Source: http://www.google.com/patents/US7039103?ie=ISO-8859-1&dq=5,960,411
Timestamp: 2014-08-29 16:01:30
Document Index: 14226952

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Patent US7039103 - Asymmetric digital subscriber line methods suitable for long subscriber loops - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign in<nobr>Advanced Patent Search</nobr>PatentsSystems and methods are described for asymmetric digital subscriber loops. A method includes utilizing a circuit having a first end and a second end, the circuit having a first amplification interface connecting the first end to the second end in a first direction, and a second amplification interface...http://www.google.com/patents/US7039103?utm_source=gb-gplus-sharePatent US7039103 - Asymmetric digital subscriber line methods suitable for long subscriber loopsAdvanced Patent SearchPublication numberUS7039103 B2Publication typeGrantApplication numberUS 10/284,057Publication dateMay 2, 2006Filing dateOct 30, 2002Priority dateMar 29, 2000Fee statusLapsedAlso published asUS6507606, US20020001340, US20030063660, WO2001073954A2, WO2001073954A3Publication number10284057, 284057, US 7039103 B2, US 7039103B2, US-B2-7039103, US7039103 B2, US7039103B2InventorsKishan Shenoi, Sandro Squadrito, Gary BogardusOriginal AssigneeSymmetricom, Inc.Export CitationBiBTeX, EndNote, RefManPatent Citations (24), Non-Patent Citations (29), Referenced by (1), Classifications (17), Legal Events (4) External Links: USPTO, USPTO Assignment, EspacenetAsymmetric digital subscriber line methods suitable for long subscriber loopsUS 7039103 B2Abstract Systems and methods are described for asymmetric digital subscriber loops. A method includes utilizing a circuit having a first end and a second end, the circuit having a first amplification interface connecting the first end to the second end in a first direction, and a second amplification interface connecting the second end to the first end in a second direction; adapting the first amplification interface to provide a first gain adjustment as a function of a first attenuation of a first communication by a first direction impedance from the transmission medium while transmitting in the first direction, the first communication within a first frequency range over the transmission medium from the first end to the second end; and adapting the second amplification interface to provide a second gain adjustment as a function of a second attenuation of a second communication by a second direction impedance from the transmission medium while transmitting in the second direction, the second communication within a second frequency range over the transmission medium from the second end to said first end. An apparatus includes a modulator for transmitting a first communication, in a first direction over a transmission medium, the modulator operably coupled to a first amplification interface for providing a first gain adjustment, based on a first attenuation of the first communication in the first direction by a first direction impedance of the transmission medium; and a demodulator operably coupled to the modulator, for receiving a second communication, in a second direction over the transmission medium, the demodulator operably coupled to a second amplification interface for providing a second gain adjustment, based on a second attenuation of the second communication in the second direction by a second direction impedance of the transmission medium.
CROSS-REFERENCE TO RELATED APPLICATIONS This application is a continuation of, and claims a benefit of priority under 35 U.S.C. 120 of U.S. Ser. No. 09/821,841 by inventors Kishan Shenoi, Sandro Squadrito and Gary Bogardus, entitled Asymmetric Digital Subscriber Line Methods Suitable for Long Subscriber Loops filed on Mar. 28, 2001 now U.S. Pat. No. 6,507,606 which in turn claims a benefit of priority under 35 U.S.C. 119(e) to U.S. Ser. No. 60/193,061, filed Mar. 29, 2000, the entire contents of which are hereby incorporated by reference for all purposes.
An early proposal to increase the information carrying capacity of the subscriber loop was ISDN (�Integrated Services Digital Network�), specifically the BRI (�Basic Rate Interface�) which specified a �2B+D� approach where 2 bearer channels and one data channel (hence 2B+D) were transported between the CO and the CPE. Each B channel corresponded to 64 kbps and the D channel carried 16 kbps. With 16 kbps overhead, the loop would have to transport 160 kbps in a full duplex fashion. This was the first notion of a Digital Subscriber Loop (�DSL�) (or Digital Subscriber Line). However, this approach presumed that POTS and 2B+D would not coexist (simultaneously). The voice codec would be in the CPE equipment and the �network� would be �all-digital�. Most equipment was designed with a �fall-back� whereby the POTS line-circuit would be in a �stand-by� mode and in the event of a problem such as a power failure in the CPE, the handset would be connected to the loop and the conventional line-circuit would take over. There are several ISDN DSLs operational today.(1-2) Asymmetric digital subscriber loop (ADSL) was proposed to provide a much higher data rate to the customer in a manner that coexisted with POTS. Recognizing that the spectral occupancy of POTS is limited to low frequencies, the higher frequencies, could be used to carry data (the so-called Data over Voice approach). Nominally, ADSL proposed that 10 kHz and below would be allocated to POTS and the frequencies above 10 kHz for data. Whereas the nominal ADSL band is above 10 kHz, the latest version of the standard specifies that the �useable� frequency range is above 20 kHz. This wide band between 4 kHz and the low edge of the ADSL band simplifies the design of the filters used to segregate the bands.
Referring to FIG. 2, a signal processing flow in a DMT-based ADSL transmission unit (�ATU�) that employs echo cancellation is depicted. The transmit (�modulation� direction) side is considered first. The data to be transmitted is first processed to include error correction by a ENC. & DEC. & ERR. & ETC. unit. It is then formatted into multiple �parallel� channels via a PARRL processing unit. It is then placed in the appropriate frequency slot via a FFT processing unit. The notion of �cyclic extension� is unique to DMT and involves increasing the sampling rate by insertion of additional samples via a CYC. EXT. processing unit. This composite signal is converted to analog via a D/A converter and coupled to the line via a 2 w-to-4 w converter. An ADSL repeater 200 is coupled to the 2w-to-4w converter.
Ideally the entire signal from the D/A converter is transmitted to the distant end via the 2 w-to-4 w converter. However, in practice some amount �leaks� from the 2 w-to-4 w converter toward a A/D converter. This leakage can be termed the �echo.�,
The receive side (�demodulation� direction) is now considered. The signal from the distant end arrives at the 2 w-to-4 w converter via the repeater 200 and is directed to the A/D converter for conversion to digital format. Subsequent processing includes line equalization via the LINE EQU. unit, fast Fourier transformation via the FFT unit and then channel equalization and data detection via the CHAN. EQU. & DET. unit. Processing is then handed to the unit that does the error detection and/or correction and reorganizing into the appropriate format. To remove the echo (the component of the transmit signal that leaks across the 2 w-to-4 w converter) an echo cancellation filter is employed. This is a digital filter that mimics the echo path and thus the output of the filter labeled �Echo Canc� is a �replica� of the echo and by subtraction of this signal from the received signal at a summation unit, the net echo can be substantially reduced. Thus 4 w operation is achieved even though the medium is merely 2 w. The spectral content of signals in the two directions can have significant overlap but are sufficiently separated by the echo cancellation technique.
Referring again to FIG. 3, the frequency range used for Upstream versus Downstream is vendor specific. Standards-compliant ADSL uses a total bandwidth of roughly 20 kHz to 1.1 MHz. In a preferred embodiment, the upstream occupies between 20 kHz and X, kHz whereas the downstream signal occupies the band between X2 kHz and 1.1 MHz. X2 should be substantially greater than X, to allow for frequency roll-off of the filters used to demarcate the upstream and down-stream bands. One suitable choice is X1=80 kHz and X2=160 kHz. The specific choice of these band edges can be made a design parameter and different �models� of the repeater can be fabricated with different choices of band edges.
Since the frequency response of the cable is not �flat� the amplifiers can be designed such that, in conjunction with the filters, they provide a rough amplitude equalization of the cable response over the appropriate frequency band, for example, approximately 10 kHz to 44 kHz upstream and approximately 60 kHz to 1 MHz downstream. The choice of frequency bands is, preferably, 20 kHz to 80 kHz for the upstream direction and 160 kHz to 1.1 MHz for the downstream direction.
The basic circuit outline 500 of the Extender unit is shown in FIG. 5. The extender unit includes a first 2 w�4 w and a second 2 w�4 w. For the case of a �load coil replacement�, the 88 mH inductors 510 would be present and the gains adjusted for compensating for (roughly) 6000 feet of cable. The same circuit arrangement would apply to the mid-span extender case wherein the 88 mH coils would not be present and the gains adjusted for X feet of cable (X could be in the neighborhood of 10,000 feet).
The following section describes relevant aspects of the DMT �data pump�. This is to compare and contrast the standardized data pump with the (non-standardized) data pump proposed herein. The essence of the new ADSL method is a better data pump, more in line with the notion of long loop behavior than the standard DMT. In particular, the new ADSL method is very well suited for modems (the ATU-R and the ATU-C) in situations where an ADSL extender (mid-span or at load coil locations) is utilized.
To understand the principle of the DMT data pump, consider the following situation. Suppose we have N(complex) samples {x(n); n=0,1,2, . . . ,(N�1)}. We can compute the (inverse) Discrete Fourier Transform (DFT) of this block of samples as {y(k); k=0,1,2, . . . ,(N�1)} as indicated in Eq. (2.4.1).
y ⁡ ( k ) = 1 N ⁢ ∑ n = 0 n = ( N - 1 ) ⁢ x ⁡ ( n ) � ⅇ + j ⁢ ⁢ 2 ⁢ π ⁡ ( n � k N ) (Eq.��2.4.1) Since the DFT is invertible, we can recover the original sample set, {x(n)} from the set {y(k)} using the (forward) DFT.
x ⁡ ( n ) = ∑ k = 0 k = ( N - 1 ) ⁢ y ⁡ ( k ) � ⅇ - j ⁢ ⁢ 2 ⁢ ⁢ π ⁢ ⁢ ( n � k N ) (Eq.��2.4.2) That is, the process of performing the IDFT (�Inverse DFT�) and then the DFT gives back the original set of samples. In DSP literature, we sometimes do not make a big distinction between the inverse and forward DFTs because they are so similar and we use FFT (Fast Fourier Transform) algorithms in either case and all FFT algorithms are geared to implement either form of DFT.
An extension of this idea is depicted in FIG. 6, below. Here we assume that a �Source� 610 generates ablock of N samples called {x(n); n=0,1,2, . . . ,(N�1)} which are processed using an inverse DFT 620 calculation (i.e. a complex matrix multiplication) to yield {y(k); k=0,1,2, . . . ,(N�1)}. These samples are converted into a serial word stream, {w(nT)}, at an effective sampling rate, fs (=1/T), of N times the rate at which the source generates blocks of samples by a parallel to serial converter 630, and converted into analog form using a digital-to-analog converter (DAC) 640. This analog signal traverses the transmission medium 650, namely the cable, and at the receiver 660 is converted into digital format at sampling rate fs to yield samples {w′(nT)}. The reverse process of conversion from serial-to-parallel is followed by a DFT calculation 680.
If we assume that the transmission medium is very wide-band and thus does not affect the signal, and that there is no additive noise (interference), and if we can compensate for any transmission delay between the DAC 640 and ADC 670, then we can, in principle, synchronize the DAC 640 and ADC 670 in a manner that w(nT)�w′(nT). That is, the serial stream of samples from the ADC 670 matches the serial stream of samples provided to the DAC 640. In this situation, each block (parallel set) of samples {x′(n); n=0,1,2, . . . ,(N�1)} provided to the �SINK� 690 will be nominally the same as the block (parallel set) of samples generated by the �SOURCE� 610. This is the underlying premise for the DMT. Each block of N samples can be viewed as a �symbol� and the symbol rate is the rate at which blocks (i.e. symbols) are generated for transmission. The sampling rate of the DAC 640 and the corresponding ADC 670 is N times this symbol rate. In the ADSL DMT standard the symbol rate is specified as 4 kHz. Thus in an ideal situation, the transmitted symbol (from the �SOURCE� 610) will be received �intact� by the receiving entity (the �SINK� 690).
Visualizing the DMT data pump as a scheme for transmitting blocks, or symbols, is appropriate if there were no transmission medium to contend with. A different viewpoint can be developed that describes more fully the action of the DMT scheme. To this end we view the sequence of N-sample symbols (blocks) as N �independent� channels wherein each channel has a sampling rate equivalent to the block rate (symbol rate), namely 4 kHz. It can be shown (see Ref. [6]) that the action of the IDFT can be viewed as a combination of interpolation, filtering and frequency translation.
In FIG. 7, the block 700 with the up-arrow and �(N)� indicates the process of over-sampling or up-sampling. The sampling frequency is increased by a factor of N by the insertion of zero-valued samples. In the frequency domain, this action is equivalent to the creation of spectral replicates. That is, the base-band spectrum is replicated at center frequencies of the form (kfs/N) where k ranges from 0 (i.e., the base-band itself) through (N�1). The low-pass filter 720, �LPF�, then �removes� all the replicates. The extent to which these replicates are attenuated depends on the frequency response of the low-pass filter 720. The low-pass filter output is representative of the input signal at the increased sampling rate, fs. This LPF-output signal is then modulated (frequency-translated) by the appropriate carrier frequency. It can be shown that the N carrier frequencies are of the form (kfs/N) where k ranges from 0 through (N�1).
In the DMT scheme the �channel separation filter�, which is nominally equivalent to the LPF 720 in FIG. 7, is equivalent to a �rectangular window�. That is, the LPF is an FIR filter (�FIR�=Finite Impulse Response) with impulse response given by {h(n); n=0,1, . . . ,(N−1)} where all N coefficients are equal and for purposes of establishing frequency response can be assumed to be unity. The frequency response can be computed as
h ⁡ ( n ) = 1 ; n = 0 , 1 , � ⁢ , ( N - 1 ) H ⁡ ( f ) = sin ⁡ [ N ⁢ ⁢ π ⁡ ( f f s ) ] sin ⁡ [ π ⁡ ( f f s ) ] ; f s = sampling��frequency (Eq.��2.4.3) The frequency response curve is of the (the digital equivalent of) �sin-x-by-x� form. As low-pass filters go it is not a very �good� response. It has transmission zeros at multiples of (fs/N) but between transmission zeros the stop-band attenuation is not that much, as little as 13 dB (approximately) close to the pass band, which is nominally up to 0.5(fs/N), but improving as the frequency is increased. One would expect that with such a weak low-pass filter, there would be significant inter-channel cross-talk. However, the DMT scheme can introduce a clever mechanism to reduce this perceived impairment.
Before we describe this technique, consider the implication of modeling the transmitter by the signal flow graph of FIG. 7. If the LPF 720 blocks were indeed good low-pass filters, then the scheme is equivalent to Frequency Division Multiplexing (FDM). Each sub-channel (distinguished via the subscript k) can be considered �independent� of any other sub-channel and occupies its own frequency slot of bandwidth (nominally) (fs/N). Further, it can be shown that the processing in the receiver, comprising the serial-to-parallel conversion followed by the DFT, is equivalent to the logical �inverse� of FIG. 7. That is, the receiver does the demultiplexing function. This is depicted in FIG. 8. Note the similarity between FIG. 7 and FIG. 8. From a Signal Processing viewpoint, the multiplexing and demultiplexing functions are �dual� operations. In fact, we can �derive� FIG. 8 from FIG. 7 by replacing the summation node with a branch point 810 and reverse the direction of the signal flow. That is, the incoming signal is processed in parallel by a bank of frequency translators followed by low-pass filters 820 followed by the reduction in sampling rate by a factor of N. In the literature the configuration of FIG. 8 is referred to as a �maximally decimated filter-bank� because the under-sampling factor (i.e., N) is equal to the number of channels and thus the overall number of samples per second is the same for the set of N sub-channels versus the combined signal.
Thus, logically speaking, we have N �independent� channels, each occupying a bandwidth of (fs/N) with its own �center frequency�. Assuming that this bandwidth is small, the effect of the intervening cable then can be modeled as a straightforward (complex) gain, that is, for all practical purposes, �flat� over this narrow band. Thus we do not need complicated equalization methods for equalizing the cable frequency response, just flat-gain equalization for each of the sub-channels.
The approach of using filter-banks that combine the filtering and modulation is not new. Ref [7] is the original patent for the �Transmultiplexer� which provided just the functionality described, namely combination of several �low-speed� (i.e., low- sampling rate) channels into a single �high-speed� (i.e., high sampling rate) channel and vice-versa. The equivalent problem of taking a single high-speed signal and splitting it into several low-speed signals and then recombining them back into the high-speed signal (without losing information) has been addressed in the theory of filter-banks and [8] is a comprehensive reference for this topic.
The DMT data pump principle is a clever method to overcome the �non-ideal� nature of the implied low-pass filter. The principle is based on the following property of the Discrete Fourier Transform (DFT). Suppose {x(n); n=0,1, . . . ,(N�1)} and {h(n); n=0,1,2, . . . , (N�1)} are two N-point sequences and {y(n), n=0,1, . . . ,(N�1)} is a third N-point sequence that is the circular convolution of the first two N-point sequences. That is,
y ⁡ ( n ) = ∑ k = 0 k = ( N - 1 ) ⁢ h ⁡ ( k ) � x ⁡ ( ( n - k ) ) ; where ( ( n - k ) ) = ( n - k ) modulo ⁡ ( N ) (Eq.��2.4.4) Note that circular convolution is similar to regular-convolution except that the indices are constrained to lie in the range 0 through (N−1) using the modulo(N) operation to map integers outside this range into this range. If we denote by {X(k); k=0,1,2, . . . ,(N�1)}, {H(k); k=0,1,2, . . . ,(N�1)}, and {Y(k); k=0,1,2 . . . ,(N�1)}, the DFTs of the three N-point sequences {x(n); n=0,1, . . . ,(N�1)}, {h(n); n=0,1,2, . . . ,(N�1)} and {y(n); n=0,1, . . . ,(N−1)}, respectively, then the transform-domain equivalent of Eq. (2.4.4) is given by
Y(k)=X(k)�H(k); k=0,1,2, . . . ,(N−1) (Eq. 2.4.5)
That is, the DFT transforms circular convolution in the �time-domain� to multiplication in the �frequency-domain�.
w ′ ⁡ ( n ) = ∑ k ⁢ w ⁡ ( n - k ) � h c ⁡ ( k ) (Eq.��2.4.6) In Eq. (2.4.6) the range of the index k encompasses all the non-zero elements of the impulse response {hc(n)} which, in general, is an infinite range, from 0 to ∞ (infinity). Note that even if the range were finite, the convolution is not a circular convolution and thus the transform-domain equivalent, assuming we use the DFT, does not follow Eq. (2.4.5). Recognizing that if {w(n)} is periodic, then the regular convolution of Eq. (2.4.6) does indeed reduce to a circular convolution, the approach taken in the DMT data pump is to mimic a periodic behavior.
Suppose the effective cable impulse response was indeed finite in duration, say K samples long. That is, hc(n)=0 for n=K, (K+1), (K+2), . . . . We modify the �parallel-to-serial� conversion from the regular, conventional, method to one in which we introduce a periodic extension. That is, from the N �parallel� samples {x(0), x(1), . . . , x(N�1)} we generate (N+K�1) �serial� samples by creating {x(N_K+1), x(N_K+2), . . . , x(N_), x(0), x(1), . . . , x(N�1)}. This periodic extension is also called a �cyclic prefix�. With this cyclic prefix, we can see that if we take the regular convolution of these (N+K�1) sequential samples with the finite impulse response {hc(n)}, and examine the latter N samples of the (regular) convolution, we get
w ′ ⁡ ( K ) = h c ⁡ ( 0 ) � x ⁡ ( 0 ) + h c ⁡ ( 1 ) � x ⁡ ( N - 1 ) + � + h c ⁡ ( K - 1 ) � x ⁡ ( N - K + 1 ) w ′ ⁡ ( K + 1 ) = h c ⁡ ( 0 ) � x ⁡ ( 1 ) + h c ⁡ ( 1 ) � x ⁡ ( 0 ) + � ⁢ + h c ⁡ ( K - 1 ) � x ⁡ ( N - K + 2 ) ⋮ w ′ ⁡ ( K + N - 1 ) = h c ⁡ ( 0 ) � x ⁡ ( N - 1 ) + h c ⁡ ( 1 ) � x ⁡ ( N - 2 ) + � + h c ⁡ ( K - 1 ) � x ⁡ ( N - K ) (Eq.��2.4.7) Denote the N samples of w′(n) for index n ranging from K through (N+K�1) by {v(n), n=0,1,2, . . . ,(N�1)}. Then examination of Eq. (2.4.7) indicates that we can identify this N-point sequence as the circular convolution of the �input� sequence {x(0), x(1), . . . , x(N�1)} and the (FIR) impulse response {hc(n)}. Thus, when we do the serial-to-parallel conversion, we choose the appropriate N consecutive samples of {W′(nT′)} from a block of (N+K−1) samples and ignore the rest. Here we have indicated the time-interval between samples for w′(t) as T′ since the effective sampling rate of the ADC and DAC is greater by a factor of (N+K�1)/N because of the inclusion of the cyclic prefix.
The inclusion of the cyclic prefix allows us to model the filtering action of the cable as being cyclic convolution, rather than regular convolution. This modeling is appropriate if (and only if) the effective cable impulse response is FIR with an impulse response length less than the size of the cyclic prefix. In the actual DMT ADSL standard, a special equalization procedure is mandated which �equalizes� the cable to the extent that, in conjunction with the equalizer, the effective impulse response is FIR.
The following section describes an even better approach to achieving the data pump, one that is better suited for long loop ADSL and which will work efficiently in conjunction with the Long Loop ADSL Extender mechanism. The principle underlying this improved method is actually quite old, predating the DMT ADSL standard by several years. In fact it has been used in a product called a �Transmultiplexer� which does a bilateral conversion between analog FDM (Frequency Division Multiplexing) and digital TDM (Time Division Multiplexing) and covered in two patents that were issued in 1978 and 1980 (see Ref. [7]).
The improved data pump is based on the principle of the Digital Filter Bank used in the Transmultiplexer. Specifically, it calls for improved filters, compared to the DMT scheme, in the configurations depicted in FIG. 7 and FIG. 8. Furthermore, we show that even though the computational burden for such filters would be greater than the computational burden in the case of the DMT (�Rectangular Window� low-pass filter), the overall computational burden is less and furthermore, the need for increasing the speed of the ADC and DAC by the factor of (N+K�1)/N is obviated.
The filter bank principle allows for filter lengths longer than N (the size of the DFT) and thus we can provide for filter characteristics that are superior to that of the N-point rectangular window called out in the DMT standard. Having a better filter characteristic implies that the channel separation is more robust and thus we do not have to resort to the cyclic prefix extension of the DMT. In particular, the filter bank principle details how a filter of length R-N can be applied. Details can be found in references [5] through [8]. Simply put, the extended length R-N can be implemented as N separate R-point FIR filters. In the �modulate� direction whereby N sub-channels are combined, the mini-FIR filters, also referred to as a �weighting network�, is positioned after the IDFT and the outputs of the N (parallel) R-point filters is converted from parallel to serial. In the �demodulate� direction, where the N sub-channels are extracted from the aggregate, the N R-point filters are positioned after the serial to parallel conversion and before the DFT computation. It can be shown that �R� does not have to be the same for the modulation and demodulation processing but it is usual to have the same length filter for both operations. The ratio, R, of the length of the DFT (N) and length of the filter (R.N), can be referred to as �the number of active taps�.
In FIG. 9 we show how the scheme depicted in FIG. 6 is modified to accommodate the longer filters for channel delineation. In the most general case the filters labeled �H� in the modulator and �G� in the demodulator could be derived from different �prototype� filters but in most cases the same design is used for both operations. We shall assume that �H� and �G� are the same for this discussion. We show the derivation for the demodulation operation here.
Denote this R�N length FIR filter as {hp(n); n=0,1,2, . . . ,(RN�1)}. This filter is considered the �prototype� filter because it is applicable to all channels. The parameter �R� is �the number of active taps�, a term which will be self-explanatory shortly but follow from the fact that the filter length is R times the size of the DFT that we will use. The signal for the k-th sub-channel, at the high sampling rate can be expressed as
x k ⁡ ( nT ) = ∑ m = 0 RN - 1 ⁢ h p ⁡ ( m ) � w ⁡ ( ( n - m ) ⁢ T ) � ⅇ - j ⁢ ⁢ 2 ⁢ ⁢ π ⁡ ( n - m ) ⁢ k N (Eq.��3.1.1) where we have taken into account that the frequency translation of {w(nT)} by the k-th carrier is achieved by multiplying by the complex exponential term.
The N R-point filters are seen to have impulse responses corresponding to the N different phases whereby the impulse response of the prototype filter can be under-sampled by a factor of N. In Eq. (3.1.1) we can split the index m which runs from 0 through (RN�1) into a double index in a manner suggested by Eq. (3.1.2) and get:
x k ⁡ ( nT ) = ∑ μ = 0 N - 1 ⁢ ∑ m = 0 R - 1 ⁢ h p ⁡ ( mN + μ ) � w ⁡ ( ( n - mN - μ ) ⁢ T ) � ⅇ - j ⁢ ⁢ 2 ⁢ ⁢ π ⁡ ( n - mN - μ ) ⁢ k N (Eq.��3.1.3) If, further, we recognize that the output of each sub-channel is re-sampled (under-sampled by a factor of N) at the lower sampling rate (4 kHz), only every N-th sample of {xk(nT)} needs to be computed. Therefore,
x k ⁡ ( nNT ) = ∑ μ = 0 N - 1 ⁢ ( ∑ m = 0 R - 1 ⁢ h μ ⁡ ( m ) � w ⁡ ( ( n - m ) ⁢ N - μ ) ) � ⅇ j2 ⁢ ⁢ π ⁢ μ ⁢ ⁢ k N (Eq.��3.1.4) Examination of Eq. (3.1.4), specifically the inner parentheses, indicates that we do N R-point FIR filters operating on the N separate phases of under-sampling the signal {w(nT)} by a factor of N. Further, the outputs of these N �sub-filters� are combined using a computation of the DFT form to yield the N sub-channel outputs (�simultaneously�). This is the theory of the digital filter bank. A similar treatment yields the dual result for the other direction.
Note the striking similarity between FIG. 3 and FIG. 10 which depict the DMT form and the Improved Data Pump form respectively (the improved data pump can also be called the �Transmux� form since it is based on the theory of the Transmultiplexer). The �back-end� processing related to data formatting, error detection and correction, coding, etc., can be the same for both data pumps. The distinction between them include the following points. First, DMT uses a cyclic prefix; the Transmux uses a Weighting Network (of R-point FIR filters). Second, DMT uses channel equalization for making the transmission medium appear �FIR�; the Transmux uses a Weighting Network (of R-point FIR filters). Third, the DMT scheme, to accommodate the cyclic prefix extension uses a line sampling rate which is greater than N-times the symbol-rate (the symbol-rate is 4 kHz for ADSL), while the Transmux scheme uses a line sampling rate of exactly N-times the symbol-rate.
Chart 1 DMT/TRANSMUX Fundamentals Key Concept:
Channel frequency response is not �flat� (equalization problem).
Over narrowband channel equalization is just a �flat gain�
Chart 2 DMT versus TRANSMUX Channel Definition Filter:
TRANSMUX uses filter of length R*N (R=�number of active taps�).
DMT assumes wideband channel is FIR. Uses cyclic extension of symbol vector to �fake� cyclic convolution.
Chart 3 DMT versus TRANSMUX EQUALIZATION REQUIREMENT:
DMT requires wideband equalization to force wideband channel to �look FIR�.
Coarse wideband (selectable 1 of M coefficient sets) Precise per-channel (adaptive wrt cable makeup) Chart 4 DMT versus TRANSMUX CHART 4
N � log(N) + M � log(M)
3 � N + 3 � M = 1728
32 � M = 2048
Chart 5 DMT versus TRANSMUX CHART 5
32 � M = 16384
One of the benefits in using a better channel definition filter is the relaxing of the attenuation requirements of the analog filters that separate the two directions of transmission in the ATU-C and the ATU-R. Because of the improved performance, less signal (power) �spreads� into the other band. In particular even with 3 active taps (R=3), the intrinsic characteristic of the Transmux scheme is to reduce the signal power in the other band by about 27 dB.
The efficacy of using more than one active tap is demonstrated in the following charts which indicate spectral occupancy. The DMT scheme frequency characteristic were computed, for the purposes of these charts, by ignoring the cyclic prefix. Thus both the Transmux scheme and DMT scheme used a symbol rate of 4 kHz and a line sampling rate of N*4 kHz, i.e., 256 kHz in the upstream direction and 2048 kHz in the downstream direction. The DMT scheme corresponds to a �rectangular window� filter or, equivalently, 1 active tap. For the Transmux scheme we assumed 3 active taps and used a Hamming frequency characteristic which, while not optional, is adequate to demonstrate the frequency behavior that can be expected.
REFERENCES 1. Walter Y. Chen, DSL. Simulation Techniques and Standards Development for Digital Subscriber Line Systems, Macmillan Technical Publishing, Indianapolis, 1998. ISBN: 1-57870-017-5.
3. �G.992.1, Asymmetrcal Digital Subscriber Line (ADSL) Transceivers,� Draft ITU Recommendation, COM 15-131.
4. �G.992.2, Splitterless Asymmetrical Digital Subscriber Line (ADSL) Transceivers,� Draft ITU Recommendation COM 15-136.
7a. U.S. Pat. No. 4,131,766, Issued Dec. 26, 1978, �Digital Filter Bank�.
7b. U.S. Pat. No. 4,237,551, Issued Dec. 2, 1980, �Transmultiplexer�.
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