This paper descriibes the performance of the Wavelet based Filtered Multitone(WFMT) modulation. The novel WFMT modulation was proposed in 2003 for improving characteristic of Wireless and DSL multicarrier systems.

1. A Wavelet based Filtered Multi-Tone
Roman M. Vitenberg
Wavetone Technologies Ltd
roman@wavetonetech.com
Abstract  This paper discusses the performance of the Such an equalizer must use an adaptive FIR filter that has at
Wavelet based Filtered Multi-Tone (WFMT) modulation. The least 64 coefficients.
novel WFMT modulation was proposed in 2003 for improving The second class of the filter-bank system comprises of
characteristics of Wireless and DSL multicarrier systems. In this transceivers, which use sub-channel signals modulated by
paper we describe a main idea of WFMT and discuss the single-side-band PAM modulation [15]. In [23] a system with
advantages of this novel modulation. The WFMT modulation in
comparison with OFDM and DMT has low level of out-of-band
Sub-band Division Multiplexing (SDM) modulation
side lobes, low sensitivity to narrowband RF interference and low developed by Rainmaker Technology LTD was described.
Peak-to-Average Power Ratio. The attractive feature of WFMT The Discrete Wavelet Multi-Tone (DWMT) modulation was
is its low implementation complexity compared with known proposed by AWARE Ltd [16]. Another version of SDM,
multicarrier architectures, that are based on FIR synthesis and named Wavelet OFDM was proposed for wireless and power
analysis filter-banks. Several main characteristics of the WFMT lines [19]. The Cosine Modulated Multi-Tone (CMT)
are illustrated by simulation results. The practically realized modulation [22] and The Cosine Modulated Filter-Bank
WFMT system is described followed by the test results. (CMFB) modulation [17], were investigated in many
contributions. Recently a perfect-reconstructed Exponentially
Keywords  FMT, WFMT, filter-bank, wavelet, PAR, OFDM,
Modulated Filter-Bank (EMFB) that uses the complex
DMT.
numbers for filter coefficients was developed [14]. All these
filter-bank systems use an overlapped spectrum of an adjacent
I. Introduction sub-channel. The division of the adjacent sub-channels in the
receiver is provided by an orthogonality of transmitted signals
Filter-bank multicarrier modulation (FBMCM) has The third class of filter-bank systems proposed by
received a significant interest in the area of broadband wired Salsberg [21] uses a special Offset Quadrature Amplitude
(DSL) and wireless (LAN) access systems. In filter-bank Modulation (OQAM) for the transmission of data over
systems the data symbols are transmitted over a number of sub-carrier bands spaced by symbol rate. In this system, the
independent sub-carriers, using a frequency division adjacent bands have significant overlapping. Successful
multiplexing (FDM) [13]. This contrasts with OFDM or DMT separation of sub-channel signals is possible thanks to an
systems, where separations of sub-channel signals are orthogonality of real and complex components of OQAM
provided using the orthogonality of the sub-carriers [1]. [15].
Over the past three decades, many different filter-bank Unfortunately the filter-bank systems described in
based multicarrier systems have been introduced. All these literature are very complex and costly so they practical
systems may be divided into three classes in accordance with realization is difficult. Up to date only two filter-bank
the type of sub-channel modulation. techniques were implemented both based on wavelet
The first class is a filtered multi-tone system (FMT) that modulation proposed by Rainmaker Technologies. The first
comprises a number of the spectrally non-overlapped is SDM that was used in prototype of the CATV
sub-channels. Each of them transmits information by double communication system [23] demonstrated by Rainmaker
side modulated QAM [2]. Because the spectrums of adjacent Technologies (now Broadband Physics) on several technical
sub-channels do not overlap, the inter-channel-interference Fairs. The second practical realization of the filter-bank
(ICI) in FMT system is very low. As a result, FMT may be technology is the Wavelet OFDM technique that was
seen as a number of single-carrier QAM systems operating in proposed by Rainmaker [19] and improved by Matsushita
parallel [15]. Hence, characteristics of this system can be Electric [20].
simply defined. In [2] an efficient implementation of FMT Panasonic has demonstrated the first industrial product
that uses polyphase techniques was described. One of the based on Wavelet OFDM in 2005 (HD-PLC - a 200 Mb/sec
FMT disadvantages is the complexity of the synthesis and modem for Power Line Communications). One of problem of
analysis filter-banks. It is clear that for achieving a high the filter-bank technique is the high sensitivity to frequency
performance, the FMT system must use the sub-channel distortion in the communication line. This requires a using of
filters with roll off factor of β ≤ 0.15 to avoid loosing more complex decision feedback equalizers in each sub-channel of
than 15% of channel bandwidth. In case of digital the system. Therefore, the filter-bank systems could be used
implementation, each sub-channel FIR filter can have a length only in the case of low phase-frequency distortion, for
of about 512~1024. The second problem is a complexity of example in CATV or Power Line networks.
FMT equalizer. The typical FMT receiver described in [2] The Wavelet based Filtered Multi-Tone (WFMT)
required one decision feedback equalizer per sub-channel. modulation was proposed by R. M. Vitenberg ( 2003) [5]. The

2. WFMT characteristics were researched in during 2003-2005 with a number of the sub-carrier n and the current time
in DATA JCE IC Design Center and in Wavetone iT ( i = 0,1,2..) .
Technologies LTD 2005-2006.
This paper presents a novel WFMT technology and its G
0 N-1 Synthesis
aM-1(iT0) Filter-Bank
characteristics. The rest of the paper is organized as follows. G
K
aM-2(iT0)
We present an overview of WFMT in Section II. In Section III, K
D1
we describe the practical system that was realized and tested IFFT
P/S X(t)
N point
by our company in 2002 - 2003. This system was developed G
Non-overlapped Wavelets
a1(iT0)
for VDSL application and provided bit rates up to 24 Mbps in K
G
a0(iT0)
the frequency band 138kHz~5200kHz; another system was K
build for transmission of CATV signals over coaxial cable [9]. 0 0
The picture of power spectrum density of the transmitted G = [ G(0) , G(1), G(2),... G(K-1) ] T0 = (N/L)T
WFMT signal illustrates the experimental results followed by
conclusions. f
Figure 2. WFMT Transmitter (without overlapping block)
II. WFMT Overview
The WFMT transmitter uses the same N point core IFFT
The Wavelet based Filtered Multi-Tone Modulation is a and transmits information over M data streams
version of the Filter-bank modulated communication system a0 , a1 ,...aM −1 each at rate 1 / T0 = L /( NT ) , where L is an
described in detail in [2], [3], [4], in which the synthesis and overlapping coefficient - number of overlapped wavelets on
analysis of sub-channel wavelets were correspondingly interval T [7]. As shown in Fig. 2, the data streams modulate
provided by IFFT and FFT cores. Unlike OFDM, the number
groups of K inputs of IFFT core to provide the sub-channel
M of sub-channels in the WFMT system is significantly less
wavelets with low level of spectrum side lobes. Some of the
than N - the number of IFFT/FFT points. Each sub-channel outermost data streams can be set to zero for spectral
wavelet is generated in this case from K harmonics (IFFT/FFT containment reasons.
points) so there is a simple expression for the number of
Now we explain the process of synthesis of the
sub-channels:
sub-channel wavelets by Inverse Fourier Transform. First, we
discuss a process of generation of prototype wavelet. The
N prototype wavelet is a base-band wavelet, whose spectrum is
M ≤ (1).
K centered on zero frequency and which has a property of shift
orthogonality. Each sub-channel wavelet can be constructed
from the prototype wavelet by shifting its spectrum to the
We start an explanation of the WFMT technique from a
correspondent carrier frequency.
comparison block schematics of OFDM and WFMT
The ideal analytic wavelet for the digital communication
transmitters shown correspondingly on Fig. 1 and Fig. 2.
system is called “Modified Gaussian” was proposed in [24].
Following this idea, the ideal wavelet is constructed from
0 N-1
Gaussian waveform:
2
aN-2(iT) / 4σ 2T 2 )
aN-3(iT) s (t ) = 1 /( 2σT π )e − ( t , where
IFFT
T denotes the eventual shift orthogonality period of the
P/S X(t)
2 2
N point
OFDM Signal
orthogonal pulse to be derived, and 4σ T is the pulse
a1(iT)
variance in time.
a0(iT) The orthogonalization trick is performed on the Gaussian
0 0 waveform, which is not shift orthogonal [24]. The Fourier
2
T 2 ( 2πf ) 2
F f
transform of s(t ) is S ( f ) = e −σ , applying
the orthogonalization trick to S ( f ) we obtain the function
2
T 2 ( 2πf ) 2
Figure 1. OFDM Transmitter e −σ
Φ( f ) =
− 8σ 2T 2π 2 ( f + l / T ) 2
As we see, the OFDM Transmitter comprises a N point ∑e
l ∈Z
IFFT core and parallel-to serial converter PS. The output
signal of the OFDM Transmitter comprises N − 2
orthogonal carriers with frequency shift: ∆F = 1 / T , where whose inverse Fourier transform φ (t ) can play role of a
T is the OFDM symbol period (without cyclic prefix). Each scaling function.
carrier is modulated by a data stream: an (iT ) in accordance A “Modified Gaussian“ wavelet W (t ) can be processed as

3. W (t ) = ψ (t ) ⋅ s (t ) , The prototype wavelet for the Cable TV System [9] that was
developed from Modified Gaussian Wavelet is shown in
where ψ (t ) is the ortogonalization function that can be figure 3. This wavelet was synthesized from 21- cosine
calculated from Φ ( f ) and S ( f ) . Function ψ (t ) provides function and provides ISI distortion less then –56 dB. Such
necessary nulls in the time domain of W (t ) . a low ISI distortion makes it possible to transmit up to 13/14
bit of information per symbol.
Figure 3 illustrates a “Modified Gaussian” wavelet that
was developed for Cable TV applications [9]. This wavelet As was shown in [7], the number of harmonics K
has bandwidth roll-off coefficient about 18% and provides defines a quality of generated wavelets, in particular the
Inter-Symbol Interference (ISI) between wavelets and a
overlapping coefficient L = 16 ( L − a number of bandwidth of sub-channels.
overlapped wavelets). The Modified Gaussian Wavelet is an We will characterize bandwidth losses of WFMT
Ideal waveform for the digital communication because
sub-channel by the roll-off factor β :
provides zero ISI and ICI distortion. However, Modified
Gaussian cannot practically realized because has non-limited ∆f
spectrum and length. β =2 , (2)
RS
where ∆f - is an excess bandwidth and RS is a symbol
rate. As was shown in [7] the roll-off factor for the WFMT
3
system may be calculated by a simple formula: β= .
K
This graph is shown in Figure 4.
Figure 3. Modified Gaussian Wavelet for Cable
TV Applications
The WFMT Modulation uses a prototype wavelet that is
very close to the Modified Gaussian Wavelet. The prototype
wavelet is synthesized in the following way:
• FIRST, The selected Modified Gaussian is
represented by FOURIER Series:
∞ Figure 4. The Roll-off factor of the WFMT sub-channel
W (t ) = ∑ Ai COS (iωt ) ,
−∞
The level of the Inter-Channel-Interference in WFMT
• SECOND, The prototype wavelet is presented by a system is very low and must be theoretically equal to zero.
part of this FOURIER Series: As we can see from Fig. 2, sub-channel wavelets in the
+m
WFMT system comprises of a number of cosine functions
PW (t ) = ∑ Ai COS (iωt ) , which all are orthogonal to cosine components of adjacent
−m
sub-channel wavelets.
The level of the Inter-Symbol Interference between
where 2m + 1 = K is a number of frequencies
wavelets depends on a form of the prototype wavelet and
used for prototype wavelet synthesis. decreases very rapidly with an increase in the number of the
• THIRD, The interpolation errors defines: wavelet components, as illustrated in Fig. 5. The minimal
− m −1 number of cosine functions that may be used for wavelet
E = 2 ∑ Ai2 synthesis is 9. In this case, the Signal/ISI ratio is about 36 dB
−∞ and wavelet may carry up to 8 bits of information. In the
• IF an interpolation error is bigger than it is necessary practical VDSL system, we used the wavelets that were
for the defined level of ISI, then the number of constructed of 11 cosine components.
frequency components K is increased by 2.
• The process is repeated while we get the necessary
level of ISI.

4. Signal / ISI front-end) board, FPGA board, and Microprocessor board.
60
dB The AFE board is based on the Analog Devices chip AD9876
that comprises of 12bit ADC and DAC. The low noise VCO
55 oscillator, placed on AFE board is controlled by 16bit DAC
MAX5204 and provides clock and symbol synchronization.
The Microprocessor board comprises of the ARM7 processor
50
that provides control of transceiver and its interface with
external equipment. The FPGA Board provides all digital
45 signals processing necessary for synthesis and analysis of
wavelets. Two XILINX FPGA are placed on the FPGA Board.
40 One of them comprises all the components of WFMT
transmitter, second- all the components of WFMT receiver.
0 5 10 15 20 25 30 K
Figure 5. Inter-Symbol Interference between
the wavelets in a WFMT Sub-channel
One of the significant advantages of the WFMT
modulation is a very precise equalization algorithm that
allows compensating the distortion of the communication
channel. This algorithm includes an independent correction
for each frequency component of a transmitted wavelet [7].
0 HMK-1*GK-1*
aM-1(lT0)
+ Detect
HMK-K*G0*
y(nT) Figure 7. WFMT VDSL Transceiver
FFT
S/P N points
HK-1*GK-1*
The transmitter prototype was realized in FPGA VERTEX2
+ Detect
a0(lT0) (3000), and uses about 1 million gates. In this design standard
H0*G0* Xilinx cores for 1024-point IFFT, RAMs, and multipliers were
used. A 1024-point core IFFT was used to obtain 44
0 sub-channels in the frequency band 200 kHz – 3 MHz. The
bandwidth of each WFMT channel is about 59 kHz.
Figure 6. WFMT Receiver Constellations from 2 to 12 were used. The system clock of
transmitter is 88 MHz. The transmitter test has shown a close
The WFMT receiver (Figure 6) consists of a matched coincidence with the simulation results. The power spectrum
filter bank. Filters are matched to the equivalent sub-channel density of a realized WFMT transmitter is shown on Figure 8.
response [7]. Instead of well-known polyphase filter-bank, the
WFMT receiver includes 1024 point FFT core that provides
analysis of frequency components of received wavelets. Each
received wavelet component on output of FFT is multiplied
on an equalizer coefficient H j for compensation of
distortion in communication channel. The information data
a i is calculated for each sub-channel by summing the
weighted (Gi ) wavelet components
III. Experimental WFMT System
For the first practical implementation of WFMT
modulation, the VDSL Application was chosen [8]. Figure
3 shows the developed WFMT VDSL Transceiver. The
Transceiver comprises of three PCB boards: AFE (analog Figure 8. PSD of WFMT VDSL downstream.

5. As can be seen from Figure 4 the WFMT Spectrum does not [6] Andrea Tonello , Roman M. Vitenberg “An Efficient Wavelet Based
Filtered Multitone Modulation Scheme WPMC 2004 –Albano Terme
comprises side lobe components practically. One of 33
, Italy , September 2004
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