Rapid Estimation Method for Data Capacity and Spectrum Efficiency in Cellular Networks


 Betty Osborne
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1 Rapd Estmaton ethod for Data Capacty and Spectrum Effcency n Cellular Networs C.F. Ball, E. Humburg, K. Ivanov, R. üllner Semens AG, Communcatons oble Networs unch, Germany Abstract System level smulatons for dervng data capacty and spectrum effcency of cellular wreless networs requre comple modelng and a consderable computatonal effort. In ths paper a combned analytcal / geometrc approach has been proposed allowng rapd performance estmaton n cellular pacet data networs. Ths s accomplshed by mappng measured or smulated ln level curves onto measured or smulated cell C/I dstrbutons. Two dfferent scenaros have been studed related to two generc traffc models wdely used n the lterature. The frst traffc model assumes a fed average pacet data call duraton whereas the second one assumes a fed average pacet data volume per subscrber. Based on these models the frst scenaro provdes very optmstc whle the second one more pessmstc performance results. Both GS/EDGE and the upcomng new IEEE Wa system have been studed n 3 frequency reuse, showng a consderable dfference of nearly 5060% n terms of spectrum effcency between both traffc models. The comparson of Wa wth GS/EDGE reveals a moderate performance advantage for the new broadband OFD system n the order of 2040% hgher spectrum effcency. Keywords Spectrum Effcency, Performance, IEEE802.6, Wa, EDGE I. INTRODUCTION A combned analytcal / geometrc method for rapd estmaton of the pacet data channel capacty and spectrum effcency n cellular wreless systems s ntroduced. The proposed method has been appled to two scenaros correspondng to two generc traffc models leadng to totally dfferent performance results. The frst scenaro assumes equal pacet call duraton for all subscrbers. In cellular envronment ths leads to consderably dfferent data volumes transferred durng the fed tme nterval snce subscrbers under good rado condtons enjoy consderably hgher data rate than subscrbers under poor rado condtons. The resultng cell throughput and consequently the spectrum effcency are too optmstc. In realty such user behavor mght be justfed n cases, where subscrbers just spend a certan fed tme perod e.g. wth webbrowsng n the Internet. The second scenaro assumes an equal data volume per subscrber. Such user behavor s observed e.g. wth download applcatons such as FTP servce or AudVdeoStreamng n drve tests. In ths case subscrbers under poor rado condtons wth low data rate occupy rado resources dsproportonately leadng to too pessmstc capacty and spectrum effcency results. Obvously n a real system mplementaton a certan mture of both traffc models s epected nducng performance results n between those provded by the studed traffc models. The proposed method s based on geometrc mappng of the measured or smulated ln level performance curves on the measured or smulated cell C/I dstrbuton. Appromatng the ln level curves by starcase functons smplfes the analytcal formulas used n the performance analyss. Detaled results for GS/EDGE [], [2] as well as for broadband IEEE AN (Wa, [3], [4]) are provded. However, there are some factors le power control, admsson control as well as specfc schedulng technques, whch cannot be taen nto account by the proposed analytcal method. But at full system load downln power control has only mnor nfluence on the cell C/I Cumulatve Dstrbuton Functon (CDF). Admsson control blocs subscrbers under very poor rado condtons avodng allocaton of channel resources n case of bad rado condtons. Furthermore the spectrum effcency can be sgnfcantly affected by means of sophstcated schedulng technques. For eample a mamum C/I scheduler gves preference to subscrbers under good rado condtons at the epense of those under moderate rado condtons thus ncreasng cell throughput and spectrum effcency whereas a proportonal farly weghted scheduler mproves the throughput of subscrbers under poor rado condtons thus degradng the overall spectrum effcency. The paper s structured as follows. Secton II descrbes the theoretcal bacground used for dervaton of analytcal formulas for the two scenaros under study concernng channel capacty and spectrum effcency. In Secton III a GS/EDGE system deployed n 3 frequency reuse has been analyzed based on measured ln level and smulated C/I CDF. Secton IV presents the data capacty and spectrum effcency acheved by a stateoftheart IEEE Wa system assumng the same frequency reuse, smulated ln level and smulated C/I CDF. Fnally the man conclusons are drawn n Secton V. II. THEORETICAL BACKGROUND A. Spectrum Effcency In a cellular networ the spectrum effcency η gven n [bps/hz/cell] s defned by: CCell CCH η () r BCH NCH r BCH wth C Cell the cell/sector throughput n [bps], N CH the number of confgured channels per cell, B CH the channel bandwdth n [Hz] and r the frequency reuse. The cell throughput C Cell s the total of the N CH ndvdual channel throughputs C CH. In a cellular rado networ rado frequency channels are allocated to cells wth a certan reuse factor r characterzng
2 CS CS 2 CS 3 CS CS 2 CS 3 Channel Throughput [bps] F 3 F 2 ) f 3 () f 2 () Channel Throughput [bps] F 3 F 2 f 3 () h 2 (); ε 2 > 0 h 3 (); ε 3 0 f 2 () F F f () h (); ε > 0 f () Fg.. Eample for a ln level performance wth three CS. the robustness of the system aganst cochannel nterference. The quantty used to descrbe the qualty of the rado ln s the CarrertoInterferenceRato (C/I) gven n db. Dependng on the multple access scheme of the rado technology deployed n the networ a rado frequency channel features a well defned structure fed by the standard. Typcally the structure of the rado frequency channel reflects the way t s desgned to accommodate one or multple communcaton channels, n the followng termed channel. Typcally a channel conssts of e.g. TDA tmeslots and frames carryng resource unts. A GPRS/EDGE Pacet Data Channel (PDCH) carres a rado bloc, a Wa OFD frame conssts of OFD symbols. The resource unts are assgned by a scheduler to dfferent users multpleed on the same channel n the cell. Typcally the resource unts for an ndvdual user are assocated wth a certan modulaton and codng scheme (CS) eperencng a certan error rate ε( C / I) dependng on the qualty of the ndvdual rado ln. Ln Adaptaton (LA) s usually appled to adjust the CS to the varyng rado condtons mamzng the user throughput. Hence n general each partcular resource unt of the channel carres dfferent payload. The total channel capacty (channel throughput) s the rato of the average effectve (related to ε ) payload of the channel resource unts and the transmsson tme per resource unt. Obvously the hghest channel throughput and consequently the hghest spectrum effcency s obtaned n a system wth 00% channel utlzaton,.e. all resource unts of the channel are permanently busy carryng traffc data. B. Ln Level Performance State of the art multrate systems support dfferent modulaton and codng schemes CS wth,,. Fg. shows an eample wth three CS. Let s defne a functon f () descrbng the throughput of a channel eplotng CS at a carrer to nterference rato C / I [ db] assumng 00% channel utlzaton. The functon f () can be wrtten as: f ( ) F ( ε ( )) (2) wth F the nomnal throughput ( ε ( ) ) of a channel utlzng CS and ε () beng the error rate of CS at C/I [db] C/I [db] Fg. 2. Appromaton of f () by step functon h (). C / I. LA automatcally selects the most sutable CS for certan C ( t)/ I( t) ( t) at tme nstant t for a partcular rado ln thus provdng optmum throughput even for a tme varyng channel [5]. The optmum throughput curve s gven by the envelope of all f () : ) ma{ f ( )},,.,. (3) There are ( ) swtchng ponts due to LA correspondng to the ntersecton ponts of the functons f () : f ( ) f ( ), 2,,. (4) Hence accordng to LA, CS s n use n a C/I range of < +, 2,,. Snce by ths notaton both the lower bound for CS and the upper bound for CS are not specfed n the followng t s assumed that CS s used from 2 down to some lmted lower C/I value whle CS s used from up to an arbtrary hgh C/I. To facltate further analytcal approach let s ntroduce the vrtual swtchng ponts and +, defnng the lower bound for CS and the upper bound for CS, respectvely. To allow for smple calculatons each functon f (),,, reflectng the channel throughput utlzng codng scheme CS has been appromated over the respectve C/I nterval < +,,, by a step (Heavsde) functon h () as follows (refer also to Fg. 2): h ( ) F ( ε ) H const. for and (5) h ( ) 0 for <. Obvously the accuracy of appromaton n (5) and hence the value of H strongly depends on the constant error rate ε chosen to represent the real one over the relevant C/I nterval for the respectve CS. As suggested by Fg. 2 the best appromaton result wll be acheved usng the epectaton value (average error rate ε, refer to Secton D) of ε () over the nterval < +. C. Cell C/I Dstrbuton Fg. 3 llustrates an eample for a CDF of C/I obtaned by system level smulatons for a heagonal cell deployment n 3 reuse (r 3) at 00% channel utlzaton. The CDF
3 Fg. 3. Cell C/I CDF (300 m cell radus, 3 reuse, 3.5GHz band, 00% channel utlzaton, downln power control off). depends manly on cell geometry, antenna confguraton (heght and pattern) as well as the propagaton model. The RF output power plays no role n nterference lmted scenaros n tght reuse, f there are no coverage problems. Table I gves an overvew of the essental parameter settngs. In the followng the cell C/I CDF s denoted by P() and the correspondng probablty densty functon by ). appng the LA swtchng ponts on the cell C/I CDF gves the porton µ of users (assumng an unform user dstrbuton over the cell area) able to use a certan CS : µ ) d P( + ) P( ),,,. (6) + In partcular µ s gven by P( 2 ) and µ by.0 P( ) snce as above defned and +. Note that µ s not necessarly equvalent to the porton of channel resource unts havng a certan CS. Ths heavly depends on the assumed traffc model as demonstrated n the followng two smulaton scenaros. TABLE I. ESSENTIAL PARAETERS OF THE RADIO NETWORK ODEL Parameter Number of stes µ Stetoste dstance Frequency reuse pattern Frequency band User dstrbuton Pathloss slope Propagaton odel BS RF TX power BS antenna oble antenna Power control (PC) Slow fadng std. devaton + P() Value 6 wrapped around on torus, 3 sectors per ste, heagonal deployment 900 m (300 m cell radus) 3.8 GHz / EDGE; 3.5 GHz / Wa unform, random postonng 38 db per decade COST W / EDGE; 2 W / Wa 65, 7.5 db, 35 m above ground, no downtlt Omn, 0 db;.5 m above ground Downln PC swtched off 8 db D. Scenaro : Channel Capacty for equal mean Pacet Call Duraton per User In the frst scenaro a traffc model s assumed, where all users occupy the channel resources for the same average tme perod ndependent of the ndvdually assgned CS and the eperenced error rate ε. The scenaro s smlar to a P ( ) p ( ) d conventonal voce traffc model havng a fed mean call holdng tme. The drawbac of the model s gven by the fact, that dfferent users obtan dfferent data volumes, e.g. users at the cell edge sufferng from poor rado condtons get sgnfcantly less data volume than users close to the base staton. The advantage of the model s ts smplcty. Obvously the C/I dstrbuton of the channel resource unts p () s dentcal to the C/I dstrbuton of the users ) and consequently the porton α of the channel resource unts havng CS corresponds to the porton µ of users able to use CS : α + + p ( ) d ) d. (7) Usng (6) t follows: α µ P( + ) P( ). The average error rate ε for CS over the nterval < + s: + ε ) ε ( ) d. (8) α The channel capacty C CH n (3) s derved by mappng the envelope g () of the throughput functons f () on the cell C/I CDF: + C ) ) d ) f ( ) d. (9) CH Usng (2) and (8) yelds: C CH + ) F ( ε ( )) d α F ( ε ). (0) Applyng the step functon appromaton for the throughput vs. C/I curves from (5) the followng easy calculaton formula has been obtaned: C α H µ H. () CH Eample: assume two user types sharng the same fully loaded channel, user type a wth µ a ½ and a ) H a 0 bps and type b wth µ b ½ and b ) H b 20 bps. Wth () the channel capacty s gven by the arthmetc mean and results n C CH ½ * 0 bps + ½ * 20 bps 5 bps. Gven the nomnal payload L, of a resource unt utlzng CS the average data payload the channel s gven by: L α L L of the resource unts on ( ε α H T µ H T (2), ) wth T the tme duraton of the resource unt. E. Scenaro I: Channel Capacty for equal mean Pacet Call Data Volume per User The second scenaro s based on a traffc model wth a fed mean data volume V per pacet call ndependent of the rado ln qualty of the dfferent users. The C/I dstrbuton of the users s stll gven by ) and the porton of users havng
4 CS s defned by µ accordng to (6). The dstrbuton p () of the channel resource unts, however, s not equal to the C/I dstrbuton of the users ) anymore, because users under poor rado condtons requre sgnfcantly more channel resources than users e.g. close to the base staton n order to transfer the same data volume V. An eample wth user type a at C/I a and user b at C/I b leads to the requred number of channel resource unts N,a and N,b respectvely: V N, a a ) T N, a and. (3) V N ), b a N, b b ) T b ) Hence the dstrbuton p () of the resource unts can be derved from )by the followng probablty transformaton: ) y) p ( ) wth Z ) Z dy. (4) y) The porton α of the channel resource unts havng CS leads to: α Z + + p ( ) d + ) d. F ( ε ( )) ) d ) Z Z + ) d f ( ) (5) Applyng the step functon appromaton from (5) and usng (8) the followng easy calculaton formula has been obtaned: µ µ ( F ( ε )) H α. (6) ( F ε H ( )) The capacty of the shared channel wth fed mean data volume s then defned by: CCH p ( ) ) d ) d Z. (7) Z The step functon appromaton accordng to (5) leads to: CCH. (8) ( F ( ε )) H The average data payload per resource unt s gven by: T L. (9) ( L ( ε H, )) The eample n Secton D wth two types of users sharng the same fully loaded channel user type a wth µ a ½ and a ) H a 0 bps and type b wth µ b ½ and b ) H b 20 bps leads wth (8) to a channel capacty of C CH (½ / 0 bps + ½ / 20 bps) bps. Wth (6) α a ½ / 0 bps 3.33 bps 0.66 and α b ½ / 20 bps 3.33 bps 0.33, thus, n contrast to the eample above wth fed mean pacet call duraton, the CS utlzaton per resource unt wth the fed mean data volume model s not equal. The rato α a / α b 2 / s recprocal to the rato H a / H b of the assumed nomnal data rates. III. NUERICAL RESULTS FOR GS/EDGE GS/EDGE supports 9 modulaton and codng schemes CS,, CS 9 utlzng both GSK and 8PSK and provdng RLC data rates up to 59.2 bps per PDCH. Fg. 4 on the rght hand sde shows the measured endtoend applcaton throughput per PDCH vs. C/I for all CS. Applcaton throughput means that all overhead ncludng TCP/IP and LLC headers are ncluded reducng the pea user data rates by roughly 35%. The measurements have been conducted on downln statc/statonary AWGN channel wth commercally avalable handset and a GSK modulated cochannel nterferer wth random payload. Ln level results based on other channel models such as TU3 or TU50 have been publshed n [6] and could also be used. In addton the statc/statonary throughput vs. C/I curves have been optmstcally appromated (assumng ε 0) by step functons H as outlned n Secton II. appng the eght LA swtchng ponts onto the cell C/I CDF for 3 reuse n Fg. 4 on the left hand sde provdes the portons µ of users to whch LA wll assgn CS accordng to the eperenced C/I at the partcular cell locaton. All data necessary for the calculatons of channel capacty and spectrum effcency by usng (), (8), and () have been collected n Table II. Obvously the 8PSK CS (CS 5,, CS 9 ) are domnantly n use wth more than 75% vs. 25% GSK modulaton even for tght 3 frequency reuse. TABLE II. ESSENTIAL EDGE DATA FOR FURTHER PROCESSING CS [db] µ H [bps] NA A. Traffc odel wth fed mean Pacet Call Duraton Insertng the data from Table II nto equaton () the channel capacty of an EDGE PDCH s obtaned for the traffc model wth fed mean pacet call duraton: 9 9 CPDCH α H µ H 35.75bps. The average data payload per resource unt s calculated accordng to (2) usng EDGE rado blocs wth four TDA frame rectangular nterleavng duraton T of 20 ms to: L C T 35.75bps 20ms 75bt. PDCH
5 µ (20%) µ (20%) µ 7 0. (0%) µ (20%) µ (5%) µ (7%) µ (6%) µ (7%) µ 0.05 (5%) Applcaton Throughput [b/s] Η 2 Η Η 5 Η Η 4 3 Η 7 Η 6 Η 9 Η C/I [db] Fg. 4. appng of a measured GS/EDGE ln level wth appromaton by step functons (rght) on the cell C/I CDF for 3 reuse (left) at full load. The spectrum effcency s calculated for frequency reuse r 3 CS 6/7 on 64QA. Data rates rangng from.5 bps up to accordng to (). The rado channel spacng n GS s bps are feasble n a 3.5 Hz channel. Hz. Thus the channel bandwdth of the EDGE PDCH s B PDCH Smlar to Fg. 4 the statc/statonary throughput vs. C/I curves 200 Hz / 8 25 Hz, snce the GS carrer ncludes eght have been optmstcally appromated n Fg. 5 by step tmeslots and one PDCH occupes one tmeslot. functons H (assumng ε 0) as outlned n Secton II. CPDCH 35.75bps η 0.47bps / Hz / Cell. appng the s LA swtchng ponts onto the cell C/I CDF r BPDCH 3 25Hz for 3 reuse n Fg. 5 on the left hand sde provdes the portons µ B. Traffc odel wth fed mean Pacet Call Volume of users to whch LA wll assgn CS accordng to the eperenced C/I at the partcular cell locaton. All data Usng (8) and (9) and the data n Table II the EDGE necessary for the calculatons of channel capacty and channel capacty and average payload per rado bloc have spectrum effcency by usng (), (8), and () have been been calculated n case of a fed mean data volume per user collected n Table III. as follows: TABLE III. ESSENTIAL WIAX DATA FOR FURTHER PROCESSING CPDCH bps and 9 µ CS [db] µ H [bps] H NA L CPDCH T 24.82bps 20ms 496bt. Tang nto account the PDCH bandwdth of 25 Hz (refer to the comments above) the correspondng spectrum effcency s gven by (): CPDCH 24.82b/ s η 0.33bps / Hz / Cell. r BPDCH 3 25Hz As epected the channel capacty as well as the spectrum effcency for EDGE s sgnfcantly hgher for the traffc model wth fed mean pacet call duraton than those obtaned for the traffc model wth fed mean pacet call volume. The dfference n the results s nearly 50%. The EDGE results for the traffc model wth fed mean pacet call volume are fully n lne wth the system level smulaton results provded e.g. n [6]  [9]. Note that the results descrbed above are only vald for PDCH allocated on transcevers (TRX) n 3 reuse,.e. PDCH allocaton on a BCCH TRX has not been consdered. The latter case would result n a lower overall spectrum effcency. IV. NUERICAL RESULTS FOR IEEE (WIAX) IEEE WAN (Wa) standard provdes 7 modulaton and codng schemes CS,, CS 7 as shown n Fg. 5 on the rght hand sde. CS s based on BPSK modulaton, CS 2/3 on QPSK, CS 4/5 on 6QA and A. Traffc odel wth fed mean Pacet Call Duraton Insertng the data from Table III nto equaton () the capacty of a Wa channel s obtaned for the traffc model wth fed mean pacet call duraton: C CS9 CS8 CS7 CS6 CS5 CS4 CS3 CS2 CS 7 7 Wa α H µ H 6.95bps. The average data payload per resource unt can be calculated accordng to (2) wth an OFD symbol duraton T of 68µs (ncludng 4µs cyclc pref) to: L CWa T 6.95bps 68µ s 472bt. The spectrum effcency s calculated for frequency reuse r 3 accordng to (). The rado channel spacng n Wa s 3.5 Hz: CWa 6.95bps η 0.66bps / Hz / Cell. r B 3 3.5Hz Wa
6 µ (20%) Η 6 Η 7 µ (0%) Η 5 µ 5 0. (20%) µ (7%) Η 3 Η 4 µ (3%) Η 2 µ 2 0. (0%) Η µ 0. (0%) B. Traffc odel wth fed mean Pacet Call Volume Usng (8) and (9) and the data n Table III the Wa channel capacty and average payload per OFD symbol have been calculated n case of a fed mean data volume per user as follows: CWa 4.3bps, and 7 H L CWa T 4.3bps 68µ s 293bt. The correspondng spectrum effcency s gven by (): CWa 4.3bps η 0.4bps / Hz / Cell. r B 3 3.5Hz Wa As epected the channel capacty as well as the spectrum effcency for Wa s sgnfcantly hgher for the traffc model wth fed mean pacet call duraton than those obtaned for the traffc model wth fed mean pacet call volume. The dfference n the results s nearly 60%. The Wa results for the traffc model wth fed mean pacet call volume are fully n lne wth the system level smulaton results provded n [0] and []. The drect comparson of Wa wth EDGE shows that about 40% hgher spectrum effcency s obtaned by Wa applyng the traffc model wth fed mean pacet call duraton and about 20% applyng the traffc model wth fed mean pacet call volume. Nevertheless t shall be ponted out, that especally under good rado condtons Wa allows for a sgnfcantly hgher user throughput than EDGE due to the hgher order modulaton schemes (64QA for Wa vs. 8PSK for EDGE) and due to the larger channel bandwdth (e.g. 3.5 Hz for Wa vs. 25 Hz for EDGE). V. CONCLUSIONS A quasanalytcal rapd estmaton method for channel capacty and spectrum effcency n wreless pacet data networs has been derved. The method s essentally based on mappng smulated or measured ln level curves of an arbtrary rado access technology on a measured or smulated cell C/I CDF. The appromaton of the ln level performance C/I [db] Fg. 5. appng of a smulated IEEE (Wa) ln level wth appromaton by step functons (rght) on the cell C/I CDF for 3 reuse (left) at full load. curves by smple step functons allows for a very easytouse calculaton procedure. The proposed approach has been manfested on two generc traffc models assumng pacet calls ether wth fed duraton or fed volume. The results obtaned are n lne wth stateoftheart system level smulaton results recently publshed n the lterature. The channel capacty and spectrum effcency have been estmated for a wdely establshed technology le GS/EDGE and an upcomng new technology such as Wa. It has been clearly stated that rrespectve of the rado technology under evaluaton the performance ndcators le channel capacty and spectrum effcency show sgnfcant dfference of % dependng on the traffc model. Future wor wll be focused on the evaluaton of an approprate mture of the generc traffc models to cope wth realstc user behavor n wreless networs. REFERENCES [] 3GPP TS , General Pacet Rado Servce (GPRS); oble Staton  Base Staton System Interface; Rado Ln Control/edum Access Control (RLC/AC) protocol. [2] 3GPP TS , General Pacet Rado Servce (GPRS); Overall descrpton of the GPRS rado nterface. [3] Draft IEEE Standard for local and metropoltan area networs, IEEE P802.6REVd/D52004, Ar Interface for Fed Broadband Wreless Access Systems, [4] Draft IEEE Standard for local and metropoltan area networs, IEEE P802.6e/D4, Ar Interface for Fed and oble Broadband Wreless Access Systems; Amendment for Physcal and edum Access Control, [5] C.F. Ball, K. Ivanov, P. Stöcl, C. asseron, S. Parolar, R. Trvsonno, Ln Qualty Control Benefts from a Combned Incremental Redundancy and Ln Adaptaton n EDGE Networs, IEEE VTC Sprng, lan, [6] C.F. Ball, K. Ivanov, L. Bugl, P. Stöcl, Improvng GPRS/EDGE EndtoEnd Performance by Optmzaton of the RLC Protocol and Parameters, IEEE VTC Fall, Los Angeles, [7] T. Halonen, J. Romero and J. elero, GS, GPRS and EDGE Performance, Wley & Sons, [8] K. Ivanov, C.F. Ball, F. Treml, GPRS/EDGE Performance on Reserved and Shared Pacet Data Channels, IEEE VTC Fall, Orlando, [9] C.F. Ball, K. Ivanov, F. Treml, Contrastng GPRS and EDGE over TCP/IP on BCCH and nonbcch Carrers, IEEE VTC Fall, Orlando, [0] C.F. Ball, E. Humburg, K. Ivanov, F. Treml, Performance Analyss of IEEE802.6 based cellular AN wth OFD256 n moble Scenaros, IEEE VTC Sprng, Stocholm, [] C.F. Ball, E. Humburg, K. Ivanov, F. Treml, Comparson of IEEE802.6 Wa Scenaros wth Fed and oble Subscrbers n Tght Reuse, 4 th IST oble & Wreless Communcatons Summt, Dresden, 2005.
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