André No Barreto Dresden University of echnoogy Address : Dresden University of echnoogy Departent of Eectrica Engineering Mobie Counications Systes Dresden 0106 Gerany e : 49-351 - 463 4660 Fax : 49-351 - 463 755 e-ai : no@ifn.et.tu-dresden.de On the downink capacity of DD CDMA systes using a pre-rake he Pre-Rake technique for the downink transission in DD-based CDMA wireess systes has been shown to provide greater capacity and a siper receiver design at the obie receiver. Nevertheess this technique is very affected by fast changing channes, since it reies on upink channe easureents for the downink transission. In this paper a sei-anaytica approach to the perforance, incuding channe coding is presented. Furtherore we anayse the pre-rake perforance, incuding its behaviour with changing channes, with and without a channe predictor. Finay we show that the pre-rake axiises the correation between the received and the desired signa, and this deonstration provides us the eans to obtain an instant power contro at bit eve that iproves perforance significanty. ey opics : Persona Counications Systes Mutipe Access echniques Modeing and Siuation of Counications Systes
On the downink capacity of DD CDMA systes using a pre-rake ABSRAC he Pre-Rake technique for the downink transission in DD-based CDMA wireess systes has been shown to provide greater capacity and a siper receiver design at the obie receiver. Nevertheess this technique is very affected by fast changing channes, since it reies on upink channe easureents for the downink transission. In this paper a sei-anaytica approach to the perforance, incuding channe coding is presented. Furtherore we anayse the pre-rake perforance, incuding its behaviour with changing channes, with and without a channe predictor. Finay we show that the pre-rake axiises the correation between the received and the desired signa, and this deonstration provides us the eans to obtain an instant power contro at bit eve that iproves perforance significanty. 1 - Introduction Code division utipe access (CDMA) based on direct sequence spread spectru techniques has been gaining a ot of ground in obie counications systes atey. his technique is aready being used in IS-95 systes under operation and ipeentation in severa countries wordwide and it is ikey to be used in the next generation of obie counication systes [3,4] currenty under standardisation. Initia studies have spread the beief that the downink capacity in CDMA systes is greater than in the upink, but soe ore recent studies [5] show that in practice the opposite can be observed, and the downink is the iiting ink in ters of capacity for CDMA systes. his is due to severa facts. Firsty, the iportance of downink power contro has been often negected. Even though the requireents are not as harsh as in the upink, different users suffer different channe ipairents and are subject to different interference patterns, and thus a ore efficient power contro schee is needed. Secondy, soft handover ipies that the sae signa can be transitted fro severa base stations at the sae tie, increasing the downink interference. And ast, the possibe capacity gains achievabe with orthogona codes are iited due to utipath propagation. In future counication systes the use of uti-user detection[6] is envisaged to increase the capacity, but its use is ore ikey in the upink ony. In the downink the high copexity of this technique akes its ipeentation prohibitive for a obie station in ters of cost and power consuption, not to ention the need for a higher André No Barreto and Gerhard Fettweis Dresden University of echnoogy Chair for Mobie Counication Systes, 0106 Dresden, Gerany <no,fettweis>@ifn.et-tu-dresden.de signaing traffic. he transission of a piot signa for each user in the upink, as proposed for the UMS standard [4], woud aso reove the need for non-coherent detection, further increasing the transission perforance and hence the capacity. hese facts ipy that the downink capacity ust be aso increased, whie keeping the obie station design as sipe as possibe. his need is even greater if we consider that, unike voice, any services to be supported by future counications services are ikey to be asyetrica, such as internet browsing and video on deand, and that in these services the downink traffic is uch higher in the downink. Another technique that has been increasingy popuar is ie Division Dupexing (DD) in which the sae carrier is used for both inks in different tie sots. One property of such systes is that, since the sae frequency is used, the channe characteristics are neary the sae in both inks, provided the channe does not change too rapidy. his is usefu when sart antennas are used, since the optiised pattern used for upink reception is aso optiised for downink transission. his fact aso ipies the knowedge of the channe ipuse response before transission, and that can be used to achieve utipath diversity gain using signa processing at the transitter, instead of epoying a Rake receiver at the obie station. his technique, known as pre-rake, was first suggested by Esaizadeh, Sourour and Nakagawa[1,], and it wi be better described and anaysed in Section, incuding channe coding. With a pre-rake transitter at the BS, the obie station needs just a atched fiter receiver instead of a Rake receiver, and can be kept sipe and cheap; the signa processing is transferred to the base station, where copexity is not such an iportant issue. But the greatest advantage obtained with the pre-rake is a substantia capacity increase, which wi be deonstrated sei-anayticay in Section and through siuation in Section 3. his is particuary iportant if the need for a capacity increase in the downink is considered, as discussed above. One ajor probe with the pre-rake is that it suffers perforance degradation in fast-changing channes, since the channe estiates used in the downink are obtained in the upink period. In Section 3 we see how this probe can be overcoe with a suitabe channe predictor. In Section 4 it wi be shown that the pre-rake axiises the correation between the desired and the received signa for a atched fiter receiver, and based on this resuts an instant power contro echanis on bit eve wi be proposed that further increases the capacity with no extra receiver copexity. On the downink capacity of DD CDMA systes using a pre-rake 1
- Syste description and perforance anaysis As a channe ode we have considered a tie-invariant baseband discrete tapped deay ine with sape spacing equa to the chip period. he copex channe ipuse response for user i is given by: h i g i, δ( k ) where L is the nuber of paths and g i, is the copex path gain of path for user i. For a syste with N users, the copex transitted signa is : sk ( ) s i i 0 d c i i i 0 where d i (k) is the copex desired sequence obtained after channe coding and copex oduation and c i (k) is the copex spreading code. he I and Q coponents of the desired signa and of the code are correated separatey, i.e. x y Re() x Re() y jix [ () I() y ] We aso assue coherent QPS oduation with unit transit power, such that c i (k)±1±j and d i ( ± 1 ± j). We wi first investigate the syste perforance with a Rake receiver. he anaysis wi be perfored for user 0, with no oss at generaity. In this configuration, the signa s(k) is transitted with no further processing. and the signa received by user 0 can be given by: r 0 g 0, d i ( k ) c i ( k ) ν (4) i 0 where ν(k) is a zero ean gaussian rando variabe with variance N 0, the power spectra density of the white gaussian noise. At the Rake receiver this signa is correated with the spreading code and integrated over sybos to obtain the decision variabe at the decoder input. Assuing axiu ratio cobining with perfect channe estiation, and considering that the data sybo is constant in sybos we have the decision variabe y 0 g 0, r 0 ( k ) c 0 0 g 0, d0 n sef n u n where n sef is the sef-interference, n u is the uti-user interference and n the gaussian noise coponent with variance (1) () (3) (5) var( n) N 0 g 0, Now et a jn, d j ( k n) c j ( k n) c 0. hen the interference coponents can be expressed as: n sef g 0, d 0 ( k ) 0 c 0 ( k ) c 0 and g 0, a 0, n ( ), n 0 n n u i 1 0 g i, g 0 d, i ( k ) c i ( k ) c 0 N 1 α g i, g d 0, i c i c 0 i 1 g i, a i, i 1 n ( ), n 0 n α N 1 g i, g a 0, i, 0 i 1 where α0 if the codes are orthogona over copex sybos and α1 otherwise. We have assued in the above equations that orthogona codes behave ike rando codes if not synchronised., what is reasonabe if we assue that orthogona codes are further correated with a scrabing code. It can be safey assued that, for n 0 or j 0, a j,n (k) are i.i.d rando variabes with equa probabiity p1/4 of assuing the vaues a jn, ( ± 1 ± j), such that var[a j,n (k)]1. Furtherore, it is cear that n sef and n u have zero ean. Hence the interference variance can be given by: var( n sef ) g 0, n ( ), n 0 n var( n u ) ( )var( n sef ) α g 0, We can assue that the interference is a gaussian rando variabe, at east for high processing gains and high nuber (6) (7) (8) (9) On the downink capacity of DD CDMA systes using a pre-rake
of users. In anaogy to a white noise process we ay then define the interference power spectra density I 0, which, since n sef and n u are independent, is equa to [ var( n sef ) var( n u )] I 0 --------------------------------------------------------- (10) g 0, A siiar anaysis can be carried out for the Rake receiver, but in this case the channe ipuse response is atched at the transitter. We have thus: s s i β i g i, d i ( k ) i 0 i 0 0 c i ( k ) where 1 β i ----------------------------- g i, (11) (1) is a noraising factor to assure that a users transit with sae power. By foowing the sae anaysis done for the Rake receiver we have at user 0 the foowing decision variabe before the decoder: y 0 β i g 0, g i, d i ( k ) i 0 0 c i ( k ) c 0 ------------------------------- g 0, d0 n se f, g 0, n u, n (13) Now the noise variance var(n )N 0, and the variance of the interference coponents are given by var( n se f, ) Siiary to equation (10), we have now (14) (15) For a given channe configuration, the bit error probabiity is a function of the bit energy to the noise pus interference power spectra density at the receiver, i.e., P e F(E b /(I 0 N 0 )). With knowedge of these functions and of the channe probabiity distribution p(g) we can obtain the ean bit error rate, as foows. where the bit energy is ---------------------------- g 0, (16) (17) for both Rake and pre-rake, with R the code rate; and the interference can be obtained fro (10) and (15). An anaytica soution of (16) for a Rake receiver without coding is possibe[7], but it is uch ore difficut for the pre-rake. Furtherore, when convoutiona channe coding is considered, the usua union bound approxiation[7] is good for high signa-to-interference ratios, but too pessiistic for ow SIR vaues, and such cases occur with a certain probabiity in Rayeigh faded environents. We have then decided for a sei-anaytica approach. We assue that the path gains g i, are independent rando variabes with ean and variance given by a particuar channe ode. hen, according to this ode, the path gains are randoy chosen and the desired signa ean; and noise and interference variance are obtained fro the equations above, and the resuts appied to the error function. For ow SIR vaues the error function F(E b /(I 0 N 0 )) was n ( ) n 0 g 0,, n var( n u, ) β i g i, i 1 n ( ), n 0 n α β i g i, i 1 [ var( n se f, ) var( n u, )] I 0, ------------------------------------------------------------------------------ BER E b ( g) E b ( g) F -------------------------- dg I 0 ( g) N 0 --- g R 0, On the downink capacity of DD CDMA systes using a pre-rake 3
obtained by siuation and approxiated by a poynoia. For high SIR vaues the union bound was used. his can be seen in Fig. 1 for a convoutiona code of rate R1/8 and constraint ength 9, which was used for the resuts shown. poynoia appr. union bound Fig. 1 - Modeing of the channe code his procedure was repeated for any different channe configurations and the average bit error rate was so obtained. We have considered a syste with processing gain G18 copex chips/bit, and the resuts are shown in Fig.. It shoud be noticed that there are ony 3 orthogona codes avaiabe in order to expoit the ow coding rate, but ore users can be supported if each group of orthogona users transits with a different scrabing code. We have used a 6-path Rayeigh faded ode with exponentia decay and 100ns rs-deay, and have considered E b /N 0 9dB. It can be seen that a substantia capacity gain can be obtained by using the pre-rake, which confirs the resuts fro [], in which however coding was not considered. We aso notice that ony a argina gain can be obtained by epoying orthogona codes in association with a pre-rake. he capacity gain is due to the fact that with a pre-rake the desired signa is received coherenty, whie the interfering signas are not, whereas with a Rake receiver both desired and interfering signas are received coherenty. Furtherore, the sei-anaytica resuts show a great accordance with the ones obtained through siuation. We saw in the previous section that a perforance iproveent can be obtained with a pre-rake, but it has a ajor drawback. Its perforance is severey deteriorated in the presence of rapidy changing channes, since the transission in the downink reies on channe easureents obtained in the previous upink period. he anaysis of this behaviour is very difficut anayticay and it has to be faced with siuation. In the resuts presented here we have used the foowing paraeters: carrier frequency 5GHz, sybo rate 18,16Mbauds and a DD frae duration of 1.5s. Accounting for guard intervas, piot signa, and considering that the sae channe has to be used for both inks, we achieve a net data rate of 64kbps in each ink, with a processing gain of G18 copex chips/bit, as in Section. he coding, processing gain and channe ode are the sae fro Section, but this tie we consider a oving obie, with a cassica dopper spectru, at various veocities. he resuts are shown in Fig. 3, in which we see the rapid deterioration of the pre-rake perforance with increasing veocity. he perforance can be however significanty iproved if we try to predict the channe characteristics using an 10-tap Wiener fiter[8]. his requires tota knowedge of the tie correation of the fading process, and can be thus seen as a iit on the perforance to be obtained using a pre-rake. he resuts so obtained are aso shown in Fig. 3. he channe paraeters are obtained fro a piot sequence in the idde of each frae, and we have assued perfect channe estiation. For the case with no prediction, we assue that the channe paraeters used for the pre-rake are the ones obtained in the upink frae. We can see that when prediction is not used the BER rapidy deteriorates for veocities above 5/s, whereas with the predictor veocities up to 15/s can be supported, which is adequate for systes with sa ces. Fig. 3 - Syste perforance in a changing environent Fig. - Perforance of a pre-rake in coparison to a Rake receiver 3 - Pre-Rake in changing channes he sae can be observed when we consider the capacity. In Fig. 4 we show the siuation resuts for a variabe nuber of users with a constant veocity of 5/s. We see that the capacity obtained with the pre-rake without prediction can be ess than the one obtained with a Rake receiver, due to the pre-rake sensitivity to Dopper fading, as shown above, but we can aso see that this can be reverted when prediction is used, at east at ow veocities. On the downink capacity of DD CDMA systes using a pre-rake 4
C i d i are ineary independent. Hence this probe can be soved using Lagrange utipiers[9]. We have the foowing Lagrange function ( s) s s λ i s ( C i γ i ) (0) i 0 By differentiating the functions p(s) and c i (s) a point of oca iniu s * is obtained if F ( s) s λ i C i 0 (1) i 0 Fig. 4 - Capacity of the pre-rake in a changing environent,and the unique soution for that equation is ceary 1 s -- λ i C i λ i C i i 0 i 0 () 4 - Pre-Rake with instant power contro As we have seen, the basic idea behind the pre-rake is that in DD systes we can assue that the channe ipuse response is known before transission. Besides that, the data sequence is aso known, so that we are abe to find the optiu transission sequence at the base station that iniises the error probabiity at a atched fiter receiver at the obie station. In rea systes we want to obtain a certain quaity of service, and there is itte point in reducing the bit rate beyond the required. We want to increase capacity, and in CDMA systes this eans to reduce the interference, and hence the transitted power. his eans that the search for the optia transission sequence can aso be seen as the search for the sequence that iniises the transitted power for given receiver perforances. In QPS the perforance is basicay a function of the correation between the received signa without noise and the desired signa. Now suppose we transit the signa vector s[re[s(0)],i[s(0)],re[s(1)],...,re[s(-1)]i[s(-1)]]. he signa received at user i is distorted by the channe atrix C i such that the received signa equas r i C i s n i (18) where n i is the noise vector. Ignoring the noise vector, we want to obtain the vector s that iniises the transitted power p(s)s s, under the constraint that the correation requireents of every user is satisfied, i.e., such that c i ( s) r i s C i γ i (19) where d i is a vector containing the desired data, incuding channe coding, spreading and scrabing. We have a syste with N constraints, with N the nuber of users, and we assue that N is ess than the diension of s. Furtherore, the derivative p (s)s 0 for any s 0, and we can assue that Rank(c (s))n, which is true if the vectors his is however nothing ess than the pre-rake. It is thus deonstrated that the pre-rake is the optia transission technique in ters of signa correation for a atched fiter receiver. he paraeters λ i can be obtained by soving the N equations obtained by substituting equation () in (19), as foows: λ j d j C j C i γ i (3) j 0 Different users are differenty affected by channe ipairents and uti-user interference, and ay have different quaity criteria. hese factors can be copensated with knowedge of the vaues λ i, which provide inforation that can be used to obtain an instant power contro, i.e., power contro can be ade on a bit-by-bit basis in order to copensate for the fuctuations in the interference eve. We now et s(k) be the transitted sequence at the transission period of the k-th bit. As in (18), the received signa can be expressed by: r i C i s v i n i (4) where v i (k)c i s(k-1) is the interference due to the deayed versions of the signa transitted during the previous bit. Siiary to (3), the N equations to be soved are now: λ j ( k )d ( k ) C j j C i d ( i k ) γ i v i di j 0 (5) Now et B(k)[d 0 (k)c 0, d 1 (k)c 1,..., d N-1 (k)c N-1 ] and v(k)[v 0 (k)d 0 (k),v 1 (k)d 1 (k),..., v N-1 (k)d N-1 (k)], then the equations (5) can be expressed in the atrix for B B λ γ v (6) Since B(k)B (k) is a syetric positive definite atrix, this On the downink capacity of DD CDMA systes using a pre-rake 5
syste can be soved with reduced copexity by using Choesky[9] decoposition. It ust be said that this anaysis appies not ony to a bit period, but by any period of ength sybos such that N, when using QPS. Anyway, the saest period at which the signa correation atters is b R, where R is the coding rate. We have siuated a syste epoying the instant power contro just suggested, and copared it with the resuts obtained with a Rake receiver and with a pre-rake. We assue as requireent that a users have the sae signa correation at reception, and after obtaining the signa power that iniises the transit power, the power is noraised, so that the sae transit power is used for a techniques. he resuts can be seen in Fig. 5 for a syste with processing gain G3 copex chips/bit, no channe coding and a 4- path channe ode. We have aso assued perfect power contro for the Rake and pre-rake situations, i.e., the received power is constant and the sae for a users. We can see that the capacity obtained with the proposed instant power contro is uch higher than the ones with either the Rake receiver or the pre-rake. his capacity gain is obtained with no further copexity at the obie station, which, as with a pre-rake, needs just a atched fiter receiver. Furtherore, through this ethod we can ake sure that a the users are treated equay and receive their fair share of the transitter power resources. his ethod can be viewed as a sort of uti-user transission schee, in which the best transission signa is estiated taking into account the interference between the different users. E b /N 0 6dB E b /N 0 9dB Fig. 5 - Perforance of the pre-rake with instant power contro 5 - Concusion In this paper we have investigated the capacity cain that can be achieved in the downink of DD CDMA systes by using a pre-rake at the base station. It has been shown that besides aowing a siper obie station receiver design, systes using the pre-rake can provide a significant capacity increase in the downink. Nevertheess the pre-rake perforance is very susceptibe to the obie veocity, and we have shown that robust pre-rake transission is feasibe with the adequate channe prediction schee, and that a arge capacity can be achieved aso at high veocities. As entioned in the Introduction, power contro is a key issue aso in the downink, and we have shown that a substantia capacity gain can be obtained if we use the a priori channe knowedge inherent to DD to provide instant power contro in conjunction with the pre-rake. 6 - References [1] Esaizadeh R. and Nakagawa M., "Pre-Rake Diversity Cobination for Direct Sequence Spread Spectru Mobie Counications Systes", IEICE rans. on Co., Aug. 1993, pp 1008-1015 [] Esaizadeh R.,Sourour E. and Nakagawa M., "Pre- Rake Diversity Cobining in ie Division Dupex CDMA Mobie Counications", Proc. of the Int Syp. on Persona, Indoor and Mobie Radio Co (PIMRC), oronto, Sep. 1995, pp 431-435 [3] Dahan E.,Gudundson B.,Nisson M.,Skod J., "UMS/IM-000 Based on Wideband CDMA", IEEE Co. Mag., Sep. 1998, pp 70-80 [4] Ojanpera.and Prasad R., "An Overview of Air Interface Mutipe Access for IM-000/UMS", IEEE Co. Mag., Sep. 1998, pp 8-95 [5] Yang J. and Rajan M., "Microce Perforance Evauation in IS-95 based CDMA Networks", Proc. of the Int Conf. on Universa Persona Co. (ICUPC), Forence, Oct. 1998, pp 899-903 [6] Moshavi S., "Muti-User Detection for DS-CDMA Counications", IEEE Co. Mag., Oct. 1996, pp 14-136 [7] Proakis, Digita Counications, McGraw Hi, New York, 1995 [8] Haykin, Adaptive Fiter heory, Prentice Ha, Engewood Ciffs, NJ, USA1991 [9] Zeider, eubner-aschenbuch der Matheatik, eubner, Leipzig, Gerany, 1996 On the downink capacity of DD CDMA systes using a pre-rake 6