1.transactions on emerging telecommunications technologies volume 15 issue 3 2004 [doi...

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EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONSEuro. Trans. Telecomms. 2004; 15:173–184 (DOI: 10.1002/ett.964)

Special Issue on Multi-Carrier Spread-Spectrum

Analysis of cellular interference for MC-CDMA and its impacton channel estimationy

Gunther Auer1*, Stephan Sand2, Armin Dammann2 and Stefan Kaiser2

1 DoCoMo Euro-Labs, Landsberger Strasse 312, 80687 Mü nchen, Germany2

German Aerospace Center (DLR), Institute of Communications & Navigation, 82234 Wessling, Germany

SUMMARY

We address the downlink of a cellular multi-carrier CDMA (MC-CDMA) system taking into accountchannel estimation. The system performance in presence of a synchronization mismatch between twointerfering base stations (BS) is analyzed in the way that a mobile terminal receives the perfectlysynchronized signal from the desired BS as well as the signal from one interfering BS with asynchronization offset. It is demonstrated through simulations that spreading and cell specific randomsubcarrier interleaving effectively decorrelates the interfering signal, independent of the synchronizationoffset. Furthermore, the robustness of the channel estimator to cellular interference is examined.Copyright# 2004 AEI.

1. INTRODUCTION

Multicarrier (MC) modulation, in particular orthogonal

frequency division multiplexing (OFDM) [1], has beensuccessfully applied to various digital communications

systems. OFDM can be efficiently implemented by using

the discrete Fourier transform (DFT). Furthermore, for

the transmission of high data rates its robustness in trans-

mission through dispersive channels is a major advantage.

For MC-CDMA, spreading in frequency and/or time direc-

tion is introduced in addition to the OFDM modulation [2–

4]. MC-CDMA has been deemed a promising candidate

for the downlink of future mobile communications systems

[5, 6], and has recently been implemented by NTT DoC-

oMo in an experimental system [7].

Recently, there has been growing interest in applying

an OFDM-based air interface to cellular systems. We

focus on a system which should be robust against inter-

ference, rather than trying to avoid interference, as this

ultimately would require inter-cell synchronization, which

comes along with a significant signaling overhead. This

means that inter-cell interference can be significant, espe-

cially if the system is to operate with high frequency reuse

factor.

For a cellular multicarrier system where adjacent basestations (BS) are not synchronized, the cellular interfer-

ence is generally dependent on the synchronization offset

between interfering base stations. For an unsynchronized

system, the interference observed at a certain subcarrier

stems from all interfering subcarriers. So, the interference

can be modeled as white Gaussian noise. For a perfectly

synchronized system, on the other hand, orthogonality

between subcarriers is preserved and the interference can

be described on the subcarrier level, which may not be

Gaussian. In such a case, spreading, cell specific random

interleaving, and scrambling of subcarriers can be used

to decorrelate the interfering and desired signal [8].

Cellular interference not only corrupts the transmitted

data but also the pilot symbols used for channel estimation.

We focus on pilot-symbol aided channel estimation

(PACE), where pilot symbols are periodically inserted in

the time-frequency grid of the multicarrier signal. Channel

Copyright # 2004 AEI Accepted 20 January 2004

* Correspondence to: Gunther Auer, DoCoMo Euro-Labs, Landsberger Strasse 312, 80687 München, Germany. E-mail: [email protected] paper has been presented in part at the 4th International Workshop on Multi-Carrier Spread Spectrum (MC-SS 2003), Oberpfaffenhofen, Germany.


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estimation is performed exclusively by using the pilot

symbols. Unlike data symbols which can be protected by

means of spreading and/or channel coding, pilots cannot

be protected in such a way. One way to mitigate this pro-

blem is to use a pilot reuse factor being larger than the fre-

quency reuse factor for the data symbols [9]. Such asystem, however, requires full synchronization between

all BSs of the cellular system, which may be difficult to

realize in practice. Therefore, we compare the perfor-

mance of a cellular MC-CDMA system with a pilot and

data reuse factor of one, with a sytem having a data reuse

of one and a pilot reuse of three. To this end, the system

performance of both approaches is investigated in a two-

cell scenario, dependent on the synchronization offset

between two interfering BSs. In Reference [8], the effects

of a synchronization offset were analyzed for a cellular

multi-carrier CDMA (MC-CDMA) system with perfect

channel state information (CSI). In this paper, the effectsof celluar interference are studied in case channel estima-

tion is taken into account.

2. SYSTEM AND CHANNEL MODEL

Figure 1(a) shows the block diagram of a MC-CDMA

transmitter for N u users. The bit stream for each user is

encoded with a convolutional code, bit interleaved by the

outer interleaver Pout, and fed to the symbol mapper. The

symbol mapper for user u assigns log2 M bits to complex-

valued data symbols, d ðuÞ½k , according to different alpha-bets, like PSK or QAM with cardinality M . Each data sym-

bol is spread with a Walsh–Hadamard sequence with a

variable spreading factor L 5 N u. Given the vector,

d½k ¼ d ð1Þ½k ; . . . ; d ð N uÞ½k T, consisting of the k th symbolof all N u users, the spreading operation results in

z

s½k ¼ C L d½k ¼ s1½k ; . . . ; s L ½k ½ T ð1Þwhere C L represents the L

N u spreading matrix. The sys-

tem load of the MC-CDMA system is N u= L and can beadjusted between 1 and 1= L . The spreading operation isused to achieve a multiple access scheme for N u users.

The spreading factor L can be significantly smaller than

the number of available subcarriers N c. In this case each

user may transmit N d ¼ N c= L data streams in parallel.The output of the spreader (1) is grouped into N d blocks,

s‘ ¼ ½sT½‘ N d; . . . ; sT½ð‘ þ 1Þ N d 1T, to yield N c spreadchips per OFDM symbol. Given a MC-CDMA system

having N c subcarriers and a frame length of N frame OFDM

symbols, the block length of the code word of one particu-

lar user is MN frame N c= L bits, which corresponds to N frame N c= L spread blocks s½k per OFDM frame, with04 k < N d N frame.

Generally, the multiple access for an OFDM-based air

interface is very flexible. CDMA can be combined with

FDMA or TDMA, termed M&Q modification in Refer-

ence [10]. To this end, the spread blocks s½k may alsobe assigned to different users, which allows to support a

maximum of N c users per OFDM symbol. Moreover, one

may choose to assign various spreading codes to one user,

in which case one user can use all N c subcarriers. For the

sake of simplicity, we will restrict to a MC-CDMA system

described above, having N u 4 L users, each user transmit-

ting N d ¼ N c= L symbols per OFDM symbol.Subsequently, the spread chips of the ‘th OFDM sym-

bol, s‘, is frequency interleaved by the inner interleaver,

PðmÞin , over one OFDM symbol to maximize the diversity

gain. More specifically, we choose a cell specific random

interleaver for PðmÞin , where m identifies the BS. The purpose

of PðmÞin is twofold: first, by increasing the distance between

adjacent spread symbols a diversity gain is achieved; sec-

ond, the inter-cell interference between adjacent BSs is

randomized. The interleaver produces the output§

X

ðmÞ‘ ¼

PðmÞin ðs‘Þ ¼ h X ðmÞ‘;1 ; . . . ; X ðmÞ‘; N ci

T

ð2Þwhere the interleaved symbol of the ‘th OFDM symbol,at subcarrier i, is denoted by X

ðmÞ‘;i . In order to distinguish

zGiven a matrix X, the operators X, XT, X H and X1 denote the con- jugate complex, transpose, Hermitian transpose, and inverse of X respec-tively.§Variables which can be viewed as values in the frequency domain, suchas X

ðmÞ‘;i , where each entry modulates a certain subcarrier, are written in

capital letters.

Figure 1. Block diagram of the MC-CDMA system; (a) trans-mitter, (b) receiver.

174 G. AUER ET AL.

Copyright# 2004 AEI Euro. Trans. Telecomms. 2004; 15:173–184


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signals from different BSs and to further randomize the

transmitted signal, X ðmÞ‘;i is scrambled by a complex cell spe-

cific random sequence, pðmÞi , to yield

X X ðmÞ‘;i ¼ pðmÞi X ðmÞ‘;i . The

scrambler has cardinality M s and the M s discrete signal

points are chosen according to a PSK constellation. An

inverse DFT (IDFT) with N DFT 5 N c points is performedon each block to yield the time domain signal x

ðmÞ‘;n ¼

IDFTf X X ðmÞ‘;i g. Subsequently a guard interval (GI) having N GI samples is inserted in the form of a cyclic prefix.

After D/A conversion, the signal xðmÞðt Þ is transmittedover a mobile radio channel. The considered MC-CDMA

receiver employs N R receive antennas, all of which are

assumed to be mutually uncorrelated. The signal trans-

mitted from BS m to receive antenna is the convolutionof the time variant channel with the transmitted signal. The

corresponding received equivalent baseband signal with-

out noise can be expressed as

zðm; Þðt Þ ¼ð max

0

hðm; Þðt ; Þ xðmÞðt Þ d ð3Þ

Assuming perfect synchronization and neglecting cellular

interferece for the moment, the received signal of the

equivalent baseband system at sampling instants t ¼½n þ ‘ N symT spl is denoted by

yð Þ‘;n ¼

4 yð Þ½n þ ‘ N sym

¼ zðm; Þ½n þ ‘ N sym þ nð Þ½n þ ‘ N symð4Þ

where nð

Þ½ represents a sample of additive white Gaussian

noise (AWGN), N sym ¼ N DFT þ N GI accounts for the num-ber of samples per OFDM symbol and T spl is the sampling

duration. After sampling and sychronization, the N sym sam-

ples are grouped together into a block. The first N GI samples

representing the guard interval are discarded. A DFT on the

remaining N DFT signal samples is performed to obtain the

output of the OFDM demodulation, Y Y ð Þ‘;i ¼ DFT

y

ð Þ‘;n

.

The last N DFT N c DFT outputs of Y Y ð Þ‘;i contain zero subcar-riers which are dismissed. Subsequently, the cell specific

scrambling sequence is removed, Y ðm; Þ‘;i ¼ pðmÞi Y Y ð Þ‘;i . We

assume the guard interval to be longer than the maximum

delay of the channel max. The received signal after OFDMdemodulation in an isolated cell, i.e. neglecting cellularinterference, is in the form [11]

Y ðm; Þ‘;i ¼ X ðmÞ‘;i H ðm; Þ‘;i þ N ð Þ‘;i ð5Þ

where X ðmÞ‘;i , H

ðm; Þ‘;i and N

ð Þ‘;i denote the transmitted symbol

from BS m having an energy per symbol of E s, the channel

transfer function (CTF) from BS m to receive antenna and AWGN with zero mean and variance N 0 respectively.

2.1. Data detection

The OFDM demodulation is performed independently for

all N R receive antennas. Maximum ratio combining

(MRC) is performed to combine the N R signals. Provided

perfect synchronization and perfect CSI the output of the

MRC unit becomes

Y Y ðmÞ‘;i ¼

X N R ¼1

H ðm; Þ‘;i Y

ðm; Þ‘;i

¼ X ðmÞ‘;iX N R ¼1

H ðm; Þ‘;i

2 |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}

H H ðmÞ2‘;i

þX N R ¼1

H ðm; Þ‘;i N

ð Þ‘;i ð6Þ

where H H ðmÞ2‘;i 2 R accounts for the coherently combined

power of the CTFs. In a practical system, the CSI H ðm; Þ‘;i

is replaced by its estimate ^ H H ð

m;

Þ‘;i . By using MRC receiveantenna diversity provides an N R-fold improvement of

the averge signal to noise ratio (SNR), as well as an addi-

tional N R-fold diversity gain, due to the mutually uncorre-

lated fading assumption.

A block diagram of a MC-CDMA receiver is depicted in

Figure 1(b). Due to frequency selective fading of the multi-

path fading channel and the random interleaving of the

spread chips, the orthogonality of the spreading sequences

cannot be maintained and multiple access interference

(MAI) occurs [12]. Various detection schemes for MC-

CDMA have been proposed in the literature, both linear

and non-linear [10, 12, 13]. An efficient compromisebetween reducing MAI and utilizing the diversity of the

frequency selective channel is the linear minimum mean

squared error (MMSE) detector [14]. Applying the MMSE

criterion to the MRC output Y Y ðmÞ‘;i =

H H ðmÞ‘;i with the constraint

of a one tap equalizer, the linear MMSE detector becomes

^ X X ðmÞ‘;i ¼

Y Y ðmÞ‘;i

H H ðmÞ2‘;i þ 1gc

ð7Þ

where gc denotes the average SNR per subcarrier, which is

gc

¼ N u

L N RE s

N 0for the single transmitter scenario.

The equalized signal sequence of OFDM symbol ‘, X̂XðmÞ‘ ,is subsequently deinterleaved by P

ðmÞ1in . Next, the sub-

block r½k ¼ ½r 1½k ; . . . ; r L ½k T containing symbol k of the N u users is despread

d̂d½k ¼ C H L r½k ¼ d̂ d ð1Þ½k ; . . . ; d̂ d ð N uÞ½k h iT

ð8Þ

yielding the soft decided values, d̂ d ðuÞ½k , corresponding tosymbol d ðuÞ½k . All soft decided values of the desired user

ANALYSIS OF CELLULAR INTERFERENCE FOR MC-CDMA AND ITS IMPACT ON CHANNEL ESTIMATION 175

Copyright # 2004 AEI Euro. Trans. Telecomms. 2004; 15:173–184


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of one frame, fd̂ d ðuÞ½k g, are combined to a serial datastream. The symbol demapper maps the data symbols into

bits, by also calculating the log-likelihood ratio (LLR) for

each bit, which serves as reliability information for the

decoder [15, 16]. According to References [15, 16] LLRs

are the optimum values which can be exploited by aViterbi decoder. The symbol demapper assumes the MAI

of fd̂ d ðuÞk g to be white Gaussian noise with zero mean andappropriately scaled variance [10, 13]. The codebits are

deinterleaved and finally decoded using a soft-in soft-out

channel decoder. We use the Max-Log MAP algorithm

for the channel decoder [17, 18], which is an approxima-

tion of the optimum maximum a posteriori (MAP) sym-

bol-by-symbol detector [19].

2.2. Channel model

We consider a time-variant, frequency selective, Rayleighfading channel, modeled by a tapped delay line with Q0non-zero taps [20]. The channel impulse response (CIR)

is described by

hðm; Þðt ; Þ ¼XQ0q¼1

hðm; Þq ðt Þ ðm; Þq

ð9Þ

where hðm; Þq ðt Þ and ðm; Þq are the complex amplitude and

delay of the qth channel tap. It is assumed that the Q0 chan-

nel taps are mutually uncorrelated and that all tap delays

are within the range

½0; max

. Due to the motion of

the mobile, hðm;

Þq ðt Þ will be time-variant caused by theDoppler effect. The CIR spectrum is band-limited by the

maximum Doppler frequency f D;max. However, the CIR

needs to be approximately constant during one OFDM

symbol, so hðm; Þ‘;q hðm; Þq ðt Þ, t ¼ ½‘T sym; ð‘ þ 1ÞT sym. The

channel of the qth tap, hðm; Þ‘;q , impinging with time delay

ðm; Þq , is a wide sense stationary (WSS) complex Gaussian

random variable with zero mean.

The CTF of Equation (5), is the Fourier transform of the

channel impulse response. Sampling the result at time

t ¼ ‘T sym and frequency f ¼ i=T , the CTF becomes

H ðm; Þ‘;i ¼ H ðm; Þð‘T sym; i=T Þ ¼

XQ0q¼1

hðm; Þ‘;q e

j2p ðm; Þq i=T ð10Þ

where T sym ¼ ð N DFT þ N GIÞT spl and T ¼ N DFTT spl repre-sent the OFDM symbol duration with and without the

guard interval.

The discrete two dimensional (2D) frequency correla-

tion function, E ½ H ðm; Þ‘;i H ðm; Þ‘þ‘;iþi ¼ Rðm; Þ HH ½i;‘, speci-fies the correlation between subcarriers and OFDM

symbols spaced i=T Hz and ‘ T sym sec apart. It is gen-erally assumed that the fading in time and frequency direc-

tion is independent. Thus, Rðm; Þ

HH ½i;‘ can be expressedin the product form

Rðm;

Þ HH ½i;‘ ¼ R0ðm;

Þ HH ½i R00ðm;

Þ HH ½‘ ð11ÞProvided that all channel taps are mutually uncorrelated,

the frequency correlation is determined by

R0ðm; Þ

HH ½i ¼XQ0q¼1

ðm; Þ 2q e j2p ðm; Þq i=T ð12Þ

where ðm; Þ 2q ¼ E ½jhðm; Þ‘;q j2 denotes the average power of

tap q. Assuming Jakes’ model [22], the correlation in time

is described by a Bessel function

R00ðm; Þ

HH

½‘

¼ J 0

ð2p‘ f D;maxT sym

Þ ð13

Þwhere f D;max is the maximum Doppler frequency and J 0ðÞaccounts for a zero-order Bessel function of the first kind.

In the above channel model shadowing is not taken into

account. While shadowing will have effects in a cellular

system, for broad band channels the effects of shadowing

will be reduced as the number of independent fading taps

increases [21]. Furthermore, power control and/or fast cell

selection may further compensate shadowing variations.

2.3. Synchronization offset

For synchronization the following parameters cause distur-

bances in the receiver [23]:

The transmitter carrier frequency oscillators may bemistuned, resulting in a carrier frequency offset, f ,

that can be modeled as a time-variant phase offset

ðt Þ ¼ f t . A carrier frequency offset will causeinter-carrier interference (ICI), i.e. the orthogonality

between subcarriers is lost.

The transmitter time scale is unknown to the receiver.Therefore, the receiver OFDM symbol window control-

ling the removal of the guard interval will usually be off-

set from its ideal setting by a time T , termed symbol

timing offset.

Generally, the received signal having a synchronization

mismatch between transmit BS m and receive antenna can be described by

yð Þðt Þ ¼ e j2p t f ðmÞ zðm; Þðt T ðmÞÞ þ nð Þðt Þ ð14Þwhere zðm; Þðt Þ was defined in Equation (3). It is assumedthat the synchronization offset is the same for all receive

176 G. AUER ET AL.



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antennas. However, the synchronization offset may be

transmitter dependent, since the BSs are assumed to oper-

ate asynchronous. In order to avoid inter-symbol interfer-

ence (ISI) and ICI due to a symbol timing offset, the

following relation must be satisfied

T ðmÞ 4T GI max ð15ÞSo, if the guard interval, T GI, is equal or longer than the

maximum delay of the channel, max, plus the symbol tim-ing offset, T ðmÞ, ISI can be avoided. Requirements for thesymbol time offset are rather relaxed, since the OFDM

symbol duration is N DFT times the sampling duration,

where N DFT is in the order of several hundreds to a few

thousands. After OFDM demodulation, a symbol timing

offset rotates the phase of the received signal, having the

same effect than a time delay induced by the channel [24].

In the absence of ISI (correct timing synchronization),

demodulation of the ‘th received OFDM symbol viaDFT yields [23, 25]

Y ð Þ‘;i ¼ J ðmÞi;i H ðm; Þ‘;i X ðmÞ‘;i þ

X N c1k ¼0k 6¼i

J ðmÞk ;i H

ðm; Þ‘;k X

ðmÞ‘;k

|fflfflfflfflfflfflfflfflffl fflfflfflffl{zfflfflfflfflffl fflfflfflfflfflfflfflffl} ICI

þ N ð Þ‘;i ð16Þ

where

J ðmÞk ;i ¼

1

N DFT e

jpEðmÞk ;i

e jpE

ðmÞk ;i = N DFT

sin

pE

ðmÞk ;i

sin

pE

ðmÞk ;i = N DFT

ð17Þ

accounts for the ICI from subcarriers k to i. The cross-sub-

carrier local frequency offsets are

EðmÞk ;i ¼ f ðmÞT þ k i ð18Þ

For perfect synchronization, f ðmÞ ¼ 0, then Equation (18)simplifies to E

ðmÞk ;i ¼ k i. Hence, the ICI term disappears

and Equation (5) is obtained. The effects of a frequency

offset are: first, a loss of orthogonality between subcar-

riers, resulting in ICI; second, the amplitudes of the DFT

outputs are reduced by approximately sin ðpEðmÞi;i Þ=ðpEðmÞi;i Þ;third, a subcarrier symbol rotation proportional to

EðmÞi;i .

2.4. Assessing the effects of cellular interference

A block diagram of how the cellular interference is mod-

eled is shown in Figure 2. It is assumed that the mobile

terminal is perfectly synchronized with the BS transmit-

ting the desired signal, which is received with an energy

per symbol of E s. The signal from the interfering BS is

received at the mobile with energy per symbol of

E s=E , having a timing offset T ðIÞ and a carrier fre-

quency offset f ðIÞ. So, E accounts for the differencein received signal power between the two interfering

BSs. It is well known that the effects of a carrier frequency

offset for OFDM on the link level are very severe [23, 25,

26]. On the other hand, considering an interfering signal

the situation is somewhat different. Basically, the powerof the interference will not change due to a synchroniza-

tion offset. However, the characteristics of the interference

might depend on the synchronization offset. After sam-

pling at the mobile terminal the received signal at receive

antenna is in the form

yð Þ‘;n ¼ zð0; Þ½n þ ‘ N sym þ n½n þ ‘ N sym

þ expð j2p f ðIÞnT splÞ ffiffiffiffiffiffiffi

E p zð I ; Þ½n nðIÞ þ ‘ N sym ð19Þ

where nðIÞ ¼ T ðIÞ=T spl is the normalized symbol timingoffset, zð0; Þ½ and zð I ; Þ½ from Equation (3) represent thereceived signal of the desired and interfering BS without

noise. Generally, signal components corresponding to the

desired and interfering BS are marked by the superscript

ð0Þ and ð I Þ respectively.In the absence of ISI (correct timing synchronization),

the DFT of yðm; Þ‘;i after descrambling, comprising the

received signal from the perfectly synchronized desired

BS and an interfering signal with a carrier frequency off-

set, is given by

Y ð Þ‘;i ¼ H ð0; Þ‘;i X ð0Þ‘;i þ

1 ffiffiffiffiffiffiffiE

p X N c1k ¼0

J ðIÞk ;i H

ð I ; Þ‘;k X

ðIÞ‘;k þ N ð Þ‘;i ð20Þ

where the ICI term from the interfering BS, J ðIÞk ;i , is

given by Equation (17). The first and second terms in

Equation (20) describe the desired and the interfering

signal respectively.

Due to cellular interference, the carrier to interference

ratio, gc, at the input of the MMSE equalizer from

Figure 2. Block diagram of the cellular MC-CDMA systemsimulator.




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Equation (20) needs to be adujusted according to

gc ¼ N R1E

þ N 0E s

L N u

ð21Þ

2.4.1. Gaussian approximation. A very simple approxima-tion is to model the entire interference as Gaussian noise,

by appropriately scaling the variance of the AWGN term.

By applying the Gaussian approximation (GA) the

received signal after OFDM demodulation in Equation

(20) is approximated by

Y ð Þ‘;i H ð0; Þ‘;i X ð0Þ‘;i þ ð Þ‘;i ð22Þ

where ð Þ‘;i denotes the resulting AWGN term having the

variance 2 ¼ N 0 þ E sE N u L . This model is very simple toimplement, since no information about the interfering

signal apart from the average signal strength is required,which makes it very attractive for system level simulations.

For large synchronization offsets ICI is the major source

of interference, so the Gaussian approximation appears

appropriate. For small synchronization offsets, however,

most interference stems from one subcarrier only, so the

resulting interference is non-Gaussian. Compared to the

received signal of the synchronized system, f ¼ 0 andT ¼ 0 in Equation (20), the Gaussian approximation is justified if Z

ð I ; Þ‘;i is an AWGN process, which implies that

either X ð I ; Þ‘;i or H

ð I ; Þ‘;i are Gaussian. In general this is not the

case, since X ð I ; Þ‘;i is randomly taken from a finite set of

complex values, while H ð I ;

Þ‘;i is Gaussian (for Rayleighfading) but not white, since adjacent subcarriers and

OFDM symbols are strongly correlated. However, in the

considered MC-CDMA system scrambling, random inter-

leaving and spreading decorrelate H ð I ; Þ‘;i . So the Gaussian

approximation is justified if H ð I ; Þ‘;i can be sufficiently

decorrelated.

3. CHANNEL ESTIMATION

Pilot-symbol aided channel estimation (PACE) is based on

periodically inserting known symbols, termed pilot sym-

bols, in the transmitted data sequence. PACE was first

introduced for single carrier systems and required a flat-

fading channel [27]. If the pilot spacing is sufficiently

close, the channel response of data symbols at an arbitrary

position can be reconstructed by exploiting the correlation

of the recived signal. When extending the idea of PACE to

multi-carrier systems, it must be taken into account that

the received signal is correlated in two dimensions, in time

and frequency. For 2D-PACE the pilot symbols are scat-

tered throughout the time-frequency grid, yielding a 2D

pilot grid. A scattered pilot grid is used, for example in

the terrestrial digital TV standard DVB-T. 2D filtering

algorithms have been proposed for PACE, based on 2D

Wiener filter interpolation [28, 29].To describe PACE, it is useful to define a subset of the

received signal sequence containing only the pilots,{

f~ X X ðmÞ~‘‘;~ii g ¼ f X ðmÞ‘;i g, with ‘ ¼ ~‘‘ Dt and i ¼~iiDf . The quantities

Df and Dt denote the pilot spacing in frequency and time,

respectively. If a scattered pilot grid is used, the received

OFDM frame is sampled in two dimensions, with rate

Df =T and DtT sym in frequency and time, respectively. Inorder to reconstruct the signal, there exists a maximum

Df and Dt, dependent on the maximum delay of the chan-

nel, max, and the maximum Doppler frequency f D;max. Byapplying the sampling theorem, the following relation

must be satisfied [29]:

Df max=T 4 bf and Dt f D;max T sym 4 1

2bt ð23Þ

where bf 51 and b t51 denote the oversampling factor in

frequency and time, respectively. According to Reference

[29], a oversampling factor of b f ; bt 2 provides a goodcompromise between performance and overhead due to

pilots.

According to Equation (11), the 2D correlation function

of the channel can be factored into a time and frequency

correlation function, which enables a cascaded channel

estimator, consisting of two one-dimensional (1D) estima-tors, termed two by 1D (2 1D) PACE. The basic idea of 2 1D-PACE is illustrated in Figure 3. First, channel esti-mation is performed in frequency direction, at OFDM

symbols ‘ ¼ ~‘‘ Dt, yielding tentative estimates for all sub-carriers of that OFDM symbol. The second step is to use

these tentative estimates as new pilots, in order to estimate

{As a general convention, variables describing pilot symbols will bemarked with a ~ (‘tilde’) in the following.

Figure 3. Principle of 2 1D pilot-symbol aided channel esti-mation (PACE).

178 G. AUER ET AL.



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the channel for the entire frame [29]. It was demonstrated

in Reference [29], that 2 1D-PACE is significantly lesscomplex to implement with respect to optimum 2D

channel estimation, while there is little degradation in

performance.

Generally, it is of great computational complexity to useall available pilots. Instead, a 2D window of size M f M tcan be slid over the whole time-frequency grid, with

M f < N c= Df and M t < N frame= Dt. Let Y ð Þ‘;i be the symbol

within the received frame to be detected. Then, the sliding

window is placed such that Y ð Þ‘;i is located within the centre

with respect to i and ‘. Only at the beginning and end of theframe, as well as near the band edges, Y

ð Þ‘;i cannot be

placed within the centre of the sliding window.

Channel estimation is performed separately for each

receive antenna . An initial estimate of the CTF atpilot positions is obtained by removing the cell specific

modulation of the pilots, H H ð0; Þ~‘‘;~ii ¼ ~ X X ð0Þ~‘‘;~ii ~Y Y ð Þ~‘‘;~ii , with~ X X

ð0Þ~‘‘;~ii

~ X X ð0Þ~‘‘;~ii

¼ 1.The estimator for 2 1D-PACE can be expressed as

b H H ð0; Þ‘;i ¼ X M tn¼1

W 00n ð‘ÞX M f m¼1

W 0mðiÞ H H ~‘‘þn;~iiþm ð24Þ

where W00ð‘Þ ¼ ½W 001 ð‘Þ; . . . ; W 00 M tð‘Þ represents afinite impulse response (FIR) interpolation filter in time

direction with filter delay ‘ ¼ Dt~‘‘ ‘. The filter in fre-quency direction W0ðiÞ ¼ ½W 01ðiÞ; . . . ; W 0 M f ðiÞdepends on the location of the subcarrier to be estimated,

i, relative to the pilot positions, i ¼ Df ~ii i.The optimal filter in the sense of minimizing the mean

squared error (MSE) is the Wiener filter [30]. The estima-

tors W0ðiÞ and W00ð‘Þ are obtained by solving theWiener-Hopf equation in frequency and time direction

respectively. For the Wiener filter in time and frequency,

the correlation functions (12) and (13) as well as the aver-

age SNR at the filter input, gc of Equation (21), are

required.

3.1. Mismatched estimator

It may be prohibitive to estimate the filter coefficients dur-

ing operation in real time. Alternatively, a robust estimator

with a model mismatch may be chosen [31]. The filters

W0ðiÞ and W00ð‘Þ are designed such that they cover agreat variety of power delay profiles and Doppler power

spectra. According to Reference [31], a rectangular shaped

power delay profile with maximum delay filter and a rec-tangular shaped Doppler power spectrum with maximum

Doppler frequency f D;filter fulfill these requirements. The

Fourier transform of a uniform power delay profile which

is non-zero within the range ½0; filter, yields the frequencycorrelation

R0 HH ½i ¼ T sinðp filter

i=T Þp filter i

e jp filter i=T ð25Þ

Accordingly, the Fourier transform of a uniform Doppler

power spectrum being non-zero within the range

½ f D;filter; f D;filter, yields the correlation in time direction

R00 HH ½‘ ¼ sinð2p f D;filter ‘T symÞ

2p f D;filter ‘ T symð26Þ

It is important to note that the parameters of the robust esti-

mator should always be equal or larger than the worst case

channel conditions, i.e. largest propagation delays and

maximum expected velocity of the mobile user, so filter5 max and f D;filter 5 f D;max. Furthermore, the averageSNR at the filter input, gfilter, which is used to generate the

filter coefficients, should be equal or larger than actual

average SNR, so gfilter5gc. In order to determine the chan-

nel estimator only filter, f D;filter and gfilter are required.

4. SYSTEM SCENARIOS

In case the mobile is near the cell/sector boundary, E in

Equation (19) will be close to one, so the carrier to inter-

ference ratio, gc, for a single antenna receiver approaches0 dB. In order to maintain a reliable connection the system

may not be operated fully loaded, so N u < L . Furthermore,we employ N R receive antennas in order to exploit spatial

diversity and to benefit from an N R–fold SNR gain. How-

ever, to achieve these gains reliable channel estimation is

essential. Moreover, the spectral efficiency is compro-

mised if N u < L for the entire system, even for users whichobserve little interference. This problem can be mitigated

if users are grouped together which are close to the cell

boundaries with 50% load ( N u ¼ L =2) and QPSK modula-tion; other users which experience little interference may

be allocated 100% load and higher order modulation.

Alternatively, a frequency reuse factor of 3 may be used

for outer parts of the cell/sector as suggested in Reference

[32]. Even for such a scheme it is of interest to closely ana-

lyze cellular interference, since the resulting sector

throughput increases if the portion of the sector having a

frequency reuse above one can be kept as small as

possible. In any case, optimization of the throughput per

cell, sector or beam is beyond the scope of this paper.




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Rather the characterization of the cellular interference is of

interest.

Cellular interference not only corrupts the transmitted

data but also the pilot symbols used for channel estimation.

Near the cell boundaries the channel estimation perfor-

mance may deteriorate, which effectively reduces theachievable throughput. One way to mitigate this problem

is to use a pilot reuse factor being larger than the frequency

reuse factor for the data symbols, r p > r d , as suggested inReference [9]. However, for interference free reception of

the pilots, such a system requires full synchronization

within all BSs of the cellular systems, which may be diffi-

cult to realize in practice.

We compare two system scenarios: first, a cellular sys-

tem with a pilot and data reuse factor of one, r p ¼ r d ¼ 1(system A); second, a cellular system with a data reuse of

one, r d

¼ 1 and a pilot reuse of three, r p

¼ 3 (system B).

While the performance of system A will degrade near thecell boundaries due to strong cellular interfence, system B

will be more sensitive to a synchronization offset.

5. SIMULATION RESULTS

The bit error rate (BER) performance of the cellular MC-

CDMA system is evaluated by computer simulations. The

system parameters of the MC-CDMA system and of the

channel model were taken from Reference [7] and are

shown in Table 1. All BSs are using exactly the same sys-

tem parameters, i.e. the same spreading length L , numberof active users N u etc. This implies that if N u decreases, the

cellular interference also decreases. However, the differ-

ence in received signal power between interfering BSs,

E , does remain constant. The channel is modeled by a

tap delay line model with Q0 ¼ 12 taps, a tap spacing of ¼ 16 T spl, with an exponential decaying power delay

profile, as illustrated in Figure 4. The independent fading

taps are generated using Jakes’ model [22], each having a

maximum Doppler frequency of f D;max ¼ 104 T sym, withT sym defined in Equation (10), corresponding to a mobile

velocity of about 3 km/h @5 GHz carrier frequency. For

the parameters of the robust channel estimator, also

depicted in Table 1, we assume that the maximum delay

of the channel, the maximum Doppler frequency and the

average SNR is known to the receiver, so filter ¼ max, f D;filter

¼ f D;max and gfilter

¼ gc. A pilot spacing of Df

¼ 3

in frequency and Dt ¼ 9 in time was used throughout.Thus, System A with r p ¼ 1 has a pilot overhead of about4% compared to an overhead of 12% for System B with

r p ¼ 3.Figure 5 shows the BER against the difference in

received signal power between the two interfering BSs,

E , for various number of users N u. Curves with solid

lines show results for a perfectly synchronized system.

Clearly, the system performance improves with decreasing

system load N u= L , since the multiple access interference(MAI) reduces with decreasing load. An error floor is

observed due to AWGN, which was set to E b=

N 0 ¼10 dB throughout. Results for a system where the cellular

interference was modeled by white Gaussian noise (WGN)

with appropriate variance, i.e. the Gaussian approximation

(GA), are also included in the graph and are drawn with

dashed lines. Generally, results for the GA are better than

Table 1. MC-CDMA system parameters.

Bandwidth B 101.5 MHz# subcarriers N c 769FFT length N DFT 1024Guard interval (GI) length N GI 226Sample duration T spl 7.4nsFrame length N frame 64Spreading Factor L 16Modulation QPSK Channel coding rate r 1/2

Parameters for mismatched channel estimator Pilot spacing freq. & time { Df , Dt} {3, 9}Filter dimension freq. & time { M f , M t} {13, 4}

Figure 4. The power delay profile of the used channel model.

Figure 5. BER versus E @E b / N 0¼ 10dB for a MC-CDMAsystem with different number of users N u and perfect CSI.

N R¼ 1.

180 G. AUER ET AL.



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the fully synchronized system. The reason is, for the linear

MMSE equalizer of Equation (7) the interference term is

assumed to be WGN, which is exactly the case for the GA.

However, it is seen in Figure 5 that the GA curves closely

match the performance of the fully synchronized cellular

system, especially for high system loads. Moreover, itwas reported in Reference [8] that the GA is accurate even

for lower spreading factors. Obviously, if results for the

GA and a perfectly synchronized system are equivalent,

cellular interference with arbitrary synchronization offsets

are accurately modeled by the GA. This is a somewhat

unexpected result since on a link level the MAI of MC-

CDMA cannot be modeled by the GA. Only for the single

user case the difference between GA and the fully synchro-

nized system is more than 0.5 dB. In this case, the interfer-

ing signal of the fully synchronized system is caused by

one user’s signal only. Therefore, the degradation with

respect to the GA increases.Since the GA accurately describes the system perfor-

mance even for a fully synchronized system, the signal

from the interfering BSs is observed as WGN at the

mobile. This means that the interfering signal, Z ð I Þ‘;i ¼

X ð I Þ‘;i H

ð I Þ‘;i from Equation (20), is sufficiently decorrelated

by cell specific interleaving, scrambling and spreading.

Figure 6(a) shows the BER versus E for the consid-

ered MC-CDMA system with half load, N u ¼ 8, having N R ¼ 1 and two receive antennas. Clearly, there is a signif-icant diversity gain if two receive antennas are used. This

is true for any system scenario. It is seen that the difference

between System A and the receiver with perfect CSI forone receive antenna is about 1 dB. It appears that the

degradation of the channel estimator due to interference

is proportional to the overall performance. If the interfer-

ence is high the performance is so poor that the additional

degradation due to channel estimation is not a major pro-

blem. On the other hand, if the interference is low, the pilot

symbols are not corrupted by interference as well. The per-

formance for System B, where the pilots are received with-

out interference, is roughly in-between the curves for

System A and perfect CSI. At high interference levels

the performance of System B is close to the case of

perfect CSI. Clearly, as the interference decreases (E

becomes larger) System B approaches the performance

of System A.

Figure 6(b) shows the BER versus E for a MC-CDMA

system with a synchronization offset between the interfer-

ing BSs and the mobile of f ðIÞ ¼ 0:5=T and nI ¼ 300.With a synchronization offset the performance of System B

remains superior, especially for high interference levels

(E is low). Since, the receiver which utilizes antenna

diversity performs better at low E , this effect is more pro-

nounced with N R ¼ 2. It appears that the interferencelevels at pilot positions of System B are still lower than

for System A. Thus, the synchronization requirements

between two interfering BSs are not as strict as between

the transmitting BS and the mobile receiver. For instance,

on the link level the frequency offset between transmitter

and receiver should not exeed 2–5% of the subcarrier spa-

cing [25]. On the other hand, the frequency offset between

two interfering BSs can be significantly higher than that,

without a degradation in performance.

Note, System B transmits zero subcarriers at a ratio of

2/25, due to the higher pilot reuse. This will result in

decreasing ICI and ISI in case of a synchronization offset,

compared to System A. This should be taken into account

when comparing System A and B.

Figure 7 compares the BER performance between

System A and B for a two antenna receiver, dependent

on the interferer frequency offset f ðIÞT . The time syn-chronization offset was set to zero. All other parameters

Figure 6. BER versus E @E b / N 0¼ 10dB for System A andB with 2 1-D PACE for N R¼ 1 and 2 receive antennas. Part(a): fully synchronized system; part (b): large sync offset( f ðIÞ ¼ 0:5=T ; ðIÞn ¼ 300) between interfering BS andreceiver.




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are the same as in the previous graph. The performance of

the receiver with perfect CSI slightly improves if the fre-

quency offset is in the range 0:2=T 4 f ðIÞ 4 0:6=T . Inthis case, the interference is further randomized.

Generally, the receiver with perfect CSI has the same

performance for f ðIÞT ¼ f ðIÞ ðT þ Þ, where is aninteger. A slight difference occurs as pilot symbols are

transmitted at a larger power than the data symbols. This

is due to the fact that the system is not fully loaded, while

the pilots are transmitted with full power. This causes the

interference level to increase at data subcarriers in case of

a synchronization offset. On the other hand, at the same

time the interference at pilot subcarriers slightly decreases

due to the same reason. As in the considered case the ratio

of pilot to data symbols in one cell is 1=26 the differencebetween f ðIÞT ¼ 0 and 1 is rather small. However, simu-lations with more pilot overhead have shown that the per-

formance slightly degrades for the unsynchronized system.

The performance of System A is rather insensitive to

changes in f ðIÞ. As expected the performance of SystemB depends on the synchronization offset, since for

f ðIÞ ¼ 0 and for f ðIÞ ¼ 1=T the pilots experience noand full interference, respectively. What is interesting, a

frequency synchronization offset for System B has little

effect on the BER as long as f ðIÞ0:5=T , the per-formance of System B approaches System A. The gap

between System A and B for large f ðIÞ is due to the factthat System B is allocated zero subcarriers.

6. CONCLUSIONS

The performance of the downlink of a celluar MC-CDMA

system with 2 1-D PACE has been analyzed.

Particularly, the impact of a synchronization offset

between the interfering BSs and mobile receiver was taken

into account. As long as perfect synchronization between

the desired BS and the mobile receiver is maintained, a

synchronization offset between an interfering base station

and the mobile has little effect on the system performance.Cell specific scrambling and interleaving, as well as,

spreading can decorrelate the cellular interference to a

great extent, such that cellular interference is observed

as white Gaussian noise. In particular, cell specific random

subcarrier interleaving has proven to be very effective.

Cellular interference causes only modest degradation on

the performance of the robust channel estimator, even if

the cellular interference for the pilots is not avoided, i.e.

pilot reuse of one. While a pilot reuse factor larger than

one can mitigate the interference of the pilot symbols, syn-

chronization requirements of the cellular system are more

stringent.

ACKNOWLEDGEMENT

The authors would like to thank Eleftherios Karipidis currently atthe Department of Electronic and Computer Engineering, Tech-nical University of Crete, Greece, for his support in implement-ing the simulation platform.

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AUTHORS’ BIOGRAPHIES

Gunther Auer received his Dipl.-Ing. Degree in Electrical Engineering from Universität Ulm, Germany, in 1996, and his Ph.D. fromthe University of Edinburgh, U.K., in 2000. From 2000 to 2001 he was a research and teaching assistant with Universitä t Karlsruhe(TH), Germany. Since 2001, he is a senior research engineer at NTT DoCoMo Euro-Labs, Munich, Germany. His research interestsinclude multi-carrier based communication systems, multiple access schemes and statistical signal processing, with an emphasis onchannel estimation and synchronization techniques.

Stephan Sand received his M.Sc. degree in electrical engineering from the University of Massachusetts Dartmouth, U.S.A. and the

Dipl.-Ing. degree in communications technology from the University of Ulm, Germany, in 2001 and 2002 respectively. He is currentlyworking toward his Ph.D. at the Institute of Communications and Navigation, German Aerospace Center (DLR), Oberpfaffenhofen,Germany. His main research interests include various aspects of mobile communications and signal processing, such as time-fre-quency methods for signal processing, space-time signal processing, MC-CDMA, channel estimation and multiuser detection.

Armin Dammann received his Dipl.-Ing. degree from the University of Ulm, Germany, in 1997. He is currently working toward hisPh.D. at the Institute of Communications and Navigation, German Aerospace Center (DLR), Oberpfaffenhofen, Germany.

Stefan Kaiser received his Dipl.-Ing. degree and Ph.D. in electrical engineering from the University of Kaiserslautern, Germany, in1993 and 1998 respectively. Since 1993, he is with the Institute of Communications and Navigation of the German Aerospace Center(DLR) in Oberpfaffenhofen, Germany, where he is currently head of the Mobile Radio Transmission Group. In 1998, he was a visitingresearcher at the Telecommunications Research Laboratories (TRLabs) in Edmonton, Canada, working in the area of wireless




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communications. His current research interests include multi-carrier communications, multiple access schemes and space time pro-cessing for mobile radio applications. Dr. Kaiser is co-organizer of the international workshop series on multi-carrier spread spectrum(MC-SS), and he is co-author of the book Multi-Carrier and Spread Spectrum Systems (John Wiley & Sons, 2003) and co-editor of thebook series Multi-Carrier Spread Spectrum & Related Topics (Kluwer Academic Publishers, 2000–2004). He is also guest editor of several special issues on multi-carrier spread spectrum of the European Transactions on Telecommunications (ETT). He is co-chair of the IEEE ICC 2004 Communication Theory Symposium. Moreover, Dr. Kaiser is organizer and lecturer of the seminar series on Wire-

less LANs at the Carl-Cranz-Gesellschaft (CCG) in Oberpfaffenhofen, Germany. He is a senior member of the IEEE and member of the VDE/ITG.


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