Chip-Level Channel Equalization in WCDMA Downlink

EURASIP Journal on Applied Signal Processing 2002:8, 757–770c© 2002 Hindawi Publishing Corporation

Chip-Level Channel Equalization inWCDMADownlink

Kari HooliCentre for Wireless Communications, P.O. Box 4500 FIN-90014, University of Oulu, FinlandEmail: [email protected]

Markku JunttiCentre for Wireless Communications, P.O. Box 4500 FIN-90014, University of Oulu, FinlandEmail: [email protected]

Markku J. HeikkilaNokia Mobile Phones, P.O. Box 50, 90571 Oulu, FinlandEmail: [email protected]

Petri KomulainenNokia Mobile Phones, P.O. Box 50, 90571 Oulu, FinlandEmail: [email protected]

Matti Latva-ahoCentre for Wireless Communications, P.O. Box 4500 FIN-90014, University of Oulu, FinlandEmail: [email protected]

Jorma LillebergNokia Mobile Phones, P.O. Box 50, 90571 Oulu, FinlandEmail: [email protected]

Received 14 August 2001 and in revised form 7 March 2002

The most important third generation (3G) cellular communications standard is based on wideband CDMA (WCDMA). Receiversbased on TDMA style channel equalization at the chip level have been proposed for a WCDMA downlink employing long spread-ing sequences to ensure adequate performance even with a high number of active users. These receivers equalize the channelprior to despreading, thus restoring the orthogonality of users and resulting in multiple-access interference (MAI) suppression.In this paper, an overview of chip-level channel equalizers is delivered with special attention to adaptation methods suitable forthe WCDMA downlink. Numerical examples on the equalizers’ performance are given in Rayleigh fading frequency-selectivechannels.

Keywords and phrases:WCDMA, multiple-access interference, channel equalization.

1. INTRODUCTION

The air interface of universal terrestrial radio access (UTRA),the most important third generation (3G) cellular mobilecommunications standard, is based on wideband code-division multiple-access (WCDMA). In 3G, cellular net-works downlink capacity is expected to be more crucialthan uplink capacity due to asymmetric capacity require-ments, that is, the downlink should offer higher capacitythan the uplink [1]. Therefore, the use of efficient down-link receivers is important. In order to avoid performancedegradation, near-far resistant (or multiuser) receivers [2]

can be used. Several suboptimal receivers feasible for prac-tical implementations have been proposed, including linearminimum mean-squared error (LMMSE) receivers [3, 4].The adaptive versions of LMMSE receivers are the mostpromising for single-user terminals. However, the adap-tive symbol-level LMMSE receivers rely on cyclostation-arity of multiple access interference (MAI), and thus re-quire periodic spreading sequences with a very short pe-riod. Hence, they cannot be applied to the frequency divi-sion duplex (FDD) mode of the WCDMA downlink, whichuses spreading sequences with a one radio frame (10ms)period.

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758 EURASIP Journal on Applied Signal Processing

In a synchronously transmitted downlink employing or-thogonal spreading codes, MAI is mainly caused by mul-tipath propagation (neighboring cells form another sourceof MAI). Due to the nonzero cross-correlations betweenspreading sequences with arbitrary time shifts, there is in-terference between propagation paths (or Rake fingers) afterdespreading, causing MAI. With a moderate or high numberof active users, the performance of a Rake receiver becomeslimited by interpath MAI. If the received chip waveform, dis-torted by themultipath channel, is equalized prior to correla-tion by the spreading code or matched filtering, there is onlya single path in the despreading. With orthogonal spreadingsequences the equalization effectively retains, to some extent,the orthogonality of users lost due to multipath propagation,thus suppressing MAI. Since the signal is equalized at thechip level, not on the symbol level, they can also be applied insystems using long spreading sequences. Such a receiver con-sists of a linear equalizer followed by a single correlator anda decision device.

The chip-level channel equalizer has proven to be one ofthe most promising terminal receivers for a WCDMA/FDDdownlink. It has drawn attention and inspired numerouspublications in recent years. Chip-level equalization has beentreated in [5, 6, 7, 8, 9, 10]. It has been addressed in mis-cellaneous contexts also earlier, as in [11]. Although chip-level equalization resembles at first glance the classical linearTDMA-type equalization (time-division multiple access), ithas several aspects characteristic for CDMA or 3G networks,thus making it an interesting research topic. These aspectsinclude efficient adaptation of the equalizer due to differ-ent training signals in CDMA, soft hand-over, and trans-mit diversity. Chip-level equalization was considered withsoft hand-over in [12, 13], and with different transmit diver-sity schemes in [14, 15]. Performance evaluations of chip-level equalizers with channel coding have been presentedin [16], and with adaptive equalizers in [17, 18]. A chipequalizer based receiver for a CDMA downlink employ-ing a long scrambling sequence and nonorthogonal chan-nelization sequences was proposed in [19]. A large vari-ety of adaptive chip-level equalizers have also been pre-sented and studied in a number of publications, includ-ing, for example, [20, 21, 22, 23, 24, 25, 26, 27]. A differ-ent approach for improving the performance of downlinkreceiver, that is, generalized Rake receiver, is discussed in[28].

The purpose of this paper is to provide an overview ofchip-level equalization and on the adaptation methods pro-posed for chip-level equalizers. The possible performancegains offered by the chip-level channel equalizers are ad-dressed, and the performance of six different adaptive chipequalizers are compared in a frequency-selective fading chan-nel. The paper is organized as follows. The system modelis defined in Section 2, and the zero-forcing and LMMSEequalizers with perfect knowledge of the channel are ad-dressed in Section 3. The adaptive versions of chip-levelequalizers are discussed in Section 4. Numerical examples forthe receivers are presented in Section 5, followed by conclud-ing remarks in Section 6.

2. SYSTEMMODEL

In this section, we present the system model used in definingthe receivers in the sequel. Only a single-base station and asingle-receive antenna are included into the system model.1

With a single-receive antenna, signal processing is restrictedto the time domain. Due to the lack of spatial characteristicsin the signal structure, moderate level other cell interferencecan be considered to be included in the white Gaussian noise.

Since the downlink is considered, all signals are syn-chronously transmitted through the same multipath chan-nel. The complex envelope of the received signal at the userterminal can be written as

r(t) =K∑k=1

rk(t) + n(t)

=K∑k=1

Mk−1∑m=0

Akb(m)k

L∑l=1

cl(t)s(m)k

(t −mTk − τl

)+ n(t),

(1)

where K is the number of users, Mk is the number of kthuser’s symbols in the observation window,2 L is the number

of paths,Ak is the average received amplitude of kth user, b(m)k

is the mth symbol of kth user, cl(t) is the time-variant com-

plex channel coefficient of lth path, s(m)k (t) is the spreading

waveform of mth symbol of kth user given by convolutionof spreading sequence and chip waveform, Tk is the symbolinterval for kth user, τl is the delay of lth path, and n(t) iscomplex white Gaussian noise process.

The discrete-time received signal after appropriate down-conversion and filtering can be written as

r =K∑k=1

DCSkAkbk + n ∈ CNcNs , (2)

where Ns is the number of samples per chip and Nc is thenumber of chips in the observation window.3 In (2), D =[d(1)1 , . . . ,d(1)L ,d(2)1 , . . . ,d(Nc)

L ] ∈ RNcNs×LNc is a path delay and

chip waveformmatrix where the column vector d(n)l containssamples from appropriately delayed chip waveform for thelth path of nth chip, C = diag(c(1), . . . , c(Nc)) ∈ CLNc×Nc is ablock diagonal channel matrix with column vector c(n) ∈ CL

containing the time-variant channel coefficients for L paths.The term DC models the combination of chip waveformand multipath channel and is common for all users; Sk =diag(s(1)k , . . . , s(Mk)

k ) ∈ CNc×Mk is a block diagonal spread-

ing sequence matrix where column vector s(m)k ∈ ΞGk

s , Ξs isthe chip alphabet, contains the spreading sequence for thekth user’s mth symbol with a spreading factor Gk. The cellspecific scrambling sequence is included in the spreadingsequences, that is, Sk = SSc(t)Sk,Ch, where the scrambling

1It is straightforward to extend the model to include multiple-base sta-tions or receive antennas.

2Thus the model allows multiple transmission rates.3Nc = GkMk , where Gk is the spreading factor for kth user. The product

GkMk is constant for all users.

Chip-Level Channel Equalization in WCDMA Downlink 759

sequence is in the diagonal matrix SSc(t) and the block di-agonal matrix Sk,Ch contains the user specific channeliza-tion sequence for the kth user. The sequences are normal-ized so that SHk Sk = I, and they are also orthogonal, thatis, SHk S j = 0 if k �= j. The average received amplitude forthe kth user is contained in a diagonal matrix Ak = AkIMk ,

4

vector bk = [b(1)k , . . . , b(Mk)k ]T ∈ ΞMk

b , Ξb is the symbol alpha-bet, contains the transmitted symbols of kth user, assumed tobe i.i.d. with unit variance, and n ∈ CNcNs contains samplesfrom a white complex Gaussian noise process with covari-ance Cnn = σ2nINcNs .

3. RECEIVERS

The chip-level version of zero-forcing and LMMSE equaliz-ers as well as the conventional Rake receiver are presented inthis section. As mentioned earlier, the multipath channel isequalized prior to despreading in the chip equalizer receivers,thus restoring to some extent the orthogonality of channel-ization codes and suppressingMAI. This means that the termDC in (2) is suppressed. The equalizer is followed by a singlecorrelator and decision device.

The equalizers treated in this paper are all linear, due tothe difficulties faced when nonlinear equalizers are consid-ered for chip-level equalization. The detection of the desireduser at chip-level is highly counter-intuitive, since it wouldignore the processing gain associated with spreading. Thus,the desired output signal of a chip-level equalizer is the to-tal transmitted signal from the base station, that is, the sumof all users’ signals. The nonlinear equalizers rely on priorknowledge of constellation of the desired signal. This infor-mation is not easily available at the terminal, since the con-stellation of all users’ signal sum is a high-order QAM withuneven spacing. The constellation order changes at framerate (100Hz) with the changing number of active users, andthe spacing in the constellation changes at power control rate(1.5 kHz). However, for example, in [29] an interesting non-linear equalizer based on soft decision cancelling was pre-sented for a WCDMA downlink.

With the introduced system model, the decision variableof the Rake receiver for arbitrary selected user 1 is given by

yR = SH1 CHDHr, (3)

that is, the received signal is filtered by the chip waveform,appropriately delayed and weighted with channel coefficientsin the Rake fingers, coherently combined and finally de-spread. The abnormal order of the maximal ratio combin-ing (MRC) and despreading has no effect on receiver perfor-mance due to the linearity of operations.

When a zero-forcing equalizer is applied, the tap coeffi-cients of the equalizer are given by

WZ = DC(CHDHDC

)−1. (4)

4The use of Ak allows power differences between different symbols of anindividual user. In here, constant power A2

k is assumed.

The first term on the right-hand side, DC, performs chipwaveform matched filtering, and is followed by the conven-tional zero-forcing equalizer [30, 31]. The decision variableafter despreading can be written as

yZ = SH1 WHZ r = SH1

(CHDHDC

)−1CHDHr. (5)

In (4), the zero-forcing equalizer is given in block form(WZ ∈ CNcNs×Nc). The filter form of the zero-forcing equal-izer is obtained by taking a middle column fromWZ .5

The second considered equalizer, an LMMSE chip-levelequalizer, can be obtained by solving

WL = argminW

E

∣∣∣∣∣WHr−

K∑k=1

SkAkbk

∣∣∣∣∣2, (6)

where E[·] denotes expectations, and the minimization iscarried out elementwise. By estimating the sum of all users’chips instead of the chips of a single user, the signal-to-noiseratio (SNR) faced in the estimation problem is significantlyimproved. It should also be noted that the chip equalizer doesnot try to suppress other users’ signals at the chip level, butjust restores the orthogonality of users. It can be shown thatfor (6)WL is given by [32]

WL =(DC

( K∑k=1

A2kSkS

Hk

)CHDH + σ2nI

)−1DC, (7)

resulting in the decision variable

yL = SH1 WHL r

= SH1 CHDH

(DC

( K∑k=1

A2kSkS

Hk

)CHDH + σ2nI

)−1r.

(8)

The standard symbol-level LMMSE equalizer [3, 4], fea-sible for DS-CDMA systems employing short spreading se-quences, is defined for user 1 by

WLs = argminW

E[∣∣WHr− b1

∣∣2], (9)

which results in the decision variable

yLs = AH1 S

H1 C

HDH

(DC

( K∑k=1

A2kSkS

Hk

)CHDH + σ2nI

)−1r.

(10)

Comparing (8) and (10), we can see that, for a given ob-servation window, the chip-level and symbol-level LMMSEreceivers are equal up to a scalar. This is an expected re-sult, since the LMMSE estimator commutes over linear (oraffine) transformations [32], like despreading. The equal per-formance of LMMSE receivers was verified numerically in[33].

5In the sequel, filter forms are denoted with lower case w.


As seen from (7), the LMMSE solution of a chip-levelequalizer depends on the spreading sequences of all userswith the period of a long scrambling code. This followsfrom the dependency between consecutive chips to be es-timated. The optimal solution changes from chip to chip,and an adaptive chip-level equalizer will not reach the exactoptimal tap coefficients. The adaptive versions of chip-levelLMMSE equalizer are built on simplifications that (i) spread-ing sequences are random, and (ii) the random spreading se-quences are white and independent from those of other users.The simplifications are unavoidable due to the nonstationar-ity of the LMMSE solution in (7).6 The LMMSE chip-levelequalizer derived according to the simplifications (or false as-sumptions) is given by

WL =(s2

K∑k=1

A2kDCCHDH + σ2nI

)−1DC, (11)

where s2 denotes the square value of chip. The decision vari-able after correlation with the spreading sequence is given by

yL = SH1 WHL r

= SH1 CHDH

(s2

K∑k=1

A2kDCCHDH + σ2nI

)−1r.

(12)

The performance losses caused by the aforementioned sim-plifications can be assessed by comparing the performancesof the equalizers given in (7) and (11) [33, 34]. Again, thechip-level equalizer in (11) is in a block form, and the equal-izer is obtained in filter form by taking amiddle column fromWL.

4. ADAPTATIONMETHODS

In this section, several methods for adapting chip-levelequalizer are discussed. WCDMA terminal receivers haveaccess to two-pilot signals, one carried on the continu-ous common pilot channel (CPICH) and another carriedon the time-multiplexed dedicated physical control chan-nel (DPCCH). The high content of pilot signals combinedwith the DS-CDMA signal structure allows accurate chan-nel response estimation in the terminal. On the other hand,pilot signals form only a small portion of the received sig-nal. Thus, for the adaptation of the equalizer, a good es-timate of the channel response and a relatively weak buttime-continuous reference signal are available. As a result,several adaptation methods that are not typical with linearTDMA equalizers have been proposed for chip-level equal-ization. In [22] equalizing was proposed to be carried out byan adaptive chip separation filter, which is based on blindlydecorrelating the multipath combined chip estimates. Themethod applies to systems employing long random scram-bling codes, in which the original transmitted multiuser chip

6The LMMSE solution cannot be considered to be cyclostationary, sincethe channel is likely to change during the spreading sequence period of10ms.

sequence is also uncorrelated. Kalman filtering was appliedfor chip-level equalization in [25]. Constrained minimumoutput energy equalizers, minimizing the energy in the sub-space of unused spreading sequences, are proposed for IS-95and CDMA2000 terminals in [21, 35, 36, 37]. However, theyrequire knowledge of unused spreading sequences, thus im-posing restrictions too strict for radio resource managementin WCDMA/FDD systems.

The most straightforward adaptation, that is, the leastmean square (LMS) adaptation based on the common pi-lot channel (CPICH), is studied in Section 4.1. The use of apilot channel as a reference signal was suggested in [7], butthe adaptation was not studied any further. In [19], a pilotchannel was proposed to be used with the stabilized fast a-posteriori error sequential technique (SFAEST) and in [38]with the multistage nested Wiener filter (MSNWF). In thefollowing, the adaptation is done at chip rate. The adapta-tion can be performed also at symbol rate, as shown in [39].7

The use of Griffiths’ algorithm [40] with a chip-level equal-izer is presented in Section 4.2, followed by the introductionof a minimum output energy equalizer constrained with thechannel response in Section 4.3. Equalizers consisting of aseparate filter and Rake receiver are referred to as prefilter-Rake equalizers in the sequel [20, 27]. In Section 4.4, adap-tive versions of a prefilter-Rake based on square-root RLS,the Levinson algorithm and Griffiths algorithm are studied.Finally, the properties of adaptive equalizers are compared inSection 4.5.

4.1. Common pilot channel based adaptation

In the adaptive equalizers discussed in Sections 4.1, 4.2, and4.3, the appropriately sampled received signal is filtered bythe chip waveform, equalized and correlated with the spread-ing sequence. The decision variable for user 1 after correla-tion with the spreading sequence is given by y = SH1 z, wherevector z contains equalizer outputs for corresponding chipintervals. The nth element of z is w(n)Hr(n), where w(n) ∈C2D+1 contains the equalizer taps and r(n) = [r(nNs − D),. . . , r(nNs), . . . , r(nNs + D)]T contains output samples fromthe chip waveform matched filter within the equalizer at nthchip interval. The number of samples per chip is given by Ns

and 2D + 1 is the number of equalizer taps.The most straightforward solution to the adaptation of

a chip-level equalizer is to use the normalized LMS (NLMS)algorithm with a common (or dedicated) pilot channel as areference signal. The receiver is depicted in Figure 1, and re-ferred to as a CPICH trained equalizer in the following. TheNLMS adaptation step for the equalizer is [41, Chapter 9]

wC(n + 1) = wC(n) + µr(n)e∗(n)rH(n)r(n)

, (13)

where 0 < µ < 2 is the adaptation step size, and e∗(n) =(s(n)−wH

C (n)r(n))∗ is the complex conjugate of error signal

between the equalizer output and reference signal s(n).

7When comparing results, one should pay attention to the channelmodel assumptions made for the fractionally spaced equalizer.


r r z yChip waveform

matched filterEqualizer Correlator

LMS + ×−

Pilot signal

Spreadingsequence

Figure 1: CPICH trained LMS equalizer.

Since the adaptation is carried out at chip level, the chipsof CPICH are used as reference samples. It should be notedthat although the error e(n) contains the signals of all activeusers, also the desired one, the equalizer does not suppressthem due to the pseudorandomness of spreading codes. Therelatively large error signal values also mean that the SNRin the adaptation is low, and small adaptation step sizes arerequired to provide sufficient averaging. The small values ofµ are partially compensated by a high adaptation rate.

4.2. Griffiths’ algorithm adapted equalizer

Several adaptation algorithms are obtained through differentapproximations of the gradient vector of the mean square er-ror cost function

J = E[∣∣d −wHr

∣∣2], (14)

where d is the desired output of the equalizer. The gradientvector is given by

∇J = −2E[d∗r] + 2E[rrH]w, (15)

where E[d∗r] is the cross-correlation vector between the in-put signal r and the desired output of the equalizer, andE[rrH] = R is the covariance matrix of the input signal [41].For example, the aforementioned standard LMS algorithm isobtained by replacing expectations with instantaneous esti-mates, that is, signal vectors r(n).

In [23], the Griffiths algorithm is used for the adaptationof a chip-level channel equalizer. The algorithm is obtainedfrom (15) by replacing the cross-correlation vector E[d∗r]with p, the channel response estimate. Instantaneous esti-mates are used for the covariance matrix R, as in the LMSalgorithm. The resulting adaptation is

wG(n + 1) = wG(n)− µ(z∗(n)r(n)− p

), (16)

where µ is the adaptation step size and z(n) is the equalizeroutput at nth chip interval.

4.3. CR-MOE equalizer

In the channel-response constrained minimum-output-energy (CR-MOE) equalizer [26], the equalizer is decom-posed into a constraint (or nonadaptive) component and anadaptive component. This is the well-known idea of the gen-

eralized side-lobe canceler, described, for example, in [41,Chapter 5]. The same approach has been applied in blindMOE multiuser receivers, in which the spreading sequenceof a desired user is used as the constraint [2, 42]. As men-tioned, the equalizer is decomposed into two parts, that is,wM = p + x. The channel response estimate p is used as thenonadaptive part, and the adaptive part x is constrained ontoa subspace orthogonal to p to avoid suppression of the de-sired signal. The mean square error J = E|d − wH

M r|2 can bewritten as J = E[d2] − 2pHp + (p + x)HE[rrH](p + x). Fora given p, the mean square error is minimized by minimiz-ing the last term of J , that is, the equalizer output energy—other terms of J are not affected by vector x. To obtain anadaptive algorithm for x, stochastic approximation is ap-plied to the gradient ∇J = E[rrH](p + x) taken with re-spect to x. The orthogonality condition is maintained at eachiteration by projecting the gradient onto the subspace or-thogonal to p. The orthogonal component of the gradientis

∇J⊥p =(r− p

pHrpHp

)rHwM, (17)

and the resulting adaptation algorithm becomes

x(n + 1) = x(n)− µz∗(n)(r(n)− zp(n)p

), (18)

where zp(n) = pHr(n)/(pHp) is the output of the channelresponse filter normalized with the energy of the channel re-sponse estimate, and z(n) = wM(n)Hr = (p(n) + x(n))Hr isthe output of the CR-MOE equalizer. The structure of thisequalizer is depicted in Figure 2.

The CR-MOE has the typical weaknesses of the MOEadaptation [2]. The orthogonality between x and the channelresponse estimate p is lost when p is updated. Thus periodicre-orthogonalization of x is required, given by

x⊥p = x − pHxpHp

p. (19)

The second problem of the MOE adaptation is the un-avoidable estimation error in p. Due to the estimation error,x has small projection on true p while maintaining orthog-onality with p. Since x is adapted to minimize output en-ergy, the projection on p translates to partial suppression ofthe desired signal component. The surplus energy χ = ‖x‖2,where ‖x‖2 = xHx, required for total suppression of the de-sired signal component is given by

χ ≥ ‖p‖2∣∣pHp∣∣2‖p‖2‖p‖2 − ∣∣pHp∣∣2 . (20)

Since the channel estimation error is usually relatively small,(|pHp|2 ∼ ‖p‖2‖p‖2), suppression of the desired signalmeans large ‖x‖2 values and significant noise enhancement.Therefore, in noisy environments the suppression remains atacceptable levels. However, to avoid the desired signal sup-pression at high SNR, ‖x‖2 values must be restricted. Onesolution is to introduce tap leakage [2], that is,


r Chip waveformmatched filter

Channelestimation

Filter p

Filter x

Adaptationalgorithm

+ Correlatory

Figure 2: Channel-response constrained minimum-output-energy (CR-MOE) equalizer.

r Chip waveformmatched filter

Channelestimation

Adaptiveprefilter

QR-RLS

Rakey

Figure 3: Prefilter-Rake receiver with inverse QR-RLS adaptation.

x(n + 1) = (1− µα)x(n)− µz∗(n)(r(n)− zp(n)p

), (21)

where α, a small positive constant, controls the tap leakage.On the other hand, large values of α cause too large tap leak-age, thus preventing efficient channel equalization. However,a predefined constant α has proven to be adequate, if p isnormalized with its energy.

4.4. Prefilter-Rake equalizer

When (3) and (12) are compared, it can be seen that theequalizer consists of a received signal’s covariance matrix in-verse, and of the part corresponding to the conventional Rakereceiver. In [20] it was suggested to actually divide the equal-izer into these parts, and to use the matrix inversion lemma(or appropriate parts of the RLS-algorithm) for the estima-tion of covariance matrix inverse R−1 (R = E[rrH]). If thechip waveform matched filter is sampled at chip rate, thecovariance matrix has a Toeplitz structure. Also the matrixinverseR−1 approaches a Toeplitz matrix with increasingma-trix dimension and finite effective length of the autocorrela-tion function. Thus the multiplication with R−1 can be effec-tively replaced by filtering r with a middle row of R−1.

The structure of prefilter-Rake with channel estimation isdepicted in Figure 3. A filter matched to the chip waveform ispreceding the prefilter, and the output of the matched filteris sampled at chip rate. The output of the prefilter is fed tothe Rake receiver performing despreading and maximal ratiocombining. There exist several possibilities for adapting the

prefilter. In the following, three methods are presented. First,a blind approach utilizing square-root RLS algorithms [27] isdiscussed, followed by a description of adaptation using theLevinson algorithm. The use of the Levinson algorithm wasproposed also in the simultaneous and independent work ofMailaender [43]. Finally, the application of Griffiths’ algo-rithm to the prefilter adaptation [18] is discussed.

Square-root RLS

The coefficients of the prefilter v(n) are given by the mid-dle column of R−1(n),8 estimate of covariance matrix in-verse R−1. The square-root matrix of R−1(n) can be up-dated using appropriate parts of the (inverse) QR-RLS al-gorithm [41, Chapter 14], or as in this paper, HouseholderRLS (HRLS) [44]. Both algorithms operate on the square-root matrix R1/2(n) of R−1, that is, R−1(n) = R1/2(n)RH/2(n).Thus the prefilter coefficients are obtained by v(n) =R1/2(n)[RH/2(n)]:,D+1, where [RH/2(n)]:,D+1 denotes the mid-dle column of RH/2(n). The square-root matrix is restrictedto a triangular matrix in the QR-RLS algorithm, whereas inthe HRLS algorithm there is no such restriction. This allowsan efficient use of block annihilation properties of House-holder reflection. The HRLS update of RH/2(n) can be writ-ten as [44]

Θ(n)

[β−1/2RH/2(n) β−1/2RH/2(n)r(n)

0T 1

]

=[RH/2(n + 1) 0

kT(n) −δ(n)

],

(22)

where 0 < β < 1 is a weighting factor and RH/2(n)r(n)is a preprocessed input vector; Θ(n) is a Householder trans-formation matrix annihilating RH/2(n)r(n) to a zero vec-tor in the postarray. The resulting adaptation algorithm forthe prefilter coefficients is tabulated in Table 1. It should benoted that prefilter-Rake does not require computation ofδ(n) or k(n) in the postarray. Although the square-root RLS

8The filtering with a prefilter is defined as vH(n)r(n).


Table 1: Prefilter adaptation with Householder RLS algorithm.

At every prefilter update

A = β−1/2RH/2(n)

a = Ar(n)

B = AHa

γ = √aHa + 1

γ = [γ(γ + 1)]−1

B = γB

RH/2(n + 1) = A− aBH

v(n + 1) = R1/2(n + 1)[RH/2(n + 1)]:,D+1 Prefilter length is 2D + 1

algorithms are computationally intensive, the filter lengthsin the chip-level equalizers are relatively short, roughly twicethe effective channel delay spread.

Levinson algorithmSince the ideal prefilter coefficients v(n) are given by amiddlecolumn of matrix inverse R−1, the prefilter coefficients can beobtained by solving periodically

R(n)v(n) = [I]:,D+1, (23)

where [I]:,D+1 is the middle column of the identity matrix,where I is the identity matrix, and 2D + 1 is the prefilterlength. Due to the Toeplitz structure of R, (23) is efficientlysolved with the standard Levinson algorithm, tabulated, forexample, in [45]. Since the covariance matrix R is Toeplitzand Hermitean, it is defined by its first row. Thus, it is suffi-cient to estimate the autocorrelation function ρ of r for non-negative delays.

Estimation of autocorrelation function can be done ei-ther directly from the received signal [32], or the estimate ρcan be calculated from the channel response estimate p andnoise power estimate σ2n by

ρ[k] = pH1:2D+1−kp1+k:2D+1 + δkσ2n (24)

for lags k = 0, . . . , 2D. Calculation of the autocorrelation esti-mate from the channel response estimate has lower complex-ity than the aforementioned possibilities, since the channelresponse estimate is required in other parts of receiver andthe autocorrelation estimate can be updated at the prefilterupdate rate. However, it is less robust against any unknowninterfering signals.

To maintain good performance, the prefilter coefficientsshould be recalculated several times during the coherencetime of the channel. Thus the update frequency can be fixed,for example, to the WCDMA slot rate (1.5 kHz), or can bemade to adapt to the velocity of the terminal. To avoid anyperformance degradations due to a compromise with theprefilter update rate, a 15 kHz update rate is used in the sim-ulation cases presented in Section 5.

Modified Griffiths’ algorithmThe ideas of Griffiths’ algorithm can be used to deriving anLMS algorithm variant for the prefilter adaptation [18]. The

gradient of mean square error cost function for the prefilterv is

∇J = −2E[d∗r] + 2E[rrH]v. (25)

The desired response of the prefilter is the received signal fil-tered with the desired prefilter, that is, d = [R−1]H:,D+1r. Thisallows a further development of the cost function gradient

∇J = −2E[rrH][R−1]:,D+1 + 2E[rrH]v

= −2[I]:,D+1 + 2E[rrH]v.

(26)

The adaptive algorithm is obtained by replacing the remain-ing expectation with an instantaneous estimate of expecta-tion, that is, with rrH. The resulting adaptation algorithm forthe prefilter can be written as

v(n + 1) = v(n) + µ([I]:,D+1 − g∗(n)r(n)

), (27)

where g(n) = v(n)Hr(n) is the output of the prefilter.Since the inverse of a Hermitean Toeplitz matrix is

Hermitean and persymmetric [46], the optimal prefilter[R−1]:,D+1 is conjugate symmetric with respect to its middleelement. This can be utilized to speed up the adaptation byforcing

vD−m(n) = 12

(vD−m(n) + v∗D+m(n)

),

vD+m(n) = v∗D−m(n), m = 0, 1, . . . , D(28)

at each adaptation step and by using filter v(n) instead of v(n)to generate the new prefilter output.

4.5. Observations on adaptive equalizers

In this section, the similarities and differences between thestudied equalizers are briefly discussed. Firstly, it should benoted that the computational requirements of the presentedequalizers are quite similar, with the exception of prefilter-Rake with square-root RLS adaptation. The complexity ofthe prefilter-Rake with RLS-type adaptation increases as aquadratic function of the number of taps, whereas the com-plexities of the other equalizers depend roughly linearly onthe number of taps. Thus, the complexity of the square-root RLS adapted prefilter-Rake is considerably higher thanthe complexities of the other presented equalizers. Also theLevinson algorithm has quadratic complexity, but the highercomplexity is effectively compensated for by the significantlylower activation rate of the Levinson algorithm.

A CPICH trained equalizer treats other received signalsthan CPICH signal as noise, whereas all other equalizers uti-lize the whole received signal from the desired base stationin the adaptation. The use of the whole received signal sig-nificantly enhances the SNR available in the equalizer adap-tation, thus providing an advantage for the other equalizersover the CPICH trained equalizer.

On the other hand, a CPICH trained equalizer does notrequire channel response estimate, whereas the other equal-izers rely on channel estimation. In prefilter-Rake receivers


Table 2: Channel parameters.

Vehicular A Channel II

Path # Power [dB] Delay [ns] Power [dB] Delay [ns]

1 0 0 0 0

2 −1 310 −3 521

3 −9 710 −6 1042

4 −10 1090 — —

5 −15 1730 — —

6 −20 2510 — —

channel estimates are needed for maximal ratio combining,but the adaptation of the prefilter can be carried out blindly.In the CR-MOE and Griffiths’ equalizers, MAI suppressionis based on channel response estimate. With the CR-MOEequalizer an inaccurate channel response estimate also resultsin self-cancellation. Thus the CR-MOE receiver can be con-sidered to be the most sensitive to channel estimation errorsof the considered equalizers.

It can be easily noted that the CR-MOE and Griffiths’equalizers have a distinctive resemblance. For example, thepart of the adaptation step orthogonal to p in (16) is equal tothe adaptation step in (18), assuming the same equalizer tapsw(n). However, the estimated channel response is directly in-serted into the equalizer in CR-MOE, whereas in Griffiths’algorithm it is gradually introduced through the adaptation.This provides a small advantage in the tracking of the chang-ing channel.

Finally, it should be noticed that the prefilter-Rake struc-ture offers an additional advantage in the soft hand-over sit-uation. Since the prefilter depends only on the properties ofreceived signal, the same prefilter can be used in the detec-tion of signals coming from different base stations. In the softhand-over situation, the prefilter is followed by more thanone Rake receiver, each of them assigned to a different basestation.

5. NUMERICAL EXAMPLES

To obtain a good understanding and comparison of the po-tential performance that the presented receivers can offer, biterror probabilities (BEPs) and signal-to-interference-plus-noise ratios (SINRs) were evaluated for the Rake receiver,zero-forcing equalizer and LMMSE equalizers with ideal co-efficients. Bit error rates (BERs) were simulated for the pre-sented adaptive chip-level equalizers.

The performance evaluations were carried out inRayleigh fading frequency-selective channels described inTable 2. The ITUs vehicular A channel model [47] was usedwith BEP and SINR evaluations. The BER simulations werecarried out in Channel II, which is a 3-path channel with anexponentially decaying average power profile. QPSK modu-lation was used employing root raised cosine pulses with aroll-off factor of 0.22. Random cell specific scrambling andWalsh channelization codes were used. The chip rate was setto 3.84Mchip/s corresponding to a 260 ns chip interval. The

received signal was modeled with two samples per chip, andchannel coding was excluded from the study.

5.1. Bit error probability andsignal-to-interference-plus-noise evaluations

BEPs were evaluated by applying the semianalytical methoddiscussed, for example, in [48]. For a linear receiver w,9

the conditional bit error probability can be expressed in theform10

Pb[E | C,b1, . . . ,bK

]= Q

(Re(∑K

k=1wHDCSkAkbk)

√σ2nwHw

),

(29)

given that the arbitrary selected desired user 1 transmittedQPSK symbol 1. The bit error probability is conditional onchannel realization, on the symbols of other users as well ason the previous and following symbols of the desired user.The BEPs were obtained by taking the average of the condi-tional bit error probabilities over a sample set of bit patternand channel realizations. A sample set size of 8000 realiza-tions was used in the evaluations.

In the same manner SINR was also evaluated. The con-ditional SINR depending on channel realization and bit pat-terns is given by

γ= Re(wHDCS1A1b1

)2σ2nwHw+

∣∣∑Kk=2wHDCSkAkbk

∣∣2+Im (wHDCS1A1b1)2 ,(30)

and a Gaussian approximation for the conditional bit errorprobability is obtained by

Pb[E | C,b1, . . . ,bK

] = Q(√

γ). (31)

Both the conditional SINR and the Gaussian approximationfor conditional bit error probability were sampled over asample set of bit pattern and channel realizations.

BEPs given by (29) and (31) were evaluated for 8 usersemploying a spreading factor of 16 and equal transmissionpowers in the vehicular A channel. The length of zero-forcingand LMMSE equalizers was set to 98 taps (49 chips), and theobservation window of the received signal was 80 chips. BEPsare presented in Figure 4 for the conventional Rake receiver,as well as for the ZF and LMMSE chip-level equalizers WL

and WL given by (7) and (11), respectively. Also the theo-retical single-user bound [49] for the considered channel isgiven in the figure.

From the results in Figure 4 it can be immediately notedthat the Gaussian approximation for BEP gives a good matchwith the BEP values obtained with (29). Also it is easily seenthat as Eb/N0 increases, the BEP of the Rake receiver saturatesdue to the MAI. The LMMSE equalizers show a significantBEP improvement when compared to conventional Rake

9Correlation with a spreading code is included in w.10Gray code mapping of symbols to bits is assumed, and the term Q2(·)

is ignored.


0 2 4 6 8 10 12 14 16 18 20

Eb/N0[dB]

10−4

10−3

10−2

10−1

100

Biterrorprob

ability

Figure 4: BEP versus Eb/N0 for 8 QPSK users with a spreading fac-tor of 16 in the Vehicular A channel. BEP (solid line) are presentedwith Gaussian approximation (dashed line) for Rake receiver (�),zero-forcing equalizer (∗), as well as for the LMMSE receivers givenby (7) (◦) and by (11) (×). Also the performance bound of channel(�) is included.

receiver, whereas the ZF equalizer attains the performance ofa Rake receiver only at high Eb/N0. The performance differ-ence between ZF and LMMSE chip-level equalizer receiversis caused by the noise enhancement typical to the ZF equal-izers [50]. The performance difference between the LMMSEequalizersWL and WL is relatively small, less than 2 dB at thepractical Eb/N0 range. Hence, it can be noted that the chang-ing chip correlations do not have a significant effect on theperformance of the LMMSE equalizer in a WCDMA down-link. However, the LMMSE equalizer defined by (11) showsmoderate saturation in performance at high Eb/N0 values.

In Figure 5, the sample distribution functions are pre-sented for the SINR γ with the Rake receiver, the ZF equalizerand LMMSE equalizers. The sample distribution functionsare given for ES/N0 values of 6 dB and 18 dB. The SINR for azero-forcing equalizer presents a strongly skewed sample dis-tribution function with a heavily weighted lower tail. Com-parison of Figures 4 and 5 reveals that the BEP performanceis dominated by the lower tail characteristics of an SINR dis-tribution, as expected. At Eb/N0 = 15dB, the BEP of the ZFequalizer is close to that of the Rake receiver. At the corre-sponding ES/N0 (18 dB), the median SINR of the ZF equal-izer is closer to the median SINR of WL, whereas the 10thpercentiles11 of SINR are almost equal for the ZF equalizerand Rake receiver. From Figure 5 we can also notice that withincreasing ES/N0 the variance of SINR increases significantlymore for the Rake receiver than for LMMSE equalizers. ThusLMMSE equalizers provide a more stable SINR performancethan the Rake receiver, which is an important advantage forradio resource management processes.

1110th percentile of a sample set is such a value x that at least 10% ofsamples are smaller than or equal to x.

−10 −5 0 5 10 15 20 25

Signal to interefence-and-noise ratio (SINR)[dB]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sampledistribu

tion

function

Figure 5: Sample distribution functions of SINR are presentedat 6 dB (dashed line) and 18 dB (solid line) signal-to-noise ratiosfor Rake receiver (�), zero-forcing equalizer (∗), as well as for theLMMSE receivers given by (7) (◦) and by (11) (×).

In Figure 6, the average and the 10th percentile of SINRare presented with respect to ES/N0. As we could expect fromFigure 5, the average SINR is not an adequate figure of merit.According to average SINR, the performance of the ZF equal-izer approaches the performance of LMMSE equalizers withhigh ES/N0. However, the 10th percentile of SINR appearsto be able to capture several performance characteristics. Itshows that the performance of the Rake receiver saturatesafter ES/N0 = 13dB (Eb/N0 = 10dB), and that the per-formances of the ZF equalizer and Rake receiver cross atES/N0 = 18dB. It also shows that the performance of theLMMSE equalizer WL starts to saturate at ES/N0 = 23dB.

The ratio of symbol energy Es to the total power PT ofbase station signal was varied by scaling the powers of in-terfering users. The ratio Es/PT describes the load of a basestation, with low Es/PT values indicating a heavily loadedsystem. At the same time, the Es/N0 values that maintainedthe 10th percentile of SINR at a predefined target value weresearched. The target values were set to−3dB and 0 dB, whichresulted in all cases 13–15% and 6–8% BEPs, respectively.The results are presented in Figure 7. The horizontal differ-ences between the curves indicate how much the transmis-sion powers of interfering users can be increased while main-taining the desired user’s transmission power constant. Theamount that the desired user’s transmission power can be de-creased while maintaining the transmission powers of inter-fering users at a constant level is also indicated by the differ-ences between the curves, as depicted in the figure.

5.2. Bit error rate simulations

The performance of adaptive chip-level equalizers were eval-uated by simulations in Rayleigh fading Channel II definedin Table 2. In the simulations, the terminal speed was as-sumed to be 60 km/h, which results in a 56Hz maximum


0 5 10 15 20 25

Signal to noise ratio [dB]

−15

−10

−5

0

5

10

15

20

25

Average

sign

alto

interefence-and-noise

ratio[dB]

(a)

0 5 10 15 20 25

SNR [dB]

−15

−10

−5

0

5

10

15

20

25

10th

percentileof

sign

alto

interefence-and-noise

ratio[dB]

(b)

Figure 6: Average (a) and 10th percentile (b) of SINR versus signal-to-noise ratio are presented for Rake receiver (�), zero-forcingequalizer (∗), as well as for the LMMSE receivers given by (7) (◦)and by (11) (×).

Doppler frequency shift at the 2GHz carrier frequency. Aspreading factor of 64 was used on the common pilot chan-nel, and the power of the pilot channel was scaled to 10%of the total transmitted power PT . Filter lengths of 19 tapswere used with the equalizers, except for the 16-tap CPICHtrained equalizer.

BERs for different Eb/N0 values are presented in Figure 8for the considered adaptive receivers, excluding the CPICHtrained equalizer. Also the performance of the LMMSEequalizer WL and the theoretical single-user bound [49] forthe considered channel are included in the figure. In Figure 8,all receivers had a perfect knowledge of the channel. The per-formance of the Rake receiver is degraded byMAI even at low

−3 −2 −1 0 1 2 3 4 5 6

ES/PT [dB]

0

2

4

6

8

10

12

ES/N

0[dB]

SNR gain of 1.4 dB

ES/PT gain of 3 dB

Figure 7: Required Es/N0 versus Es/PT is presented for −3dB (solidline) and 0 dB (dashed line) target values of 10th percentile of SINRwith Rake receiver (�) and LMMSE receivers given by (7) (◦) andby (11) (×).

0 2 4 6 8 10 12 14 16 18 20

Eb/N0 (dB)

10−3

10−2

10−1

100

Biterrorrate

Rake receiverGriffiths equalizerCR-MOE equalizer

Prefilter-Rake with GriffithsPrefilter-Rake with HRLSPrefilter-Rake with Levinson

LMMSE

Performance bound

Figure 8: Bit error rates versus Eb/N0 for 4QPSK users (spread-ing factor 8) and common pilot channel (spreading factor 64) withknown channel response in Channel II.

Eb/N0 values, whereas the adaptive equalizers attain almostthe performance of the LMMSE receiver at low Eb/N0 values.At high Eb/N0 values the prefilter-Rake receivers provide bet-ter performance than CR-MOE or Griffiths’ equalizers. How-ever, the performance differences remain at a moderate level.

To see the effect of channel estimation, the channel co-efficients were estimated with a common pilot channel anda moving average smoother spanning over two slots. BERsare presented in Figure 9 for different Eb/N0 values and in


0 2 4 6 8 10 12 14 16 18 20

Eb/N0 (dB)

10−3

10−2

10−1

100

Biterrorrate

Rake receiverCPICH-trained equalizerGriffiths equalizerCR-MOE equalizer


LMMSE

Performance bound

Figure 9: Bit error rates versus Eb/N0 for 4 QPSK users (spread-ing factor 8) and common pilot channel (spreading factor 64) withestimated channel response in Channel II.

−2 0 2 4 6 8 10 12 14

Es/PT (dB)

10−3

10−2

10−1

Biterrorrate

Rake receiverCPICH-trained equalizerGriffiths equalizerCR-MOE equalizer


LMMSE

Figure 10: Bit error rates versus Es/PT at Eb/N0 = 12dB (Es/N0 =15dB) with estimated channel response in Channel II.

Figure 10 with respect to the ratio of the desired user’s sym-bol energy Es to the total transmitted power PT . DifferentEs/PT values were obtained by simulating different numbersof equal power users employing a spreading factor 64.

Comparing Figures 8 and 9, it can be noted that the per-

formance of a CR-MOE equalizer is affected by channel es-timation errors. However, the performance degradation dueto channel estimation is not severe. It is slightly surprisingto see that the prefilter-Rake and Rake receivers are not sig-nificantly affected by channel estimation. This indicates thattheir performances are limited by other factors, like MAI inthe case of the Rake receiver.

From the results it can be seen that both prefilter-Rake receivers as well as CR-MOE and Griffiths’ equaliz-ers provide performance improvements when compared tothe conventional Rake receiver. The performance gain alsoincreases with increasing Eb/N0 (Figure 9) and decreasingEs/PT (Figure 10), that is, when MAI becomes more domi-nant. However, at high Es/PT values (low number of users)the Rake receiver provides equal or better performance thanthe CR-MOE or Griffiths’ equalizer. From Figure 10 it canbe noted that with decreasing numbers of users and, thus,MAI, the performance of prefilter-Rake and Rake receiversapproach the performance of the LMMSE receiver.

The CPICH trained equalizer provides performance im-provement over the Rake receiver at a relatively high Eb/N0

range (Figure 9) or in severe MAI situations (Figure 10). TheCPICH trained equalizer suffers from insufficient adaptationcaused by low SNR in the adaptation. The SNR is especiallylow at high Es/PT values, indicating low CPICH power. Atthe same range also the BER of the equalizer saturates as seenin Figure 10.

6. CONCLUSIONS

One approach to improve the performance of WCDMAdownlink receivers was studied in this paper, namely, channelequalization prior to despreading. The presented receivers,consisting of a channel equalizer, a correlator, and a decisiondevice, restore to some extent the orthogonality of users, and,thus, suppress MAI when orthogonal spreading sequencesare employed.

The zero-forcing and LMMSE solutions for chip-levelchannel equalizers were defined and the effects of WCDMAdownlink signal structure to the equalizers were addressed.The performance of chip-level channel equalizers was stud-ied with respect to bit error probability and signal-to-interference-plus-noise ratio in a frequency-selective fadingchannel.

An overview of several adaptation methods proposed forthe chip-level channel equalizers was given. Adaptive chip-level channel equalizers based on training with a common pi-lot channel, on MOE equalization constrained with channelresponse, on the Griffiths’ algorithm, as well as on the combi-nation of a blind prefilter and Rake were studied. The perfor-mance of the equalizers was numerically evaluated and com-pared to the performance of the Rake receiver in a Rayleighfading multipath channel. The results show significant per-formance improvements when chip-level channel equalizersare employed instead of the conventional Rake receiver in aWCDMA downlink. The prefilter-Rake receivers appear asthe most promising adaptive solution for the equalizers.


ACKNOWLEDGMENTS

The research at the University of Oulu has been supported bythe Academy of Finland, Nokia, and Texas Instruments.

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Kari Hooli received his M.S. degree inelectrical engineering from the Universityof Oulu, Finland in 1998. Since 1998, hehas been a Research Scientist at CentreforWireless Communications, University ofOulu. Currently, he is pursuing Dr.Tech. de-gree in electronic engineering with reseachinterests in statistical signal processing, in-terference suppression, and CDMA systems.

Markku Juntti was born in Kemi, Fin-land, in 1969. He received his M.S. (Tech.)and Dr.Tech. degrees in electrical engineer-ing from University of Oulu, Oulu, Fin-land in 1993 and 1997, respectively. Dr.Juntti has been a Research Scientist andResearch Project Manager at Telecommu-nication Laboratory and Centre for Wire-less Communications, University of Oulu in1992–1997. In academic year 1994–1995 hewas a Visiting Research Scientist at Rice University, Houston, Tex.In 1998 he was an Acting Professor at the University of Oulu. In1999–2000 he was with Nokia Networks, Radio Access Systems inOulu as a Senior Specialist of W-CDMA Research and Solutions.Dr. Juntti has been a Professor of Telecommunications at Universityof Oulu since 2000. He is also ResearchManager of UMTS Researchat Centre for Wireless Communications, University of Oulu. Dr.Juntti consults the telecommunication industry, for example, bytraining its personnel. Dr. Juntti’s research interests include com-munication theory and signal processing for wireless communica-tion systems as well as their application in wireless communicationsystem design. He is an author in book “W-CDMA for UMTS”published by Wiley. Dr. Juntti is a member of IEEE. He was Sec-retary of IEEE Communication Society Finland Chapter in 1996–1997 and the Chairman for years 2000–2001. He has been Secretaryof the Technical Program Committee of the 2001 IEEE Interna-tional Conference on Communications (ICC ’01), and Chairmanof the Technical Program Committees of 1999 Finnish Signal Pro-cessing Symposium (FINSIG ’99) and the 2000 Finnish WirelessCommunications Workshop (FWCW ’00).

Markku J.Heikkila received his M.S. degreein electrical engineering from the Universityof Oulu, Oulu, Finland, in 1997. He is cur-rently a Senior Research Engineer in Nokia,Research and Technology Access, Finland.From 1996 to 1997, he was employed as aResearch Assistant at the Telecommunica-tion Laboratory of the University of Oulu.Since 1997, he has been with Nokia, Fin-land. His research interests include multi-antenna transmission and reception techniques, space-time codingand baseband signal processing algorithms.


Petri Komulainen was born in Kiuruvesi,Finland, in 1971. He received the M.S.(Dipl. Eng.) degree in 1996 from the pro-gramme of Information Engineering of theUniversity of Oulu, Finland, with a thesison turbo codes. In 1997, he worked as aVisiting Research Scholar at the New Jer-sey Institute of Technology (NJIT), Newark.Since then he has worked for Nokia MobilePhones in Oulu, Finland, specialising in theresearch and development of various WCDMA terminal receiveralgorithms.

Matti Latva-aho received the M.S. in elec-trical engineering, Lic.Tech., and Dr.Tech.degrees from the University of Oulu, Fin-land in 1992, 1996, and 1998, respectively.From 1992 to 1993, he was a Research En-gineer at Nokia Mobile Phones, Oulu, Fin-land. During the years 1994–1998 he wasa Research Scientist at TelecommunicationLaboratory and Centre for Wireless Com-munications at the University of Oulu. Cur-rently, Professor Latva-aho is Director of Centre for Wireless Com-munications at the University of Oulu. His research interests in-clude future broadband wireless communication systems and re-lated transceiver algorithms. Professor Latva-aho has publishedmore than 50 conference or journal papers in the field of CDMAcommunications.

Jorma Lilleberg was born in Rovaniemi,Finland, in 1953. He received the DiplomaEngineer and Licentiate of Technology de-grees in electrical engineering at the Uni-versity of Oulu, Oulu, Finland in 1979 and1984, respectively and the Doctor of Tech-nology degree at the Tampere Universityof Technology, Tampere, Finland in 1992.From 1992 to 1993 he worked at the Tech-nical Research Center of Finland, in Oulu,Finland as an acting Research Professor and Chief Scientist. SinceAugust 1993 he has been working at Nokia Mobile Phones, Oulu,Finland as a Principal Scientist and NMP Fellow. Dr. Lilleberg’s re-search interest is in digital communications theory and the appli-cation of statistical signal processing methods to digital radio re-ceivers. He has published several tens of research papers and holds9 patents. He is also a Docent to the University of Oulu, Oulu, Fin-land where he has given lectures on estimation theory and guideddoctoral students.

Chip-Level Channel Equalization in WCDMA Downlink

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