Throughput-Delay Analysis of a Multi-Channel Packet CDMA Scheme in a Fading Environment

Transcription

1 Throughput-Dely Alysis of Multi-Chel Pcet CDMA Scheme i Fdig Eviromet Weipig u, A. Chocligm y, d Lurece B. Milstei Deprtmet of Electricl d Computer Egieerig Uiversity of Clifori, S Diego 9500 Gilm Drive, L Joll, CA , USA AbstrctI this pper, we lyze the throughput d dely performce of multichel wireless ccess protocol usig CDMA i the presece of Ryleigh fdig. M equl-cpcity trffic chels, ech of which is ssiged uique orthogol spredig code, re shred by N mobile users (N M) o the upli (mobile-to-bse sttio li). Trsmissio ttempts o the upli re mde bsed o the busy/idle sttus of the M receivers, which is brodcst by the bse sttio, every slot, o the dowli (bse sttio-to-mobile li). A i.i.d. fdig chel model is used to describe the pcet success/filure process. Alyticl expressios for the verge per chel throughput d dely re derived. Simultio results re show to verify the lysis. I. INTRODUCTION Next geertio wireless etwors re evisged to support high dt rtes, pcet orieted trsport, d multimedi trffic hdlig. The desig of efficiet d robust wireless medi ccess protocols, d the evlutio of their performce i the presece of chel fdig, re ey techicl issues []-[]. High cpcity wireless etwors c be relized either by ssigig sigle widebd chel or by usig multiple rrow bd chels. The ltter pproch, which we will cosider i this pper, is prticulrly ttrctive whe cotiguous wide bdwidth spectrum is ot vilble. I multichel system, there re severl idepedet chels, d user c trsmit o y of these chels bsed o suitble ccess protocol. The performce of multichel slotted ALOHA systems, where multiple equl-cpcity chels re shred by my users, hs bee lyzed i [5], [6]. However, these studies ssumed determiistic chel model tht did ot cosider the effect of multipth fdig o the system performce. I fct, mobile rdio chels re severely ffected by time-vryig losses due to distce, shdowig (blocge due to buildigs, trees, etc.), d multipth fdig. Medi ccess cotrol schemes usig code divisio multiple ccess (CDMA) re becomig populr for pcet commuictio i wireless eviromets becuse of their robustess to iterferece, bility to perform well uder multipth coditios, d eed for less regultory d frequecy coorditio efforts. Erlier studies o both rdom d slotted CDMA protocols iclude [7], [8]. I [9], [0], we preseted medi ccess protocol tht mes This wor ws prtilly supported by TRW Systems Itegrtio Group, Airtouch Commuictios, d the MICRO progrm of the Stte of Clifori. ya. Chocligm is presetly with Qulcomm, Ic., S Diego, CA 9 use of the upli (mobile-to-bse sttio li) chel sttus iformtio, which is coveyed to the mobiles through busy/idle flg o the dowli (bse sttio-to-mobile li) brodcst. The throughput performce of system tht uses sigle trffic chel o the upli ws lyzed i correlted Ryleigh fdig eviromet. I [], we exted this protocol to utilize multiple trffic chels o the upli by ssigig uique, orthogol spredig code to ech chel, d lyze the throughput performce. I this pper, we further lyze the dely performce of the proposed multichel protocol i the presece of fdig. The detiled descriptio of the proposed multichel ccess protocol is preseted i Sectio. I Sectio 3, we lyze the throughput d dely performce of the protocol i the presece of fdig. Numericl d simultio results re preseted i Sectio. Coclusios d res of future wor re provided i Sectio 5. II. MULTICHANNEL PACKET CDMA PROTOCOL Cosider pcet commuictio wireless etwor where N mobile users shre M equl-cpcity trffic chels (N M) o the upli to commuicte with the bse sttio. All the upli chels re sychroized d slotted to oe pcet durtio. Ech upli chel is ssiged uique, orthogol spredig code such tht the pcets trsmitted o give chel re spred usig its ssiged spredig code. I other words, ll the users i the etwor c use y oe of M differet spredig codes followig the ccess rules. The bse sttio is provided with M receivers, ech tued to differet spredig code, to demodulte ll the upli chels trffic. Bsed o the busy/idle sttus of the M receivers, the bse sttio brodcsts M-bit busy/idle word, every slot, o the dowli. The busy/idle flg correspodig to ech chel is set or reset depedig o whether or ot the dt pcets re beig trsmitted o tht chel. Ech messge geerted t the mobiles cosists of two segmets, mely the heder segmet d the dt segmet. The heder segmet is of oe pcet legth. It crries premble for spredig code cquisitio, d cotrol iformtio lie the destitio ddress, the umber of pcets i the dt segmet, etc. The dt segmet, which represets the ctul trffic, cosists of rdom umber of pcets. Trsmissio ttempts re mde by the mobiles oly t the slot boudries by sedig the heder pcet. The mobile, oce it receives messge to be set to the bse sttio, first checs the sttus of the busy/idle word which it periodiclly receives from the bse sttio o the dowli. If ll the

2 M busy/idle flgs idicte busy sttus, the mobile refris from mig trsmissio ttempt, d reschedules the ttempt to lter time. If oe or more flgs idicte idle sttus, the the mobile rdomly pics oe of these idle chels, d mes trsmissio ttempt by sedig heder pcet o the upli slot of the chose chel. If the heder pcet is received successfully (without pcet loss due to fdig or collisio), the bse sttio sets the correspodig chel s flg busy for subsequet slots, where is the umber of pcets i the dt segmet of tht messge. This permits the mobile to sed ll the dt pcets i those slots. Durig these slots, other mobiles would receive busy sttus flg for this chel d so they would ot me trsmissio ttempts o it. The bse sttio resets the flg bc to idle sttus fter slots. If the heder pcet is lost (due to collisio or fdig), the the bse sttio will ot respod with busy sttus flg, but will cotiue to sed the correspodig chel s flg s idle. This is idictio to the mobile tht the heder pcet ws lost, d so it hs to reschedule its trsmissio ttempt to lter time. Note tht, i cse of error-free busy/idle word receptio t ll the mobiles, collisios re possible oly durig the heder pcet trsmissios d ot durig the trsmissio of pcets i the dt segmet. III. PERFORMANCE ANALYSIS The lysis of the system dely performce is obtied by expdig the pproch employed i []. As i [], sigle cell system with o iter-cell iterferece is cosidered. Busy/idle word is ssumed to be received istteously, d error-free by ll the mobiles. The effect of cpture is igored. All the mobiles trsmissios re ssumed to be power cotrolled such tht the slowly vryig distce d shdow losses re perfectly compested, wheres the rpidly vryig multipth fdig remi ucompested. The multipth fdig is cosidered to be frequecy o-selective, the effect of which is described s multiplictive complex fuctio, (t). The evelope of (t) hs i.i.d. Ryleigh distributio. Bsed o model of The pcet success/filure process i the presece of fdig i [9, 0], the verge pcet error rte, P E,isgiveby P E, e,f () where F is the fdig mrgi of the li. New messges rrive t the mobiles with probbility i ech slot. Ech mobile is ssumed to hve buffers to hold oe messge. Newly rrivig messges re reected util the stored messge is successfully set to the bse sttio. The legth of the dt segmet of ech messge,, mesured i iteger umber of pcets, is ssumed to follow geometric distributio with prmeter g m, d probbility mss fuctio P [ i] gm (, g m ) i, i ; ; 3; 0 otherwise. I y give slot, ech mobile c be i y oe of the three sttes, mely,idle/heder stte, dt tx stte, d bclogged stte. Refer to Figure. I the idle/heder stte, the mobile remis idle or geertes ew messge with probbility, rdomly chooses idle upli chel (if vilble), d trsmits the heder () o ew messge ew heder success IDLE/HEADER N-- sed dt pcets DATA_T messge completed ew heder filure/ ll chels busy old heder success BACKLOGGED Fig.. Mobile stte trsitio digrm old heder filure pcet i the upli slot. If the heder pcet trsmissio is successful, themobilemovesfromtheidle/heder stte to the dt tx stte, i which it trsmits the dt pcets cotiuously util ll the pcets i the messge re set, d the moves bc to the idle/heder stte. The mobile moves from the idle/heder stte to bclogged stte if ll the upli chels re foud busy upo rrivl of messge. Similrly, if the heder pcet is lost due to collisio or bd chel coditios, the mobile moves from the idle/heder stte to the bclogged stte. I the bclogged stte, the mobile rechecs the sttus of the upli chels fter rdom umber of slots. This retrsmissio ttempt dely is ssumed to be geometriclly distributed with prmeter g r. If mobile i the bclogged stte fils to retrsmit its heder pcet successfully, it stys i this stte util its heder pcet trsmissio is successful, fter which it moves to the dt tx stte. A. Throughput Performce Let x t be the umber of mobiles i the dt tx stte d y t be the umber of mobiles i the bclogged stte t the ed of slot t. The two dimesiol rdom process fx t ;y t g is fiite stte Mrov chi. Bsed o the coditiol probbility tht mobiles simulteously trsmit heder pcets d c s of those pcets re successfully received t the bse sttio, the oe step trsitio probbility tht the system moves from (x t ; y t ) t time slot t to (x t+ l; y t+ m) t time slot t +is give by mi(m,;) P ;lm N,, (, ),, 0 c s0 gr, (, g r),+ gm cs+,l, (, g m) l,c s f (c s; M, ); (3) where M is the totl umber of spredig codes (i.e., the umber of upli chels), N is the totl umber of mobiles, N M, 0 ; l M, 0 ; m N,, m, + c s,dthe coditiol probbility f (c s ; M, ), which is the probbility

3 tht c s heder pcets re successfully received, coditioed o mobiles out of N,, mobiles i idle/heder stte d mobiles i bclogged stte trsmit heder pcets over M, chels, c be evluted by recursive expressio s f (c s; M, ) where p (i) i0 i6, i(, p (i) f (c s, i; M,, ) +p () f (c s,, ;M,, )(, PE) +p () f (c s, ;M,, )PE; () M, ),i ( M, )i is the probbility tht i pcets out of pcets re trsmitted over the rbitrrily chose chel. The iitil coditios for f (c s ; M, ) c be foud i []. Let P (P ;lm ) be the probbility trsitio mtrix d f g, 0 M, 0 N,, deote the stedy-stte probbility vector. c be clculted by solvig the set of lier equtios P ; (5) d usig the coservtio reltioship M 0 0 (6) The etwor throughput,, which is defied s the verge umber of pcets successfully received per time slot, is obtied from the verge umber of successful dt pcets, EfS d g, d the verge umber of successful heder pcets, EfS h g, i the stedy stte s EfS d g + EfS h g; (7) where EfS d g M 0 M 0 P, (, P E) P E (8) (, P E) EfSg(, PE) P M EfS g 0 is the verge umber of users i the dt tx stte. The verge umber of successful heder pcets, EfS h g, is obtied s EfS h g M M N,l 0 0 l0 m0 mi(m,;) (, ),,, g cs+,l c s0 c s N,, gr,,+ (, g r) m (, g m) l,c s f (c s; M, ) (9) Filly, we obti the verge per chel throughput, i.e., the verge umber of pcets successfully received per slot per chel, s c M (0) B. Dely Performce The messge trsfer dely is the time elpsed betwee the rrivl of messge t the mobile d the successful completio of its trsmissio to the bse sttio. This dely cosists of two compoets, mely, ) the umber of slots elpsed to chieve successful heder pcet trsmissio, d ) the umber of slots elpsed durig the dt pcets trsmissio. The verge messge trsfer dely, EfDg,isgiveby EfDg EfD h g + EfD d g; () where EfD h g is the expected umber of slots it tes to chieve heder pcet success, d EfD d g is the expected umber of slots spet for dt trsmissio. EfD d g is othig but the expected legth of the messge. For geometric distributio of messge legth with prmeter g m, EfD d g is give by EfD d g g m () EfD h g c be obtied by evlutig the expected umber of heder pcets lost, EfF h g, d the expected umber of witig slots (excludig the lost heder pcets) elpsed util the success of the heder pcet, EfW r g. The expressios for EfW r g d EfF h g re give by EfW rg M, (, g r) g r (3) d EfF h g 0 (, g r) M 0 M M N,l ; mi(m,;) (, c s) 0 0 l0 m0 c s0 N,, (, ),, g,,+ r (, g r), g cs+,l l,c m (, g s m) f (c s; M, );() The expressio for EfD h g is the give by EfD h g + E ff hg + E fw rg E fs h g (5) Note tht the i (5) is to ccout for the successful heder pcet slot i the dely expressio. IV. RESULTS AND DISCUSSION Numericl results for the verge per chel throughput of the proposed multichel protocol obtied from (7) d (0) for M 3, N 5, g m 0, dg r 0 re plotted i Figure. The vrious vlues of fdig mrgis cosidered re 5, 0, d 0 db. Results for o fdig cse (i.e., F! ) relso plotted. From (), the g m vlue of 0. correspods to verge messge legth of 0 dt pcets. Liewise, the prmeter g r

4 lysis results F5dB, F0dB,...F0dB,..Fifiity ++++simultio results M3, N5, gm0., gr0. Averge per chel throughput 0. Averge per chel throughput 0. N5, gm0., F0dB, gr0....m; M; M Fig.. Averge per chel throughput, c, vs ew messge rrivl rte, Fig.. Effect of umber of chels, M, o the verge per chel throughput.. Normlized me messge dely lysis results F5dB, F0dB,...F0dB,..Fifiity ++++simultio results M3, N5, gm0., gr0. Normlized me messge dely M M M3 N5, F0dB, gm0., gr Fig. 3. Normlized me messge dely vs ew messge rrivl rte, Fig. 5. Effect of umber of chels, M, o the ormlized me messge dely. 0 mes tht the verge time betwee retrsmissio ttempts is 5 slots. I dditio to the lysis, the proposed protocol ws simulted s well, d the throughput performce collected over millio slots of simultio is lso show i Figure. The lies represet the lyticl results d the mrers represet the simultio poits. Whe there is o fdig (tht is, pcet losses re oly due to heder pcet collisios), the protocol is foud to offer mximum throughput o the order of 0.9. Whe the chels re fdig, mximum throughputs s high s the o fdig cse c still be chieved, provided the fdig mrgi is mitied better th 0 db. With prcticl vlues of fdig mrgi, sy 0 db, the resultig mximum throughput is i excess of. Whe the fdig mrgi decreses to 5 db, the mximum throughput degrdes to 3. For the bove set of system prmeters, the messge trsfer dely performce of the proposed protocol is show i Figure 3. The curves represet the verge dely vlues obtied from (), d ormlized to the verge legth of the messge, icludig the heder pcet (i.e., +g m ). A ormlized me messge dely of uity t low rrivl rtes implies tht the messges get trsmitted immeditely o rrivl without y witig/retrsmissio delys. Both icresed messge rrivl rtes d lower fdig mrgis re see to icrese the ormlized de- ly beyod uity. Eve whe there is o fdig, the ormlized dely icreses beyod uity t high rrivl rtes (e.g., ormlized dely of.8 t ), which is mily due to heder pcet collisios d subsequet reschedulig of trsmissio ttempts. Lie the throughput, the dely performce t fdig mrgi of F 0dB is very close to the o fdig cse. Compred to the o fdig cse, the dely performce worses by 5% d 0%, respectively, t fdig mrgis of 0 db d 5 db. Note tht the lyticl d simultio results i Figures d 3 closely gree, thus verifyig the lysis. The effect of the umber of chels, M, o the throughput d dely chrcteristics of the proposed protocol is show i Figures d 5. The plots re prmeterized by differet vlues of M ; ; 3 t N 5, F 0dB, g m 0, dg r 0. At low rrivl rtes, sigle chel system (M ) offers higher throughput th multichel system (M ; 3). This is becuse, i the bsece of eough trffic t the mobiles, ll the chels go uderutilized. Also, this better throughput performce of sigle chel system hs ssocited icrese i dely performce compred to multichel system, s see from Figure 5. At high rrivl rtes, the throughput performce behvior reverses (i.e., the sigle chel system offers less throughput th mutlichel system). Here, sigle chel system loses more

5 Averge per chel throughput New heder pcet rrivl rte, lmd M3, N5, F0dB, gm Old heder pcet rrivl rte, gr Fig. 6. Effect of gr d o the verge per chel throughput, c. Normlized me messge dely New heder pcet rrivl rte, lmd M3, N5, F0dB, gm Old heder pcet rrivl rte, gr Fig. 7. Effect of gr d o the ormlized me messge dely. cpcity through higher collisio rtes th does multichel system. Further, the dely performce t high rrivl rtes is sigifictly better i multichel system th i sigle chel system (e.g., ormlized dely of.9 d 6.7, respectively, for M 3d M whe ). I Figures 6 d 7, the effect of the prmeter, g r, o the throughput d dely chrcteristics of the proposed protocol t vrious vlues of ew messge rrivl rte,, is show s 3-D cotour plots for N 5, M 3, F 0 db, d g m 0. The reso for the bell-shped curve is tht if g r is too smll (i.e., more witig slots i the bclogged stte), more slots will go uutilized durig the witig period, d if g r is high, more slots will witess collisio resultig i decresed throughput d icresed dely performce. V. CONCLUSIONS We lyzed the throughput d dely performce of multichel wireless pcet CDMA scheme i the presece of Ryleigh fdig. The proposed scheme mde use of multiple slotted chels, ech of which employed uique spredig sequece. The efficiecy of the protocol is high becuse the trsmissio ttempts o the upli chels re mde bsed o the busy/idle sttus of the receivers, which is brodcst by the bse sttio, every slot, o the dowli. The resultig rchitecture is highly flexible i the sese tht the system c be scled up or dow simply by ddig or removig chels bsed o the bdwidth eeds of the etwor. I dditio, the cocept of heder pcet for ech messge resulted i sigifictly low overhed time employed for the code cquisitio. Further ogoig ivestigtios iclude the effect of cpture d retrsmissio of erroeous dt pcets o the system performce. It must be oted tht the Ryleigh fdig is ssumed to be i.i.d. i this pper, which is good model for fst movig users i multipth eviromet. A extesio of the curret multichel protocol lysis to dopt correlted fdig process, which is suit for slowly movig users, will be useful future wor. REFERENCES [] K. Phlv, d A. H. Levesque, Wireless Iformtio Networs, Joh Wiley, New Yor, 995. [] W.-C. Wog, Pcet reservtio multiple ccess i metropolit micocellulr rdio eviromet, IEEE Jl. Sel. Ares Commu., vol., o, 6, pp , August 993. [3] F. Borgoovo, M. Zorzi, L. Frtt, V. Trecordi, d G. Bichi, The cpture-divisio pcet ccess (CDPA) for wireless persol commuictios, IEEE Jl. Sel. Ares Commu., vol. SAC-, pp , My 996. []. Qiu, d V. O. K. Li, Dymic reservtio multiple ccess (DRMA) A ew multiple ccess scheme for persol commuictio system, Wireless Networs, pp. 7-8, Jue 996. [5] W. Yue, The effect of cpture o performce of multichel slotted ALOHA systems, IEEE Trs. Commu., vol. 39, pp. 88-8, Jue 99. [6] Z. Zhg, d Y.-J. Liu, Commets o The effect of cpture o performce of multichel slotted ALOHA systems, IEEE Trs. Commu., vol., o. 0, pp , October 993. [7] D. Rychudhuri, Performce lysis of rdom ccess pcet-switched code divisio multiple ccess systems, IEEE Trs. Commu., vol. COM-9, o. 6, pp , Jue 98. [8] A. Polydoros, d J. Silvester, Slotted rdom ccess spred-spectrum etwors A lyticl frmewor, IEEE Jl. Sel. Ares Commu., vol. SAC-5, o. 6, pp , July 987. [9] A. Chocligm, L. B. Milstei, d M. Zorzi, Performce of wireless medi ccess protocol o Mrovi fdig chel, Proc. IEEE GLOBECOM 96, pp , Lodo, November 996. [0] A. Chocligm, M. Zorzi, L. B. Milstei, d P. Vetrm, Performce of wireless ccess protocol o Mrovi fdig chel with cpture d urelible feedbc, submitted to IEEE Trs. Commu. [] A. Chocligm, W. u, d L. B. Milstei, Performce of multichel pcet CDMA protocol i fdig eviromet, to pper i Proc. IEEE VTC 97, Phoeix, My, 997.