Analysis of Non-Linear Response in DS-CDMA Satellite Systems

Transcription

1 Alyss of No-Ler Respose DS-CDMA Stellte Systems MARIO REYES-AYALA, EDGAR ALEJANDRO ANDRADE-GONZALEZ, JOSÉ ALFREDO TIRADO-MÉNDEZ, HILDEBERTO JARDÓN AGUILAR Electrocs Deprtmet Metropolt Autoomous Uversty S Pblo 8, Col. Reyos Tmulps, Azcpotzlco, ZIP Code, Mexco Cty MEXICO Secto of Commuctos CINVESTAV-IPN Av. IPN 58, Col. S Pedro Zcteco, Zp Code 76 Mexco Cty Aprtdo postl -7, 7 Mexco Cty MEXICO mr@correo.zc.um.mx Abstrct: - Ths pper shows lgorthm to clculte sychroous DS-CDMA stellte lks wth o-ler respose mplfers, where the probblty error, ctve devce prmeters, hrmocs, termodulto products d bck-off compesto, re used to evlute the performce of the system. The lyss of crrer to terferece rto s crred out for N-crrer up-lk, where sgle crrer uses DS-CDMA. Key-words: - Hrmocs, Itermodulto, DS-CDMA, lk budget, HPA, crrer to terferece rto. Itroducto The ture of Frequecy Dvso Multple Access (FDMA) mples tht the recever chel hs to mplfy set of crrers frequecy tervls. Stellte systems wth Code Dvso Multple Access (CDMA) requre lso FDMA, becuse the bdwdth s very lrge. The the o-ler trsfer chrcterstc of the mplfers used erth d spce sttos geerte lot of spurous sgl. I ths pper, we lyze dgtl stellte commucto system where Drect Sequece Code Dvso Multple Access (DS-CDMA) s used to mxmze the umber of smulteous users the trsmsso med. I ths techque, the stellte trspoders detfy the erth stto (up-lk), wth pseudordom sequece (PN). The legth d rte of the sequece determe the spred bdwdth d umber of smulteous user of the system. The rchtecture employed to obt pseudo-rdom sequeces s med PN sequece geertor, d the fetures of the most mportt cofgurtos re show []. I mult-crrer systems the o-ler effects re cresed, termodulto products geerto reduces the power of the desred crrers [], [], [], [5]. Ths behvor s cused by ctve devces, becuse ther resposes re o-ler. There re two m techques to cheve CDMA, Drect Sequece d Frequecy Hoppg (FH), but FH-CDMA s more sesble to Doppler effect, s cosequece of stellte veloctes. The, DS-CDMA s the oly prctcl choce to use spred spectrum stellte commucto. I secto two, the crrer to terferece rto s preseted. The bck-off clculto for sgle crrer s lyzed secto three. The cse for rbtrry umber of crrers the up-lk s lyzed detl secto four. The m results d coclusos re preseted secto fve d sx. C/I Dgtl Stellte Systems The totl crrer to ose rto s determed by (). C N T = N u + N d + N C + I () Where (C/N) T s totl crrer to ose rto, (C/N) u s the uplk crrer to ose rto, (C/N) d s the dowlk crrer to ose rto, (C/N) s the crrer to termodulto ose rto, d (C/I) s the crrer to terferece rto. 5 Issue, Volume 7, Aprl 8

2 Hrmocs geerto for sgle toe the HPA c be clculted by equto (), [], [], [5]. ( ) = cos( ω ) x t A ct f ( t) + x( t) + x ( t) + x ( t) () Where x(t) s the crrer, A s the mpltude of the crrer, ω c s the gulr frequecy of the crrer, f(t) s the o-ler mgtude respose fucto, d flly,, d re costts. The complete hrmocs tht re geerted the HPA s show the Tble. TABLE. HARMONICS FOR A SINGLE CARRIER Ampltude Frequecy A + D. C. A A + A A ω c ω c ω c Itermodulto c be determed by equtos (), (), (5) y (6). y s ( t ) A cos ( ω t ) s ( t ) A cos ( ω t ) x( t) s ( t) + s ( t) ( t) + x( t) + x ( t) + x ( t) + L = () = () = (5) (6) Where x(t) s the put sgl; A d A re the mpltude of the crrers; ω d ω re the gulr frequeces of the crrers; y(t) s the o-ler mgtude respose fucto; d,, d re costts. The complete termodulto products tht re geerted by the o-ler respose of the HPA s show the Tble. TABLE. INTERMODULATION PRODUCTS FOR TWO CARRIERS Ampltude Frequecy + ( A + A ) D. C. A + A ( A + A ) ω A + A ( A + A ) ω A ω A ω A A ω ± ω A ω A ω A A ω ± ω A A ω ± ω The totl crrer to ose rto s very mportt to determe the rto of eergy per bt to ose desty d error probblty s well. The error probblty for o-ler mgtude respose for DS-CDMA s llustrted [], where the lyss ssume sgle crrer the up-lk. Bck-Off for sgle crrer The mplfers hve o-ler respose f the put power level s hgh d t s possble to employ polyoml model, the output level predcto. The put bck-off s clculted by (7). [ BO ] [ EIRP ] [ EIRP ] = (7) R Where: [BO] s the put bck-off, dbw; [EIRP R ] s the rel up-lk EIRP, dbw; d [EIRP S ] s the EIRP for HPA sturto, dbw. The put bck-off s the uplk compesto eeded to sturte stellte S 6 Issue, Volume 7, Aprl 8

3 HPA. I order to use ormlzed curve of TWT oler respose, t s ecessry to defe R TWTA. TWTA [ EIRP ] [ EIRP ] R = / (8) R Where: R TWTA s the rel to sturto EIRP Rto. It s obvous tht respose of prtculr TWTA my be modfed, f ts TWT s chged, becuse ech tube hs prtculr respose. The followg equtos offer wy to obt ormlzed predcto for TWTA o-ler put-output rto []. R α P = (9) TWTA p ( + β R ) p TWTA TWTA R α q Q = () ( + β R ) q TWTA Z P + Q S = () Where: α P, β P, α q d β q re TWT coeffcets; P s the -phse ormlzed o-ler respose, d; Q s the -qudrture ormlzed o-ler respose. [ EIRP ] [ EIRP ]Z R S S, S, = () Where: Z s the mgtude of ormlzed oler respose. It s possble to bck wth the rel o-ormlzed prmeters. Flly, we c obt the output bck-off the rel mplfer, s cosequece of compestg the put power level. [ ] [ EIRP ] [ EIRP ] BO =, () O S, S R S Where: [BOo] s the output bck-off, dbw; [EIRP R,S ] Is the rel output EIRP, dbw; d, [EIRP S,S ] s the output EIRP sturto, dbw. I ths pper, we use three TWT devces to compre the o-ler respose stellte HPA, see Tble. TABLE. TWT DEVICES USED IN SIMULATION TWT TWT TWT α p β p α q β q The TWT d TWT re commercl tubes, d TWT s del tube, where there s ot phse dstorto. Bck-Off for N-Crrer I the prevous secto, the mpltude o-lertes hve bee lyzed d modeled. But, my dgtl stellte commuctos systems, the modulto techques employed to trsmt re very sesble to Doppler effect. The velocty of the LEO stelltes some PCS stellte systems cuses lrge Doppler shft the crrer frequecy. The the lyss of phse o-lertes re qute mportt stellte pplctos speclly o-geo orbts. Cosder the mult-crrer put sgl equto (). v = { A cos( t + θ ( t) )} = ω () Where θ (t) s the modulted phse, d s the umber of crrers the system. It s possble to express ths set s crrer hvg me gulr frequecy, equtos () d (5). R ( ) ( ω t + θ ( t) ) v = R t cos (5) ( t) = [ A cos[ ( ω ω ) t + θ ( t) ] = = [ [( ) ( ) ] A se ω ω t + θ t + (6) [ Ase[ ( ω ω ) t + θ ( t) ] ( ) = θ t = t [ [( ) ( ) ] (7) A cos ω ω t + θ t = ω + ω ω = (8) Where ω d ω re the gulr frequeces of the frst d lst crrers the system, respectvely. 7 Issue, Volume 7, Aprl 8

4 I the mpltude-phse o-ler behvor the TWTA, the correspodg output sgl V(t) s determed by equto (9). ( t) = G[ R( t) ] { t + θ ( t) F[ R( t) ]} ω V cos + (9) Where G[R(t)] d F[R(t)] represet the mpltude d phse trsfer chrcterstcs of the TWTA, respectvely. The mpltude of the dvdul output crrer s determed by () []. P t Pt B = () Where P t s the totl put power, W. The thrdorder termodulto products re the most mportt, becuse ther mpltudes re frequetly the hghest. The mpltudes of these termodulto products c be obted usg () d () [5]. V V,,, P P =... t 5 t + [.5 + 5( ) ] + () P P =... t 5 t + + ( ) + () Flly, the crrer to terferece rto c be computed by (). I B = r D,, +,, ( r, ) V D ( r, ) V,, () Where D, (r,) d D,, (r,) re the umber of thrd-order termodulto products tht fll rght o the r-th crrer. The ctve devce selected to obt the results preseted the followg secto ws the TWTA. Ths devce hs moderte o-ler respose. AM-PM coverso s oe of the most mportt problem to solve dgtl stellte commuctos, becuse phse d frequecy modultos re lmost lwys chose s cosequece of ose level d very hgh med tteutos. bck-off clculted for prctcl system s llustrted Tble. TABLE. OUTPUT BACK-OFF P t [BO ] A B B [BO o ] I Fgure, the output bck-off correspodg to Tble s show. 5 Results The m results obted ths work, were the output bck-off d crrer to terferece rto the DS-CDMA mult-crrer stellte system. The output 8 Issue, Volume 7, Aprl 8

5 I Fgure s possble to detfy the mmum of output bck-off. Ths prmeter should be short order to mxmze the totl crrer to ose rto. Fg. Output Bck-Off. The crrer to terferece rto clculted s llustrted Tble 5 d Fgure. TABLE 5. CARRIER TO INTERFERENCE RATIO P t [BO ] V, V,, [C/I r] E-6-5.E E-6 -.E E E E E E E E E E-5-6.6E E E E E E-5-9.5E E E E-5 -.5E E-5 -.E E E E-5 -.6E E-5 -.E E E E-5 -.5E E-5 -.5E E-5 -.6E E E E E E- -.58E E- -.5E E- -.79E-.86 Fg. Crrer to terferece rto. The mult-crrer cse for bck-off clculto s llustrted Fgure. Fg. Output Bck-Off versus crrer verge power. I the Fgure the output bck-off s show for lrge tervl of crrer mpltude. It s possble to djust the lk order to reduce the output bckoff. 9 Issue, Volume 7, Aprl 8

6 Lk budget ws clculted by VSt softwre. VSt s prelmry softwre to tech dgtl stellte systems the Metropolt Autoomous Uversty, where we ehce ts fetures costtly. Fg. Output Bck-Off versus crrer mpltude. The Fgure 5 shows tht the coeffcet B does ot vry sgfctly, f the operto pot s er the best cse for output bck-off geerto. Fg. 5 Output Bck-Off versus B. 6 Coclusos The o-ler behvor of the devces used to mplfy the sgl the trspoders, cuses severl effects tht c reduce the performce of the system: hrmocs, termodulto products, AM-AM d AM-PM, re some of the most mportt spect to tke cosderto. I ths pper the crrer to terferece rto hs bee computed for DS-CDMA stellte systems, where o-ler resposes (phse d mgtude) re cosdered, besdes some results hs bee plotted order to compre the bck-off compesto for rbtrry umber of crrers. Refereces: [] De Gudez R., Gett F., Luse M. L., Advces Stellte CDMA Trsmsso for Moble d Persol Commuctos, Proceedgs of the IEEE, Jury 996. [] Shmbo O., Effects of Itermodulto AM/PM Coverso d Addtve Nose Multcrrer TWT Systems. Proceedgs of the IEEE, Februry 97. [] H T., Dgtl Stellte Commucto Systems, Mc-Grw-Hll 99. [] Stellte Hd book, ITU, Greoble. [5] Prtt T., Bost, C., Allut, J., Stellte Commuctos, Wley. [6] Srwte D. V. d Pursley M. B. Crosscorrelto Propertes of Pseudordom d Relted Sequeces, Proceedgs of the IEEE, Vol. 68, No. 5, My 98. [7] Pursley M. B., Roefs H. F. A., Numercl Evlutos of Correlto Prmeters for Optml Phses of Bry Shft-Regster Sequeces, IEEE Trsctos Commuctos, Vol. COM-7, No., Oct [8] Be Jem Z., Belghth S., Geerto of Bry Sequeces wth good AIP usg the Logstc Mp- Applcto to DS-CDMA Decorreltg Recever, rd WSEAS It. Cof. O Electrocs, Hrdwre, Wreless & Optcl Commuctos, Slzburg Austr, Februry. [9] Veljovc Z., Pejovc M., Rdusovc I,. Petrovc Z., A Model for OFDM-CDMA System wth Plot Toe, rd WSEAS It. Cof. O Electrocs, Hrdwre, Wreless & Optcl Commuctos, Slzburg Austr, Februry. [] Reyes-Ayl M., Adrde-Gozlez E. A., Ro-Frco J., QPSK d BPSK Sychroous Sequece DS-CDMA Stellte Lks, 8th WSEAS It. Cof. O Commuctos, Athes, Greece, July. [] Reyes-Ayl M., Adrde-Gozlez E. A., Ro-Frco J., No-Ler Mgtude Respose for Sychroous Sequece DS-CDMA Stellte Lks, 9th WSEAS It. Cof. O Commuctos, Athes, Greece, July 5. Issue, Volume 7, Aprl 8

7 [] Wescott R. J. Ivestgto of multple FM/FDM Crrers through Stellte TWT Opertg er to Sturto, Proceedgs of the IEEE, Vol., No. 6, 967. [] Sevy J. L., The Effect of Multple CW d FM Sgls pssed through Hrd Lmter or TWT, IEEE Trsctos Commuctos, Vol. COM-, No. 5, 966. [] Spoor H., Itermodulto Nose of FDM/FM Commuctos through Hrd Lmter, IEEE Trsctos Commuctos, Vol. COM-5, No., 967. [5] Shft P. D., Lmtg of Severl Sgls d ts Effect o Commucto System Performce, IEEE Trsctos Commuctos, Vol. COM-, No., 965. Issue, Volume 7, Aprl 8