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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 5, MAY 2001 899

Code Timing Acquisition for DS-CDMA in FadingChannels by Differential Correlations

Tapani Ristaniemi, Member, IEEE, and Jyrki Joutsensalo, Member, IEEE

AbstractIn this paper, we propose simple and efficientalgorithms for the code timing acquisition in the direct-sequencecode-division multiple-access communication system. The es-sential assumption is that a preamble or an unmodulated pilotchannel is available for the desired user. Then the correlationmatrix

R ( )

of the sampled data, where

is suitably chosentime lag, contains the timing information only of desired user,while the contributions of uncorrelated interferers and noiseare suppressed out. Hence, compared to the conventional ap-proach, more interference suppression is achieved. Coarse delayestimates are then obtained by matched filter (MF) or multiplesignal classification-type approaches. In the latter case, only

L

eigenvectors are computed, whereL

is the number of resolvablepaths. If only one path exists, an additional procedure is proposedto both approaches, by which the estimation accuracy is greatlyimproved with negligible increase in computation. More precisely,the chip timing offset due to chip-asynchronous sampling can bedetermined by solving a system of two second-order polynomialsfor each chip interval. Therefore, only at most

2 C

hypotheses areneeded, where C is the processing gain.

All the proposed methods are computationally quite simple, con-taining mainly MF-operations, or at most computation of only feweigenvectors. Mean acquisition time analysis is carried out semi-analytically. Numerical experiments speaks for the possibility ofachieving significant performance gains compared to conventionalacquisition, especially in the presence of strong multiple-access in-terference, making them attractive options to be attached for thenext generation mobile receivers.

Index TermsCode acquisition, code-division multiple access,differential correlation.

I. INTRODUCTION

WIDE-BAND code-division multiple-access (WCDMAor CDMA) technology is a strong candidate for futureglobal wireless mobile communications. WCDMA [1] has been

selected as an air interface solution, e.g., in UMTS (Universal

Mobile Telecommunication System) standard, which will

Paper approved by R. Kohno, the Editor for Spread-Spectrum Theory andApplications of the IEEE Communications Society. Manuscript received March30, 1999; revised November 25, 1999 and July 20, 2000. The work of T. Ris-taniemi was supported by the Academy of Finland. This paper was presentedin part at the Second IEEE Signal Processing Workshop on Signal ProcessingAdvances in Wireless Communications (SPAWC), Annapolis, MD, May 1999,the 1999International Workshop on Mobile Communications (IWMC), Chania,Greece, June 1999, the Sixth IEEE International Conference on Electronics,Circuits, and System (ICECS), Paphos, Cyprus, September 1999, and the 50thIEEE Vehicular Technology Conference (VTC-Fall), Amsterdam, The Nether-lands, September 1999.

The authors are with the Department of Mathematical Information Tech-nology, University of Jyvskyl, FIN-40351 Jyvskyl, Finland (e-mail:[email protected]; [email protected]).

Publisher Item Identifier S 0090-6778(01)04088-0.

provide a multitude of services, especially multimedia and high

bit rate packet data.

CDMA is based on spread-spectrum technique, where

the idea is to spread the narrow-band information signal

into a common wide frequency band before transmission. In

direct-sequence (DS) CDMA, the spreading is performed by

wide-band noise-like signal, which simultaneously identifies

each user in the system. This pseudonoise is also called the

code or the chip sequence of a particular user.

The final objective in the reception of a DS-CDMA system is

to estimate the symbols which carry the data, but a prerequisite

task is to get the local code generator synchronized to that ofreceived signal. This means estimation of the propagation delay,

which gives the required knowledge to the receiver about the

phase of thespreading code. In addition,the strengthsof possible

multipaths and carrier phase must be estimated. In this paper,

we consider only code timing estimation, because it tends to be

the most challenging task, and because the other parameters can

be estimated given a reliable delay estimate [2], [3].

Conventional CDMA systems rely on single-user techniques,

such as matched filter (MF) [4], in both delay estimation and

detection. Although simple, they are inadequate if the code or-

thogonality conditions are perturbed. This happens even in syn-

chronous system with orthogonal codes due to the existence of

multipaths with different delays. Moreover, if the desired signalis much weaker than the interfering signals, which is commonly

known as a nearfar problem, single-user techniques can totally

collapse. In the uplink (e.g., mobile to base) communication,

nearfar problem can be mitigated by power control, but if used

in downlink (e.g., base to mobile) communications, it actually

causes nearfar effect for the downlink receiver. (This is the

case, e.g., in the WCDMA concept, where equal performance is

offered to each mobile user, regardless of their locations.) The

work of Verd [5] meant, however, that it is possible to eliminate

the effects of multiple-access interference (MAI) and nearfar

problem. This optimum multiuser detector, although computa-

tionally demanding and requires all the system parameters to be

known, initiated the development of lower complexity nearfarresistant techniques for both detection [6], [7] and delay/channel

estimation [8], [9].

Code timing acquisition refers to coarse delay estimation,

where themaximal acceptable error is half a chip duration. In [8]

and [9] a subspace approach was considered, which was based

on multiple signal classification (MUSIC) [10]. However, their

performance is found to be inadequate in highly loaded systems

[11], when the signal might not have subspace structure any-

more. Since acquisition takes place before actual data detection,

training symbols or preamble can be used. This was utilized

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900 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 5, MAY 2001

in [11] and [12]. Both maximum-likelihood-based algorithms

modeled the training symbols as desired signal and all the in-

terference as colored non-Gaussian noise that is uncorrelated

with the desired signal. The algorithm in [11] was found to be

nearfar resistant and tolerate high system loading. In addition,

the accuracy of the delay estimate was achieved by solving a

second-order polynomial for each chip interval. A major limita-

tion, however, is that the method cannot be extended to fadingchannels. This is mainly because of the need of long training pe-

riod, during which the channel may have a (sample) mean too

close to zero. This disadvantage was removed by receiver di-

versity in [13], which allowed shorter training. The algorithm

in [12] also has limitations in extension to the fading channels,

and moreoverlooses its nearfar resistance in highly loaded sys-

tems. The computational complexity of all those algorithms is

also still quite high from the downlink signal processing point of

view. Most promising performance with low computation was

found in [14], where the effects of interference were suppressed

by correlating the MF output with a delayed version of it. The

idea behind differential correlation is the following: when only

1s are sent to desired user, its contribution in the receivedsignal at the symbol level is only the fading process, whose

time-correlatedness can be exploited. Basically the same idea

was exploited also in [15], with the exception that the differen-

tial correlation was performed prior to matched filtering. This

was due to the special shift-and-add-property of -sequences,

which makes the proposed algorithm sensitive to the choice of

spreading code.

In this paper, we adopt the same spirit as in [14], although the

derivation of the algorithm is different. This is mainly because

we assume periodic (or short) spreading codes, and analyze

the properties of the correlation matrix of the received and sam-

pled data with nonzero time lags. In short, we call it a differ-

ential correlation matrix. In addition, two extensions are made.

First, the assumption of periodic codes makes it possible to con-

sider also eigenvalue-based approaches. We do this by applying

MUSIC [10], which has also earlier been applied to CDMA syn-

chronization in [8] and [9]. In those papers, however, MUSIC

was applied to the data correlation matrix withzero time lag, and

problems arose in high system loads due to the disappearance of

signal subspace structure. In the context of this paper it is rea-

sonable to apply MUSIC even in highlyloaded systems, because

differential correlations effectively filters interference prior to

actual delay estimation. Therefore, the signal subspace dimen-

sion is significantly reduced while still preserving the desired

information, making the circumstances favorable for MUSIC.Second, we assume arbitrary delays, and propose a simple way

to accurately estimate the chip timing offset in single-path case.

This is an important task since the estimation errors in chip tim-

ings maycause serious performance losses in symbol estimation

[16]. In this paper we show that differential correlations enable

determining the fractional part of the delay by solving a system

of two second-order polynomials for each chip interval.

Numerical simulations with DS-CDMA downlink data

are included in the paper, as a goal to estimate the delays

of a desired user in the system. These values are then used

as input parameters for the mean acquisition time analysis,

which is hence carried out semianalytically. As main reference

Fig. 1. Channel model (L = 3 paths). x ( t ) is the data to be sent, z standsfor delaying by d chips, and a ( t ) denotes path i attenuation in time.

methods we use conventional noncoherent and coherent MF.

Comparisons are also made with the recently reported con-

strained minimum output energy-based algorithm [17], and

subspace-based MUSIC.

The rest of the paper is organized as follows. Section II con-

tains problem formulation. In Section III, differential correla-

tions based algorithms for delay estimation are derived. Sec-tion IV contains mean acquisition time analysis and numerical

experiments, and conclusions are collected in the last section.

II. PROBLEM FORMULATION

A. Notations

Throughout the paper, lower and uppercase boldface letters

denote vectors and matrices, respectively. In addition, we denote

the following:

complex conjugate;

transpose, and Hermitian transpose;

expected value;

sign-function;th vector;

Frobenius norm;

matrices with all entries 0 and 1, respectively.

B. Signal Model

The signal model studied in this paper is a baseband down-

link model with a fading multipath channel, and additive white

Gaussian noise. The channel model is depicted in Fig. 1. The

base station sends a signal

, which containsthe information of symbols of users.

Here is th users th symbol, is th users chip se-

quence. ,where is the symbol duration. We assume that the channel is

fixed during one symbol, i.e.,

inFig.1. iscalled an attenuation factor ofthe thpath, which

is a complex number and may vary from symbol to symbol. The

received signal hence has the form

(1)

where is the number of resolvable paths, is the chip dura-

tion, and is the delay of the th path, where

with integer and . The delay of each path is
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RISTANIEMI AND JOUTSENSALO: CODE TIMING ACQUISITION FOR DS-CDMA IN FADING CHANNELS 903

Fig. 2. Conventional noncoherent MF and DC-MF. The decision is performedby a threshold element, after cumulating the information from a predeterminednumber of data vectors. T is a symbol duration.

A. MF-Type Approach

The simplest way to estimate the delay is to try and match the

known code to the data as well as possible. That is, to find the

solution for

(24)

Here is a replica of the users code, corresponding

tothe fractional test delay . Formally, if wefirstdefine

a cyclic shift of the chip sequence as

(25)

then we may write as

(26)

The delay estimator (24), which we label DC-MF (Differen-

tial Correlations based MF), was the main contribution of our

earlier work [19]. Notice that as all ones preamble is used, the

conventional noncoherent MF is exactly DC-MF with . It

is also worth noticing that, since (24) equals

(27)

DC-MF includes, indeed, only MF-operations. Moreover, it

tells that DC-MF is applicable also in the system with aperiodic

(long) codes, since only the MF outputs are needed. Estimator

of form (27) would be the practical implementation of DC-MF,

and is depicted in Fig. 2.

B. MUSIC-Type Approach

In practice, the estimate will always contain some con-

tributions of interfering users andnoisedue to the finite lengthof

the preamble. But if would have exactly the form of (12),

or equally (19), it could be rewritten by eigenvalue decomposi-

tion as

(28)

Here is a diagonal matrix, whose diagonal elements are

nonzero eigenvalues of , and is a dimensional

matrix, containing the related eigenvectors on its columns. But

then MUSIC [10] could be used to estimate the delays. Due to

finite number of samples, will be in practice asymmetric,

and it must be first symmetrized to achieve real eigenvalues

and orthonormal eigenvectors. Therefore, we define symmetric

, for which MUSIC is applied. Moreprecisely, the delay estimation is performed as

(29)

where consists of principal eigenvectors of .

We label this estimator as DC-MUSIC (differential correlations-

based MUSIC).

MUSIC has been applied to CDMA chip timing acquisi-

tion also earlier in [8] and [9], but it should be stressed that

DC-MUSIC is totally different from those. The difference

between traditional MUSIC and DC-MUSIC arise from the

development of the autocorrelation matrix, whose principaleigenvectors are computed. In traditional MUSIC, a matrix

is computed, i.e., the time lag for the data is zero.

As was seen earlier, has a signal subspace of dimension

. Considering the data model (3), can be as high

as due to multipath fading, and even in nonfading

case is still as large as . In a highly loaded system,

when does not obey subspace structure anymore,

and this causes the failure of MUSIC. In DC-MUSIC, on the

other hand, the first thing to do is to filter the interference and

noise out as much as possible by differential correlations, i.e.,

by estimating instead of . In theory, is of rank

, which is a big enough rank reduction to make circumstances

favorable for MUSIC. Equally important, the rank is reducedwhile still preserving the desired information. In practice, as the

interference cannot be suppressed totally due to a finite number

of vector samples, principal eigenvectors of symmetrized

are estimated, after which MUSIC is applied.

C. Timing-Offset Estimation

Up to this point we have considered only the coarse delay

estimation by fractional test delays, which is clearly enough to

achieve an estimation error less than half of a chip duration. The

accuracy of the estimate can then be achieved in the tracking

mode. Of course, accuracy could also be achieved by using

smaller step sizes for the test delays. However, differential cor-relations enable actual solving of the fractional part of the delay.

Namely, we show in the following that in a frequency-flat fading

channel it is enough to solve a system of two second-order poly-

nomials for each chip interval.

Assume only one resolvable path exists. Suppose is

the propagation delay, so that the differential correlation ma-

trix becomes , where we have denoted

[see (19)]. Recall that

by (20). According to (4) and (5), we have moreover

, where and are

defined in (25), being just a and times shifted replicas

of the desired chip sequence, respectively. Suppose now that we
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use the test codes exactly and . This is because

the truedelaylies between and . Considering the MF-type

approach, we immediately have (see details in Appendix B)

(30)

where . Notice that these quantities

are known, since they are (up to scaling) just values of the code

autocorrelation function with time lag chips. For example, for

-sequences , and . Hence, only two

unknowns, and are included in (30). The solutions for

can be found (see details in Appendix C) to be equal to

(31)

where

(32)

We can also rewrite (32) as

(33)

which is more a suitable expression in the case of aperiodic

codes. Equation (31), which we label ADC-MF (accurate

DC-MF), is a closed-form expression for the timing offset ,

for which we need only the information about the hypotheses

and . ADC-MF is summarized in Table I.

Also the MUSIC-type approach could be used. This is be-

cause has only one nonzero eigenvalue,

and the related eigenvector is . Replacing by

in (30), we would have

(34)

Since is unknown, as being a function of , we end up

with (31) and (32). Naturally, is replaced by

in (32). Analogously, we label this approach as ADC-MUSIC(accurate DC-MUSIC), and summarize it also in Table I.

Remark 4: A slightly modyfied version of (31) could also be

used in case of multipaths. This is because

i.e.

(35)

TABLE IALGORITHMS ADC-MF AND ADC-MUSIC FOR TIMING OFFSET ESTIMATION

Letting now , (30) would accordingly have more of a

general form

Assuming impulse-like code autocorrelation, i.e., for

, we would end up with(30), where in addition .

This would accordingly lead to an estimator

(36)


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Fig. 3. Code acquisition process.

IV. ANALYSIS

A. Performance Measures

In this paper, we consider delay estimation only in a parallel

manner. This is because the goal is to compare the performance

of the methods without considering any threshold setting. Max-

imum selection is used to determine the delay, i.e., the strongest

peak from the delay spectrum is selected. The definition of ac-

quisition is the case where any multipath component is found.

The performance measure, probability of acquisition, is defined

as

# of acquisitions

# of trials(37)

The other performance measure is mean acquisition time,

which measures the average time spent in the acquisition

process. This issue is profoundly considered in [20]. The

acquisition scheme is illustrated in Fig. 3. A preamble ofsymbols is sent, which is processed in the receivers acquisition

mode. In case of misacquisition, a request for the new preamble

is sent, which takes a time of symbols.

Suppose a while that it takes no time to request a new pre-

amble, i.e., . Then the average time needed for acquisi-

tion is

(38)

In practice, however, , since each misacquisition pays

an additional price of symbols by which a new preamble is

requsted. This additional time is on average

(39)

The mean acquisition time is thus

(40)

Fig. 4. Typical fading process. The lines indicates the real andimaginary partsof the time-varying path attenuation factor for M = 5 0 0 symbols.

The third performance measure is root mean-square error

(RMSE). It measures the accuracy of the delay estimation

according to

(41)

where is the true delay, and is the number of realizations.

If the delay estimations are unbiased, the RMSE values can be

directly compared to the CramerRao bound (CRB). CRB is the

lower bound for the variance of any unbiased estimator. The an-

alytical forms of CRBs in different type of channels are derived,

e.g., in [9], [11], and [16].

B. Numerical Experiments

We compare the methods in the downlink environment with

theRayleigh fading channel. The data rate is assumed to be

kbit/s, carrier frequency GHz, and mobile speed

km/h. This results in normalized Doppler shifts at most

. According to Jakes doppler

power spectrum [18], and related autocorrelation function of the

channel, thecoherent integrationintervalof symbols

is reasonable, and is used from now on unless otherwise stated.

The typical fading process at the symbol level is seen in Fig. 4.

The methods for delay estimation are: DC-MF (24),DC-MUSIC (29), ADC-MF and ADC-MUSIC (Table I),

MUSIC [9], CMOE [17], and conventional noncoherent and

coherent MF [4]. Any parameters such as time-varying path

strengths, and codes of the interfering users are not assumed

to be known. Only the code of the desired user is known. In

addition, a preamble is available for the desired user

. Gold codes of length are used. Signal-to-noise

ratio (SNR) in the chip-MF output is always 10 dB. Both

frequency-selective and flat fading channels are considered. In

frequency-selective fading channels the number of resolvable

paths is either or . The number of users is varied

from to . Therefore, the total number of sources
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Fig. 5. Probability of acquisition as a function of the number of users in anequal energy two-path Rayleigh fading channel. All the interfering users are10 dB stronger. The length of the preamble is M = 4 0 0 , and the average SNR

is 10 dB.

Fig. 6. Mean acquisition time as a function of the number of users in an equalenergy two-path Rayleigh fading channel. All the interfering users are 10 dBstronger. The length of the preamble is M = 4 0 0 , and the average SNR is10 dB.

is , while the maximum signal subspace

dimension is . Therefore, highly loaded systems arise.

In one simulation, each parameter value is fixed, and the delaysare estimated from the peaks of the delay spectra. All the

measured quantities are averaged over 1000 simulations.

1) Setup A: Varying System Load: The channel has two

equal energy paths, and all the interfering users are

10 dB stronger. Maximum selectionis used to find any multipath

component. The probabilities of acquisition are measured as a

function of the number of users . Fig. 5 shows

the performance with varying system load, when the length of

the preamble is . Noncoherent MF predictably fails

due the strong MAI, as well as MUSIC due to the high system

loading. On the other hand, CMOE would need more an accu-

rate estimate for the inverse of the autocorrelation matrix. The

Fig. 7. Probability of acquisition as a function of MAI in an equal energytwo-path Rayleigh fading channel. The system included K = 1 0 users. Thelength of the preamble is M = 4 0 0 , and the average SNR is 10 dB.

Fig. 8. Mean acquisition time as a function ofMAI inan equal energy two-pathRayleigh fading channel. The system included K = 1 0 users. The length of thepreamble is M = 4 0 0 , and the average SNR is 10 dB.

remaining methods have nearly equal performance when only a

few users occupy the system, but the methods based on differ-

ential correlations are clearly the most tolerant against system

loading. Quite remarkably, DC-MF reaches a probability of ac-quisition as high as 0.963, even though all the 14 interfering

users (i.e., the case ) are 10 dB stronger. Fig. 6 shows

the corresponding mean acquisition times.

One can notice that DC-MF seems to have better acquisi-

tion capability than DC-MUSIC. The reason for this is that the

MF-type approach in general works well as the code autocor-

relation function is impulse-like. With shorter codes, the code

autocorrelation function gets worse, and the use of DC-MUSIC

is more reasonable. This is demonstrated later in Setup D.

2) Setup B: Varying Level of MAI: In this experiment we

study the effect of increasing the level of MAI. The system in-

cludes users in an equal energy two-path Rayleigh


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Fig. 9. Probability of acquisition as a function of the preamble length in anequal energy two-path Rayleigh fading channel. The system included K = 1 0users,and all theinterferingusers are10 dB stronger. TheaverageSNR is 10dB.

Fig. 10. Meanacquisitiontime as a function of thepreamblelengthin an equalenergy two-path Rayleigh fading channel. The system included K = 1 0 users,and all the interfering users are 10 dB stronger. The average SNR is 10 dB.

fading channel. The length of the preamble is , and

the average SNR is 10 dB.

Fig. 7 shows the achieved probabilities of acquisition as a

function of MAI per interfering user. One can see that real dif-ferences are noticed after MAI of 8 dB, after which DC-MF is

able to retain the performance the best. With MAI of 12 dB per

interfering user, DC-MF still gives a probability of acquisition

equal to 0.915, while coherent MF drops down to 0.608. Fig. 8

shows the corresponding mean acquisition times.

3) Setup C: Varying Number of Symbols: In this experiment

we study the effect of increasing the length of the preamble.

The system includes users and all the interfering users

are 10 dB stronger. The achieved probabilities of acquisition are

seen in Fig. 9. Again, noncoherent MF fails in the nearfar sce-

nario, which is predictable, as well as MUSIC due to the high

system load. CMOE usually performs better as more symbols

Fig. 11. Relative number of acquired paths in L = 3 path Rayleigh fadingchannel as a function of the preamble length. The system included K = 2users, and the random codes were of length C = 7 . Average SNR was 10 dB.

TABLE IINUMBER OF CASES A CERTAIN PATH IS ACQUIRED IN A K = 2 USER SYSTEMWITH RANDOM CODES OF LENGTH C = 7 . PREAMBLE LENGTH IS M = 5 0 0 SYMBOLS, AND AVERAGE SNR IS 10 dB. FRACTIONAL PARTS ; i = 1 ; 2 ; 3 ;

ARE UNIFORMLY DISTRIBUTED OVER ( 0 ; 1 )

are available [17]. This is because the estimation for the inverse

of the autocorrelation matrix thus becomes more accurate.

However, in this setup the strong MAI is too much for CMOE,

even if as many as symbols are available. The fact

that the proposed methods are asymptotically invariant with re-

spect to the interfering users and noise can be predicted from

the figure, in which the probability of acquisition seems to tend

to 1. The figure also tells the fact that the performance of the

proposed methods depends essentially on the length of the pre-

amble, because the goal is to average interference out. For this

reason, it is understandable that the methods fail if the preambleis too short. However, this is also the problem for the reference

methods, which may suffer even more.

In Fig. 10 the mean acquisition times in symbols are plotted.

Due to reliable estimations, the acquisition time for DC-MF is

usually no more than the length of the preamble.

4) Setup D: Search of Multiple Paths: In this experiment we

demonstrate the ability of DC-MUSIC to find the most paths.

users are given random codes of length in

path Rayleigh fading channel. The paths have 5 dB differences

in power. Fig. 11 shows the average amount of acquired paths

as a function of the preamble length. It is seen that DC-MUSIC

always found the most paths. Quite remarkably, DC-MUSIC
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Fig. 12. RMSE (chips) as a function of number of users in a single-pathRayleigh fading channel. The length of the preamble is M = 5 0 0 symbols,

and the average SNR is 10 dB.

found average nearly 2.5 paths out of 3, as sym-

bols are available. Table II shows the case in more

detail. Namely, it tells the number of cases when each path

is acquired. It is quite noticeable how frequently DC-MUSIC

acquired also the weaker paths ( 5- and 10-dB paths with

probabilities 0.882 and 0.640, respectively) compared to the

other methods, which had serious problems in acquiring even

the second strongest path.

5) Setup E: Single-Path Channel: In the first experiment,

we study the achieved accuracy in a system with

users. Now, all the users are equally strong. The channel is fre-

quency-flat fading, and ADC-MF and ADC-MUSIC are applied

for the first time. The accuracy for all the other methods are

achieved by using more delay candidates. More precisely, the

increment for the delay candidate was always as small as

chip. Recall that ADC-MF and ADC-MUSIC uses an increment

equal to one chip, only.

Fig. 12 shows the achieved accuracies in RMSE. CMOE

seems also to yield quite accurate estimates, and performs

better than the proposed methods, when the system load is

low. However, it must be pointed out that there is no MAI inthis experiment. Hence, it is expected that in the presence of

MAI, the RMSE of CMOE will degrade significantly, as can

be seen from Setup B. Also MUSIC performs better than theproposed ones, but only when the system load is low. Coherent

MF seems to perform nearly the same as the proposed methods.

However, we must stress that both ADC-MF and ADC-MUSIC

actually solves the fractional part of the propagation delay

from two successive outputs of the differential correlator, thus

needing much less computation than the reference methods.

The negligible difference of ADC-MF and ADC-MUSIC is

also understandable, since differential correlations effectively

filters the interference, giving thus not much possibilities for

MUSIC to improve the accuracy any more.

The second experiment is dedicated for the comparison of

the accuracy of ADC-MF and ADC-MUSIC to the CramerRao

Fig. 13. RMSE as a function of preamble length in single-path time-invariantchannel with K = 5 users, the average SNR of 0 dB.

lower bound (CRB). Although the estimators turned out to be

approximately unbiased, the bias is estimated for each fixed pa-

rameter value. This is taken into account in the final RMSE cal-

culation, giving an adequate measure for the CRB comparison.

The system includes users, and the averageSNR is 0 dB.

The single-path time-invariant channel is assumed, and hence

the data model coincides with that of [11, pp. 8889], where the

CRB is derived. The RMSE curves are seen in Fig. 13, from

which we notice that neither methods attain the CRB. This was

also the case in [9] with MUSIC. One can also see that the co-

herent integration improves the accuracy of ADC-MF to that of

ADC-MUSIC.

V. CONCLUSION

In this paper, simple and accurate code timing acquisitionin DS-CDMA system was studied. It was shown that when aconstant preamble or an unmodulated pilot channel is availablefor the desired user, the receiver can efficiently filter noise andinterferers out by differential correlations and suitably chosentime lags. Therefore, it is possible to estimate the desired usersdelays even when huge number of interferers exist. Two typesof methods were proposed, labeled as (A)DC-MF and (A)DC-

MUSIC, whose main characteristics were as follows: they are computationally simple, containing only MF-op-

erations (DC-MF) or at most computation of few, say, eigenvectors (DC-MUSIC);

they efficiently filter interfering users and additive noiseout prior to actual delay estimation, regardless of the codenonorthogonalities due to multipath propagation;

they can effectively utilize the time correlation of thefading process;

DC-MF performs equally or better than conventional ap-proach, though they are computationally equally simple;

DC-MUSIC is suitable especially for the acquisition ofmany, possibly less powerful paths;
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DC-MUSIC performs well when the processing gain issmall;

an additional procedure can be attached to both methods,improving the estimation accuracy by a negligible in-crease in computation.

These features were verified by numerical experiments in down-link environment, making the proposed methods attractive op-

tions to be attached for the next generation mobile receivers.Future research in the context of the paper include, e.g., moreefficient interference suppression mechanisms, which are vitalespecially when short preambles are used. Also the possibilityof using the methods for tracking purposes via decision feed-back is our ongoing subject.

APPENDIX A

A. Derivation of (19)

First, from (8) we have

. . .

(42)

where the second equation follows from , and the

third is due to definition . Therefore we have

(43)

from which (19) immediately follows.

APPENDIX B


Recall from Section III that

and (44)

(45)

Thus, we first may write

(46)

Defining , we have

(47)

from which the first equation in (30) follows. The derivation of

the second one is entirely similar and is omitted.

APPENDIX C


To shorten notations, define and

. Taking square roots on both

sides of (30), we have

(48)

(49)

which is a system of equations with two unknowns, and

. Dividing (48) by (49) we obtain

(50)

By simple algebraic manipulations it leads to

(51)

from which (31) is obtained by denoting .

REFERENCES

[1] T. Ojanper and R. Prasad, Wideband CDMA for Third Generation Mo-

bile Communications. Norwood, MA: Artech House, 1998.

[2] H. V. Poor, On parameter estimation in DS/CDMA formats, in Ad-

vances in Communications and Signal Processing, W. A. Porter and S.

C. Kak, Eds. New York: Springer-Verlag, 1989. .

[3] K. K. Chawla and D. C. Sarwate, Parallel acquisition of PN sequences

in DS/SSsystems,IEEETrans. Commun., vol. 42,pp. 21552164,May

1994.

[4] J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-

Hill, 1995.

[5] S. Verd, Minimum probability of error for asynchronous Gaussian

multiple-access channels, IEEE Trans. Inform. Theory, vol. IT-32, pp.

8596, Jan. 1986.

[6] R. Lupas and S. Verd, Linear multiuser detectors for synchronous

code-division multiple-access communications, IEEE Trans. Inform.

Theory, vol. 35, pp. 123136, Jan. 1989.

[7] U. Madhow and M. L. Honig, MMSE interference suppression for di-

rect-sequence spread-spectrum CDMA, IEEE Trans. Commun., vol.

42, pp. 31783188, Dec. 1994.[8] S. Bensley and B. Aazhang, Subspace-based channel estimation for

code division multiple access communication systems, IEEE Trans.

Commun., vol. 44, pp. 10091020, Aug. 1996.

[9] E. Strm, S. Parkvall,S. Miller, andB. Ottersten, Propagationdelayes-

timation in asynchronous direct-sequence code division multiple access

systems, IEEE Trans. Commun., vol. 44, pp. 8493, Jan. 1996.

[10] R. Schmidt, Multiple emitter location and signal parameter estimation,

IEEE Trans. Antennas Propagat., vol. AP-34, pp. 276290, Mar. 1986.

[11] D. Zheng, J. Li, S. L. Miller, and E. G. Strm, An efficient code-timing

estimator for DS-CDMA signals, IEEE Trans. Signal Processing, vol.

45, pp. 8289, Jan. 1997.

[12] S. E. Bensley and B. Aazhang, Maximum likelihoodsynchronization of

a singleuser for code division multiple access communication systems,

IEEE Trans. Commun., vol. 46, pp. 392399, Mar. 1998.


12/12


[13] Z.-S. Liu, J. Li, and S. L. Miller, An efficient code-timing estimator for

receiver diversity DS-CDMA systems, IEEE Trans. Commun., vol. 46,

pp. 826835, June 1998.

[14] M. H. Zarrabizadeh and E. S. Sousa, A differentially coherent PN code

acquisition receiver for CDMA systems, IEEE Trans. Commun., vol.

45, pp. 14561465, Nov. 1997.

[15] C.-D. Chung, Differentially coherent detection technique for direct-se-

quence code acquisition in a Rayleigh fading channel, IEEE Trans.

Commun., vol. 43, pp. 11161126, Feb./Mar./Apr. 1995.[16] S. Parkvall, Near-Far Resistant DS-CDMA Systems: Parameter Esti-

mation and Data Detection, Ph.D. dissertation, Royal Inst. of Technol.,

Oct. 1996.

[17] M. Latva-Aho, Advanced Receivers for Wideband CDMA Systems,

Doctoral dissertation, Acta. Univ. Ouluensis, C 125, Sept. 1998.

[18] J. D. Parsons, The Mobile Radio Propagation Channel. London, U.K.:

Pentech, 1992.

[19] J. Joutsensalo and T. Ristaniemi, Single-user synchronization in fading

channel, Proc. IEEE Signal Processing Workshop on Signal Processing

Advances in Wireless Communications, pp. 133137, May 912, 1999.

[20] A. Polydoros and C. Weber, A unified approach to serial search spread-

spectrum code acquisitionPart II: A matched filter receiver, IEEE

Trans. Commun., vol. COM-32, pp. 550560, May 1984.

Tapani Ristaniemi (M00) was born in Kauhava,Finland, in July 1971. He received the M.Sc. degreein pure mathematics, the Ph.Lic. degree in appliedmathematics, and the Ph.D. degree in telecommuni-cations from the University of Jyvskyl, Jyvskyl,Finland, in 1995, 1997, and 2000, respectively.

He is Senior Research Scientist at the Departmentof Mathematical Information Technology, Universityof Jyvskyl, Jyvskyl, Finland. His research in-

terests include signal processing and radio resourcemanagement for wireless communication systems.

Jyrki Joutsensalo (M94) was born in Kiukainen,Finland, in July 1966. He received the diploma en-gineer, licentiate of technology, and doctor of tech-nology degrees from the Helsinki University of Tech-nology, Espoo, Finland, in 1992, 1993, and 1994, re-spectively.

Currently, he is Professor of Telecommunicationsat the Department of Mathematical InformationTechnology, University of Jyvaskyla. His currentresearch interests include signal processing forwireless radio communications and data networks.

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