Outage Probability for GPRS over GSM Voice Services

Transcription

1 Outage Prbability fr GPRS ver GSM Vice Services Shaji Ni, Yg Liag ad Sve-Gustav Häggma Helsii Uiversity f Techlgy, Istitute f Radi Cmmuicatis, Cmmuicatis Labratry, P.O. Bx 3, Otaaari 8, 5 Es, Filad, Fax: , i@tiltu.hut.fi. Abstract Geeral acet radi service (GPRS) is desiged fr trasmittig acet data ad sused t tae its radi resurce frm the l f chaels uused by GSM vice services. Obviusly, the itrducti f GPRS affects the vice services. I this aer the utage rbability f -frequecy hig ad frequecy hig systems with differet frequecy reuse factr has bee calculated i rder t ivestigate thse effects. The umber f uused vice chaels allcated t GPRS deeds the differece betwee the utage level f the existig GSM etwr ad the maximum accetable level. Fr bth -frequecy hig ad frequecy hig systems, GPRS affects the QS f vice services f the etwr with small reuse factr are higher tha that f the etwr with large reuse factr. GPRS will reduce the cell service area, but the reducti ercetage f the cell service area fr the system with small reuse factr is higher tha that fr the system with large reuse factr. excet fr causig a degradati f the QS f vice services. Therefre, a relimiary resurce laig fr GPRS is required t guaratee the quality f service fr vice users. A methd t calculate the utage rbability f the GSM-GPRS etwr fr bth the -frequecy hig ad the frequecy hig systems has bee reseted i [4], but the aer ly discussed the utage rbability fr the system with a frequecy reuse factr f 7. I this aer, we fcus discussis f the utage rbability fr systems with differet frequecy reuse factrs i rder t rvide sme guidelies fr system evaluati ad laig, as well as the admissi ctrl. This aer is rgaized as: i secti II, the calculati riciles f the utage rbability fr the GSM-GPRS etwr are exlaied; i secti III, the umerical results f the utage rbability fr systems with differet frequecy reuse factrs are reseted ad the quality f service (QS) f vice services affected by GPRS is discussed; fially the cclusis are give i secti IV. I. INTRODUCTION The curret methd f data trasmissi i the a- Eurea Glbal System fr Mbile Cmmuicatis (GSM) ad the America Advaced Mbile Phe Stadard (AMPS) cellular etwrs is circuit switchig. This techique reserves the traffic chael fr the etire cmmuicati time, ad wastes the radi resurce whe data traffic ccurs i bursts with lg silet itervals. I the develmet f GSM hase +, the Eurea Telecmmuicatis Stadard Istitute (ETSI) has secified [] a geeral acet radi service (GPRS) ver the GSM t icrease the utilizati efficiecy f the radi resurce ad rvide a set f additial services. The GPRS is desiged t utilize thse chaels uused by the circuit switched services t trasmit shrt bursts f acet data. Hwever, the itrducti f GPRS it GSM etwrs withut allcatig ew sectrum will icrease the iterferece rbability f circuit switched services. I additi, the hysical chael allcated t GPRS is shared by a few data users simultaeusly. The cchael iterferece t the vice users might vary raidly ad dramatically i the time iterval frm ms t a few secds deedig the trasmitted acet data size, because the lcatis f thse acet data users culd be largely differet. This effect culd drive the system it a uredictable ad ustable situati A. System mdel II. OUTAGE PROBABILITY All sigals are assumed t exeriece Rayleigh fadig with resect t a lcal mea sigal stregth, while the lcal mea sigal stregth exerieces lg-rmal slw fadig (with a stadard deviati σ s ) based a mea value, which determied by the ragati lss law f a iverse η-th wer f distace. The desired sigal ad iterferig sigals, ad amg the differet idividual iterferig sigal are statistically mutually ideedet. The slw fadig is assumed t be ucrrelated ad the variace is the same fr all cells. The wer ctrl algrithm is assumed t cmesate the athlss ad slw fadig artly (<α<) [, 3]. The wer ctrl errr is csidered as a lgrmal radm variable with a zer mea ad a stadard deviati σ e. Vice activity detecti is assumed t be used i the system. Usig the disctiuus trasmissi (DTX) methd, the trasmitted wer f a user is reduced t a lw level durig seech auses, ad its iterferece t ther users is assumed t be zer. Fr a vice user, the active time f seech is abut 4% f his call durati i average, ad the rest f the call durati is i listeig state. Therefre, whe a chael is used fr trasmittig vice, the activity factr is abut 4%. The selective

2 autmatic reeat request (ARQ) rtcl is used fr GPRS data trasfer. The MAC rtcl [] is develed t multilex u t eight differet MSs f GPRS t e hysical chael. Differet acet data lgical chaels ad the PDTCH ca als be multilexed the same hysical chael. Due t the umber f chaels available fr GPRS ad the multilexig mechaism, a chael accmmdatig a few GPRS users, ca be assumed t be i the trasmittig state all the time, if the users requestig service are large eugh. Therefre, the activity factr f a chael carryig the acet data traffic is used as % here as csiderig a high lad f GPRS traffic. B. Outage Prbability The utage rbability f a system is the rbability that the istataeus sigal wer t iterferece wer rati (S/I) falls belw a secified threshld γ ad deted as { } P ( utage) = Pr S / I < γ () A methd t calculate the utage rbability f the GSM-GPRS etwr fr bth the -frequecy hig ad the frequecy hig systems has bee reseted [4]. This methd taes it accut the Rayleigh fadig, wer ctrl errr, disctiuus trasmissi, ad frequecy hig. Accrdig t [4], the average utage rbability fr withut frequecy hig system is: P ( utage ) = w { + π N j= d q= i= + Nd Nv l l= = wj + d ex( cx ax ) [ j l wi + d ex( cx ax ) } () q i l where w i is the weight f the -it Gauss-Hermite quadrature frmula ad x i is the abscissa f the i-th zer f Gauss-Hermite lymial [5]; N v ad N d are the umber f cchaels used by vice users ad data users simultaeusly i M iterferig cells resectively, σ = σq = ( + α ) σs + σ e, σ = ( α) σs + σ, e a = σ l /, c = σ l /, α α η α α η d = γ( r r / r), d = γ ( r r / r ) q q q, r is the distace frm the desired mbile t its hst base stati; r (r r q ) is the distace frm the desired mbile t the -th iterferig base stati f vice (r data) user i dwli, r the distace frm the hst stati t lcati f the cchael vice (r data) user i the -th iterferig cell i uli; r (r r q ) refers t distace frm lcati f the cchael vice (r data) user i the -th iterferig cell its w base stati. The utage ] rbability is maily deedet the lcatis f mbiles, the frequecy reuse factr ad the chael lad by GSM vice services ad GPRS. Fr frequecy hig systems, each chael i a cell is ccuied by vice r data users with the same rbability, Nv( ) Vf + Nd( ) = (3) Nt Nh( ) where N t is the umber f time slts er TDMA frame ad N h () is the umber f distict frequecy carriers i cell ; N v () ad N d () are the umber f chaels usig i cell by vice users ad data users resectively. Here we assume the umber f frequecy carriers allcated t differet cells are the same. Because each f N = N v () + N d () c-chaels i cell is equally liely t cause iterferece ad they are mutually exclusive, the rbability f iterferece frm the i-th mbile i the -th cell shuld use /N. The average utage rbability with frequecy hig [4] is P ( utage ) = π w { + π N [ M l l= = w j in = j= + d ex( cx ax ) i j l ] } (4) α α η where di = γ( r r i / ri ) ; r is the distace frm the desired mbile t its hst base stati; r i is the distace frm the desired mbile t the -th iterferig base stati f the i-th mbile i dwli, r the distace frm the hst base stati f the desired mbile t the i- th mbile i the -th iterferig cell i uli; r i refers t distace frm mbile i i iterferece cell t its w base stati. III. NUMERICAL RESULTS I this secti, we will give sme umerical results f the utage rbability f the uli affected by trasmittig the GPRS traffic i the GSM radi etwr resurce. The effects f GPRS the utage rbability fr systems with differet frequecy reuse factrs are ur mai fcus. A. System mdel A hexagal cell s cellular system with midirectial ateas is assumed t be used. A cetral cell which is tae as the cell with desired mbiles has six iterferig cells. The ragati lss exet η ad stadard deviati σ s f the slw fadig are same fr all cells ad assumed t be 4 ad 8 db resectively. The vice chael activity factr is assumed t be.4, ad the acet data chael activity factr is %. Fr wer ctrl, the algrithm artly cmesatig the ath lss

3 ad shadwig is chse with α =.5 [, 3]. The threshld value f SIR is db. The umber f hysical chaels are 3 (4 8) available i a cell. It is sused that 3 chaels are reserved fr the etwr sigalig, thus, ly 9 chaels are available fr traffic i a cell. Suse the GSM etwr erated at a blcig rbability f fr vice services. Fr a cell with 9 traffic chaels, a average traffic lad f.4 Erlags is the surted. The average umber f vice calls i the system is E() = ρ(-p b ) =.4 98% =.6. This average umber f vice calls is csidered i ur calculatis ly. Based the average situati with chaels used fr vice services, a few chaels are assumed t be allcated t GPRS ad the utage rbability is calculated. The system arameters are listed i Table. TABLE. System arameters. frequecy reuse factr frm 3 t 9 ragati lss exet η = 4 std. deviati f the slw fadig σ s = 8 db vice chael activity factr.4 GPRS chael activity factr % wer ctrl (artly cmesati) α =.5 [, 3] std. deviati f wer ctrl errr σ e = ad db SIR threshld value γ = db ttal umber f traffic chaels 9 vice traffic lad (P b =%).4 Erlags chaels simultaeusly used by vice The mbile statis are uifrmly distributed with a idetical umber i each cell. The utage rbability is calculated thrugh a series f Mte Carl simulatis based geeratig a large umber f sashts. I each sasht lcatis f users are radmly geerated, ad a ure radm chael allcati algrithm is used t assig chaels t users i the cetral (desired) cell as well as i each iterferig cell, accrdig t the csidered umber f simultaeus users. Due t the radm chael allcati, fr the -frequecy hig system there always exist sme gd chaels with less cchael users ad bad chaels with mre cchael users, but fr the frequecy hig system the quality f every chael is the same because f the iterferece diversity. Frm the system laer s it f view, the system shuld guaratee the quality f the wrst chael with the largest umber f cchael users. Therefre, fr the -frequecy hig system the utage rbability f each sasht is calculated frm the wrst chael. I a simulati, sashts are geerated ad the utage rbability f each sasht is calculated by () r (4). The distributi f the utage rbability i a give cell deeds lcatis f the mbile statis i this cell ad its iterferig cells. Istead f givig a cumulative distributi fucti (CDF) f the utage rbability, we ly shw the.9 ercetile value, called 9% wrst case utage rbability. The 9% wrst case utage rbability is btaied by srtig thse sashts values i icreasig rder ad chsig the 9th value. B. Results The fllwig results are calculated fr a SIR threshld value f db ad the average situati f traffic chaels used by vice services i each cell simultaeusly. Fig. ad Fig. shw the 9% wrst case utage rbability f the -frequecy hig system as fucti f the frequecy reuse factr ad with the umber f chaels used fr GPRS as a arameter. Fig. ad Fig. crresd t the erfect wer ctrl (σ e = db) ad the wer ctrl with a errr f db stadard deviati (σ e = db) i the system resectively. As see frm the figures, the utage rbability icreases by abut 5%-% wheever the umber f chaels used fr GPRS icreases by e. The utage rbability icrease f the etwr with a small frequecy reuse factr caused by GPRS is higher tha that f the etwr with a large frequecy reuse factr. Therefre, the GPRS affects the QS f vice services f the etwr with small size reuse factr mre N v =, σe = db (K) Fig. The 9% wrst case utage rbability f the -frequecy hig system (erfect wer ctrl, σ e = db). N v ad dete the umber f chaels simultaeusly used by vice services ad GPRS resectively Nv =, σe = db Fig. The 9% wrst case utage rbability f the -frequecy hig system (wer ctrl with a errr f db stadard deviati, σ e = db). N v ad dete the umber f chaels simultaeusly used by vice services ad GPRS resectively. = =

4 Nv =, σe= db = Fig. 3 The 9% wrst case utage rbability f the frequecy hig system (erfect wer ctrl σ e = db). N v ad dete the umber f chaels simultaeusly used by vice services ad GPRS resectively Nv =, σe= db = Fig. 4 The 9% wrst case utage rbability f the frequecy hig system (wer ctrl with a errr f db stadard deviati, σ e = db). N v ad dete the umber f chaels simultaeusly used by vice services ad GPRS resectively. By cmarig the utage rbability f the same reuse factr ad same umber f chaels used by GPRS i Fig. ad, we fid that the wer ctrl errr causes the icrease f the utage rbability i the system with large umber f GPRS chaels higher tha that i the system with small umber f GPRS chaels. Therefre, the wer ctrl errr has mre imact the system erfrmace whe mre chaels are allcated t GPRS. This feature is als metied i the aer [4]. Fig. 3 ad 4 shw the 9% wrst case utage rbability f the frequecy hig system as fucti f the frequecy reuse factr ad with the umber f chaels used fr GPRS as a arameter. Fig. 3 ad 4 crresd t the erfect wer ctrl ad the wer ctrl with a errr f db stadard deviati i the system resectively. The erfrmace f the frequecy hig system i the utage rbability is much better tha that f the -frequecy hig system. Hwever, the geeral behavir f the utage rbability affected by GPRS is similar t that f the -frequecy hig system Nv =, σe= db K=4, K=4, K=4, = K=4, K=7, K=7, K=7, = K=7, Fig. 5 The 9% wrst case utage rbability -frequecy hig systems with the reuse factr (K ) f 4 ad 7 resectively Nv =, σe= db K=9, K=9, K=9, = K=9, K=, K=, K=, = K=, Fig. 6 The 9% wrst case utage rbability -frequecy hig systems with the reuse factr (K )f 9 ad resectively. I this aer, a arameter, the cell service area, is defied as the area ver which a secified utage rbability limit is achieved. I rder t ivestigate the cell service area f existig vice services affected by GPRS, we simulate the utage rbability distributed with the rmalized radius (r/r, R is the cell radius) i the desired cell. I each simulati, the lcati f the mbile stati i the desired cell is restricted t a circle with a radius r, ad lcatis f mbiles i iterferig cells are radmly geerated i thse cells. Fig. 5 ad Fig. 6 shw the 9% wrst case utage rbability frequecy hig systems with the reuse factr f 4, 7, 9 ad resectively. The figures shw that GPRS will reduce the cell service area, but the reducti ercetage f the cell service area fr the system with small reuse factr is higher tha that fr the system with large reuse factr. Fig. 7 ad Fig. 8 shw the 9% wrst case utage rbability distributed with rmalized radius (r/r) fr the frequecy hig systems with the reuse factr f 4,

5 7, 9 ad resectively. The behavir f the cell service area shriig as the itrducti f GPRS is similar t that f the -frequecy hig system. I summary, GPRS which dyamically shares radi resurce with GSM vice services may t reduced the caacity f vice services, hwever, the system erfrmace will be degraded, e.g., utage rbability will icrease ad cell service area decrease, due t the additial iterferece ctributed by acet data trasmissi. The hysical chael allcated t GPRS is shared by a few GPRS users simultaeusly. The cchael iterferece t the vice users might vary raidly ad dramatically i the time iterval frm ms t a few secds deedig the trasmitted acet data size, because the lcatis f thse acet data users culd be largely differet. This effect culd drive the system it a uredictable ad ustable situati excet fr causig a degradati f the QS f vice services. Therefre, a relimiary resurce laig fr GPRS is required t guaratee the quality f service fr vice users. The umber f uused vice chaels allcated t GPRS deeds the differece betwee the utage level f the existig GSM etwr ad the maximum accetable level. REFERENCES [] GSM 3.6, V5.., Digital cellular telecmmuicati system (Phase +);geeral acet radi service (GPRS); Service descriti (Stage ), Dec [] GSM 3.64, V5.., Digital cellular telecmmuicati system (Phase +); geeral acet radi service (GPRS); verall descriti f the GPRS radi iterface (Stage ), Nv [3] J. F. Whitehead, Sigal level based dyamic wer ctrl fr cchael iterferece maagemet, i Prc. 993 IEEE Veh. Techl. Cf., May 993, [4] Shaji Ni, Yg Liag, Sve-Gustav Häggma, Outage Prbability i GSM-GPRS Cellular Systems with ad withut Frequecy Hig, t be aeared i Wireless Persel Cmmuicatis. [5] M. Abramwitz ad I. A. Stegu (Ed.), Hadb f mathematical fuctis, Dver Publicatis, Ic., New Yr, 97, IV. CONCLUSIONS I this aer, the effects the quality f vice services due t the itrducti f GPRS it GSM etwr are ivestigated by calculatis f the utage rbability. The utage rbability f -frequecy hig system ad frequecy hig system with differet frequecy reuse factrs has bee calculated. Sice GPRS icreases the utage rbability f existig GSM vice services, all thse uused vice chaels might t be used fr carryig GPRS traffic. The umber f uused vice chaels allcated t GPRS deeds the differece betwee the utage level f the existig GSM etwr ad the maximum accetable level. Fr bth -frequecy hig system ad frequecy hig system, GPRS affects the QS f vice services f the etwr with small reuse factr are higher tha that f the etwr with large reuse factr. The wer ctrl errr has mre imact the system erfrmace whe mre chaels are allcated t GPRS. GPRS will reduce the cell service area, but the reducti ercetage f the cell service area fr the system with small reuse factr is higher tha that fr the system with large reuse factr. ACKNOWLEDGMENTS The rject is fiacially surted by Nia Research Ceter, Sera, Techlgy Develmet Ceter f Filad ad Helsii Telehe Cmay Nv =, σe = db K=4, K=4, K=4, = K=4, K=7, K=7, K=7, = K=7, Fig. 7 The 9% wrst case utage rbability frequecy hig systems with the reuse factr (K) f 4 ad 7 resectively Nv =, σe = db K=9, K=9, K=9, = K=9, K=, K=, K=, = K=, Fig. 8 The 9% wrst case utage rbability frequecy hig systems with the reuse factr (K) f 9 ad resectively.