A Complexity Cost Function for the Signal Processing in a WCDMA. Basestation for dimensioning of a Software Defined Radio.

Transcription

1 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. Paul Buns and Mak Reed Naional IT Ausalia Ausalian Naional Univesiy anbea 000 AT, Ausalia paulbuns@simplexiy.com.au Absac - This pape deemines he cos funcion fo a newok of WDMA- FDD Base Saions (Node-B s fo he pupose of dimensioning a Sofwae Defined Radio (SDR implemenaion. An SDR achiecue is poposed and he cos funcion is expessed in ems of cell diamee and signal pocessing load. The cos funcion is developed in ems of a lage numbe of sysem paamees. Based on ceain assumpions a cell diamee is deemined which minimizes he cos funcion and heefoe povides he minimal compuaional complexiy SDR.

2 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. I. INTRODUTION The cellula infasucue indusy ypically segmens cells ino Maco, Mico and Pico cells. uenly he signal pocessing inensive pas of he physical laye in mos WDMA s (and Ue s ae implemened by fixed funcion applicaion specific inegaed cicuis (ASI s ha have been designed fo he wos-case cell dimensions and use-densiy. This wos-case allows a small se of ASI devices o mee he Laye 1 signal pocessing equiemens fo all classes of. The lieaue includes many efeences fo he capaciy and dimensioning of DMA ai-inefaces (including [1],[9],[10] & [11], hese all assume ha he signal pocessing is dimensioned fo he wos case cell dimensions and use-densiy and hey do no conside he cos due o complexiy fo an SDR implemenaion. Pacical signal pocessing powe esuls fom SDR implemenaions of WDMA using TMS306x DSP s have been published in [7] fo WDMA-TDD and in [8] whee a six-finge WDMA Rake eceive design is deailed. The heoeical SDR equiemens fo WDMA ae esimaed in [6] whee i is ecognized ha he signal pocessing powe of a DMA sysem inceases wih boh numbe of uses and lage cell size. These efeences also do no conside he cos due o complexiy.

3 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 3 Theefoe his pape ses abou o deemine a cos funcion fo a newok of WDMA s implemened using Sofwae Defined Radio (SDR and hen show ha he cos funcion has a minimum and coesponding opimum cell size. In Pa II we deail he newok level analysis, in Pa III we popose an SDR achiecue and in Pa IV we develop he cos funcion using he esuls of Pa II. In Pa V we esimae he paamees equied o evaluae he cos funcion and in Pa VI we povide numeical esuls. II. NETWORK LEVEL ANALYSIS onside a poion of a WDMA cellula newok wih aea A p whee each seco coves he same aea and is pefecly hexagonal. Le us assume ha he aea uses 10 degee cell secoizaion (i.e. 3 secos pe. Using [4] and [5] whee he s ae placed in he cone of a hexagon wih diamee D, he seco aea S is hen S D 3/ 4 The numbe of s (base ansceive saions equied o sevice A p is hen N AP / 3S Le us now conside ha A p is a uni aea whee (1 ( N / 3 3D (3 Assuming ha A p conains a unifom densiy of uses ρ whee each use geneaes T k elangs of affic duing he busies hou, each in A p will be equied o suppo a maximum of T elangs of affic i.e.

4 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 4 T 3( ρtk S The elaionship beween affic and seco diamee is hen (4 T 3( ρt k 3D / (5 Because signal pocessing esouces fo a single use ae a funcion of he seach window, i is moe inuiive o expess he seco aea using he seco adius in chips. Fo WDMA he chip ae is 3.84 Mcps [3], heefoe he adio wave will avel 3x10 8 /3.84x10 6 mees (~ 78 mees along is ajecoy duing a chip peiod. In mos cellula ansmission envionmens he waves aiving a he eceive will have efleced off one o moe objecs ceaing a muli-pah envionmen whee each wave can avel a diffeen disance and heefoe ake a diffeing amoun of ime, in some cases hee is no diec wave. Delay spead d is used o measue he diffeence in aival imes of he vaious mulipah waves a he eceive whee he mean and vaiance is a funcion of seveal facos including physical envionmen. The seach windows fo he Pah Seach and Access funcions in a WDMA eceive ae fixed in size (ime equivalen o a discee numbe of chips c, his effecively disceizes he cell diamee. As delay inceases, wave aenuaion also ends o incease, so fo pacical puposes an uppe bound fo d is used. As he posiion of he ansmie is no known by he eceive, Pah Seach and Access funcions mus seach ove he combined up and downlink diec pah ime plus he uppe bound on delay spead. The cell diamee in mees can hen be expessed as 8 3e10 R 6 (3.84e10 (1 + The elaionship beween N and seach window ime is hen d (6

5 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 5 Le N (7.68e e10 3(9e10 16 d (7 Then β 9 (7.68e10 ( (9e10 d 16 (8 N β Use densiy is ypically quoed pe km so using he esuls of (5 & (6 we ge (9 T 3( ρtk 8 3 3e (7.68e10 (1 + ρtk T β d (10 (11 Esimaes fo he level of affic pe uni aea ρt k ae povided in [], voice affic is classified as eihe: mobile (MS ρt k 500 E/km, pesonal saion oudoos (PS o ρt k E/km o pesonal saion indoos (PS I ρt k E/km /floo. These affic figues ae specified o epesen a ypical dense ciy envionmen. III. SOFTWARE DEFINED RADIO ARHITETURE Le us assume ha he hadwae fo each consiss of k wideband eceive divesiy channels and k wideband ansmi divesiy channels. Wideband is defined hee o mean ha each channel is capable of pocessing a numbe of 5 MHz WDMA-FDD caies. Fo pacical puposes we shall conside a maximum of 4

6 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 6 caies (o 0 MHz of bandwidh pe seco and assume ha he caie powe is sufficien o mee he needs of he fowad link. Seco 1 Seco Seco 3 Divesiy hannel k LNA Divesiy hannel 1 Wideband Analog Muli- aie Receive Fon-End Wih AD and DD's Bus PA Divesiy hannel 1 Divesiy hannel k Wideband Muli-aie Analog Tansmie Fon-End Wih DA and DU's Swich N DSP 1 DSP DSP Resouce Resouce onolle & RN ineface RN Fig 1 SDR Achiecue The DD s povide ove-sampled daa o he DSP esouces a a ae of F OSF imes he chip-ae i.e. 3.84F OSF million samples pe second (MSPS. IV. SIGNAL PROESSING REQUIREMENTS Le Y be an esimae of he signal pocessing equiemen fo ou WDMA SDR measued in million of insucions pe second (MIPS. Le us assume ha on he chip-ae pocessing side he consiss of a down-link conol channels, b downlink affic channels, c up-link access channels and d up-link Pah Seaches and Rake Receives. Theefoe hee will be a+b down-link anspo channels and c+d up-link anspo channels. Le hee be k channels of eceive divesiy and k channels of ansmi divesiy. These funcions ae hosed on he DSP devices of one o moe DSP esouces.

7 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 7 Le DL be he numbe of chip-ae signal pocessing MIPS equied pe down-link conol channel, le UL be he symbol-ae MIPS pe up-link anspo channel, le UL P be he chip-ae MIPS equied pe chip ( c pe up-link Pah Seache and so on, hen he oal signal pocessing equiemen is Y ak DL ( c + d UL + bk DL T + ( a + b DL + ck UL A Assuming symmeical up and down-links, bdt and + dk UL P + dul R + (1 Y c( k UL a( k DL A + DL + T ( k DL T + DL + k UL P R + (13 Subsiuing fo T Y c( k UL a( k DL A and eaanging + DL ρtk + β [ k DL + DL + k UL ] T (14 P R + Y UL ρtk kul β + a( k DL 3 P + DL ρtk ( k DL + T + DL β R + ck UL A + (15 One can see fom (15 ha as he cell ges vey lage, he MIPS conibued by he Pah Seaching funcion dominae he equaion. In a pefec implemenaion each signal pocessing esouce will be capable of deliveing Y DSP MIPS. Taking accoun of he efficiency Φ in implemenaion (diven by achiecue, compile efficiency ec, he numbe of DSP esouces N DSP equied fo he will be N DSP Y φ Y DSP (16

8 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 8 If eceive is he cos of each fon end eceive, ansmi he cos of each fon end ansmie and fixed is he cos of he base hadwae (powe supplies, swich, conolle ec, hen he cos of each is N + k + k + DSP DSP eceive ansmi Whee he cos o populae he poion A p (in km of he Newok wih s is fixed (17 The cos pe squae kilomee is hen N A P N (18 Theefoe using he esul fom (9 N N ' ' N + k + k + ( ' DSP DSP eceive ansmi fixed N β Theefoe using he esuls fom (15 & (16 (19 (0 β φy DSP ρt kkul β 3 P ρt k( k DL + DSP ( ' ckul A + a k DL + DL N T + DL β R + + k eceive + k ansmi + fixed (1 V. SIGNAL PROESSING REQUIREMENTS FOR WDMA In his secion, we esimae he signal pocessing equiemens fo he physical laye of a WDMA. The scope of his pape does no allow fo an in-deph esimaion of he pocessing equiemens (in MIPS fo evey laye-1 funcion in a. As (15 indicaes ha Pah Seaching is he bigges conibuo fo lage cell size, we esic ou analysis o his impoan funcion. Fig deails he majo blocks in a ypical diec sequence spead specum eceive.

9 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 9 Fom Digial Down onvee I Q Typically 4 X 1.88 Mega samples pe sec (DMA000 o 4 X 3.84 Mega samples pe second (WDMA oelao ode Geneaion I Q Fine Finge Tacking hannel Esimaion Phase Roaion Delay Equalizaion "Rake Finge 1" 4 3 Maximal Raio ombining To Symbol Pocessing I Q Pah Seache Finge 1 Finge Finge 3 Finge 4 Peak Deecion Theshold Fig Spead Specum Receive (Repined fom Sofwae Defined Radio fo 3G, 00, epoduced wih pemission The inpu o pah pocessing is a sequence of L samples whee L is equivalen o he coelaion sequence lengh. A seach is pefomed peiodically evey u (pah updae ime seconds on a complex inpu signal and consiss of hee majo opeaions, coelaion (de-speading and summing, powe calculaion and peak deecion. oelaion and powe calculaions ae epeaed wih he de-speading code shifed a 1/F OSF chip inevals acoss he seach window. The esulan c F OSF powe calculaions ae seached o find candidae peaks. An esimae fo he numbe of insucions (in MIPS he DSP mus pefom pe pah seach insance UL P is calculaed by adding he equied MIPS fo coelaion UL P plus hose fo powe calculaion UL PP and hose fo peak deecion UL PD. UL UL P P PP PD (

10 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 10 The pe chip ( c MIPS fo a single insance of UL P is calculaed by muliplying he ove-sampling faco by he coelaion sequence lengh muliplied by he numbe of insucions I P equied o implemen he funcions opeaions and divided by he pah updae ime u by 1e10 6 ie. F LI OSF P ULP 6 1e10 u Powe calculaion is pefomed only once pe coelaion so UL PP is found by F OSF PP ULPD 6 1e10 u I (3 (4 Peak deecion is pefomed on he powe calculaions fom he enie seach window, so as we ae esimaing he numbe of MIPS pe seach chip, we define I PD as he numbe of insucions pe seach chip. As an example le F OSF 8, L56 (a suiable speading faco fo voice, u 10 ms (UMTS fame size, allows fo medium mobiliy uses, I P 16 insucions pe coelaion, I PP 8 insucions pe powe calculaion and I PD insucions pe peak deecion. Using hese values esuls in a value of 3.3 MIPS pe use pe seach chip pe channel of eceive divesiy. By using he same echnique as fo Pah seaching, he pocessing equiemens fo he ohe funcions wee calculaed (using daa fom Table 3 and hen lised in Table.

11 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 11 Vaiable Symbol MIPS Symbol MIPS pe DL anspo channel DL 69 hip MIPS pe DL conol channel DL 3 hip MIPS pe DL affic channel DL T 3 Symbol MIPS pe UL anspo channel UL 70 hip MIPS pe UL access channel pe c UL A 3.3 hip MIPS pe UL pah seach pe c UL P 3.3 hip MIPS pe UL ake eceive UL R TABLE Laye-1 MIPS pe Funcion VI. NUMERIAL RESULTS The cos funcion fom (1 was hen evaluaed using he daa fom Tables and 3 fo hee values of ρt k and a ange of cell sizes in chips. The esuls wee nomalized o he minimum cos and he cell size was conveed fom chips o kilomees (assuming d 0.5 and ploed in Fig 4. Vaiable Symbol Values pe Jusificaion Speading Faco 56 Suiable fo voice Symbol Rae 15 kbi/sec Fo speading faco 56 oelaion Sequence L 56 Povides adequae pocessing gain and false Lengh alam ae # of Rake Finges 4 Typical value fo accepable pefomance Ove sampling faco F OSF 8 Typical value fo accepable pefomance Pah updae ime 0.01 sec UMTS fame ae and ypical value fo medium mobiliy uses ~100 km/h. Receive Divesiy k Minimum fo 3GPP pefomance Tansmi Divesiy k 1 Minimum fo 3GPP pefomance # of DL conol channels a Minimum as specified in [1] # of UL access channels c 4 i.e. 8 pe seco fo accepable missed deecion ae Delay spead d 0.5 Typical value assuming hexagonal cells MIPS pe DSP Resouce Y DSP 19,00 Assumes 8 x 400 MIPS commecial DSP s DSP uilizaion efficiency Fixed esouce cos fixed 1 Typical figue DSP esouce cos DSP 0.5 Based on 8 high end DSP s Fon-end eceive cos eceive 1.5 Typical figue Fon-end cos ansmie Φ 0.5 Typical figue fo embedded sofwae indusy ansmi 1.5 Typical figue

12 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 1 TABLE 3 Paamees 4 ( N ' Relaive cos pe squae kilomee ell diamee (D kilomees 500 Elang 1000 Elang 1500 Elang Figue 4 Relaive cos funcion vs cell diamee D As he affic densiy (ρt k inceases he minimum poin of he cos funcion becomes less pominen, Fig 4 illusaes ha a ρt k 500 E/km he minimum occus a 34 chips o 885 mees, a 1000 E/km his shifs o 7 chips o 703 mees and a 1500 E/km he opimum c is 3 chips o 599 mees. The assumpion of a maximum of 0 MHz specum uilizaion is valid fo each of he esed cases, howeve he assumpion becomes invalid fo affic densiies beyond abou 300 E/km, a his poin he minimum of he cos funcion occus a he same poin whee 4 full UMTS caies ae equied pe seco. VI. ONLUSIONS In his pape we have developed a complexiy cos model fo a basesaion in a DS/DMA sysem, modeled lagely on 3GPP. We have shown, fo a give cell size he complexiy cos associaed wih such an SDR implemenaion. We have also shown ha fo a given load ha an opimal cell size exiss which minimizes he oveall sysem cos of he implemenaion.

13 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 13 In geneal fo a unifom affic densiy deploymen cos ises apidly as cell size shinks due o an D incease in cell sies equied and he dominaion by he fixed coss. As cell size inceases he cos funcion becomes dominaed by he cos of poviding DSP esouces fo pah seaching. This pape has demonsaed ha he cos of deploying sofwae defined s in a WDMA newok can be minimized by choosing an opimum cell size. APPENDIX I A lowe bound on he capaciy of a DMA newok is pesened in [1], his analysis povides he pobabiliy (1-P ha a given qualiy of sevice (QoS in ems of Bi Eo ae (BER is exceeded fo he fowad and evese link. The evese link equaion 16 fom [1] is epoduced hee as (5 whee N s is he numbe of uses pe seco, α is he voice aciviy aio (se o 3/8 and δ is defined by equaion whee W is he speading bandwidh, D is he infomaion bandwidh, E b /N o is he signal o noise aio necessay fo he given QoS, η is he backgound noise and S is he eceived use signal powe. 1 P Ns 1 k 0 Ns 1 k α (1 α k δ W / R E / N b Ns 1 k 0 δ k 0.47N Q 0.078N s η S s (5 (6 Evaluaing (5 fo WDMA whee α 3/8, W5 MHz, R15 kbi/sec, E b /N o 3.16 (5 db and η/ S 1.5 indicaes ha he evese link can suppo appoximaely 14

14 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 14 uses pe seco wih a 1% blocking ae o fo 99% of he ime wih a BER of 1E-3 o bee. REFERENES [1] K. S. Gilhousen, I. M. Jacobs, R. P. Padovani, A. J. Viebi, On he apciy of a ellula DMA Sysem, IEEE Tansacions On Vehicula Technology, Vol 40, No, May [] I.T.U, Recommendaion ITU-R M.687- Inenaional Mobile Telecomunicaions-000 (IMT-000, [3] E.T.S.I., TS Univesal Mobile Telecommunicaions Sysem (UMTS Physical laye Geneal Descipion. [4] I.T.U, Recommendaion ITU-R M.15 Guidelines fo Evaluaion of Radio Tansmission Technologies fo IMT-000, [5] E.T.S.I., TR Univesal Mobile Telecommunicaions Sysem (UMTS Selecion pocedues fo he choice of adio ansmission echnologies of he UMTS, [6] P. Buns, Sofwae Defined Radio fo 3G, Aech House 00.

15 A omplexiy os Funcion fo he Signal Pocessing in a WDMA Basesaion fo dimensioning of a Sofwae Defined Radio. 15 [7] Bonne,., G. aie, A. Enou, P. Humble, G. Monalbano, A. Nodio, and D. Nussbaum, A Sofwae Radio Tesbed fo UMTS TDD Sysems, Ocobe 000. [8] Implemenaion of a WDMA Rake Receive o a TMS306x DSP Device, Texas Insumens Applicaion Repo SPRA680, July 000. [9] H. Holma and A. Toskala, WDMA fo UMTS: Radio Access fo Thid Geneaion Mobile ommunicaions, Wiley 00 [10] J. Laiho, A. Wacke amd T. Novosad, adio Newok Planning and Opimisaion fo UMTS, Wiley 00. [11] Lee, J.S., Mille, L.E., "DMA Sysems Engineeing Handbook", Aech House [1] ETSI, ETSI TS Univesal Mobile Telecommunicaions Sysem (UMTS; Speading and Modulaion (FDD, V 4..0, Decembe 001.