MACRO-DIVERSITY VERSUS MICRO-DIVERSITY SYSTEM CAPACITY WITH REALISTIC RECEIVER RFFE MODEL

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1 MACRO-DIVERSITY VERSUS MICRO-DIVERSITY SYSTEM CAACITY WITH REALISTIC RECEIVER RFFE MODEL I Ouachani, Duhamel, K Gosse, S Rouquette-Léveil and D Bateman *Laboatoie des Signaux et Systèmes 3 ue Joliot-Cuie Gif su Yvette - FRACE **Cente de Recheche de Motoola - ais- Les Algoithmes Gif-su-Yvette Cedex - FRACE ABSTRACT This pape studies the evolution of Multiple-Input Multiple- Output (MIMO) system capacity in the context of maco-divesity antenna configuations, with espect to system paametes such as the distance between mobile devices In this context, we edefine an accuate channel model by poposing a ealistic configuation of the RF font-end (RFFE) the The impact of this impoved model on system capacity is fist checked in the mico-divesity context, when compaing ou esults with the model classically used in the liteatue This new model is shown to explain some phenomena obeved in actual implementations Then, in the maco-divesity context, we concentate on the usefulness of adding antennas, depending on the distance to the tansmitte o eceive The obtained esults ae stongly impacted by the RFFE model 1 ITRODUCTIO Wieless netwoking constitutes an impotant component of futue infomation technology applications To impove the eliability of communication ove the wieless channels and combat the fading, many papes have focused on the use of divesity techniques One of the most studied technique is the use of multiple antennas at wieless tansmittes and eceives It exploits the spatial micodivesity ceated by seveal antennas colocated on the same mobile device [1][] Howeve, spatial divesity can also be exploited by joint pocessing of signals tansmitted o eceived by sepaated devices, access points o teals This type of divesity is known as maco-divesity evious woks addessing the maco-divesity [3, 4,, 6, 7, 8] have been published The ealiest woks have focused on the uplink in cellula netwoks in ode to impove the systems coveage and enlage the cells size The measue of the link quality has been eithe (i) the instantaneous o local mean signal-to-noise atio (SR) o (ii) signal-to-intefeence (+ noise) atio (SIR) [3][4], o (iii) the coesponding bit-eo-ate (BER) [6][7] In this pape, the main objective is to assess the impact of system paametes values, such as distance between devices, on the capacity and the outage capacity of maco-divesity based system This point-to-multipoint communication link is met when a given communicating teal can tansmit infomation though seveal communication outes, eithe in decentalized netwoks o in systems in which access points can shae eceived infomation In this context, it is necessay to edefine a pope channel model adapted to the maco-divesity situation, in connection with the popagation model, since the elative distance between communicating devices plays an impotant ole due to path loss effects This equies also to edefine ealistic constaints on emitting powes In that pupose, we popose a model of the eceive adio fequency font-end (RFFE), enabling to specify elationships between eceive SR values and emitted/tansmitted powes in vaious opeating zones In ode to assess the impact of the ealistic RFFE model (pesented in section 3) and the elated impoved channel model on the system capacity, we fist addess the case of point-to-point multiple-tansmit multiple-eceive (MIMO) communications (micodivesity), and compae ou esults to the ones obtained with classical MIMO channel models [1] [], ie without taking into consideation the eceive RFFE model It is shown that the RFFE exhibits two main opeating modes, one of which esults in an unusual channel behavio The impact of these opeating modes is fist evaluated in a micodivesity scenaio (section 4), in tems of the egodic and outage capacities Then, in section, we concentate on the maco-divesity context itself The objective is to evaluate the impact of inceasing the numbe of antenna (possibly at some distance of the othe ones) on the egodic and outage capacities This study thus povides means of evaluating whethe consideing additional antennas that ae at some distance as pat of a multi-antenna eceive has a lage potential impact o not MIMO SYSTEM RESETATIO We focus on a MIMO system that employs n T tansmitting and n R eceiving antenna elements In the mico-divesity context, the n T tansmitting antennas ae co-located, as ae the n R eceiving antennas In the maco-divesity context, the tansmitting antennas and the eceiving ones ae dispatched on mobile teals Assume we have T x tansmitting teals and R x eceiving teals, and n Tj and n Ri (j = 1 T x, i = 1 R x) denote the numbe of antennas co-located on the j th tansmitting teal and i th eceiving teal espectively This system is denoted as an (n T1, n T,, n TTx )x(n R1, n R,, n RRx ) MIMO, and the distance between the j th tansmitting teal and the i th eceiving one is denoted by D i,j The input/output elation of the MIMO system is descibed by the following equation: y = Hx + b (1) whee x = [x 1 x x Tx ] T is the tansmitted vecto; x i denotes the n Ti 1 vecto tansmitted by the i th teal b = [b 1 b b Rx ] T denotes the additive white Gaussian noise vecto, which covaiance matix cov{b} = diag{cov{b 1 }, cov{b },, cov{b Rx }}

2 AGC G Othe devices (1,G1) (,G) (3,G3) G( + ) ADC + * Fig Receive model scheme s (,G) with cov{b i } is given by Fig 1 Simplified eceive scheme 1 cov{b i } = n Ri 1 C A whee i, (i = 1n R) is the noise powe intoduced by the i th eceived signal The channel matix is given by () H = {H i,j} i=1rx, j=1t x (3) whee H i,j denotes the channel matix containing the individual channels fom the j th tansmitting antenna to the i th eceiving antenna In this pape, the enties h k,l i,j of the matix {Hi,j}i=1Rx, j=1tx ae assumed independent Rayleigh flat fading, ie they ae ciculalysymmetic Gaussian with zeo mean, independent eal and imaginay pats, having vaiance σi,j/ The vaiance σi,j is given by the path loss σi,j = K o(d i,j/d o) δ whee d o = 1m is a efeence distance, δ is the path loss exponent; K o = (c/4πd of c) is the channel powe gain at the efeence distance 3 MODEL OF THE RADIO-FREQUECY RECEIVER FROT-ED Classically, the RFFE is modelled only by additive white Gausian noise (AWG), which epesents the themal noise of the components, a model which implicitly assumes a pefect behavio of the Automatic gain Contol (AGC) inside the eceive Hee, we will take into account a diffeent, yet pactical point of view, of the effect of the AGC on the oveall system pefomance in tems of capacity Geneally, the eceive RFFE is mainly composed of thee pats: in the fist pat, the eceived signal is filteed in ode to emove adjacent band signals Then, the amplifying block (second block, delimited by the dashed ectangle in Fig 1) multiplies the eceived signal by some gain G, so that the signal dynamic ange is adapted to the ADC input ange The gain G is adjusted by the Automatic Gain Contol AGC device And finally, the ADC convets the analog signal to a digital one A geneic AGC consists of a (Low oise) Amplifie, with a constant gain and a noise figue 1 followed by a vaiable gain amplifie with a gain G and intoducing a noise figue All othe components ae gouped in the thid block having a constant gain G 3, and intoducing a noise figue 3 This eceive RFFE model can be simplified into the scheme plotted in Fig Thee, the eceived signal is fist affected by the additive themal noise; it is then amplified by the gain G = G G 3 adjusted by the AGC, and it is finally sent to the ADC The themal noise can be gatheed into a single noise souce at the input of the eceive, and its powe is given by = KT B ( ) (4) G whee K is the Boltzmann constant, T is the tempeatue; KT is -174 dbm/hz at oom tempeatue, and B is the signal bandwidth The eceive RFFE can be descibed by, the dynamic ange, the amplifies gains These paametes associated to the themal noise lead to a chaacteisation of the vaiation of the SR vesus the eceived powe, as explained below 31 Dynamic ange The dynamic ange of the eceive expessed in db is the diffeence between the blocking level and the eceive sensitivity The blocking level and the sensitivity ae the imum powe and imun powe suppoted by the eceive electonic components 3 Amplifie gain The RFFE global gain is given by G = G G 3 Because of individual components limitations, the amplifies ae not always able to povide the necessay gain to compensate fo the channel fadings In fact, when the eceived powe is lowe than some theshold, hee denoted by AGC, the amplifying gain in the AGC is bounded by G To simplify the model, we assume that the umum of the dynamic ange of G (ie G ) coesponds to Hence, the vaiation of the gain has two modes When is in [, AGC ], the amplifying block gives the imum gain G When the eceived powe inceases in [ AGC, ], the amplifying block gain G deceases linealy till equals the eceive blocking level At this stage, the gain G = G This desciption intoduces thee modes fo the AGC: in a fist mode, (satuation) the gain is set to G In the noal mode (whee the AGC plays its ole: the signal at the entance of the ADC has its noal value Finally, when >, the eceived signal dynamic ange is outside the opeating ange of the ADC, thus intoducing undesiable clipping effects In the sequel, we will not addess this thid mode In Fig 3(a), only the two fist modes ae pesented 33 Receive SR Given these models of the noise floo and of the gains, the instantaneous SR at the input of the ADC eads: SR = = KT B( G ) whee is the eceived powe Define the eceived powe sat coesponding to a gain G sat, so that we have: 3 = ( G sat 1 + G 1 ) This value delimits two appoximations of the SR with diffeent behavios: ()

3 G G G (db) (a) SRsat SR (b) SR at the output of the RFFE block and the eceived powe on a given eceive antenna This new elationship also depends on the way the multi-antenna font-end is designed, in tems of numbe of analog RFFE blocks and in tems of AGC stategies In any case, the esulting SR vs eceived powe elation affects capacity We compae below the esults obtained with the standad and the impoved multi-antenna RFFE models AGC Fig 3 (a)amplifie gain vaiation vesus the eceived powe, (b)sr vaiation vesus the eceived powe If sat, the amplifie gain G is lage and the expession of the noise powe simplifies to: = KT B ( 1 + /), a constant noise powe Thus the SR vaies linealy with the eceived signal powe : SR = 3 db sat KT B( 1 + ) If sat : the gain G is small, and 1 + is negligible compaed to 3 G Consequently, the themal noise simplifies to: = KT B 3 G Since G is vaiable, the noise powe is no moe constant and the SR expession can be appoximated by: SR = (6) G1 G KT B 3 (7) (dbm) We conclde fom the AGC behavio that the poduct G is constant Thus, The SR is constant fo [ sat, Consideing the two SR expessions above, the vaiation of the SR vesus the eceived signal powe is plotted on Fig 3(b) Fom the explanations given above, the eceive dynamic ange can be divided into thee intevals: [ and [ sat, ], AGC ], [ AGC, sat ] Since the pefomance of the system is investigated in tems of capacity, which depends only on the noise powe, only two intevals [ sat, ] and [, sat ], denoted by I 1 and I espectively, ae of inteest to us It is to point out that the noal zone fo eceive pocessing is: [ AGC, sat ], since we ae outside the satuation zone of the AGC and the satuation zone of the SR 4 MIMO SYSTEMS EXLOITIG MICRO-DIVERSITY In this section, we focus on a MIMO system that uses n T tansmitting and n R eceiving antenna elements, in a mico-divesity scenaio The aim hee is to calculate the system capacity This computation is based on the popagation model, and on the signal and noise vaiances as given by the RFFE model Unde the classical assumptions made by Foschini [], the SR is the same on all eceive banches, and is expessed as: SR = whee is the aveage eceived powe on each banch This is the standad model Hee, the extension of the single antenna RFFE model descibed in section 3 to the MIMO case puts into question these assumptions, and leads to a modified elation between the (8) ] 41 Multiple-antenna eceive model In a multiple-antenna eceive, thee stategies can be applied in the font-end design: (1) one RFFE block is assigned fo each antenna and the AGC of each banch is communicating with the AGCs of the othe ones, so that the same gain is applied on all banches, () one RFFE block is assigned fo each antenna and the AGC of each banch is independent of the AGCs of the othe ones, thus diffeent gains ae applied on the eceive banches, (3) a single RFFE block is assigned to all antennas, the eceive compaes all the eceived powes and selects the highest one This case does not fully exploit divesity and will not be futhe consideed hee Remembeing the single antenna RFFE model pesented in subsection 3, it is clea that the instantaneous noise powe depends of the eceived signal powe, o, in othe wods, of the channel fading coefficients Thus, in the MIMO setting, the final value of the SR i eceived on the i th banch depends on the AGC stategy 4 Simulation esults Conside again RFFE chaacteistics matching with the physical laye specifications of the IEEE 811a standad, as summaized in table 1 The Rayleigh fading vaiances ae given by the path loss, which is chaacteized by the following paametes chosen fo a typical indoo channel without shadowing: the path loss exponent is δ = 31, the opeating fequency is f c = GHz and K o = 33 1 The total tansmit powe is fixed to e = dbm fo all systems B is assumed to be equal to 16MHz, coesponding to typical WLA bands (KT B = 7dB) Table 1 aametes of a typical IEEE 811a eceive -8 dbm -88 dbm AGC -68 dbm G 6 db sat -48 dbm G 17 db - dbm SR sat 4 db ADC -3 dbm SR 3 db We now compute the egodic capacity fo the x system, in the mico-divesity context, consideing the two eceive RFFE models, which will be compaed to the standad system coesponding to Foschini s assumptions We fist investigate the vaiation of the eceived powe vesus the distance D between one tansmitte and one eceive, in ode to give the bounds of the zones coesponding to the thee signal powe intevals: [-8 dbm, -68 dbm], [-68 dbm, -48 dbm] and [- 48 dbm,- dbm] The eceived powe vesus D is given in Fig 4 In summay, the noal woking egion of the RFFE block is whee the distance between the tansmitte and the eceive is in [6m, 3m], when the eceive gain is below G and the SR is vaying linealy with the eceived signal powe

4 Rceived powe in dbm SR satuation G = f( ): linea 48 dbm SR=g( ): linea G = f( ): linea 68 dbm SR = g( ):linea G = G distance in mete 8 dbm Fig 4 Received powe vesus the distance between the tansmitte and the eceive (SISO case) In the following, we use U 1 and U to denote the intevals [1m, 6m] and [6m, 76m], espectively Fig illustates the vaiation of the egodic capacity vesus the distance sepaating the tansmitte to the eceive; we note that the egodic capacities when using eithe communicating AGCs o independent ones, ae the same in all the eceive dynamic ange Futhe, when we compae the egodic capacity when consideing the modelled RFFE blocks to the standad system, we note that they have diffeent behavio in the SR satuation zone, ie when D U 1 When D tends to zeo, the standad system capacity conveges to infinity wheeas the system capacity when consideing the RFFE models satuates This behavio is obseved in eal systems Egodic Capacity in bps/hz U 1 x MIMO context, e = dbm standad system RFFE model, independent AGCs RFFE model, communicating AGCs U till D = 78m system consisting of T x tansmitting teals and R x eceiving ones, in the maco-divesity context is denoted by: the T x R x maco-divesity MIMO system In the following, we pesent the simulation esults fo some scenaios, keeping the same simulation paametes as consideed in section 4 We conside the scenaio whee the two eceives ae located at the same place and the two tansmittes ae mobile aound Then we compae its pefomance to the 1x MISO system in ode to study the impact on the egodic capacity of adding a second tansmitte at a cetain distance fom the fist one In Fig 6 and Fig 7, the cuve with stas is plotted fo (1,1)x(1,1) system whee one tansmitte is located at a fixed distance fom the eceives and the othe one is moving fa away, being always fae fom the two eceives than the fist tansmitte Fig 6 depicts the vaiation of the egodic capacity when = 1m, while Fig 7 is the coesponding cuve fo = 7m Clealy, when the distance of the second tansmitte goes to infinity, the capacity should convege to that of a 1 SIMO system This is clealy seen on Fig 6, since the convegence is fast, while on Fig 7, it is seen that the impact of the second tansmitte extends to a much wide zone If we look at the impovement bought by the maco-divesity (adding the second tansmitte), we can see that the fae the fixed tansmitte is the bette is the incease in the global system capacity If we look in moe details at the nea suounding egion of the two eceives, we can note a supising behavio of the egodic capacity As it is shown in Fig 8, stating fom the case the two tansmittes ae located at the same distance = D in U 1, then one of them stats moving close the two eceives, the system egodic capacity deceases Roughly speaking, this can be explained by the fact that in this egion the SR satuates This seems to be due to the fact that, when the tansmitte is becog neae to the two eceives, the eceived powe inceases consequently thus inceasing the intoduced noise (since it is popotional to the eceived powe), which causes a decease in the system egodic capacity D in mete Fig Egodic capacity, x MIMO mico-divese system with vaious -antenna eceive RFFE models To conclude, we can say that when the distance sepaating the tansmitte to the eceive is sufficiently high, both the standad and the impoved models povide almost the same esults Howeve, when the eceive is close to the tansmitte, the eceive SR satuates in the ealistic model, thus esulting in a moe accuate estimate of the pefomances; Thus, it is shown that the use of the classical model in this egion could esult in an oveestimation of the pefomance MIMO SYSTEMS EXLOITIG MACRO-DIVERSITY We now focus on maco-divesity systems, when the antennas ae dispatched on diffeent mobile teals We estict ou simulations to the case whee each teal has a single antenna We concentate on scenaios whee the distances between all the eceive (o tansmit) mobiles decease so that we move smoothly fom a maco-divesity to a mico-divesity configuation The 6 COCLUSIOS In this pape, the evolution of the capacity in both the macodivesity and mico-divesity contexts have been investigated, with espect to the system paametes such as the distance between the mobile teals Fo both contexts, we have poposed a ealistic channel model which involves an accuate model of the eceive adio font-end In the mico-divesity context, it was seen that ou esults ae simila to those povided by the model classically used in the litteatue, when the distance sepaating the tansmitte to the eceive is highe than a given theshold Howeve, when the distance between the tansmitte and the eceive tends to zeo, the modelled MIMO system egodic capacity satuates wheeas the standad MIMO system one tends to infinity This new model allows to pedict a behavio obseved in actual implementations In the maco-divesity situation, it was shown that the coveage aea of the SISO system is stongly inceased by adding a mobile tansmitte Futhemoe, adding a mobile tansmitte to the 1x(1,1) SIMO system, composed of one fixed tansmitte and two colocated eceives, has diffeent impact on the system egodic capacity, depending on the distances between the tansmittes and

5 the eceives Fom a pactical point of view, the good news ae that maco-divesity is popotionnally moe useful in difficult situations (when the eceives and the tansmittes ae fa away) than when they ae close The SR satuation zone was also shown to be subject to somewhat unexpected phenomena (binging one antenna close deceases capacity) Finally, it was shown that adding antennas significantly inceases the MIMO system pefomance in most maco-divesity scenaios, and that the new RFFE model explain some phenomena obseved in actual implementations Egodic capacity in bps/hz x: Rx1=Rx, d 1 =1m 1x (indep AGCs): Tx1=Tx d in mete Fig 6 Compaing the (1,1)x(1,1) system egodic capacity, when the eceives ae in the same place, to the 1x(1,1) one fo = 1 m Egodic capacity in bps/hz x: Rx1=Rx, d 1 =7m 1x (indep AGCs): Tx1=Tx [] GJ Foschini and MJ Gans, On Limits of Wieless Communications in a Fading Envionment when Using Multiple Antennas, Wieless esonal Communications, vol 6, pp , 1998 [3] RC Benhadt, Macoscopic divesity in fequency euse adio systems, IEEE Jounal on Selected Aeas in Communications, vol, pp 86 87, June 1987 [4] L-C Wang, G L Stübe, and C-T Lea, Effects of Ricean fading and banch coelation on a local-mean-based macodivesity cellula system, IEEE Tansactions on Vehicula Technology, vol 48, pp , Ma 1999 [] A M D Tukmani, efomence evaluation of a composite micoscopic plus macoscopic divesity system, in IEE oceedings I, Communication, Speech, Vision, Feb 1991, vol 138, pp 1 [6] Zang J and V A Aalo, Effect of macodivesity on aveageeo pobabilities in a Ricean fading channel with coelated log-nomal shadowing, IEEE Tansactions on Communications, vol 49, pp 13 17, Jan 1 [7] A A Abu-Dayya and C Beaulieu, mico- and macodivesity MDSK on shadowed fequency-selective channels, IEEE Tansactions on Communications, vol 43, pp , Aug 199 [8] S Mukhejee and D Avido, Effect od micodivesity and coelated macodivesity on outages in a cellula system, IEEE Tansactions on Wieless Communications, vol, no 1, pp 8, Jan d in mete Fig 7 Compaing the (1,1)x(1,1) system egodic capacity, when the eceives ae in the same place, to the (1,1)x1 one fo = 7 m 6 = 1m = 3m = 6m 4 Egodic capacity in bps/hz D Fig 8 Capacity behavio in the suounding egion of the two eceives 7 REFERECES [1] IE Telata, Capacity of Multi-antenna Gaussian Channels, Technical epot, AT & T Bell Labs, 199