Performance Anayss of an Enhanced DQRUA/C-CDA Protoco wth an LPRA Scheme for Voce Traffc Jae Yoon Park Korea Teecom R&D Group, Woomyun-dong 17, Seou, 137-792, Korea Seung Yeob Nam Dept. of EECS, KAIST, Daeon, 305-701, Korea Dan Keun Sung Dept. of EECS, KAIST, Daeon, 305-701, Korea Jemn Chung Korea Teecom R&D Group, Woomyun-dong 17, Seou, 137-792, Korea Abstract Ths paper presents a comparatve evauaton of a modfed verson A-Protoco of the Dstrbuted-Queueng Request Update utpe Access DQRUA/ut-Code Code Dvson utpe Access C-CDA protoco and an enhanced verson P-Protoco of the DQRUA/C-CDA protoco wth a attce poo for request accesses LPRA scheme n a packet-based voce traffc envronment. Anaytca resuts agree wth the smuaton ones and show that the P-Protoco outperforms the A-Protoco n terms of the packet oss rate for voce traffc. I. INTRODUCTION In the future generaton wreess packet networks t s mportant to deveop approprate mutpe access technques n order to provde varous types of servces [1]. Lu et a.[2] proposed a DQRUA protoco based on mut-code C CDA for wreess packet networks whch features a pggybackng PGBK mechansm to reduce the number of access requests and a bandwdth-on-demand far-sharng round-robn BoD- FSRR transmsson schedung pocy wth a maxmum capacty power aocaton CPA approach n a sot-by-sot bass to fuy utze rado resources. Due to these good features ths protoco can be apped to rea-tme traffc as we as nonreatme traffc. The modfed verson of the DQRUA/C- CDA protoco A-Protoco s the same as the the orgna DQRUA/C-CDA protoco caed the orgna protoco hereafter except that rea-tme traffc has hgher prorty than the non-rea-tme traffc n the A-Protoco. Thus f the A- Protoco s apped to data traffc ony, t s the same as the orgna protoco. We prevousy derved the anaytca resut for the A- Protoco ony [3] and ntroduced smuaton resuts for an enhanced verson of the DQRUA/C-CDA protoco wth an LPRA Lattce Poo for Request Accesses scheme P- Protoco n [4] n order to reduce request cosons. However, the mathematca anayss of the P-Protoco has not been avaabe thus far. Heren, focusng on voce traffc ony, we mathematcay anayze the system performance n terms of the packet oss rate for voce traffc. The rest of ths paper s organzed as foows: Secton II ntroduces the enhanced DQRUA/C-CDA protoco wth an LPRA scheme. Notatons used n anayzng the system performance are descrbed and anaytca resuts are obtaned n Secton III. In Secton IV, anaytca and smuaton resuts are compared for both A-Protoco and P-Protoco. Fnay, concudng remarks are gven n Secton V. II. THE ENHANCED DQRUA/C-CDA PROTOCOL WITH AN LPRA SCHEE P-PROTOCOL The orgna protoco was proposed for data traffc ony, especay for hgh data rate traffc usng ts mut-code, BoD- FSRR, CPA, and pggybackng schemes [2]. The concept of an LPRA was ntroduced [4]. The P-Protoco has a new sot structure based on an LPRA scheme proposed for upnk where each tme sot s dvded nto a number of sma mnsots and severa codes are assgned for requests and request packets are transmtted concurrenty wth datavoce packets of other cas durng a tme sot. It s necessary to reserve an addtona capacty margn for concurrent request accesses besdes background nose. Thus, n the P-Protoco, capacty for data transmsson s smaer than for the orgna protoco or A-Protoco by a capacty margn for concurrent request accesses. Snce request attempts are dspersed on the LPRA, actua nterference on data transmsson due to request attempts s sma n the P-Protoco. Fg. 1 shows a sot structure of the proposed P-Protoco where propagaton deay s negected and a tme sot can be dvded nto +2mnsots for request accesses consderng guard tme [5]. Frst mnsots are avaabe for requests and the ast two mnsots are used for recepton of a request acknowedgment and a transmsson permsson from the BS. There are two access schemes,.e., Schemes I and II, n the P-Protoco. A random scheme Scheme I and a desgnated scheme Scheme II are dstngushed dependng on the methods whch seect a request code and a request mnsot based on an LPRA scheme. Both schemes yed ow request access deays due to few or no cosons durng request accesses. In Scheme I request packets can be sent n one of many mnsots wth a randomy chosen code concurrenty wth data packets of other cas durng a tme sot. Request packets are assumed to code ony when both the same code and the same mnsot are seected. Hence, the number of code cosons of request packets can be greaty reduced due to an LPRA scheme. Scheme II s the same as Scheme I except that access requests are attempted n the pre-aocated mnsot poston wth a request access code assgned durng the ca admsson contro CAC procedure. The LPRA sze s defned as the product of 0-7803-7376-6/02/$17.00 c 2002 IEEE. 743
Fg. 1. Power n-sot Voce k-th tme sot on the upnk Power N rc2-1 N rc2-2 Code no. for access requests 1 0 0 1-2-1 k-th tme sot on the downnk Req. Transmsson Ack. Permsson Aocated for access request LPRA Voce The k-th tme sot structure of the P-Protoco. n-sot no. for access requests the number of request mnsots per tme sot and the number of codes assgned for request accesses. Thus, ths scheme s avaabe when the LPRA sze s equa to or arger than the number of admtted cas. If the LPRA sze s arge enough to aocate unque request access postons on the LPRA to a admtted cas, Scheme II s better than Scheme I because there s no request coson n Scheme II. III. ATHEATICAL ANALYSIS FOR VOICE TRAFFIC In order to derve the voce packet oss probabty for the P- Protoco, system mode and assumptons n [3] are used n ths paper. A. Notatons E1 event that a source s n the S p state n tme sot under the condton that the source s n the ON state E2 event that a source s n the ON and S p states n tme sot E3 event that a request packet experences a coson E4 event that a source cannot receve transmsson permsson E5 event that a request packet experences nether cosons nor corrupton E6 event that a voce packet bt experences corrupton n S 1 n Fg.2 b L r ength of a request packet L v ength of a voce packet number of request mnsots per tme sot N1 number of sources whch were n the ON and S p states n the prevous tme sot N2 number of sources whch were n the OFF state n the prevous tme sot t N3 N br N cb N cb2 N mr N off N on N or N p N rc N rc2 N rp N s N w P off on P on off P b r P b1 P b2 P c P cc P P m P mm P p P p P pg number of sources whch were n the ON and S np states n the prevous tme sot number of requests n the mnsot to whch a bt beongs number of corrupted bts on a voce packet n a tme sot number of corrupted bts on voce packet transmsson n the unoccuped parts of request packets durng the span of a voce packet that s, n the S 2 n Fg.2b number of requests n a mnsot number of sources n the OFF state n the prevous tme sot number of sources n the ON state n the prevous tme sot number of requests from the other sources except the target source number of sources n the S p state number of codes for access requests n a tme sot n the A-Protoco number of codes for access requests n a tme sot n the P-Protoco mnmum number of recever-code pars accommodatng channe capacty, except for the capacty margn for background nose n a BS number of sources n the system number of sources watng for transmsson permsson transton probabty of a voce source from the OFF to ON state transton probabty of a voce source from the ON to OFF state bt error probabtes of voce packets n one actua access request part wth r other requests of mnsots bt error probabty of voce packets n the S 1 n Fg.2b bt error probabty of voce packets n the S 2 n Fg.2b probabty that a request packet experences cosons n the A-Protoco probabty that a request packet experences cosons or corrupton n the P-Protoco voce packet oss probabty voce packet corrupton probabty due to AI at the ar nterface n the A-Protoco voce packet corrupton probabty due to AI at the ar nterface n the P-Protoco probabty that a source s n the S p state under the condton that the source s n the ON state n a tme sot steady-state probabty of P p probabty of a voce packet dscarded due to PGBK nformaton oss 0-7803-7376-6/02/$17.00 c 2002 IEEE. 744
Fg. 2. Detaed tme sot structure for the P-Protoco: a The proposed tme sot structure b The modfed structure for performance anayss. P r r probabty that a request packet s corrupted n the case that there are r other requests durng a mnsot P s successfu packet transmsson probabty P u probabty for non-recept of transmsson permsson due to capacty mt S np a source s n the state whch has receved no request acknowedgment or transmsson permsson S p a source s n the state whch has receved both request acknowedgment and transmsson permsson T number of correctabe bts n an encoded voce packet δ an addtona capacty margn for access requests n the P-Protoco. B. Anaytca dervaton of the voce packet oss probabty P for the P-Protoco Some parts of the equatons derved n [3] for the A-Protoco are modfed n order to obtan P for the P-Protoco because of concurrent transmsson of request packets and voce packets. In other words, request packet corrupton may occur n the P-Protoco because the power eve of request packets s reduced to essen the AI amount from other request and/or voce packets. Hence, cacuaton of P cc and P mm for the P- Protoco s dfferent from that of P c and P m for the A-Protoco. Now we cacuate P cc. P cc 1 P {E5 N s 1 1 0 0 P {E5 N on, N p P {N p N on P {N on, where P {E5 N on, N p N s 1 n0 [P {E5 N on, N p, N or n P {N or n N on, N p ]. 1 The detaed sot structure of the P-Protoco s depcted n Fg.2a. Heren, however, the sot structure shown n Fg.2 b s used for the performance anayss because the request packet error probabtes and the bt error probabtes of voce packets n the P-Protoco may vary dependng on the number of requested packets for each mnsot due to concurrent transmsson of voce packets and request packets. In Fg.2 b, the ength of a voce packet can be dvded nto two parts. The frst part s for actua access requests S 1 n the fgure. The second part s S 2, n whch there are no access requests. In Eqn.1 we can derve P {E5 N on, N p, N or n P {N mr r N on, N p, N or n P {E5 N on, N p, N or n, N mr r n 1 r r 1 1 n r 1 1 L r 1 P r r + 1 n 1 r 1 L r 1 1 n r 1 P r r+1 Scheme I, n 1 r r 1 1 n r 1 P r r+1 Scheme II. Snce the performance resuts of Schemes I and II of the P- Protoco are very smar as w be shown n Fg.4 n Secton IV ater, we cacuate the voce packet oss rate for Scheme II ony. Assumng that packets of ength L are transmtted over a memoryess bnary symmetrc communcaton channe wth a bt error probabty of P b usng a BCH FEC codng scheme that can correct up to T errors, the packet error probabty P E can be expressed as P E L T +1 L P b1 P b L. 2 Snce the bt error probabty of request packets s assumed to be constant durng a mn-sot, the packet error probabty 0-7803-7376-6/02/$17.00 c 2002 IEEE. 745
Error probabty 0.14 0.12 0.1 0.08 0.06 0.04 Packet error probabty of request packet Bt error probabty of voce packet P {N or n N on, N p Ns 1 n 1 P on off P on off P off on n 1 P off on Ns 1 n. 4 Hence, substtutng Eqn.4 obtaned n [3] and Eqn.3 nto Eqn.1 yeds 0.02 0 0 2 4 6 8 10 Number of request packets Fg. 3. Bt error probabtes of voce packets and request packet error probabtes accordng to the number of request packets per mnsot n the P-Protoco. of request packets can be obtaned from Eqn. 2 n the A- Protoco. However, Eqn. 2 cannot be used for voce packets of the P-Protoco because the bt error probabty dffers from mn-sot to mn-sot dependng on the number of request packets attempted n each mn-sot. A voce packet s sad to be ncorrecty receved f the number of bts n error durng a tme sot s greater than the number of correctabe bt errors T. In the A-Protoco, the bt error probabtes of voce packets are ndependent of the number of voce packets because power eves of voce packet transmssons are assumed to be optmay controed [2]. However, n the P-Protoco the bt error probabtes may vary dependng on the number of request packets from mn-sot to mn-sot because of concurrent transmsson of voce packets and request packets. Fg. 3 shows that bt error probabtes of voce packets and request packet error probabtes accordng to the number of request packets per mn-sot n the P-Protoco. Thus, f exacty two requests are attempted n every mn-sot, the same nterference eve as voce packet at a basc rate transmsson s acheved except for guard tme ntervas between mn-sots. However, f the number of request packets s ess than two n a mn-sot, voce packets durng the span of the mn-sot n the P-Protoco experence ess nterference than n the A-Protoco. From Fg.3 we can approxmate P r r+1 as a near functon such that: P r r +1 Ar + B where A and B are constants. P {E5 N on, N p, N or n n 1 r r 1 1 n r 1 A B Ar 1 A B A n. 3 P {E5 N on, N p N s 1 n0 Ns 1 n 1 A B A n N s 1 N s 1 n Ns 1 n 1 P on off P on off P off on n 1 P off on N s 1 n 1 P on off P on off P off on n 1 P off on N s 1 n 1 A B A n. 5 Lettng n m smpfes P {E5 N on, N p 1 A B A N s 1 1 P on off P on off N s 1 Ns 1 P off on m 1 P off on Ns 1 m m m0 A N s 1 1 P on off P on off N s 1 Ns 1 m P off on m 1 P off on N s 1 m m m0 1 A B A 1 P on off A N s 1 P on off. 6 Therefore, P cc s obtaned as { s 1 P cc 1 1 A B A 1 P on off 0 0 A N s 1 P on off Ns 1 π on1 π on N s 1 Pp1 P p 7 0-7803-7376-6/02/$17.00 c 2002 IEEE. 746
{ A + B + A s 1 1 P on off 0 0 P p1 P p Ns 1 π on1 π on N s 1 { + A s 1 N s 1 P off on 0 0 Pp 1 P p Ns 1 π on1 π on N s 1. 8 And from Eqn.12 n [3], we have { s 1 α β Ns 1 P p 1 P p 0 0 Ns 1 π on 1 π on N s 1 [1 π on β+π on [P p +α1 P p ]] N s 1. 9 Dfferentatng both sdes of Eqn.9 wth respect to α and β and assgnng α 1and β 1, we can obtan the foowng equatons. s 1 0 0 s 1 0 0 Pp1 P p Ns 1 π on1 π on N s 1 N s 11 P p π on. 10 N s 1 Pp1 P p Ns 1 π on1 π on N s 1 N s 11 π on. 11 Substtutng Eqns.10 and 11 nto Eqn.8, we obtan a smpfed form of P cc as foows: P cc A+B+ A 1 P on off N s 11 P p π on + A P off onn s 11 π on. And we now cacuate P mm. P mm P {N cb > T T 1 P {N cb T,N cb2 where T Lv L r 1 T Lr k k0 P b2 1 P b2 Lv Lr P b1 k 1 P b1 L r k, 12 and P b1 P {E6 s 1 0 0 N s 1 n0 [P {E6 N on, N p, N or n P {N or n N on, N p ]P {N p N on P {N on, P {E6 N on, N p, N or n P {N br r N on, N p, N or n P {E6 N on, N p, N or n, N br r n 1 r r 1 1 n r P b r. We can approxmate P b r from Fg.3 as foows: P b r r + Y where and Y are constants. Hence, P {E6 N on, N p, N or n n 1 r r 1 1 n r r + Y Y + n. In a smar manner descrbed n Eqn.5, P {E6 N on, N p can be obtaned as P {E6 N on, N p N s 1 N s 1 Ns 1 n! n! 1 P on off P on off P off on n 1 P off on Ns 1 n Y+ n Y + 1 P on off + N s 1 P off on. Therefore, P b1 s approxmated as s 1 P b1 0 0 Y+ 1 P on off+ N s 1 P off on P p 1 P p Ns 1 πon1 π on Ns 1 Y + 1 P on off N s 11 P p π on + P off onn s 11 π on. 13 Therefore, we can cacuate P mm from Eqns.12 and 13. We can obtan P for the P-Protoco after repacng P c and P m by P cc and P mm, respectvey, n Eqn.4 n [3]. 0-7803-7376-6/02/$17.00 c 2002 IEEE. 747
TABLE I SIULATION PARAETERS VOICE TRAFFIC Parameters Vaue ax. number of cas n the system 128 Requred E b /I o of voce packets 2.6 db Processng gan 64 Request packet sze, L r 31 bts Voce packet sze, L v 1023 bts Voce packet corrupton probabty, P m of A-Protoco 0.0116 Tme sot duraton 11.75 ms Voce source rate 32 kbps Voce actvty 0.35 P on off 1/30 P off on 1/55 FEC for request packets BCH31,11,5 FEC for voce transmsson packets BCH1023,648,41 Voce packet deay mt, D max 1 tme sot Number of codes for LPRA, N rc2 13 Number of mnsots for LPRA, 10 System capacty reservaton factors of A-Protoco and P-Protoco 1, 2 IV. PERFORANCE EVALUATION FOR VOICE TRAFFIC A smuaton envronments and termnooges of the P- Protoco, except some parameters sted n Tabe I, are dentca to those n the orgna DQRUA/C-CDA protoco and the A-Protoco [2, 3]. Fg. 4 ustrates the voce packet oss rate for a varyng number of voce cas. It shows that the anaytca and smuaton resuts are n good agreement. In the P-Protoco voce packet osses occur because of cosons or corrupton of request packets reated to P cc, droppng due to the channe capacty mt P u, corrupton due to AI on voce packet transmssons P mm, and dscardng due to PGBK nformaton oss P pg. When the number of mobe cas s ess than approxmatey 110, domnant factors affectng voce packet osses are P cc, P mm, and P pg. The request coson probabty graduay ncreases as the number of mobes ncreases. However, the request coson or corrupton probabty ncreases ony sghty because of a decrease n request cosons by usng the LPRA scheme n the P-Protoco. As the ncreasng number of mobes mts the avaabe channe capacty, the packet oss rate starts to rapdy ncrease because P u ncreases. The number of voce packets dscarded due to PGBK nformaton oss s proportona to the number of corrupted voce packets because voce packet corrupton on the ar nterface due to AI affects the pggybackng nformaton oss drecty, from the reaton P pg 1/P on off 1 1/P on off P mm. The packet oss rates for the P-Protoco are better than for the A-Protoco, not ony because the actua nterference eve caused by access requests s ess than the reserved nterference margn for access requests, but aso because t yeds ess Fg. 4. Voce packet oss rate 0.04 0.035 0.03 0.025 0.02 0.015 A-Protoco Smuaton A-Protoco Anayss Scheme I of P-Protoco Smuaton Scheme II of P-Protoco Smuaton Scheme II of P-Protoco Anayss 0.01 60 70 80 90 100 110 120 130 Number of voce mobe cas Comparson of anayss and smuaton resuts for voce traffc. packet corrupton due to AI than the A-Protoco. V. CONCLUDING REARKS We derved anaytca resuts of an enhanced DQRUA/C-CDA protoco wth an LPRA scheme P-Protoco for voce traffc. athematca anayss focused on the performance measure of voce packet oss probabty for the P-Protoco. The accuracy of ths formua was verfed by smuaton. These resuts show that the P-Protoco yeds better performance than the A-Protoco n terms of the voce packet oss rate because the LPRA scheme contrbutes to fewer request cosons and ess nterfered packet transmsson. REFERENCES [1] S. Ohmor, Y. Yamao, and N. Nakama, The future generatons of mobe communcatons ased on broadband access technooges, IEEE Commun. ag., pp. 134-142, Dec. 2000. [2] Z. Lu,. J. Karo,. E. Zark, and K. Y. Eng, Channe access and nterference ssues n mut-code DS-CDA wreess packet AT networks, Wreess Networks, pp. 173-193, 1996, J.C. Batzer AG, Scence Pubshers. [3] J. Y. Park, S. Y. Nam, D. K. Sung, and S. H. Km, Performance Anayss of a odfed DQRUA/C-CDA Protoco for Voce Traffc, n Proc. APCC, pp. 744-748, Oct. 2000. [4] J. Y. Park, D. K. Km, and D. K. Sung, An enhanced DQRUA/C- CDA protoco for wreess packet networks, IEICE Trans. Commun., vo. E83-B, no.7, pp. 1567-1571, Ju. 2000. [5]. J. Karo, Z. Lu, and K. Y. Eng, An effcent demand-assgnment mutpe access protoco for wreess AT networks, Wreess Networks, pp. 269-279, 1995, J.C. Batzer AG, Scence Pubshers. 0-7803-7376-6/02/$17.00 c 2002 IEEE. 748