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Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2007, Article ID 49525, 9 pagesdoi:10.1155/2007/49525

Research Article

Equalization of Multiuser Wireless CDMA DownlinkConsidering Transmitter Nonlinearity Using Walsh Codes

Stephen Z. Pinter and Xavier N. Fernando

Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada M5B 2K3

Received 25 February 2006; Revised 11 November 2006; Accepted 13 November 2006

Recommended by David I. Laurenson

Transmitter nonlinearity has been a major issue in many scenarios: cellular wireless systems have high power RF amplifier (HPA)nonlinearity at the base station; satellite downlinks have nonlinear TWT amplifiers in the satellite transponder and multipath con-ditions in the ground station; and radio-over-fiber (ROF) systems consist of a nonlinear optical link followed by a wireless channel.In many cases, the nonlinearity is simply ignored if there is no out-of-band emission. This results in poor BER performance. Inthis paper we propose a new technique to estimate the linear part of the wireless downlink in the presence of a nonlinearity usingWalsh codes; Walsh codes are commonly used in CDMA downlinks. Furthermore, we show that equalizer performance is sig-nificantly improved by taking into account the presence of the nonlinearity during channel estimation. This is shown by using aregular decision feedback equalizer (DFE) with both wireless and RF amplifier noise. We perform estimation in a multiuser CDMAcommunication system where all users transmit their signal simultaneously. Correlation analysis is applied to identify the channelimpulse response (CIR) and the derivation of key correlation relationships is shown. A difficulty with using Walsh codes in termsof their correlations (compared to PN sequences) is then presented, as well as a discussion on how to overcome it. Numericalevaluations show a good estimation of the linear system with 54 users in the downlink and a signal-to-noise ratio (SNR) of 25 dB.Bit error rate (BER) simulations of the proposed identification and equalization algorithms show a BER of 106 achieved at anSNR of25 dB.

Copyright 2007 S. Z. Pinter and X. N. Fernando. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

1. INTRODUCTION

The quality of channel estimation has a prominent impact onthe accuracy of equalization and hence system performance.The general wireless CDMA downlink for cellular networksis shown in Figure 1. In order to properly equalize this chan-nel, an accurate estimation of both the nonlinear and linearchannel parameters is required. Some example systems arecellular CDMA network downlink, radio-over-fiber (ROF)[1] downlink, and satellite downlink. In all these cases, thesystem of interest consists of a mildly nonlinear part followedby a linear part, in that particular order. This interconnectionis considered a Hammerstein system. The breakdown of thenonlinear/linear downlink systems as described above is thefollowing:

(1) wireless CDMA network downlink: RF amplifier/wire-less channel;

(2) satellite downlink: TWT amplifier/wireless channel;(3) ROF downlink: optical channel/wireless channel.

Some of the dominant issues associated with the above sys-tems include intersymbol interference (ISI), RF amplifiernonlinearity, and the presence of noise. In order to limitthe effects of these distortions, estimation and subsequentlyequalization of the concatenated channel should be done.The most common approach is to ignore the nonlinearity

and just attempt to estimate the linear channel. This will re-sult in inferior equalization performance. The goal in thispaper is to estimate first the channel parameters, and thendevise appropriate equalization.

Some work in identifying Hammerstein systems has beendone by Billings and Fakhouri [2]. In [2], the Hammersteinmodel was analyzed in a single control signal (or single user)continuous-time baseband environment. Correlation analy-sis was used to decouple the identification of the linear andnonlinear component subsystems by using white Gaussianinputs. The generation of white noise inputs has practicaldifficulties, therefore in this paper we substitute the whiteGuassian inputs with the summation of multiple Walsh code

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2 EURASIP Journal on Wireless Communications and Networking

Central basestation

RF amplifier

nonlinearity

F(

)

Access point

Multipath wireless

channel

To mobile unit

To mobile unit

To mobile unit

.

.

....

Figure 1: General wireless downlink.

F(

)q(t) r(t)

(a) Single complex-valued sys-tem.

FI( )

FQ( )

q(t) r(t)

90

(b) Two real-valued systems.

Figure 2: Inphase and quadrature phase model for a nonlinear system.

sequences. We then apply the concept of Hammerstein rep-resentation and correlation analysis to a multiuser CDMAdiscrete-time passband communication system. The use ofWalsh codes for estimation of the downlink is attractive be-cause these spreading codes are already widely used in spreadspectrum communications [3].1 Any mildly nonlinear sys-tem that can be described by an lth-order polynomial can beidentified using our technique. Other Hammerstein systemidentification methods involve frequency domain techniques

[5], subspace-based state-space system identification [6], andnoniterative algorithms based on orthonormal functions [7].

The wireless downlink has a nonlinear element (e.g.,HPA) common to all users, but each user will have a sep-arate multipath wireless channel. We considered this mul-tiuser scenario, where a summation of Walsh codes travelsthrough this concatenated channel. Following the channelestimation, the downlink is equalized. A decision feedbackequalizer (DFE) is used to equalize for the wireless channeldispersion. It is shown that equalizing for the nonlinearity isnot a strict requirement, however, consideration of the non-linearity is required for the accurate estimation and equaliza-tion of the linear channel.

Although the work in this paper is tailored to a multiuserCDMA communication system, it can also be applied to areasoutside of the communication field where a parallel connec-tion of multiple linear systems is encountered in series witha single nonlinearity.

1 3G systems use scrambling codes as opposed to Walsh codes. Our ap-proach is still justified since 3G downlink systems use both an initialchannelization code spreading (i.e., orthogonal Walsh code) followed bya scrambling code spreading [4]. So in 3G downlink systems, Walsh codesare still used, only in combination with scrambling codes, and we be-lieve that system identification with Walsh codes will be of interest to re-searchers in this area.

2. MULTIUSER CDMA DOWNLINK SYSTEM MODEL

In this section the theory for a multiuser CDMA downlinkwill be presented with the help of discrete-time nonlinearsystems theory discussed in [2]. But before proceeding withthe estimation theory, a short section regarding complex no-tation will be discussed.

2.1. Passband complex consideration

Communication signals and systems are passband. In orderto use baseband signal processing, communication signalsin the passband (i.e., real-valued signals [8]) must be ap-propriately translated from the passband to the baseband.Generally, this translation results in complex-valued base-band signals [8]. Therefore, in a passband system, the sig-nals as well as the channel impulse response (CIR) and non-linear component are complex valued. We now show howthese complex-valued quantities can be split into real-valuedquadrature components for easy handling.

When an RF signal undergoes a nonlinear transforma-tion one of the major concerns is the AM-AM and AM-

PM distortions. The complex-valued nonlinear system inFigure 2(a) introduces both of these distortions [9]. It hasbeen shown in [10, 11] that a bandpass memoryless nonlin-earity can be modeled with a baseband complex nonlinearmodel. Then the nonlinear distortion can be expressed byinphase and quadrature phase components that are real. Letthe input signal in Figure 2(a) be given as

q(t) =A(t)cosct+ (t)

. (1)

Then the output r(t) is

r(t) = R

A(t)

cos

ct+ (t) +

A(t)

, (2)

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S. Z. Pinter and X. N. Fernando 3

x1(n)

x2(n)

xN(n)

F( )u(n) q(n)

namp(n)

h1(n)

h2(n)

hN(n)

nw(1)(n)

nw(2)(n)

nw(N)(n)

r1(n)

r2(n)

rN(n)

.

.

.

.

.

....

.

.

.

Base station Nonlinearity Accesspoint

Wireless channel To mobileunits

Figure 3: Downlink in a multiuser CDMA environment with a single nonlinearity (amplifier) and separate wireless channels for each user.

where R is the AM-AM distortion and is the AM-PM dis-tortion. The output r(t) can also be expressed as

r(t) = RA(t)

cos

A(t)

cos

ct+ (t)

R

A(t)

sin

A(t)

sin

ct+ (t)

,

(3)

using the trigonometric identity cos(A + B) = cos(A)cos(B) sin(A)sin(B). Equation (3) can then be written as

r(t) = riA(t)

cos

ct+ (t)

rq

A(t)

sin

ct+ (t)

,

(4)

where

riA(t)

= R

A(t)

cos

A(t)

,

rqA(t)

= R

A(t)

sin

A(t)

.

(5)

Equation (4) shows that the bandpass nonlinearity can beseparated into an inphase component and a quadraturephase component with only AM-AM distortion. Therefore,the two real-valued systems shown by the quadrature modelin Figure 2(b) are equivalent to the complex-valued systemshown in Figure 2(a). Similarly, the bandpass CIR can alsobe separated into inphase and quadrature phase components[8].

Mathematically, real quantities are easier to work with

and therefore the quadrature model is the representation ofchoice in this paper. As a result of this, it can be stated thatfor the linear system in this paper the real-valued inphase andquadrature phase components are estimated individually. Allvariables introduced hereafter are real quantities unless oth-erwise specified.

2.2. Wireless channel estimation theory

This section presents an investigation into the estimation ofthe wireless channel of the downlink in a multiuser CDMAenvironment using Walsh codes. As mentioned in Section 1,the system of interest consists of a mildly nonlinear part

Table 1: Symbol descriptions for the downlink.

Symbol Description

xj (n) Input Walsh code spreading sequence, 1 j N

u(n) Compound Walsh signal input

F() Nonlinear function

namp(n) RF amplifier Gaussian noise

q(n) Signal sent through multiple wireless channels

hj(n) Wireless channel impulse response, 1 j N

nw(j)(n) Wireless channel Gaussian noise, 1 j N

rj(n) Signal sent to mobile units, 1 j N

(HPA) followed by a linear part (wireless channel), whichcan be modeled by a Hammerstein system. An investigationinto the single signal estimation of a Hammerstein systemhas been covered in [2], but Gaussian inputs were used andthere was no extraction of the termRuw1 (). In this section,the theory is extended to the multiuser case where varyingwireless channels are encountered for each mobile user. It isalso shown that multilevel testing (via the Vandermonde ma-trix) alleviates anomalies that would otherwise be encoun-tered with direct correlation.

The scenario of a multiuser CDMA downlink is shownin Figure 3 (all signals used in analyzing the downlink, alongwith their descriptions, are shown in Table 1). In this sce-nario: (1) the base station generates an independent Walshcode for each user and combines them, (2) the combined sig-nal is then transmitted through the common nonlinear linkfollowed by the addition of HPA noise, (3) the signal is thentransmitted through separate wireless channels followed bythe addition of an independent wireless channel noise,2 and

2 Different initial seed settings are used during simulation to ensure in-dependence.

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finally, (4) the signal is sent to the mobile user for furtherprocessing. This scenario generates a multitude of signal im-pairments such as: (1) ISI from the wireless channels, (2)different path loss affecting dynamic range, (3) addition ofwireless and RF amplifier noise, and (4) carrier regrowth, in-band distortion, and cross-multiplication of terms, all result-

ing from the nonlinearity.The channel of interest in the estimation theory to followwill be that of the first user, and so the output signal usedin all following derivations will be r1(n). The first step in theestimation is to define the output of the system. Accordingto the theorem of Weierstrass [12], any function which iscontinuous within an interval may be approximated to anyrequired degree of accuracy by polynomials in this interval.Therefore, the output of the nonlinear system plus the am-plifier noise is given by a polynomial of the form

q(n) =A1u(n) +A2u2(n) + +Alu

l(n) + namp(n), (6)

where u(n) is a compound input of Walsh codes (of length

Nw) that can be written asu(n) = x1(n) + x2(n) + + xN(n), (7)

where N is the number of Walsh codes (or equivalently thenumber of users). The system output r1(n) can be expressedby the convolution

r1(n) = q(n) h1(n) + nw(1)(n). (8)

Substituting for q(n) from (6) and expanding the convolu-tion give

r1(n) =A1

m=

h1(m)u(n m) +A2

m=

h1(m)u2(n m)

+ +Al

m=

h1(m)ul(n m)

+

m=

h1(m)namp(n m) + nw(1)(n),

(9)

which can be written in a more compact form as

r1(n) =l

k=1

Ak

m=

h1(m)uk(n m)

+

m=h1(m)namp(n m) + nw(1)(n)

noise terms.

(10)

As a summation of the output of the isolated lth order kernel,the above equation becomes

r1(n) = w1(n) + w2(n) + w3(n) + + wl(n) + noise terms.(11)

Expressing the output in the form of (11) is a crucial stepin developing the correlation relationships that follow. Bystudying the correlation between the outputr1(n) and the in-put u(n), as well as the output of the first-order kernel w1(n)and the input u(n), the linear and nonlinear systems can beestimated.

3. CORRELATION RELATIONSHIPS

The next step in the estimation of the concatenated channelis to further process the input-output relations, as definedabove, by utilizing correlation relationships.

3.1. Generalized input-output correlation

A commonly defined output is used in this derivation. Theoutput is given by r(n), where r(n) = rj(n), 1 j N.Using the input u(n) and the general output r(n), the cross-covariance between them can be written as

Rur() =r(n) r(n)

u(n ) u(n )

. (12)

The cross-covariance relationship is used widely throughoutthis section. From this point onward, r(n), q(n), namp(n),u(n), and xj(n), nw(j)(n) for 1 j N will refer to their re-spective signals with the mean removed. In some cases [12],a mean level is added to the input to ensure that both oddand even terms in (11) contribute to the first-order input-output cross-correlation. However, in this case, only the out-put of the first-order kernel is of interest (discussed shortly)and hence a mean level is not needed. With means removed,the cross-covariance can be written as

Rur() = r(n)u(n ). (13)

Substituting (11) into the above equation and assuming theinput and noise processes to be statistically independent, thatis, namp(n)u(n ) = 0 for all and nw(j)(n)u(n ) = 0forall , give

Rur() = w1(n) + w2(n) + + wl(n)u(n )= w1(n)u(n)+w2(n)u(n)+ +wl(n)u(n)

= w1(n)u(n)+w2(n)u(n)+ +wl(n)u(n)

=Ruw1 () +Ruw2 () + +Ruwl(),

(14)

which can be written in a more compact form as

Rur() =l

k=1

Ruwk (). (15)

However, ifRur() is evaluated directly as defined above, the

termsl

k=2Ruwk () give rise to anomalies associated withmultidimensional autocovariances [13]. This problem can beovercome by isolating Ruw1 () using multilevel input test-ing. This step is crucial for successful estimation of the wire-less channel. Multilevel testing is possible under the condi-tion that the output can be expressed by (11). It should benoted that if the channels were linear there would be no needto isolateRuw1 () becauseRuw1 () =Rur().

Multilevel testing is implemented prior to the nonlin-earity by using the signal mu(n), where m = l for allm = l, and repeating ltimes. For example, with a third-order

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nonlinearity, the output at the mobile user can be written as

r(n) =

A1u(n) +A2u2(n) +A3u

3(n) + namp(n)

h1(n)

+ nw(j)(n)

= A1u(n) h1(n) +A2u2(n) h1(n)

+A3u

3

(n)

h1(n) + namp(n)

h1(n) + nw(j)(n)= w1(n) + w2(n) + w3(n) + noise terms.

(16)

With the multilevel input 1u(n), the above equation be-comes

r1 (n) =

A11u(n) +A221u

2(n) +A331u

3(n) + namp(n)

h1(n)

+ nw(j)(n)

=A11u(n) h1(n) +A221u

2(n) h1(n)

+A331u

3(n) h1(n) + namp(n) h1(n) + nw(j)(n)

= 1w1(n) + 21w2(n) +

31w3(n) + noise terms,

(17)

which when used to findRur() gives the following modifiedform of (15):

Rurm () =l

k=1

kmRuwk (), m = 1,2, . . . , l (18)

where rm is the response of the system to multilevel inputs.An important condition when using multilevel inputs is

that the number of multilevel inputs used should be equalto the highest polynomial order. This ensures that the algo-rithm works in the presence of any order nonlinear function.Representing (18) in matrix form gives

Rur1 ()

Rur2()

Rurl()

=

1 21

l1

2 22

l2

l 2l

ll

Ruw1 ()

Ruw2 ()

Ruwl()

. (19)

To check the above matrix for singularities, it is dividedinto two matrices as follows:

1 0 0

0 2 0 0

0 0

0 0 l

1 1 21

l11

1 2 22

l12

1 l 2l

l1l

. (20)

The matrix on the left-hand side (LHS) of (20) is clearlynonsingular for m = 0. The matrix on the right-handside (RHS) of (20) is the Vandermonde matrix which has anonzero determinant given by

1i

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1000

500

0

500

1000

1500

Amplitude

1000

500 0 500 1000

Lag

(a) Autocovariance of Walsh code of index 396.

1000

500

0

500

1000

1500

Amplitude

1000 500 0 500 1000

Lag

(b) Autocovariance of Walsh code of index 882.

150

100

50

0

50

100

150

Amplitude

1000

500 0 500 1000

Lag

(c) Cross-covariance of the above two Walsh codes.

Figure 4: Covariance properties of individual Walsh codes of length210 for two different code indices.

that, as more and more users are added, this compound in-put of Walsh codes starts to resemble a white noise-like pro-cess. This is an interesting outcome because it is known thatidentification of the downlink is possible under the condi-tion that the input is white noise-like (see [2, 13]). The au-tocovariance of the input u(n) is shown in Figure 5. There issome resemblance observed between this autocovariance andthat of a PN sequence, given byRxixi () = Nci(). Asidefrom the amplitudes at nonzero lags, the autocovariance ofthe summation of Walsh codes can be approximated by the

1

0

1

2

3

4

5

6

104

Am

plitude

1000 500 0 500 1000

Lag

Figure 5: Autocovariance of a summation of Walsh codes.

relationship3

Ruu() NwN(), (26)

where N is the number of Walsh codes. Applying the aboveapproximation to (23) gives

Ruw1 () =A1NwNNw1m=0

h1(m)(m ). (27)

Using the convolution properties of the impulse functiongives

Ruw1 () =A1NwNh1() (28)

where the estimated CIR can be found by solving the aboveexpression. Therefore, it has been shown that the CIR canbe estimated by utilizing the autocovariance property ofsummed Walsh codes. Using a greater number of Walshcodes results in even better covariance properties and hencea more accurate identification.

4. ESTIMATION: SIMULATION RESULTSAND DISCUSSION

The simulation package used for all simulations hereinwas MATLAB with Simulink. The simulations were per-formed with Figure 3 implemented as a Simulink model. TheSimulink model was used mainly as a means to gather theinput-output data of the system. All the initializations andidentification calculations (i.e., correlations) were performedin MATLAB by sending the Simulink inputs/outputs to theMATLAB workspace.4

3 Under the condition that the code indices for the Walsh codes occupythe entire range of indices available for that certain code length, in equalintervals.

4 MATLAB and Simulink are the trade names of their respective owners.

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4.1. Simulation parameters andchannel characteristics

4.1.1. CIR and polynomial

All CIRs used in the simulations satisfied the property of unitenergy, that is,

n |h(n)|

2 = 1. This ensured no amplification

from the wireless channel.The major source of nonlinearity is the RF amplifier,

which can be modeled using an lth-order polynomial. Anymildly nonlinear system that can be described by an lth-orderpolynomial can be identified using our technique. For exam-ple, in the case of ROF, the polynomial is third-order with asaturating characteristic (see [14, 15]).

4.1.2. Number of users andWalsh code length

Fifty four users were simulated at the base station. Simu-lations were performed with a Walsh code length of 1024(Nw = 210).

4.1.3. Noise

The SNR between the base station and access point was set to25 dB, and the wireless noise power for each mobile user wasset equal to the amplifier noise power.

4.1.4. Cross-covariance

Lang and Chen showed in [16] that, for 10th degree se-quences, the average Walsh code cross-covariances are ap-proximately 2.53 times larger than PN sequence cross-covariances. However, the adverse effect of these cross-

covariances is minimal because they are relatively small whencompared to the large autocovariance value. This can also beseen by comparing Figures 4(c) and 5. From these figures it isfound that the maximum amplitude of the cross-covarianceis approximately 0.208% of the maximum autocovariance.

4.1.5. Quality of fit

The quality of fit of the estimated CIR to the actual CIR wasmeasured by defining a normalized estimation error param-eter

= Lk=0

hactual (k) hest(k)

2

Lmax, (29)

where Lmax is the largest CIR memory amongst all users.Dividing by Lmax makes independent of CIR memory. Asmaller means a better CIR estimate.

4.1.6. Synchronous communication

Synchronization can be achieved for all signals in the down-link. The buffer period needed for the simulation of asyn-chronous communication is not needed. All signals can startat the same time and data is collected from the start of thesimulation to the end (i.e., the time needed to cover one pe-riod, Nw).

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

Amplitude

0 5 10 15 20 25 30 35 40 45

Delay (nTc)

Actual CIREstimated CIR

Figure 6: Poor channel impulse response (CIR) estimate.

0.4

0.2

0

0.2

0.4

0.6

0.8

1

Amplitude

0 5 10 15 20 25 30 35 40 45

Delay (nTc)

Actual CIREstimated CIR

Figure 7: Good channel impulse response (CIR) estimate with = 1.462 104.

4.2. Wireless channel identification

Two CIR estimates are presented in this section, they are de-fined as good and poor. The reason for this is to show thatat this point there is still an inconsistency between estimatesand that the quality of the estimate depends on the charac-teristics of the CIR (a major factor being the spread betweenmultipath arrivals). Note that the linear CIRs have been es-timated in the presence of a nonlinearity. We performed alarge number of trials by varying the gain of each path usingthe Rayleigh fading model. The worst and the best case esti-mation errors from these trials were = 4.241 103 and = 1.462 104. These two cases are shown in Figures 6and 7, respectively. Most of the time was smaller than the

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Channel Equalizernamp(n)

+/

1

nw(n)

x(n)

Basestation

Nonlinearity Wirelesschannel

r(n)F( ) h(n) DFE

q(n) q(n)

Figure 8: Block diagram for downlink equalization.

mean value, which we found gives a reasonably good chan-nel estimate. Note that since there is a greater spread betweenmultipath arrivals in the poor estimate ofFigure 6, the al-gorithm is not so accurate but it is still able to recover thegeneral structure of the desired CIR.

4.3. Nonlinearity identification

Once the CIRs are known, the internal signal q(n) must beestimated so that polynomial fitting can be done between thesignals u(n) and q(n). The accuracy of the nonlinear identi-fication is highly dependent on the CIR estimates and so itis important that the CIR estimation algorithm works well.One possible method to estimate the internal signal is by de-convolving h1,...,N(n) with their respective outputs r1,...,N(n).Estimating the nonlinearity is left for future work.

5. HAMMERSTEIN-TYPE DOWNLINK EQUALIZATION

The downlink has a static nonlinearity followed by a dynamiclinear time dispersive wireless channel. This is a Hammer-

stein system. Although the nonlinear portion of the Ham-merstein system has not been estimated, equalization can stillbe performed on the linear wireless channel of the downlink.The structure of the equalizer is shown in Figure 8. The re-ceiver consists only of a DFE arrangement that compensatessolely for the wireless channel dispersion. Even though thepolynomial is not compensated for, the simulation results ofthe equalization still show a good improvement in terms ofbit error rate (BER). Note that the equalization is done fora single user, but the channel is estimated under a multiuserenvironment. The nonlinearity is common for all the users;however, the wireless channel varies for different users.

The number of DFE taps was derived based on the mem-

ory of the CIR (L was varied from 9 to 13). In order to com-pletely eliminate postcursor interference, the number of FBFtaps must satisfy the condition K2 L [8]. The number ofFFF taps is chosen to be approximately 2L (which is com-mon in the literature). Hence, the DFE parameters for thesimulations were as follows: FFF taps were varied from 18 to26 and FBF taps were varied from 9 to 13.

A large number of error rate simulations were performedand the BER from an average CIRestimate was found. Sim-ulations were also done to find the BER resulting from nottaking the nonlinearity into account during the channel esti-mation process. These two BERs are plotted in Figure 9. Wecan see from this figure that a very good improvement in

10 9

10 8

10 7

10 6

10 5

10 4

10 3

BER

10 15 20 25 30 35

SNR(dB)

Average CIR estimate (nonlinearity not considered)Average CIR estimate

Figure 9: BER of the downlink using the average CIR estimate;this is the most realistic outcome.

the BER can be achieved with the proposed algorithm whichtakes the nonlinearity into account during channel estima-tion.

When the channel has a few strong paths (typical in arural environment with few buildings) the proposed non-linear channel estimation works very well. Figure 10 showsthis best case (when the estimation error is small). Under thisscenario the performance error is even better. An acceptableBER for transmitting data is 106. Our algorithm can achieve

this BER at an SNR of about 25 dB (with the good CIR esti-mate), which is comparable to the DFE BER curves obtainedin [8, 17].

This paper shows the usefulness of an estimation algo-rithm that takes into account the nonlinear nature of thechannel.

6. CONCLUSION

This paper presented a method for identification of the mul-tiuser CDMA downlink using the correlation properties ofWalsh codes. We improved the single user identification per-formed in [2] to accommodate multiple users and we showed

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10 9

10 8

10 7

10 6

10 5

10 4

10 3

BER

10 15 20 25 30 35

SNR(dB)

Good CIR estimate (nonlinearity not considered)Good CIR estimate

Figure 10: BER of the downlink using the good CIR estimate.

the effect of both wireless and RF amplifier noise. It wasshown that using a summation of Walsh codes, as opposed tosingle Walsh codes, makes identification of the Hammersteinsystem possible. In a synchronous CDMA environment, theproposed identification algorithm works well with 54 users,and even better with additional users because the correlationproperty improves. Equalization of the downlink showed aBER of 106 achieved at an SNR of 25dB.

Some concerns regarding the practicality of the estima-tion algorithm arise when considering the effect that mul-tilevel testing has at the system level. However, with powercontrol algorithms used in CDMA systems, the multileveltransmission is inherently done. For example, when a mo-bile unit moves away from the base station, its received powerwill drop; the base station will then increase the transmittedpower (typically in 1 dB steps) until the power is acceptable.So, one of our ideas to overcome this problem of multileveltesting is to record data during the adjustment of power withpower control algorithms. Assuming there is little change inthe wireless channel impulse response while gathering data,this technique can provide the multilevel testing required for

estimation.

REFERENCES

[1] X. N. Fernando and S. Z. Pinter, Radio over fiber for broad-band wireless access, PHOTONS: Technical Review of theCanadian Institute for Photonic Innovations, vol. 2, no. 1, pp.2426, 2004.

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