A SINR Maximizhg RAKE Receiver for DS-CDMA Downlinks

Massimiliano Lenardi Abdekader Medles Dirk T.M. Slock Institut E&om*, 2229 route des C+tes, B.P. 193,

06904 Sophia Antipolis Cedex, FRANCE Tel: +33 4 9300 291012606; Fax: +33 4 9300 2627

e-mail :{lenardi, medles, slock}@eurecom. fr

Abstract

The RAKE receiver is a matchedjlter (MF), matched to the operations of spreading, puke shape filtering and chan- neljltering. An S I ” maximizing linear receiver may per- form much better. In the downlink, in which the channel is the same for all intracell signals, and with orthogonal codes and cell-dependent scrambling, good S I ” pet$or- mance can be attained with a RAKE-like receiver. In par- ticular, we replace the pulse-shape MF by another filter, and the sparse channel MF by another sparse filter. The firstfilter is chosen to facilitate the desigdhdqtation of the sparse fiter, the coe&ients of which are optimized for mar- imum SINR. In the presence of intercell interference (other base stations), but using multiple teceiver antenna a d o r oversampling with respect to the chip rate, good SINR per- formance can be attained with these structured linear re- ceivers.

1. INTRODUCTION

In the FDD mode of the Wideband CDMA (WCDMA) option of the 3GPP UMTS proposal for cellular wireless communications, both uplink and downiink use DS-CDMA communications. This paper focuses on the downlink, where a set of orthogonal periodic spreadiog sequences are used, to take advantage of the synchronicity (between users) of the downlink. To limit interference between cells though, a cell-

dependent scrambling gets added which does not destroy the orthogonality between the inrracell users. Due to the scrambling (which can be Considered as a stationary chip

‘ W s neearch i s parciatly Jnppoaed by its industrial parmers: Ascom, Swissann, ?bomson-CSF, IBM France, CEGETTX. Motorola, Fhmce T~~ Hitachi Europe and Texas I”ents . ?he workl*ding to this papa was also partidly snppmed by the French RNRT (National Network fa T e k u ” m ’cationsResearcb)pFojedAUBE

rate sequence), the received signal is cyclostationary at the chip rate. The conventional receiver for DS-CDMA com- munications is the RAKE receiver. The RAKE receiver is a matched filter 0, matched to the operations of spreading, pulse shape filtering and channel filtering. Such a MF does not maximize the SDR, but only the SNR. The RAKE re- ceiver is a restricted linear optimal receiver in the sense that it would be optimal if only the additive white noise (and not any interference) would be present. Even though the received signal is cyclostationary at the

chip rate (and not at the symbol rate. so that signal sub- spaces do not exist) linear multiuser detectom (MUD) can be meaningfully applied to achieve much improved perfor- mance (SINR) over the RAKE receiver. The general linear MMSE receiver is time-varying however, due to the pres- ence of the scrambler. For such a receivez spanning several symbol periods, the complexity for applying the filter can be quite high, due to the multiplications of signals with ar- bitrarily valued coefficients at chip rate. And of come, the complexity for producing the time-varying filter coefficients is enormous.

However, structurally constrained linear detectors exist that show a reasonable complexity/performance trade-off. Indeed, apart from synchronicity. another characteristic of the downlink is that all intracell signals pass through the same channel (if the BS does not apply beamfoxming). So, considering only the intracell interference (and not the inter- cell interference and noise). a receiver consisting of a zero- forcing equalizer followed by a descrambler and a correla- tor would be optimal (maximize SIR). Indeed, the equalizer restores orthogonality of the codes (which was destroyed by the delay spread of the multipath channel) so that a simple correlator then suffices to pick out the signal with the code of interest while perfectly suppressing all other (orthogo- nal) codes. Such a receiver is also suboptimal though smce the zero-forcing equalizer enhances the noise and intercell interference. The RAKE maximizes the SNR while this re- ceiver maximizes the SIR (counting the intercell mterfer-

0-7803-65 14-3/00/$10.0002000 IEEE 1283

ence witb the noise). Theperfo”criteri0n that needs to be optimized though is the SINR.

In [l] we proposed a g e “ i linear receiver, the

equal=-plusuxrelatororrelatorvers [2] as special cases. The svuctllre is the same of the RAKE receiver, but the channel and pulse shapematchedfilters m replaced by an equalizer filter that is designed to maximize the SINRat theoutput of the receiver. So the receiver is a cascade of a linear (short- term) time-invariant equahzer. a descmnblez and a m- lator. So the overall linear receiver is time-varying but the time-variation is completely concenW in the descram- b k . It tums out that the optimal design of the equalizer that leads to maximum SINR at the output of the overall receiver leads to the MMSE equal~zer (with the received signal be- ing cyclostationary at chip rate). In [3] we studied different lower-amplexity ionplementations of the equalizer, includ- ing a cascade of a pulse shape matched filter and a sparse filter, whose coefficients were optimized to maximize the output SINR. In this paper we propose to replace the pulse shape matched filter by a pulse shape equalizer, using possi- bly multiple antermas to beuer handle intercell interference also.

~ ~ x - S I N R receiver, Which en~0m-s the RAKE and the

Figure 1. Dawnlink signa0 model BS-MS

Stacking the M samples per chip period in vectors, we get for the sampled received signal at the MS antenna j

K N-1

= C C h{bk,l-i +4 3 (2) k l i=o

where

2. MULTIUSER DOWNLINK SIGNAL MODEL

Rg. 1 shows the downlinir: signal model in baseband, be tween the mobile receiver and the main base station. Signals coming from other BSs am of the same structure. but pass- ing through different channels, and included in the additive noise u(t). The K users are assumed to transmit linearly modulated signals over the s a m linear multipath channel. The symbol and chip periods T and T, are related through the spreadtng factor L: T = LT,, which is assumed here to be common for all the users. The totaJ chip sequence bl is the sum of the chip sequences of all the users, each one given by the product between the nth symbol of the kth

self the product of a periodic Walsh-Hadamard (with unit

and a basestation specific unit magnitude complex scram-

U s e t and all apefiodiC Spfeading S e q U e n O e WkJ Which is it-

m%y) spreadtug ’ Ck,L-l] 9

bling Sequence 81 With VaI‘hlKX 1, WkJ = Ck.1 mod L81:

T c k = [ck,O Ck.1

K K bt = bk,I = xak,[;jwk,l -

k= 1 k=l

The chip sequence b1 gets transformed into a continuous- time signal by filtering it with the pulse shape p(t) and then passes through the multipath propagation channel h(t) to yield the received signal ~ ( t ) . The receiver samples M times per chip the lowpass filtered received signal.

HUE represents the vectori~ed samples of the overall channel, including pulse shape, propagation channel and re- ceiverfilterfortheMSantennaj(j = l . . . J ) .Theoverall channel is assumed to k e a delay spread of N chips. In the case of multipath, the channel model is

antenna j , {a,} represent the complex amplitudes of the path p with the correspondent Belays {T’} which are equal for all P MS antermas. If we model the scrambling sequence and the symbol sequences as independent i.i.d. se quences, then the chip sequence bl is a sum of K m d e p - dent white noises (chip rate i.i.d. sequences, hence station- ary). The invacell contribution to $ then is a stationary (vector) process (the continuous-time counterpart is cyclo- stationary with chip period). The intercell interference is a sum of contributions that are of the same fonn as the m- tracell contribution. The remaining noise is assumed to be white stationary noise. Hence the sum of intercell interfer- ence and noise, 4, is stationary. In the case of multiple MS antennas, the total received signal from a BS is

J

= a e j (5 ) j=l

where ej is a unit vector of size J with a 1 in position j . The total channel is then hi = hi @ ej.

3.MAX-SINRRECEIVERSTRUC"URE

As shown in Fig. 2, the receiver is constrained to be a chip rate filter f followed by a descrambler and a mrrelator with the spreading code of the user of interest, which is here assumed to be user 1. So the receiver has the same struc- ture as a RAKE receiver, except that the channel matched filter gets replaced by a general filter f. If a sparse (path- wise) representation is used for the channel, then the chan- nel matched filter leads to a RAKE structure with one fin- ger per path. In Fig. 2, the operation "SE"' denotes a se- rial to parallel conversion which stacks the L most recent inputs into a vector. The conelator can also be viewed as a matched filter, matched to the spreading code filter, but here it is simply depicted as an inner product on a downsampled vectorhi signal.

'f-d

Figure 2. The downlink receiver structure

While the RAKE is one particular instance of the proposed receiver structure, anothex special case is the equalizer re- ceiver. To describe this case more precisely, let h(z) =

hlz-' be the M J x 1 FIR chamel transfer function and f (2) = xkt fit-' the 1 x MJ FIR filter transfer function of length I c y . Tbe cascade of channel and filter gives f (z)h(z) = ~ ~ ~ - 2 a ~ z - ~ = a(%). In particular, for a zero-forcing (ZF) equalizer with a delay of d chips, we get f (t)h(t) = zed. In general, we can write for the filter-channel cascade

where 7(.) is a block Toeplitz filtering matrix and

(7)

In the noiseless case (and no intercell mterference), the use ofaZFequalizerleadstoFiZ= [O.--O]andi?~,~ = al,,, (ad = 1). A RAKE receiver cOrreSpOndS to f = hH. ad = llh112, I = N, Where h = [hz-, - - - h:]'.

The analysis done in 121 shows that, due to the orthog- onality of the spreading codes and to the i.i.d. character of the scrambler, the SINR at the receiver output, r, is

a = [ao---az+~-2], ad = [0 - . . 0ad O - . - O ] ad=[ao...aa-lOaWt--.az+~-2] . -

where 4 = E 1ak,,J2, dw = xEl and ~ Z Y Y = Rvv+&7(h')TH(h'). The choice for the filter

f that leads to maximum receiver output SINR is unique up to a scale factor and can be found as the solution to the following problem

f M A X = arg max r==g min f R y y f H f:fh=l f f h=1

* f MAX (9)

The maximum SINR becomes (ayAX = 1)

As pointed out in [2]. this receiver corresponds to the cas- cade of an (unbiased if ad = 1) MMSE receiver for the de- sired user's chip sequence, followed by a descrambler and a mla tor . In the noiseless case, the MMSE receiver f M A X becomes a ZF equalizer.

4. Path-Wise Receiver Structures

Figure 3. The pathub equalker RAKE struc- ture (PWEQ-RAKE)

The equalizer filter f presented in section 3 re- places at the same time the pulse shape and the channel matched filters, leaving complete freedom to the optimiza- tion process. Other possibilities arise when we impose a particular structure on the receiver. We shall here focus on structured equalizers that are the cascade of a short spa- tiotemporal FIR filter followed by a sparse spatiotemporal filter. The RAKE is a particular instance of this structure, with the FIR filter being the pulse shape matched filter per antenna, and the sparse filter being the 2D matched filter to the 2D sparse propagation channel. We shall here con- sider several choices for the short FIR filter, with the sparse filter portion being optimized for max SINR The receiver depicted in Fig. 3 is one possible instance of the constrained receiver structure considered here.

4.1. Pulse-Shape MF (GRAKE)

The pulse shape adopted by the 3G UMTS nom is a mot raised cosine (RRC) with roll-off 0.22. The short FIR

1285

filter in this case is simply the pulse shape matched filter, as in the RAKE receiver. However, the sparse propagation channel matched filter keeps its sparse structure, but its co- efficients are optimized for maximum SINR. This receiver structure was introduced in 141 as the GRAKE and inde- pendently in [3]. To analyze this receiver structure, we can write the overall channel h in (4) as

h = TH(p 8 I J ) hmOp = Pzhsp (11)

where TH@ 8 IJ) is the convolution matrix of the root raised cosine p(t) and hpop is the vector of samples of the

filter is the cascade of the channel impulse response and the pulse shape equalizer and hence also the cascade of the sparse propagation channel and the equalized pulse shape (cascade of the pulse shape and its MMSE equalizer). This equalized pulse shape should have approximately one sig- nificant nonzero coefficient. Hence, the sparse filter with one tap per path appears to be well adapted in this case.

The spatiotemporal FIR MMSE equalizer for the pulse shape is of the form

(14)

(12)

Optimizing the coefficients of the spatiotemporal (tempo- rally) sparse filter g , for maximum SINR at the output of the overall receiver, we get for the SINR (15)

~ G R A K E = .: Optimizing the coefficients of the spatiotemporal (tempo- rally) sparse filter gIP for maximum SINR at the output of the overall receiver, we get for the SINR

(overall equalizer) is now again factored into a short FIR filter, being the pulse shape equalizer, and an optimized (sparse) filter:

f =gpopT(P@IJ)=gspPsp-

f = s ,opnF) = gap%.

(hHPg (PWRyuPg)-' Psph)-' - U& *

(13) For improved performance, the tap positions m gpop do not necessarily correspond to the taps in the propagation channel hptop. Also, i n m m g the number of taps be- yond the number of paths (such that more than one tap per path is available) will obviously improve performance, but at the cost of an increase in complexity. In the GRAKE, the channel impulse response as seen at the input of the sparse filter is the channel impulse response filtered by the pulse sh& matched filter, or hence the sparse propagation chan- nel filtered by the pulse shape correlation sequence. This se- quence would be a delta function if no oversampling would be used. In the case of oversampling however, it leads to a number of no112ebo samples. Hence, putting one tap per finger in the sparse filter of the receiver does not appear to be optimal.

4.2. Path-Wue Equalizer (PWEQRAKE)

In the unconstrained equaiizer-codator receiver, the optimal equalizer fMAx is essentially a MMSE equalizer hHR&. Hence, a logical choice for the short FIR filter in the path-wise structured equalizer would be a pathwise equalizer, or hence a MMSE pulse shape equalizer. The re- sulting receiver is depicted in Fig. 3. One may remark that in that case, the channel as seen at the input of the sparse

43. Averaged PWEQRAKE (APWEQRAKE)

The spatiotemporal MMSE equalization of the pulse shape leads to a nonnegligible complexity unless Q is kept very small. To simplify the equalization operation, we can average the RX signal covariance matrix over the antennas to obtain &y with which we construct a temporal pulse shape equalizer

F=piZ&, - (17)

We then apply this temporal equalizer to each antenna sig- nal, hence

-

F = F 8 I j . (18)

The SINR for the APWEQRAKE can be obtained by sub- stituting the spatiotemporal pulse shape equalizer F from (14) in (16) by the temporal one in (18). An altemative strategy would be to have an optimized temporal equalizer per antenna instead of an averaged one.

1286

5. simulations

m-.

IS- .

Simulations were perfomed to evaluate the output SINR of the various receiver structures as a function of S N R In the four figures, the SINR curves are averaged over 100 re- alizations of the channei, which is either "Indoof-like or "Vehicular"-like. The spreading factor is 32 and 9 users are present in the cell of interest and in the neighboring cell. The SIR between the signals teceived from the 2 base sta- tions is OdB . All users in a cell are at the same power level. The pulse shape equalizer spread Q Cprediction order'') is typically 2 for PWEQRAKE and 4 for APWEQRAKE, to have comparable complexity to the GRAKE or RAKE. Typ-

where R stands for RAKE. From the previous discussion, one may think that without oversampling, the PWEQIUKE would not be able to improve upon the GRAKE, but the last figure shows the contrary. References

> i d y r M A X > rPWEQR > rAPWEQR r C R > rR

i _ - - - I

.................... ;. ................... . . , . - ; - 7 _ -

4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . .

I. Ghauri and D. T. M. Slock, "Linear receivers for the DS-CDMA downlink exploiting or thogdty of spreading sequences," m Pmc. 32nd Asilomur Con$ on Signals, Systems & Computers, (Pacific Grove, CA), November 1998.

ceiver with Intmcell Intexfmce Cancellation for a DS-CDMA Synchronous Downlink with Orthogonal Codes," in Pmc. VTC 2000, (Tokyo, Japan), May 2OOO. M. Lenardi and D. T. M. Slock, "SINR Maximizing Equalizer Receiver for DS-CDMA," m Pmc. ECJSIPCO 2000, (Tmpere, Finland), Sept. 2000.

eralized RAKE Receiver for Interfemce Suppression," IEEEJ. Sel. Areas Communic., vol. 18, pp. 1536-1545, Aug. 2000.

M. L e n d and D. T. M. Slo~k, "A RAKE Re-

G. Bottodey, T. Ottos~n and Y.-P.E. Wmg, "A Gen-

I5

I O

- 3 5 - z i O -

4-

m - a 9 . I B I F l ~ l l L I 2 Y S . ~ ~ ~ I m Y C ~ . ~ ~ . I

m-. .... ..!.. .... ...) ........I .... ....I ......... I ........ .!.. ..... ..!.. .... ...!......... ....... ' .... . . . . . . . . _ _ - - . . . . . . . . . . . . . . . . . . . . . . . . . . _ _ j _ - - - . . . . . . . . . . . . . . . . . . . . .

,I-. .... .~ ............................................ .,_.. ............ ~ ....................... .- . . . . . . . . . . . . . . . . :

-

-

.

Figure 5. Vehicular, M=2, J=2.

Figure 6. Vehicular, M=2, J=1.

- -----.---I . . . _ - - . . ........................................ -.- . . . . . . . . . . . . . . . . . .

. . Ur. max-SlNR

- - A V PW -RAID .,

. .

-I" t / 1 -I

-15 -10 -5 0 5 10 15 20 25 30 35 EbMOWBJ

Figure 4. Indoor, M=2, J=2. Figure 7. Vehicular, kl , J=2.

1287