Implementation of a High-Performance Assignment Scheme for Orthogonal Variable-Spreading-Factor Codes in WCDMA Networks

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1 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Implementaton of a Hgh-Performance Assgnment Scheme for Orthogonal Varable-Spreadng-Factor Codes n WCDMA Networs JUI-CHI CHEN * Department of Computer Scence and Informaton Engneerng, Asa Unversty, Tawan ABSTRACT In WCDMA, channelzaton s acheved by assgnng OVSF codes to dfferent users. The codes n a Node-B are valuable and lmted. Much research has been devoted to devsng OVSF code-assgnment strateges to support as many users as possble. A number of the strateges suffer from a code-set fragmentaton problem, whch ncreases the call blocng probablty (CBP) on the Node-B. In order to resolve ths ssue some strateges have appled code-exchange and reassgnment polces but ncreased the correspondng complexty. Ths paper proposes a Best-ft Least Recently Used (BLRU) code-assgnment scheme wthout reassgnment to approach an optmal method. Furthermore, we devse a revsed verson, Queue-assst BLRU (QBLRU), to mprove system utlzaton and to obtan an even lower CBP than the optmal method does. Consequently, code-assgnment smulaton results present a QBLRU scheme that has a low CBP and the hghest utlzaton, whch s a hgh performance OVSF code-assgnment scheme whch should be useful for WCDMA networs. ey words: WCDMA, Channelzaton, OVSF code, Code assgnment, Sngle code, Multcode, BLRU, QBLRU.. INTRODUCTION In Wdeband-CDMA (WCDMA) networs, orthogonal varable-spreadngfactor (OVSF) codes support a varety of wdeband servces from low to hgh data rates (Adach, Sawahash & Suda, 998; 3GPP, 7). Both the forward and the reverse lns n WCDMA can apply only one OVSF code, a sngle code, multple OVSF codes n parallel, or multcode, to match the data rate requested by a user (3GPP, 7; Dnan & Jabbar,998 ; Doh, Oumura, Hgash, Ohno & Adach, 996). From the pont of vew of a code-lmted system, the OVSF codes are valuable and scarce. Several sngle-code and multcode assgnment schemes have been wdely studed to support as many users as possble ( Adach et al., 998; Yang & Yum, ; Chen & Hwang, 6; Yen & Tsou, 3; Chao, Tseng & Wang, 3; Chen & Ln, 6; Mnn & Su, ; araoc & ava, 7; Cruz-Perez, Vazquez-Avla, Segun-Jmenez & Ortgoza-Guerrero, 6). Comparng the sngle-code schemes wth the multcode schemes by a number of crtera, e.g., system complexty, nter-path nterference and nter-channel nterference, one can fnd that none of them provdes obvous superorty (S. J. Lee, H. W. Lee & D.. Sung, 999; Agn & Gourgue, 999; Ramarshna & Holtzman, 998; Dahlman & Jamal, 996). In addton, a number of the schemes suffer from * E-mal: r@asa.edu.tw 9

2 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, code-set fragmentaton, called code blocng n (Mnn & Su, ), whch ncreases the call blocng probablty (CBP) on a cell (one or few cells n a Node-B whch denotes the 3G base staton). Some schemes have appled code-exchange and reassgnment polces to resolve ths ssue, but they ncreased the correspondng complexty due to the extra effort of dealng wth the reassgnment process. In ths paper, we propose an effcent code-assgnment scheme wthout reassgnment, a Best-ft Least Recently Used (BLRU) scheme, to approach a reassgnment-based optmal method, such as that n (Mnn & Su, ), n consderaton of the CBP and the system utlzaton. The BLRU scheme needs nether code exchange nor reassgnment to reduce the complexty. Moreover, a revsed verson, Queue-assst BLRU (QBLRU), s proposed here to mprove the utlzaton and to obtan even lower CBP than the optmal method. The remander of ths paper s organzed as follows. The OVSF code s descrbed n Secton II. Secton III llustrates the proposed code-assgnment schemes. Secton IV presents two queung models for performance evaluaton and verfes the theoretcal analyss by smulaton. Code-assgnment smulaton results are presented n Secton V, whle concludng remars are stated n Secton VI.. THE OVSF CODE. OVSF Codes Generaton In WCDMA, one spreadng operaton s the channelzaton that transforms each data symbol nto a number of chps. The number of chps per data symbol s called the spreadng factor. The data symbols are frst spread n channelzaton operaton and then scrambled n a scramblng operaton (3GPP, 7). The channelzaton codes are OVSF codes that preserve the orthogonalty between channels of dfferent rates. As shown n Fgure, a code tree recursvely generates the OVSF codes based on a modfed Walsh-Hadamard transformaton (3GPP, 7). For example, C ch, SF unquely descrbes the codes, where SF s the spreadng factor of a code, s the code number, and SF = n. Varable spreadng factors are used for low and medum-hgh data rates. In the reverse ln the spreadng factors for data transmsson range from to 56, whle n the forward ln the factors vary from to 5, wth restrctons on the use of the factor 5. Upon requrng hgher data rates, a user can employ the multcode transmsson and parallel code channels. Up to sx parallel codes are used to rase the data rate, that can accommodate Mbps f the codng rate s / (Holma & Tosala, ). Wthout loss of generalty, the data rates descrbed later are normalzed by the basc data rate R b that represents an OVSF code wth SF max. Let all codes wth the same spreadng factor SF be n the same level log (SF) n the code tree. In other words, any code n the level log (SF) s assocated wth the data rate SF max R. b SF

3 SF= SF= SF= SF=8 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8,, = {}, = {,}, = {, }, = {,,,}, = {,,, } 3, = {,,, }, = {,,,},8,8 3,8,8 5,8 6,8 7,8 8,8 SF= SF= SF= SF=8 Fgure. A code tree for generaton of the OVSF codes.. Code-lmted Capacty Test Let U stand for the -th user (call) n a cell. The data rate R for U can be n j expressed n a polynomal as R = r j *, where r j {,}, n = log (SF max ), j= R SF max, and R s the value of a multplcaton of R b. Before a code assgnment, the cell has to chec ts avalable system capacty. There are two methods for measurng the system capacty, nterference-lmted test and code-lmted test. In the code-lmted test, the system capacty s equal to SF ma x Rb n a sngle cell. Then the nonblocng condton can be defned n j= R j + R SF max R b. () The user U wll be rejected (bloced) f the above nequalty s unsatsfed. In fact, because the number of OVSF codes s lmted, the cell may run out of codes. Then the new ncomng calls at ths moment wll be rejected..3 Sngle Code and Multcod The objectve of OVSF code assgnment s to support as many users as possble. Wth the sngle-code assgnment scheme, the user equpment (UE) transmts ts sgnal on only one channel wth a varable data rate and requres only one RAE recever (combner), whch s a rado recever desgned to resolve and compensate the effects of multpath fadng. On the other hand, wth the multcode assgnment scheme, the UE can use more than one channel to transmt ts sgnal, whch requres multple RAE recevers. On the other hand, wth the multcode assgnment scheme, the UE can use more than one channel to transmt ts sgnal,

4 Avalable code Bloced code Assgned code J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, whch requres multple RAE recevers. A general OVSF multcode system assgns multple codes to offer exactly the bandwdth requested by the UE. Therefore, the system capacty and the number of RAE recevers n the UE determne the data rate provded for a user. The CBP on the general multcode system has a poor lower bound no matter what code-assgnment scheme s used (R. J. Chen & W. E. Chen, ). Ths s explaned by the exact multcode approach beng mpractcal. To avod the lmtatons of the bound, n practcal applcatons we use two alternates, approxmate sngle-code assgnment and approxmate multcode assgnment, to provde the data rate requested. Hence, the data rate R for call can be assgned wth an approxmate sngle-code rate wrtten as φ(r ) = [log (*R -)]. () It can also be assgned wth an approxmate multcode rate lmted n π codes, whch can be expressed as: φ ( π, R ) = log ( R φ ( π, R )) where π equals the number of RAE recevers n the UE., π = (3) + φ( π, R ), π,. Code-set Fragmentaton After a sequence of code assgnment and release operatons, the OVSF code tree conssts of many fragmental nodes. Ths fragmentaton wll degrade the performance of the code assgnment. For nstance, as shown n Fgure, a new call x requestng a unprovded sngle code Cch, wll be rejected, although the cell has 3 8 enough overall capacty (the aggregaton of C, ch, C, and ch,8 C s equal to the ch,8 x code Cch, ). Ths stuaton s the code-set fragmentaton, whch results n less code-assgnment flexblty, hgher CBP, and lower utlzaton.,,,,, 3,,,8,8 3,8,8 5,8 6,8 7,8 8,8 Avalable code Bloced code Assgned code Fgure. An example of OVSF code blocng due to the code-set fragmentaton.

5 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, 3. HIGH-PERFORMANCE OVSF CODE-ASSIGNMENT SCHEME In a statc code assgnment, assgnng a code at random results n a lot of fragmental codes. A dynamc optmal assgnment approach, such as that n (Mnn & Su, ), can gather the unused codes together dynamcally so as to assgn them wth more flexblty. However, ths approach suffered from addtonal overhead for code exchange and reassgnment. Although the overhead was mnmzed as much as possble, t ncreased the system complexty n terms of both software and hardware. In ths secton, we propose four code-assgnment schemes for mantanng low complexty, mtgatng the fragmentaton, obtanng low CBP and mprovng utlzaton. 3. Best-ft Least Recently Used Scheme Intutvely, a good approxmaton to the optmal soluton s based on the observaton that codes assgned frst wll have a hgher probablty of beng released frst. The popular least recently used (LRU) polcy can be consdered for mnmzng the number of fragmental codes, decreasng the code-set fragmentaton and reducng the system complexty. Frst, a compact data structure can be devsed to store the OVSF code table and the unused code lst smultaneously. Fgure 3 shows the prmary structure of a code entry n the code table. The codeword s a bnary sequence that represents an OVSF code by tang ts prefx SF bts. The real feld for the codeword can be absent f the Decmal Walsh Code Generatng Functon (DWCGF) s further appled. The DWCGF formula derves the codeword n only constant tme and saves about 89 percent of space, whch s expressed as δ ( SF, γ ) = δ ( SF, γ )*( SF + ) + [( γ ) mod ]*[ SF * δ ( SF, γ )], () where ( C ) C γ = + = SF max SF factor SF. + φ, δ(, ) =, and C s a code wth the spreadng φ Code No. Codeword Used Flag SF PREV NEXT 8 bts 56 bts bt 8 bts 8 bts 8 bts Fgure 3. The prmary structure of a code entry n an OVSF code table. Subsequently, we translate the decmal value of δ(sf, γ) to a sequence of 3

6 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, bnary dgts and retreve the least sgnfcant SF bts. Where dgt represents + and dgt represents, ths maps the result to an OVSF code. An example for OVSF code generaton va DWCGF s presented n Table I. Gven a code ndex and the spreadng factor SF, the cell obtans the correspondng codeword wth O(log (SF maz )) by recursve DWCGF. Table. An Example for OVSF code generaton va DWCGF SF CGF Walsh code OVSF code Decmal SF bts Code word Code δ(,) () C, δ(,) (,) C, δ(,) (,-) C, δ(,) (,,,) C, δ(,) 3 (,,-,-) C, δ(,3) 5 (,-,,-) C,3 δ(,) 6 (,-,-,) C, 8 δ(8,) (,,,,,,,) C 8, δ(8,) 5 (,,,,-,-,-,-) C 8, δ(8,3) 5 (,,-,-,,,-,-) C 8,3 δ(8,) 6 (,,-,-,-,-,,) C 8, δ(8,5) 85 (,-,,-,,-,,-) C 8,5 δ(8,6) 9 (,-,,-,-,,-,) C 8,6 δ(8,7) (,-,-,,,-,-,) C 8,7 δ(8,8) 5 (,-,-,,-,,,-) C 8,8 The Used Flag feld s set to false ntally and wll be changed to true when the codeword n the same entry s assgned. The feld SF stores the current spreadng factor assocated wth the code entry. Both the PREV and NEXT felds are used for the unused code lst. The lst, therefore, s embedded n the code table; that s, there s no other addtonal memory requred to store the lst. In addton, the code table embeds the OVSF code tree, all codeword entres, and used code records. An example of the embedded OVSF code tree s shown n Fgure. Each code C has a dynamc left chld code C and a rght chld code C + SF max /(*SF). When a user requres a code wth SF = 8, the cell wll splt Code 93 (SF = ) nto two codes, Code 93 and Code 5, wth SF = 8. The feld SF of each code entry wll be changed dynamcally accordng to the current status. After release, Code and Code 65 wth SF = wll be merged nto Code wth SF =. Thus the code table smultaneously mantans the code tree. Moreover, the table requres only 56 code entres and saves 55 nodes and 5 lns for a fxed OVSF code tree. Fgure 5 shows the unused code lst organzed by a logcal double-lned lst and ordered by the spreadng factor. In fact, the lst s also embedded n the code table as descrbed above.

7 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Code No. É SF SF = φ =56 65 É 9 SF = 9 É SF = 93 8 É 5 8 É Code Table SF = φ = 3 Embedded OVSF Code Tree (Vrtual and Dynamc) Fgure. An example for whch the code table embeds the OVSF tree. SFponter[] SFponter[] SFponter[log φ] (Front) SFponter[log φ + ] (Rear) SFponter[log SF max ] Head Assgnment (The Best-ft entry) }SF = SF max / φ Release (Natural LRU queueng) Tal Fgure 5. The unused OVSF code lst organzed by a logcal double-lned lst. The data rate R for call s a multplcaton of R b, whle ts approxmate sngle-code rate s φ(r )= [log (*R -)]. Subsequently, the admtted code for call s represented by the prefx SF max /φ bts of the codeword ndexed by SFponter [log (φ)]. Ths s the best-ft strategy. If none of the unused codes have the same spreadng factor as SF max /φ but SF s greater than SF max /φ, the best-ft code must be splt. Otherwse, f the ndex SFponter [log (φ)] s NIL, the call wll be rejected. The best-ft strategy n BLRU s most straghtforward to select an unused code from the set of avalable codes. It always chooses the code wth the best spreadng 5

8 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, factor frst. Furthermore, searchng for a LRU code s unnecessary, because the correspondng SFponter ponts to the front of the best-ft entres, and each entry group wth the same spreadng factor s a natural LRU queue. Moreover, tmestamps or tme counters are also unnecessary. The BLRU procedure for sngle-code assgnment s descrbed n the followng. Notaton > s a remar. In Step 3 φ(r ), slghtly hgher than R, s the approxmate sngle code converted from an arbtrary data rate R for call. Step checs f the code rate φ s greater than the remanng code rates n the cell. If so, call wll be rejected. Step 5 checs f there s a code wth SF SF max /φ. If not, call wll be rejected (because of code blocng). Step 7 decdes f the best-ft code needs to splt. Steps 8- perform the code splttng, a smple way that changes the SF felds n the splt entres and modfes two PREV and NEXT lns. Step 3 executes the LRU code assgnment and retreves the front element n the entry group wth SF = SF max /φ. On the other hand, a released code wll be nserted nto the rear poston of the group wth SF = SF max /φ. Code mergng wll be executed f necessary. Fnally, the output wll be an assgned code number C f call s accepted or a NIL f call s rejected. The extra effort for BLRU s the mantenance of the ponters from SFponter (Adach et al., 998) to SFponter [log (SF max )]. The whle loop on Steps 9- totally requres, at most, log (SF max ) tmes, so the BLRU scheme runs O(log (SF maz )). In fact, t can be seen as a constant tme because SF max = 56 or 5. Procedure BLRU( R for call ): Step. Code No. C NIL. Step. SF max Maxmum spreadng factor. Step 3. φ(r ) [log (*R -)]. Step. If φ > (SF max UsedDataRates), then Step 5 > Call rejected. Step 5. If SFponter [log φ]. SF = NIL, then Step 5 > Call rejected. Step 6. SFponter [log φ]. CodeNo s the best-ft choce. > Accept call and apply the best-ft strategy. Step 7. If SFponter [log φ]. SF = SF max /φ, then Step 3 > LRU code assgnment. Step 8. CSF SFponter [log φ]. SF. Step 9. Whle (CSF < SF max /φ) > Code splttng. Step. Splt one code wth the spreadng factor CSF nto two codes wth CSF. Step. CSF CSF. Step. Modfy SFponter [log φ] and Felds PREV and NEXT. Step 3. Retreve the front element n the entry group wth SF = SF max /φ. Step. C SFponter [log φ]. CodeNo. 6

9 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Step 5. Return (C ). 3. Queue-assst BLRU Scheme In addton, we ntroduce a relax concept nto the BLRU scheme, as llustrated n Fgure 6. Ths polcy s the Queue-assst BLRU (QBLRU) scheme. Observng the characterstcs of Posson arrval, we now that the nter-arrval tme follows the exponental dstrbuton and the arrval events are ndependent (memoryless). A cell may have burst ncomng calls. Whle the system load s gettng heavy and a burst of calls s arrvng, the OVSF avalable codes n the cell may be nsuffcent to support all of the calls. Ths nsuffcency yelds more calls rejected and hgher CBP. Nevertheless, after the burst, few or no call present n a subsequent short perod of tme. The cell may have more avalable codes used nadequately. Ths mples that the utlzaton may be reduced. Therefore, brngng a tme-lmted queue for BLRU lets the cell put the wll-be-rejected calls nto the queue temporarly. The queue relaxes the burst and defers the calls for a short perod of tme (a few seconds n the real world), durng whch a number of the calls may be served. The cell wll actually reject the calls havng wated over the perod n the queue. Then the CBP wll be decreased, and the utlzaton wll be ncreased. Deferred f necessary Tme C all requests Fgure 6. A relax concept from the characterstcs of Posson arrval.. PERFORMANCE EVALUATION Ths secton proposes two performance evaluaton models used on OVSF sngle-code and multcode systems. The models are consdered for an optmal soluton, e.g., the dynamc code-assgnment strategy n (Mnn & Su, ). We adopt a computer-asssted teratve procedure to solve the equlbrum equatons and conduct the CBP and utlzaton formulas. In the experment, the models had approxmately the same results as the smulatons.. M X /M/c/c codel for an OVSF Sngle-code System An OVSF code-assgnment system can be seen as a mult-channel queue, 7

10 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, whch has more than one server n parallel, wth batch arrval. Let the customers arrve n groups followng a Posson process wth mean group arrval rate λ. The probablty sequence {x } for a sngle-code system or An OVSF code-assgnment system can be seen as a mult-channel queue, whch has more than one server n parallel, wth batch arrval. Let the customers arrve n groups followng a Posson process wth mean group arrval rate λ. The probablty sequence {x } for a sngle-code system or {x } for a multcode system governs arrvng group sze,.e., an arrvng group has the sze and wth the probabltes x and x respectvely. Let the servce tmes (call holdng tmes) be ndependently exponentally dstrbuted wth parameter μ. In general, the number of OVSF codes wth the maxmum spreadng factor c = SF max s the system capacty n a cell,.e., the cell has totally cr b rate resources. The c basc-rate codes can be explaned as parallel multple servers to serve c channels smultaneously. A new call wth R b can be seen as a group arrval wth the sze. From another aspect, a served call wth R b can be seen as a contnuous basc-rate code released smultaneously. Therefore, the OVSF sngle-code system can be modeled on a batch-arrval M x /M/c/c model. Assume that the sngle-code system can support the varable rate rangng from to. The arrvng group sze X for the system has a dstrbuton P(X = ) = x,, where X has mean E[]. The average arrvng group sze s g = = P( X = ) = x, where the probablty densty functon for x can be any computable dstrbuton. Let λ be the batch arrval rate wth the group sze of Posson user stream, where λ = P( X = ) λ = x λ, P ( X = ) = x =, log (c), and, = = {, N}. s the admtted maxmum request rate n the system; n practce, t s usually one-fourth of the maxmum spreadng factor (Holma & Tosala, ). To obtan the steady-state probablty P m for the model, we apply ts equlbrum equatons as wrtten below. for a multcode system governs arrvng group sze,.e., an arrvng group has the sze and wth the probabltes x and x respectvely. Let the servce tmes (call holdng tmes) be ndependently exponentally dstrbuted wth parameter μ. In general, the number of OVSF codes wth the maxmum spreadng factor c = SF max s the system capacty n a cell,.e., the cell has totally cr b rate resources. The c basc-rate codes can be explaned as parallel multple servers to serve c channels smultaneously. A new call wth R b can be seen as a group arrval wth the sze. From another aspect, a served call wth R b can be seen as a contnuous basc-rate code released smultaneously. Therefore, the OVSF sngle-code system can be modeled on a batch-arrval M x /M/c/c model. Assume that the sngle-code system can support the varable rate rangng from to. The arrvng group sze X for the system has a dstrbuton P(X = ) = x,, where X has mean E[]. The average arrvng group sze s g = = = P( X = ) = x, where the probablty densty functon for x can be any computable dstrbuton. Let λ be the batch arrval rate wth the group sze of Posson user stream, where = 8

11 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, λ = ( X = λ = x λ, P( X = ) = x =, log (c), and, P ) = = {, N}. s the admtted maxmum request rate n the system; n practce, t s usually one-fourth of the maxmum spreadng factor ( Holma & Tosala, ). To obtan the steady-state probablty P m for the model, we apply ts equlbrum equatons as wrtten below. = λ = P μp, where log (c). (5) mμ mn( log ( c m), ) mn( log m, ) + λ = Pm λ = = P m + ( m + ) μpm +, c P c = λ P c = where m c. (6) μ, whch can be used for verfcaton. (7) Let P * = ; then * λ P = μ. (8) = μ ( m + ) μ, mn( log ( c m), ) mn( log m, ) * * * m+ = m + λ P λ m P m = = P where m c. (9) Accordng to the normalzng condton P =, we fnally have the equlbrum probabltes of all states as follows: c = P m = P * m c = P *, where m c. (). Call Blocng Probablty and System Utlzaton Here two measures of the M x /M/c/c model, the CBP and utlzaton, are evaluated for two cases n whch the arrvng group sze has a constant value and a negatve exponental dstrbuton. Frst, f a new sngle-code call fnds that the avalable capacty cannot satsfy ts rate requrement, a rate- code, t wll be rejected. Hence the CBP of the model can be wrtten as Ω = P + c P c q q= = log ( q+ ) = λ λ, where c = SF max and log (c). () 9

12 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Second, observng the sngle-code system for a long perod of tme T, we can express ts average utlzaton as follows: Ψ = λ ( ) = q + cμ c Pq = c, () where c = SF max, log (c), and /μ s the mean call holdng tme. In theoretcal analyss, the CBP and utlzaton were calculated for ρ rangng from.3 to.8 and λ from. to., where μ =.5, the maxmum group sze s 8 ( = 3), and the average arrvng group sze g = The group sze s dstrbuted unformly, that s, λ = λ = λ = λ 8 = λ/. In smulaton here, the CBP s regarded as the rejected calls dvded by the total calls, whle the utlzaton s defned by Ψ smulaton = N = SF max ( T duraton ) ( T total SF max SF ), (3) where N s the number of successful calls durng the total smulaton tme T total, and SF s the spreadng factor of the -th successful call wth the duraton T. duraton Moreover, SF max = c, and SF max /SF ranges from to. The other parameters n the smulaton are the same as those n the theoretcal analyss. Fgure 7 ndcates that both the CBP and the utlzaton ncreases when ρ ncreases; moreover, the theoretcal results are close to the smulaton results. Thus, the sngle-code system can use the proposed model for evaluatng ts performance accurately. CBP CBP-Smu. Utlzaton Utlzaton-Smu. Fgure 7. Comparson between theortcal and smulaton results n consderaton of the CBP and utlzaton.

13 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8,.3 Batch Arrval wth Negatve Exponental Dstrbuton In fact, one can apply any computable dstrbutons, e.g., constant, exponental, geometrc, and other dstrbutons, for mappng the behavor of the arrvng group sze. The negatve exponental dstrbuton s gven by P Z (Z=z) =θe -θz, where z. It can be the probablty functon for x, where θ = /E[]. Therefore, the probabltes for countable arrval elements can be wrtten as follows: = = = = x P = E E Z Z PZ Z e e e [ ] e [ ] ( ) ( ) θ θ θ θ = = =. () Fgure 8 depcts three dfferent negatve exponental dstrbutons wth the maxmum group sze = 6 ( = ) and the average arrvng group sze of the batch arrval g, where g = E[] = P( ). = Table presents an approxmate result between the theoretcal analyss and the smulaton, where λ vares from.7379 to.75, μ =.5, and the arrvng group sze s dstrbuted exponentally (λ : λ : λ : λ 8 : λ 6 =.636:.3:.86:.3:.) wth = and g = The results demonstrate that the theoretcal analyss has approxmate values as good as the smulaton. E[] = (g =.8895) E[] = (g = ) E[] = 3 (g =.76) Fgure 8. Negatve exponental dstrbutons wth the maxmum group sze = 6 and the average arrvng group sze of the batch arrval g.

14 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Table. Performance comparson between theoretcal and smulaton results usng negatve exponental arrval-group dstrbuton MaxSF Call Blocng Probablty System Utlzaton c ρ theoretcal smulaton theoretcal smulaton M X /M/c/c Model for an OVSF Multcode System Smlarly, the batch-arrval M X /M/c/c model can depct a general OVSF multcode system (Crome, Chaudhry & Grassmann, 979; Abol nov & Yasnogordsy, 97; aba, 97). An approxmate OVSF multcode system s a subset of the model, whch can be modeled on M φ(x) /M/c/c. Let λ be the batch n arrval rate wth the group sze of Posson user stream, where λ = x λ, x =, = n c, and, n N. The varable n s the hghest data rate that a call can n request. Then the average group sze g s equal to x. Therefore, the = equlbrum equatons of the model can be expressed n the followng. mn( c m, n) mn( m, n) mμ + λ Pm = λ P = = n λ P = μp, where n c. (5) = m + ( m + ) μpm +, where m c. (6) n cμ P c = λ P. (7) = In the same way as the teratve procedure, we can obtan the equlbrum probabltes of all states Pm, where m c. The CBP of the batch-arrval MX/M/c/c model can be: c Ω = Pc, f n =. n n n, P, f. c + P c q λ λ c n q= = q+ = (8)

15 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, whle the average utlzaton of the M X /M/c/c model can be expressed as: n c λ ( Pq ) = q = c + Ψ =, (9) cμ where c n and /μ s the mean call holdng tme per rate- user. 5. SIMULATION RESULTS By smulaton, ths secton compares the CBP and utlzaton between the followng approaches: random assgnment, dynamc optmal reassgnment, BLRU, and QBLRU. The CBP can be vewed as the rejected calls dvded by the total calls, whle the utlzaton can be expressed as (S. J. Lee et al., 999). The smulaton uses the followng assumptons and parameters. Mean call arrval rate: λ = -68 calls per unt tme; Posson arrval. Mean call holdng tme: /μ = 5 unts of tme; an exponental dstrbuton. Call request data rate: an exponental dstrbuton. Maxmum spreadng factor: SF max = 56. The number of RAE recevers n the UE: π. Capacty test: code-lmted. QBLRU-8: the QBLRU scheme wth the maxmum queung tme = 8 unts of tme. QBLRU-6: the QBLRU scheme wth the maxmum queung tme = 6 unts of tme. Random: an assgnment scheme that assgns a new arrval ts requred rate wth randomly arbtrary avalable codes n a cell. Optmal: a dynamc optmal reassgnment scheme, such as that n (Mnn & Su, ). Fgures 9 and present the results by usng multcode wth the mean request data rates R b and 6R b. The mean arrval rate λ s denoted on the horzontal axs, whle the average CBP for a long perod of tme s ndcated on the vertcal axs. From the fgures, QBLRU has the lowest CBP always; BLRU has a close result to the Optmal scheme, but the Random approach s the worst one. The nterestng regon s n the rght upper corner n Fgure, where the mean arrval rate ranges from to 68. In ths regon, the BLRU and QBLRU schemes outperform the Optmal scheme. When the arrval rate s hgh enough, the fragmentaton wth a moderate number of fragmental codes may result n more total calls accepted n the proposed schemes than those accepted n the Optmal scheme. Optmal accepted a new hgh-rate user, but the proposed schemes allowed several new low-rate users. Although QBLRU-6 has the lowest CBP, a long watng tme s unacceptable. Throughout ths paper we suppose that the maxmum queung tme of QBLRU-8 s acceptable. 3

16 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Indeed, low CBP cannot guarantee hgh utlzaton. Fgure show the comparson of the utlzaton between the fve approaches. Optmal adopts a dynamc code-exchange strategy that has the best flexblty for assgnng the avalable codes. Therefore, Optmal has the hghest utlzaton, and QBLRU-8 and QBLRU-6 have the closest results to t. On the other hand, Fgures and 3 dsplay the results of usng a sngle code wth the mean request data rate = 6R b. The proposed schemes are slghtly nferor to Optmal. The reason for the nferorty s that only one RAE recever n the UE cannot adequately use the avalable fragmental codes n the cell. Optmal BLRU QBLRU-8 QBLRU-6 Random Fgure 9. Comparson of the CBP between fve approaches usng multcode (π = and the mean data rate = R b for each call). Optmal BLRU QBLRU-8 QBLRU-6 Random Fgure. Comparson of the CBP between fve approaches usng multcode (π = and the mean data rate = 6R b for each call).

17 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Optmal BLRU QBLRU-8 QBLRU-6 Random Fgure. Comparson of the utlzaton between fve approaches usng multcode (π = and the mean data rate = 6R b for each call). In fact, the optmal scheme n (Mnn & Su, ) can gather the unused codes together dynamcally and has no code-set fragmentaton. The fragmentaton from sngle-code transmsson s the underbelly of the QBLRU and BLRU schemes, because t cannot be avoded. When multcode transmsson s allowed, the schemes suffer from lttle fragmentaton. Code blocng ssues could be resolved naturally wthn more RAE recevers. The BLRU scheme presents the close result to Optmal; QBLRU s more outstandng than Optmal. The superorty of QBLRU comes from an assumpton of a Posson arrval. The QBLRU schemes defer the wll-be-rejected calls for a perod of tme so as to obtan a lower CBP than Optmal does. Fgure shows the comparson of the CBP wth regard to other dfferent maxmum queung tmes. The longer the call watng tme s, the lower the CBP becomes. It s just for reference, because a long watng tme s unacceptable n the real world. Optmal BLRU QBLRU-8 QBLRU-6 Random Fgure. Comparson of the CBP between fve approaches usng sngle code (π = and the mean data rate = 6Rb for each call). 5

18 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Optmal BLRU QBLRU-8 QBLRU-6 Random Fgure 3. Comparson of the utlzaton between fve approaches usng sngle code (π = and the mean data rate = 6Rb for each call). BLRU QBLRU-8 QBLRU-6 QBLRU-3 QBLRU-6 QBLRU-9 Fgure. Comparson of the CBP between sx approaches usng multcode wth dfferent maxmum queung tmes (π = and the mean data rate = Rb for each call). In summary, QBLRU has a low CBP and the hghest utlzaton. However, BLRU wors effcently; QBLRU needs an extra auxlary queue but effectvely decreases the CBP and mproves the utlzaton. These proposed schemes, wthout code-exchange and reassgnment processes, have low complexty and hgh performance. 6. CONCLUDING REMARS 6

19 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, Many OVSF code-assgnment strateges have been nvestgated n the lterature. Several dynamc optmal strateges need code-exchange and reassgnment processes, so they ncrease the correspondng complexty. We have proposed BLRU and QBLRU schemes to mprove the utlzaton and to obtan an even lower CBP than the optmal strateges do. The proposed schemes need nether code-exchange nor reassgnment process to reduce the complexty greatly. In addton, we have presented two useful models for evaluatng the CBP and utlzaton on OVSF code-assgnment systems. As a result, the code-assgnment smulaton results demonstrate that the QBLRU scheme has the lowest CBP and the hghest utlzaton. However, the QBLRU scheme should be useful for the OVSF code assgnment n WCDMA networs. REFERENCES C. Chao, Y. Tseng & L. Wang, Reducng nternal and external fragmentatons of OVSF codes n WCDMA systems wth multple codes. Proc. of IEEE WCNC 3, E. Dahlman &. Jamal (996). Wde-band servces n a DS-CDMA based FPLMTS system. Proc. of IEEE VTC 96, pp E. H. Dnan & B. Jabbar (998). Spreadng codes for drect sequence CDMA and wdeband CDMA cellular networs. IEEE Commun, Mag., 36(9), 8 5. F. Adach, M. Sawahash & H. Suda (998). Wdeband CDMA for next generaton moble communcatons systems. IEEE Commun. Mag., 36(9), F.A. Cruz-Perez, J.L. Vazquez-Avla, A. Segun-Jmenez & L. Ortgoza-Guerrero (6). Call admsson and code allocaton strateges for WCDMA systems wth multrate traffc. IEEE Journal on Selected Areas n Commun., (), Harr Holma & Antt Tosala (). WCDMA for UMTS. Hoboen, New Jersey, USA: John Wley & Sons Inc. I. W. aba (97). Blocng and delays n M (x) /M/c bul arrval queung systems. Management Scence, 7, 5. L. M. Abol nov & R. M. Yasnogordsy(97). Investgaton of many channel nonstatonary Marov systems wth non-ordnary nput flow. Engneerng Cybernetcs, (), L. Yen & M. Tsou (3). An OVSF code assgnment scheme utlzng multple Rae combners for W-CDMA. Proc. of IEEE ICC 3, M. araoc & A. ava (7). A New Dynamc OVSF Code Allocaton Method based on Adaptve Smulated Annealng Genetc Algorthm (ASAGA). Proc. of IEEE PIMRC 7, 5. M. V. Crome, M. L. Chaudhry & W.. Grassmann (979). Further results for the queung system M X /M/c. Journal of the Operatonal Research Socety, 3(8), M.-X. Chen & R.-H. Hwang (6). Effcent OVSF code assgnment and reassgnment strateges n UMTS. IEEE Trans. on Moble Computng, 5(7),

20 J. C. Chen / Asan Journal of Arts and Scences, Vol.,,No., pp. 9-8, P. Agn & F. Gourgue (999). Comparson between multcode wth fxed spreadng and sngle code wth varable spreadng optons n UTRA/TDD. Proc. of IEEE SPAWC'99, R. J. Chen & W. E. Chen (). A lower bound on blocng probablty of an OVSF mult-code system n WCDMA n Proc. of 3Gwreless, pp S. J. Lee, H. W. Lee & D.. Sung (999). Capactes of sngle-code and multcode DS-CDMA systems accommodatng multclass servces. IEEE Trans. on Vehcular Tech., 8(), S. Ramarshna & J. M. Holtzman (998). A comparson between sngle code and multple code transmsson schemes n a CDMA system. Proc. of IEEE VTC 98, T. Doh, Y. Oumura, A. Hgash,. Ohno & F. Adach (996). Experments on coherent multcode DS-CDMA. IEICE Trans. Commun., E79-B(9), The Thrd Generaton Partnershp Project [3GPP] (7). Techncal Specfcaton 5.3, v7.., Spreadng and modulaton (FDD) (Release7). T. Mnn &. Y. Su (). Dynamc assgnment of orthogonal varable-spreadng-factor codes n W-CDMA. IEEE Journal on Selected Areas n Commun., 8(8), 9. Y.-S. Chen & T.-L. Ln (6). Code placement and replacement schemes for WCDMA Rotated-OVSF code tree management. IEEE Trans. on Moble Computng, 5(3), 39. Y. Yang & T. P. Yum (). Maxmally flexble assgnment of orthogonal varable spreadng factor codes for multrate traffc. IEEE Trans. on Wreless Commun., 3(3), Ju-Ch Chen receved hs B.S. and M.S. degrees n Computer Scence and Informaton Engneerng from Natonal Chao Tung Unversty, Tawan, n 993, 995, respectvely and hs Ph.D. degree n Computer Scence from Natonal Chung Hsng Unversty, Tawan, n 6. He s currently an Assstant Professor n the Department of Computer Scence and Informaton Engneerng of Asa Unversty, Tawan. Hs research nterests nclude wreless multmeda communcatons and moble computng. 8