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

Transcription

1 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 Abstract Call admsson control (CAC) s essental to guarantee the sgnal qualty n CDMA systems. Sgnal-tonterference-and-nose rato (SINR) s used as a crteron for user admsson by comparng the SINR wth a predefned threshold value (SINR th ). The choce of the SINR th value s restrcted by two opposng factors: the sgnal qualty and the network utlzaton. Settng SINR th at hgh value s desrable to ncrease the sgnal qualty. However, SINR th shouldn t exceed a certan lmt to keep the blockng probablty ( b ) below a mum value. In ths paper, we derve an upper bound of SINR th (SINR th-ub ) for mult-class CDMA systems wth mperfect power control. SINR th-ub of class (SINR th-ub (), =,,., ) s determned by fndng the relatonshp between the blockng probablty of all classes and SINR th (). Then, SINR thub() s determned as the hghest value of SINR th () that keeps the blockng probablty of all classes below the correspondng mum values. Keywords Call admsson control; mperfect power control; multple-class CDMA systems I. INTRODUCTION It s known that CDMA systems have soft capacty lmts, whch means that the hgher the system loadng, the worse the sgnal qualty the users can get. Hence, call admsson control (CAC) s usually requred n CDMA networks to lmt the system loadng n order to preserve the sgnal qualty. Sgnal to nterference and nose rato (SINR) based CAC s proposed n the lterature as an effectve technque to guarantee the sgnal qualty n terms of a mnmum SINR (SINR mn ) for admtted users (e.g., [, ]). SINR mn corresponds to the mum tolerable bt error rate (BER). In SINR-based CAC schemes, SINR of the reverse lnk s measured and then compared wth a predefned threshold value (SINR th ). The ncomng call s admtted only f the measured SINR s hgher than SINR th. erfect power control s usually assumed n the reverse lnk of CDMA systems such that the receved power and SINR are kept constant for all users regardless of ther locatons or channel condtons. In realty, however, the receved power and SINR fluctuate around the targeted values due to the power control (C) command errors and Mohamed H. Ahmed Faculty of Engneerng and Appled Scence Memoral Unversty of Newfoundland St. John s, Canada mhahmed@engr.mun.ca delay. It has been shown that SINR, n ths case, can be accurately modeled by the lognormal dstrbuton [, ]. Two factors affect the choce of the value for SINR th : network utlzaton and sgnal qualty. If SINR th s chosen hgh, the servce qualty wll mprove and the outage probablty ( out ) wll decrease but that wll lower the resource utlzaton and ncrease the blockng probablty ( b ). On the other hand, a low value of SINR th can reduce ( b ) but wll ncrease out. Ths s because C becomes nfeasble f the number of admtted users per cell exceeds a certan lmt. If C turns out to be nfeasble, out ncreases snce SINR converges to a lower level than the target value (SINR ) as shown n Fg. (b). It has to be emphaszed, though, that outage can also take place (but wth a much smaller probablty compared to the nfeasble C case) even f C s feasble due to SINR fluctuaton around the target value as shown n Fg. (a). An upper bound of SINR th n sngle class CDMA networks has been derved n [] such that b can be kept below a mum value. A lower bound of SINR th (SINR thlb), that keeps out below a mum value ( out_ ), has been derved n sngle-class [] and mult-class [7] CDMA networks. In ths paper, we derve an upper bound of SINR th (SINR th-ub ) n mult-class CDMA networks. The upper bound s derved such that the blockng probabltes of all classes are kept below specfed values. The dervaton of SINR th-ub s presented n Secton II. Then, the results for a dual-class case are presented n Secton III. Fnally, conclusons are gven n Secton IV. II. UER BOUND OF SINR THRESHOD As mentoned above, SINR th_ub s determned as the hghest value of SINR th that keeps b of all classes below the correspondng mum values ( b_ ). Hence, b dependence on SINR th has to be determned frst. Usng the law of total probablty, the blockng probablty of class ( b ()) can be expressed as ( N N N ) b ( ) K ( ),,, () = N N = N = = b N, N,, N

2 - m= m< mn - mn Tme-ndex Tme-ndex (a) (b) Fg.. SINR fluctuatons around the mean value (a) feasble C (b) nfeasble C. where ( ) s the condtonal blockng b N, N, K, N probablty of class gven the number of actve users (per cell) n all classes (N, N,, N ), s the number of classes and (N, N,, N ) s the ont probablty of havng N users of class, N users of class,, and N users of class. Wth mperfect C, SINR can be modeled as a lognormally-dstrbuted random process. Hence, ( ) s gven by N, N, K, b N SINR th ( ) m( ) ( ) =,, Q () K N σ ( ) N, N where m() and σ() are the mean and the standard devaton of (), respectvely and the superscrpt denotes that SINR s expressed n s. The condton of C feasblty s that N s less than the mum number of users of class (N ) gven the number of users n other classes (N, ). Therefore, when C s feasble (N <N ), m() converges to the target SINR value ( SINR ()) as shown n Fg. (a). When C becomes nfeasble (N >N ), m() starts to degrade as shown n Fg. (b) and ts value wll depend on the number of actve users. By extendng the analyss gven n [], t can be shown that N s gven by N η ow = + ( + ) () R N, () f SINR S = where f s the rato of the nter-cell nterference to the ntracell nterference, R s the rato of the receved power of class to that of class, η o s the nose power spectral densty, W s the spreadng bandwdth, S s the target receved power level of class. It can be shown that R s gven by [7] ( + f ) ( ) ( f ) SINR + + SINR R = + SINR ( ) SINR ( ) ( ) Hence, t can be easly shown that m() s gven by SINR ( ) N N m( ) = log N > N ( )( ) ( ) N + f + R N + ηow / S = () The number of actve users can be modeled by a multdmensonal Markovan chan as shown n Fg. for a two class network. β, () µ µ µ β, () µ β, () µ β, () β, () µ β β ), (), (,,,, µ µ, () µ β µ β, () β, () µ µ µ β, () β, () β β, (), (),,,, µ µ µ β, () β, () β µ, () µ µ µ β β, () β, () β, (), (),,,, µ β,() β, () β, (),,,, µ µ Fg.. Two dmensonal Markov chan representng a two class network. µ ()

3 where µ and µ are the average call departure rates of classes and, respectvely, whle β, () and β, () are the average rates of admtted traffc at state (, ) of classes and, respectvely, and they are gven by β () = λ () & β () = λ (),, N =, N =, N =, N = where λ and λ are the mean arrval traffc rate of class and class respectvely. For a system wth classes, t can be shown that the state probabltes (ont probabltes) can be determned as follows [9] ( N = x, N = y,.., N = z)= + = = x y Λ Λ... Λ k= z M k... ( Λ Λ... Λ, () ) Y where Λ s the average traffc ntensty of class n Erlang per cell and t s equal to λ /µ, whle M and Y are constants gven by M= x and Y= y ( () ) ( ) N = w, N = y,.., ( ) N =, N = w,.., z ( ( ) ) N =, N =,.., N = w ( () ) ( ) N = w, N = y,.., ( ) N =, N = w,.., k... ( ( ) ) N =, N =,.., N = w... Blockng orbablty TABE I. ARAMETERS OF THE TWO CASSES OF SERVICE arameter Voce Vdeo Transmsson rate kbps kbps Mnmum SINR (SINR mn ) (for the outage condton) - - Target SINR (SINR ) (for the C algorthm) - - Maxmum Blockng robablty ( b_ ) % % Standard devaton of SINR (σ) SINR th () Class Class class class Fg.. Blockng probablty dependence on SINR th () at SINR th ()= In order to determne SINR th_ub gven the mum values of b for all classes ( b _ (), =,,, ), an ntal small value for SINR th s assumed. Then, the Markovan model s used to determne the transton probablty for each state. The blockng probablty for each class s calculated and compared wth b _ for that class. If the blockng probabltes of all classes are below the correspondng mum values, SINR th s ncreased and the process s repeated. The mum SINR th that keeps b below b _ for all classes s consdered the upper bound of the SINR threshold value (SINR th_ub ). Blockng robablty class class class class III. RESUTS A CDMA system wth two classes (=) s consdered here. The frst class (=) represents voce servce, whle the second class (=) represents vdeo servce. The parameters of these two classes are lsted n table I. The dependence of b () and b () on SINR th () at SINR th ()= & on SINR th () at SINR th ()=- s shown n Fgs. &, respectvely at Λ = & Λ = Erlang/cell SINR th () Fg.. Blockng probablty dependence on SINR th () at SINR th ()=

4 As expected, b () decreases monotoncally wth the decrease of SINR th () and so does b () wth the decrease of SINR th (). Also, t s apparent that b () has a strong dependence on SINR th () and less dependence on SINR th (). kewse, b () has a strong dependence on SINR th () and less dependence on SINR th (). For nstance, and as shown n Fg., a - dfference n SINR th () causes a one order of magntude change n b () but t causes a very slght change n b (). Smlarly, and as shown n Fg., a dfference n SINR th () causes a one order of magntude change n b () but t makes a small change n b (). Ths shows that the blockng rate of one class has more senstvty to the SINR threshold value of ts class than the SINR threshold value of the other class. Fgs. and depct SINR th-ub () versus Λ and Λ at SINR th ()=- and respectvely. Also, Fgs. 7 and show SINR th-ub () versus Λ and Λ at SINR th ()=- and - respectvely. As expected, SINR th-ub () and SINR th-ub () are monotoncally decreasng functons of both Λ and Λ. These four Fgs. show that the domnant factor n determnng SINR th-ub s Λ. In the four curves the SINR thub decreases slowly wth the ncrease of Λ for small values of Λ. On the other hand the effect of Λ s much stronger as SINR th-ub monotoncally decreases wth the ncrease of Λ. For example, n Fg., wth the ncrease of Λ from to Erlang/cell, at Λ =, SINR th-ub () decreases by only. ; whle the same Fg. shows that the ncrease of Λ by Erlang/cell, at Λ =, SINR th-ub () decreases by.. Ths result s expected as the ncrease of class arrval rate makes the network more loaded compared wth the network load for the same ncrease of class arrval rate. It s also evdent that at hgh values of Λ and Λ, there s no fnte value for SINR th-ub () and SINR th-ub (). For example, n Fg. at Λ = Erlang/cell and Λ = Erlang/cell SINR th-ub ()=-. Ths means that the arrval rates of both classes are so hgh that the network cannot satsfy the mum blockng rate constrants of the two classes. In such a case, at least one of the blockng rates constrants wll be volated. IV. CONCUSIONS An upper bound of SINR th (SINR th-ub ) has been derved n mult-class CDMA systems wth mperfect power control. SINR th_ub s determned by fndng the relatonshp between b and SINR th of all classes and then fndng the hghest value of SINR th that keeps all blockng probabltes of all classes ( b (), =,,., ) below the correspondng mum values ( b_ (), =,,., ). The numerc results are obtaned for a dual class system (=). ower control nfeasblty and SINR fluctuaton due to mperfect power control are taken nto consderaton. SINR th-ub has been determned for a CDMA system wth two classes of servce. Furthermore, the dependence of SINR th-ub on the traffc arrval ntensty of dfferent classes has been analyzed. Results show that SINR th-ub s vtal to keep the blockng probablty below the mum value. REFERENCES [] 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., no., May 99, pp. -. [] 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., no., Jan., pp. 9-. [] A. Vterb and A. Vterb, Erlang capacty of a power controlled CDMA system, IEEE Journal on Selected Areas n Communcatons (JSAC), vol., no., Aug. 99, pp. 9. [] S. Aryavstakul and. Chang, Sgnal and nterference statstcs of a CDMA system wth feedback power control, IEEE Trans. on Communcatons, vol. 9, Feb., pp. 9-. [] D. Km, On upper bounds of SIR-based call admsson threshold n power-controlled DS-CDMA moble systems, IEEE Communcatons etters, vol., no., Jan., pp. -. [] M. Ahmed and H. Yankomeroglu, SINR threshold lower bound for SINR-based call admsson control n CDMA networks wth mperfect power control, IEEE Communcaton etters, Aprl, pp. -. [7] M. Ahmed and H. Yankomeroglu, A ower Bound on SINR Threshold for Call Admsson Control n Multple-Class CDMA Systems wth Imperfect ower-control, roc. IEEE Globecom. [] A. Sampath,. 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. -. [9] A. eon-garca, robablty and Random rocesses for Electrcal Engneerng, nd ed., Addson-Wesley Inc., 99 (Secton., pp. 7-77)

5 SINR th-up ()(db) SINR th-up () (db) Λ Λ Λ Λ Fg.. SINR th-ub () dependence on Λ and Λ (SINR th ()=- ) Fg.7. SINR th-ub () dependence on Λ and Λ (SINR th ()=- ) SINR th-ub () (db) SINR th-ub () Λ Λ Λ Λ Fg.. SINR th-ub () dependence on Λ and Λ (SINR th ()= ) Fg.. SINR th-ub () dependence on Λ and Λ (SINR th ()=- )