The demand for provision of multi-media applications and other broadband services over telecommunications networks has created a need to transmit high bit rate traffic over a pair of copper wires. This requirement has led to the development of different Digital Subscriber Line (DSL) transmission schemes. Several examples of variations on the DSL technology are represented below, which are often denoted by the term xDSL (where x is a variable, when the discussion is about DSL in general).                Asymmetric DSL (ADSL)—that is called “asymmetric” because the downstream data transmission rate is greater than the upstream transmission. In particular, ADSL works this way due to the fact that most Internet users look at, or download, much more information than they send, or upload.        High bit-rate DSL (HDSL)—that receives and sends data at the same speed, but it requires two lines that are separate from the normal phone line.        ISDN DSL (ISDL)—that is slower than most other forms of DSL, however has an advantage for Integrated Services Digital Network (ISDN) customers in the fact that they can use their existing equipment, but the actual speed gain is typically only 16 Kbps, while ISDN runs at 128 Kbps.        Rate Adaptive DSL (RADSL)—This is a popular variation of ADSL that allows the modem to adjust the speed of the connection depending on the length and quality of the line.        Symmetric DSL (SDSL)—This scheme receives and sends data at the same speed and uses only a single line instead of the two used by HDSL.        Very high speed DSL (VDSL)—A rather fast connection, VDSL is asymmetric, but only works over a short distance using standard copper phone wiring.        Voice-over DSL (VoDSL)—This scheme allows multiple phone lines to be combined into a single phone line that also includes data-transmission capabilities.        
Two of the above technologies, ADSL and VDSL, currently dominate the industry. The VDSL technology can be regarded as an evolution of ADSL and represents the next step in the DSL technology for two-way broadband network access. Four modulation techniques (line codes) have been proposed in the art for xDSL, such as: Discrete Multi-Tone modulation (DMT) modulation, carrierless amplitude and phase (CAP) modulation, Discrete Wavelet Multi-Tone (DWMT) modulation and Filtered Multi-Tone (FMT) modulation. More specifically:
DMT modulation is the discrete time implementation of orthogonal frequency division multiplexing (OFDM), where the available bandwidth is divided into a plurality of subchannels (e.g., 255 subchannels), each subchannel with a small bandwidth, e.g., about 4 kHz (or 1000 cycles per second). Traffic is allocated to the different sub-channels in dependence on noise power and transmission loss in each sub-channel. Usually, each sub-channel carries multi-level pulses capable of representing up to 15 data bits. Poor quality sub-channels carry fewer bits, or may be completely shut down (see, for example, U.S. Pat. No. 5,479,447, Chow, et al.). DMT modulation can effectively achieve this sub-channel arraying within the one transceiver set by utilizing the Inverse Fast Fourier Transform (IFFT) to create individual carriers and its counterpart, the Fast Fourier Transform (FFT) for demodulation. DMT can use FDM for upstream/downstream multiplexing, although DMT does not preclude a TDMA multiplexing strategy. This modulation method is mainly used hitherto in ADSL.
CAP operates by dividing the signals on the telephone line into three distinct bands. More specifically, voice conversations are usually carried in the zero- to 4-KHz band, used in all standard phone circuits. Moreover, the upstream channel is used that is carried in a band between 25 and 160 KHz. Likewise, the downstream channel begins at 240 KHz and goes up to a point that varies with such conditions as line length, line noise and the number of users in the switch, but it has a maximum of about 1.5 megahertz (MHz).
CAP is closely related to quadrature amplitude modulation (QAM). QAM typically generates a double sideband suppressed carrier signal constructed from two multi-level pulse amplitude modulated (PAM) signals applied in phase quadrature to one another. In other words, in a QAM signal, there are two carriers (i.e., the I signal and the Q signal), each having the same frequency but differing in phase by 90 degrees (one quarter of a cycle). Mathematically, one of the signals can, for example, be represented by a sine wave, and the other by a cosine wave. The two modulated waves are combined at the source for transmission. At the destination, the waves are separated, the data is extracted from each, and then the data is combined into the original modulating information. CAP modulation produces the same form of signals as QAM without requiring in-phase and quadrature components of the carrier to first be generated. The CAP technique, employing the three channels widely separated, minimizes the possibility of interference between the channels on one line, or between the signals on different lines.
DWMT is a multi-carrier technique utilizing a Wavelet Transform to create and demodulate individual carriers. The generation of the subchannels and their modulation is being done by an inverse fast wavelet transform (IFWT) and the corresponding demodulation by a fast wavelet transform (FWT). Contrary to DMT technique, DWMT uses overlap in the time domain in order to achieve a higher spectral containment of the subchannels in the frequency domain. The subchannels of a DWMT system have half the frequency spacing between their subchannels, compared with DMT, and employ one-dimensional PAM instead of QAM. The drawback of this technique is the increased complexity due to longer filter lengths and the necessity of buffering the previous transmit blocks. The advantage is that the spectral overlap between the subchannels is much smaller than in case of DMT.
It should be noted that only two of these line codes, namely CAP and DMT, can practically be used for VDSL systems. In particular, the DMT line code provides significantly better performance of a VDSL system than the CAP line code. That is a reason why only DMT line code has been standardized for VDSL systems by T1E1 Committee (Contribution T1E1.4/2003-188; “Olympic gold for DMT”; Alcatel; Jun. 18, 2003). On the other hand, the DWMT line code has better theoretical characteristics than DMT, but has not been yet realized because of its very hard implementation complexity.
One of the recognized problems associated with DMT is a poor separation between the subchannels. U.S. Pat. No. 5,497,398 to Tsannes et al. proposed a technique for ameliorating the problem of signal degradation associated with subchannel loss. This technique allows to obtain a superior burst noise immunity. This was achieved by replacing the Fast Fourier Transform (FFT) with the lapped transform, thereby increasing the difference between the main lobe and side lobes of the filter response in each sub-channel. The lapped transform can provide wavelets, as was disclosed by M. A. Tsannes et al. in an article “The DWMT: A Multicarrier Transceiver for ADSL using M-band Wavelets”, ANSI, T1E1.4 Contribution 93-067, March 1993.
One of the common disadvantages of DMT and DWMT techniques is related to the fact that they typically use a large number of subchannels (namely, 2048 or 4096 for VDSL), that leads to a rather complex and costly equipment. Moreover, DMT and DWMT systems suffer from difficulties during equalization and synchronization.
The recently proposed FMT modulation is a multi-carrier technique that partially addresses the drawbacks of the CAP, DMT and DWMT modulation techniques. In general terms, the FMT modulation is achieved by splitting the data into several streams, each of them applied to one of the inputs of a filter-bank where the filters are frequency-shifted versions of a prototype filter that achieves a high level of spectral containment, such that intersymbol interference (ISI) is negligible compared to other noise signals. Because of implementation complexity, the number of subchannels is considerably less than in DMT. An implementation of an FMT scheme will be described herebelow in detail.
FIG. 1 shows a block-diagram of a VDSL system employing a filter-bank modulation and demodulation concepts (see, for example, G Cherubini, et al., “Filtered Multi-tone Modulation for Very High-Speed Digital Subscribe Lines”, IEEE Journal on Selected Areas in Communications, 2002, V. 20, N. 5, P. 1016-1028).
Accordingly, a group of M modulation symbols Ak(i), i=0, 1, . . . , M−1 are provided in parallel at the rate of 1/T to a set of M filters 105 with transfer functions H(eJ2πf), and impulse response h(k). The efficient realization can be achieved in the critically sampled case (i.e., M=K)), when the filters 105 are selected as the frequency-shifted versions of a baseband filter, (referred to as a prototype filter). The notation ↑ K indicates upsampling by a factor of K by means of up-samplers 106, i.e., insertion of K−1 zeros between two consecutive input signals. The set of M filters 105 represents a so-called synthesis filter-bank 107. The filter-bank 107 generates a transmitted signal at the transmission rate of K/T. An output of each baseband prototype filter 105 is connected to a corresponding up-converter 110 that shifts a baseband spectrum of this filter in frequency to the corresponding subcarriers.
A transmitted FMT line signal Xn is formed by summing output signals of all M up-converters 110 by an adder 112. The transmitted signal Xn is transferred through a communication channel (cable) 115 with the frequency response C(f). An arrived signal Yn passed through the cable 115 is fed to M down-converters 117. Each of them shifts a signal of the corresponding subchannel to the baseband, and provides the shifted signal to an input of the corresponding Equalizer (EQi) 119 configured for eliminating intersymbol interference (ISI) within the subchannel. For each subchannel, a signal provided by an output of the Equalizer 119 passes to a corresponding analysis prototype filter 121 with the frequency response G(f). An analysis filter-bank 123 constituted by M filters 121 is followed by down-samplers 125. The notation ↓ K indicates down-sampling by a factor of K by means of the down-samplers 125.
Preferably, characteristics of the filter-banks 107 and 123 are chosen to satisfy a “perfect reconstruction” constraint, in order to ensure that transmission is free of intersymbol interference (ISI) and interchannel interference (ICI). In particular, a matched filtering, i.e., G(f)=H*(f) should be fulfilled for the “perfect reconstruction” of the received signal. (Hereinafter the symbol “*” denotes complex conjugation). The following orthogonal conditions are imposed for the design of the filter banks for the “perfect reconstruction” of the received signal:
                                                                                                              ∑                    n                                    ⁢                                                                                    h                                                  (                          i                          )                                                                    ⁡                                              (                        n                        )                                                              ⁢                                                                  h                                                  (                          i                          )                                                *                                            ⁡                                              (                                                  n                          -                          kM                                                )                                                                                            =                                  δ                  k                                            ,                                                                          i                =                0                            ,              1              ,              …              ⁢                                                          ,                              M                -                1                                                                                                                                              ∑                    n                                    ⁢                                                                                    h                                                  (                          i                          )                                                                    ⁡                                              (                        n                        )                                                              ⁢                                                                  h                                                  (                          j                          )                                                *                                            ⁡                                              (                                                  n                          -                          kM                                                )                                                                                            =                0                            ,                                                          i              ≠              j                                                          (        1        )            where δ denotes the Kronecker symbol. The elements of a set of orthogonal filter impulse responses that satisfy Eq. (1) are referred to as wavelets.
The form of the prototype wavelet is very impotent for its spectral characteristics and very critical for the performance of the multi-carrier system (see, for example, U.S. Pat. No. 6,278,686 to Michel Alard). FIG. 2 illustrates an example of a prototype wavelet 201, which can be generated by a baseband prototype filter. In turn, FIG. 3 illustrates a spectrum 301 of the prototype wavelet 201.
Because the transmission channel is not ideal, the orthogonality between subchannels is destroyed at the receiver whenever amplitude and phase distortions are introduced by the transmission medium. In order to maintain orthogonality, various modulation techniques utilize various approaches. For example, DMT modulation systems extend cyclically each block of M transmit symbols prior to transmission. On the other hand, FMT technique employs another approach, whereby spectral overlap between the subchannels is avoided. FIG. 4 shows a typical example of the transmission spectrum of a VDSL system employing FMT modulation and demodulation scheme described above.
The key advantages of application of the FMT modulation to xDSL, when compared to other types of aforementioned modulation techniques, can be summarized as follows. FMT provides a flexibility to adapt to a variety of spectrum plans for allocating bandwidth for upstream and downstream transmissions. FMT modulation allows a high-level of subchannel spectral containment, and thereby avoids disturbance by echo and self-NEXT (near-end crosstalk). Furthermore, disturbance by a narrowband interferer, e.g., from AM or HAM radio sources, does not affect neighboring subchannels as the side lobe filter characteristics are significantly attenuated. Likewise, FMT modulation does not require synchronization of the transmissions at both ends of a link or at the binder level, as is needed for DMT xDSL. Finally, there is no need for cyclic extensions in the form of cyclic prefix or suffix.
A main disadvantage of the prior art FMT modulation scheme is associated with its complexity and significant difficulty of its implementation. For example, the synthesis filter-bank of the 64 subchannels VDSL system employing FMT modulation (hereinafter FMT VDSL system) includes 64 FIR filters, each of them having 128 taps. In turn, an FMT receiver for such a system must comprise not only 64 FIR filters of the analyses filter bank, but also 64 equalizers. In turn, each of the equalizers must be adaptive and comprise minimum 32 changeable parameters. Moreover, FMT system has to include 64 up-converters and 64 down-converters. Therefore, notwithstanding the good theoretical results, the FMT modulation for the VDSL was not yet realized on a mass scale.