FMT

iii

Contents
Chapter 1. Introduction 1
Chapter 2. The Multipath Radio Channel 3
2.1. Exponentially decaying Rayleigh Fading Channel 3
Chapter 3. Introduction to Multi Carrier Modulation for Broadband
Communication Systems
5
3.1. OFDM Modulation 6
3.1.1. Effects of multipath and Cyclic Prefix (CP) solution 8
3.1.2. OFDM generation 8
3.1.3. Virtual Carriers 9
3.1.4. Performance with Frequency and Timing Errors 10
3.1.5. The Peak to Average Power Problem 13
3.2. OFDM/DMT conclusion 13
Chapter 4. Filtered Multitone Modulation 15
4.1. FMT as a Multirate Filter Bank (General Principles) 16
4.1.1. FMT Transmitter 16
4.1.2. FMT Receiver 20
4.1.3. Perfect reconstruction condition 22
4.1.4. Prototype design 23
4.2. OFDM as a filter bank 27
4.3. Virtual Carriers 28
4.4. Conclusion 30
Chapter 5. Equalization in FMT 31
5.1. Per subchannel DFE: Computation of the MMSE equalizer coefficients
based on channel estimation
33
5.2. Efficient FMT equalization schemes 36
5.2.1. Frequency domain DFE 36
5.2.2. Time Domain DFE 38
5.2.3. Complexity 39
5.2.4. Achievable bit rate and loading algorithms 40
5.2.5. Simulation results 41
5.3. Precoding 44
5.4. Adaptive equalizers in FMT 45
5.4.1. Adaptive Decision Feedback Equalization 46
5.4.2. Simulation results 50
5.4.3. Proposed simplified adaptive algorithms 52
5.4.4. Further improvement in outdoor environments 53
5.4.5. Simulation results 55
5.4.6. Conclusions about the proposed scheme 56
Chapter 6. Conclusions, future improvements and usage 59
References 61
iv

Appendix A: The Multipath Channel 63
Appendix B: Computation of the DFE coefficients 69
Appendix C: Precoding 75

v

Symbols/Acronyms

ADC Analog to Digital Converter
ADSL Asymmetric Digital Subscriber Line
AWGN Additive White Gaussian Noise
BPSK Binary Phase Shift Keying
BWA Broadband Wireless Access
CP Cyclic Prefix
DAB Digital Audio Broadcasting
DAC Digital to Analog Converter
DFE Decision Feedback Equalizer
DFT Discrete Fourier Transform
DMT Discrete Multitone
DVB Digital Video Broadcasting
DWMT Discrete Wavelet Multitone Modulation
FDM Frequency Division Multiplex
FFT Fast Fourier Transform
FIR Finite Impulse Response
FMT Filtered Multititone
ICI Inter Carrier Interference
ISI Inter Symbol Interference
LMS Least Mean Squares
LOS Line of Sight
MCM Multicarrier Modulation
OFDM Orthogonal Frequency Division Multiplexing
P/S Parallel to Serial
PAPR Peak to Average Power Ratio
PDF Probability Density Function
PR Perfect Reconstruction
PSD Power Spectral Density
QAM Quadrature Amplitude Modulation
QPSK Quadrature Phase Shift Keying
RC Raised Cosine
RLS Recursive Least Squares
RMS Root Mean Square
RRC Root Raised Cosine
S/P Serial to Parallel
SNR Signal to Noise Ratio
TDM Time Division Multiplex
THP Tomlinson Harashima Precoding
VC Virtual Carrier
VDSL Very High-speed Digital Subscriber Lines


Notation


M
Number of subchannels
T
FMT symbol period
k
Index for samples with sampling period equal to the FMT symbol period T
vi

n
Index for samples with sampling period equat to T/M
h
(i)
(k)
=h(kM+i), i-th polyphase componet of h(n)
h
(i)
(n)
= h(n)e
j2πi/M
transmitter filter of the i-th subchannel
A
(i)
(k)
QAM or QPSK symbol of the i-th subchannel
x

Column vector x
x

Matrix x
γ Overlap

vii

Publications


The following publications, appended at the end of the thesis, relate to the work in
this thesis:

1. Inaki Berenguer, Ian J. Wassell, “FMT Modulation: Receiver Filter Bank
definition for the Derivation of an Efficient Implementation”, Proc. IEEE 7
th

International OFDM Workshop, Hamburg, Germany, Sept. 2002

2. Inaki Berenguer, Ian J. Wassell, “Efficient FMT equalization in outdoor
broadband wireless systems”, Proc. IEEE International Symposium on
Advances in Wireless Communications, Victoria, Canada, Sept. 2002.

viii

1














Chapter 1. Introduction


This thesis addresses Filtered Multitone (FMT) modulation, a multicarrier
modulation technique initially introduced in 1999 for Very High Speed Digital
Subscriber Line (VDSL) applications [1][2] that can also be used in Broadband Fixed
Wireless Systems.

High data rate wireless communications are limited not only by additive noise but
often more significantly by the Intersymbol Interference (ISI) owing to multipath
propagation [3]. The effects of the ISI are negligible so long as the delay spread of the
multipath channel is significantly shorter than the duration of one transmitted symbol.
This implies that the symbol rate is limited by the channel memory. Multicarrier
modulation is an approach to overcome this limitation [4][5][6]. Here, a set of
subcarriers is used to transmit the information symbols in parallel in so-called
subchannels. This allows a higher data rate to be transmitted by ensuring that the
subchannel symbol duration exceeds that of the channel memory.

There are several approaches to multicarrier transmission. The spectral partitioning
can generally be realized in the form of overlapping or non-overlapping subbands.

The multicarrier techniques used in today’s standards (Digital Audio Broadcast,
ADSL, HIPERLAN/2, Terrestrial Digital Video Broadcasting, etc [7]) are based on
sinc(f) overlapping methods in which adjacent carriers are at the nulls of the sinc(f)
function (see Fig. 1 (a)). A guard interval is added to each transmitted symbol to
avoid ISI which occurs in multipath channels and destroys orthogonality. At the
receiver, the guard interval is removed. If the guard interval length is longer than the
maximum delay in the radio channel, zero ISI occurs and the orthogonality between
subcarriers is maintained. In this case, the multipath channel only changes the
amplitude and the phase of the subcarrier signals which can be easily equalized with a
set of complex gain coefficients. However, the longer the delay spread of the channel,
the higher the transmission inefficiency. These methods are known as Discrete
Multitone Modulation (DMT) or Orthogonal Frequency Division Multiplexing
(OFDM) when used in wireless systems [7].
2

(a)

(b)

Fig. 1 Subchannel frequency response of the first 5 subchannels (M=64) (a) OFDM and (b) FMT
with overlap=16
In contrast, in FMT modulation, the spectral partitioning is based on non-
overlapping methods. This filter bank modulation technique is based on M-branch
filters that are frequency shifted versions of a low pass prototype (uniform filter
bank). The prototype filter, achieves a high level of spectral containment such that the
Interchannel Interference (ICI) is negligible compared to the other noise signals in the
system and the subcarriers can be considered close to orthogonal, whatever the length
of the multipath channel (see Fig.1 (b)). In this way, FMT does not need the use of the
cyclic prefix used in DMT/OFDM to maintain subcarrier orthogonality in the
presence of multipath, thereby, improving the total throughput. However, per
subchannel equalization is needed in order to reduce the remaining intersymbol
interference [1].

These improvements are at the expense of higher complexity owing to filter bank
implementation and equalization requirements.

The remainder of the thesis is organized as follows:

Chapter 2 gives an overview of the wireless radio channel characteristics.

Chapter 3 gives an overview of conventional multicarrier modulations used to combat
the effects of multipath propagation, highlighting the main problems that FMT is
trying to solve.

Chapter 4 describes the FMT modulation from the point of view of filter bank theory.
It presents the low pass prototype filter that is the basic element of the filter bank and
proposes methods and parameters for its design. An efficient FMT implementation
using the M polyphase components of the prototype filter and the Fast Fourier
Transform (FFT) will be introduced. Reasons for the introduction of equalization will
also be presented.

Chapter 5 will present and also propose different equalization architectures based on
channel estimation or adaptive algorithms. The performance of the various
equalization architectures proposed will be investigated via the use of computer
simulations.

Chapter 6 draws conclusions and discusses areas for future research.
3












Chapter 2. The Multipath Radio Channel


Multicarrier Modulation techniques were originally conceived to transmit data in
time dispersive or frequency selective channels without the need for the use of
complex channel equalization [5][8]. To understand how this can be achieved, the
multipath wireless channel is described in Appendix A and some parameters that are
useful to describe the severity of different multipath environments are presented.

The systems under consideration will operate in the range from 2.5 to 17GHz.
Measurements confirm that these channels have similar characteristics and may be
modelled in a similar way [10].

2.1. Exponentially decaying Rayleigh Fading Channel

We now present the exponentially decaying Rayleigh Fading Channel Model [15]
used in the simulations conducted in this thesis. This channel was agreed by the IEEE
802.11 WLAN specification to be a baseline model for comparison of modulation
methods. The multipath model is selected to be a Rayleigh fading model with an
exponentially decaying power profile.

In this channel, the RMS delay spread τ
RMS
completely characterizes the path delay
profile. The model is simple to analyze and simulate. With a proper choice of the
delay spread values it represents realistic conditions.

The channel is assumed static throughout the transmitted packet and is generated
independently for each packet.

The impulse response of the channel is composed of complex samples with random
uniformly distributed phase and Rayleigh distributed magnitude with average power
decaying exponentially with equidistant delays, i.e.

∑
−
=
−=
1
max
0
)()()(
K
k
s
kTtkkc
δα

(1)
where c(k) is the channel impulse response and T
s
is the sampling period.

Each of the equi-spaced coefficients of the impulse response α(k) are defined as:
4

)
2
1
,0()
2
1
,0()(
22
kk
jNNk
σσα
+=

(2)
RMS
T
s
kT
k
e
/
2
0
2
−
=
σσ

(3)
RMS
T
s
T
e
/
2
0
1
−
−=
σ

(4)
where is a zero mean Gaussian random variable with variance
(produced by generating a N(0,1) random variable and multiplying it by
σ
)2/,0(
2
k
N
σ
RMSs
TT
e
/−
−
2/
2
k
σ
k
/√2) and
is chosen so that the condition ∑ =1 is satisfied to ensure same
average received power:
2
0
1=
σ
2
k
σ
1
)1(
1
)1()1(
/
/
0
//
0
/
2
0
0
2
=
−
−=−==
−
−
∞
=
−−
∞
=
−
∞
=
∑∑∑
RMSs
RMSsRMSsRMSsRMSs
TT
TT
k
TkTTT
k
TkT
k
k
e
eeee
σσ
(5)

The number of samples to be taken in the impulse response should ensure sufficient
decay of the impulse response tail, e.g. K
max
=10T
RMS
/T
s
.

For example, in HIPERLAN/2, the sampling rate is 1/T
s
=20MHz, and for an indoor
channel at 5GHz, the NLOS delay spread
σ
RMS is
40ns. If we consider taps with a
dynamic range of 30dB, K
max
in Eq. (1) will be equal to 5. In Fig. 2 we show a single
realization of this channel and the power profile with these parameters.


Fig. 2 Power profile (x) and a single realization (o)

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