Pre-distortion Linearization for 64-QAM Modulation in Ka-Band Satellite Link

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Wilfrid Bates
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1 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August Pre-dstorton Lnerzton for 64-QAM Modulton n K-Bnd Stellte Lnk P. Sojood Srdrood,, G.R. solt nd P. Prvnd Summry In ths pper the effcency of lnerzton for pre-dstorton n 64-QAM modulton, utlzed n K-bnd stellte lnk for DVB-RCS servces, s nvestgted. The lnerzton s smulted by Mtlb-Smulnk, for GEO Stellte nd DVB- RCS servce. A A power mplfer wth 1dB bck-off s used n ths stellte lnk, nd to conclude the results, the spectrum nd eye-dgrm n both trnsmtter nd recever sde re evluted. Key words: Pre-dstorton, Modulton, Power Amplfer, A Irn Telecommuncton Reserch Centre. Power Amplfer Before pplyng lnerzton technques, studyng of nonlnerty chrcterstcs of power mplfers s mportnt. To evlutes non-lnerty effects n hgh power mplfers, polynoml s utlzed to justfy output to nput trnsfer functon []. The output of the system cn be expressed by 3 rd order polynoml, shown by Eq.1 3 y =. x +. x + x (1) Introducton The new generton of stellte recevers for DVB-RCS servces n K-bnd re utlzng hgher order modulton such s 64-QAM nd hgher effcency A power mplfers. One of the most expensve prts of stellte communcton systems s the output power mplfer, whch hs the most power consumpton. There s trde off between workng n the lner re nd the mxmum effcency. Lnerzton technques ncrese the effcency by keepng the lnerty of power mplfers. To hve enough lnerty the mplfer should functon t low output level. Dstnce between operton pont nd sturton pont s so clled Bck-Off. Lnerzton reduces the Bck-Off. Tble. 1. Shows the mount of mprovement for mult crrer system usng predstorton [1]. Tble 1: Lnerzton Benefts Pre-dstorton No Yes TX Power 10W 10W PAR 9dB 9dB Bckoff 1dB 9dB PA Power Rtng 160W 80W Effcency 9% 18% Power Dsspton 101W 45W In the Eq.1, 1 s the lner gn of the mplfer, nd nd 3 re the non-lner gns respectvely. The block dgrm of power mplfer s llustrted n Fg. 1, where v ( nd v o ( re nput nd output sgnls of systems respectvely. To show the non-lnerty ffect of the mplfer, the system s tested wth two tones, wth dfferent frequences, the output sgnl nd then the nonlnerty ffect due to A power mplfer s evluted. But pplyng two tones n Eq. nto the polynoml n Eq.1, the output of hgh power mplfer nd the out spectrl effects s clrfed. v ( 1 t = Acos( ω + Acos( ω ) Fg.1. Block dgrm of nput nd output of power mplfer The result of spectrl expnson for the output spectrum, when two tones re ppled to the nput, s llustrted n Fg., nd certnly ll coeffcents n Eq. 1 re rel. Generlly the output of the system cn be expressed by Eq.3. () v 3 o ( = 1 v ( + v ( + 3v ( (3) Mnuscrpt receved August 5, 008. Mnuscrpt revsed August 0, 008.

. spectrl expnson for the output spectrum, when two tones re ppled to the nput. Ordnrly, the functon of power mplfer s descrbed by AM-AM nd AM-PM chrcterstcs.

2 48 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August 008 Fg.4 llustrtes the result of test wth two tone nputs, nd obvously the ffect of non-lnerty of the mplfer s observed n the output spectrum. Fg.. spectrl expnson for the output spectrum, when two tones re ppled to the nput. Ordnrly, the functon of power mplfer s descrbed by AM-AM nd AM-PM chrcterstcs. The AM-AM chrcterstc cn be extrcted from the non-lner polynoml, stted n Eq.3, lthough AM-PM chrcterstc cn not be extrcted. But the AM-PM chrcterstc cn be extrcted by Eq. 5. The AM-AM nd AM-PM chrcterstcs of the power mplfer re shown by g nd g, respectvely []. ϕ Fg.4. () nput of A mplfer (b) output of A mplfer. 3. Bsebnd Pre-dstorton Mthemtclly, pre-dstorton system hs n nverse functon of the hgh power mplfer [3-11]. Pre-dstorton system nd the hgh power mplfer re cscded together s chn, nd t s llustrted n Fg.5 v ( = g( v ( v ( = g ( v ( ) e o g ( v ( ) = +. v ( g ( v ( ) = ϕ + ϕ. v ( ϕ v ( 5 5 jgϕ ( v ( ) v 4 + ϕ. v ( 4 ( (4) In the A hgh power mplfer wth Sleh modelng, the AM-AM nd AM_PM chrcterstc re ntroduced by Eq.5 nd Eq.6. αr r) = (5) 1+ β r π α pr P( r) = (6) 3 1+ β r p The non-lner chrcterstcs re drwn n Fg. 3 verses nput voltge. Fg.5. cscded of mplfer nd pre-dstorton unte. If v d ( s the tme domn output sgnl of hgh power mplfer, the totl output of the system s expressed by Eq.7. (7) v ( = g( f ( v ( v ( f ( v ( v ( o It s clered tht the hgh power mplfer s lner when the mount of G n Eq.8 s constnt. G = g( f ( v ( v ( f ( v ( ) (8) A pre-dstorton system chnges the shpe of nput dt of mplfer so tht the totl chrcterstc of system s lner. In other words we cscde two non-lner systems so tht the output to nput of the whole system s lner. Ths wll be done only f the power mplfer functons ner ts sturton pont. For lnerzton of A power mplfer, n 64-QAM modulton, pre-dstrcton system s desgned, wth the followng desgn steps. Suppose tht we express the mpltude nd phse of every symbol n 64-QAM modulton by Eq.9. x( = cos( wct + ϕ( (9) We cn descrbe the output of the mplfer nd predstorton by Eq.10. Fg.3. The non-lner chrcterstcs of A wth sleh model.

IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August 008 49 y( = f FP f FA FA + P twt )cos( w t + FA c + ϕ( : functon of A AM/AM conversons.

As the rton of output to nput should be constnt, the condtons n Eq.11 should become true: f FA = k (11) FP + P FA = 0 Therefore Eq.

6 llustrtes the block dgrm of desgned Predstorter, to clculte 64-QAM symbols. Fg.7. Smulnk Model Fg.8 nd Fg.

3 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August y( = f FP f FA FA + P twt )cos( w t + FA c + ϕ( : functon of A AM/AM conversons. P : functon of A AM/PM conversons. : functon of mpltude. FP : functon of phse. (10) prmeters nd the mount of BER re mesured fter recevng the sgnl v stellte lnk. As the rton of output to nput should be constnt, the condtons n Eq.11 should become true: f FA = k (11) FP + P FA = 0 Therefore Eq.1 shows the reltonshp between the mpltude nd the phse of pre-dstorter: 1 1 FA = f ( k (1) FP( = P F 1 α ( r) = + β r 4β r f α 1 β (13) Fg.6 llustrtes the block dgrm of desgned Predstorter, to clculte 64-QAM symbols. Fg.7. Smulnk Model Fg.8 nd Fg.9 llustrte the ffect of non-lnerty nd lso the lnerzton ffect by the pre-dstorter n the smulton respectvely. Fg. 8 shows the spectrum of trnsmtted sgnl, fter the power mplfer wthout predstorton. Fg.9 shows tht the level of frst sde lobe n receved sgnl wth pre-dstorter s 0dB lower thn the receved sgnl wthout pre-dstorted lso the bndwdth s hlf of the non pre-dstorted stte. Fg.6. Pre-dstorted system 4. System Model A GEO stellte lnk n 30GHz s utlzed for testng of pre-dstorter. Pseudo rndom dte s used s nput besde 64-QAM modulton. The pre-dstorter s locted before A, wth the prmeters descrbed before. The bckoff of system s 1dB, nd the free spce loss s lmost 13dB. The nose temperture n recever s 60 K. The utlzed pulse shpng s rsed-cosne nd the test s done wth nd wthout pre-dstorter. Fg. 7 llustrtes the smulton block dgrm, used for the smulton wth MATLAB/Smulnk. The rndom bnry strems pssng through rsed-cosne flter nd 64-QAM modultor re sent to the nput of the pre-dstorton sub-system. We use Sleh model for A ccordng to the prmeters shown n Eq.5 nd Eq.6. Ultmtely, the spectrum Fg.8. Spectrum n recever nd trnsmtter wth nonlner mplfer wthout usng lnerzer.

50 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August 008 Fg.9. Spectrum n recever nd trnsmtter wth nonlner mplfer wth usng lnerzer.

10, the eye-dgrm s llustrted, whle the power mplfer s non-lner, nd n Fg.11 the eye-dgrm of the power mplfer s llustrted, when pre- dstorton system s cscde wth the power mplfer. Fg.1 nd Fg.

When the mount of α s lrge, nd consequently the bndwdth nd the nose power s ncresed, the mount of BER s ncresed. Fg.13 Illustrtes the mount of BER wthout pre-dstorton.

4 50 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August 008 Fg.9. Spectrum n recever nd trnsmtter wth nonlner mplfer wth usng lnerzer. The effect of lnerzton cn be evluted by the eyedgrm of the system for output symbols n two stted. As t s seen n Fg.10 nd Fg.11, the eye-openng s much more n the lnerzed system. In Fg.10, the eye-dgrm s llustrted, whle the power mplfer s non-lner, nd n Fg.11 the eye-dgrm of the power mplfer s llustrted, when pre- dstorton system s cscde wth the power mplfer. Fg.1 nd Fg.13 show the dvntges of usng dt predstorton n term of BER performnce for dfferent rolloff fctor wth nd wthout dt pre-dstorton. As t s llustrted n Fg.1, the mount of error s mnmums when α = When the mount of α s lrge, nd consequently the bndwdth nd the nose power s ncresed, the mount of BER s ncresed. Fg.13 Illustrtes the mount of BER wthout pre-dstorton. Obvously, s the mount of bck-off s 1dB, nd lso 64- QAM modulton s senstve to non-lnerty of A, the mount of BER s hgh. Comprng Fg.1 nd Fg.13, 5 the mount of BER s mproved by Ths result enbles the 64-QAM modulton scheme to be effcently utlzed n stellte communcton systems not worry bout non-lner dstorton. Fg 10. eye dgrm n recever wth nonlner mplfer wthout usng lnerzer. Fg 11. eye dgrm n recever wth nonlner mplfer wth usng lnerzer.

5 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August pre-dstorton technques. Also, ths method for dt predstorton cn be used for hgher level modulton. References Fg.1. BER for dfferent roll off fctor wth Pre-dstorton Fg.13. BER for dfferent roll off fctor wthout Pre-dstorton In the method, presented n [1] for DVB-MODEM wth QPSK modulton, the sde lobe s mproved bout 10dB. In the method presented n [13] wth 16-QAM for moble stellte, the mount of mprovement of the sde lobes s 13dB. In [14] the pre-dstorton method for lnerzton n 16-QAM modulton nd wthout roll-off prmeter s mplemented. The results of smultons show tht the method, offered n ths pper, mproves the mount of sde lobe by 0dB, wth consderng the roll off ffect. Therefore, the offered method confrms better performnce thn the bove references. 5. Concluson In ths pper the effcency of lnerzton for bsebnd pre-dstorton n 64-QAM modulton, utlzed n K-bnd GEO stellte lnk for DVB-RCS servces, s nvestgted. A A power mplfer wth bout 1dB bck-off s used n ths stellte lnk, nd the spectrum nd eye-dgrm n both trnsmtter nd recever sde re evluted. Smulton results show tht stellte communcton lnk cn beneft from 64-QAM modulton schemes, usng our [1] G. Copelnd, Dgtl Power Amplfer Lnerzton, Texs Instruments Inc., 003. [] R. Sperlch, Adptve Power Amplfer Lnerzton by Dgtl Pre-Dstorton wth Nrrowbnd Feedbck usng Genetc Algorthms Doctorl Thess, School of Electrcl nd Computer Engneerng Georg Insttute of Technology August 005. [3] R.Schornstedt, N. Rozro, C.Hyes, J. Seter, nd A. Ktz, Performnce of Mult-Crrer 16-QAM Over Lnerzed AA Stellte Chnnel, 0 th AIAA Interntonl Communcton Stllte Systems Conference nd Exhbt, 1-15 My 00, Montrel, Quebec, Cnd. [4] M.Cote, L.Erup, M.Lmbert, N.McSprrron, Implementton Chllenges nd Synergstc Benefts of DVB-RCS nd DVB-S, Dgtl Vdeo Brodcstng over Stellte: Present nd Future, 006. The Insttuton of Engneerng nd Technology Semnr, Nov. 006, pges: 1-33, London, UK. [5] A. Ktz, AA Lnerzton, The Mcrowve journl, Vol. 39, No 4, pp , Aprl [6] H. Alsdy, M. Ibnkhl, A. Btd, A Smple Dt Pre-Dstorton Technque for Stellte Communcton : Desgn & Implementton on Alter DSP Bord, CF-SAT , 005. [7] A. Sleh, Frequency- Independent nd Frequency- Dependent Nonlner Models of A Amplfers, IEEE Trnsctons on Communctons, Vol. 9, No 11, Nov [8] Ernst Aschbcher, Prototype Implementton of two effcent lowcomplexty Dgtl Pre-dstorton Algorthms, EURASIP Journl on dvnce n sgnl processng, Vlo.008, Artcle ID [9] Young Yun Woo, Adptve Dgtl Feedbck Pre-dstorton Technque for Lnerzng power Amplfer, IEEE Trnsctons on Mcrowve Theory nd Technques, VOL. 55, NO.5, My 007. [10] Nm Sfr, Block bsed Predstorton for Amplfer Lnerzton n Burst Type Moble stellte Communctons, EUMW 005. [11] Jnng Zho, Error Anlyss nd Compenston Algorthm for Dgtl Predstorton Systems, Prs Onlne, VOL.,No. 6, 006. [1] Ten M. Nguyen, Modelng of HPA nd HPA Lnerzton Through Predstorter, IEEE Trnsctons on Brodcstng, 49(), pp (Jun. 003). [13] Nm Sfr1, Block bsed Predstorton for Amplfer Lnerzton n Burst Type Moble stellte Communcton, Europen Mcrowve Conference (EuMC) No35, Prs, FRANCE vol. 54 (), no 6 (334 p.) 006. [14] Hshm lsdy, A smple Dt Pre-dstorton technque for stellte Communcton: Desgn & Implementton on Alter DSP Bord, CF-SAT , 005. Acknowledgments Ths reserch ws supported by Irn Telecommuncton Reserch Center.

5 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August 008 Sojood Srdrood Prvn receved the B.S. degree n Communcton Engneerng from Tehrn Polytechnc Unversty 001.

technology n communcton network. She s stll workng on the smlr felds. Modulton & Codng. Rez Solt receved the B.S. degree n Electrcl Engneerng from Isfhn Unversty of Technology n Irn n 1990 nd M.

Durng 1995-008, he styed n Irn Telecommuncton Reserch Center (ITRC) s Project Mnjer n stellte communcton systems, nd Pymn Prvnd receved the B.S.

6 5 IJCSNS Interntonl Journl of Computer Scence nd Network Securty, VOL.8 No.8, August 008 Sojood Srdrood Prvn receved the B.S. degree n Communcton Engneerng from Tehrn Polytechnc Unversty 001. Durng 00 untl now, she styed n Irn TeleCommuncton Reserch Center (ITRC), Mnstry of Posts nd Telecommunctons of Irn to study stellte RF lnks, next generton ccess network, Ethernet technology n communcton network. She s stll workng on the smlr felds. Modulton & Codng. Rez Solt receved the B.S. degree n Electrcl Engneerng from Isfhn Unversty of Technology n Irn n 1990 nd M.S. degree n Communcton from Khjeh Nsr Tous Unversty of Technology n Irn n Durng , he styed n Irn Telecommuncton Reserch Center (ITRC) s Project Mnjer n stellte communcton systems, nd Pymn Prvnd receved the B.S. degree n Electrcl Engneerng from Irn Unversty of Scence & Technology n Durng 1990 untl now, he hs styed n Irn Telecomm. Reserch Center, Mnstry of ICT of Irn to reserch on Stellte Communctons, Subsystems, Technologes, nd Mcrowve nd Mlllter RF devces etc. He s stll workng on the smlr felds.

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