An Efficient FMT Algorithm
Roman M. Vitenberg
Data-JCE Electronics
Andrea Tonello
Udine University
Tel Aviv, ISRAEL
Udine, ITALY
Abstract—The Filtered Multitone (FMT) Modulation
is a new communication technology that uses for
data transmission the orthogonal wavelets. This
paper describes a new efficient FMT algorithm,
which may be used for practical realization of high
performance Wireless Systems.
Keywords-component; Wireless, FMT, modulation,
wavelets.
INTRODUCTION
The Filtered Multitone Modulation was proposed by
group of researches from IBM as alternative technology
for xDSL [1]. This technology is based on Wavelet
theory and uses complex filter-banks for synthesis and
analysis of multi-channel signal.
I.
The theoretical aspects of FMT for Wireless
Application were developed by Cambridge University [2]
and Udine University [3]. It was shown that in many
cases FMT modulation might guarantee better
performance than OFDM.
A most significant advantage of FMT is absence of
out of band side lobes and high rejection of narrowband
RF noise. The FMT receiver is working as high order
bandpass filter and minimizes requirements to analogy
components of the System. A second advantage of FMT
before OFDM is absence of guard time interval (cyclic
prefix) that is necessary for OFDM. The cyclic prefix in
OFDM Systems takes up to 25% of OFDM symbol that
means: the FMT may have up to 25% better performance.
The FMT advantages are not realized up today
because of high complexity of synthesis and analysis
filter-banks, which were proposed for theoretical study of
FMT.
Data-JCE Electronics developed a new efficient FMT
algorithm in 2002 –2003 years. This algorithm lets
realize a low complexly FMT core.
SYNTHESIS OF A PROTOTYPE WAVELET
Suppose that our prototype wavelet shell be
II.
a) Symmetrical in time relative to its maximum.
b) limited in time.
From this two limitation follows that the prototype
wavelet W (t ) is a sum of cosine components with
frequencies Fn  k *1 / T , where T is a wavelet length
and k = 0,1,2…
We suppose that our wavelet comprises only N
cosine components, so:
N 1
W (t )   a k Cos(k / T );
k 0
and we will be look for W(t) that stay orthogonal for N
=> min.
It may be shown that N is relative small and depends
from acceptable level of the ISI (inter-symbol
interference).
Figure 1 demonstrates dependence of the ISI from N for
wavelets those were used for realization of an efficient
FMT algorithm.
The minimal number of cosine components for
prototype wavelet synthesis is 9. For practical prototype
of FMT system was used a prototype wavelet constructed
from 11 components.
So low number of frequency components lets
possibility to use IFFT for prototype wavelet synthesis.
Figure 2 illustrates how a prototype wavelet may be
produced by IFFT.
Figure 3 illustrates a new architecture of the FMT
Transmitter that uses IFFT for forming all sub-channel
wavelets.
Signal / ISI
60
dB
55
0
50
D0 w
D1
45
127/T
0
K
w
K
IFFT
128 point
w
P/S
DM-1
0
5
10
15
20
25
N
30
X(t)
Multicarrier spectrum
K
40
Synthesis
Filter-Bank
t127
t126
0
0
0
t1
t0
Figure 1.
a1
a2
a3
a4
0
127/T
126/T
125/T
124/T
123/T
Synthesis of baseband
prototype wavelet
t127
t126
w = a0,a1, a2,..a(K-1)/2
IFFT
128 point
0
a4
a3
a2
a1
a0
a0 a1
a2
5/T
4/T
3/T
2/T
1/T
0
a4
Figure 3.
W(t)
P/S
Each sub-channel wavelet is generated by group of k
IFFT inputs (in our example k=9). A resulting FMT line
signal X (t ) appears on IFFT output. Number of IFFT –
points defines a number of sub-channels  of FMT
System.
t1
t0
Prototype wavelet
spectrum
a3
f
a3 a2
a1
a4
t
f
0
0
T/2
T
127/T
1/T
Figure 2.
The FMT system that comprises about 100 subchannels needs only 1024-point IFFT core. There no
need frequency up-converters and prototype wavelet
filters.
Figure 4 shows PSD of FMT Transmitter that was
realized in accordance with described efficient algorithm.
For example there is used 128-point IFFT core. Only
9 inputs of this core are used for wavelet synthesis. All
other inputs are connected to ground (0). The prototype
wavelet W (t ) may be modulated by amplitude and carry
information. In this case amplitudes ak of frequency
components are modulated by information signal.
III.
SYNTHESIS OF SUB-CHANNEL WAVELETS.
The FMT System uses in general number  of
frequency sub-channels; each of them transmits a
correspondent sub-channel wavelet. The sub-channel
wavelet is a prototype wavelet shifted to carrier
frequency of correspondent sub-channel. A common
realization of FMT system comprises  frequency upconverters in transmitter and  prototype wavelet filters.
Figure 4
IV.
an input of multiplayer that provides a multiplying of
each wavelets frequency component on corresponding
equalization coefficient. The sequence of corrected
frequency components passes to demodulator that
decodes an information data.
ANALYSIS OF SUB-CHANNEL WAVELET
A transmitted FMT line signal X (t ) passes through
communication channel. As result a received signal
Y (t ) appears on an input of FMT Receiver. After
amplifying and A/D conversion, the received FMT signal
comes to input of analyses block that provides decoding
of sub-channels wavelets.
The constellation diagram of received wavelet signal is
shown on Figure 7. The FPGA prototype System was
designed for VDSL Application but the same FMT core
may be used for wireless systems.
Figure 5 illustrates how this wavelet decoding may be
provided by FFT core.
t127
t126
127/T
Analysis of sub-channel
wavelet
L=6
0
0
FFT
128 point
S/P
Y(t)
0
Sub-channel
Sub-channel
Wavelet
Wavelet
t1
t0
0
a4
a3
a2
a1
a0
a1
a2
a3
a4
Sub-channel wavelet
spectrum
a2 a1 a0 a1 a2
a3
a3
0
a4
a4
T
0
127/T
1/T
f
fc
Figure 5.
Figure 7.
Analysis of sub-channel wavelet is provided by analysis
its frequency components by FFT. Because each
frequency component may be processed independently,
the distortions of a communication channel may be easily
compensated.
The simple Equalizer that may be used in proposed FMT
architecture is shown on Figure 6.
t127
t126
127/T
V.
THE FILTERED MULTITONE MODULATION (FMT) IS A
NEW
TECHNOLOGY THAT MAY BE SUCCESSEFULY
USED FOR WIRELINE AND WIRELESS COMMUNICATIONS.
THE PROPOSED EFFICIENT FMT ALGORITHM GIVES
POSSIBILITY TO REALIZE THE
FMT ADVANTAGES
WITHOUT USING COMPLEXLY FILTER-BANKS.
Efficient equalization and
demodulation of subchannel line signal
0
CONCLUSIONS
REFERENCES
0
Equalizer
P/S
FFT
128 point
S/P
W(t)D
rei + j*im i
Equlization
coefficients
sequence
0
Sub-channel
Sub-channel
line Signal
Wavelet
D*C(f)
t1
t0
0
Weghting
coefficients
sequence
0
efficiency
demodulator
ai
T
Information
D
The wavelets frequency components from FFT block
outputs passes to parallel/serial converter and comes to
G. Cherubini, E. Eleftheriou, S. Oelser : “ Filtered
Multitone Modulation for Very High-Speed Digital
Subscribe Lines”, IEEE Journal of Selected Areas in
Communications, VOL.20, NO. 5, 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.
[3] Andrea Tonello “Discrete Multi-Tone and Filtered
Multi-Tone
Architectures
forBroadband
Asynchronous
Multi-User
Communications”
Wireless personal Multimedia Communications
Symposium - Aalborg, Denmark - September 9-12,
2001
[1]
Figure 6.