A Lower Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control

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1 A ower Bound on SIR Threshold for Call Admsson Control n Multple-Class CDMA Systems w Imperfect ower-control Mohamed H. Ahmed Faculty of Engneerng and Appled Scence Memoral Unversty of ewfoundland St. John s, Canada mhahmed@engr.mun.ca Halm Yankomeroglu Broadband Communcatons & Wreless Systems Centre Carleton Unversty Ottawa, Canada halm@sce.carleton.ca Abstract Call admsson control (CAC s essental to guarantee e sgnal qualty n CDMA systems. Sgnal-to-nterference-andnose rato (SIR s used as e crteron for user admsson by comparng e SIR w a predefned reshold value (SIR. owerng s reshold level s desrable to reduce e blockng rate. However, a lower bound of SIR s vtal to keep e outage probablty ( out below a mum value. In s paper, we derve s lower bound of SIR (SIR -lb for mult-class CDMA systems w mperfect power control. SIR -lb of class (SIR -lb (, =, 2,., s determned by fndng e relatonshp between out ( (=, 2,., and SIR ( (=, 2,., where s e number of classes. Then, SIR -lb ( s determned as e lowest value of SIR ( at keeps e outage probablty of all classes below e correspondng mum values. Keywords Call admsson control; mperfect power control; multple-class CDMA systems I. ITRODUCTIO Unlke TDMA/FDMA systems, CDMA systems have soft capacty lmts. Ths means at e hgher e system loadng, e worse e sgnal qualty e users can get. Hence, call admsson control (CAC s usually used n CDMA networks to lmt e system loadng n order to preserve e sgnal qualty. Sgnal to nterference and nose rato (SIR based CAC s proposed n e lterature as an effectve technque to guarantee e sgnal qualty n terms of a mnmum SIR (SIR mn for admtted users (e.g. [, 2]. SIR mn s correspondng to e mum tolerable bt error rate (BER. In ese CAC schemes, SIR of e reverse lnk s measured and en compared w a predefned reshold value (SIR. The ncomng call s admtted only f e measured SIR s hgher an SIR. erfect power control s usually assumed n e reverse lnk of CDMA systems such at e receved power and SIR are kept constant for all users regardless of er locatons or channel condtons. In realty, however, e receved power and SIR fluctuate around e targeted values due to power control command errors and delay. It has been shown at SIR n s case can be modeled by e lognormal dstrbuton [3, 4]. If perfect power control would be realzable, SIR can be chosen equal to SIR mn. Due to e SIR fluctuatons, however, SIR has to be carefully chosen. A hgh value of SIR can lead to a low outage probablty ( out =(SIR<SIR mn but at e expense of a hgh blockng probablty ( b. On e oer hand, a low value of SIR can reduce ( b but w a hgh outage probablty. Ths s because C becomes nfeasble f e number of admtted users per cell exceeds a certan lmt. If C turns out to be nfeasble, out ncreases snce SIR converges to a lower level an e target value (SIR as shown n Fg.. It has to be emphaszed, ough, at outage (SIR<SIR mn can also take place (but w a much smaller probablty compared to e nfeasble C case even f C s feasble due to SIR fluctuaton around e target value as depcted n Fg.. A hgher bound of SIR has been derved n [] such at b can be kept below a mum value. In [6], we have derved a lower bound of SIR (SIR -lb n sngle-class CDMA networks. In s paper, we extend e work presented n [6] to e case of mult-class CDMA networks. The lower bound s derved such at e outage probabltes of all classes are kept below specfed values. The dervaton of SIR -lb s presented n Secton II. Then, e results for a dualclass case are presented n Secton III. Fnally, conclusons are gven n Secton IV. II. OWER BOUD OF SIR THRESHOD The lower bound of SIR (SIR -lb s determned usng e followng steps: The outage probablty of class ( out ( s determned as a functon of SIR (, SIR mn (, mean and standard devaton of SIR( and mean traffc ntensty (for all classes,.e. for all values of. The mean of SIR( s determned whle oer parameters (SIR mn (, standard devaton of SIR( and mean traffc ntensty are assumed to be gven. SIR -lb ( s determned as e lowest value of SIR ( at keeps out ( (for all values of below e mum acceptable value ( out_ (.

2 - m=sir SIR m<sir -4-4 SIR -6 SIR -6-8 SIR mn -8 SIR mn Tme-ndex Tme-ndex (a (b Fg.. SIR fluctuatons around e mean value (a feasble C (b nfeasble C. Assumng e numbers of users n dfferent classes are ndependent random varables, e outage probablty of class ( out ( can be expressed as out 2= = ( ( ( ( = ( out, 2, K, where ( s e condtonal outage probablty out, 2, K, of class gven e number of actve users (per cell n all classes (, 2,, and s e number of classes. W mperfect C, SIR can be modeled as a lognormallydstrbuted random process. Hence, ( can be out, 2, K, expressed as SIR = Q mn out, 2, K, 2 ( m( σ ( where m( and σ( are e mean and e standard devaton of SIR (, respectvely where e superscrpt denotes at SIR s expressed n s. As shown n Fg., when C s feasble, m( converges to e target SIR value ( SIR ( (2 (, but when C becomes nfeasble m( starts to degrade and ts value depends on e number of actve users n dfferent classes (, 2,,. Hence, m( can be expressed as SIR ( m( = log ( ( + f + R j j + ( ηow / S j = j > (3 where f s e rato of e nter-cell nterference to e ntracell nterference, R j s e rato of e receved power of class j to at of class, η o s e nose power spectral densty, W s e spreadng bandwd, S s e target balanced receved power level of class and s e mum number of users n class gven e number of users n oer classes ( j j. It can be shown at R j s gven by [7] ( + f ( f SIR + + SIR R j = + SIR SIR ( ( whle can be shown (usng a smlar analyss to at gven n [8] to be gven by (4 η ow ( = + ( + ( R j j, f SIR S j= j It s apparent from (2-( at ( s out, 2, K, constant and does not depend on e number of users n dfferent classes (, 2,, as long as C s feasble. When C becomes nfeasble, ( ncreases out, 2, K, monotoncally by e ncrease of e number of users. Ths trend s shown n Fg. 2 for e dual class case (=2. Snce e number of class users per cell ( can be modeled as a osson process, ( n ( s gven by ( = exp ( α α! where α ι s e average admtted traffc ntensty of class n Erlang per cell whch s gven by (6

3 Fg. 2. out,2 ( dependence on and 2 n a dual class CDMA system ( ( α = Λ (7 where Λ s e average arrvng traffc ntensty of class n Erlang per cell and b ( s e blockng probablty of class, whch s a functon of e reshold value of SIR of class (SIR ( as follows SIR ( = b Q b ( m σ ( ( From (, (2, (6, (7 and (8 out ( can be expressed as a functon of SIR j as follows ( = out 2 = = j = ( SIR mn ( m Q σ ( SIR m Λ j Q σ ( j! SIR j m ( exp Λ jq σ ( (8 (9 The lower bound of SIR ( (SIR _lb ( s determned as e lowest value of SIR ( at keeps e outage probablty of all classes smaller an e correspondng mum values ( out (k< out_ (k k=, 2,,. Snce a closed form for SIR -lb ( cannot be obtaned, SIR -lb ( s determned numercally. III. RESUTS A CDMA system w two classes (=2 s consdered here. The frst class (= represents voce servce whle e second class (=2 represents vdeo servce. The parameters of ese two classes are lsted n table I. The dependence of out ( and out (2 on SIR ( and SIR (2 s depcted n Fg. 3 at Λ =3 Erlang/cell, = Erlang/cell, SIR (2= (Fg. 3 (a and SIR (=-6 (Fg. 3 (b. As expected, out ( and out (2 ncrease monotoncally w e reducton of SIR ( or SIR (2. Also, t s apparent at out ( and out (2 have a strong dependence on SIR ( or SIR (2. A 2 or 3 dfference n SIR ( or SIR (2 can lead to a one order of magntude change n out ( and out (2. It s clear at out (2 s e lmtng factor snce e lowest value of SIR ( and SIR (2 (correspondng to out (= out (2= out_ =. s mposed by out (2. Ths s not surprsong snce class 2 (vdeo servce has hgher SIR mn as shown n Table I. However, s s not always e case. For nstance, f out_ of any (or bo of e two classes s ncreased to.3 (or hgher, out ( wll be e lmtng factor for SIR ( as shown n Fg. 3 (a. In fact, whch servce class s e lmtng factor for SIR s dependent on e loadng value of e two classes, SIR of e oer class, out_ of bo classes and e relatve values of SIR mn of bo classes. Fgs. 4 and depct SIR -lb ( versus Λ and at SIR (2=- and respectvely. As expected, SIR lb( s a monotoncally ncreasng functons of bo Λ and. However, SIR -lb ( has less dependence on at SIR (2=- 9 an at at SIR (2=-. Ths s because when SIR (2=, hgh blockng rate s encountered by class 2 users. Therefore, changng does not have a strong mpact on e outage probabltes of e two classes ( out ( and out (2. Also, t s apparent at e dependence of SIR -lb ( on Λ s hgher at lower values of. For nstance, at = SIR -lb ( ncreases from -7. to -6.8 by ncreasng Λ from to Erlang/cell, whle at =, SIR -lb ( ncreases from to -6. by ncreasng Λ from to Erlang/cell. It s also evdent at for some ranges of Λ and, ere s no fnte value for SIR -lb (. For example, at small values of Λ and ere s no need for any bound (.e. SIR -lb (=- snce t s possble to admt all arrval traffc wout volatng e constrants on e outage probabltes ( out (< out_ ( and out (2< out_ (2. On e oer hand, at large values of (>2 Erlang/cell at SIR (2=-, t s found at e outage constrants of class 2 users ( out (2 becomes hgher an e mum value ( out_ (2 regardless of e value of SIR -lb ( (.e. SIR -lb (=. TABE I. ARAMETERS OF THE TWO CASSES OF SERVICE arameter Voce Vdeo Transmsson rate 6 kbps 64 kbps Mnmum SIR (SIR mn -8-2 Target SIR (SIR -2-6 Maxmum outage robablty ( out_ % % Standard devaton of SIR (σ

4 .3.3 Class Class 2..9 Class Class Outage robablty ( out.2. Outage robablty ( out SIR ( ( SIR (2 ( (a (b Fg. 3. Outage probabltes dependence (a on SIR ( at SIR (2= and (b on SIR (2 at SIR (=-6. Smlar trends can also be observed n Fgs. 6 and 7 for SIR -lb (2 at SIR (=-6 and -4 respectvely. For nstance, SIR -lb (2 shows less dependence on Λ at SIR (=-4 an at at SIR (=-6. For example at = Erlang/cell, SIR -lb (2 ncreases from -.8 to by ncreasng Λ from to Erlang/cell at SIR (=-6, whle SIR -lb (2 changes from - to -.9 for e same ncrease n Λ at SIR (=-4. Also, t s apparent at for small values of Λ and, ere s no need for any bound on SIR (2 (SIR -lb (2=-. For example n Fg. 7, for < Erlang/cell all arrvng users can be admtted wout volatng e constrants on e outage probabltes ( out (< out_ ( and out (2< out_ (2. These results show at when strngent admsson condtons are mposed on e traffc of a certan class, e change of e traffc ntensty of s class does not have a strong mpact on e value of SIR -lb. Moreover, e results show at at low values of traffc ntensty, e constrants on e outage probablty can be guaranteed wout mposng any constrants on SIR. IV. COCUSIOS A lower bound of SIR (SIR -lb has been derved n mult-class CDMA systems w mperfect power control. SIR _lb s determned by fndng e relatonshp between out and SIR of all classes and en fndng e lowest value of SIR at keeps all outage probabltes ( out (, =, 2,., below e correspondng mum values ( out_. The analyss s developed for any number of classes (. However, e numerc results are obtaned for a dual class system (=2. It s assumed at outage occurs due to power control nfeasblty and SIR fluctuaton due to mperfect power control. SIR -lb has been determned for a CDMA system w two classes of servce. Furermore, e dependence of SIR -lb on e traffc arrval ntensty of dfferent classes has been analyzed. Results show at SIR -lb s vtal to keep e outage probablty below e mum value. Furermore, results ndcate at e value of SIR -lb of some class s strongly dependent on e traffc ntensty of s class and to some extent on e traffc ntensty of oer classes as well. Fndng an upper bound of SIR for multple-class CDMA wll be consdered n future work. REFERECES [] Z. u and M. El Zark, SIR-based call admsson control for DS- CDMA cellular systems, IEEE Journal on Selected Areas n Commun. (JSAC, vol. 2, no. 4, May 994, pp [2] I.-M. Km, B.-C. Shn, and D. ee, SIR-based call admsson control by ntercell nterference predcton for DS-CDMA systems, IEEE Communcatons etters, vol. 4, no., Jan., pp [3] A. Vterb and A. Vterb, Erlang capacty of a power controlled CDMA system, IEEE Journal on Selected Areas n Communcatons (JSAC, vol., no. 6, Aug. 993, pp [4] S. Aryavstakul and. Chang, Sgnal and nterference statstcs of a CDMA system w feedback power control, IEEE Trans. on Communcatons, vol. 49, Feb., pp [] D. Km, On upper bounds of SIR-based call admsson reshold n power-controlled DS-CDMA moble systems, IEEE Communcatons etters, vol. 6, no., Jan. 2, pp [6] M. Ahmed and H. Yankomeroglu, SIR reshold lower bound for SIR-based call admsson control n CDMA networks w mperfect power control, submtted to IEEE Communcaton etters. [7] M. Ahmed, H. Yankomeroglu, and B. Hashem, Rado Resource Management n Wreless Multmeda etworks, IEEE Globecom 2 (tutoral. [8] A. Sampa,. Kumar, and J. Holtzman, ower control and resource management for a multmeda CDMA wreless system, IEEE Internatonal Symposum on ersonal, Indoor and Moble Communcatons (IMRC 9, 99, pp. 2-2.

5 SIR -lb ( ( SIR -lb ( ( Λ Λ 3 Fg.4. SIR -lb ( dependence on Λ and (SIR (2=- Fg.. SIR -lb ( dependence on Λ and (SIR (2= SIR -lb (2 ( Λ 3 SIR -lb (2 ( Λ 3 Fg.6. SIR -lb (2 dependence on Λ and (SIR (=-6 Fg.7. SIR -lb (2 dependence on Λ and (SIR (=-4

An Upper Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control

An Upper Bound on SINR Threshold for Call Admsson Control n Multple-Class CDMA Systems wth Imperfect ower-control Mahmoud El-Sayes MacDonald, Dettwler and Assocates td. (MDA) Toronto, Canada melsayes@hotmal.com