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

Final Research Project

Parallel interference cancellation in beyond 3G multi-userand multi-antenna OFDM systems

David Sabater DinterMay 2003

Universitat KaiserslauternFachbereich ElektrotechnikLehrstuhl fur hochfrequente

Signalubertragung- 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-userand multi-antenna OFDM systems

David Sabater DinterMay 2003

Betreuer: Prof. Dr.-Ing. habil. Dr.-Ing E.h. P.W. BaierDipl.-Ing. A. Sklavos

Bearbeiter: David Sabater Dinterc/ Cami de Son Vich, 1207150 Andratx, Islas Baleares (Spain)

Statement

I hereby assure that I did not use other aid than the ones mentioned within the text to write thisthesis.

Die vorliegende Diplomarbeit wurde von mir selbstandig 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 opportunityin 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 succesfulcompletion of this diploma thesis.

I would like to thank the invaluable support received from my supervisor Dipl. -Ing. AlexandrosSklavos throughout the duration of this project. He helped me to explain perfectly all that I hadthought 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 Jose y Ute con todo mi carino, si no fuera por ellos,yo no estaria aqui, tambien se lo dedico a mis hermanos Malena, Matias y Patrick, me sientoafortunado por tener una familia asi. Tambien para mi abuela Margarita por su confianza yaprecio. Dankeschon Oma.

Gracias a todos mis amigos de Kaiserslautern, de Mallorca y sur de la peninsula, ya que sinellos hubiera sido imposible hacer todo esto. Moltes gracies 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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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

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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

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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 communicationnetwork, by means of transmission of signals in the radio frequency (RF) band. 100 years agoG. Marconi managed to set up a radio link across the Atlantic, an accomplishment for whichhe was awarded the Nobel prize in 1909. A fact that G. Marconi would probably not haveguessed is that thanks to decisive advances in technology, mobile communications is a radicallychanging 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 surpassconventional 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 onthe 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 overlappingfrequency bands to different users. The first generation of analog cellular systems included theAdvanced Mobile Telephone System (AMPS) in the USA, the Total Access CommunicationSystem (TACS) in Europe, the C-450 system in Germany and Portugal, the Nordic MobileTelephones (NMT) in Scandinavian countries and the Nippon Telephone and Telegraph (NTT)system in Japan [PGH95, Stu01].

1.2.2 Second generation

Parallel to the evolution of mobile communications, decisive progress in digital communicationstook place. The increase of the device density in integrated circuits (ICs) and the developmentof low rate speech coders spawned the second generation of mobile radio systems. Due to thisfact, the integration of the mobile radio systems in the digitalized Public Switched TelephoneNetworks (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. Incontrast to the first generation where FDMA was used, in the second generation Time Division


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Multiple Access (TDMA) and Code Division Multiple Access (CDMA) are used, thanks to thedigital technology CDMA with analog transmission applied in the signal processing techniquescan 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 wholeavailable 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 frequencydomain. On the receiver, linear filtering with a synchronized replica of the spreading code isapplied 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 ofmobile radio systems the Groupe Speciale Mobile (GSM) was established by the ConferenceEuropeene des Postes et Telecommunications (CEPT) at 1982 which was later renamed toGlobal System of Mobile communications [PGH95, OP98]. In 1988, the European Telecom-munication and Standardization Institute (ETSI) was founded and GSM became the TechnicalComittee Special Mobile Group (TC SMG).

In the United States an important factor considered by the standardization of second generationmobile radio systems was the need of backwards the compatibility to AMPS due to the largenumber of analog handsets already in operation. The Electronic Industry Association (EIA) andthe 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 theversion of IS-54 with a digital control channel, and is the most commonly used term whenreferring to US-TDMA. Backwards compatibility to the analog AMPS system was enabled bythe 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 initiatedin 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 laterrenamed to International Mobile Telecommunication 2000 (IMT-2000) [IMT]. The 3G Partner-ship Project (3GPP) was initiated in 1998 to coordinate research activities and standardizationaround the world. 3GPP does not contribute directly to ITU and is formed by Organizationalpartners, such as ETSI (Europe), Association of Radio Industries and Business (ARIB) and theTelecommunications Technology Association (TTA) (Korea) and T1 (USA). Several companiestake part in 3GPP as market representation partners and other standardization bodies [3GP]. InEurope, research concerning 3G mobile radio system is known under the term Universal MobileTelephone System (UMTS), began in 1990. In 1998, WCDMA was selected for the FDD mode


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and time division CDMA (TD-CDMA) [KB93] for the TDD mode of UMTS. An importanttarget 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, andfor 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 towardsthe definition and design of beyond 3G systems have started in many parts of the world and isfar from being immature. With the expected development of new mobile multimedia services inthe 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 fromfirst 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. Dueto 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 expensivethan scarce 50 billion ¤ for 3G in Germany) , the support of high data rates requires systemdesigns which make optimum use of the assigned frequency spectrum and thus guarantee a highspectrum efficiency.

��

��

��

��

vehicular

pedestrian

stationary

3rd Generation

0.1 10 100

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

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Fig. 1.1 shows that variable and specially high data rates will be requested, which should beavailable 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 physicallayer with interference suppression is considered by the majority of the scientific community tobe the leading the candidate for the beyond 3G mobile radio systems, due to its inherent abilityto 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 discernbetween 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 basestations (BSs). The transmitted information is then properly forwarded from the core networkof 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 transmittedwirelessly from the BSs to the MTs. To accomplish the bidirectional flow of information in theair interface, different time or frequency resources are used for the UL and DL transmissions ina mobile radio system. Time division duplexing (TDD) is used if different time slot groups aredevoted 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 amultitude of transmitters and receivers. In the UL (DL) the transmitters are the MTs (BSs) andthe 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 ofeach 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 mobileradio 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 ofthe receivers. The mobile radio system consisting of the MIMO channel, the transmitters andthe 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 MIMOsystem is depicted. Groups of inputs and outputs of the MIMO channel of Fig. 1.2 are bundledtogether to indicate the antenna elements of a single transmitter or receiver, respectively. Insome state of the art mobile radio systems, as e.g. in TD-CDMA [Kle96], signals corresponding


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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. Thisjoint processing across antenna elements can be generalized to a joint processing across moretransmitters 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 normallyno communication possibility between dislocated transmitters or receivers which means thatsignals 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), whichinvolves inversion of the MIMO channel and can be impractical for large dimensions of theMIMO 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 thereceived signal.

The Parallel Interference Cancellation (PIC) as joint detector (JD) will be investigated in thisthesis, it will be studied in the context of a multi-user and multi-antenna system, based onOFDM. Different performance measures will be introduced to assess PIC with different refine-


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ment techniques and to compare the results with ZF detector. Finally a modified data estimaterefinement technique in PIC detector will be introduced and investigated. All the investigationswill 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 ofthe 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 availablebandwidth is divided into a number of narrower frequency bands, then the spectra do not overlapand each of the simultaneously active users is assigned one of the non overlapping frequencybands.

A parallel transmission technique is effective in combatting the effects of amplitude and delaydistortion, and impulse noise because each subchannel occupies a relatively to the whole systembandwidth. In order to get an efficient use of the available spectrum, the spectra of the differentsubchannels are allowed to overlap.

Multicarrier modulation is a technique of transmitting data by dividing the data into severalinterleaved, or not, bit streams and use these to modulate several carriers. A special case ofmulticarrier modulation with spectra overlap is the OFDM where the carrier spacing is carefullyselected 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 asKINEPLEX, ANDEFT and KATHRYN.

In 1971, Weinstein and Ebert applied the discrete Fourier transform (DFT) to parallel datatransmission systems as part of the modulation and demodulation process. If DFT is used at thereceiver 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 requiredby 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 frequencysubchannels, both transmitter and receiver are implemented using efficient FFT techniques thatreduce 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 mobilecommunications, and high-density recording. Systems realizing the OFDM technique for mul-tiplexed QAM using DFT, carrier stabilization, clock frequency control and trellis coding arealso implemented.

2.3 Basic principles of OFDM

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In the 1990s, OFDM was employed for wideband data communications over mobile radio FMchannels, high-bit-rate digital subscriber lines (HDSL, 1.6 Mbps), asymmetric digital subscriberlines (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 envelopemodulation 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

�� ! "$# �%&(' # � "

� &*) � " �,+.- �0/21435� �7698�;:=<>@?� � � �A8B�C�D�E�,�9�C�GFH�IFH�C�J: �

�� <>�K�MLN�C�POQ�MRS�C�J: � (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 partsof the OFDM signal, which have to be multiplied by a cosine and sine of the desired carrierfrequency to produce the final OFDM signal.

�� "$# �%&(' # �! "

� &() � " �T+.- �0/2143G� �7698�� A8B�C�D�E�,�A�C�GFH�MFH�C�P: �

�� <>�K�MLS�C�JOU�MR=�C�;: � (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, allsubcarriers have the same phase and amplitude, but in practice the amplitudes and phases maybe modulated differently for each subcarrier. Each subcarrier has exactly an integer numberof 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 / th from (2.2) is demodulated by downconverting the signal with a frequency of VW andthen 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 demodulatedsubcarrier / , this integration gives the desired output � V )

� " (multiplied by a constant factor�

),which is the QAM value for that particular subcarrier. For all other subcarriers, the integration


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��

� ��

�� ! ��

�#" �%$'&)(+*-,/.0$213&41+5�6�798:6

�#" �%$+&�(+*;$<,=.>&@?!6A$213&41+5�6�798:6

Figure 2.1. OFDM modulator

Time

PSfrag replacements

Amplitude

�CB 1 �

Time

Figure 2.2. Example of four subcarriers within one OFDM symbol

is zero, because the frequency difference � � 8 / � B � produces an integer number of cycles within


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the integration interval�

, such that the integration result is always zero.

�� ).W� � �T+.- � 8 /21435�

/� � � �98B�C�D�E�

�� " # �%&(' # �! "

� &() �� " �T+.- �0/21435� �7698�� A8B�C�D�E��

�� "$# �%&(' # � "

� &*) �� "� �� ).W�� ,+>- � 8 /2143G�

/� � � �A8B�C�D�E�� V )

�! "� (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( 3 � � ),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 maximumof each subcarrier spectrum, all other subcarrier spectra are zero. Because an OFDM receiveressentially 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 othersubcarriers. Basically, Fig. 2.3 shows that the OFDM spectrum fulfills Nyquist’s criterium foran 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 onesubcarrier 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 transformof �� 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 sincethe hardware complexity of an adder is significantly lower than that of a multiplier of phaserotator, only the multiplications are used here. Then, the IFFT drastically reduces the amountof calculations by exploiting the regularity of the operations in the IDFT.

�� # �%&*' � � & �T+.- ��/.173

�� T� (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 withmultipath delay spread. By dividing the input datastream in � � subcarriers, the symbol duration


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Amplitude

Time

Figure 2.3. Spectra of individual subcarriers

is made �� times larger, which also reduces the multipath delay spread, relative to the symboltime, by the same factor. To eliminate intersymbol interference almost completely, a guardtime is introduced for each OFDM symbol. The guard time is chosen larger than the expecteddelay spread, such that multipath components from one symbol cannot interfere with the nextsymbol. The guard time could consist of no signal at all. In that case, however, the problem ofIntercarrier Interference (ICI) would arise. ICI is crosstalk between different subcarriers, whichmeans they are no longer orthogonal.

This effect is illustrated in Fig. 2.4. In this example, a subcarrier 1 and a delayed subcarrier 2 areshown. When an OFDM receiver tries to demodulate the first subcarrier, it will encounter someinterference from the second subcarrier, because within the FFT interval, there is no integernumber of cycles difference between subcarrier 1 and 2. At the same time, there will be crosstalkfrom the first to the second subcarrier for the same reason. To eliminate ICI, the OFDM symbolis cyclically extended in the guard time, as shown in Fig. 2.5. This ensures that delayed replicas


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PSfrag replacements

Part of subcarrier #2causing 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 2causes ICI on subcarrier 1 and vice versa

of the OFDM symbol always have an integer number of cycles within the FFT interval, as longas the delay is smaller than the guard time. As a result, multipath signals with delays smallerthan the guard time cannot cause ICI. As an example of how multipath affects OFDM, Fig. 2.6shows received signals for a two-ray channel, where the dotted curve is a delayed replica of thesolid curve. Three separate subcarriers are shown during three symbol intervals. In reality, anOFDM receiver only sees the sum of all these signals, but showing the separated componentsmakes it more clear what the effect of multipath is. From the figure, It can seen that the OFDMsubcarriers are BPSK modulated, which means that there can be 180-degree phase jumps atthe symbol boundaries. For the dotted curve, these phase jumps occur at a certain delay afterthe 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 destroythe orthogonality between the subcarriers, it only introduces a different phase shift for eachsubcarrier. The orthogonality does become lost if the multipath delay becomes larger than theguard time. In that case, the phase transitions of the delayed path within the FFT interval of thereceiver. The summation of the sine waves of the first path with the phase modulated waves ofthe delayed path no longer gives a set of orthogonal pure sine waves, resulting in a certain levelof interference.

2.4 Parameterization of an OFDM system

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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, oftenconflicting 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, theguard time should be about two to four times the root-mean-squared delay spread. This valuedepends on the type of coding and QAM modulation. Higher order QAM (like 64-QAM) ismore sensitive to ICI and ISI than QPSK; while heavier coding obviously reduces the sensitivityto such interference.

2.5 OFDM signal processing

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14

PSfrag replacements

First arriving pathReflection delay

Reflection delay

Guard time

Guard time

FFT integration timePhase 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 durationmuch larger then the guard time. It cannot be arbitrarily large, however, because a larger symbolduration means more subcarriers with a smaller subcarrier spacing, a larger implementationcomplexity, and more sensitivity to phase noise and frequency offset, as well as an increasedpeak-to-average power ratio. Hence, a practical design choice is to make the symbol durationat 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 directlyas the requiered -3 dB bandwidth divided by de subcarrier spacing, which is the inverse of thesymbol 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 subcarrieris defined by the modulation type, coding rate, and symbol rate.

An additional requirement that can affect the chosen parameters is the demand for an integernumber of samples both within the FFT/IFFT interval and in the symbol interval. The onlysolution 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 extensionhas 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 paralleldata stream is then coded using a forward error correcting (FEC) scheme and mapped to acomplex symbol alphabet. Both operations can be done in one module if coded modulationis 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 infrequency. Then a cyclic prefix (CP) is inserted to avoid ISI due to multipath propagation in themobile radio channel. Finally, the transmission filter forms the continuous time signal that isupconverted into high frequency for its transmission over the channel.

At the receiver the received signal is downconverted and sampled to obtain the discrete signalafter the reception filter. The received block is windowed to remove the cyclic prefix and thesamples are converted from time into frequency domain by the FFT module. Then, dependingon the used modulation scheme, the amplitude and phase shifts of each subchannel have to beequalized and the received complex symbols are inversely mapped and decoded. Finally, theoriginal serial data stream is obtained.

2.5O

FD

Msignalprocessing

22ndM

ay2003

16

IFFT

RECEIVER

Serial

Parallel

Parallel

Serial

mappingand

Coding cyclic

insertionprefix

filter

transmission

sampling&

filterreception

(windowing)removalprefixcyclic

FFT

equalization&

estimationchannel

remapping&

decoding

datainput

dataoutput

TRANSMITTER

Mobile RadioChannel

Figure2.7.System

modelof

anO

FDM

transmission

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 theproblematic regarding the efficient coverage of the theoretically infinite geographical area, thecellular system invented by Bell Labs in 1979 [McD79] is applied in the mobile radio systemsof 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 inorder to accomplish radio coverage. Mobile terminals (MTs) are served by the nearest BS andthe area responsability of each BS is termed cell.

To avoid interference situations between the individual radio links of the MTs of neighboringcells 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 wouldlead to a waste of resources. In the cellular concept, the frequency band assigned to the mobileradio operator, is distributed among cells of a particular group, termed cluster and the numberof 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 interferencebetween 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 sizeof 4 is used but in 3G mobile radio system (UMTS), unity cluster size is used and the resultingintercell interference is mitigated by the use of spread spectrum techniques in each cell. Fig. 3.1shows the architecture of a conventional cellular system. Each cell contains a BS, and the MTsof each cell communicate solely with this BS. All BSs are connected to a central entity termedcore network in Fig. 3.1, which, in the case of GSM, consists of the base station controllers andthe mobile switching centers [MP92]. The core network can be considered the data source anddata sink in the communication with the MTs.

An alternative air interface architecture to cellular systems are service area (SA) based systems[WMS

)02, SWC

)02, SWC

)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 centralunit (CU). The CUs in their turn are connected to the core network. Each such group definesa 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 havea SA with a number of APs, which are connected to a CU. Fig. 3.2 shows the architecture of aSA-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 �� APsof the SA and fed to the CU, where they are jointly processed. The aim of this joint processingconsists in exploiting the signal energies received by the �� APs of the SA in a optimum way,

3.1 Service area concept versus cellular concept

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18

PSfrag replacements

core network

BSMS

cell

Figure 3.1. Conventional cellular system with 12 cells and cluster size 4

C UC 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-SAmultiple access interference (MAI). The CU jointly detects the signals radiated by � MTs ofthe SA and provides the data transmitted by the MTs at its output. This means that in the ULthe 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 waythat the transmit signals for each MT have minimum powers and cause minimum interferenceat other MTs, and the complexity of the MTs can be kept low. This means that in the DL theCU performs joint transmission (JT) [MBW

)00].

3.2 Transmission model of uplink transmission

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19

The rationale of SA based systems can be applied in both single, that is isolated SAs, andconglomerates of SAs corresponding to conventional cellular networks. Each CU has to beconnected to a core network, into which- in the case of the UL - the data coming from the MTsis 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

)00].

In the case of a SA-based system, intra-SA MAI, corresponding to the intercell MAI of cellularsystems, is combated by JD and JT, see above. Because in the case of a SA-based systemthe SAs are larger than the cells of a conventional cellular system, a larger number of links isincluded in the interference mitigation processes, producing an improvement of the spectrumefficiency.

For the present thesis only UL transmission in a SA based mobile radio system an iterative datadetection algorithm for JD is investigated.


The transmission model of the uplink transmission of the service area based system is explainedwith detail in this chapter. As it is explained in section 3.1, a SA consists of � simultaneouslyactive MTs, � � APs and a CU, as shown in Fig. 3.3. Each MT utilizes, in the general case, thewhole 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 theDL transmission, the CU generates AP specific signals which are transmitted from the APs inthe SA. This asymmetric distribution of signal processing tasks between the APs and the CUis beneficial in terms of cost of deployment as the cost per AP is reduced. Consequently, thespacial diversity inherent in the SA based system can be cost efficiently increased by installinga 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� �G � , compiled into the vector

� � k � � �� k � � � E� � k �

�� k � �G � (3.1)

The � data vectors� � k � , k � �G � , of (3.1) can be compiled to the total data vector

� ��

� � � � � (3.2)


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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 notnecessarily 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 � ,on each subcarrier n � , n � � �5 � � , i.e., in each subcarrier � , � data symbols are sentsimultaneously.

With the � � � transfer function matrices

�� k � k � � �

��

� � k � k � � � � <. . .

< � � k � k � � �

!#""$ � k � �G � � k � ��G � � � (3.4)

3.3 Subcarrierwise investigation

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21

the total � � �� transfer function matrix

��

��

�� ...

. . ....��

! ""$ � (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 ofnoise

�� , the vector �� : �� (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 jointlyprocessed by the CU to obtain the estimates

�� (3.7)

of�

of (3.2) free from intra-SA interference which resulted from the simultaneous operationof 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 OFDMsystem, by defining the n � subcarrier specific � �� matrices

�� n � �

��

� � � � � � n � � � � � � � n �...

. . ....� � � � � � � n � � � � � � � � n �

! ""$ (3.8)

Using the matrix of (3.8) the total � � �� transfer function matrix by a reordering of itselements, takes the blockdiagonal form

��

��

�� < << �� <...

.... . .

...

< < ��

!#""""$ (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 �

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 oftransmissions 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 � �� n � �� n �� n � � �G ��P� (3.10)

and from the total data vector�

of (3.6) the �� partial data vectors

� � n � � �� n � ��

� � n � �� n � ��5 � �P� (3.11)

for every subcarrier n � , n � � �5 � � , are formed [WSC02]. With the channel transfer matri-

ces��

n �

of (3.8) describing the MIMO channel at each subcarrier, the partial received signalvectors

�� n � of (3.10) and the partial data vectors� � n � of (3.11), the transmission model of

(3.5) can be rewritten in the subcarrierwise form�� n � � �� n � � � n � : �� n � � n � � �G � �P (3.12)


3.4.1 Theory of mobile radio propagation

During transmission, in the mobile radio channel, the transmitted signal suffers from threenearly 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, atthe receiver antenna, a multitude of waves arrives from many different directions withdifferent 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 MTand moving objects in the mobile radio channel, changes in the phases and amplitudesof the arriving waves occur, resulting in time-variant multipath propagation. Even smallmovements 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 referredto 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 tofast fading, longer distances have to be covered to significantly change the shadowingconstellation. The varying signal strength due to shadowing is called slow fading and canbe described by a log-normal distribution [Par92].


22nd May 2003

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� Path loss predicts how the mean signal power decays with distance from the APs. Infree 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 receiverand transmitter, the signal power typically decreases with a power higher than two and istypically in the order of three to five [Rap96].

The mobile radio channel is given by the time-variant channel impulse response �� E�� or by

the time-variant channel transfer function�� ;�E�� , which is the Fourier transform of

�� E�� .The channel impulse response

�� represents the response of the channel at time � due to animpulse applied at time � 8 � . 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 shortperiods of time or small spatial distances. In environments with multipath propagation, thechannel impulse response is composed of a large number of scattered impulses received over�� different paths,

�� E��G� # �%� ' �� K�T+.-�

/;� 143 �� :� ��4�� 8 � �4�T� (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

�� 4�� (3.14)

depends on the velocity � of the MT, the speed of light � , the carrier frequency � � , and the angleof incidence � � of a wave assigned to the � th path.

The description of the correlation functions of the channel impulse response �� E�� is sufficient

to characterize the fast fading of the mobile radio channel [Bel63]. The autocorrelation functionof

�� E�� is defined as

� �� G� �1"!$# �� E�� % �� E� :� ��& (3.15)

Under the presumption that the WSS random processes �� E�� E�� are uncorrelated for � �

not equal � � , called uncorrelated scattering (US), the autocorrelation function (3.15) simplifiesto

� �� 5�(' �� )� �� 8 � � �T� (3.16)

where ' �� is the delay cross-power spectral density [Bel63]. The mobile radio channelcharacterized by (3.16) is referred to as WSSUS channel. The fourier transform of ' �� in � yields the scattering function [Bel63]

* �� 5��,+# + '

�� T+.-��(8 /2143 ��" �-� � � ��T (3.17)


22nd May 2003

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The scattering function is real-valued and provides a measure of the average power output ofthe channel as a function of the delay � and the Doppler frequency �� .By integrating the scattering function

* �� over the Doppler frequency � the delay powerspectrum

' �� +# +

� �� ,� �� 9� (3.18)

is obtained, which is identical to the delay cross-power spectral density ' �� at � equal to0. The delay power density spectrum gives the average power of the channel output as a functionof the delay � and can be viewed as a scattering function averaged over all Doppler shifts. Themean delay � , the delay spread �� , and the maximum delay �� are characteristic parametersof a multipath channel and can be determined from the delay power density spectrum. If theduration

� � of the transmitted symbol is significantly larger than the maximum delay �� , thechannel produces a negligible amount of ISI. This effect is exploited with MC transmissionwhere 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 quantifiedby their mean delay and the delay spread [Par92]. The mean delay is the first moment of thedelay power density spectrum resulting in

� � +� � ' �� +� ' �� (3.19)

The normalization with +� ' �� is applied because ' �� is not a probability density function.

The delays are measured relative to the first detectable path at the receiver. The delay spread isthe standard deviation of the delay power density spectrum and is given by

��$� +� �� 8 � �

�' �� +� ' �� (3.20)

The coherence bandwidth � � �� of a mobile radio channel is the bandwidth over which thesignal propagation characteristics are correlated and is proportional to the reciprocal of thedelay spread �� . The coherence bandwidth can be defined as the bandwidth over which thefrequency correlation function is above 0.5 and, thus, can be approximated by [Rap96, Skl97]

� � � �� ?�� (3.21)

The frequence correlation function is the Fourier transform of the delay power density spectrum' �� , i.e., �

� � �5�� +# + '

�� >�,+>-�*8 /.173 � �� (3.22)

The channel is said to be frequency selective if the signal bandwidth�

is larger than the co-herence bandwidth � � � � . On the other hand, if

�is smaller than � � �E� , the channel is said

to be frequency non-selective or flat. The coherence bandwidth of the channel is of importancefor 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 MCtransmission, frequency diversity is exploited if the separation of subcarriers transmitting thesame information exceeds the coherence bandwidth. The maximum achievable frequency diver-sity is approximated by the ratio between the signal bandwidth

�and the coherence bandwidth� � � � .

�� (3.23)

and, consequently, depends on the delay spread � � of the channel, cf. (3.21).By integrating the scattering function � �� ) � over the delay � , the Doppler power densityspectrum � �� G�

� +# +

� �� ,�� (3.24)

is obtained. The Doppler power density spectrum gives the average power of the channel outputas a function of the Doppler frequency � and can be viewed as a scattering function averagedover all delays. The frequency dispersive properties of multipath channels are most commonlyquantified 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 � ��,� isthe duration over which the channel characteristics can be considered as time-invariant and isproportional to the reciprocal of the maximum Doppler frequency. The coherence time canbe defined as the time over which the time correlation function is above 0.5 and, thus, can beapproximated by [Ste94, Rap96]

� ��

�� 3 � �� (3.25)

The time correlation function is the inverse Fourier transform of the Doppler power densityspectrum

� �� . i.e., �� G�

� +# +

� �� >�T+.-� /2143 �� -� � ��9 (3.26)

If the duration��

of the transmitted symbol is larger than the coherence time � �� , the channelis said to be time selective. On the other hand, if

��is smaller than � �� , the channel is said

to be time non-selective. The coherence time of the channel is of importance for evaluatingthe performance of FEC coding and interleaving techniques that try to exploit the inherent timediversity � � of the mobile radio channel. Time diversity can be exploited if the separationbetween successive time slots carrying the same information exceeds the coherence time. Anumber of �� successive time slots create a time frame of duration

� �� of a time frame and thecoherence time � �� ,

� � �� (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 subcarriersand 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, orpolarization diversity which are not within the scope of this thesis can additionally increase theoverall diversity and are described in [Lee74, Lee93, Rap96, Stu01]. It should be noted thatspace diversity, also known as antenna diversity, is a popular form of diversity used in wirelesssystems [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 atthe receiver. The application of the central limit theorem leads to a complex-valued Gaussianprocess is zero-mean. The magnitude of the corresponding channel transfer function� � � � �,� � �� ,� � (3.29)

is a random variable, for brevity denoted by a, with a Rayleigh distribution given by [Pro95]

� � � � �1 �� #�� "�� <>� (3.30)

where � � ! # � � � �P�E�� & (3.31)

is the average power. The phase is uniformly distributed in the interval � <>� 143 . This channelis said to be a Rayleigh fading channel and best agrees with the propagation characteristic ofmacrocells.

In the case that the multipath channel contains a LOS or dominant component in addition tothe randomly moving scatterer, the channel impulse response can no longer be modeled aszero-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]

� � � �G�1 � � �� 6�� : �7�� # �� #�� " � �� ) � � ��

1 �� 6�� 6�� : �7�� <> (3.32)

The Rice factor �� 6�� is determined by the ratio of the power of the dominant path to the powerof the scattered paths at the receiver. The average power

�is given according to (3.31) and

� � � @�is the zero-order modified Bessel function of first kind. The phase is uniformly distributed inthe interval � <>� 173 � . This channel is said to be a Ricean fading channel and best agrees with thepropagation 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 Cooperationin the field of Scientific and Technical research (COST) in the action point 207, that correspondsto 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 approachis related to the physical description of the channel and is based on the implementation of adiscrete multipath scenario [Kai98].

The COST 207 channel models basically determine the various propagation scenarios by con-tinuous, exponentially decreasing delay power density spectra ' �� . Every environment can bemodeled by a number of �� discrete paths, where each path has the same amplitude and isspecified by its propagation delay � � . Each propagation delay is chosen according to the prob-ability density function of � within the given interval � � � � � �� . The probability densityfunction of � is proportional to the delay power density spectrum ' �� . The average power

� �per path is chosen to be

�� , normalizing the power of the channel according to (3.33).� �

� �%� ' �

� � �� (3.33)

The �� are modelled with isotropic scattering, i.e., the angles of incidence � � are taken from auniform distribution in the interval � <>� 143 � . Each path has a phase � uniformly distributed overthe interval � <.� 143 � .The channel transfer function implemented by the COST 207 channel models can be written as

�� n � � � � � � �D�G� ��

� �%� ' � �T+.-�

� 143 vfc

c � iT � � �� p � :, p �� ,+.-�(8 143 nF � � p � � (3.34)

being n � subcarrier number, � symbol slot number,� � is subcarrier spacing,

� � the OFDMsymbol duration which includes the guard time duration, � , the velocity of the MT, � � , the lightvelocity, �4� , the carrier frequency, � 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 !�� B � � ratio, at the input of the CU,where ! � is the energy per bit at the received signal and � � B 1 is the two sided power spectraldensity of the noise at the APs.


22nd May 2003

28

environment �� in � s ' �� hilly terrain 100 1-74 0.01 1 � <>� 143 � � <>� 1 � � � #��

(HT) 75-100 0.01 1 � <>� 143 � �*�7?.� 1 < � � <>�� E# � � � �

bad urban 100 1-68 0.01 1 � <>� 143 � � <>�,?�� # � � � �(BU) 69-100 0.01 1 � <>� 143 � � ?.� � < � � <. ?!� �E# ��

typical urban 100 1-100 0.01 1 � <>� 173 � � <>�� # �� (TU)

rural area 100 1-100 0.01 1 � <>� 143 � � <.� <> �� #��

(RA)

Table 3.1. COST 207 channel model parameters. The power per path is normalized to� �U�

� B �� , the angles of incidence � � are taken from a uniform distribution in the interval � <>� 143 � ,the propagation delays � � are chosen within the given interval � � � � � �� proportional to theassigned delay power density function ' ��

To perform such simulations, a well defined ! � B � � ratio must be present. Equivalently, it isassumed that the MTs employ such a power control scheme, that constant ! � is present for agiven channel snapshot. Hence, ! � B � � will depend only on the noise power. The receivedsignal

�� n � ��

�� n �� n �...�� n �

! """$ �

��

� � � � � � n � � � � � � � n � � � � � � � n �� n � � � � � � � n � ......

. . ....� � � � � � � n � � � � � � � � n �

!#""""$

�� n �

� �� n �...

� � � � n �

! """$

at the � � APs at a specific subcarrier n � can be written as superposition of � partial receivedsignals

�� n ��

��

� � � � � � n �� n �...� � � � � � � n �

! """"$

� �� n �� n � � k ��G � � (3.35)

each corresponding to a certain data symbol�� n �

.

With the assumption of QPSK, i. e.,�� n �� n � � 1 � k ��G � � � n � ��G ��P� (3.36)


22nd May 2003

29

then with�� n � and

�� n �of (3.35) and with (3.36), the received energy

� � � � � �1 �� n � �� n �� 1 �� n � � �� n � �� n � �� n �

� � � �� n � �� n � �(3.37)

corresponding to a single data symbol � � � � n � , depends on the energy scaling induced by thechannel. Thus, if channel columns of channel matrix is normalized as

� � � � � � � �� n � �� n � � � (3.38)

a well defined received energy per QPSK modulated data symbol � � k � n � is obtained. Mathemat-

icaly seen, (3.38) is totally equivalent with having an arbitrary value for�� n � �� n �

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 � �� n � � � � �� n � �� n � � �� k � �G � � n � �

�G �� , in this case fast power control at the MT occurs and means !�� B � � is the real

! � B � � .� Normalizing in average energy one, i.e.,

� � �� n � �� n � � �� k � �G � � n � ��G �� , slow power control and ! � B � � is the ! � B � � averaged over all � �� channelsexperienced by the � � � data symbols

� � � � n � .

In this way a comparison of� versus ! � B � � can be applied.


22nd May 2003

30

50 100 150 200 250 300 350 400 450 5000

0.5

1

1.5

2

2.5

3

3.5

k=1k=2k=3k=4

PSfrag replacements

� �� k � n �� k � n �

�Figure 3.4.

� �� n �� n �normalization using averaging over all �� subcarriers,

� �� ?2� 1

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 � � k � �5 � � n � � �G �� , 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 nonlinear maximum a posteriori (MAP) detector is applicable in the described SA based mobileradio system, as its complexity is reduced due to the subcarrierwise equalization. Complexityof 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 theknowledge of the employed modulation alphabet � to deliver the estimated vector�� n �� + n ��

� � � � n � � �� n � � � � n � ��G ��P� (4.1)

according to the maximum a posteriori (MAP) principle. If all data vectors� � n ��

�are

equiprobable, then the optimum detector is the one following the maximum likelihood vectorestimation (MLVE) principle and producing the estimated vector [WSC02]�� n �� + n � ��

� � � �� n � � � � n � � � � n � � �G � �P (4.2)

Expression (4.2) for the MLVE detector can be simplified to the form�� n �� n �� ! �� n � 8 ��

n � � � n � � � � n � ��G ��P� (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 � with a lower complexity than the optimum

MLVE detector of (4.3) in the same subcarrierwise transmission system model, in a linear wayfrom the received signal

�� n � , since optimum detector with subcarrierwise involves exhaustivesearches among a set of �

�possible data vectors

� � n � .Due to the fact that the a priori knowledge concerning the data symbols

� � n � is not exploited bylinear 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 �

,different linear detectors can be designed.

The most simple suboptimum receiver consists of a bank of filters (MF), matched on the MIMOchannel transfer matrix

��of (3.4), yielding the estimates as

�� n ��

n � ��

n � #

� �� n � �� n � � (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 ��

n � ��

n � #

� �� n � �� n �

��

n � ��

n � #

� �� n � ��

n � � � (4.5)

where��

n � ��

n �

is, in the general case, a non diagonal matrix and then there will be inter-ference between different data symbols

�, as�� n ��

� � � � n � : � �� n � : 7: � � � � n � : : � �

� �� n � � (4.6)

with � � , k � �5 � , being the complex elements of k-th row of��

n � ��

n �

, and the non zerocontributions of � ��

�� , in (4.6) represent interference.

If the minimal distance �� 8 ��

n � �� n �

is the target criterion which the linearly obtained

candidate estimated vector�� n �

must satisfy and in (3.5) additive white noise�� with correlation

matrix [WSC02] �� (4.7)

is assumed, then the zero-forcing (ZF) detector

�� n ��

n � % � ��

n � � # � ��

n � % � �� n � (4.8)

results, which totally suppresses the interferences between active MTs at the expense of a noiseenhancement.

22nd May 2003

33

5 Parallel interference cancellation

5.1 Introduction

The task of the CU in the uplink JOINT [WMS)

02] is to remove the intra-SA interferenceresulting from the simultaneous operation of the MTs by jointly processing the received signalsof the APs. Various algorithms can be employed to perform the JD process at the CU, such asZF detection [SWC

)02] or optimum MLVE detection [WMS

)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 motivatedand 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 theparallel 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 processwhich is indeed highly beneficial in terms of computational complexity for linear detectors suchas ZF involving matrix inversion. Moreover, the complexity reduction makes the applicationof the optimum non-linear MLVE detector possible, as shown in Section 4.2. However, nosignificant complexity reduction can be achieved with subcarrierwise equalization in the caseof 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)

02].According to the principle of JOINT, the signals received

�� of (3.6) at the various APs will bejointly processed at the CU.

Instead of working with the received signal�� , the scaled estimates of matched filter output

��

� �� (5.1)

with �� % � �� (5.2)

can be used, as it is a set of sufficient statistics for�� [For72].

Every element�� k � n � , k = 1... � � n � � �G �� , 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 signalsbelonging 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 eachiteration � � ��0 , after processing with the forward path matrix

�� % � �� #

�

� (5.3)

the inter-SA interference is approximately reconstructed with the feedback matrix

�� % � �� (5.4)

and subsequently substracted from�

� of (5.2). In (5.4) the operator � � �� is used on a squarematrix and returns a matrix with the off-diagonal elements of its argument.

filter bankmatched

estimate refinementand

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�� ;� of the data symbol estimates�� ;� 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

�� ;� 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 refinementat all, as Fig. 5.2 shows.

demod

filter bankmatched

FEC

��

��

��

�� !��"$#%�&�'��#(�

Figure 5.2. Iterative detection with no estimate refinement

In each iteration, the refined estimates

�� P� � �� ;� (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 � � �� (5.6)

The a-priori knowledge of (5.6) can be exploited at the CU to refine the estimates�� ;� gained

at each iteration � by applying hard quantization on the continuous valued estimates�� ;� with

5.5 Estimate refinement by soft quantization

22nd May 2003

36

respect to the symbol constellation � , as�� ;�G� �� ! � � � �� P�A8 � �� (5.7)

As Fig. 5.3 shows, the data symbol estimates�� ;� of each iteration � are quantized to the

modulation constellation � used.

demod

FEC

��

��

��

�� !#" �� $&%'�)(�*

�,+-�/.0�1��/�2$3� ! (4� �5�,(6�

Figure 5.3. Iterative detection with hard estimate refinement


In order to improve the basic estimate refinement by hard quantization which consits in a innersign function, a estimate refinement by soft quantization is introduced, justified on the basis thatit minimizes mean-square error.

The optimal nonlinear PIC detector, shown in Fig. 5.4, with respect to the error

� � � �� k �7 8 � � k �7 � �

� �� k �7 8 � � � � k �7 � �� k �7 � �

:98 �� k �7� �� k �7 � � (5.8)

where � � � �� represent the number of bits of the data symbols�� k �

, transmitted per eachMT � k � �G � , is explained in this section.


22nd May 2003

37

The error� � � ��

�k �7 8 �

�k �7 �

of (5.8) becomes minimal if the refined estimates

�� k �7 � � � � � k �7� �� k �7 � � (5.9)

are produced by the PIC detector. Because ��k �7 � # 8�� &�� k ��G � � � � �5 � , the

log-likelihood ratios

� � � � k �7 � �� k �7 � ��

��k �7 � : � � �� k �7

� ��k �7 � 8�� k �7

!$ � (5.10)

of the a-posteriori probabilities� �

��k �7 �� k �7 , of the modulated bits �

�k �7 , can be used,

which can be expressed depending on the log-likelihood ratios� � ��

�k �7 � � � k �7 � , of the conditional

probabilities� � ��

�k �7 � � � k �7 � � , of the estimates

��k �7 and on the log-likelihood ratios

� � � � k �7 � ,

of the a-priori probabilities� �

��k �7 �� , of the modulated bits �

�k �7 , as

� � � � k �7 � �� k �7 � ��

� ��k �7 � � � k �7 � : �

� � ��k �7 � � � k �7 ��8��

!$� ��

� � �� k �7� � � k �7 �

:��

��k �7 � : �

� ��k �7 ��8��

!$� �� k �7

(5.11)

With (5.10), and assuming that all ��k �7 � k ��G � � � � �G � , are equiprobable, i.e.

� � � � k �7� � < (5.12)

holds, using (5.11), (5.12) and

� �� k � � : � � �� k � � �T+.-� � � �� k �7

� � � k �7 � ��T+.-� � � �� k �7

� � � k �7 � : � ��

�T+.-� � � �� k �7� � � k �7 � B 1 �

�T+.-�� k �7� � � k �7 � B 1 � :=�T+.-�*8 � � �� k �7

� � � k �7 � B 1 �(5.13)

� �� k � ��8�� k � � �

�T+.-� � � �� k �7� � � k �7 � : ��

��,+>-�*8 � � �� k �7 � � � k �7 � B 1 �

�T+.-� � � �� k �7� � � k �7 � B 1 �2: �T+.-�*8 � � �� k �7 � � � k �7 � B 1 �

(5.14)(5.9) becomes

�� k �7 � � �� k �7 � � � k �7 �1

!$ � k ��G � � � � �G � (5.15)

To calculate the refined estimates��k �7 as in (5.15), the log-likelihood ratios

� � ��k �7 � � � k �7 � , i.e.,

the probabilities� � ��

�k �7 � � � k �7 �� , need to be calculated. To accomplish such a task, it is


22nd May 2003

38

assumed that additive white gaussian noise�� with mean value � � < and variance � �� is

superimposed at the demodulated bits ��k �7 giving rise to noisy estimates

�� k �7 � � � k �7 : �� G � � k ��G � (5.16)

Due to (5.15) each estimate��k �7 is also gaussian distributed with mean value �

�k �7 and variance� �� . With the probability distribution functions

-� �� k �7 � � � k �7 � � � � �� 143 �� T+.-

�8 �143 � ��

� �� k �7�� (5.17)

of��k �7 and the corresponding probabilities

� � ��k �7 � � � k �7 �� , the refined estimates

�� k �7 � � � � � � 1 ��k �7

� �� k ��5 � � � � �G � � (5.18)

can be calculated from (5.15).

Clearly, the assumption of the white and gaussian nature of�� is not close to reality, but it

helps to considerably simplify expressions and on the other hand, the errors produced by thisassumption have only a marginal impact on the performance of the PIC detector.

estimation

demod

mod

filter bankmatched

FEC

�� !��"�

#$ #%

&&' �"(*),+-� &. �"(/�&&' �"(/�

01

023 ��4� 56�-� 38793;: � 3 5 3 ��

�<� �

=?>A@ <BDC EGFHJI BDC EKFHML

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 ErrorRate (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 ofthe data detector. In addition, another performance measures can be used to analyze, designand understanding of the various detectors. Spectral radius in the case of PIC and multiuserefficiency are introduced in this chapter for the study of the performance of JD in OFDM uplinktransmission 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 thanone 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 thereceived transmission power

� � � n � " of each transmitted data symbol � � � � n � , the SNR of thatdata symbol of a JD detector can be calculated as� � � � � � n � "

� � :��

V '� �

� ' � � V � � � " ' �� n � V � � 8 � � � n � " � � � ��0�� n � � �G �� P (6.2)

The decreased SNR

�� of (6.1) relative to the SNR

� � of (6.2) results in bit-error-rates � � � n �� IR � � � n �� holds, due to the presence of other MTs that are introducing MAI.

Equivalently, in the single user scenario, to achieve the same BER � � � n �� as in multiuser

scenario � � � n �� , lower transmission power

�k � n � "� of the data symbol

�� k � n �than that of a

multiuser scenario, is required because no MAI is present and the background noise keeps thesame level. This can be mathematically explained by

� � � n �� n �� (6.3)

6.2 Multiuser efficiency

22nd May 2003

40

then with (6.3) � � � n � � � � � n �� 0 � � n � ��G ��P� (6.4)

Finally the multiuser efficiency � � � � n � � � � ��0� � � n � � �G � �P� is defined as ratio betweenenergies

� � � n �� and � � � n � in single user scenario and in multiuser scenario respectively, when

they have the same BER,

� � � � n � � � � � n �� n � � � �� n �� ' � �� n � �� 0� � � n � ��5 � �P� (6.5)

It can be explained as follows, the more MTs in the service area, the higher transmission poweris required for the MT

�to hold the BER, then, the lower multiuser efficiency � � � � n � is.

In (6.5) the multiuser efficiency depends on the background noise level. The asymptotic mul-tiuser efficiency �

� � � n �� , is introduced to measure the multiuser system performance regardingonly to the MAI [Ver98]

��k � n �� + � � k � n � � k � �G � � n � ��5 � �P (6.6)

In order to calculate the assymtotic multiuser efficiency �� n �� , from (6.5), the multiuser effi-

ciency � � � � n � can be calculated as

� � � � n � � � � � n � "� � � � n � "

�� n �� ' � �� n � ��

� �k � n �� k � n ��

�� k � n �� ' � k � n � � �

�

� �k � n �� k � n ��

�� k � n �� k � n ��

�� k � n �� ' � k � n � � � ��

k � n �� k � n ��

(6.7)

� k � �G � � n � ��5 � �;� (6.8)

where

� �k � n �� and

� �k � n �� represents the SNR at output of MF and JD detectors respectively.

Since��

k � n �� and��

k � n �� 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 �� can becalculated as

��k � n �� + �

�k � n � �

�� k � n �� k � n ��

� k ��5 � � n � � �G ��P (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 � . Assuming that the

superimposed noise is Gaussian and white with covariance matrix�� (6.10)

data estimates�� k � n �

with an SNR

� � � � n �� n � ��

�

1 � �� n � � � ��

n � #

��&@&� (6.11)

�9� � � 8H�7� �� : �P� � ��0 � � � ��0� � �;�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

�� iswhite and wide sense stationary with the power � � and neglecting MAI

� � � � � �� n � ��

�

1 � � � � �� n � � � ��

n � �� & & � (6.12)

�9� � � 8H� � �� : �P� � � ��0 � � � �� P�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 �

whencomparing the cases of (6.12) and (6.13), the SNR degradation

� � � � � � ��

� � �� n � � � ��

n � #

� ��

� � �� n ��

n � �� (6.13)

� ��0� � � � ��0 ��P�is introduced, as a performance measure. This degradation is, as said, the price to be paid for the

unbiasedness of the estimates�� n �

in the form of an enhancement of the noise level inducedby the JD process.

The presence of other users in the channel can only decrease the SNR of��

so that the SNR ofJD is always upper bounded by that of matched filter� � � � � �� k ��5 � � n � � �G � �P� (6.14)

It has to take in account that degradation � quantifies the performance loss due to the existenceof 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 � and asymptotic multiuser efficiency �� n �� can be

calculates as follows. From (6.14), the SNR degradation � � � � n � can be obtained as

� � � � n � ��

k � n �� k � n ��

�� k � n �� ' � k � n �

�

� �k � n �� k � n ��

�� k � n �� k � n ��

�� k � n �� ' � k � n � ��

k � n �� k � n �� (6.15)

� k � �G � � n � ��5 � �;� (6.16)

where

� �k � n �� and

� �k � n �� represents the SNR at output of MF and JD detectors respectively,��

k � n �� and��

k � n �� are constants which actually only depend on the system matrix��

. From(6.8) and (6.16), the relation of SNR degradation � � � � n � and asymptotic multiuser efficiency

�� n �� of data symbol

�� k � n �for JD can be drawn as

�� n ��

� � � � n � � k ��G � � n � ��G ��P (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) �

� �� % � �� #

� �� % � �� (6.18)

at the � th iteration the estimated�� ;� is�� ;�G� �

� 8� � � �� % � �� #

�

� � �� % � �� - 8 �7�T� (6.19)

at the output of the PIC detector.

With the eigenvalues � � � �� of

�� , with matrices

��, (5.3) and

��, (5.4)��

� � � �� % � �� #�

� � � � � �� % � �� (6.20)

the iterative process of Fig. 5.2 converges only if the spectral radius

' � �� G� �� + # � � � � � � � � � � & (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),�� % � �� #

� �� % � �� (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 inChapter 6, are used to assess the performance of the PIC detector, a special case is introducedand 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, thatthe energy of the partial received signal

�� k � n � , at the APs of the SA caused by the transmissionof a single data symbol � � k � n � is constant for all data symbols � � k � n � � k � �5 � � n ��G �� . 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 thesame 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 allsimulations.

The fixed parameters are:

� Carrier frequency �76G� ?2 ?�� System used bandwidth

� � 1 <�� 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 PICis the convergence, an important performance measure for the PIC detector is the spectral radiusdescribed in Section 6.4.

Consequently an investigation regarding spectral radius is developed in this section, taking inaccount that a frozen channel is used in all simulations.

The spectral radius for each subcarrier can describe the convergence in the case of no refinementestimation. In Figs. 7.1 and 7.2 the cumulative distribution function (cdf) of spectral radius ' ,is shown for the case of a scenario where PIC is performed subcarrierwise and a sufficientlylarge 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 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PSfrag replacements

� � 1 � � MTs

non convergenceconvergence

�

��

Figure 7.1. CDF of the spectral radius in the channel with � � 1 0� � MTs and �� APs

observed that with � � 1 MTs in all subcarriers PIC detector converges, as in all subcarriersholds 'NL � . On the other hand, in the case of 3 and 4 MTs, PIC in only 60% and 10% ofthe subcarriers converges, respectively. It can be observed from Fig. 7.2, that in the case of� �N�� APs when � � 1 or � �� MTs are active in the SA PIC detection converges inall the subcarriers. With � � �

or � ��? MTs some subcarriers with non-convergent andconvergent results are present and finally with � � � , � � � or � �� MTs, PIC does notconverge at any subcarrier. If the fully loaded case is taken into account, then by comparingthe cases of Fig. 7.1 and 7.2 it can be seen that with � �� MTs active in the SA, there existabsolutely 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, moreMAI exists and less subcarriers that PIC detector converge are present. Therefore spectralradius is also a measure of how much MAI is present and how it is affecting each subcarrier inthe 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 ' � n � .The case of PIC with no estimate refinement which converges to the ZF detector is explainedin 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 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PSfrag replacements

� � 1 �� MTs

non convergenceconvergence

�

��

Figure 7.2. CDF of the spectral radius in the channel with � � 1 0� � MTs and �� APs

radius ' � � � � � � <> � 1 � ? , so in the figure can be observed that the BER of the PIC detector atthe 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 � � � 1 at which does PIC not con-verge, as it is characterized by spectral radius ' � � � � � � �� <�<>�� , in the case of a fully loaded casewith � � �

MTs and � � � �APs, the performance of different estimate refinement techniques

can be observed and it can be remarked that the estimates�� n � � � � 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

100

AWGNMFZF1−iter2−iter3−iter4−iter5−iter

PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.3. PIC with � � MTs and � �=� �APs ? iterations with no quantization in the

subcarrier n � � 1 <�< with spectral radius ' � � � � � � <. � 1 � ?

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.4. PIC with � � �MTs and � �=� �

APs ? iterations with no quantization in thesubcarrier n � � � 1 with spectral radius ' � � � � � � ��@<�<.��

Finally Fig. 7.6 demonstrates the clearly superior performance of soft quantization when iscompared to the cases of no and hard quantization.


22nd May 2003

47

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.5. PIC with � � �MTs and � � � �

APs ? iterations with hard quantization in thesubcarrier n � � � 1 with spectral radius ' � � � � � � ��@<�<.��

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�


APs ? iterations with soft quantization in thesubcarrier n � � � 1 with spectral radius ' � � � � � � ��@<�<.��

As it can be seen from Figs. 7.7 - 7.9, in the case of a spectral radius ' � � � � � close to zero, MAI


22nd May 2003

48

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.7. PIC with � � 1 MTs and � �=� �APs ? iterations with no quantization in the

subcarrier n � � with spectral radius ' � � � � � � <.@< �<>�

−10 −5 0 5 10 15 2010

−4

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.8. PIC with � � 1 MTs and � � � �APs ? iterations with hard quantization in the


7.4 Special case

22nd May 2003

49

in a SA is also close to zero. Consequently, the� performance of all multiuser detectors such

as MF, ZF and PIC will coincide with the single user bound. Mathematically stated

'�� <� � � #

��

� �� &�� <�� n � ��

n ��

(7.1)

where � � �� the eigenvalues of the � � � matrix��

n � ��

n �

which means that�� ;�G� <>� � � 1 � (7.2)

i.e., a reconstruction of interference does not take place, as MAI is absent.

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.9. PIC with � � 1 MTs and � � � �APs ? iterations with soft quantization in the


7.4 Special case

The case of� � 1 (7.3)

exhibits special interest when no data estimate refinement techniques are applied, i.e., if�� n � � �� n �(7.4)

7.4 Special case

22nd May 2003

50

holds. If (7.3) holds, PIC with no estimate refinement as shown in Fig. 7.11 performs betterthan estimate refinement by hard or soft quantization of Figs. 7.12 and 7.13 respectively in theeven iterations

� � 1 � � � � �� (7.5)

of the case of 2MTs. Moreover in Fig. 7.11 can be seen that at all even iterations PIC with noestimate refinement manages to effectively remove all MAI from the MF estimates.

The transfer matrix �� n � �

� � � ��

� � (7.6)

will be used. With��

n �

of (7.6), the MF output with the feedback matrix��

n �

of (5.3) applied

�� n � �� n � � ��

n � ��

n � % � �� n � �

��

� � � n � : � % � : � �� : � � � % �

� �� n �

� � � � n � : � � : � %�� : � � � %�

� � � � n �! "$ (7.7)

of (4.4), and the��

n � ��

n �

matrix, with matrices��

of (5.3) and��

of (5.4)

�� n � ��

n � �

�� < � % � : � �

� : � � � % �� : � %�� : � � � %� <

! "$ � (7.8)

the estimates�� n � � <�� <�� n � � � � � �� n � �� n �� n � � 1 � � ��

n � �� n � 8 ��

n � ��

n � �� n � � �7� � �

��8� � � : � %� � � � % � : � � �� : � % � � � � � �I: � %� � � �

� � � � � � n �� n � �

�� n � � �� n � �� n � 8 ��

n � ��

n � �� n � � 1 � �

�� n � : � � % � : � � � � � � : � %� �

�

� � : � � � % � �� : � � � %� � �

� � � n �

� �� n � : � � % � : � � �

� � � � : � %� �� : � � � % � � � �5: � � � %� �� n �

! """"""$

(7.9)

are present at the output of the parallel interference canceler at the first three iterations. From(7.9) it can be seen that at iteration � � 1 all intra-SA interference free estimates are yielded,except from the scaling factor

� � 1 �G��8� � � : � %� � � � % � : � � �� 5: � % � � � � � � : � %� � � � (7.10)

7.4 Special case

22nd May 2003

51

0

0.2

0.4

0.6

0.8

1

00.2

0.40.6

0.81

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

��

��

Figure 7.10. Scaling factor � � 1 � as a function of � � and � � , if � � � � � � �

For the simple case of � � � � � �� Fig. 7.10 shows the dependence of � � 1 � of (7.10) on � � and

� � . It is to be seen that if � � � � � �� , � � 1 � � <> ? , i.e., no bit errors will be induced by the scalingof

� � n � with � � 1 � .

Assume that the interference free estimates are present also at the end of an arbitrary eveniteration, � � 1 � , which means that�� n � � 1 �Q�5� � � 1 �Q� � � n � (7.11)

holds. Then, with the matrices� ��

n � ��

n � �

� � � 8 � � 1 �E�� (7.12)

and

��M8 ��

n � ��

n � ��

n � �� n � �

�� 8 � % � : � �

� : � � � % �8 � � : � %�� : � � � %� �

! "$

��

� � � n � : � % � : � �� : � � � % � �

� � � n �� n � : � � : � %�

� : � � � %� �� n �

! "$

��8

� � � : � %� � � � % � : � � �� 5: � % � � � � � �5: � %� � � �� n �

� � � 1 � � � n � � (7.13)

7.4 Special case

22nd May 2003

52

at the next even iteration � � 1 � : 1 , the estimates�� n � � 1 � : 1 � � �� n � �� n � 8 ��

n � ��

n � �� n � � 1 � : �7�

� �� n � �� n � 8 ��

n � ��

n � � ��

n � �� n � 8 ��

n � ��

n � �� n � � 1 �Q�

��M8 ��

n � ��

n � ��

n � �� n � : � ��

n � ��

n � � �� n � � 1 �Q�

� � � 1 � � � n � : � ��8 � � 1 �E� � � 1 �Q� � � n �� 1 �Q� : � � 1 �A8 � � 1 � � � 1 �Q�� n � (7.14)

free from interference are present at the output of the PIC detector. With (7.9), (7.11) and (7.14)is shown with the method of induction that for the case of two MTs, at every even iteration� � �� 1 � � � � �G � , interference free estimates are present at the output of the PICdetector.

This interference free nature of the estimates�� n � � 1 � : 1 �T� � � �G � , can be justified

as follows. For the two MT case, the estimates�� n � � �;� at every even iteration � are the MF

output��n � of (4.4) multiplied with the matrix � 8 ��

n � ��

n �

of (7.13), which in the 2 MT casecorresponds except a complex scaling factor to the decorrelator matrix� �

� � �� n � % � ��

n � � � # � ��

n � % � ��

n � � # � of (4.8) removing all interference in

��n � .

7.4 Special case

22nd May 2003

53

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100

AWGNMFZF1−iter2−iter3−iter4−iter5−iter6−iter7−iter8−iter

PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.11. Case of � � 1 MTs and � � � �APs � iterations in the case of no quantization in

the subcarrier n � � � � with spectral radius ' �� <> ��<

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.12. Case of � � 1 MTs and � � � �APs � iterations in the case of hard quantization

in the subcarrier n � � � � with spectral radius ' �� <> ��<

7.5 PIC with improved estimate refinement

22nd May 2003

54

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.13. Case of � � 1 MTs and � �Q� �APs � iterations in the case of soft quantization

in the subcarrier n � � � � with spectral radius ' �� <> ��<


In this section a modification of the refinement techniques by hard and soft quantization isintroduced.

An improvement in� can be obtained just starting the estimate refinement after the second

iteration, taking advantage of the special case of � � 1 MTs as explained in Section 7.4where in the second iteration intra-SA interference free estimates are yielded in the case whenno refinement technique is applied, except from the scaling factor (7.10). Thanks to start theestimate refinement after the second iteration in which case the estimates data vector

�� 1 � isclean from interference,

�� and the subsequent iterative estimations can be more accuratelyestimated, resulting in a improvement in

� .

The Figs. 7.14 - 7.18 are shown the performance obtained using this modification, comparedwith the standard estimate refinement by hard or soft quantization and without estimate refine-ment.


22nd May 2003

55

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.14. PIC with � � 1 MTs and � � � �APs ? iterations with no quantization in the

subcarrier n � � �7?.� that PIC converges

−10 −5 0 5 10 15 2010

−4

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.15. PIC with � � 1 MTs and � � � �APs ? iterations with hard quantization in the



22nd May 2003

56

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100

AWGNMFZF1−iter2−iter3−iter4−iter5−iter6−iter7−iter8−iter9−iter10−iter

PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.16. PIC with � � 1 MTs and � � � �APs � < iterations with hard quantization

starting at the third iteration in the subcarrier n � � �7?.� that PIC converges

−10 −5 0 5 10 15 2010

−4

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.17. PIC with � � 1 MTs and � � � �APs ? iterations with soft quantization in the


Comparing Fig. 7.14 with Fig.7.15, with no refinement technique and with refinement tech-nique by hard quantization respectively, it can be observed that the performance of the PIC

7.6 PIC performance over all subcarriers

22nd May 2003

57

detector when no refinement technique is applied is better than the case of hard quantization.Moreover PIC with no estimate refinement converges and with hard quantization does not con-verge. In Fig. 7.16 with refinement technique by modified hard quantization, the improvementin� respect Fig. 7.15 with standard refinement technique by hard quantization can be ob-

served, in this case PIC converges, moreover it has the same performance as Fig. 7.17 with softquantization. Finally Figs. 7.17 and 7.18 show the improvement in terms of

� gained in the

case when estimate refinement by soft quantization is modified.

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.18. PIC with � � 1 MTs and � � � �APs � < iterations with soft quantization starting

at the third iteration in the subcarrier n � � � ?.� that PIC converges


Finally results about the performance over �� 1 is investigated to extend the results for thecase using subcarrierwise investigation.


22nd May 2003

58

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.19. PIC with � � MTs and � � � �APs � iterations without refinement estimate

over �� 1 subcarriers

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.20. PIC with � � MTs and � � � �APs � iterations with hard quantization over

�� 1 subcarriers


22nd May 2003

59

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

��

Figure 7.21. PIC with � � MTs and � � � �APs � iterations with hard quantization starting

at the third iteration over � � � 1 subcarriers

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.22. PIC with � � MTs and � �B� �APs � iterations with soft quantization over

�� 1 subcarriers


22nd May 2003

60

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.23. PIC with � � MTs and � � � �APs � iterations with soft quantization starting

at the third iteration over � � � 1 subcarriers

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100

AWGNZFMF1−iter2−iter3−iter4−iter5−iter6−iter7−iter8−iter9−iter10−iter

PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.24. PIC with � � MTs and � � � � APs � < iterations without estimate refinementover �� 1 subcarriers

In figures 7.19 to 7.28, can be observed the performance of application of estimate refinementtechniques and the improvement of the modification of the estimate refinement technique ex-


22nd May 2003

61

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100

AWGN1−iter2−iter3−iter4−iter5−iter6−iter7−iter8−iter9−iter10−iterZF

PSfrag replacements

� < � � � � � � ! � B � � � B � �

��

Figure 7.25. PIC with � � MTs and � � � � APs � < iterations with hard quantization over�� 1 subcarriers

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100

AWGN1−iter2−iter3−iter4−iter5−iter6−iter7−iter8−iter9−iter10−iterZF

PSfrag replacements

� < � � � � � � ! � B � � � B � �

� �

Figure 7.26. PIC with � � MTs and � � � � APs � < iterations with hard quantizationstarting at the third iteration over � � � 1 subcarriers


22nd May 2003

62

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.27. PIC with � �� MTs and � � � � APs � < iterations with soft quantization over�� 1 subcarriers

−10 −5 0 5 10 15 20

10−3

10−2

10−1

100


PSfrag replacements

� < � � � � � � ! � B � � � B � �

�

Figure 7.28. PIC with � � MTs and � � �� APs � < iterations with soft quantization startingat the third iteration over � � � 1 subcarriers


22nd May 2003

63

tended in the case of � � MTs.

As can be observed from Figs. 7.19 to 7.28, the extension of the improved version of estimaterefinement technique for PIC at the case of 3 MTs results in a performance improvement ifcompared to PIC with standard estimate refinement techniques. Although no theoretical proofis supplied in the present thesis as was done for the case of 2 MTs, it can be intuitively supportedthat the improved estimate refinement technique for PIC brings performance improvement alsofor larger number K of active MTs in the SA. A detailed proof can be a topic of future research.

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8 Summary

8.1 Conclusions

In the present thesis, the concept for beyond 3G mobile radio systems is described. A servicearea concept is introduced in order to combat the performance limiting interferences presentin the cellular mobile communication systems, with each service area consisting of a varioussimultaneously active mobile terminals, a number of fixed access points and a central unit per-forming signal processing. About uplink transmission, the main characteristic of this servicearea system is that with the aid of joint detection of the transmit signals from the mobile ter-minals performed at uplink transmission, all interferences between the simultaneously activemobile terminals using the same bandwidth is drastically reduced. Moreover the use of OFDMsubcarrierwise in the described service area based system allows for intersymbol interferencefree communication and for simple equalization in the frequency domain.

Through this subcarrierwise equalization the service area based system is equivalent with anumber of smaller parallel systems, a fact that affects in a reduced computational complexityin the case of optimum multiuser operating with the maximum likehood principle and subop-timum linear detector zero-forcing. In this thesis the parallel interference cancellation detectoris introduced, according to which the multi access interference is iteratively reconstructed andsubtracted from the received signal. Parallel interference cancellation detector is compared interms of performance with suboptimum linear detector, due to the reduced computational com-plexity.

Using standardized COST 207 channel models, the performance of parallel interference can-cellation detector compared with suboptimum linear detector has been investigated for a frozenchannel, with the same snapshot using the same parameters of the channel, as well as for anumber of system loads. A fact that can be observed in simulations results is that parallel in-terference cancellation detectors could achieve the same performance with a reduction of thecomplexity as suboptimum linear detector zero-forcing in the case of no estimate refinementand with estimate refinement by hard quantization depending on the load system. With esti-mate refinement by soft quantization the performance of the parallel interference cancellationdetector is improved, having better performance than zero-forcing detector in cases with nor-mal load. Moreover with the improvement raised in this thesis, in this normal system load,the performance is more improved. On the other hand in the case of full load system, the PICdetector can not substract all the multi access interference producing error flow, this thing is nottoo important taking in account that the fully loaded system case should not be never present.

8.2 Outlook

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8.2 Outlook

More investigations have to be done to perform the parallel interference cancellation techniquesand his estimate refinement techniques, the modification raised in this thesis could be a nicepoint to begin with investigations, investigate about in which cases odd or even iterations arebetter, depending on the load of the system, could determine the better iteration to start therefinement technique. The same occurs with the convergence of the iterative process with thedifferent estimate refinement techniques, that they affect to the performance of the parallelinterference cancellation, they should be mathematically investigated.

In the case of fully loaded systems forward error coding can be investigated in order to improvethe performance of parallel interference cancellation detectors. And extend all investigations toliving channels to compare the results in front of frozen channels.

Another estimate refinement techniques should be investigated such Turbo multiuser detection,exploiting also knowledge of the employed forward error coding.

References

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

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