Intermodulaton Dstorton n Swtched Multbeam Antennas for Cellular Rado Systems Mattas Wennström, Anders Rydberg and Tommy Öberg Sgnals and Systems Group, Uppsala Unversty, ox 528, SE-75 20 Uppsala, Sweden, Emal:mw@sgnal.uu.se ASTRACT The performance of swtched multbeam antennas for cellular rado systems s nvestgated when the transmt amplfer s of a multcarrer (MCPA) type. The MCPA nonlnearty generates ntermodulaton dstorton n the transmtted sgnal that s spatally fltered by the array radaton pattern. Hence, the ntermodulaton dstorton becomes drecton-dependent, and the drecton of the generated ntermodulaton products of any order s derved. It s shown by usng Monte Carlo smulatons how the downlnk carrer to nterference rato depends on the freuency reuse dstance and on the MCPA lnearty measured as ts nose power rato (NPR). For reuse factor one systems, whch s made possble by use of multbeam antennas, the lnear co-channel nterference domnates the nterference. On the contrary, for a reuse factor seven system t s shown that a weak nonlnearty drectly gves a degradaton n carrer to nterference rato (CIR) due to ntermodulaton dstorton. However the reuse factor seven system has a large CIR overhead due to the ncrease n CIR usng a multbeam antenna, and the outage probablty s thereby only slghtly affected.. INTRODUCTION The deployment of swtched multbeam antennas at base statons (S) n cellular TDMA/FDMA systems has ether shown to mprove the capacty or to extend the rado coverage by ncreasng the carrer to nterference rato (CIR). The reduced nterference levels allows for a reducton n freuency reuse dstance, thereby ncreasng the spectrum effcency of the cellular system []. One drawback wth the use of array antennas at the S stes s the ncreased amount of hardware compared to a conventonal S. For each antenna and for each freuency channel a sngle carrer power amplfer s reured for the downlnk transmsson. Thus, to reduce sze, cost and power consumpton of the S, multcarrer power amplfers (MCPA) have been suggested for use n multantenna S [2]. The co-amplfcaton of several carrers on dfferent freuences n an MCPA generates ntermodulaton products (IMP) due to the nonlnearty and due to the non-constant envelope of the combned sgnal. Often the thrd order IMP are consdered (of type 2 - and ), as they fall onto other freuency channels that are used n the system and thereby, cannot be removed by flterng. To meet the reurements n the moble system specfcaton of allowed spurous emsson, lnearsaton of MCPA:s s reured. Although lnearsaton technues sgnfcantly reduces the ntermodulaton dstorton n the output sgnal, some resdual ntermodulaton dstorton remans, and t s useful to know to what level the ntermodulaton has to be suppressed by the lnearser, as a lower level mples a more expensve lnearsaton method. The problem addressed n ths paper s how the lnearty reurements on the transmt MCPA depends on the freuency reuse dstance for a system usng swtched multbeam antennas at the S. The lnearty of the MCPA s defned by usng the nose power rato (NPR) measured from a standardzed NPR test [3]. A cellular system wth a total of freuency channels eually dstrbuted over cells s assumed n ths paper. The freuency channels n each cell are further dvded n a sector-trunkpool scheme where each 20 sector has a unue set of freuency channels assgned to t. The moble statons (MS) n the sector wll receve nterference of two types. Frst, lnear nterference comes from S n the (prmarly) frst ter of co-channel S. Secondly, ntermodulaton nterference s generated n the MCPA n the same S as the MS s connected to, and f the set of freuency channels used n the sector are eually spaced, t can be shown that the generated ntermodulaton products falls onto the same set of freuences. Note that the ntermodulaton nterference s emtted wth low power, but the MS s usually close to the S, hence the sgnal has a low path loss. Compare wth the lnear co-channel nterference from frst ter S, whch s transmtted at hgh power, but the larger S to MS dstance gves a hgh path loss. Hence, there s a pont n the degree of MCPA lnearty, where the major nterference at the MS changes from beng lnear nterference, from frst ter S, to ntermodulaton nterference, from own S. One property of MCPA:s n conjuncton wth multbeam antennas s that the radated IMP wll be spatally fltered by the beam-pattern of the antenna array [5],[6]. Ths mples that n some drectons the generated IMP wll be suppressed by the sde lobe level of the multbeam radaton pattern and n other drectons, the IMP power wll be amplfed by the antenna array gan by coherent addton of the IMP from all antennas. Hence, the carrer to nterference rato at the MS n the system depends on the poston and beam allocaton of the other users n the cell and n neghborng cells. A Monte Carlo smulaton s used to estmate the outage probablty, whch s the probabl-
R f V ty that the carrer to nterference rato (CIR) for a MS fall below some threshold. The outage probablty s evaluated for dfferent MCPA lneartes and at dfferent freuency reuse dstances. 2. CO-CHANNEL INTERFERENCE ON THE DOWNLINK The freuences n a cluster are assumed to be planned accordng to a fxed channel allocaton scheme as seen n Fg.. Furthermore, each sector s eupped wth an el- 8,20,32,... 9,2,33,... 5,7,29,... 6,8,30,... 7,9,3,... 4,6,28,..,23,35,... 2,24,36,... 2,4,26,... 3,5,27,... 0,22,34,...,3,25,... Fgure : Assgnment of freuency channels to sectors n a fxed channel allocaton scheme wth cluster sze K=4 cells. ement antenna array, hence fxed beams can be formed n each sector and thus beams n each cell. In the S transmt path, each antenna s preceded by an MCPA wth maxmum and mnmum output power per carrer of 43 and 3 dm respectvely. The power regulaton per transmtted carrer s performed n 2 d steps and s based on the receved sgnal strength of the uplnk sgnal averaged over the fast multpath fadng. Path loss compensaton s done for half of the loss, followng the deas n [7]:! #%$ '&)( *+-,/.0 () Here,,.0 s the MS-S lnk gan, that s, the uotent between the receved power at the S and the transmtted $ power from the MS, whch s assumed known and s constant that has to be adjusted for optmal performance of the system, see [7]. After the power regulaton (), the power s adjusted to be n the nterval between mnmum and maxmum output power. A. Intermodulaton Interference Consder a S wth transmt MCPA s operatng n t s nonlnear regon, close to saturaton to maxmze the power effcency of the amplfer. The power of the receved IMP at the MS s a functon of the array pattern, the nonlnear characterstcs of the amplfers and the spatal dstrbuton of the MS [8]. In the remanng part of the paper, the study s restrcted to the thrd order ntermodulaton products that falls n band,.e. at the freuences 2. 3 and. 4. Ths s justfed by the fact that these IMP terms contans most of the ntermodulaton energy. Furthermore, assume that the freuency channels n Fg. are eually spaced, that s, the center freuences are related as 56 87:9; (2) where s the center freuency of freuency channel 7, 9; s the freuency channel separaton and 5 s a reference freuency. In each sector, the center freuences of the used freuency channels are related as =<> 9? where s the cluster sze. It s easy to verfy that wth ths freuency plannng, the generated thrd order IMP falls onto other freuences used n the downlnk n the same sector. For example freuency channel 3 and 25 generates IMP on channel (2 >A@ 4CD > ) whch s also used n that sector, see Fg... Calculatng the MCPA Output Sgnal If the complex gan of an MCPA as a functon of the nput power of a sngle carrer s measured, the AM/AM and AM/PM converson characterstcs of the amplfer s obtaned. These are commonly used to descrbe the nonlnearty. When smulatng MCPA:s n conjuncton wth array antennas, each of the IMP n each of the MCPA:s output sgnal must be separately calculated, because ther relatve phases and ampltudes wll affect the radaton pattern of each IMP. A commonly used method uses the fast Fourer transform (FFT) to yeld the output power at arbtrarly freuences from a nonlnear devce wth a mult-tone nput. Wth more than one IMP on the same freuency n the output sgnal, the FFT method fal to dstngush between them, as t gves only the sum of the total IMP on that freuency. Instead, Shmbo [9] proposed a method by fttng the AM/AM and AM/PM characterstcs to a essel seres expanson. Wth ths method t s possble to fnd an analytcal expresson for the ampltude and phase of the desred sgnals and each of the IMP:s n the output of a nonlnear amplfer wth a mult-tone nput. Hence, ths method suts our needs. Shmbo s method s descrbed below. If EGFIHKJ and L FIHKJ are the AM/AM and AM/PM characterstcs of the amplfer, fnd the coeffcents M6NOQP n a essel seres expanson by solvng arg MSNTO > N (U(U( NOQV!W g h mn\o!p ]:^ _a`t^cbcbcbd^ XZY\[ _de E!FjHKJlk Pdr > Otsvu > FIMCwxHJ for all ampltudes H n the nput ampltude nterval. Here u > s the st order essel functon and note that the coef- zy { (3)
V N J F F Ë J ± ¾ Ì fcents O P are complex. Assume that the nput conssts of phase modulated (~ ZF lj ) carrers wth ampltude H and wrte the nput as k.\0 F lj Qn/ ˆ < Š n/ˆ p p r > HKKk where s the center freuency of freuency channel. The output sgnal of the MCPA can be wrtten as kœt ˆ Fj lj UŽ t FI 6J k ` n ˆ < n/ˆ p pu Gš (5) where s the set œ R- > N N (-(U( N W?ž N (4) (6) to restrct the output to the n band frst and thrd IMP. Now, defne the set s as s Rx > N N (U(-( N W ž s (7) to consder the output n the freuency channel wth center freuency s only. Usng the coeffcents from the least suare ft n euaton (3), the complex voltage gan for the :th component n the output at freuency s and can be wrtten as [9] Fj s J Pdr > OQP u FIM vh J (8) where u s the essel functon of order. Note that the output ampltude of the desred carrer at freuency s s gven by Fj s J wth s R (U(-( N & N sx ĵª N & N (-(U( W. C. The Far Feld Radaton Pattern Now consder the receved power at the MS n drecton from broadsde of the array and on a dstance from the S. Assume an element, G2 -spaced lnear array, where s the wavelength of the carrer freuency n the center freuency channel. Furthermore we assume a smple fxed beamformer, whch can be mplemented as the fast Fourer transform (FFT), or f mplemented n hardware, a utler matrx. The phase of the beamformer weght appled to sgnal 7 at antenna s denoted =0. The far feld radated power n the drecton of the s :th sgnal component can then be calculated as C T! Fj sj Fj s Jl F J ± 0 r > k t ` n/ U²v l³ n0 >Apjµ nº¹tpjp where F J s the ndvdual antenna element gan n drecton. Usng the FFT or the utler matrx, we have the (9) property =0 F J 9 [5], where 9 s the phase gradent over the antennas n the array for sgnal 7. The phase gradent 9 belongs to a set V, of dfferent phase gradents, unue for each beam the beamformng network can generate.»v ½¼ 2¾ À > s r 5 (0) The fnte set»v s a closed group under multplcaton and addton, followng modulo- algebra. These propertes mples that the man-lobe drecton of the desred sgnals are also man-lobe drectons for the IMD (f no AM/PM amplfer converson s assumed). Usng the FFT beamformng, (9) s smplfed to where T! Â:F FI s J 2 Fj s Jt F Á Y\[ FIÃÂ:F JlJ Á Y[ F Â:F JlJ 9 ¾ Á Y[ F () JlJ ( (2) For example, the drecton of the maxmum radated IMP for a 2 Ä product can be found as»å=æ ^ ÈÇÉÊ Á Y\[ÃË 2 9 Ä39 ( (3) It s easly verfed that (3) maxmzes () for the 2 product. 3. SIMULATION SETUP The purpose of the smulaton s to calculate the cumulatve dstrbuton functon of the CIR at the MS n the fully loaded system. We smulate wth a cluster sze ÎÍ NtÏ)N=Ð and a frst ter of nterferng S. Each cell shape s assumed to be hexagonal and the MS are unformly area dstrbuted wthn a cell. We assume that a four element antenna array are employed n each sector ( Ï ). The antenna elements have a ÊQÑ Á J radaton pattern wth ÒÓ & senstvty (the front to back rato s Ô d). The power! receved at the MS from the S transmttng at power s, after averagng over the fast multpath fadng, Õ%T! Ì ÖSØ (4) where s the S to MS dstance, Ù s the path loss exponent (set to 4) and s a lognormal dstrbuted random Ø varable wth mean 0 d and standard devaton 4 d. The MS are randomly placed n each cell and the MS used for the CIR estmaton s pcked from the center cell, to avod edge effects. The beam wth the hghest receved sgnal strength (RSSI) on the uplnk for one partcular user s chosen as the beam for the downlnk transmsson and the power s regulated accordng to (). The users can be separated by usng e.g. a tranng seuence method.
H Ô Ï A. The Transmt MCPA The S s assumed to be eupped wth MCPA:s capable of amplfyng a maxmum of eght smultaneous carrers. The number of used freuency channels per cell s 2,2 and 24 n the ÐvNtÏ)N cases respectvely. As a measure of the lnearty of the MCPA, the nose power rato (NPR) s defned as the rato between the lnear output power densty to the spectrum densty wthn a pre-located notch[3]. When the number of co-amplfed carrers s small (e.g. four), we use the ntermodulaton dstorton rato (IMR) as a lnearty measure nstead, due to the large errors nvoked when removng one carrer n the NPR measurement. IMR s defned as the rato between lnear output power per tone to the hghest ntermodulaton dstorton power, assumng that all nput carrers are of eual ampltude but wth ndependent phases. The AM/PM dstorton s neglected n ths study, t s often s small n a lnearzed amplfer, but the amplfer AM/AM s modeled accordng to Cann s model [0] EGFIHKJ Ú H Û o š!þuš ÜSÝ ` ß (5) where Ú s the small sgnal amplfcaton, àå s the output saturaton level as the nput ampltude and»á â controls the knee sharpness, or the transton smoothness between the lnear and nonlnear regon. In the smulatons, the values â ã & N Å ã are used. The nput backoff, defned as the average nput power compared to the nput saturaton pont, s adjusted to gve the desred NPR.. Performance Crtera To evaluate the performance of the swtched beam antenna system, the area averaged probablty of a receved CIR at a MS exceedng a target value äå. The outage probablty as the probablty that CIR s below a pre-defned power protecton rato. A power protecton rato of 5 d were used n the smulatons. 4. SIMULATION RESULTS Fg. 2 and Fg. 3 shows the performance of the Ð and Ï system respectvely for dfferent NPR. Four carrers are co-amplfed n each MCPA. The degradaton due to the ntermodulaton dstorton s smlar n the cluster sze, although we have a degradaton n CIR compared to Ð due to the reduced reuse dstance and hence ncreased nterference levels, as can be seen as a shft of the curves to the left n Fg. 3. The nterference n these cases are lnear co-channel nterference transmtted by the S n the frst ter and ntermodulaton dstorton from the S n the same sector as the MS s connected to. We see that when NPR s decreased, the nterference s domnated by ntermodulaton dstorton. When the reuse dstance s reduced to æ, see Fg. 4, the NPR=4 d concde wth the deal MCPA curve for low CIR. Ths mples that the lnear nterference from the S n the frst ter s the domnatng nterference. When NPR s decreased, the amplfer s workng closer to the saturaton pont and the nterference becomes more domnated by ntermodulaton dstorton. Fg. 5 shows a 5 5 NPR=28 d NPR=38 d NPR=48 d 0 5 0 5 20 25 30 35 Γ T [d] Fgure 2: Area-averaged probablty for dfferent MCPA lneartes measured as NPR. The curves shows the downlnk wth 4-element antenna arrays n each sector and cluster sze K=7. 5 5 NPR=24 d NPR=33 d NPR=42 d 0 5 0 5 20 25 30 Γ [d] T Fgure 3: Area-averaged probablty for dfferent MCPA lneartes measured as NPR. The curves shows the downlnk wth 4-element antenna arrays n each sector and cluster sze K=4. comparson of the outage probabltes for the three cluster szes consdered. We see that the Ï system s slghtly more senstve to ntermodulaton than the Ð system, due to the reduced reuse dstance, hence when NPR s decreased, a MS can be nterfered by ntermodulaton from S n the frst ter. Note that the asymptotc value of the outage probablty for the ½ case s 0.79 when NPR goes to nfnty, hence the system s nterference lmted due to the short reuse dstance, even wth deal MCPA:s. 5. CONCLUSION The performance of a swtched multbeam antenna system usng transmt MCPA:s n a cellular FDMA network has
R that partcular freuency channel. 5 5 NPR=22 d NPR=33 d NPR=4 d 0 5 0 5 Γ T [d] Fgure 4: Area-averaged probablty for dfferent MCPA lneartes measured as NPR. The curves shows the downlnk wth 4-element antenna arrays n each sector and cluster sze K=. Pr{SIR>5 d 0.7 0.6 0.5 Asymptote for K= K=7 K=4 K= 0.4 20 25 30 35 40 45 50 55 60 NPR [dc] Fgure 5: -Pr R-çè A EvkW for dfferent cluster szes as a functon of MCPA lnearty. been studed by smulatons on the downlnk channel. The IMP wll be spatally fltered by the array radaton pattern and s often radated n another drecton than the drecton where the two, or the three sgnals that generate the IMP are drected. The multbeam antenna makes the system more robust to nonlneartes, for Ð, the CIR s severely reduced when the nonlnearty s present, by ntermodulaton dstorton from the own S. However, the multbeam antenna has ncreased the CIR to such an extent that the outage probablty éêìë *í $ W s only slghtly affected. For æ systems the lnear nterference stuaton s severe and every d degradaton n MS CIR s expensve, hence the outage probablty wll be largely affected when the NPR s decreased. Hence, t was demonstrated that by usng a multbeam antenna n Ð freuency planned network, we can use the generated CIR overhead to use a less complex or less expensve lnearsaton method. To reduce the ntermodulaton dstorton at the MS, t s possble allocate new mobles to freuences so that the generated ntermodulaton man beam ponts n drectons where no moble exsts on REFERENCES [] M.D.Austn M.J.Ho, G.L.Stuber, Performance of swtched-beam smart antenna systems, IEEE Transactons on Vehcular Technology, vol. 47, pp. 0 9, 998. [2] J.McGeehan G.Tsoulos, M.each, Space dvson multple acess (SDMA) feld trals. Part 2: Calbraton and lnearty ssues, IEE Proc. - Radar, Sonar and Navgaton, vol. 45, pp. 79 84, 998. [3] N.orges de Carvalho J.Pedro, On the use of multtone technues for assessng RF components ntermodulaton dstorton, IEEE Transactons on Mcrowave Theory and Technues, vol. 47, pp. 2393 2402, 999. [4] T.S.Rappaport P.Carder, Combned effects of narrowbeam antennas and fractonal loadng factor n forward lnk cellular communcaton systems, n Proceedngs of Vehcular Technology Conference, Pscataway, USA, 999, pp. 074 078. [5] M.Wennström, Smart antenna mplementaton ssues for wreless communcatons,, Techncal report, Sgnals and Systems Group, Uppsala Unversty, Sweden, 999, Techncal Lcentate Thess, http://www.sgnal.uu.se/publcatons/ abstracts/l99.html. [6] W.A. Sandrn, Spatal dstrbuton of ntermodulaton products n actve phased array antennas, IEEE Transactons on Antennas and Propagaton, vol. 22, pp. 864 868, 973. [7] M.Ljungberg C.Carnehem, S-O Jonsson, FH- GSM freuency hoppng GSM, n Proceedngs of Vehcular Technology Conference, Stockholm, Sweden, 994, pp. 55 59. [8] S.Sowelam K.J. Maalouf, R.C.Gaus, Error rate estmaton n a mult-channel actve phased array, n IEEE Internatonal Conference on Communcatons, New York, USA, 998, pp. 402 406. [9] O.Shmbo, Effects of ntermodulaton, AM-PM converson, and addtve nose n multcarrer TWT systems, Proceedngs of the IEEE, vol. 59, no. 2, pp. 230 239, 97. [0] A.J.Cann, Nonlnearty model wth varable knee sharpness, IEEE Trans. on Aerospace and Electronc Systems, vol. 6, pp. 874 878, 980.