Parallel Interference Cancellation in beyond 3G multi-user and multi-antenna OFDM systems

Final Research Project
Parallel interference cancellation in beyond 3G multi-user
and multi-antenna OFDM systems
David Sabater Dinter
May 2003

Universität Kaiserslautern
Fachbereich Elektrotechnik
Lehrstuhl für hochfrequente
Signalübertragung- und Verarbeitung
-Grundlagen der Elektrotechnik-
Prof. Dr.-Ing. habil. Dr.-Ing E.h. P.W. Baier
final research project
Parallel interference cancellation in beyond 3G multi-user
and multi-antenna OFDM systems
David Sabater Dinter
May 2003
Betreuer: Prof. Dr.-Ing. habil. Dr.-Ing E.h. P.W. Baier
Dipl.-Ing. A. Sklavos
Bearbeiter: David Sabater Dinter
c/ Cami de Son Vich, 12
07150 Andratx, Islas Baleares (Spain)

Statement
I hereby assure that I did not use other aid than the ones mentioned within the text to write this
thesis.
Die vorliegende Diplomarbeit wurde von mir selbst¨andig auf Initiative von Herr Dipl.-Ing.
A. Sklavos angefertigt. Bei der Erstellung habe ich mich ausschließlich der angegebenen Hilfs-
mittel bedient.
Kaiserslautern, May 2003
(David Sabater Dinter)

Acknowledgements
Sincere gratitude is expressed to Prof. P. W. Baier for presenting me this great opportunity
in working on such an interesting concept of beyond third generation mobile radio systems.
I would like to thank all the members of the Research Group for RF Communications, Uni-
versity of Kaiserslautern, Germany, who contributed in some way or another in the succesful
completion of this diploma thesis.
I would like to thank the invaluable support received from my supervisor Dipl. -Ing. Alexandros
Sklavos throughout the duration of this project. He helped me to explain perfectly all that I had
thought and to understand deep concepts. Thank You very much for all Alex.
Thanks to Prof. Ignaci Furio of the ”Universidad de las Illes Balears”for bring me the opportu-
nity to work in another country with another people and in a very interesting concept.
Este trabajo se lo dedico a mis padres José y Ute con todo mi cariño, si no fuera por ellos,
yo no estaría aquí, también se lo dedico a mis hermanos Malena, Matías y Patrick, me siento
afortunado por tener una familia así. También para mi abuela Margarita por su confianza y
aprecio. Dankeschön Oma.
Gracias a todos mis amigos de Kaiserslautern, de Mallorca y sur de la península, ya que sin
ellos hubiera sido imposible hacer todo esto. Moltes gràcies a tots.
Kaiserslautern, May 2003
(David Sabater Dinter)

Contents
1 Introduction 1
1.1 Mobile radio systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Evolution of mobile communications . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 First generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.2 Second generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.3 Third generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.4 Beyond 3G mobile radio systems . . . . . . . . . . . . . . . . . . . . 3
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 Objectives of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 OFDM modulation technique 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 History of OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Basic principles of OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Generation of subcarriers using the IFFT . . . . . . . . . . . . . . . . 8
2.3.2 Guard time and cyclic extension . . . . . . . . . . . . . . . . . . . . . 10
2.4 Parameterization of an OFDM system . . . . . . . . . . . . . . . . . . . . . . 13
2.5 OFDM signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

CONTENTS
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II
3 Investigated system 17
3.1 Service area concept versus cellular concept . . . . . . . . . . . . . . . . . . . 17
3.2 Transmission model of uplink transmission . . . . . . . . . . . . . . . . . . . 19
3.3 Subcarrierwise investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Channel models used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.1 Theory of mobile radio propagation . . . . . . . . . . . . . . . . . . . 22
3.4.2 Channels with exponentially fading power delay spectrum . . . . . . . 27
3.4.3 Power control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Non-iterative multiuser detection 31
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Optimum nonlinear detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Linear joint detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5 Parallel interference cancellation 33
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2 General model of PIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.3 PIC with no estimate refinement . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.4 Estimate refinement by hard quantization . . . . . . . . . . . . . . . . . . . . 35
5.5 Estimate refinement by soft quantization . . . . . . . . . . . . . . . . . . . . . 36
6 Performance investigation 39
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.2 Multiuser efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.3 Signal-to-noise ratio degradation . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.4 Spectral radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

CONTENTS
22nd May 2003
III
7 Results 43
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
7.2 Spectral radius of PIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
7.3 PIC performance over one speciﬁc subcarrier . . . . . . . . . . . . . . . . . . 44
7.4 Special case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.5 PIC with improved estimate reﬁnement . . . . . . . . . . . . . . . . . . . . . 54
7.6 PIC performance over all subcarriers . . . . . . . . . . . . . . . . . . . . . . . 57
8 Summary 66
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
8.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
References 68

22nd May 2003
1
1 Introduction
1.1 Mobile radio systems
The elementary target of a mobile radio system is provide seamless and qualitative commu-
nication between mobile users or between mobile users and users of a fixed communication
network, by means of transmission of signals in the radio frequency (RF) band. 100 years ago
G. Marconi managed to set up a radio link across the Atlantic, an accomplishment for which
he was awarded the Nobel prize in 1909. A fact that G. Marconi would probably not have
guessed is that thanks to decisive advances in technology, mobile communications is a radically
changing field, dominantly present in every aspect of worldwide research and economy. Repre-
sentative about this phenomenon is that the number of mobile cellular subscribers will surpass
conventional fixed lines during the first decade of this century as indicated by the forecasts.
In what follows a brief outline of the evolution of the mobile communications will be performed.
1.2 Evolution of mobile communications
1.2.1 First generation
In the 80’s several analogue cellular network came into operation around the world, based on
the cellular concept invented by Bell Labs in 1979 [McD79]. Frequency modulation (FM)
and frequency division multiple access (FDMA) [Pro95] were used. According to FDMA,
active users are separated in the frequency domain, by means of assignment of non overlapping
frequency bands to different users. The first generation of analog cellular systems included the
Advanced Mobile Telephone System (AMPS) in the USA, the Total Access Communication
System (TACS) in Europe, the C-450 system in Germany and Portugal, the Nordic Mobile
Telephones (NMT) in Scandinavian countries and the Nippon Telephone and Telegraph (NTT)
system in Japan [PGH95, Stü01].
1.2.2 Second generation
Parallel to the evolution of mobile communications, decisive progress in digital communications
took place. The increase of the device density in integrated circuits (ICs) and the development
of low rate speech coders spawned the second generation of mobile radio systems. Due to this
fact, the integration of the mobile radio systems in the digitalized Public Switched Telephone
Networks (PSTNs) could be performed more naturally. Another improvement thanks to the dig-
italization was the provision of new services aside from speech, such as data communication. In
contrast to the first generation where FDMA was used, in the second generation Time Division

22nd May 2003
2
Multiple Access (TDMA) and Code Division Multiple Access (CDMA) are used, thanks to the
digital technology CDMA with analog transmission applied in the signal processing techniques
can be used.
In TDMA, the time axis is subdivided in separate non overlapping time slots. Each user is as-
signed a separate slot to transmit and receive information, during which the user uses the whole
available bandwith. Often TDMA can be combined with FDMA. CDMA uses a set of orthog-
onal or quasi-orthogonal codes to spread the information to be transmitted in the frequency
domain. On the receiver, linear filtering with a synchronized replica of the spreading code is
applied to recover the information [Pro95].
With the need of a transition from the multiple standards of many European national radio sys-
tems characterizing the first generation to a Europe-wide standard for the second generation of
mobile radio systems the Groupe Spéciale Mobile (GSM) was established by the Conférence
Européene des Postes et Télécommunications (CEPT) at 1982 which was later renamed to
Global System of Mobile communications [PGH95, OP98]. In 1988, the European Telecom-
munication and Standardization Institute (ETSI) was founded and GSM became the Technical
Comittee Special Mobile Group (TC SMG).
In the United States an important factor considered by the standardization of second generation
mobile radio systems was the need of backwards the compatibility to AMPS due to the large
number of analog handsets already in operation. The Electronic Industry Association (EIA) and
the Telecommunications Industry Association (TIA) adopted the TDMA based Interim Standard
(IS-) 54 [TIA92, PGH95, OP98], also known as US-TDMA or digital AMPS. IS-136 is the
version of IS-54 with a digital control channel, and is the most commonly used term when
referring to US-TDMA. Backwards compatibility to the analog AMPS system was enabled by
the use of the same carrier spacing of 30 kHz.
1.2.3 Third generation
The need for high data rates and spectrum efficiencies as well as for a global standard initiated
in 1992 research and standardization activities for mobile radio systems of the third generation
(3G) [OP98]. The term initially used to describe the 3G systems in International Communica-
tion Union (ITU) was Future Public Land Mobile Telephone System (FPLMTS) which was later
renamed to International Mobile Telecommunication 2000 (IMT-2000) [IMT]. The 3G Partner-
ship Project (3GPP) was initiated in 1998 to coordinate research activities and standardization
around the world. 3GPP does not contribute directly to ITU and is formed by Organizational
partners, such as ETSI (Europe), Association of Radio Industries and Business (ARIB) and the
Telecommunications Technology Association (TTA) (Korea) and T1 (USA). Several companies
take part in 3GPP as market representation partners and other standardization bodies [3GP]. In
Europe, research concerning 3G mobile radio system is known under the term Universal Mobile
Telephone System (UMTS), began in 1990. In 1998, WCDMA was selected for the FDD mode

22nd May 2003
3
and time division CDMA (TD-CDMA) [KB93] for the TDD mode of UMTS. An important
target of the standardization of UMTS is that the bit rates offered should be determined in ac-
cordance with the Integrated Services Digital Network (ISDN) rates. In particular, 144 Kpbs
(rate of 2B+D ISDN channels) is offered with full coverage and supporting full mobility, and
for limited coverage and mobility, 1920 Kbps (rate of H12 ISDN channel) should be available.
1.2.4 Beyond 3G mobile radio systems
As 3G systems already operate in some parts of the world, research activities directed towards
the definition and design of beyond 3G systems have started in many parts of the world and is
far from being immature. With the expected development of new mobile multimedia services in
the coming years, new technical approaches will be necessary for the future mobile communi-
cations systems. Looking the approximately 10 years of time span observed for 2G or 3G from
first research to the deployment of the system, a new air interface and complete network con-
cepts for beyond 3G systems are already being discussed in research since last year 2000. Due
to the new mobile multimedia services, data services will dominate over pure voice services.
Moreover, in the future the allotted frequency bands will be a scarce resource (more expensive
than scarce 50 billion ¤ for 3G in Germany) , the support of high data rates requires system
designs which make optimum use of the assigned frequency spectrum and thus guarantee a high
spectrum efficiency.
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vehicular
pedestrian
stationary
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Mobility
Wireless LAN
Beyond 3G
Data rate [Mbps]
Figure 1.1. General Requirements for Beyond 3G generation mobile communication systems

1.3 Outline of the thesis
22nd May 2003
4
Fig. 1.1 shows that variable and specially high data rates will be requested, which should be
available at a variety of mobility scenarios. Moreover asymmetric data services between up-
and downlink should be supported.
Orthogonal Frequency Division Multiplexing (OFDM) transmission techniques at the physical
layer with interference suppression is considered by the majority of the scientific community to
be the leading the candidate for the beyond 3G mobile radio systems, due to its inherent ability
to mitigate the effects of multipath propagation, which pose a limit at the achievable data rates.
1.3.1 Objectives of the thesis
Concerning wireless transmissions in the air interface of a mobile radio system one can discern
between uplink (UL) and downlink (DL) transmissions, depending on the direction of the in-
formation flow in the wireless links. In the UL, information is sent from the mobile terminals
(MTs) of the mobile subscribers via the air interface of the mobile radio system to the fixed base
stations (BSs). The transmitted information is then properly forwarded from the core network
of the mobile radio system until the desired communication partners are reached. In the DL,
mobile subscribers are the endpoints of communication links and information is transmitted
wirelessly from the BSs to the MTs. To accomplish the bidirectional flow of information in the
air interface, different time or frequency resources are used for the UL and DL transmissions in
a mobile radio system. Time division duplexing (TDD) is used if different time slot groups are
devoted to UL and DL, whereas is different (paired) frequency bands are used for UL and DL,
frequency division duplexing (FDD) is said to be used.
In UL as well as in the DL, the air interface of a mobile radio system is a system consisting of a
multitude of transmitters and receivers. In the UL (DL) the transmitters are the MTs (BSs) and
the receivers the BSs (MTs) of the mobile radio system. In the general case, transmitters and re-
ceivers employ multiple element antennas and the signals impinging at the antenna elements of
each receiver are the signals from all transmitters, along with noise signals, which represent sig-
nals stemming from sources other than the transmitters the mobile radio system. Equivalently,
signals from a single transmitter are received from all receivers. Hence, the channel of a mobile
radio system can be modelled as a linear, time variant multiple input multiple output (MIMO)
channel, in which the inputs are the antennas of the transmitters and the outputs the antennas of
the receivers. The mobile radio system consisting of the MIMO channel, the transmitters and
the receivers is then modelled as a MIMO system, as Fig. 1.2 shows.
In Fig. 1.2 the general case of an air interface of a mobile radio system modelled as a MIMO
system is depicted. Groups of inputs and outputs of the MIMO channel of Fig. 1.2 are bundled
together to indicate the antenna elements of a single transmitter or receiver, respectively. In
some state of the art mobile radio systems, as e.g. in TD-CDMA [Kle96], signals corresponding

22nd May 2003
5
SISO channel
MIMO channel
PSfrag replacements
¢¡¤£
¢¡¦¥
¢¡¨§
© £
© ¥
© §
Figure 1.2. Air interface of a mobile radio system modelled as a MIMO system
to different antenna elements of a single transmitter or receiver are jointly processed. This
joint processing across antenna elements can be generalized to a joint processing across more
transmitters or receivers of the MIMO channel of Fig. 1.2 only if the transmitters or receivers,
respectively, are not spatially separated. In the case of spatial separation there exists normally
no communication possibility between dislocated transmitters or receivers which means that
signals are processed independently by each transmitter or receiver.
Signals from different users should be jointly detected to suppress multiple access interference
(MAI) and increase the spectrum efﬁciency of the mobile radio system, therefore the develop-
ment of a interference suppresion technique must be carried out. State of the art Joint Detection
(JD), is with the employment of the suboptimum joint linear detector, zero forcing (ZF), which
involves inversion of the MIMO channel and can be impractical for large dimensions of the
MIMO system, due to this, special attention deserves the concept of parallel interference can-
cellation (PIC), according to which the MAI is iteratively reconstructed and subtracted from the
received signal.
The Parallel Interference Cancellation (PIC) as joint detector (JD) will be investigated in this
thesis, it will be studied in the context of a multi-user and multi-antenna system, based on
OFDM. Different performance measures will be introduced to assess PIC with different reﬁne-

22nd May 2003
6
ment techniques and to compare the results with ZF detector. Finally a modiﬁed data estimate
reﬁnement technique in PIC detector will be introduced and investigated. All the investigations
will take in account different channel characteristics of the channel.

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2 OFDM modulation technique
2.1 Introduction
2.2 History of OFDM
The concept of OFDM can be better comprehended by looking back to its history. At the end of
the 1960s a parallel data transmission was proposed, system Frequency Division Multiplexing
(FDM) is a technique which was used for analog systems. According to FDM the available
bandwidth is divided into a number of narrower frequency bands, then the spectra do not overlap
and each of the simultaneously active users is assigned one of the non overlapping frequency
bands.
A parallel transmission technique is effective in combatting the effects of amplitude and delay
distortion, and impulse noise because each subchannel occupies a relatively to the whole system
bandwidth. In order to get an efficient use of the available spectrum, the spectra of the different
subchannels are allowed to overlap.
Multicarrier modulation is a technique of transmitting data by dividing the data into several
interleaved, or not, bit streams and use these to modulate several carriers. A special case of
multicarrier modulation with spectra overlap is the OFDM where the carrier spacing is carefully
selected so that each subcarrier is orthogonal to the other subcarriers.
In the 1960s, the OFDM technique was used in several high-frequency military systems such as
KINEPLEX, ANDEFT and KATHRYN.
In 1971, Weinstein and Ebert applied the discrete Fourier transform (DFT) to parallel data
transmission systems as part of the modulation and demodulation process. If DFT is used at the
receiver and correlation values with the center of frequency of each subcarrier are calculated,
the transmitted data with no crosstalk can be recovered.
Moreover, to eliminate the banks of subcarrier oscillators and coherent demodulators required
by frequency-division multiplex, completely digital implementations could be realized on spe-
cially developed hardware performing the fast Fourier transform (FFT), which is an efficient im-
plementation of the DFT. Using this method, if ¢¡ is the number of nonoverlapping frequency
subchannels, both transmitter and receiver are implemented using efficient FFT techniques that
reduce the number of operations from
¥
¡ in DFT to £¡ log £¡ in FFT.
In the 1980s, the application of OFDM was investigated on high-speed modems, digital mobile
communications, and high-density recording. Systems realizing the OFDM technique for mul-
tiplexed QAM using DFT, carrier stabilization, clock frequency control and trellis coding are
also implemented.

2.3 Basic principles of OFDM
22nd May 2003
8
In the 1990s, OFDM was employed for wideband data communications over mobile radio FM
channels, high-bit-rate digital subscriber lines (HDSL, 1.6 Mbps), asymmetric digital subscriber
lines (ADSL, up to 6 Mbps), very-high-speed digital subscriber lines (VDSL, 100Mbps), dig-
ital audio broadcasting (DAB), and high-definition television (HDTV) terrestrial broadcasting
[vNP84].
2.3.1 Generation of subcarriers using the IFFT
An OFDM signal consists of a superposition of subcarriers modulated by constant envelope
modulation such as phase shift keying (PSK) or quadrature amplitude modulation (QAM). Tak-
ing ¡£¢¥¤§¦©¨ as the complex QAM symbols, ¡ as the number of subcarriers,
¡ as the
OFDM symbol duration, and as the carrier frequency, one OFDM symbol starting at ¦ !
can be expressed by
#%$
'¦ (0)
132
465
£
7
8@9
5
1 2
4
8BA 1 2
4
)DCFE
$HGPIRQS$
UTWV
¤YXa`bdc
¡
$
eVfg!hiD¢Wg!qprsprg!tX
¡
#%$
'¦ `b¢uwvxg!€yw‚ƒg!tX
¡ (2.1)
In the literature, often the equivalent complex baseband notation is used, which is given by (2.2).
In this expression, the real and imaginary parts correspond to the in-phase and quadrature parts
of the OFDM signal, which have to be multiplied by a cosine and sine of the desired carrier
frequency to produce the final OFDM signal.
#%$
'¦
1 2
465
£
7
8@9
5
132
4
8@A 1 2
4
)„CFE
$HGPIRQq$
UTWV
¤
¡
$
eVfg!hiD¢eg!qprwprg!€X
¡
#%$
'¦ `b¢uwvƒg!ty…w‚ag!YX
¡ (2.2)
Fig. 2.1 shows the operation of the OFDM modulator specific for QAM data in a block dia-
gram. Fig. 2.2 shows an example of four subcarriers of an OFDM signal. In this example, all
subcarriers have the same phase and amplitude, but in practice the amplitudes and phases may
be modulated differently for each subcarrier. Each subcarrier has exactly an integer number
of cycles in the interval
¡ , and the number of cycles between adjacent subcarriers differs by
exactly one. This property accounts for the orthogonality between the subcarriers. For instance,
if the G
th from (2.2) is demodulated by downconverting the signal with a frequency of †‡ and
then integrating the signal over
¡ seconds, the result is as written in (2.3). In the intermediate
result, it can be seen that a complex carrier is integrated over
¡ seconds. For the demodulated
subcarrier G
, this integration gives the desired output
†
A 1
4 (multiplied by a constant factor
¡ ),
which is the QAM value for that particular subcarrier. For all other subcarriers, the integration

22nd May 2003
9
¢¡¤£¦¥¨§©

§£§©©¡¤©
!$#%§ § ')( !
0 ¥132%§©
¡54 7698A@CBEDGFH6PIQ8RICST¦UWVXT
¡54 76C8)@CBY6`DaFb8dc3Te6PIQ8RICST¦UWVXT
Figure 2.1. OFDM modulator
Time
g replacements
Amplitude
¡gf I
¡
Time
Figure 2.2. Example of four subcarriers within one OFDM symbol
is zero, because the frequency difference $
¤ V
G

f ¡ produces an integer number of cycles within

22nd May 2003
10
the integration interval
¡ , such that the integration result is always zero.
#%$
'¦
¢¡¤£ AF‡
¡£ )„CFE
$
V
GPIRQS$
G
¡
$
WVfg!hi
12
4 5
£
7
8@9
5
132
4
8@A 12
4
)„CFE
$HGPIRQS$
UTWV
¤
¡
$
eVfg!hi¦¥¨§
¦
1 2
465
£
7
8@9
5
1 2
4
8BA 12
4
¡¤£AF‡
¡¤£ )DCbE
$
V
GPIRQq$
G
¡
$
eVfg!hi¦¥¨§ ¦
†
A 132
4
¡ (2.3)
The orthogonality of the different OFDM subcarriers can also be demonstrated in another way.
According to (2.1), each OFDM symbol contains subcarriers that are nonzero over a
¡ -second
interval. Hence, the spectrum of a single symbol is a convolution of a group of Dirac pulses lo-
cated at the subcarrier frequencies with the spectrum of a square pulse that is one for a
¡ -second
period and zero otherwise. The amplitude spectrum of the square pulse is equal to sinc(Q

¡ ),
which has zeros for all frequencies that are an integer multiple of 1/
¡ . This effect is shown in
Fig. 2.2, which shows the overlapping sinc spectra of individual subcarriers. At the maximum
of each subcarrier spectrum, all other subcarrier spectra are zero. Because an OFDM receiver
essentially calculates the spectrum values at those points that correspond to the maxima of indi-
vidual subcarriers, it can demodulate each subcarrier free from any interference from the other
subcarriers. Basically, Fig. 2.3 shows that the OFDM spectrum fulfills Nyquist’s criterium for
an intersymbol interference free pulse shape. The pulse shape is present in the frequency do-
main and not in the time domain, for which the Nyquist criterium usually is applied. Therefore,
instead of ISI, it is intercarrier interference (ICI) that is avoided by having the maximum of one
subcarrier spectrum correspond to zero crossings of all the others.
The complex baseband OFDM signal as defined by (2.2) is in fact the inverse Fourier transform
of £¡ QAM input symbols. The time discrete equivalent is the inverse discrete Fourier trans-
form (IDFT), which is given by (2.4), where time is replaced by a sample number © . In prac-
tice, this transform can be implemented very efficiently by the inverse fast Fourier transform
(IFFT). An point IDFT requires a total of
¥
complex multiplications which are actually
only phase rotations. Of course, there are also additions necessary to do an IDFT, but since
the hardware complexity of an adder is significantly lower than that of a multiplier of phase
rotator, only the multiplications are used here. Then, the IFFT drastically reduces the amount
of calculations by exploiting the regularity of the operations in the IDFT.
#%$
© ¦
2
5
£
7
8B9 8 )„CFE
$GFIUQ ¤©
„¢ (2.4)
2.3.2 Guard time and cyclic extension
One of the most important beneficial characteristics of OFDM is the efficient way it deals with
multipath delay spread. By dividing the input datastream in ¡ subcarriers, the symbol duration

22nd May 2003
11
Amplitude
Time
Figure 2.3. Spectra of individual subcarriers
is made £¡ times larger, which also reduces the multipath delay spread, relative to the symbol
time, by the same factor. To eliminate intersymbol interference almost completely, a guard
time is introduced for each OFDM symbol. The guard time is chosen larger than the expected
delay spread, such that multipath components from one symbol cannot interfere with the next
symbol. The guard time could consist of no signal at all. In that case, however, the problem of
Intercarrier Interference (ICI) would arise. ICI is crosstalk between different subcarriers, which
means they are no longer orthogonal.
This effect is illustrated in Fig. 2.4. In this example, a subcarrier 1 and a delayed subcarrier 2 are
shown. When an OFDM receiver tries to demodulate the ﬁrst subcarrier, it will encounter some
interference from the second subcarrier, because within the FFT interval, there is no integer
number of cycles difference between subcarrier 1 and 2. At the same time, there will be crosstalk
from the ﬁrst to the second subcarrier for the same reason. To eliminate ICI, the OFDM symbol
is cyclically extended in the guard time, as shown in Fig. 2.5. This ensures that delayed replicas

22nd May 2003
12
g replacements
Part of subcarrier #2
causing ICI on subcarrier #1
Delayed subcarrier #2
Subcarrier #1
Guard time FFT integration time = 1/Carrier spacing
OFDM symbol time
Figure 2.4. Effect of multipath with zero signal in the guard time; the delayed subcarrier 2
causes ICI on subcarrier 1 and vice versa
of the OFDM symbol always have an integer number of cycles within the FFT interval, as long
as the delay is smaller than the guard time. As a result, multipath signals with delays smaller
than the guard time cannot cause ICI. As an example of how multipath affects OFDM, Fig. 2.6
shows received signals for a two-ray channel, where the dotted curve is a delayed replica of the
solid curve. Three separate subcarriers are shown during three symbol intervals. In reality, an
OFDM receiver only sees the sum of all these signals, but showing the separated components
makes it more clear what the effect of multipath is. From the figure, It can seen that the OFDM
subcarriers are BPSK modulated, which means that there can be 180-degree phase jumps at
the symbol boundaries. For the dotted curve, these phase jumps occur at a certain delay after
the first path. In this particular example, this multipath delay is smaller than the guard time ,
which means there are no phase transitions during the FFT interval. Hence, an OFDM receiver
”sees”the sum of pure sine waves with some phase offsets. This summation does not destroy
the orthogonality between the subcarriers, it only introduces a different phase shift for each
subcarrier. The orthogonality does become lost if the multipath delay becomes larger than the
guard time. In that case, the phase transitions of the delayed path within the FFT interval of the
receiver. The summation of the sine waves of the first path with the phase modulated waves of
the delayed path no longer gives a set of orthogonal pure sine waves, resulting in a certain level
of interference.

2.4 Parameterization of an OFDM system
22nd May 2003
13
Guard time / cyclic prefix FFT integration time = 1/carrier spacing
OFDM symbol time
Figure 2.5. OFDM symbol with cyclic extension
2.4 Parameterization of an OFDM system
The choice of various parameters of an OFDM system is a tradeoff between various, often
conﬂicting requirements. Usually, there are three main requirements to start with: bandwidth,
bit rate, and delay spread. The delay spread directly dictates the guard time. As a rule, the
guard time should be about two to four times the root-mean-squared delay spread. This value
depends on the type of coding and QAM modulation. Higher order QAM (like 64-QAM) is
more sensitive to ICI and ISI than QPSK; while heavier coding obviously reduces the sensitivity
to such interference.

2.5 OFDM signal processing
22nd May 2003
14
g replacements
First arriving path
Reflection delay
Reflection delay
Guard time
Guard time
FFT integration time
Phase transitions
OFDM symbol time
Figure 2.6. Example of an OFDM signal with three subcarriers in a two-ray multipath channel.
The dashed line represents a delayed multipath component
Now that the guard time has been set, the symbol duration can be fixed. To minimize the signal-
to-noise ratio (SNR) loss caused by the guard time, it is desirable to have the symbol duration
much larger then the guard time. It cannot be arbitrarily large, however, because a larger symbol
duration means more subcarriers with a smaller subcarrier spacing, a larger implementation
complexity, and more sensitivity to phase noise and frequency offset, as well as an increased
peak-to-average power ratio. Hence, a practical design choice is to make the symbol duration
at least five times the guard time, which implies a 1 dB SNR loss because of the guard time.
After the symbol duration and guard time are fixed, the number of subcarriers follows directly
as the requiered -3 dB bandwidth divided by de subcarrier spacing, which is the inverse of the
symbol duration less the guard time. Alternatively, the number of subcarriers may be deter-
mined by the required bit rate divided by the bit rate per subcarrier. The bit rate per subcarrier
is defined by the modulation type, coding rate, and symbol rate.
An additional requirement that can affect the chosen parameters is the demand for an integer
number of samples both within the FFT/IFFT interval and in the symbol interval. The only
solution to this problem is to change one of the parameters slightly to meet the integer constraint.
Until now, how the basic OFDM signal is formed using the IFFT and adding a cycling extension
has been described.

22nd May 2003
15
The system model of an OFDM transmission technique is shown in Fig. 2.7.
The high rate input data stream is divided into many low rate parallel data streams. Each parallel
data stream is then coded using a forward error correcting (FEC) scheme and mapped to a
complex symbol alphabet. Both operations can be done in one module if coded modulation
is applied. These complex symbols are the input for the inverse fast Fourier transform (IFFT)
module which computes the time samples corresponding to the set of parallel subchannels in
frequency. Then a cyclic prefix (CP) is inserted to avoid ISI due to multipath propagation in the
mobile radio channel. Finally, the transmission filter forms the continuous time signal that is
upconverted into high frequency for its transmission over the channel.
At the receiver the received signal is downconverted and sampled to obtain the discrete signal
after the reception filter. The received block is windowed to remove the cyclic prefix and the
samples are converted from time into frequency domain by the FFT module. Then, depending
on the used modulation scheme, the amplitude and phase shifts of each subchannel have to be
equalized and the received complex symbols are inversely mapped and decoded. Finally, the
original serial data stream is obtained.

2.5OFDMsignalprocessing
22ndMay2003
16
IFFT
RECEIVER
Serial
Parallel
Parallel
Serial
mapping
and
Coding cyclic
insertion
prefix
filter
transmission
sampling

filter
reception
(windowing)
removal
prefix
cyclic
FFT
equalization

estimation
channel
remapping

decoding
data
input
data
output
TRANSMITTER
Mobile Radio
Channel
Figure2.7.SystemmodelofanOFDMtransmission

22nd May 2003
17
3 Investigated system
3.1 Service area concept versus cellular concept
Mobile radio systems have to serve a large number of mobile subscribers. To cope with the
problematic regarding the efficient coverage of the theoretically infinite geographical area, the
cellular system invented by Bell Labs in 1979 [McD79] is applied in the mobile radio systems
of the first, second and third generation. According to the cellular system, mobile radio oper-
ators distribute a number of base stations (BSs) over the geographical area of responsibility in
order to accomplish radio coverage. Mobile terminals (MTs) are served by the nearest BS and
the area responsability of each BS is termed cell.
To avoid interference situations between the individual radio links of the MTs of neighboring
cells utilizing the same frequencies, different frequency bands may be assigned to each cell.
However, given the theoretically infinite size of the area to be covered, such a solution would
lead to a waste of resources. In the cellular concept, the frequency band assigned to the mobile
radio operator, is distributed among cells of a particular group, termed cluster and the number
of cells forming a cluster is called cluster size.
As attenuation of electromagnetic waves grows with the distance of propagation, a specific par-
tial frequency band of a cell is reused after a sufficiently large distance, because the interference
between MTs of the two cells using the same frequencies can be considered to be negligible.
In this way, the whole geographical area is covered with clusters of cells. In GSM cluster size
of 4 is used but in 3G mobile radio system (UMTS), unity cluster size is used and the resulting
intercell interference is mitigated by the use of spread spectrum techniques in each cell. Fig. 3.1
shows the architecture of a conventional cellular system. Each cell contains a BS, and the MTs
of each cell communicate solely with this BS. All BSs are connected to a central entity termed
core network in Fig. 3.1, which, in the case of GSM, consists of the base station controllers and
the mobile switching centers [MP92]. The core network can be considered the data source and
data sink in the communication with the MTs.
An alternative air interface architecture to cellular systems are service area (SA) based systems
[WMS
A
02, SWC
A
02, SWC
A
01]. In the SA based air interface architecture, instead of individ-
ual BSs access points (AP) are introduced with groups of such APs being linked to a central
unit (CU). The CUs in their turn are connected to the core network. Each such group defines
a SA, and the MTs of each SA communicate with the SA specific CU via all APs of the SA.
Instead of a number of cells - each with a BS- of a conventional cellular systems we now have
a SA with a number of APs, which are connected to a CU. Fig. 3.2 shows the architecture of a
SA-based system as opposed to the cellular system architecture, shown in Fig. 3.1.
In the UL, the transmit signals of the simultaneously MTs of a SA are received by ¢¡ APs
of the SA and fed to the CU, where they are jointly processed. The aim of this joint processing
consists in exploiting the signal energies received by the £¡ APs of the SA in a optimum way,

3.1 Service area concept versus cellular concept
22nd May 2003
18
PSfrag replacements
core network
BS
MS
cell
Figure 3.1. Conventional cellular system with 12 cells and cluster size 4
C U
C U
c o r e n e t w o r k
S A
A P
M T
C U
Figure 3.2. Architecture of a SA-based system, example with 3 SAs
and in simultaneously combating the impacts of intersymbol interference (ISI) and intra-SA
multiple access interference (MAI). The CU jointly detects the signals radiated by MTs of
the SA and provides the data transmitted by the MTs at its output. This means that in the UL
the CU performs joint detection (JD) [Ver98].
In the DL, each MT of a SA is supported by transmit signals radiated by ¢¡ APs of the SA.
These signals are generated in the CU based on the data for each MT of the SA in such a way
that the transmit signals for each MT have minimum powers and cause minimum interference
at other MTs, and the complexity of the MTs can be kept low. This means that in the DL the
CU performs joint transmission (JT) [MBW
A
00].

3.2 Transmission model of uplink transmission
22nd May 2003
19
The rationale of SA based systems can be applied in both single, that is isolated SAs, and
conglomerates of SAs corresponding to conventional cellular networks. Each CU has to be
connected to a core network, into which- in the case of the UL - the data coming from the MTs
is fed, and which - in the case of the DL - provide the data to be fed to the MTs.
In the case of conventional cellular systems in each cell only the MAI originating in the cell,
that is intracell MAI, can be avoided or mitigated by schemes as JD and JT [Kle96, MBW
A
00].
In the case of a SA-based system, intra-SA MAI, corresponding to the intercell MAI of cellular
systems, is combated by JD and JT, see above. Because in the case of a SA-based system
the SAs are larger than the cells of a conventional cellular system, a larger number of links is
included in the interference mitigation processes, producing an improvement of the spectrum
efficiency.
For the present thesis only UL transmission in a SA based mobile radio system an iterative data
detection algorithm for JD is investigated.
The transmission model of the uplink transmission of the service area based system is explained
with detail in this chapter. As it is explained in section 3.1, a SA consists of simultaneously
active MTs, ¡ APs and a CU, as shown in Fig. 3.3. Each MT utilizes, in the general case, the
whole bandwidth
¡
available to the SA for its data transmissions. The £¡ APs deployed in the
SA, are communicating with all MTs over the MIMO wireless channel. The APs, however,
do not perform any signal processing.
The task of joint processing of the AP signals is assigned to the CU, connected to the ¢¡
APs. It is assumed in the thesis that the APs do not perform signal processing tasks. Instead,
received signals in the UL transmission are forwarded to the CU for processing, and in the
DL transmission, the CU generates AP specific signals which are transmitted from the APs in
the SA. This asymmetric distribution of signal processing tasks between the APs and the CU
is beneficial in terms of cost of deployment as the cost per AP is reduced. Consequently, the
spacial diversity inherent in the SA based system can be cost efficiently increased by installing
a larger number of APs.
The MTs are simple OFDM transmitters using all ¢¡ available subcarriers for their trans-
mission, each transmitting after FEC coding and modulation, complex data symbols
¢
k £¤ ¦¥ ,
©¦ ¨q , compiled into the vector
§ ¢
k¥ ¦
¨

¢
k£
£ ¥ i
¢
k£

¥© ¢ k ¦ ¨q (3.1)
The data vectors
§ ¢
k¥ , k ¦ ¨q , of (3.1) can be compiled to the total data vector
§
¦
¨
§ ¢ £ ¥
§ ¢ § ¥ © ¢ (3.2)

22nd May 2003
20
AP
AP
MT
MT
MT
AP
CU
¡£¢¥¤
¡§¦¨¤
¡§©¤
£ !
#$#§#
Figure 3.3. Service area at uplink transmission, MTs communicating with £¡ APs
containing all ¡ data symbols transmitted from the MTs during UL.
In the general case, the number of data symbols
¢
k £¤ ¥ of (3.1) sent by each MT does not
necessarily equal the number ¢¡ subcarriers. However, the simplifying assumption of
¦ £¡ (3.3)
is made, without loss of generality. Due to (3.3), each MT k sends a single data symbol
¢
k£ n
2
¥ ,
on each subcarrier n¡ , n¡ ¦ ¨S ¡ , i.e., in each subcarrier © ¡ , data symbols are sent
simultaneously.
With the ¡ transfer function matrices
%
¢
k£ k' ¥
¦
()
)
0
12
¢
k£ k' £
£ ¥
`
...
`
12
¢
k£ k' £

2
¥
354
4
6 ¢ k ¦ ¨q ¢ k¡ ¦ ¨q ¡ ¢ (3.4)

3.3 Subcarrierwise investigation
22nd May 2003
21
the total ¡ £¡¡ £¡ transfer function matrix
%
¦
()
)
0
%
¢ £ £
£ ¥

%
¢ § £
£ ¥
...
...
...
%
¢ £ £
§ ' ¥

%
¢ § £
§ ' ¥
3 4
4
6 ¢ (3.5)
describing the MIMO channel of uplink transmission in the SA can be defined.
After transmission through the MIMO channel transfer matrix
%
of (3.5) and superposition of
noise
%¢ , the vector
%£ ¦
% §
X
%¢ (3.6)
contains the complex amplitudes of the received signals by the £¡ APs over all £¡ subcarriers.
The received signals contained in the vector
%£ of (3.4) received by the ¢¡ APs are jointly
processed by the CU to obtain the estimates
¤§
¦
¥ ¤§
¢ £ ¥
¤§
¢ § ¥ §¦
(3.7)
of
§
of (3.2) free from intra-SA interference which resulted from the simultaneous operation
of the MTs at the same bandwidth
¡
. In other words, the CU exploits the spatial diversity
inherent in the MIMO wireless channel of the SA to suppress the interference between the
active MTs [WSC02].
3.3 Subcarrierwise investigation
A significant reduction of complexity of joint detection can be achieved in the SA-based OFDM
system, by defining the n¡ subcarrier specific ¡¨ matrices
%
¢
n
2
¥
¦
()
)
0
12
¢ £ £
£ £ n
2
¥

12
¢ § £
£ £ n
2
¥
...
...
...
12
¢ £ £
§ ' £ n
2
¥

12
¢ § £
§ ' £ n
2
¥
3 4
4
6 (3.8)
Using the matrix of (3.8) the total ¡ £¡© ¢ ¡ transfer function matrix by a reordering of its
elements, takes the blockdiagonal form
%
¦
()
)
)
)
0
%
¢ £ ¥
` `
`
%
¢ ¥ ¥
`
...
...
...
...
` `
%
¢

2
¥
354
4
4
4
6
(3.9)
The block-structure of
%
essentially means that the SA-based OFDM system is equivalent to
£¡ parallel transmission systems each at one subcarrier. Moreover,
%
¢
n
2
¥
of (3.9) describes

3.4 Channel models used
22nd May 2003
22
the MIMO channel of the SA in a specific subcarrier n¡ . Taking profit by the independence of
transmissions at different subcarriers the complexity of the system can be significantly reduced,
because equalization can be performed subcarrierwise.
For this purpose from the received signal vector
%£ of (3.6), the ¡ partial received signal vectors
%£ ¢
n
2
¥ ¦¡ 1¢ ¢ £ £ n
2
¥
1¢ ¢ § ' £ n
2
¥¤£ ¢ n¡ ¦ ¨q £¡€¢ (3.10)
and from the total data vector
§
of (3.6) the ¢¡ partial data vectors
§ ¢
n
2
¥ ¦
¨

¢ £ £ n
2
¥ ¥
¢ § £ n
2
¥ © ¢ n¡ ¦ ¨S ¡€¢ (3.11)
for every subcarrier n¡ , n¡ ¦ ¨S ¡ , are formed [WSC02]. With the channel transfer matri-
ces
%
¢
n
2
¥
of (3.8) describing the MIMO channel at each subcarrier, the partial received signal
vectors
%£ ¢
n
2
¥ of (3.10) and the partial data vectors
§ ¢
n
2
¥ of (3.11), the transmission model of
(3.5) can be rewritten in the subcarrierwise form
%£ ¢
n
2
¥ ¦
%
¢
n
2
¥ § ¢
n
2
¥ X
%¢ ¢
n
2
¥ ¢ n¡ ¦ ¨q ¡€ (3.12)
3.4.1 Theory of mobile radio propagation
During transmission, in the mobile radio channel, the transmitted signal suffers from three
nearly independent effects which are characterized as follows:
¥ Multipath propagation occurs as a consequence of reflections, scattering, and diffrac-
tion of the transmitted electromagnetic wave at natural and man-made objects. Thus, at
the receiver antenna, a multitude of waves arrives from many different directions with
different delays, attenuation, and phases. The superposition of the waves results in ampli-
tude and phase variations of the composite received wave. Due to the mobility of the MT
and moving objects in the mobile radio channel, changes in the phases and amplitudes
of the arriving waves occur, resulting in time-variant multipath propagation. Even small
movements on the order of the wavelength may result in a totally different wave superpo-
sition. The varying signal strength due to time-variant multipath propagation is referred
to as fast fading.
¥ Shadowing is caused by obstruction of the transmitted waves by hills, buildings, walls,
etc., resulting in more or less strong attenuation of the signal strength. Compared to
fast fading, longer distances have to be covered to significantly change the shadowing
constellation. The varying signal strength due to shadowing is called slow fading and can
be described by a log-normal distribution [Par92].

22nd May 2003
23
¥ Path loss predicts how the mean signal power decays with distance from the APs. In
free space, the mean signal power decreases with the square of the distance from the MT.
In a mobile radio channel, where often no direct LOS path exists between the receiver
and transmitter, the signal power typically decreases with a power higher than two and is
typically in the order of three to five [Rap96].
The mobile radio channel is given by the time-variant channel impulse response
2 $¡
¢i or by
the time-variant channel transfer function
1¢ $
Y¢i , which is the Fourier transform of
2 $£
¢i .
The channel impulse response
2 $¡
¢ represents the response of the channel at time due to an
impulse applied at time V

. The mobile radio channel is assumed as a wide-sense stationary
(WSS) random process, i.e., the channel has a fading statistic that remains constant over short
periods of time or small spatial distances. In environments with multipath propagation, the
channel impulse response is composed of a large number of scattered impulses received over
¥¤ different paths,
2 $¡
¢iq¦
5 ¤
7
¤ 9
£§¦
¤u)„CFE©¨
GY$ IRQ
£ X¤R
$¡
V

¤R„¢ (3.13)
where ¦
¤ , £ ,¤ and
¤ are the amplitude, the Doppler frequency, the phase, and the propaga-
tion delay, respectively, associated with the th path. The Doppler frequency
£ ¦!
R
#%$')(10 (3.14)
depends on the velocity
!
of the MT, the speed of light #
, the carrier frequency , and the angle
of incidence 0 ¤ of a wave assigned to the th path.
The description of the correlation functions of the channel impulse response
2 $£
¢i is sufficient
to characterize the fast fading of the mobile radio channel [Bel63]. The autocorrelation function
of
2 $£
¢i is defined as
(
$¡ £ ¢
¥ ¢12 q¦
¨
I4365
2 $¡ £ ¢i
2 7 $£ ¥ ¢i X2 18 (3.15)
Under the presumption that the WSS random processes
2 $¡ £ ¢i
2 $¡ ¥ ¢i are uncorrelated for £
not equal ¥ , called uncorrelated scattering (US), the autocorrelation function (3.15) simplifies
to
(
$¡ £ ¢
¥ ¢12 S¦@9
$¡ £ ¢12 A
$¡ £ V
¥ „¢ (3.16)
where 9
$¡
¢12 is the delay cross-power spectral density [Bel63]. The mobile radio channel
characterized by (3.16) is referred to as WSSUS channel. The fourier transform of 9
$£
¢12 in
2 yields the scattering function [Bel63]
B $¡
¢ S¦
DC
5 C
9
$£
¢12 )„CFE§¨@V
GPIRQ
42 E ¥ $
2 „ (3.17)

22nd May 2003
24
The scattering function is real-valued and provides a measure of the average power output of
the channel as a function of the delay
and the Doppler frequency ) .
By integrating the scattering function
B $¡
¢¡ over the Doppler frequency the delay power
spectrum
9
$¡
¦
C
5 C
¢ $£
¢D W¢ (3.18)
is obtained, which is identical to the delay cross-power spectral density 9
$£
¢12 at 2 equal to
0. The delay power density spectrum gives the average power of the channel output as a function
of the delay
and can be viewed as a scattering function averaged over all Doppler shifts. The
mean delay
, the delay spread £¥¤ , and the maximum delay §¦©¨
are characteristic parameters
of a multipath channel and can be determined from the delay power density spectrum. If the
duration
¡ ! of the transmitted symbol is significantly larger than the maximum delay ¦©¨
, the
channel produces a negligible amount of ISI. This effect is exploited with MC transmission
where the duration per transmitted symbol increases with the number of subcarriers and, hence,
the amount of ISI decreases. Residual ISI can be eliminated by the use of a guard interval, cf.
Section 2.3. The time dispersive properties of multipath channels are most commonly quantified
by their mean delay and the delay spread [Par92]. The mean delay is the first moment of the
delay power density spectrum resulting in

¦
C

9
$¡

C
9
$¡

(3.19)
The normalization with
C
9
$£

is applied because 9
$¡
is not a probability density function.
The delays are measured relative to the first detectable path at the receiver. The delay spread is
the standard deviation of the delay power density spectrum and is given by
£¤6¦
C
$¡
V

¥
9
$¡

C
9
$¡

(3.20)
The coherence bandwidth $
2 of a mobile radio channel is the bandwidth over which the
signal propagation characteristics are correlated and is proportional to the reciprocal of the
delay spread £¤ . The coherence bandwidth can be defined as the bandwidth over which the
frequency correlation function is above 0.5 and, thus, can be approximated by [Rap96, Skl97]
$
2
¨
c£¤
(3.21)
The frequence correlation function is the Fourier transform of the delay power density spectrum
9
$¡
, i.e.,
$
2 S¦
C
5 C
9
$£
b)DCbE©¨BV
GFIUQ
2! #

(3.22)
The channel is said to be frequency selective if the signal bandwidth
¡
is larger than the co-
herence bandwidth $
2 . On the other hand, if
¡
is smaller than $
2 i , the channel is said
to be frequency non-selective or flat. The coherence bandwidth of the channel is of importance
for evaluating the performance of spreading and frequency interleaving techniques that try to

22nd May 2003
25
exploit the inherent frequency diversity ¢¡ of the mobile radio channel. In the case of MC
transmission, frequency diversity is exploited if the separation of subcarriers transmitting the
same information exceeds the coherence bandwidth. The maximum achievable frequency diver-
sity is approximated by the ratio between the signal bandwidth
¡
and the coherence bandwidth
$
2 .
£¡
¨
$
2
¢ (3.23)
and, consequently, depends on the delay spread £ ¤ of the channel, cf. (3.21).
By integrating the scattering function ¤ $¡
¢A over the delay
, the Doppler power density
spectrum
¢
¡¦¥ $
q¦
C
5 C
¢ $¡
¢D

(3.24)
is obtained. The Doppler power density spectrum gives the average power of the channel output
as a function of the Doppler frequency and can be viewed as a scattering function averaged
over all delays. The frequency dispersive properties of multipath channels are most commonly
quantified by the maximum occurring Doppler frequency )¨§© . If in the case of MC transmis-
sion the subchannel spacing is significantly larger than the maximum Doppler frequency §© ,
the channel produces a negligible amount of ICI. The coherence time of the channel $
2 D is
the duration over which the channel characteristics can be considered as time-invariant and is
proportional to the reciprocal of the maximum Doppler frequency. The coherence time can
be defined as the time over which the time correlation function is above 0.5 and, thus, can be
approximated by [Ste94, Rap96]
$
2

¨ Q
§© (3.25)
The time correlation function is the inverse Fourier transform of the Doppler power density
spectrum
¢
¡¦¥ $
. i.e.,

$
2 q¦
C
5 C
¢
¡¦¥ $
b)„CFE©¨
GPIRQ
2 E W (3.26)
If the duration
¡ of the transmitted symbol is larger than the coherence time $
2 ¥ , the channel
is said to be time selective. On the other hand, if
¡ is smaller than $
2 , the channel is said
to be time non-selective. The coherence time of the channel is of importance for evaluating
the performance of FEC coding and interleaving techniques that try to exploit the inherent time
diversity ¡ of the mobile radio channel. Time diversity can be exploited if the separation
between successive time slots carrying the same information exceeds the coherence time. A
number of ! successive time slots create a time frame of duration
¡ ¡ of a time frame and the
coherence time $
2 ,
¡
¡ ¡!
$
2
¢ (3.27)
which, consequently, depends on the maximum Doppler frequency §© of the channel, cf.
(3.25).
A system exploiting frequency and time diversity can achieve the overall diversity
¦ #¡$ ¡ (3.28)

22nd May 2003
26
The system design allow one to optimally exploit the available diversity . For instance, in sys-
tems with MC transmission the same information should be transmitted on different subcarriers
and in different time slots, achieving uncorrelated fading in both dimensions. In MC systems,
a time slot corresponds to an OFDM symbol. Further diversity schemes like space, angle, or
polarization diversity which are not within the scope of this thesis can additionally increase the
overall diversity and are described in [Lee74, Lee93, Rap96, Stü01]. It should be noted that
space diversity, also known as antenna diversity, is a popular form of diversity used in wireless
systems [BPS97].
Several probability distributions can be considered in attempting to model the statistical char-
acteristics of the fading process. A simple and often used approach is obtained from the as-
sumption that there is a large number of scatterer in the channel that contribute to the signal at
the receiver. The application of the central limit theorem leads to a complex-valued Gaussian
process is zero-mean. The magnitude of the corresponding channel transfer function
$
¢ §D ¦
¡£¢
$
¢ §D
¡
(3.29)
is a random variable, for brevity denoted by a, with a Rayleigh distribution given by [Pro95]
$
¦
¦
I
¦
¤
¢ 5¦¥
4¨§©
¢
¦
`b¢ (3.30)
where
¤
¦ 3 5
¡ ¢ $
€¢i
¡
¥
8 (3.31)
is the average power. The phase is uniformly distributed in the interval ¨ `b¢
IRQ
. This channel
is said to be a Rayleigh fading channel and best agrees with the propagation characteristic of
macrocells.
In the case that the multipath channel contains a LOS or dominant component in addition to
the randomly moving scatterer, the channel impulse response can no longer be modeled as
zero-mean. Under the assumption of a complex-valued Gaussian process for the channel im-
pulse response, the magnitude of the channel transfer function has a Rice distribution given by
[Pro95]
$
¦
q¦
I
¦
$
¡ T X Ü
¤
¢ 5
§ !#
5¦¥
4 ¢ § !$
A
£ ¥
§©%

'
I
¦)(
¡ T
$
¡ T X Ü
¤ 0 ¢
¦1
`b (3.32)
The Rice factor ¡ T is determined by the ratio of the power of the dominant path to the power
of the scattered paths at the receiver. The average power
¤
is given according to (3.31) and
%
$
d
is the zero-order modified Bessel function of first kind. The phase is uniformly distributed in
the interval ¨ `b¢
IUQ
¨ . This channel is said to be a Ricean fading channel and best agrees with the
propagation characteristic of micro- and picocells.

22nd May 2003
27
3.4.2 Channels with exponentially fading power delay spectrum
Taking into account the requirements of future mobile radio systems, the European Cooperation
in the field of Scientific and Technical research (COST) in the action point 207, that corresponds
to digital land mobile radio comunications, defined a propagation model for macrocell scenarios
[CHA88]. The philosophy of modeling the mobile radio channel with the COST 207 approach
is related to the physical description of the channel and is based on the implementation of a
discrete multipath scenario [Kai98].
The COST 207 channel models basically determine the various propagation scenarios by con-
tinuous, exponentially decreasing delay power density spectra 9
$£
. Every environment can be
modeled by a number of ¡ discrete paths, where each path has the same amplitude and is
specified by its propagation delay
¤ . Each propagation delay is chosen according to the prob-
ability density function of
within the given interval ¨

¤ £
¦ ¡£¢ ¢

¤ £
¦©¨
. The probability density
function of
is proportional to the delay power density spectrum 9
$¡
. The average power
¤
¤
per path is chosen to be
£§ ¤ , normalizing the power of the channel according to (3.33).
¤
¦
§ ¤7
¤ 9
£ ¤
¤ ¦ ¨ (3.33)
The ¥ are modelled with isotropic scattering, i.e., the angles of incidence 0 ¤ are taken from a
uniform distribution in the interval ¨ `b¢
IRQ
¨ . Each path has a phase ¤ uniformly distributed over
the interval ¨ `F¢
IRQ
¨ .
The channel transfer function implemented by the COST 207 channel models can be written as
% $
n¡ ¦ ¢ © ¡ ¡ !hq¦
¨
§ ¨
§ ¤7
¤ 9
£ )„CFE©¨ © $ IRQ vfc
c iT! $ )(
$
0 p XD p )DCFE©¨@V© IRQ
nF!

p ¢ (3.34)
being n¡ subcarrier number, © ¡ symbol slot number,
¦ ! is subcarrier spacing,
¡ ! the OFDM
symbol duration which includes the guard time duration,
!
, the velocity of the MT, # , the light
velocity, R , the carrier frequency, 0 p, the angle of incidence of a wave assigned to the th path,
p, the phase associated with the th path, and
p, the propagation delay of the path th.
Table 3.1 shows the macrocell environments defined in the COST 207 study.
3.4.3 Power control
In order to asess the performance of the considered SA-based system, the bit error rate (BER)
produced by joint detection will be measured for a given 3
f
ratio, at the input of the CU,
where 3 is the energy per bit at the received signal and f I
is the two sided power spectral
density of the noise at the APs.

22nd May 2003
28
environment ¡ ¤
¤ ¤ 0 ¤

¤ in ¡ s 9
$¡

hilly terrain 100 1-74 0.01 1 ¨ `b¢
IRQ
¨ `b¢
I
0 )
5£¢¥¤ ¦ ¤¨§ §© £
(HT) 75-100 0.01 1 ¨ `b¢
IRQ
¨BÜcF¢
I
` 0 `b¨ )
£ ¦i5 ¤ § §© £
bad urban 100 1-68 0.01 1 ¨ `b¢
IRQ
¨ `b¢Dc 0 )
5 ¤ § §© £
(BU) 69-100 0.01 1 ¨ `b¢
IRQ
¨ cF¢ ¨ ` 0 `F c3)
¦i5 ¤¨§ §© £
typical urban 100 1-100 0.01 1 ¨ `b¢
IUQ
¨ `b¢ 0 )
5 ¤¨§ §© £
(TU)
rural area 100 1-100 0.01 1 ¨ `b¢
IRQ
¨ `F¢ `b 0 )
5£¥¤
¥ ¤ § §© £
(RA)
Table 3.1. COST 207 channel model parameters. The power per path is normalized to
¤
¤…¦
¨
f
¨ , the angles of incidence 0 ¤ are taken from a uniform distribution in the interval ¨ `b¢
IRQ
¨ ,
the propagation delays
¤ are chosen within the given interval ¨

¤ £
¦ ¡£¢ ¢

¤ £
¦©¨
proportional to the
assigned delay power density function 9
$£

To perform such simulations, a well defined 3
f
ratio must be present. Equivalently, it is
assumed that the MTs employ such a power control scheme, that constant 3 is present for a
given channel snapshot. Hence, 3
f
will depend only on the noise power. The received
signal
%£ ¢
n
2
¥ ¦
()
)
)
0
1¢ ¢ £ £ n
2
¥
1¢ ¢ ¥ £ n
2
¥
...
1¢ ¢ § ' n
2
¥
3 4
4
4
6
¦
()
)
)
)
0
12
¢ £ £
£ £ n
2
¥ 12
¢ £ £
¥ £ n
2
¥

12
¢ £ £
§ £ n
2
¥
12
¢ ¥ £
£ £ n
2
¥ 12
¢ ¥ £
¥ £ n
2
¥ ...
...
...
...
12
¢ § ' £
£ £ n
2
¥

12
¢ § ' £
§ £ n
2
¥
354
4
4
4
6

()
)
)
0

¢ £ £ n
2
¥

¢ ¥ £ n
2
¥
...

¢ § £ n
2
¥
3 4
4
4
6
at the ¡ APs at a specific subcarrier n¡ can be written as superposition of partial received
signals
%£ ¢
n
2
¥ ¦
()
)
)
)
0
12
¢ £ £
£ n
2
¥
12
¢ ¥ £
£ n
2
¥
...
12
¢ § ' £
§ £ n
2
¥
3 4
4
4
4
6

%! ¢ § £ n
2
¥

¢ £ n
2
¥ ¢ k ¦ ¨q ¢ (3.35)
each corresponding to a certain data symbol

¢ £ n
2
¥
.
With the assumption of QPSK, i. e.,
1

¢ £ n
2
¥$# 1

¢ £ n
2
¥
¦
I
¢ k ¦ ¨q ¢ ¢ n¡ ¦ ¨q £¡€¢ (3.36)

22nd May 2003
29
then with
%£ ¢
n
2
¥ and
%! ¢ § £ n
2
¥
of (3.35) and with (3.36), the received energy
¢ ¥ ¦
¨
I
¡£¢ %£ ¢
n
2
¥ #¥¤ %£ ¢
n
2
¥ ¦ ¦
¨
I
¡£§

¢ £ n
2
¥ # %! ¢ £ n
2
¥ #¨¤ %! ¢ £ n
2
¥

¢ £ n
2
¥©
¦
¡ § %! ¢ £ n
2
¥ #¨¤ %! ¢ £ n
2
¥ © ¢
(3.37)
corresponding to a single data symbol
¢ £ n
2
¥ , depends on the energy scaling induced by the
channel. Thus, if channel columns of channel matrix is normalized as
¢ ¥ ¦
¡ § %! ¢ £ n
2
¥ #¥¤ %! ¢ £ n
2
¥ © ¦ ¨ (3.38)
a well deﬁned received energy per QPSK modulated data symbol
¢
k£ n
2
¥ is obtained. Mathemat-
icaly seen, (3.38) is totally equivalent with having an arbitrary value for
¡§ %! ¢ £ n
2
¥ #¨¤ %! ¢ £ n
2
¥ ©
and scaling the transmitted data symbols in order to obtain the desired received energy
¢ ¥ ,
i.e., with the real-world power control.
Two methods of normalization are applied in the present thesis:
¥ Normalizing to one, i.e.,
%! ¢ £ n
2
¥ #¥¤ %! ¢ £ n
2
¥
¦
¡ § %! ¢ £ n
2
¥ #¨¤ %! ¢ £ n
2
¥ © ¦ ¨¢ k ¦ ¨q ¢ n¡ ¦
¨q £¡ , in this case fast power control at the MT occurs and means 3
f
is the real
3
f
.
¥ Normalizing in average energy one, i.e.,
¡ § %! ¢ £ n
2
¥ #¥¤ %! ¢ £ n
2
¥ © ¦ ¨¢ k ¦ ¨q ¢ n¡ ¦
¨q £¡ , slow power control and 3
f
is the 3
f
averaged over all £¡ channels
experienced by the ¡ data symbols
§ ¢ § £ n
2
¥ .
In this way a comparison of
versus 3
f
can be applied.

22nd May 2003
30
50 100 150 200 250 300 350 400 450 500
0
0.5
1
1.5
2
2.5
3
3.5
k=1
k=2
k=3
k=4
PSfrag replacements
12
¢¡
£ k£ n
2
¥$#
¢
12
¢¡
£ k£ n
2
¥
© ¡
Figure 3.4.
12
¢¡
£
£ n
2
¥$#
¢
12
¢¡
£
£ n
2
¥
normalization using averaging over all ¢¡ subcarriers,
£
¦
¤
¢ ¡ ¦ cP¨
I

22nd May 2003
31
4 Non-iterative multiuser detection
4.1 Introduction
The detection process at the CU should be carried out jointly for the ¡ data symbols
¤§
¢
k£ n
2
¥
¢ k ¦ ¨S ¢ n¡ ¦ ¨q £¡ , of the MTs. Depending on the optimization criterion,
based on the system model of (3.6), different JD techniques can be applied. In this chapter, var-
ious possibilities for the JD algorithm are presented. It turns out that the overall optimum non
linear maximum a posteriori (MAP) detector is applicable in the described SA based mobile
radio system, as its complexity is reduced due to the subcarrierwise equalization. Complexity
of JD can be further reduced by applying suboptimum linear JD algorithms.
4.2 Optimum nonlinear detection
The optimum nonlinear detector in the subcarrierwise system model for the CU exploits the
knowledge of the employed modulation alphabet to deliver the estimated vector
¤§
¢
n
2
¥
¡£¢ ¦
¥¤§¦ ¨
C
© n
2
¢ $ § ¢
n
2
¥ ¡ %£ ¢
n
2
¥ ¦ ¢ n¡ ¦ ¨q £¡€¢ (4.1)
according to the maximum a posteriori (MAP) principle. If all data vectors
§ ¢
n
2
¥
§
are
equiprobable, then the optimum detector is the one following the maximum likelihood vector
estimation (MLVE) principle and producing the estimated vector [WSC02]
¤§
¢
n
2
¥
¡£!#%$ ¦
¥¤§¦ ¨1
C
© n
2 %
¢ $ %£ ¢
n
2
¥ ¡ § ¢
n
2
¥ ¦ ¢ n¡ ¦ ¨q ¡€ (4.2)
Expression (4.2) for the MLVE detector can be simpliﬁed to the form
¤§
¢
n
2
¥
¡£!'%$ ¦
¥¤§¦ ¨)(10
© n
2
¢32 %£ ¢
n
2
¥ V
%
¢
n
2
¥ § ¢
n
2
¥ 2 ¥
¦ ¢ n¡ ¦ ¨q £¡€¢ (4.3)
in the case that the superimposed noise at the APs is Gaussian.
4.3 Linear joint detection
Linear JD algorithms can be used to estimate
§ ¢
n
2
¥ with a lower complexity than the optimum
MLVE detector of (4.3) in the same subcarrierwise transmission system model, in a linear way
from the received signal
%£ ¢
n
2
¥ , since optimum detector with subcarrierwise involves exhaustive
searches among a set of
§
possible data vectors
§ ¢
n
2
¥ .
Due to the fact that the a priori knowledge concerning the data symbols
§ ¢
n
2
¥ is not exploited by
linear JD schemes, linear detectors are inherenty suboptimal sacriﬁcing system performance for

4.3 Linear joint detection
22nd May 2003
32
a lower complexity detection. Depending on the chosen criterion for the data estimates
¤§
¢
n
2
¥
,
different linear detectors can be designed.
The most simple suboptimum receiver consists of a bank of ﬁlters (MF), matched on the MIMO
channel transfer matrix
%
of (3.4), yielding the estimates as
¤§
¢
n
2
¥
¡ ¡ ¦
¨
¥ ( ¥¦
¨ %
¢
n
2
¥ #¨¤ %
¢
n
2
¥ © ©
5
£ %
¢
n
2
¥ #¥¤ %£ ¢
n
2
¥ ¢ (4.4)
which is inefﬁcient for the multiuser case, because interference is treated as noise [KKKB96].
In the case of absence of noise, the expression of (4.4) will be
¤§
¢
n
2
¥
¡ ¡ ¦
¨
¥ ( ¦
¨ %
¢
n
2
¥ #¥¤ %
¢
n
2
¥ © ©
5
£ %
¢
n
2
¥ #¥¤ %£ ¢
n
2
¥
¦
¨
¥ ( ¥¦
¨ %
¢
n
2
¥ #¨¤ %
¢
n
2
¥ © ©
5
£ %
¢
n
2
¥ #¥¤ %
¢
n
2
¥ §
¢ (4.5)
where
%
¢
n
2
¥ #¥¤ %
¢
n
2
¥
is, in the general case, a non diagonal matrix and then there will be inter-
ference between different data symbols
§
, as
¤§
¢ £ n
2
¥
¡ ¡ ¦
¦
£ § ¢ £ £ n
2
¥ X
¦
¥ § ¢ ¥ £ n
2
¥ X UX
§ ¢ ¡
£ n
2
¥ X X
¦
§ § ¢£¢
£ n
2
¥ ¢ (4.6)
with ¦
, k ¦ ¨S , being the complex elements of k-th row of
%
¢
n
2
¥ #¨¤ %
¢
n
2
¥
, and the non zero
contributions of ¦
¥¤ ¢
£§¦
¦ ¨©¨¨¨ ¢
£¦
¦
£
, in (4.6) represent interference.
If the minimal distance
2 %£ V
%
¢
n
2
¥ ¤§
¢
n
2
¥ 2
is the target criterion which the linearly obtained
candidate estimated vector
¤§
¢
n
2
¥
must satisfy and in (3.5) additive white noise
%¢ with correlation
matrix [WSC02] %
¦ £
¥
(4.7)
is assumed, then the zero-forcing (ZF) detector
¤§
¢
n
2
¥

¡ ¦
¥ %
¢
n
2
¥
7

%
¢
n
2
¥ ¦ 5
£
%
¢
n
2
¥
7
%£ ¢
n
2
¥ (4.8)
results, which totally suppresses the interferences between active MTs at the expense of a noise
enhancement.

22nd May 2003
33
5 Parallel interference cancellation
5.1 Introduction
The task of the CU in the uplink JOINT [WMS
A
02] is to remove the intra-SA interference
resulting from the simultaneous operation of the MTs by jointly processing the received signals
of the APs. Various algorithms can be employed to perform the JD process at the CU, such as
ZF detection [SWC
A
02] or optimum MLVE detection [WMS
A
02]. Therefore, the application
of alternative detection techniques for the elimination of the intra-SA interference of reduced
complexity due to exhaustive searches among a set of
§
data vector
¤§
¢
k¥
, is well motivated
and suboptimum non-linear detectors can be employed, which iteratively subtract the approx-
imatively reconstructed intra-SA interference from the received signal. Such a detector is the
parallel interference canceller (PIC), the principles of which are described in the next section.
As described in section 3.3 subcarrierwise equalization may be employed for the JD process
which is indeed highly beneficial in terms of computational complexity for linear detectors such
as ZF involving matrix inversion. Moreover, the complexity reduction makes the application
of the optimum non-linear MLVE detector possible, as shown in Section 4.2. However, no
significant complexity reduction can be achieved with subcarrierwise equalization in the case
of PIC. Therefore, PIC will not be performed subcarrierwise.
5.2 General model of PIC
The system model considered is the service area of JOINT at uplink transmission [SWC
A
02].
According to the principle of JOINT, the signals received
%£ of (3.6) at the various APs will be
jointly processed at the CU.
Instead of working with the received signal
%£ , the scaled estimates of matched filter output
%
¦
¨
%
¢ £ ¥ ¤
%
¢ § ¥ ¤ © ¢ (5.1)
with
%
¦
% 7

%£ ¢ (5.2)
can be used, as it is a set of sufficient statistics for
%£ [For72].
Every element
1¡
¢
k£ n
2
¥ , k = 1... ¢ n¡ ¦ ¨q £¡ , of
%
of (5.2) contains in the noise free case,
aside from the useful signal energy from MT k, at subcarrier n¡ energy portions of signals
belonging to the other active MTs giving rise to intra-SA interference.

5.2 General model of PIC
22nd May 2003
34
The principle of block parallel interference cancellation (PIC) is illustrated in Fig. 5.1. In each
iteration ¦ ¨H
, after processing with the forward path matrix
%
¦
¨
¥ ( ¦
¨ % 7

% © ©
5
£
¢ (5.3)
the inter-SA interference is approximately reconstructed with the feedback matrix
%
¦ ¥ ( ¥¦
¨ % 7

% © (5.4)
and subsequently substracted from
%
of (5.2). In (5.4) the operator ¥ ( ¥¦ $
is used on a square
matrix and returns a matrix with the off-diagonal elements of its argument.
filter bank
matched
estimate refinement
and
decoding
¡
¢
¡
£
¤
¤
¥ ¦¨§©
¤
¤
¥ ¦¨§ ¤

¦§

Figure 5.1. General model of iterative detection
Target of the estimate refinement and decoding block in Fig. 5.1 is to produce refined estimates¤¤§ $
Y of the data symbol estimates
¤§ $
Y at each iteration of the PIC detector so that MAI can
be more efficiently reconstructed and subtracted from the MF estimates
%
of (5.2). Moreover,
the estimate refinement and decoding block demodulates and evaluates the forward error coding
(FEC) code of the data symbol estimates
¤§ $
Y of each iteration producing estimates
¤!
(p) of
the uncoded data bits !
.

5.3 PIC with no estimate refinement
22nd May 2003
35
5.3 PIC with no estimate refinement
The most primitive case regarding estimate refinement, is not to apply any estimate refinement
at all, as Fig. 5.2 shows.
demod
filter bank
matched
FEC

¡
¢
£
¢
¤
¥
¥
¦ §©¨
¥
¥
¦ §©¨ ¥

§©¨

!#%$')(0213046578905@
Figure 5.2. Iterative detection with no estimate refinement
In each iteration, the refined estimates
¤¤§ $
€ ¦
¤§ $
Y (5.5)
of
§
are present at the output of the estimate refinement block.
5.4 Estimate refinement by hard quantization
A first step towards the enhancement of the PIC detector with no refinement, is to exploit knowl-
edge concerning the modulation alphabet of the data symbols

¢
k£ n
2
¥ (5.6)
The a-priori knowledge of (5.6) can be exploited at the CU to refine the estimates
¤§ $
Y gained
at each iteration by applying hard quantization on the continuous valued estimates
¤§ $
Y with

5.5 Estimate refinement by soft quantization
22nd May 2003
36
respect to the symbol constellation , as
¤¤§ $
Yq¦
¥¤§¦ ¨ ( 0
© 132
¢ ¡ ¡ ¤§ $
€eV
§ ¡$¡
¥
¦ (5.7)
As Fig. 5.3 shows, the data symbol estimates
¤§ $
Y of each iteration are quantized to the
modulation constellation used.
demod
FEC

¡

¢
£
£
¤ ¥§¦©¨
£
£
¤ ¥§¦ £

¥¦

!$#%('0)21
354
#)26879!A@0B
)DCE#GFHI!$#G)P6Q)
3
@R)2S)D@T#
Figure 5.3. Iterative detection with hard estimate refinement
In order to improve the basic estimate refinement by hard quantization which consits in a inner
sign function, a estimate refinement by soft quantization is introduced, justified on the basis that
it minimizes mean-square error.
The optimal nonlinear PIC detector, shown in Fig. 5.4, with respect to the error
¡ § ¨

¢
k¥U V
¢
k¥U
©
¥
© ¦
¨

¢
k¥U V
¡ ¢
¢
k¥U
¡

¢
k¥U ¦ ©
¥
XWV
¥¤ ¢
¢
k¥U
¡

¢
k¥U ¦ ¢ (5.8)
where ¦ ¨ ¨¨¨
represent the number of bits of the data symbols
¤§
¢
k¥
, transmitted per each
MT ¢ k ¦ ¨q , is explained in this section.

22nd May 2003
37
The error
¡ § ¨

¢
k¥U V
¢
k¥U
©
¥
© of (5.8) becomes minimal if the reﬁned estimates

¢
k¥U ¦
¡ ¢
¢
k¥U
¡

¢
k¥U ¦ ¢ (5.9)
are produced by the PIC detector. Because
¢
k¥U

5 V¨¢ ¨ 8%¢ k ¦©¨q ¢ ¦ ¨S
, the
log-likelihood ratios
¢
¢
k¥U
¡

¢
k¥U ¦ ¦¢¡0
(
0
£ ¨

¢
k¥U ¦ X ¨
¡

¢
k¥U
©
£ ¨

¢
k¥U ¦ V§¨
¡

¢
k¥U
©
3
6 ¢ (5.10)
of the a-posteriori probabilities
£ ¨

¢
k¥U ¦¥¤ ¨
¡

¢
k¥U
© , of the modulated bits
¢
k¥U , can be used,
which can be expressed depending on the log-likelihood ratios
¢

¢
k¥U
¡

¢
k¥U ¦ , of the conditional
probabilities
£ ¨

¢
k¥U
¡

¢
k¥U ¤ ¨
© , of the estimates

¢
k¥U and on the log-likelihood ratios
¢
¢
k¥U ¦ ,
of the a-priori probabilities
£ ¨

¢
k¥U ¦¥¤ ¨
© , of the modulated bits
¢
k¥U , as
¢
¢
k¥U
¡

¢
k¥U ¦ ¦¢¡0
(
0
£ ¨

¢
k¥U
¡

¢
k¥U ¦ X ¨
©
£ ¨

¢
k¥U
¡

¢
k¥U ¦ V¨
©
3
6

¢

¢
k¥U
¡

¢
k¥U ¦
X¦¡0
(
0
£ ¨

¢
k¥U ¦ X ¨
©
£ ¨

¢
k¥U ¦ V¨
©
3
6

¨§
¢
k¥U©
(5.11)
With (5.10), and assuming that all
¢
k¥U ¢ k ¦ ¨q ¢ ¦ ¨q
, are equiprobable, i.e.
§
¢
k¥U© ¦ ` (5.12)
holds, using (5.11), (5.12) and
£ ¨

¢
k¥ ¦ X ¨
¡

¢
k¥ © ¦
)„CFE©¨
¢

¢
k¥U
¡

¢
k¥U ¦
)„CFE©¨
¢

¢
k¥U
¡

¢
k¥U ¦ X ¨
¦
)„CFE©¨
¢

¢
k¥U
¡

¢
k¥U ¦ f I

)„CFE§¨
¢

¢
k¥U
¡

¢
k¥U ¦ f I
Xa)„CFE©¨BV
¢

¢
k¥U
¡

¢
k¥U ¦ f I

(5.13)
£ ¨

¢
k¥ ¦ V¨
¡

¢
k¥ © ¦
¨
)„CFE©¨
¢

¢
k¥U
¡

¢
k¥U ¦ X ¨'
¦
)DCbE©¨BV
¢

¢
k¥U
¡

¢
k¥U ¦ f I

)„CFE©¨
¢

¢
k¥U
¡

¢
k¥U ¦ f I
PX )„CFE©¨BV
¢

¢
k¥U
¡

¢
k¥U ¦ f I

(5.14)
(5.9) becomes

¢
k¥U ¦ § ¥0
(
0
¢

¢
k¥U
¡

¢
k¥U ¦
I
3
6 ¢ k ¦ ¨q ¢ ¦ ¨q
(5.15)
To calculate the reﬁned estimates

¢
k¥U as in (5.15), the log-likelihood ratios
¢

¢
k¥U
¡

¢
k¥U ¦ , i.e.,
the probabilities
£ ¨

¢
k¥U
¡

¢
k¥U ¦¥¤ ¨
© , need to be calculated. To accomplish such a task, it is

22nd May 2003
38
assumed that additive white gaussian noise
1
©¡ with mean value ¡ ¦ ` and variance £
¥
is
superimposed at the demodulated bits
¢
k¥U giving rise to noisy estimates

¢
k¥U ¦
¢
k¥U X
1
©¢ ¢ ¦ ¨q
¢ k ¦ ¨q (5.16)
Due to (5.15) each estimate

¢
k¥U is also gaussian distributed with mean value
¢
k¥U and variance
£
¥
. With the probability distribution functions
E
¨

¢
k¥U
¡

¢
k¥U ¦ ¤ ¨
© ¦
¨
§ IRQ
££
)„CFE
¥
V
¨
IRQ
£
¥

¨

¢
k¥U¥¤ ¨
©
¥
¦ (5.17)
of

¢
k¥U and the corresponding probabilities
£ ¨

¢
k¥U
¡

¢
k¥U ¦¥¤ ¨
© , the reﬁned estimates

¢
k¥U ¦ § 0
'
I

¢
k¥U
£
¥

0 ¢ k ¦ ¨S ¢ ¦ ¨q
¢ (5.18)
can be calculated from (5.15).
Clearly, the assumption of the white and gaussian nature of
1
©¦ is not close to reality, but it
helps to considerably simplify expressions and on the other hand, the errors produced by this
assumption have only a marginal impact on the performance of the PIC detector.
estimation
demod
mod
filter bank
matched
FEC
§©¨
!#%$' (0)21'3!4
56 57
889 4@BADCE 8F 4@G889 4@G
HI
HP
Q (!R)2STE QVUWQYX Q S Q '
$
`§ ¨
acbed `fhg2iqprtsfhg2iuprwv
Figure 5.4. Iterative detection with soft estimate reﬁnement

22nd May 2003
39
6 Performance investigation
6.1 Introduction
The main performance measure of interest in digital communications in general, is Bit Error
Rate (BER) of the data detection algorithms measured with respect to the Signal-to-Noise Ratio
(SNR), which depends on the transmission power, noise, and MAI, present at the input of
the data detector. In addition, another performance measures can be used to analyze, design
and understanding of the various detectors. Spectral radius in the case of PIC and multiuser
efﬁciency are introduced in this chapter for the study of the performance of JD in OFDM uplink
transmission with different detection techniques.
6.2 Multiuser efﬁciency
In wireless communication channels, the transmitted signal is corrupted by noise and by com-
munications between other MTs and APs. In the case of multiuser detection when more than
one MT are active, the detector needs more received power to produce a given output SNR,
relative to a single-user k ¦ ¨ data detection scenario.
When only one MT is active in the SA, with its received transmission power denoted by
© ¥
and the variance of Gauss noise
%¢ denoted by £
¥
, the SNR at input of a MF detector can be
presented as [Ver98]
¡ ¡ ¦
© ¥
£
¥ ¢ (6.1)
which represents the SNR of a single-user data detection scenario.
If k MTs are simultaneously active in the SA and communicate over ¡ subcarriers, with the
received transmission power
© ¢ £ n
2
¥
4
of each transmitted data symbol
¢ £ n
2
¥ , the SNR of that
data symbol of a JD detector can be calculated as

¡ ¦
© ¢ £ n
2
¥
4
£
¥
X£¢
§
†
9
£ ¢
2
¤9
£ © ¢
†
£
¤¥
4
9
¥ £ n
2
£†
£
¤ V
© ¢ £ n
2
¥
4 ¢
£
¦ ¨H¦¥ ¢ n¡ ¦ ¨q ¨§ ¡€ (6.2)
The decreased SNR

¡ ¡ of (6.1) relative to the SNR

¡ of (6.2) results in bit-error-rates
¢ £ n
2
¥¡
$
£ s‚
¢ £ n
2
¥¡ ¡ $
£ holds, due to the presence of other MTs that are introducing MAI.
Equivalently, in the single user scenario, to achieve the same BER
¢ £ n
2
¥¡ ¡ $
£ as in multiuser
scenario
¢ £ n
2
¥¡
$
£ , lower transmission power
© ¢
k£ n
2
¥
4
of the data symbol
¤§
¢
k£ n
2
¥
than that of a
multiuser scenario, is required because no MAI is present and the background noise keeps the
same level. This can be mathematically explained by
¢ £ n
2
¥¡ ¡ $
£ ¦
¢ £ n
2
¥¡
$
£ (6.3)

6.2 Multiuser efficiency
22nd May 2003
40
then with (6.3)
© ¢ £ n
2
¥

© ¢ £ n
2
¥
¢
£
¦ ¨H ¢ n¡ ¦ ¨q £¡€¢ (6.4)
Finally the multiuser efficiency
¢ £ n
2
¥ ¢
£
¦ ¨H ¢ n¡ ¦ ¨q ¡€¢ is defined as ratio between
energies
© ¢ £ n
2
¥
and
© ¢ £ n
2
¥ in single user scenario and in multiuser scenario respectively, when
they have the same BER,

¢ £ n
2
¥ ¦
© ¢ £ n
2
¥

© ¢ £ n
2
¥
¡ ¡
£¢¥¤ n
2
¦ ¥ ¢¨§
¥ 9
¡
£¢©¤ n
2
2 ¢¨§
¥ ¢
£
¦ ¨H ¢ n¡ ¦ ¨S ¡€¢ (6.5)
It can be explained as follows, the more MTs in the service area, the higher transmission power
is required for the MT
£
to hold the BER, then, the lower multiuser efficiency
¢ £ n
2
¥ is.
In (6.5) the multiuser efficiency depends on the background noise level. The asymptotic mul-
tiuser efficiency
¢ £ n
2
¥ , is introduced to measure the multiuser system performance regarding
only to the MAI [Ver98]

¢
k£ n
2
¥ ¦ ¡(1¨
C

¢
k£ n
2
¥ ¢ k ¦ ¨q ¢ n¡ ¦ ¨S ¡€ (6.6)
In order to calculate the assymtotic multiuser efficiency
¢ £ n
2
¥ , from (6.5), the multiuser effi-
ciency
¢ £ n
2
¥ can be calculated as

¢ £ n
2
¥ ¦
© ¢ £ n
2
¥
4

© ¢ £ n
2
¥
4

¡
£¢©¤ n
2 ¦ ¥ ¢§
¥ 9
¡
£¢©¤ n
2 2 ¢§
¥
¦
¢
k£ n
2
¥¡ ¡ ¢
k£ n
2
¥¡

k¤ n
2 ¦ ¥ ¤
9 k¤ n
2 2
¤
¦
¢
k£ n
2
¥¡ ¡ £
¢
k£ n
2
¥¡ £
¨
1 ¢
k£ n
2
¥¡
1 ¢
k£ n
2
¥¡ ¡

k¤ n
2 ¦ ¥ ¤
9 k¤ n
2 2
¤
¦
1 ¢
k£ n
2
¥¡
1 ¢
k£ n
2
¥¡ ¡
(6.7)
¢ k ¦ ¨q ¢ n¡ ¦ ¨S ¡Y¢ (6.8)
where
¢
k£ n
2
¥¡ ¡ £
and
¢
k£ n
2
¥¡ £
represents the SNR at output of MF and JD detectors respectively.
Since
1 ¢
k£ n
2
¥
¡ and
1 ¢
k£ n
2
¥
¡ ¡ of (6.8) are constants which actually only depend on the system matrix%
, described in (3.5), with (6.6) and (6.8), the asymptotic multiuser efficiency
¢ £ n
2
¥ can be
calculated as

¢
k£ n
2
¥ ¦ ¡(1¨
C

¢
k£ n
2
¥ ¦
1 ¢
k£ n
2
¥¡
1 ¢
k£ n
2
¥¡ ¡
¢ k ¦ ¨S ¢ n¡ ¦ ¨q £¡€ (6.9)

6.3 Signal-to-noise ratio degradation
22nd May 2003
41
6.3 Signal-to-noise ratio degradation
Applying JD delivers MAI free estimates of the sent data symbols
§ ¢
k£ n
2
¥ . Assuming that the
superimposed noise is Gaussian and white with covariance matrix
%
¦ £
¥
(6.10)
data estimates
¤§
¢
k£ n
2
¥
with an SNR
¢ £ n
2
¥¡ ¦

¤§
¢ £ n
2
¥

¥
I
£
¥¡ ¨ %
¢
n
2
¥ #
¢
%
¢
n
2
¥ ©
5
££¢
8d8
¢ (6.11)
¤W¦
$ £
VrÜ £¡ © ¡ X © ¡€¢
£
¦ ¨H ¢ © ¡ ¦ ¨H ¡Y¢
are present at the output of the JD linear detector with ¢¡ OFDM subcarriers.
The optimal detection technique, as far as the SNR of the data estimate is concerned and inter-
ference is ignored, is the MF, which delivers the estimates (3.6), considering that the noise
%¢ is
white and wide sense stationary with the power £
¥
and neglecting MAI
¢ £¤ 2
¥¡ ¡ ¦

¤§
¢ £ n
2
¥

¥
I
£
¥ ¤ ¨ %
¢
n
2
¥ #
¢
%
¢
n
2
¥ ©¦¥ 8 8 ¢ (6.12)
¤W¦
$ £
Vr¨ £¡ X © ¡€¢
£
¦ ¨H ¢ © ¡ ¦ ¨ ¡€¢
represents the output of the optimal detector MF with ¡ OFDM subcarriers.
Comparing the SNR of (6.12) and (6.13), can be observed that there occurs an SNR reduction
when applying JD. To quantify the mentioned SNR reduction of the estimates
¤§
¢ £ n
2
¥
when
comparing the cases of (6.12) and (6.13), the SNR degradation

¢ £¤ 2
¥ ¦
¢ £¤ 2
¥¡ ¡ ¢ £¤ 2
¥¡
¦
¨ %
¢
n
2
¥ #
¢
%
¢
n
2
¥ ©
5
£ ¢

¤ ¨ %
¢
n
2
¥$#
¢
%
¢
n
2
¥ ©¦¥ ¢ (6.13)
£
¦ ¨H ¢ © ¡ ¦ ¨H £¡€¢
is introduced, as a performance measure. This degradation is, as said, the price to be paid for the
unbiasedness of the estimates
¤§
¢ £ n
2
¥
in the form of an enhancement of the noise level induced
by the JD process.
The presence of other users in the channel can only decrease the SNR of
¤§
so that the SNR of
JD is always upper bounded by that of matched filter ¢ £¤ 2
¥¡ ¡
¢ £¤ 2
¥¡ ¢ k ¦ ¨S ¢ n¡ ¦ ¨q ¡€¢ (6.14)
It has to take in account that degradation quantifies the performance loss due to the existence
of others users in the channel in JD with linear detectors.

6.4 Spectral radius
22nd May 2003
42
Finally a relation between degradation
¢
k£ n
2
¥ and asymptotic multiuser efficiency
¢ £ n
2
¥ can be
calculates as follows. From (6.14), the SNR degradation
¢ £ n
2
¥ can be obtained as

¢ £ n
2
¥ ¦
¢
k£ n
2
¥¡ ¡ £
¢
k£ n
2
¥¡ £

k¤ n
2
¦ ¥ 9 k¤ n
2
2
¦
¢
k£ n
2
¥¡ ¡ ¢
k£ n
2
¥¡
¨
1 ¢
k£ n
2
¥
¡ ¡1 ¢
k£ n
2
¥
¡

k¤ n
2
¦ ¥ 9 k¤ n
2
2
¦
1 ¢
k£ n
2
¥
¡ ¡1 ¢
k£ n
2
¥
¡
(6.15)
¢ k ¦ ¨q ¢ n¡ ¦ ¨S ¡Y¢ (6.16)
where
¢
k£ n
2
¥¡ ¡ £
and
¢
k£ n
2
¥¡ £
represents the SNR at output of MF and JD detectors respectively,
1 ¢
k£ n
2
¥
¡ and
1 ¢
k£ n
2
¥
¡ ¡ are constants which actually only depend on the system matrix
%
. From
(6.8) and (6.16), the relation of SNR degradation
¢ £ n
2
¥ and asymptotic multiuser efficiency

¢ £ n
2
¥ of data symbol
¤§
¢
k£ n
2
¥
for JD can be drawn as

¢ £ n
2
¥ ¦
¨

¢ £ n
2
¥ ¢ k ¦ ¨q ¢ n¡ ¦ ¨q £¡€ (6.17)
6.4 Spectral radius
Regarding only in the PIC detector, when no data estimate refinement techniques are applied,
with
%
the MF output (4.5)
%
¦
¨
¥ ( ¥¦
¨ % 7

% © ©
5
£ % 7

%
¨
¤§
¢ (6.18)
at the th iteration the estimated
¤§ $
Y is
¤§ $
Yq¦
%
V
¨
¥ ( ¥¦
¨ % 7

% © ©
5
£
¥ ( ¥¦
¨ % 7

% © ¨
¤¤§ $
E V Ü„¢ (6.19)
at the output of the PIC detector.
With the eigenvalues
£ ¢ ¢¡
§

2 of
%
%
, with matrices
%
, (5.3) and
%
, (5.4)
%
%
¦
¨
¥ ( ¥¦
¨ % 7

% © ©
5
£
¥ ( ¦
¨ % 7

% © ¢ (6.20)
the iterative process of Fig. 5.2 converges only if the spectral radius
9
$
%
%
q¦
¨
C 5
¡

£ ¡
¢ ¢
¡

§

2
¡
8 (6.21)
of
%
%
is smaller than one. In the case of convergence, the estimates
¤§ $£¢
of (6.19) correspond
to the ZF estimates of (4.8),
¤§ $¤¢
¦
¥ ¨
¥ ( ¥¦
¨ % 7

% © ©
5
£ % 7

% ¦ ¨
%
(6.22)

22nd May 2003
43
7 Results
7.1 Introduction
In this chapter an investigation concerning PIC detectors is developed for Beyond 3G systems,
for a SA based system in the uplink transmission. Different performance measures described in
Chapter 6, are used to assess the performance of the PIC detector, a special case is introduced
and finally a modification of the PIC estimate refinement is applied and investigated.
It is assumed that the MTs employ such a power control scheme described in Section 3.4, that
the energy of the partial received signal
%£ ¢
k£ n
2
¥ , at the APs of the SA caused by the transmission
of a single data symbol
¢
k£ n
2
¥ is constant for all data symbols
¢
k£ n
2
¥ ¢ k ¦ ¨S ¢ n¡ ¦
¨q £¡ . This fact is expressed by a proper normalization of the channel transfer matrix
%
.
It is to be remarked that all the simulations have been performed over a frozen channel with the
same parameters fixed for all simulations, i.e., the same snapshot of a channel with exponen-
tially fading power delay spectrum, according to the COST 207 channel model, is used in all
simulations.
The fixed parameters are:
¥ Carrier frequency UTq¦ cP c¡
¢£¢
¥ System used bandwidth
¡
¦
I
`¡¤
¢£¢
¥ Length of channel impulse response in taps ¥ ¦ ¨
7.2 Spectral radius of PIC
As one of the most important aspects about the PIC detectors due to the iterative nature of PIC
is the convergence, an important performance measure for the PIC detector is the spectral radius
described in Section 6.4.
Consequently an investigation regarding spectral radius is developed in this section, taking in
account that a frozen channel is used in all simulations.
The spectral radius for each subcarrier can describe the convergence in the case of no refinement
estimation. In Figs. 7.1 and 7.2 the cumulative distribution function (cdf) of spectral radius 9 ,
is shown for the case of a scenario where PIC is performed subcarrierwise and a sufficiently
large number £¡ of subcarriers is used. In the case of ¡ ¦
¤
APs seen in Fig. 7.1, it can be

7.3 PIC performance over one specific subcarrier
22nd May 2003
44
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PSfrag replacements
¦
I

¤
MTs
non convergenceconvergence

¡£¢
¤
¥¦
Figure 7.1. CDF of the spectral radius in the channel with ¦
I
H
¤
MTs and £¡ ¦
¤
APs
observed that with ¦
I
MTs in all subcarriers PIC detector converges, as in all subcarriers
holds 9xv ¨ . On the other hand, in the case of 3 and 4 MTs, PIC in only 60% and 10% of
the subcarriers converges, respectively. It can be observed from Fig. 7.2, that in the case of
¡x¦¨§ APs when ¦
I
or ¦¨© MTs are active in the SA PIC detection converges in
all the subcarriers. With ¦
¤
or ¦'c MTs some subcarriers with non-convergent and
convergent results are present and finally with ¦ , ¦ or ¦§ MTs, PIC does not
converge at any subcarrier. If the fully loaded case is taken into account, then by comparing
the cases of Fig. 7.1 and 7.2 it can be seen that with ¦§ MTs active in the SA, there exist
absolutely no subcarriers in which PIC is convergent.
Finally it can be observed that with more MTs with the same number of APs in the SA, more
MAI exists and less subcarriers that PIC detector converge are present. Therefore spectral
radius is also a measure of how much MAI is present and how it is affecting each subcarrier in
the convergence of PIC detectors.
In this section the performance over one specific subcarrier is studied, where the subcarrier © ¡
is chosen according to its spectral radius 9
¢
n
2
¥ .
The case of PIC with no estimate refinement which converges to the ZF detector is explained
in Section 6.4. Fig. 7.3 represents a subcarrier in which PIC detector converges with spectral

22nd May 2003
45
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PSfrag replacements
¦
I
§ MTs
non convergenceconvergence

¡£¢
¤
¥¦
Figure 7.2. CDF of the spectral radius in the channel with ¦
I
H § MTs and £¡ ¦ § APs
radius 9
¢ ¥ ¥ ¦ `b
¤ I
§ c , so in the figure can be observed that the BER of the PIC detector at
the fourth iteration finally converges to the BER of ZF detector, in the case of '¦ © MTs and
¡ ¦
¤
APs.
Observing the Figs. 7.4 - 7.6 simulated in the subcarrier n¡ ¦ ¨
I
at which does PIC not con-
verge, as it is characterized by spectral radius 9
¢ £
¥ ¥ ¦ ¨ ``b¨¨ , in the case of a fully loaded case
with ¦
¤
MTs and ¡ ¦
¤
APs, the performance of different estimate refinement techniques
can be observed and it can be remarked that the estimates
¤§
¢
n
2
¥ $
¨ of the first iteration coincide
with the MF estimates of (4.5).
Moreover from Figs. 7.4 and 7.5 the advantage gained in terms of
when exploiting the
knowledge of the discrete nature of the sent data symbols by hard quantization can be observed.

22nd May 2003
46
−10 −5 0 5 10 15 20
10
−3
10
−2
10
−1
10
0
AWGN
MF
ZF
1−iter
2−iter
3−iter
4−iter
5−iter
PSfrag replacements
¨ ` ¡
¦ £ $
3
f

f
¥

Figure 7.3. PIC with ¦ © MTs and ¡a¦
¤
APs c iterations with no quantization in the
subcarrier n¡ ¦
I
`` with spectral radius 9
¢ ¥ ¥ ¦ `F
¤ I
§ c
−10 −5 0 5 10 15 20
10
−3
10
−2
10
−1
10
0
AWGN
MF
ZF
1−iter
2−iter
3−iter
4−iter
5−iter
PSfrag replacements
¨ ` ¡
¦ £ $
3
f

f
¥

Figure 7.4. PIC with ¦
¤
MTs and ¡a¦
¤
APs c iterations with no quantization in the
subcarrier n¡ ¦ ¨
I
with spectral radius 9
¢ £
¥ ¥ ¦ ¨d``F¨¨
Finally Fig. 7.6 demonstrates the clearly superior performance of soft quantization when is
compared to the cases of no and hard quantization.

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