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.
A Wavelet based Filtered Multi-Tone Roman M. Vitenberg Wavetone Technologies Ltd email@example.com Abstract This paper discusses the performance of the Such an equalizer must use an adaptive FIR filter that has atWavelet 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 ofcharacteristics of Wireless and DSL multicarrier systems. In this transceivers, which use sub-channel signals modulated bypaper we describe a main idea of WFMT and discuss the single-side-band PAM modulation . In  a system withadvantages of this novel modulation. The WFMT modulation incomparison with OFDM and DMT has low level of out-of-band Sub-band Division Multiplexing (SDM) modulationside 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 wasis its low implementation complexity compared with known proposed by AWARE Ltd . Another version of SDM,multicarrier architectures, that are based on FIR synthesis and named Wavelet OFDM was proposed for wireless and poweranalysis filter-banks. Several main characteristics of the WFMT lines . The Cosine Modulated Multi-Tone (CMT)are illustrated by simulation results. The practically realized modulation  and The Cosine Modulated Filter-BankWFMT system is described followed by the test results. (CMFB) modulation , 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 complexDMT. numbers for filter coefficients was developed . 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 byreceived a significant interest in the area of broadband wired Salsberg  uses a special Offset Quadrature Amplitude(DSL) and wireless (LAN) access systems. In filter-bank Modulation (OQAM) for the transmission of data oversystems the data symbols are transmitted over a number of sub-carrier bands spaced by symbol rate. In this system, theindependent sub-carriers, using a frequency division adjacent bands have significant overlapping. Successfulmultiplexing (FDM) . This contrasts with OFDM or DMT separation of sub-channel signals is possible thanks to ansystems, where separations of sub-channel signals are orthogonality of real and complex components of OQAMprovided using the orthogonality of the sub-carriers . . Over the past three decades, many different filter-bank Unfortunately the filter-bank systems described inbased multicarrier systems have been introduced. All these literature are very complex and costly so they practicalsystems may be divided into three classes in accordance with realization is difficult. Up to date only two filter-bankthe 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 firstcomprises a number of the spectrally non-overlapped is SDM that was used in prototype of the CATVsub-channels. Each of them transmits information by double communication system  demonstrated by Rainmakerside modulated QAM . Because the spectrums of adjacent Technologies (now Broadband Physics) on several technicalsub-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 wasseen as a number of single-carrier QAM systems operating in proposed by Rainmaker  and improved by Matsushitaparallel . Hence, characteristics of this system can be Electric .simply defined. In  an efficient implementation of FMT Panasonic has demonstrated the first industrial productthat uses polyphase techniques was described. One of the based on Wavelet OFDM in 2005 (HD-PLC - a 200 Mb/secFMT disadvantages is the complexity of the synthesis and modem for Power Line Communications). One of problem ofanalysis filter-banks. It is clear that for achieving a high the filter-bank technique is the high sensitivity to frequencyperformance, the FMT system must use the sub-channel distortion in the communication line. This requires a using offilters with roll off factor of β ≤ 0.15 to avoid loosing more complex decision feedback equalizers in each sub-channel ofthan 15% of channel bandwidth. In case of digital the system. Therefore, the filter-bank systems could be usedimplementation, each sub-channel FIR filter can have a length only in the case of low phase-frequency distortion, forof 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  The Wavelet based Filtered Multi-Tone (WFMT)required one decision feedback equalizer per sub-channel. modulation was proposed by R. M. Vitenberg ( 2003) . The
WFMT characteristics were researched in during 2003-2005 with a number of the sub-carrier n and the current timein 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-Bankcharacteristics. 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 D1we describe the practical system that was realized and tested IFFT P/S X(t) N pointby 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 Kbuild for transmission of CATV signals over coaxial cable . 0 0The picture of power spectrum density of the transmitted G = [ G(0) , G(1), G(2),... G(K-1) ] T0 = (N/L)TWFMT signal illustrates the experimental results followed byconclusions. f Figure 2. WFMT Transmitter (without overlapping block) II. WFMT Overview The WFMT transmitter uses the same N point core IFFTThe Wavelet based Filtered Multi-Tone Modulation is a and transmits information over M data streamsversion of the Filter-bank modulated communication system a0 , a1 ,...aM −1 each at rate 1 / T0 = L /( NT ) , where L is andescribed in detail in , , , in which the synthesis and overlapping coefficient - number of overlapped wavelets onanalysis of sub-channel wavelets were correspondingly interval T . As shown in Fig. 2, the data streams modulateprovided by IFFT and FFT cores. Unlike OFDM, the number groups of K inputs of IFFT core to provide the sub-channelM of sub-channels in the WFMT system is significantly less wavelets with low level of spectrum side lobes. Some of thethan N - the number of IFFT/FFT points. Each sub-channel outermost data streams can be set to zero for spectralwavelet 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 thesub-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 communicationtransmitters shown correspondingly on Fig. 1 and Fig. 2. system is called “Modified Gaussian” was proposed in . 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 . 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 ∈ZIFFT core and parallel-to serial converter PS. The outputsignal of the OFDM Transmitter comprises N − 2orthogonal carriers with frequency shift: ∆F = 1 / T , where whose inverse Fourier transform φ (t ) can play role of aT 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
W (t ) = ψ (t ) ⋅ s (t ) , The prototype wavelet for the Cable TV System  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- cosinecalculated from Φ ( f ) and S ( f ) . Function ψ (t ) provides function and provides ISI distortion less then –56 dB. Suchnecessary 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 thatwas developed for Cable TV applications . This wavelet As was shown in , the number of harmonics Khas bandwidth roll-off coefficient about 18% and provides defines a quality of generated wavelets, in particular the Inter-Symbol Interference (ISI) between wavelets and aoverlapping 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 WFMTIdeal waveform for the digital communication because sub-channel by the roll-off factor β :provides zero ISI and ICI distortion. However, ModifiedGaussian cannot practically realized because has non-limited ∆fspectrum and length. β =2 , (2) RS where ∆f - is an excess bandwidth and RS is a symbol rate. As was shown in  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 isvery close to the Modified Gaussian Wavelet. The prototypewavelet is synthesized in the following way: • FIRST, The selected Modified Gaussian isrepresented 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.
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 WFMTmodulation is a very precise equalization algorithm thatallows compensating the distortion of the communicationchannel. This algorithm includes an independent correctionfor each frequency component of a transmitted wavelet . 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 spectrumfilter bank. Filters are matched to the equivalent sub-channel density of a realized WFMT transmitter is shown on Figure 8.response . Instead of well-known polyphase filter-bank, theWFMT receiver includes 1024 point FFT core that providesanalysis of frequency components of received wavelets. Eachreceived wavelet component on output of FFT is multipliedon an equalizer coefficient H j for compensation ofdistortion in communication channel. The information dataa i is calculated for each sub-channel by summing theweighted (Gi ) wavelet components III. Experimental WFMT System For the first practical implementation of WFMTmodulation, the VDSL Application was chosen . Figure3 shows the developed WFMT VDSL Transceiver. TheTransceiver comprises of three PCB boards: AFE (analog Figure 8. PSD of WFMT VDSL downstream.
As can be seen from Figure 4 the WFMT Spectrum does not  Andrea Tonello , Roman M. Vitenberg “An Efficient Wavelet Based Filtered Multitone Modulation Scheme WPMC 2004 –Albano Termecomprises side lobe components practically. One of 33 , Italy , September 2004sub-channels was disabled for demonstration of possible  Andrea Tonello, Roman M. Vitenberg “An Efficient Implementationrejection of RF narrowband noise. The rest of 32 sub-channels of a Wavelet Based Filtered Multitone Modulation Scheme” ISSPITwere modulated by QAM-64 random symbols. The WFMT 04 ITALY, ROME, December 2004.receiver is realized in FPGA XILINX VERTEX2 (3000) and  Roman M.Vitenberg: “A practical implementation of a Waveletuses about 1.5 million gates. A constellation diagram shown on Based Filtered Multitone Modulation”, WOSM’05 Conference .figure 9 illustrates the WFMT receiver performance. Tenerife, December 2005  Roman M. Vitenberg: " A WFMT Transmitter for Cable TV Applications", WSEAS Conference, Madrid, February 15-17, 2006.  Roman Vitenberg: "Peak-to-Average Ratio in WFMT System", AIC WSEAS Conference, Elounda, Crete, Greese, August 2006.  Roman M. Vitenberg: " Effect of Frequency offset and Phase Noise on WFMT Systems", WSEAS Conference , Lisbon, September 2006.  Roman M. Vitenberg: "An Approach to Design of a Multicarrier Downlink transmitter for Low Earth Orbit Satellite", WSEAS Conference, Venice, November 2006.  Vaidyanathan, P.P. "Filter banks in digital communications" Circuits and Systems Magazine, IEEE Volume 1, Issue 2, Date: Second Quarter 2001,  Viholainen, A.; Stitz, T.H.; Alhava, J.; Ihalainen, T.; Renfors, M. "Complex modulated critically sampled filter banks based on cosine and sine modulation",Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on.  Peiman Amini, Ronald Kempter , Behrouz Farhang-Boroujeny: "A Comparison of alternative filterbank multicarrir methods for Fig.9. WFMT Receiver Constellation Diagram cognitive radio systems", ECE Departament, University of Utah, USA, 2006.  Stuart D. Sandberg, Michael A. Tzannes: " Overlapped Discrete Multitone Modulation for High Speed Copper Wire IV. Conclusions Communications", IEEE Journal on Selected Areas in Communications 13(2995) December, No. 9, New York, NY, US. We have presented results of a study of a novel WFMT  Umehara, D.; Nishiyori, H.; Morihiro, Y. "Performance Evaluation ofmodulation. During 2003~2006 main characteristics of the CMFB Transmultiplexer for Broadband Power Line Communications under Narrowband Interference", Power Line Communications andWavelet based Filtered Multi-tone modulation have been Its Applications, 2006 IEEE International Symposium ondefined. It was shown that WFMT modulation has significant Date: 26-29 March 2006, Pages: 50 - 55advantages in comparison with others filter-bank systems such  B. Fargang-Boroujeny :"Multicarrier modulation with blind detectionas low complexity and simple equalizing. The FPGA based capability using cosine modulated filter banks", IEEE Transaction onhardware implementation of a WFMT transceiver was Communications, vol 51, no 12, Dec. 2003developed and tested. The experimental results are very close  Rainmaker Technologies Inc. : "RM Wavelet Based (WOFDM) PHYto the simulations and show good spectral characteristic of the Proposal for 802.16.3, Rev 0.0" , IEEE Contribution IEEE 802.16.3C-01/12, 18 Jan. 2001.new technology. 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