Direct Sequence Spread Spectrum II

Transcription

1 DS-SS II 7. Dire Sequene Spread Speru II ER One igh hink ha DS-SS would have he following drawak. Sine he RF andwidh i ie ha needed for a narrowand PSK ignal a he ae daa rae R, here will e ie a uh noie in he DS-SS reeiver and he ER will go up aordingly. I i rue ha he wider peru of he DS-SS ignal onain ie a uh noie, u ju a he reeiver proeing allowed u o ge rid of oher DS-SS ignal, o oo i allow u o ge rid of o of hi noie. he ignal plu noie i Afer de-preading we have n A o n 7.) n A o n 7.) Conider he er n. n i noie. Mulipliaion y doe no hange he apliude of n, i iply aue oe ign flip on an already rando proe. So we an ju all hi a new noie proe n n. n and n will have he ae variane hene he ae peral deniy. hen k ) k) k A o n o d A k n d ) o A k X k 7.3) Ju a for narrowand PSK, he la inegral over a ie inerval hene i will inlude peral oponen in a andwidh R / aou he arrier frequeny. herefore n /. I follow ha he ER will e exaly he ae a for PSK E P e Q 7.4) We ee ha here i no ER penaly for uing DS-SS. he fa he de-preading proeing effeively redue he noie power fro o, i.e., y a faor of an e hough of a a proeing gain of Gpro 7.5) owever, keep in ind ha in hi iuaion he gain i ju ouneraing he inreae in noie aued y he preading. he iporan poin i ha here i no lo of power effiieny in uing DS-SS. EE43: RF Engineering for eleouniaion So udon, Wahingon Sae Univeriy 5/3/7

2 DS-SS II 7. Channelizaion ow one igh hink, Okay, here i no power effiieny penaly for DS-SS, u wha aou andwidh effiieny? You have o ue ie a uh andwidh a you d need o do narrowand PSK a he ae i rae. So one uer i he aking up andwidh ha ould uppor uer. owever, i urn ou ha any differen link an operae over hi andwidh iulaneouly. Suppoe you wan o have wo link ha rani daa rea and repeively. For exaple, a ae aion i o operae downlink o wo oile. Give eah link i own P equene, ay, ) and ). hen he ranied ignal i he u of he wo DS-SS ignal. A o 7.6) hee oupy he ae andwidh. A he reeiver we une o one of hee y uliplying y he orreponding preading equene. o une o link we d have followed y A o A o 7.7) k) k o d A k), k, k k Le ay ha i i periodi wih period, ha i i repea afer hip. hen he la inegral aove vanihe if i j i j i j d i j d 7.8) 7.9) In oher word we need o find wo uually orhogonal inary veor, or ode, of lengh. hi i eay. Le e any equene of hip. hen we only need o ake ure ha ½ he hip in are he ae a he orreponding hip in while he oher ½ are differen. hen / /. For exaple, if he hip in are,,, hen ould have hip,,,. If we ould find hree uually orhogonal ode, hen hree link ould operae independenly. ow any uually orhogonal inary veor ode ) of lengh an you have? hi i analogou o aking how any uually orhogonal veor you an have in an dienional pae. he anwer i. So, DS-SS ue ie ore andwidh per uer han narrow-and ehod, u we an fi uer ino he ae peru. here i no lo in andwidh effiieny. oe, however, ha hi idea only work if he all he ode are aligned. You anno find ode ha are uually orhogonal for arirary relaive hif. We diu hi elow. An exaple of e of orhogonal inary veor i he Walh ode. he following reurion forula provide Walh ode for any lengh equal o a power of. EE43: RF Engineering for eleouniaion So udon, Wahingon Sae Univeriy 5/3/7

3 DS-SS II ) ere i an arix and i negaion, ha i, you flip he i. For exaple, he ode of lengh and 4 are 4 7.) he IS-95 CDMA ye ue Walh ode of lengh 64 o ipleen hannelizaion of hi or on he downlink fro he ae aion o he oile). You igh noie ha he fir ode will alway e all zero. In hi ae on and here would e no preading. hi i rue. owever, following Walh oding, all ignal are uliplied y a o-alled peudo-rando hor ode. hi ahieve he deired preading for all hannel. More aou hi when we diu CDMA ellular ye. Unynhronized Channel he Walh ode are orhogonal only if hey are ynhronized. Conider he la wo row of 4. oie ha if we hif he fourh row,,, ) o he righ one hip we ge,,, ), whih i he hird row. So, if on uplink we ried o ue differen Walh ode for differen oile, we ould ge a ignal uh a A ) ) o 7.) a he ae aion due o he differen ie delay on he wo differen link. We aue ha he wo apliude are he ae. In praie, CDMA ye uually eploy hande power onrol o ry and ahieve hi, i.e., ha ignal fro all oile arrive a he ae aion wih equal power level. A we ve ju noed, and ay e orhogonal, u and ) will no e for an arirary. So, le forge rying o have perfe orhogonaliy. Inead le he i h link ue i own P preading equene i having a period uh longer han hip. We require only ha differen equene e unorrelaed. In ha ae i i, u ) i j ) i equally likely o e or, i.e., i opleely rando. ow de-pread 7.) wih ) o ge A o A ) ) o 7.3) EE43: RF Engineering for eleouniaion So udon, Wahingon Sae Univeriy 5/3/7

4 DS-SS II 7.4 he eond er here i rando, i.e., noie, eaue and are unorrelaed. I ha a andwidh eaue he preading equene do) enered on he arrier frequeny. And, ine ) ) i ha he ae power a he fir er he ignal). So, i i analogou o 7.) where here he ignal of oile appear a noie o oile. Aue we have oile in a ell eah produing P ignal power a a ae aion. For now, negle noie a he reeiver. Inead, onider ha for any ignal, he oher ignal are effeively noie. Eah ha a power peral deniy deniy of he inerferene noie i P /. herefore he oal power peral Sine he i energy i P we have I ) P 7.4) For PSK and QPSK) E I P P ) 7.5) E P e Q 7.6) I For a given ER hi will fix he value of E / I. For exaple, E / I 5, or 7 d, give P e Q ).8%. hen we an olve for he nuer of uer ha an e uppored a hi ER 7.7) E / I oie ha hi i a of lii. Equaion 7.5) how ha eah ie we add a new uer he E / I degrade for all uer, u here i no hard lii a here i in a ye in whih you run ou of hannel. Equaion 7.7) would e valid for a ingle ell wih no ouide inerferene and no reeiver noie. In CDMA ye, however, all ell ue he ae frequeny. Eah oile ue a differen ode. I i no iple o alulae he inerferene fro oher ell. hi an e aouned for y a faor. If uer in our ell generae inerferene I, and if all oher ell have a iilar load, hen he inerferene o our ell fro all oher ell i I. aed on iulaion, a EE43: RF Engineering for eleouniaion So udon, Wahingon Sae Univeriy 5/3/7

5 DS-SS II 7.5 rough eiae i ha i on he order of. A he ae ie, a phone hannel i only aive for a fraion of he ie. A well-deigned ye an effeively op raniing during ilene. If i he fraion of ie a voie hannel i aive, hen he inerferene i redued y hi faor. So he oal inerferene fro all oure wih raniion only during voie aiviy, i approxiaely ) ) P /. Adding in he reeiver noie peral deniy, we have E I Solving for he nuer of oile we have P 7.8) P ) ) 7.9) ) E / I P Uing ypial nuer of. 5,, E / I 5 hi eoe 5 P 5 P 7.) A an exaple, ake 9. kz and 64. hen.88mz. In he lii of no noie ) we ge 64/5 4. If we ue eoring, hen hi i he nuer of uer per eor. he nuer of uer per ell i herefore 4. Copare hi o an analog ye wih a hannel andwidh of 3 kz, no eoring, and an 7 reue paern. In hi ae a andwidh of.88mzgive u 4 oal hannel or aou 6 per ell. herefore he CDMA ye give 7 ie he apaiy per andwidh relaive o he analog ye. Referene. Garg, V. K., IS-95 CDMA and da, Prenie all,, IS Ki, K. I., ed., andook of CDMA Sye Deign, Engineering, and Opiizaion, Prenie all,, IS Rappapor,. S., Wirele Couniaion: Priniple and Praie, nd Ed.,Prenie all,, IS Mark, J. W. and W. Zhuang, Wirele Couniaion and eworking, Prenie all, 3, IS EE43: RF Engineering for eleouniaion So udon, Wahingon Sae Univeriy 5/3/7