Opportunities for Adaptivity in the UMTS TerminalReceiver: The Path-Search Function

Jordy Potman, Marijn Damstra, Fokke Hoeksema and Kees Slump

University of Twente, Faculty of EEMCS,

Signals and Systems Group,

P.O. box 217 - 7500 AE Enschede - The Netherlands

Phone: +31 53 489 2773 Fax: +31 53 489 1060

E-mail: j.potman@utwente.nl

Abstract—Wireless communication systems will have tobecome more and more flexible. In the Adaptive WirelessNetworking project we try to develop such a flexible wire-less communication system by developing algorithms foradaptive implementation of the digital signal processingfunctions in wireless communication systems. Within thelimits of a wireless communication system standard thereare two kinds of adaptivity: algorithm-selection adaptiv-ity and algorithm-parameter adaptivity. In this paper wefocus on algorithm-selection adaptivity in the UMTS pathsearch function. Therefore we describe two path searchalgorithms: a Power Delay Profile (PDP) based algorithmand a Maximum Likelihood Estimate (MLE) based algo-rithm. We study and compare the performance of thesealgorithms under a number of multipath channel condi-tions by means of simulations.

The MLE based algorithm is able to resolve a largernumber of paths, especially when the paths are closelyspaced, at the cost of an increased computational com-plexity. Therefore, using algorithm-selection adaptivity inthe UMTS path search function seems to be useful. TheMLE based algorithm is used when there are strong closelyspaced path and the PDP based algorithm is used in allother conditions, appears to be useful. However, in orderto be conclusive a few points will still have to be studied.

Keywords— adaptive signal processing, path search,UMTS

I. Introduction

Wireless communication systems will have to be-come more and more flexible for a number of reasons:

1. The number of wireless communication standardskeeps increasing. Future wireless communication sys-tems will have to support a number of these standards,for example for backwards compatibility.2. The types of traffic that wireless communicationsystems have to transport cover a wide range, fromrelatively low-rate voice traffic to high-rate packet ormultimedia data. The Quality of Service (QoS) re-quirements and thus the performance requirementsof the wireless system that are associated with these

types of traffic vary significantly. A flexible wirelesscommunication system can thus save power by adjust-ing the Digital Signal Processing (DSP) it performs tothe performance requirements.3. The digital signal processing that has to be per-formed in wireless communication systems in orderto achieve the desired performance under worst casewireless channel conditions is becoming increasinglycomplex. Under normal, non worst case, wirelesschannel conditions, simpler processing would havebeen sufficient and the more complex processing onlyleads to higher power consumption. A flexible wire-less communication system can thus save power byadjusting the processing it performs to the channelconditions.

In the Adaptive Wireless Networking (AWgN)project [1] we develop such a flexible wireless com-munication system. The project consists of two activ-ities. In the first activity we develop algorithms foradaptive implementation of DSP functions in wire-less communication systems. This allows the wire-less communication system to adjust the DSP it per-forms to the QoS requirements and the wireless chan-nel conditions. Currently the focus is mainly on algo-rithms for adaptive implementation of the DSP func-tions in the Universal Mobile Telecommunication Sys-tem (UMTS) terminal receiver. In the second activitythe mapping of wireless communication system algo-rithms to a heterogeneous reconfigurable System on aChip (SoC) architecture is studied. The reconfigura-bility of the SoC architecture allows the implemen-tation of different wireless communication standardsusing the same hardware.

In this paper we will focus on algorithms that aresuitable for an adaptive implementation of the pathsearch function in the UMTS terminal. The paper isorganized as follows: In Section II our view on adap-tivity in DSP functions for wireless communicationsystems is given. Section III gives an overview of the

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DSP functions that have to be performed in an UMTSterminal. In Section IV two algorithms for the pathsearch function are explained in more detail and inSection V the performance of these two algorithms iscompared. Finally in Section VI conclusions aboutthe suitability of the two path search algorithms foradaptive implementation of the path search functionin UMTS are given.

II. Adaptivity

Wireless communication standards usually define alarge number of DSP functions that have to be per-formed to implement that particular standard. Thestandards usually do not define the algorithms thathave to be used to implement these functions, so thealgorithms can still be chosen by the implementor ofthe standard. Apart from allowing products to becompetitive it makes it possible to develop an imple-mentation of the standard in which the algorithm thatis used to implement a DSP function is adaptively se-lected based on, for example, QoS requirements orwireless channel conditions.

When a particular algorithm is selected for imple-mentation of a DSP function, the parameters of thealgorithm, if any, can still be freely selected. It istherefor also possible to adaptively select the param-eter values of the algorithm based on, again, QoS re-quirements or wireless channel conditions.

So two kinds of adaptivity can be distinguished:

• Algorithm-selection adaptivity : the algorithm usedto implement a DSP function is selected adaptively.• Algorithm-parameter adaptivity : parameter valuesof an algorithm are adapted.

In this paper we focus on algorithm-selection adap-tivity in the path search function of the UMTS termi-nal. In this paper, two algorithms to implement thepath search function will be described in Section IV.But first the role of the path search function in theUMTS terminal receiver will be briefly explained inthe next section.

III. UMTS Terminal DSP Functions

The main processing chain of the UMTS terminalreceiver roughly performs the following DSP func-tions [2]: receive filtering, descrambling and despread-ing, channel decoding and Cyclic Redundancy Check(CRC) checking, see Fig 1.

The descrambling and despreading function re-quires a number of supporting DSP functions: thecell search, channel estimation and path search func-tions. The cell search function finds the scrambling

FromADC Receive

FilterDescrambling /Despreading

ChannelDecoding

CRCChecking

CellSearch

PathSearch

ChannelEstimation

ToHigherLayers

Fig. 1. UMTS terminal receiver DSP functions

codes and timing of the cells in the neighborhood ofthe terminal. The channel estimation function findsthe scaling and phase rotation of the received signalintroduced by the wireless channel. In this paper wefocus on the path search function. The path searchfunction finds the delays and attenuations of the pathsof the multipath wireless channel between base stationtransmitter and terminal receiver. In the next sectiontwo algorithms for the path search function will bediscussed.

IV. Algorithms for the UMTS Path Search

Function

The path search algorithms that can be found inliterature can roughly be divided in three classes:Power Delay Profile (PDP) based algorithms, Max-imum Likelihood Estimate (MLE) based algorithmsand subspace based algorithms [3]. In this sectionan algorithm from the class of PDP based algorithmsand an algorithm from the class of MLE based al-gorithms will be described in more detail. Both al-gorithms make use of the fact that the transmissionof the Primary Common Pilot Channel (PCPICH) inUMTS results in a transmitted signal component thatonly consists of the scrambling code of the base sta-tion.

A. A Power Delay Profile Based Path Search Algo-

rithm

In [4] a PDP based path search algorithm is de-scribed. In this subsection the operation of this algo-rithm is summarized. Refer to Fig. 2 for an overviewof the algorithm.

The multipath wireless channel will cause the ar-rival of multiple delayed copies of the transmitted sig-nal at the receiver. This received signal r(p), where p

295

h(t) averageset

threshold

selectmaxima

comparecode

generator

x(t) r(t)

s(p)

y(n,m) z(n,m)

Threshold

z (n,m)maxdelays

source channel

ADCr(p)

sampling

Fig. 2. Power Delay Profile based path search algorithm

is a discrete-time time index, can be expressed as

r(p) =

L∑

l=1

hl(p)s(p − τl

Tc) + w(p). (1)

The termL

∑

l=1

hl(p)s(p − τl

Tc) (2)

represents the multiple copies of the scrambling codeonly component of the transmitted signal that arriveat the receiver. In the equations above L is the num-ber of paths in the channel, hl(p) are the complexchannel coefficients of the paths, s(p) is the scram-bling code, τl are the delays of the paths and Tc is thechip duration. The other components of the receivedsignal, such as the user data channels, and the Addi-tive White Gaussian Noise (AWGN) are contained inw(p).

The received signal r(p) is first correlated with thecomplex conjugate of the scrambling code s∗(p)

y(n,m) =1

N

N−1∑

p=0

r(nF + m + p)s∗(p), (3)

where n is the frame index, F is the frame length,m is the correlation index, N is the correlation win-dow size, m ∈ [0, P − 1] and P is the correlationlength. The obtained correlated signal y(n,m) con-tains a number of peaks for the different delays

y(n,m) =1

N

N−1∑

p=0

L∑

l=1

hl(p)δ(m − τl

Tc) + w̃(n,m). (4)

Here δ(m− τl

Tc) results from the autocorrelation of the

scrambling code s(p) and w̃(n,m) is the correlatednoise.

To find a PDP z(n,m) the correlated signal y(n,m)is averaged with the correlated signal from the previ-ous M frames

z(n,m) =1

M

M−1∑

k=0

|y(n−k,m)|2 m ∈ [0, P −1]. (5)

s(t, )èl

s(t, )èLLth path

u(t)

xL(t)

xl(t)

lth path

1st paths(t, )è1

x1(t)

N0 Lâ

2n (t)L

N0âl

2n (t)

l

N0 1â

2n (t)1

y(t)

Fig. 3. Alternative view of the multipath received signalmodel

Local maxima in the PDP are detected by checkingthe height of each sample in the PDP. If it exceeds theheight of both the preceding and subsequent sample alocal maximum is found. A path is found when a localmaximum exceeds a threshold. In [4] the threshold isset to:

η =1

P

P−1∑

m=0

z(n,m)(2 +4√M

). (6)

The performance of a path searcher using a PDPbased path search algorithm will be evaluated in Sec-tion V.

B. A Maximum Likelihood Estimate Based Path

Search Algorithm

In [5] a MLE based path search algorithm is de-scribed. In order to be able to comprehend the opera-tion of this algorithm as summarized in this section, itis useful to consider an alternative view of the multi-path received signal model of the previous subsection.

The complex baseband signal u(t) of the transmit-ter travels to the receiver through a channel via Lpaths [6], see Fig. 3. Each path contributes to thecomplex baseband signal y(t) in the receiver. Thecontribution of the lth path with complex gain αl anddelay τl is:

s(t, θl) = αlu(t − τl) θl , [αl, τl] (7)

Each signal is corrupted by complex white gaussiannoise nl(t), which leads to xl(t). The signal xl(t) isdefined as:

xl(t) = s(t, θl) +

√

N0βl

2nl(t), (8)

n(t) =L

∑

l=1

nl(t) nl(t) =√

βln(t). (9)

The noise n(t) is divided over xl(t) by the factors βl,with

∑Ll=1 βl = 1. The received signal y(t) is related

296

to the signals xl(t) as follows:

y(t) =

L∑

l=1

xl(t). (10)

The complex baseband received signal y(t) cantherefore be described as the sum of the path signalsand a complex white gaussian noise term n(t):

y(t) =L

∑

l=1

s(t, θl) +

√

N0

2n(t). (11)

Using this description a likelihood function can nowbe defined in terms of y(t) and the path parametersθ , [θ1, . . . , θL]T :

Λ(θ; y) ,1

N0

[

2

∫

Do

<(

s∗(t,θ)y(t)

)

dt −

∫

Do

||s(t,θ)||2dt

]

. (12)

In (12) Do denotes the time span over which pathsare searched (the correlation window), s(t,θ) =∑L

l=1 s(t, θl). By maximizing the likelihood functionthe estimates of the path parameters are found:

θ̂ML(y) ∈ arg maxθ

{Λ(θ; y)}. (13)

As the complexity of this calculation requires a vastamount of computational power, the likelihood func-tion is split up into L parts (see (10)):

Λ(θl;xl) ,1

N0βl

[

2

∫

Do

<(

s∗(t, θl)xl(t)

)

dt −

∫

Do

||s(t, θl)||2dt

]

, (14)

(

θ̂l

)

ML(xl) ∈ arg max

θl

{Λ(θl;xl)}. (15)

The maximization (15) of the derived likelihoodfunction (14) can be carried out by Expectation Max-imization (EM). As the data xl(t) is not available, itis estimated in terms of the conditional expectation ofxl(t) using y(t) and a previous estimate of the chan-nel parameters θ̂. Each iteration µ of the algorithmis divided into two steps. The expectation step pro-vides an estimate x̂l(t) of xl(t) and the maximizationstep calculates the value of θl that maximizes the like-lihood function.Expectation step:

x̂l(t, θ̂(µ)) , Eθ̂(µ)

[

xl(t)∣

∣

∣y

]

(l = 1, . . . , L). (16)

Signaldecomposition

MLE of1st path

MLE of

th pathl

MLE ofLth path

Sufficientconvergence

ì ì= + 1

x1 è(ì(t, ))

xl(t, )è( )ì

xL(t, )è( )ì

è( )ìè( )0 è( )ì+1

è ( )ì+1L

è ( )ì+1l

è ( )ì+11

No

Yes

èMLy(t)

^

^

^ ^

^

^

^^ ^

^

^

^

^

Sufficientconvergence

Expectation Maximization

Fig. 4. MLE based path search algorithm using Expecta-tion Maximization

Maximization step:

θ̂l(µ + 1) = arg maxθl

{

Λ(

θl, x̂l

(

t, θ̂(µ))

)

}

(l = 1, . . . , L). (17)

A general diagram of the MLE based path searchalgorithm using EM is shown in Fig. 4 [6]. It canbe implemented by first estimating the signals x̂l(t)using the estimate of θ̂ from the previous iteration.This decomposition of y(t) follows from (10), θ̂(0) isthe initial value. The next step is to carry out Lmaximum likelihood estimations to find all values forθ̂. If the algorithm has converged sufficiently θ̂ML isassigned its value.

A more detailed description of this MLE based pathsearch algorithm using EM can be found in [3] andthe references therein. In the next section the perfor-mance of a MLE based path searcher using EM willbe evaluated

V. Performance Comparison of the Path

Search Algorithms

The PDP and MLE path search algorithms de-scribed in the previous section have been implementedin a UMTS physical layer simulator in order to beable to compare their performance in various multi-path channel models.

Figure 5 shows the average number of path delaysthat the PDP and MLE path searchers estimate cor-rectly in the Vehicular B channel model for variousSignal to Noise Ratios (SNRs). See Table V for thepath delays and path powers in the Vehicular B chan-nel model. The figure shows that on average the PDPalgorithm finds one path less than the MLE algorithm.

Figure 6 shows the percentage of correctly esti-mated paths in the Vehicular B channel model forboth algorithms split out over the path delays. Thefigure shows that the PDP based path searcher neverfinds the weakest path in the channel. The PDP

297

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

-10 -5 0 5 10 15 20 25SNR (dB)

Avera

ge

nu

mb

er

of

co

rrect

path

dela

yesti

mate

s

PDP

MLE

Fig. 5. Vehicular B - Average number of correctly esti-mated path delays (average over 12 frames; 6 paths arepresent)

Vehicular B 0 300 8900 12900 17100 20000 ns

-2.5 0.0 -12.8 -10.0 -25.2 -16.0 dB

TABLE I

Vehicular B channel

path searcher also finds either the first or the secondpath in the channel, but cannot find the two paths atthe same time (the sum of the detection percentagesequals 100%). This explains the fact that the PDP al-gorithm on average finds one path less than the MLEalgorithm

Figure 7 shows the average number of path delaysthat the PDP and MLE path searchers estimate cor-rectly in the Office B channel model for various SNRs.See Table V for the path delays and path powers inthe Office B channel model. Only the MLE algorithmbenefits from the increasing Signal to Noise Ratio(SNR). On average the PDP algorithm finds about

MLE

0

20

40

60

80

100

120

0 300 8900 12900 17100 20000

delay (ns)

co

rrect

esti

mati

on

(%)

SNR = -5 dB SNR = 0 dB

SNR = 5 dB SNR = 10 dB

SNR = 15 dB SNR = 20 dB

PDP

0

20

40

60

80

100

120

0 300 8900 12900 17100 20000

delay (ns)

co

rrect

esti

mati

on

(%)

SNR = -5 dB SNR = 0 dB

SNR = 5 dB SNR = 10 dB

SNR = 15 dB SNR = 20 dB

Fig. 6. Vehicular B - Percentage of correctly estimatedpath delays (SNR = -5 to 20 dB)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

-10 -5 0 5 10 15 20 25SNR (dB)

Avera

ge

nu

mb

er

of

co

rrect

path

dela

yesti

mate

s

PDP

MLE

Fig. 7. Office B - Average number of correctly estimatedpath delays (average over 12 frames; 6 paths are present)

Office B 0 100 200 300 500 700 ns

0.0 -3.6 -7.2 -10.8 -18.0 -25.2 dB

TABLE II

Office B channel

one path, whereas the MLE algorithm finds two tothree paths depending on the SNR.

Figure 8 shows the percentage of correctly esti-mated paths in the Office B channel for both algo-rithms split out over the path delays. It can be clearlyseen that paths can only be detected when they areat least 100 ns separated in time. Both algorithmsmiss the paths at 100 and 300 ns. Again, the weakpaths are detected better by the MLE algorithm, itdoes find the weak paths at 500 and 700 ns. TheOffice B channel clearly shows that both path searchalgorithms have a resolution below which they cannotseparate two closely spaced paths from each other.

PDP

0

20

40

60

80

100

120

0 100 200 300 500 700

delay (ns)

co

rrect

esti

mati

on

(%)

SNR = -5 dB SNR = 0 dB

SNR = 5 dB SNR = 10 dB

SNR = 15 dB SNR = 20 dB

MLE

0

20

40

60

80

100

120

0 100 200 300 500 700

delay (ns)

co

rrect

esti

mati

on

(%)

SNR = -5 dB SNR = 0 dB

SNR = 5 dB SNR = 10 dB

SNR = 15 dB SNR = 20 dB

Fig. 8. Office B - Percentage of correctly estimated pathdelays (SNR = -5 to 20 dB)

298

PDP

MLE

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7 8 9 10

Oversample factor

Reso

luti

on

(ns)

Fig. 9. Resolution as function of the oversample factor

All simulations presented thus far have been carriedout with a sample rate of 1/Tc = 3.84 MHz implyingan oversampling factor of one (no oversampling). Theresolution of the path search algorithms can be im-proved by increasing the oversample factor. Figure9 shows the resolution of the PDP and MLE pathsearchers as a function of the oversample factor. Itcan be seen that if two paths are spaced 131 ns apartthe MLE algorithm is still able to separately detectboth paths with an oversample factor of one. ThePDP algorithm already requires an oversample factorof three in order to be able to separate these paths.

The presented simulation results show that theMLE path search algorithm can better detect weak orclosely spaced paths than the PDP based path searchalgorithm. Unfortunately the complexity of the MLEbased path searcher is higher than the complexity ofthe PDP based path searcher. Figure 10 shows the ra-tio of the number of operations (multiply, add, etc) ofthe MLE and PDP algorithms, the complexity ratio,as a function of the number of paths that have to befound for various values for the maximum number ofiterations µ that the MLE path searcher is allowed toperform. The figure shows that the complexity ratioincreases linearly with the number of paths that haveto be estimated and with the maximum number of it-erations µ. Especially for larger values of µ the MLEpath searcher gets excessively more complex than thePDP based path searcher.

So far all simulations of the MLE path searcher havebeen performed with a maximum number of iterationsµ of 50. Figure 11 shows the average power estimatesof the MLE for the paths in the Vehicular B chan-nel and 15 dB SNR for various values of µ. For µequal to ten the algorithm is not capable of findingthe weakest path of the channel model at 17100 ns.

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7

Number of paths to be estimated

Rati

oM

LE

/P

DP

mu = 50

mu = 30

mu = 20

mu = 10

mu = 1

Fig. 10. Ratio of MLE/PDP complexity as function of µ(N = 2560, P = 340)

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

0 5000 10000 15000 20000 25000

delay (ns)

po

wer

(dB

)

mu = 50

mu = 40

mu = 30

mu = 20

mu = 10

Fig. 11. Vehicular B MLE - Average power in path withcorrect delay estimates as function of µ (15dB SNR)

For twenty iterations the power estimates differ fromthe power estimates for higher numbers of iterations,but all paths are detected. So the complexity of theMLE path searcher can in this case be reduced with-out sacrificing the performance a lot by lowering themaximum number of allowed iterations to 20.

A more elaborate study of the performance andcomplexity of the PDP and MLE path search algo-rithms can be found in [3].

VI. Conclusions and Future Work

In the AWgN project we want to develop adaptivewireless communication systems. Within the limitsof a wireless communication standard we distinguishtwo kinds of adaptivity: algorithm-selection adaptiv-ity and algorithm-parameter adaptivity. In this paperwe have studied two algorithms that can possibly beused for algorithm-selection adaptivity in the UMTSpath search function: a Power Delay Profile (PDP)based algorithm and a Maximum Likelihood Estimate(MLE) based algorithm.

299

The MLE based path search algorithm on averagedetects more paths than the PDP based path searchalgorithm. This is due to the fact that the MLE basedpath searcher can detect weak paths better than thePDP based path searcher, as can be clearly seen inthe Office B channel simulations of Fig. 8.

The MLE based path searcher is also better at re-solving closely spaced paths. The MLE based pathsearcher can detect paths that are a spaced a factorthree closer to each other than the PDP based pathsearcher for the same oversample factor as can be seenin Fig. 9.

The better performance of the MLE based pathsearcher comes at the cost of an increased computa-tional complexity. The relative computational com-plexity of the MLE path searcher to the PDP pathsearcher increases linearly with the number of pathsL that have to be resolved and the maximum num-ber of iterations µ that the MLE algorithm is allowedto perform. By keeping the value of µ relatively small(say 20) the complexity of the MLE path searcher canbe kept within limits.

The PDP and MLE based path search algorithmscan be suitable candidates for algorithm-selectionadaptivity in the UMTS path search function. Fromour research it can be concluded that the MLE basedpath search algorithm has to be used in channels withstrong closely spaced paths. In channels with weakclosely spaced paths the additional paths that theMLE algorithm will find will be weak and thereforewill not contribute a lot to the bit error rate perfor-mance of the receiver. So in all other conditions thePDP algorithm has to be used, because the(averageover 12 frames; 6 paths are present) computationalcomplexity of the MLE algorithm is too high to jus-tify the relatively small improvement in performance.

However in order to be conclusive a few points willhave still to be studied:

• While we know what the performance of the PDPand MLE path searchers is in terms of number of re-solved paths, we have not yet studied the influenceof the number of resolved paths on the bit error rateperformance.• The detection of closely spaced paths by the PDPalgorithm can be improved by using the Teager-Kaiseroperation [7].• There are some alternatives to the MLE algorithm,such as the SAGE algorithm [6], that have a reducedcomputational complexity.

In our future work we will address these issues andfocus on the measurement and control functions that

are required in a path searcher implementation thatswitches between the PDP and MLE based pathsearch algorithms.

Acknowledgment

This research is supported by the Freeband Knowl-edge Impulse program, a joint initiative of the DutchMinistry of Economic Affairs, knowledge institutionsand industry.

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