Performance analysis of qam modulations applied to the linc transmitter

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 42, NO. 4, NOVEMBER 1993 399 Pe o mance Analysis o QAM Modula ions Applied o he LINC T ansmi e Fe nando J. Casade all, Membe , IEEE, and An onio Valdo inos, S uden Membe , IEEE, Abs ac - Fu u e mobile adiocommunica ions sys ems will use linea modula ions because hey show a highe spec um e iciency han classical FM modula ions. Fu he mo e, in o de o use hese modula ions in hand-po able equipmen , powe e iciency is also eques ed o he powe ampli ie s. To ob ain bo h powe and spec um e iciency, a LINC' ansmi e can be conside ed. In his pape , we p esen an analysis o he e ec o di e en ypes o imbalances be ween he pa allel signal pa hs in a LINC ansmi e . The sys em deg ada ions a e desc ibed in e ms o adjacen channel ejec ion, ( UR ). Classical aised cosine (Nyquis il e ed) 4, 16, and 64 QAM modula ion pa e ns a e aken in o accoun , and in all cases, uppe bounds o adjacen channel ejec ion as unc ion o he gain and phase imbalances as well as o he gua d band be ween adjacen channels a e p esen ed. Mo eo e , he impac o hese imbalances in he sys em pe o mance, cha ac e ized by means o he signal- o-noise a io (SNR) inc emen needed o main ain a ixed e o a e, is also conside ed. The esul s show ha gain and phase imbalance be ween bo h RF pa hs could be a se ious limi a ion o he LINC ansmi e pe o mance. I. INTRODUCTION N MOBILE adio sys ems, he ela i e ine icien use I o he spec um by exis ing ypes o FM modula ions such as MSK, GMSK, TFM, e c., has esul ed in c owd- ing on he a ailable channels. They a e s ill widely used because hei cons an en elope p ope y is app op ia e o using powe -e icien nonlinea ampli ie s. Howe e , in he nex gene a ions o digi al cellula adio sys ems, he use o Quad a u e Ampli ude Modula ion (QAM) pa e ns will be equi ed, [l], because hey ha e a highe spec um e iciency han he p e iously men ioned FM modula ions. Bu , since QAM p esen s a noncons an en elope, i will be necessa y o conside linea powe ampli ie s which a e less e icien han he classical class-C powe ampli ie s cu en ly in use wi h he FM- ype modula ions. In o de o achie e bo h spec um and powe e iciency, se e al classical linea izing echniques o powe ampli ie s ha e been p oposed in he echnical li e a u e, [2]-[5]. These echniques a e usually ca ego ized as: Feed- o wa d, Feed- back, P edis o ion, and LINC ansmi e . Among hem, in ou opinion, one o he mos p omising is he LINC ansmi e , Manusc ip ecei ed Decembe 20, 1991; e ised Feb ua y 18, 1992, and July 16, 1992. This pape was suppo ed by he CICYT (Spain) unde G an TIC90714. The au ho s a e wi h he Depa men o Signal Theo y and Communica ions, Uni e sidad Poli 'ecnica de Ca alunya, Apdo. 30.002, 08080 Ba celona, Spain. IEEE Log Numbe 9208915. ' Ac onym o Linea ampli ica ion using Nonlinea Componen s [ .DIGITAL o( ) 1 SIGNAL I PROCESSOR I D.S.P. I I I I I L GO_MPONE_NI_' y-@-- j I k T+i I I I Fig. 1. Schema ic diag am o he LINC ansmi e . because i does no use a eedback loop, he eby gua an eeing comple e ci cui s abili y. The basic p inciple o he LINC ansmi e is o ep esen any a bi a y bandpass signal, which may ha e bo h ampli ude and phase a ia ions, by means o wo signals which a e o cons an ampli ude and only ha e phase a ia ions [5]. These wo angle modula ed signals can be ampli ied sepa a ely using e icien high-powe nonlinea de ices. Finally, he ampli ied signals a e passi ely combined o p oduce an ampli ude mod- ula ed signal. Fig. 1 shows he schema ic d awing o such sys em whe e S( ) = G . [a( ) . COS (wo + 4)] Sl( ) = V/a[sin (wo + 4 + $@)I &( ) = V/a[si i (q + 4 - $( )] (1) wi h $( ) = sin-' [@)/VI, and max [n( )] 5 V. Ob iously, he componen sepa a o is a nonlinea de ice ha could nowadays be implemen ed using digi al signal p ocessing (DSP) echniques. In a p ac ical LINC ansmi e , he e a e se e al mecha- nisms ha deg ade he o e all pe o mance; e.g., he powe gain and he delay (o phase) imbalance be ween he wo RF pa hs o he e o s due o he digi al signal p ocessing uni p oduces impe ec gene a ion o he cons an ampli ude phase-modula ed signal componen , SI ( ) and SZ ( ). Some heo e ical [7] and p ac ical [6] wo ks ha e been add essed o cha ac e ize he impac o hese ci cui mal unc- ions on he sys em pe o mance conside ing he ypical wo one as linea i y es . Howe e , o ou knowledge, he e is no ye a comple e cha ac e iza ion o hese e ec s when digi al modula ions a e conside ed in which hese deg ada ions p o- duce enhancemen o he signal powe spec um ha p oduces 400 4 Qm A,=O. 9 A,=O .6 A,=O .3 8=0.2 3.2490 5.8481 9.7469 8=0.5 2.6388 4.7498 7.9163 8=0.7 2.5745 4.9581 8.2635 p=O.9 2.9460 5.3028 8.8379 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 42, NO. 4, NOVEMBER 1993 9.7469 17.544 29.24 22.743 40.936 68.228 7.9163 14.249 23.748 18.471 33.248 55.414 8.2635 14.874 24.709 19.281 34.706 57.844 8.8379 15.908 25.514 20.622 37.119 61.865 TABLE I VALUES OF THE V PARAMETER AS FUNCTION OF THE MODULAT~ON PATTERN AND ROLL-OFF FACTOR in e e ence on he adjacen channels, hus limi ing he sys em spec um e iciency. This pape p esen s an analysis o he e ec o he e o s on he sys em pe o mance caused by he imbalance be ween he pa allel RF pa hs. In pa icula , hey ha e been cha ac e ized using wo c i e ia: adjacen channel ejec ion (UR), ha is, he a io be ween he powe in he use ul channel wi h espec o he powe in he adjacen channel, and also by he signal- o-noise a io (SNR) inc emen needed o main ain a ixed bi e o a e (BER). 4,16, and 64 QAM modula ions pa e ns wi h squa e oo aised cosine pulse shape ha e been conside ed. Mo eo e , he sensi i i y o he gain and phase imbalances o a LlNC ansmi e ha e also been compa ed o he one ob ained when a con en ional QAM modula o is conside ed [8]. 11. IMBALANCE ANALYSIS An M-QAM modula ed signal could be exp essed as S( ) = x( ) . cos (uo ) + y( ) . sin (wo ) (2) wi h m k=-ca m k=-cc whe e x( ) is he in-phase (I) componen , y( ) he quad a u e (Q) componen , {ak} and {bk} being he symbol se s ans- mi ed in I and Q channels, h",;( ) a squa e oo aised cosine pulse shape, and T he symbol pe iod. A e some algeb aic e o om (1) and (2) i can be ob ained: S,( ) =I,( ). cos(w0 ) Sz( ) = IZ( ) . cos (wo ) + Ql( ) . sin (we ) + Q2( ) . sin (we ) (3) whe e: Fo he oll-o ac o s and he QAM modula ions consid- e ed in he pape , he V alue is gi en in Table I using he a io A, = max[a( )]/V as pa ame e , whe e a( ) is he QAM signal en elope gi en by: a( ) = &q ) + yZ( ). When he e o s due o he RF p ocessing a e conside ed, he gene a ed signal could be exp essed as: S( ) = Gl[Il( ) cos (wo ) + Ql( ) sin (we )] + Gz[Iz( ) cos (we + Ad) + Q2( ) sin (we + Ad)] whe e G1 and Gz a e he ol age gain o each b anch and Ad is he phase imbalance be ween he wo RF b anches. Taking in o accoun he exp essions Il( ), Ql( ), I2( ), and Q2( ), he exp ession S( ) esul s in S( ) = GI . [Si( ) + S2( ) + i( )] whe e i( ) = {AG. sin (A+) . Q2( ) - [l - AG . COS Ad] . I2( )} COS (wo ) - {AG . sin (A#) .12( ) + [l - AG . cos Ad] . Q2( )} sin (wo ) is a esidual in e e ing signal ha appea s due o he im- balances, and AG = G2/G1. The signal i( ) in oduces in e e ing powe in he adjacen channel limi ing he spec um e iciency o he sys em. To analyze he e ec o hose imbalances, he powe spec- um o he gene a ed signal, W( ), mus be compu ed. In o de o ob ain W( ), a pseudo andom sequence o 16384 QAM symbols is p oduced. Wi h his sequence a se o 131 072 signal samples a e gene a ed. Eigh samples pe symbol pe iod ha e been assumed. Then, he o iginal sampled sequence is CASADEVALL AND VALDOVINOS: QAM MODULATIONS APPLIED TO LINC TRANSMITTER 401 40 I - I” m F . GE 4-3-2-10 12 3 4 No malized F equency Fig. 2. Powe Spec um o 4-QAM pa e n o a gain imbalance o 0.25 dB. di ided in o 64 sequences wi h 2048 samples o each one. Fo each sequence he Fas Fou ie T ans o m is e alua ed using a Hanning window so as o dec ease he side lobes. The inal spec um is compu ed as he a e age o he 64 spec a p e iously calcula ed. In Fig. 2, he powe spec um o a aised cosine 4-QAM modula ion wi h a oll-o ac o equal o 0.5 is shown. A 0.25 dB o imbalance be ween bo h RF pa hs gain is aken in o accoun . F om he igu e i can be seen ha he undesi ed powe spec um ex ends u he han he use ul bandwid h, causing in e e ence in he adjacen channels. The adjacen channel ejec ion alue, U,, is ob ained by means o he compu a ion o he use ul and in e e ing powe using a nume ical p ocedu e. Tha is: UR(dI3) = 10. log,, being: whe e B, is he gua d band be ween he use ul and he adjacen channel and /3 he oll-o pa ame e o he squa e oo aised cosine il e . 111. RESULTS A. Gain Imbalance Fi s o all, he e olu ion o he adjacen channel ejec ion, UR (dB), agains he gain imbalance has been s udied using he oll-o ac o as pa ame e and conside ing di e en alues o he gua d band be wen he adjacen channels. F om he ob ained esul s, i can be concluded ha he sys em pe o mances a e almos insensi i e o he oll-o alue, wha e e i is he QAM modula ion conside ed. Fo his eason, om now on, only he oll-o alue o 0.2, as ypical 80 LG 70 -0 0 60 !+ 50 z + u w h 1 2 48 Q L u 5 30 w u 4 - s 26 I@ 0.01 0.1 1 10 100 GAIN IMBALANCE (AG) (dBI Fig. 3. Adjacen channel ejec ion e sus he gain imbalance o 4-QAM modula ion pa e n wi h he ampli ude o he phase modula ed signals o he peak en elope alue a io as pa ame e . o mobile adio communica ion sys ems, will be conside ed. Mo eo e , when he sys em pe o mances o he di e en modula ion pa e ns conside ed in he pape a e compa ed, i is ound ha he di e ences in he adjacen channel ejec ion alues a e lowe han 3 dB. Fo his eason, i could be concluded ha he sys em is also insensi i e o he modula ion pa e n, because o all he QAM modula ions conside ed in he pape , he LINC ou pu spec a look simila o he one shown in Fig. 2. On he o he hand, in Fig. 3, he in luence o he A, pa ame e in he sys em pe o mances is shown. No ice ha his pa ame e de ines he app op ia e alue o he ampli ude o he phase modula ed signals Sl( ) and S,( ). As shown in Table I, he lowe he A, alue is, he highe he ampli ude (V/2) o he phase modula ed signals. F om he igu e i can be seen ha no gain is ob ained by dec easing he A, alue; ha is, inc easing V. The e o e, om now on we will main ain o A, a conse a i e alue o 0.9. Taking in o accoun ha in p ac ical si ua ions UR alues g ea e han 50 dB could be needed, om his igu e i can also be seen ha o gua an ee hese pe o mances, gain imbalance alues as low as 0.1 dB a e equi ed. Finally, he e olu ion o he adjacen channel ejec ion agains he gain imbalance using he no malized gua d band as pa ame e is shown in Fig. 4. In his igu e, i is shown how he adjacen channel ejec ion inc eases app oxima ely 0.5 dB e e y ime he no malized gua d band inc eases 0.1, i espec i e o he gain imbalance alue. In summa y, conside ing he esul s shown abo e, he ollowing uppe bounds, wi h a maximum e o o 3 dB, could be pu o wa d o cha ac e ize he sys em pe o mances: 1. 4-QAM: UR(dB) 2 32.5 - 19.2. log10 (AG) + 5. (AB,T) 2. I6-QAM: 402 80 E 10 E 0 60 g 50 L c 0 W h 1 w < I C1 5 40 5 30 w 0 < h 9 20 10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 42, NO. 4, NOVEMBER 1993 0.01 0.1 1 10 10O GAIN IMBALANCE (AG) (dB) PHASE IMBALANCE (A@) (deg ees1 Fig. 5. Adjacen channel ejec ion e sus he phase imbalance o 4-QAM Fig. 4. Adjacen channel ejec ion e sus he gain imbalance o 4-QAM modula ion pa e n wi h he no malized band gua d as pa ame e . modula ion pa e n wi h he no malized gua d band as pa ame e . 3. 64-QAM: when phase imbalances up o 5 deg ees a e conside ed. These uppe bounds could be exp essed as 1. 4-QAM: UR(dB) 2 28.5 - 19.0. loglo (AG) + 7. (ABgT) UR(dB) 2 48.0 - 20.5. log," (A$) + 5. (ABgT) AG being he gain imbalance in dB, and ABgT he no malized gua d band anging be ween 0 and 1. 2. 16-QAM: B. Phase Imbalance I he wo pa h signals ha e wo di e en delay alues a he inpu o he combine , he signals do no combine in phase, and his esul s again in a high deg ee o dis o ion. Following he same me hod used o he gain imbalance, he e olu ion o he adjacen channel ejec ion agains he phase imbalance, Aqb, has also been s udied. F om he ob ained e- sul s, i can newly be concluded ha he sys em pe o mances a e e y insensi i e o he modula ion ype. Again, his can be explained no icing ha 4, 16, and 64 QAM spec a o S( ) o di e en phase imbalances a e e y simila , and consequen ly, he same beha io can be expec ed. On he o he hand, when he e ec o he oll-o ac o in he sys em pe o mances is conside ed, i may be no iced ha he sys em also emains insensi i e o he alue o he oll-o coe icien . I is also impo an o emphasize ha e en small phase imbalances a e able o p oduce high deg ading e ec s on he sys em pe o mances. Fo example, a sys em wi h only one deg ee o phase imbalance has an adjacen channel ejec ion o a ound 50 dB, bu i he phase imbalance inc eases up o 5 deg ees, hen adjacen channel ejec ion dec eases o only 33 dB. Finally, he e olu ion o he adjacen channel ejec ion agains he phase imbalance using he no malized gua d band as pa ame e is shown in Fig. 5. As in he gain imbalance case, i can be seen in his igu e ha he adjacen channel ejec ion inc eases app oxima ely 0.5 dB e e y ime he no - malized gua d band inc eases 0.1, independen ly o he phase imbalance alue. Simila ly o he p ocedu e ollowed o gain imbalances, we a e also able o ob ain he sys em pe o mance uppe bounds 3. 64-QAM: UR(dB) 2 44.5 - 21 .2. loglo (A4) + 7. (ABgT) wi h Aq5 in deg ees. I . EFFECTS OF THE IMBALANCES ON THE BIT ERROR RATE The e ec s o hese imbalances on he bi e o p obabili y a e u he analyzed. In o de o emphasize he in luence o he imbalances, a sys em ee o he in e symbol in e e ence p oblem induced by he channel is conside ed; ha is, a Nyquis equi alen impulse esponse is assumed. Then, a he ou pu o he cohe en demodula o , he in-phase, z( o), and he quad a u e, ,( o), componen s a he sampling ins an , can be exp essed as: -k1 -71( o) - k2 . Y2( 0)1 + n ( 0) c( o) = ko . M o) + kl . q( 0) y( o) = ko . [q( o) - k1 .p( o) -h . Y2( ") + k2 .Yl( O)l + n,( o) (4) 1 whe e: o) * h0N5( )l = o 30 hN( - kT)I = , = a0 k=-co q( o) = ~( ) * hON.5( )l = o CASADEVALL AND VALDOVINOS: QAM MODULATIONS APPLIED TO LINC TRANSMITER 403 Q3 = bk . hN( - kT)( = o = bo k=-m 7l( ) = [C( ) . X( )] * hi5( ) 72( ) = [C( ) . y( )] * h;;5( ) (5) being h~ ( ) he aised cosine Nyquis pulse, 1 - . (1 + AG. COSA~), 2 1+AG. COSA~' 1 - AG. COSA~$ 1+AG. COSA~' ko kl = k2 = (6) AG . sin Ad and n l and nq a e espec i ely he I and Q alues o noise a sampling ins an . In he abo e exp ession, pe ec ca ie and iming eco e y ha e been assumed, and he e o e, he e is no in e symbol in e e ence. In o de o es ima e he bi e o p obabili y, he quasi- analy ic me hod [9] has been used. Fo a speci ied powe o whi e Gaussian noise a he h eshold de ec o inpu , he e o p obabili y o he i h symbol wi h espec o he in- phase channel could be e alua ed as in (7), ound a he bo om o he page. whe e yZz is he i h ecei ed sample and 5'; and Sz", a e he lowe and uppe h esholds. An equi alen exp ession could be ob ained o he quad a u e channel 1. A e some algeb aic ope a ions, we can ob ain he exp ession o he noise a iance ound a he bo om o he The o al bi e o p obabili y o a sequence o N symbols Page (8). is compu ed as: (9) whe e A4 is he numbe o cons ella ion poin s. A G ay encoding p ocess has also been conside ed, wi h he esul o only one bi e o o each symbol e o . V. RESULTS To cha ac e ize he in luence on he bi e o p obabili y o he gain and phase imbalances, he inc emen on he SNR necessa y o gua an ee a ixed BER has been compu ed. In pa icula , he alues lop3 and lop6, as ep esen a i e a ge s o oice and da a ansmission ha e been conside ed. 4 Fig. 6. Recei ed cons ella ion diag am o 16-QAM wi h 1.5 dB gain imbalance. A. Gain Imbalances When only gain imbalance is conside ed, k1 = 0 and k2 # 0 in exp ession (4). F om his exp ession, i may be no iced ha he ecei ed in-phase componen depends on 72 ( ) which is di ec ly dependen on he quad a u e componen , as shown in (5). This c oss- alk be ween he in-phase and quad a u e channels leads o an impo an e ec o o a ion on he ecei ed signal cons ella ion, as can be seen o 16 QAM wi h 1.5 dB o gain imbalance in Fig. 6. This e ec can be compensa ed a he ecei e by using a s anda d ca ie eco e y ci cui . Conside ing a oll-o ac o equal o 0.2 and a BER alue o lop3, he inc emen on he SNR needed o compensa e a gain imbalance be ween he wo RF pa hs is shown in Fig. 7(a). In his igu e, he esul s co esponding o bo h sys ems wi h and wi hou phase ca ie op imiza ion a e depic ed. F om he ob ained esul s, i can be concluded ha he highe he modula ion o de , he mo e sensi i e is he modula ion o he gain imbalance. Fo example, o a 4-QAM modula ion pa e n, he sys em is almos insensi i e when he phase op imiza ion is pe o med, and i i is no pe o med, he sys em only needs an inc emen o abou 2 dB a mos in he SNR o cope wi h 2 dB o gain imbalance be ween bo h RF b anches. I 16-QAM modula ion is conside ed, wi h he same inc emen in he SNR, he sys em is able o cope wi h gain imbalance alues equal o 3 dB and 0.5, depending 404 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 42, NO. 4, NOVEMBER 1993 -5 -4 -3 -2 -I 0 I 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 GAIN IMBALANCE (dB1 GAIN IMBALANCE (dB) (a) (b) Fig. 7. Inc emen o he SNR as unc ion o he gain imbalance o a p e- ixed BER equal o lop3. Dashed lines indica e no ca ie eco e y ci cui conside ed. Roll-o ac o equal o : (a) 0.2, (b) 0.5. 0246818 0245818 PHASE IMBALANCE (deg ees) PHASE IMRALAKE (deo eesl (a) (b) Fig. 8. Inc emen o he SNR as a unc ion o he phase imbalance o a p e- ixed BER equal o lo 3. Dashed lines indica e no ca ie eco e y ci cui conside ed. Roll-o ac o equal o: (a) 0.2, (b) 0.5. on he p esence o absence o he ca ie eco e y ci cui . Finally, o 64-QAM modula ion, hese alues educe o 0.6 and 0.2, espec i ely. No ice ha o a gain imbalance o 1.2 dB (10% app oxima ely), he 64-QAM modula ion deg ades in app oxima ely 6 dB he SNR needed o gua an ee a BER o lop3; ha is, wi h espec o an ideal LINC ansmi e , i is necessa y o inc ease ou imes he alue o he ansmi ed powe o main ain he same sys em quali y. Simila esul s a e ob ained o a BER o lop6. When a oll-o ac o equal o 0.5 is conside ed, he ob ained esul s a e shown in Fig. 7-b. In his case, he sys em pe o mance is sligh ly be e han he ob ained esul s, conside ing a oll-o ac o equal o 0.2; bu in gene al, he same ideas and conclusions ob ained be o e apply in his case. Finally, i is also impo an o emphasize ha he conclu- sions ob ained in he p e ious pa ag aph could be ex ended o o he BER's. B. Phase Imbalance Fig. 8 shows he e olu ion o he inc emen in he SNR needed o compensa e he e ec o he phase imbalance o he same oll-o alues. This igu e shows only posi i e alues o he phase imbalance because nega i e alues p oduce he same esul s. On he o he hand, looking a he exp ession (4), when only he phase imbalance is conside ed, hen K1 # 0 and K2 # 0, and as a esul , he c oss- alk be ween he in- phase and he quad a u e channels appea s. Fo his eason, esul s conside ing wo si ua ions ha e been ob ained. In he i s case, he ca ie eco e y loop is able o compensa e o his e ec , [lo], bu in he second case, i is no . Again, om he ob ained esul s, i could be concluded ha he highe he modula ion o de , he mo e sensi i e he modula ion o he phase imbalance. Fo a BER alue equal o and 4-QAM modula ion pa e n, he sys em only needs an inc emen o 0.1 dB in he SNR o cope wi h alues o phase imbalance as high as 10 deg ees be ween he wo RF channels when no c oss- alk appea s, and 0.2 dB i c oss- alk is conside ed. Howe e , when 16-QAM modula ion is aken in o accoun , o a 3-dB inc emen in he SNR, he sys em is able o cope wi h a phase imbalance alue equal o 6 deg ees i a ecei ed signal wi hou c oss- alk is conside ed, bu i is only able o cope wi h up o 5 deg ees in he case o c oss- alk; while o 64- QAM modula ions, wi h he abo e men ioned SNR inc emen , he maximum phase imbalance alues educe o only 2.3 and 2 deg ees, espec i ely. Simila esul s a e ob ained o a bi e o alue o CASADEVALL AND VALDOVINOS: QAM MODULATIONS APPLIED TO LINC TRANSMITTER 405 TABLE I1 INCREMENT OF THE SNR AS FUNCTION OF THE GA~N IMBALANCE (a), AND THE PHASE IMBALANCE (b), FOR A PREFIXED BER EQUAL TO lop4. COMPARISON BETWEEN A CONVENTIONAL QAM MODULATOR, [8], AND A LINC TRANSMITTER Conside ing a oll-o ac o equal o 0.5, he inc emen on he SNR needed o compensa e o he phase imbalance is shown in Fig. 8(b). The igu e also shows he sensi i i y o 64-QAM modula ion as ega ds he phase imbalances, in compa ison o he 4-QAM modula ion ha is able o cope wi h up o 10 deg ees o he phase imbalance alue wi h a SNR deg ada ion lowe han 0.2 dB. Howe e , o 64-QAM modula ion, he phase imbalance canno be g ea e han 3 deg ees o main ain deg ada ion lowe han 3 dB on he SNR. Finally, i is wo hwhile o compa e he sensi i i y o a LINC ansmi e o a con en ional QAM modula o . In Table I1 a compa ison be ween he esul s ob ained in [8] o a con en ional QAM modula o and hese ob ained o he LINC ansmi e is p esen ed. In Table II(a) i can be seen ha he LINC ansmi e is less sensi i e o he gain imbalances o all he modula ion pa e ns. Howe e , he con en ional QAM modula o p esen s a be e beha io o phase imbalances, as is shown in Table II(b). In any case, i mus be emembe ed ha in he con en ional QAM modula o , comple ely linea il e ing and powe ampli ica ion a e assumed; whe eas, he LINC ansmi e allows he use o highly non-linea powe ampli ie s wo king close o i s sa u a ion poin and, as a esul , o inc ease he sys em powe e iciency. VI. CONCLUSIONS In his pape , he e ec o he RF signal p ocessing impai - men s in a LINC ansmi e has been analysed. In pa icula 4, 16, and 64 QAM modula ion pa e ns wi h aised cosine Nyquis il e ing and wo di e en kinds o pa h imbalances a e conside ed. Fi s o all, he sys em deg ada ions a e desc ibed in e ms o he adjacen channel ejec ion, and analy ical uppe bounds ha e been ob ained o all he analyzed cases. Mainly, he gain imbalance be ween bo h powe ampli ie s, bu also he phase imbalance, appea s as a se ious limi a ion o he pe o mances o he LINC ansmi e . The in luence o he RF imbalances on he bi e o p ob- abili y has also been analyzed. F om he ob ained esul i can be concluded ha 4-QAM modula ion emains almos insensi i e o he e ec o hose imbalances. The same applies o 16 QAM, in case he imbalances emain below easonable limi s. On he con a y, since 64-QAM o highe modula ions a e e y sensi i e o he e ec o hese imbalances, ca e ul implemen a ions a e equi ed. ACKNOWLEDGMENT The au ho s wish o acknowledge he anonymous e iewe s o hei sugges ions which ha e led o imp o emen s in he wo k. REFERENCES R. S eele, “Deploying pe sonal communica ion ne wo ks,” IEEE Com- mun., pp. 12-15, Sep . 1990. J. Yamas, “An HF dynamic ange ampli ie using eed o wa d ech- niques,” RF Design, pp. 50-59, July 1987. V. Pe o ic, “Applica ion o Ca esian eedback o HF SSB ansmi - e s,” in P oc. Ins . Elec . Eng. Con on H.F: Commun. Sys . Techniques, pp. 81-85, 1985. A. A. Saleh and J. Salz, “Adap i e linea iza ion o powe ampli ica ion in digi al adio sys ems,” Bell Sys em Technical J., pp. 1019-1033, Ap . 1983. D. C. Cox, “Linea ampli ica ion wi h non-linea componen s,” IEEE T ans. Commun., pp. 1942-1945, Dec. 1974. S. A. He zel, A. Ba eman, and J. P. McGeehan, “A LINC ansmi e ,” in P oc. 41”‘ IEEE Veh. Technol. Con$, S . Louis, MO, pp. 133-137. F. Casade all, J. J. Olmos, “On he beha io o he LINC ansmi e ,” in P oc. 40 h IEEE Veh. Technol. Con$, May 6-9, 1990, O lando, FL, pp. 20-34. H. Sa i, G. Ka am, “Compensa ion o modem impe ec ions by adap i e il e ing,” in P oc. GLOBECOM’86, 1986, pp. 51 1-516. M. J. Je uchim, “Techniques o es ima ing he bi e o a e in he simula ion o digi al communica ion sys ems,” IEEE J. Selec . A eas Commun., ol. SAC-2, pp. 153-170, Jan. 1984. S. Mo idi, H. Sa i, “Analysis o decision- eedback ca ie eco e y loops wi h applica ion o 16-QAM digi al adio sys ems,” in P oc. In . Con Commun. (ICC’83), 1983, pp. 671475. 406 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 42, NO. 4, NOVEMBER 1993 Fe nando J. Casade all (M’87) was bo n in Ba celona, Spain, in 1955. He ecei ed he Enginee o Telecommunica ion and Ph.D. deg ees om he Escola Wecnica Supe io d’Enginye s de Teleco- municaci ’o de Ba celona (ETSITB), Uni e si a Poli ’ecnica de Ca alunya (UPC), Spain, in 1977 and 1983, espec i ely. In 1978 he joined he ETSETB, whe e he was an Associa e P o esso om 1983 o 1991. He is cu en ly a P o esso in he Signal Theo y and Communica ions Depa men , UPC. His esea ch in e es s include equaliza ion echniques o digi al ibe op ic sys ems and digi al communica ions, wi h pa icula emphasis on digi al adio and i s pe o mance unde mul ipa h p opaga ion condi ions, especially cellula and pe sonal communica ion sys ems, mul ipa h ecei e design, and digi al signal p ocessing. He is ac i ely pa icipa ing in he Eu opean esea ch p og ams COST231 and RACE. An onio Valdo inos was bo n In Ba bas o, Spain, in 1966. He ecei ed he Enginee o Telecommu- nica ion deg ee om he Escola n’ecnica Supe- io d’Enginye s de Telecomunicaci ’o de Ba celona (ETSETB), Uni e sj a Poli ‘ecnica de Ca alunya (UPC), Spain, in 1990. In 1991 he joined, unde a esea ch g an , he Signal Theo y and Communica- ions Depa men , UPC, Spain, whe e he is cu en ly pu suing he Ph.D. deg ee in he a ea o mobile adio communica ion sys ems. P esen ly, he is an Assis an P o esso in he UPC.