obtaied. For the PA, a Wieer model is used, which meas that the model cosists o a cascade o a 5th-order FIR ilter modelig the memory eects ad a polyomial modelig the actual oliear behaviour. Sice there is a LTI chael at the iput o the oliearity, the parallel Hammerstei model is ot able to perectly model the PA, ad there will iheretly be some residual SI due to a model mismatch. I this paper, the used igure-o-merit is the SINR o the detector iput sigal. The PH oliear chael model has oliearity order 5, ad the ilter legths o the PH model are 5 or all the braches. Furthermore, 1 OFDM symbols, or 32 samples, are used or their estimatio i each realizatio. For estimatig the liear SI chael oly, ormal liear leastsquares estimatio is employed with the same umber o samples ad the same ilter legth. Figure 4 shows the SINR vs. trasmit power whe oly liear SI cacellatio is employed, ad whe the proposed oliear SI cacellatio structure is used. Both o these curves are plotted or three dieret values o atea separatio. The proposed oliear techique allows usig approximately 1 db higher trasmit power tha with liear SI cacellatio, regardless o the amout o atea separatio. Furthermore, with atea separatio o 5 db, the oliear SI cacellatio techique achieves the same idelity as without

5 RF cacellatio: 3 db, PA gai = 2 db = 15 dbm, P1dB PA = 24.5 dbm, M, N = 32, P c RF cacellatio: 3 db, PA gai = 2 db Trasmit power = 2 dbm, M, N = 32, P c SINR (db) 5 1 SINR (db) Noliear cacellatio, At. sep. = 3 db Liear cacellatio, At. sep. = 3 db 2 Noliear cacellatio, At. sep. = 4 db Liear cacellatio, At. sep. = 4 db 25 Noliear cacellatio, At. sep. db Liear cacellatio, At. sep. db Trasmit power (dbm) 15 Noliear cacellatio, At. sep. = 3 db Liear cacellatio, At. sep. = 3 db 2 Noliear cacellatio, At. sep. = 4 db Liear cacellatio, At. sep. = 4 db 25 Noliear cacellatio, At. sep. db Liear cacellatio, At. sep. db (dbm) Fig. 4. SINR at detector iput with ad without oliear cacellatio or various TX powers, ad or dieret amouts o atea separatio. Fig. 6. SINR at detector iput with ad without oliear cacellatio or various PA IIP3 igures. 6 RF cacellatio: 3 db, PA gai = 2 db = 15 dbm, P1dB PA = 24.5 dbm, M, N = 32, P c 6 RF cacellatio: 3 db, PA gai = 2 db Trasmit power = 2 dbm, M, N = 32, P c 5 5 Digital SI atteuatio (db) Noliear cacellatio, At. sep. = 3 db Liear cacellatio, At. sep. = 3 db Noliear cacellatio, At. sep. = 4 db 1 Liear cacellatio, At. sep. = 4 db Noliear cacellatio, At. sep. db Liear cacellatio, At. sep. db Trasmit power (dbm) Digital SI atteuatio (db) Noliear cacellatio, At. sep. = 3 db Liear cacellatio, At. sep. = 3 db Noliear cacellatio, At. sep. = 4 db 1 Liear cacellatio, At. sep. = 4 db Noliear cacellatio, At. sep. db Liear cacellatio, At. sep. db (dbm) Fig. 5. The amout o achieved digital cacellatio with ad without oliear modelig or various TX powers, ad or dieret amouts o atea separatio. ay SI up to a trasmit power o 2 dbm. Thus, the proposed techique allows extedig the operatig rage o the device i a sigiicat maer. Furthermore, cosiderig that the umber o samples used or the estimatio is oly 32, this is a promisig result. The achieved amouts o digital SI atteuatio, correspodig to Fig. 4, are show i Fig. 5. Here, the amout o achieved digital cacellatio is deied as the decrease i the power o the total SI sigal i the digital domai. It ca be observed that i the liear operatig regio o the PA, a higher amout o digital cacellatio is achieved with liear processig, as a lower umber o parameters has to be estimated tha with oliear processig, which suers rom over-parameterizatio. Takig a look back at Fig. 2, this behavior is atural sice the power o the oliear distortio is well below the thermal oise loor with these lower trasmit powers. However, as the trasmit power icreases, the power o the PA-iduced Fig. 7. The amout o achieved digital cacellatio with ad without oliear modelig or various PA IIP3 igures. oliear distortio becomes more sigiicat, ad the gai achieved by perormig oliear SI cacellatio icreases. The poit at which oliear SI cacellatio becomes more beeicial tha liear cacellatio depeds o the amout o aalog SI atteuatio. With very high trasmit powers, the amout o achievable SI supressio with the proposed oliear SI cacellatio algorithm starts decreasig due to the quatizatio oise loor ad model mismatch. The latter is caused by the dierece betwee the cosidered Wieer PA model, ad the parallel Hammerstei model used or estimatig the oliearity coeiciets. Figure 6 illustrates SINR vs. IIP3 o the PA, agai with three dieret values o atea separatio. The purpose is to id out whether a lower-quality PA with a lower IIP3 igure could be used i oliear SI cacellatio is employed. I these simulatios, the value o the 1 db compressio poit is always chose as 9.5 db higher tha the IIP3 igure. Fig. 6 coirms

6 that a less liear PA ca ideed be used with the proposed oliear SI cacellatio algorithm, by demostratig up to 15 db reductio i IIP3 compared to usig liear SI cacellatio oly. With higher values or atea separatio, it is possible to achieve the ideal SINR o 15 db eve with a IIP3 igure o 14 dbm whe usig the proposed oliear SI cacellatio algorithm. With liear processig, this is ot possible, as ca be observed rom Fig. 6. However, it is importat to ote that usually the liearity requiremets or the PA are also set by the spectrum emissio stadards, ad thus it might ot be possible to decrease the IIP3 igure beyod a certai poit. The correspodig amout o achieved digital cacellatio is show i Figure 7. It ca be observed that the amout o atea separatio does ot sigiicatly aect the achievable digital SI atteuatio with a trasmit power o 2 dbm. Furthermore, with a less liear PA, the dierece betwee the perormaces o liear ad oliear cacellatio algorithms is airly large. However, as the liearity o the PA improves, the diereces i the achieved digital SI atteuatio decrease. V. CONCLUSION This article studied the eects ad digital cacellatio o PA iduced oliear sel-itererece i ull-duplex trasceivers. It was irst show through trasceiver system power calculatios i a LTE uplik-like sceario that the PA oliearities are a sigiicat problem with trasmit powers exceedig about 1 dbm. A oliear digital sel-itererece cacellatio techique was the proposed to hadle both the liear ad oliear sel-itererece simultaeously. Waveorm simulatios demostrated the proposed caceller s ability to exted the usable trasmit power rage by at least 1 db, or alteratively, to make it possible to use a lower-quality PA i the trasmitter. This is see as a major step ahead towards practical deploymet o ull-duplex radio commuicatios with practical low-cost RF circuits, ad i particular, with practical oliear power ampliiers. As uture work, we will cosider implemetig a actual ull-duplex trasceiver with a typical oliear PA, ad evaluate the perormace o the proposed digital cacellatio algorithm uder realistic coditios. REFERENCES [1] M. E. Kox, Sigle atea ull duplex commuicatios usig a commo carrier, i Proc. 13th Aual Wireless ad Microwave Techology Coerece (WAMICON), 212, pp [2] J. I. Choi, M. Jai, K. Sriivasa, P. Levis, ad S. Katti, Achievig sigle chael ull duplex wireless commuicatio, i Proc. 16th Aual Iteratioal Coerece o Mobile Computig ad Networkig. ACM, 21, pp [3] M. Jai, J. I. Choi, T. Kim, D. Bharadia, S. Seth, K. Sriivasa, P. Levis, S. Katti, ad P. Siha, Practical, real-time, ull duplex wireless, i Proc. 17th Aual Iteratioal Coerece o Mobile Computig ad Networkig. New York, NY, USA: ACM, 211, pp [4] A. Sahai, G. Patel, ad A. Sabharwal, Pushig the limits o ull-duplex: Desig ad real-time implemetatio, Departmet o Electrical ad Computer Egieerig, Rice Uiversity, Techical Report TREE114, Jul [5] M. Duarte ad A. Sabharwal, Full-duplex wireless commuicatios usig o-the-shel radios: Feasibility ad irst results, i Proc. 44th Asilomar Coerece o Sigals, Systems, ad Computers, 21. [6] D. Bharadia, E. McMili, ad S. Katti, Full duplex radios, i SIG- COMM 13, Hog Kog, Chia, August 213. [7] E. Everett, A. Sahai, ad A. Sabharwal, Passive sel-itererece suppressio or ull-duplex irastructure odes, 213. [Olie]. Available: [8] D. Korpi, T. Riihoe, V. Syrjälä, L. Attila, M. Valkama, ad R. Wichma, Full-duplex trasceiver system calculatios: Aalysis o ADC ad liearity challeges, submitted ad uder review i IEEE Trasactios o Wireless Commuicatios, 213. [9] L. Dig, G. Zhou, D. Morga, Z. Ma, J. Keey, J. Kim, ad C. Giardia, A robust digital basebad predistorter costructed usig memory polyomials, IEEE Trasactios o Commuicatios, vol. 52, o. 1, pp , 24. [1] M. Isaksso, D. Wisell, ad D. Roow, A comparative aalysis o behavioral models or RF power ampliiers, IEEE Trasactios o Microwave Theory ad Techiques, vol. 54, o. 1, pp , 26. [11] L. Attila, P. Hadel, ad M. Valkama, Joit mitigatio o power ampliier ad I/Q modulator impairmets i broadbad direct-coversio trasmitters, IEEE Trasactios o Microwave Theory ad Techiques, vol. 58, o. 4, pp , 21. [12] H. Ku ad J. Keey, Behavioral modelig o oliear r power ampliiers cosiderig memory eects, IEEE Trasactios o Microwave Theory ad Techiques, vol. 51, o. 12, pp , 23. [13] Y. Choi ad H. Shirai-Mehr, Simultaeous trasmissio ad receptio: Algorithm, desig ad system level perormace, IEEE Trasactios o Wireless Commuicatios, vol. PP, o. 99, pp. 1 19, 213. [14] S. Hayki, Adaptive Filter Theory (3rd Ed.). Upper Saddle River, NJ, USA: Pretice-Hall, Ic., [15] M. Duarte, C. Dick, ad A. Sabharwal, Experimet-drive characterizatio o ull-duplex wireless systems, IEEE Trasactios owireless Commuicatios, vol. 11, o. 12, pp , Dec. 212.