POWER PENALTIES CAUSED BY MODEM IMPAIRMENTS IN SPREADING METHOD WITH IMPROVED INTERFERENCE TOLERANCE Noboru Izuka 1 and Yoshimasa Daido 2

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1 POWER PEALTIES CAUSED BY MODEM IMPAIRMETS I SPREADIG METHOD WITH IMPROVED ITERFERECE TOLERACE oou Izuka and Yoshiasa Daido Infoation and Counication Las., Japan Teleco -9- Hatchooi, Chuo-ku, Tokyo, Japan, noou.iizuka@japan-teleco.co.jp Digital Infoation Media Design Coe, Kanazawa Institute of Technology 7- Ohgigaoka, onoichi, Ishikawa, Japan, daido@info.kanazawa-it.ac.jp ABSTRACT This pape theoetically estiates powe penalties caused y ode ipaients in a poposed speading ethod. The ethod has a ette ultiple access intefeence toleance than a vaiale length othogonal speading ethod when the piay odulation is a ulti-level QAM signal. The poposed ethod also has flexile ultiple data ate tansission capaility fo wieless ultiedia counication systes that can accoodate uses with vaious data ates. The ethod is ased on a ulti-caie odulation, and the nue of su-caies is aitay intege. The theoetical estiation suggests that the powe penalties ae the sae as that of the piay odulation. Assuing the piay odulation of 6 QAM, the penalties ae estiated fo a caie phase eo, a decision tiing eo, and aplitude distotions.. ITRODUCTIO Afte a poposal of an othogonal CDMA syste [], othogonal speading ethod studies ae acceleated []-[4]. In the speading ethods, a pocess gain is a ultiple of two. A ulti-ate tansission capaility of the syste is attained y adopting ulti-codes o vaiale length othogonal codes whee the use data ate is one of an intege ultiple o a ultiple of two of the specified it ate, espectively. Howeve, the uses want to select vaious data ates, oe flexily. Recently, we have poposed a speading ethod with an aitay use data ate [5]-[7]. The aitay use data ate gives oe flexile ulti-ate tansission capaility than the conventional ethod. Figue shows ipoved ulti-ate tansission capaility y the poposed ethod. Because the tansitted data ate is a discete value in the conventional ulti-code ethod, the total data ate of the poposed ethod is lowe than that of the conventional ethod. Theefoe, the poposed ethod can effectively use a wieless esouce in a cell when a ase-station accoodates uses with vaious data ates such as audio, video o we access. An intefeence toleance is ipotant in CDMA systes ecause the intefeence level liits a syste capacity. When the piay odulation is a ulti-level signal, the toleance is paticulaly ipotant ecause the highest level odulation gives the highest use data ate in ulti-ate CDMA systes [8][9]. The poposed ethod has a ette toleance of ultiple access intefeence when the piay odulation is a ulti-level QAM signal [7]. Figue shows siulated pefoances of the poposed ethod and conventional vaiale length othogonal speading ethod in the pesence of the intefeence. The poposed ethod has a ette pefoance ecause the ethod has a lowe fouth oent of the intefeence distiution [7]. This pape theoetically estiates powe penalties caused y ode ipaients in the poposed ethod.. OVERVIEW OF PROPOSED METHOD The poposed speading ethod is coposed of the following steps. Figue shows a odulato lock diaga of the poposed speading ethod. ( Data of all uses ae aanged as a seial sequence. ( The seial sequence is conveted M paallel sequences, and each sequence is divided into - syol locks. ( Data in diffeent sequences ae egulaly exchanged, and new M paallel sequences ae otained. (4 Each lock in the new sequence is tansfoed y Fouie tansfo, and new locks of data ae otained. Eleents of the new lock ae tansfoed data. (5 The eleents of locks in the diffeent sequences ae andoly exchanged. (6 Invese Fouie tansfo is calculated fo each sequence. (7 Thus otained M paallel sequences ae allocated fo M su-caies. In this speading ethod, powe level of each use is adjusted efoe step ( when powe contol is adopted. Fo step (, k-th data in n-th lock of -th sequence ae descied as a (. Steps ( and ( suggest that the uses can select any it ates. When one o two uses ae counicating, unifo powe distiution aong the sequences is desied to educe intefeence to suounding sevice aea. To this

2 oject, step ( is applied. Data allocation fo the sequences is eaanged in the anne deteined y the following equations. whee = a ( ( p p = + k od(m. ( The syol od(m eans odulo M. If thee ae patially vacant locks, existing syols cause intefeence to coesponding syols in suounding sevice aea. Step (4 is necessay to educe the intefeence ecause Fouie tansfo of the lock unifies the powe distiution. Fouie tansfo of the data sequence ( is calculated, i. e., c lkπ fo l =,,..., ( j nl = exp k = of final sequence is allocated to one of the su-caies fo ω to ω M. The nue of su-caies M is aitay intege. Fo de-spead in the eceive, invese pocesses fo step ( to (7 ae ade with the invese ode.. THEORETICAL ESTIMATIO OF POWER PEALTIES.. Signal Flow Equations Output signal v s (t of the tansitte is given as s M = n= k = ( jω t f ( t ( n + k T v ( t e exp = s (7 whee f s (t is ipulse esponse of tansit filte and T is syol peiod. Spacing ω of su-caies is assued to e equal to andwidth of ase-and signal with spectal shaping, i. e., Rando ixing in step (5 copesses the intefeence y the pocess gain. The ando ixing is ade y using M-level ando nue x l, ω = ω (8 ω = π ( + α /T (9 whee d = ( λ nl c nl (4 λ = + x l od(m. (5 As can e undestood y the equation (4, this pocess is ando exchanges of the data in the diffeent sequences. The M-level ando sequence is used as a long code to diffeentiate a cell o a secto in a cellula syste. The ando sequence plays the sae ole as M sequence o Gold sequence in the pesent CDMA systes [8][9]. Finally, invese Fouie tansfo is calculated fo each sequence, i. e., e j lkπ fo l =,,..., (6 = d nl exp l= The invese tansfo is adopted in ode to educe an aveage-to-peak powe atio without ovehead [7]. Each Received signal v (t can e witten as v ( t = M = n= k= e exp ( jω t ( t ( n + k T W ( t f ( s + whee W (t is theal noise. Su-caie sepaation given y eqs. (8 and (9 eans that eceive filte extacts only desied su-caie coponent, i. e., v ( t = n= k = e exp ( j φ ( t ( n + k T W ( t f + ( whee f(t is convolution of ipulse esponses of tansit and eceive filtes. W (t is theal noise at the out put of eceive filte, and φ is caie phase eo of - th su-caie.

3 De-spead stats fo Fouie tansfo which is invese of step (6 in speading ethod. Suppose data in -th lock ae estoed with tiing eo t, Fouie coefficient exp(-jlπk/ is ultiplied at tiing t+kt, i. e., v l exp( j φ exp( enp n= k = p = f ( t ( n + p k + = T W l jlπk fo l =,,..., ( ' np n= ( ' v = exp( j { c f ( t c f ( t nt 5p φ + n= q= c p ( ' nq 'ξ = ( f ( t + ( n T } + W p fo p =,,..., (6 whee Σ eans n equal to zeo and equal to zeo ae eliinated in the second and thid tes, espectively. Since v 5p is Fouie coefficient, invese Fouie tansfo is calculated to otain data sequence (, i. e., whee l = W ( t + kt exp( jl k / k = W π ( Sustitution of eq. (7 to eq. ( gives the following equation. 6k φ k ' n= ( ' + np [ δ k, + sδ p, s f ( t + ( n T n= p= = s= + δ k, sδ p, + s f ( t ( + n T ]} + W ( t + kt ( ' v = exp( j { f ( t f ( t nt fo k =,,..., (7 v 4p = dnp n= q= exp( j φ ξ f ( t + ( n T + Wp = ( whee ξ is given as ξ = δ fo p =,,..., (4 [ exp( jqπ / / ] s= [ exp( jqπ / / ] + s= fo > exp[ jsπ ( p q / ] fo = exp[ jsπ ( p q / ] fo < (5 Despite coplex ipession of eq. (7, inte-syol intefeence aong the data, is the sae as that of the piay odulation. This can e confied fo each value of k. Fo k equal to zeo, ' n= ( ' v = exp( j { f ( t f ( t nt 6 φ + n= = ( ' n f ( t ( + n T } + W ( t (8 This equation eans that all the data in -th sucaie except ( cause intefeence when ode ipaient exist. This situation is exactly the sae as that of piay odulation. Fo othe values of k, the siila equations ae otained all of which show intesyol intefeence is the sae as that of piay odulation. In eq. (5, δ is Konecke s delta which is one fo p equal to q, and zeo othewise. ext, invese exchange of step (5 is caied and data in -th lock ae eaanged to coect nue of su-caie.. Powe Penalties Caused y Mode Ipaients Tale suaizes calculation conditions. The piay odulation is 6 QAM. The oll-off facto is.. Good channel condition without fequency selective fading is assued. As the ode ipaients, following fou factos ae consideed: (a caie phase eo,

4 ( decision tiing eo, (c linea aplitude distotion, and (d quadatic aplitude distotion. Figue 4 shows powe penalty caused y caie phase eo: hoizontal axis shows φ in degee. Powe penalties ae estiated fo of -, -6 and -9. As pointed out in., powe penalty is the sae as that of 6 QAM. Figue 5 shows powe penalty caused y tiing eo: thee cuves in this figue coespond to of -, -6 and -9, siila to Figue 4. In this figue, an effect of inte-syol intefeence is estiated with a chaacteistic function ethod []. As can e seen fo the figue, toleale tiing eo is wide enough to adjust equipent with negligile penalty. Figue 6 shows powe penalty caused y the intesyol intefeence coesponding to linea aplitude distotion. In this figue, of -6 is assued. As can e seen fo the figue, powe penalty is significantly educed coesponding to an incease of the nue of su-caies. In this pape, digital filtes ae assued to ake spectal shaping. So, aplitude distotion is caused y analog filtes at the output of tansitte and at the input of eceive. Thus, aplitude distotion is specified as aplitude vaiation within total andwidth. Reduction of the penalty at a lage nue of su-caies coesponds to eduction of vaiation of aplitude within andwidth of a su-caie. Since penalty caused y the inte-syol intefeence ecoe negligile at a lage nue of sucaies, powe penalty is estiated y consideing vaiation of SR aong su-caies. In Figues 7 and 8, total powe of ulti-caie signal is assued constant. Figue 7 shows powe penalty caused y linea aplitude distotion fo 64 su-caies. Figue 8 shows the penalty caused y quadatic aplitude distotion. Judging fo Figues 7 and 8, the analog filtes can e adjusted in the ange whee powe penalty caused y aplitude distotion can e negligile. 4. COCLUSIO This pape descies theoetical estiations of powe penalties caused y ode ipaients in the poposed speading ethod with an ipoved toleance of ultiple access intefeence. The penalties ae estiated when the piay odulation is 6 QAM, assuing ipaient factos of a caie phase eo, a decision tiing eo, and aplitude distotions. The esults show that the penalties ae the sae as that of the piay odulation. REFERECES [] K. S. Gilhousen, I. M. Jacos, R. Padovani, A. J. Vitei, L. A. Weave, J. and C. E. Wheatley III, "On the capacity of a cellula CDMA syste", IEEE Tansactions on Vehicula Technology, vol. 4, no., 99, pp. -. [] E. H. Dinan and B. Jaai, "Speading codes fo diect sequence CDMA and wideand CDMA cellula netwoks", IEEE Counications Magazine, no. 9, 998, pp [] K. Fazel and L. Papke, "On the pefoance of convolutionally coded CDMA / OFDM fo oile counication syste", Intenational Syposiu on Pesonal, Indoo and Moile Radio Counications, Yokohaa, Japan 99, pp [4] S. Haa and R. Pasad, "Oveview of ulticaie CDMA", IEEE Counications Magazine, no., 997, pp. 6-. [5]. Izuka, T. Yuge and Y. Daido, "Multi-caie othogonal speading ethod fo ulti-ate tansission with pocess gain of any natual nue", Euopean Confeence on Wieless Technology, London, U.K.,, pp [6]. Izuka, T. Yuge and Y. Daido, "Multi-caie othogonal speading ethod with factional ulti-code assignent in pesence of decision tiing eo", CDMA Intenational Confeence, Seoul, Koea,, Session A- (CD-ROM Poceedings. [7]. Izuka, T. Yuge and Y. Daido, "Speading ethod with ipoved toleance of intefeence fo ulti-level odulation", Intenational Syposiu on Counication Systes, etwoks and Digital Signal Pocessing, Staffod, U.K.,, pp. 7-. [8] P. Bende, P. J. Black, M. S. Go, R. Padovani,. T. Sindhushayana and A. J. Vitei, "CDMA/HDR: A and-efficient high-speed wieless data sevice fo noadic uses", IEEE Counications Magazine, no. 7,, pp [9] M. Sawahashi, K. Higuchi, H. Ataashi and. Miki, "High-speed packet wieless access in WCDMA and its adio li pefoance", IEICE Tansactions, vol. J84-B, no.,, pp [] Y. Daido, E. Fukuda, Y. Takeda and H. akaua, "Theoetical evaluation of signatues and CR penalties caused y ode ipaients in ultilevel QAM digital adio odes", IEEE Tansactions on Counications, vol. 4, no. 7, 986, pp

5 Total it ate (Mps Conventional 4 uses uses use Poposed 4 5 Bit ate / use (Mps Figue : Multi-ate tansission capaility ipoved y poposed ethod Seial-Paallel Convesion FFT IFFT Input Regula Exchange FFT. FFT Rando Exchange IFFT. IFFT Multi-Caie Modulation Output Figue : Block diaga of odulato Multi- Level Rando Sequence Geneato - Tale : Calculation conditions - - Theal noise SF = 8 SF = = M = 8 = M = Conventional Piay odulation: 6 QAM Roll-off facto:. Channel condition: Static Mode ipaients: Caie phase eo Decision tiing eo Linea aplitude distotion Quadatic aplitude distotion.5-4 Poposed CIR afte de-spead (db SF: Speading facto M: ue of su-caies : FFT length Powe penalty (db Figue : Siulated pefoance in pesence of ultiple access intefeence [7] 4 5 Caie phase eo (degee Figue 4: Powe penalty caused y caie phase eo

6 4 6 Powe penalty (db Powe penalty (db Decision tiing eo (degee Linea aplitude distotion (db Figue 5: Powe penalty caused y decision tiing eo Figue 7: Powe penalty caused y linea aplitude distotion (64 caies, SR vaiation aong caies 5 Powe penalty (db caies 6 caies 8 caies Powe penalty (db Linea aplitude distotion (db Quadatic aplitude distotion (db Figue 6: Powe penalty caused y linea aplitude distotion (Inte-syol intefeence Figue 8: Powe penalty caused y quadatic aplitude distotion (64 caies, SR vaiation aong caies