1. Field of the Invention
The present invention generally relates to discrete multi-tone communication systems, and more particularly to a discrete multi-tone communication system using discrete Hartley transform for modulation and demodulation.
2. The Prior Arts
Discrete multi-tone (DMT) is a multi-carrier modulation (MCM) technique commonly applied in wireline communications such as digital subscriber loops (xDSL) including ADSL, ADSL2, ADSL2+, and VDSL, and power-line communications such as HomePlug. The basic idea of DMT is that a large number of sinusoids (i.e., subcarriers) are modulated by complex-valued quadrature amplitude modulation (QAM) symbols derived from an input bit stream, and transmitted in parallel. Performing a modulation on the complex valued constellation points generates samples of the continuous-time signal to be transmitted during a DMT symbol period. At the receiver, the QAM symbols are recovered by performing a demodulation on the analog-to-digital-converted received signal. A typical DMT system for xDSL is shown in
The modulation and demodulation operations performed by the IDFT and DFT can be expressed mathematically as follows:
where
Xk or Yk is the complex transmission symbol on the k-th subchannel in frequency domain, xn or yn is the n-th transmission sample in time domain, and N is the number of points for the IDFT/DFT.
The FEQ or, as it is used behind the DFT, the DFT-based FEQ can be implemented using various algorithms. For example, the MMSE (minimum mean-square error) algorithm tries to minimize the estimated error between the equalized signal and the transmitted signal. Among these algorithms, the LMS (least mean square) algorithm is most popular in terms of VLSI implementation. The LMS algorithm in the DFT-based FEQ consists of three operations: filtering, error estimation, and coefficient updating, expressed mathematically as follows:
Filtering: Ŷk=Yk·Wk*=(Yk,R+jYk,I)·(Wk,R−jWk,I) (3)
Error estimation: Ek=Xk−Ŷk (4)
Coefficient Updating: Wk(n+1)=Wk(n)+μkYkEk* (5)
where the subscripts R and I represent the real part and imaginary part of a complex number respectively, the superscript asterisk (*) denotes the complex conjugate operation, Yk is the DFT output, Xk is the training symbol of the k-th subchannel of the DMT system, Wk is the FEQ coefficient of the k-th subchannel, and μk is the updating step-size of the FEQ for the k-th subchannel. An embodiment of the DFT-based FEQ is illustrated in
Prior arts have suggested replacing the DFT with discrete Hartley transform (DHT) so as to reduce the computing complexity from complex to real multiplication involved in DFT, as DHT itself is real-valued operation. With such a substitution, the DFT-based DMT system shown in
The modulation and demodulation operations performed by the IDHT and DHT can be expressed mathematically as follows:
where cas(·)=cos(·)+sin(·), and N is the number of points for the IDHT/DHT and is the same as that for the IDFT/DFT. Similarly, the C2RT and R2CT can be expressed as follows:
C2RT: Hk=Xk,R−Xk,I (8)
R2CT: Yk=Yk,R+jYk,I={tilde over (H)}k,E−j{tilde over (H)}k,O (9)
where {tilde over (H)}k,E and {tilde over (H)}k,O are the even and odd parts of the {tilde over (H)}k respectively, which can be obtained by:
A DMT system is provided herein. As described above, in practice, the IDFT and DFT of a conventional DMT system can be replaced by the IDHT with a preceding complex-to-real transformation (C2RT), and by the DHT with a succeeding real-to-complex transformation (R2CT) at the transmitting end and the receiving end respectively. With the present invention, the DFT and the DFT-based FEQ at the receiving end of a conventional DMT system is replaced by the DHT and a DHT-based FEQ, omitting the use of R2CT.
At the transmitting end, the DMT system of the present invention performs modulation either by IDFT or by the IDHT along with C2RT while, at the receiving end, the demodulation is just realized by the DHT. The DHT-based FEQ directly equalizes each of the 0-th to (N−1)-th, subchannels output from the DHT as R2CT is omitted, where N is the number of points of DHT. Finally, each of the 0-th to
subchannels of the DMT system is obtained by combining the k-th and (N-k)-th subchannels of the DHT-based FEQ for k=0, 1, . . . ,
The LMS algorithm can also be adopted for the DHT-based FEQ, which is very suitable for VLSI implementation. The LMS algorithm of the DHT-based FEQ also contains the filtering, error estimation and coefficient updating operations.
The foregoing and other objects, features, aspects and advantages of the present invention will become better understood from a careful reading of a detailed description provided herein below with appropriate reference to the accompanying drawings.
a is a schematic diagram showing a DMT system for xDSL according to a first embodiment of the present invention.
b is a schematic diagram showing a DMT system for xDSL according to a second embodiment of the present invention.
The following descriptions are exemplary embodiments only, and are not intended to limit the scope, applicability or configuration of the invention in any way. Rather, the following description provides a convenient illustration for implementing exemplary embodiments of the invention. Various changes to the described embodiments may be made in the function and arrangement of the elements described without departing from the scope of the invention as set forth in the appended claims.
a and 4b are schematic diagrams showing a DMT system for xDSL according to two embodiments of the present invention. As illustrated, at the transmitting end, the modulation can be realized either by IDFT alone or by IDHT with a preceding C2RT. In the following, for simplicity, the first embodiment of
As illustrated, the DMT system of the present invention is similar to the prior arts in terms of architecture where, at the transmitting end, the system of the present invention performs modulation by the C2RT plus IDHT while, at the receiving end, the demodulation is now realized by the DHT only, omitting the R2CT. A major characteristic of the present invention is that a DHT-based FEQ is invented and employed to directly equalize each of the real-valued 0-th to (N−1)-th subchannels (i.e., {tilde over (H)}k of eq. (7)) output from the DHT.
The mathematical model for the DHT-based FEQ has been derived by the present inventor based on the MMSE criteria as the cost function of the equalization's residual error, and is presented in “DHT-Based Frequency Domain Equalizer for DMT Systems” in Proceedings of European Signal Processing Conference (Proc. of EUSIPCO'05). Using the LMS algorithm, the mathematical model of the DHT-based FEQ is as follows, which also contains the filtering, error estimation, and coefficient updating operations:
Filtering:
Error estimation:
Coefficient Updating:
where the subscripts R and I represent the real part and imaginary part of a complex number respectively, {tilde over (H)}k and {tilde over (H)}N-k are k-th and (N-k)-th subchannels output from DHT, Xk is the training symbol of the k-th subchannel of the DMT system, Ŷk is the k-th subchannel output from the DHT-based FEQ, μk is the updating step-size of the DHT-based FEQ. In an embodiment of the present invention, the coefficients Sk and Ck can be derived from Wk,R and Wk,I, which are the real and imaginary part of coefficients Wk from the DFT-based FEQ as follows:
In an alternative embodiment, the coefficient updating operation can also be carried out as follows:
where sgn(x) is the x's quantized value, which represents a +1 if the x≧0 and −1 if x<0.
An embodiment of the DHT-based FEQ is illustrated in
subchannels of the DMT system is obtained by combining the k-th and (N-k)-th subchannels of the DHT-based FEQ for k=0, 1, . . . ,
A comparison of the computing complexity for a single tone operation between the conventional approach (DHT+R2CT along with DFT-based FEQ) and the present invention (DHT+DHT-based FEQ) along the receive path is listed in Table 1:
In Table 1, the R2CT is considered only requiring 2-addition for each tone since the ½-term in Eq. (10) and (11) can be ignored for VLSI realization. From Table 1, it can be seen that the computing complexity of the DHT-based FEQ is the same as the DFT-based FEQ. In addition, it could be concluded that the present invention requires less computing complexity as it omits the 2N-addition (2 for each tone) of the R2CT.
Simulation results of data rates on a number of test loops under the conventional approach (DHT+R2CT along with DFT-based FEQ) and the present invention (DHT+DHT-based FEQ) are listed in Table 2:
As illustrated, the DHT-based FEQ and the DFT-based FEQ have identical data rates. Also by performance analysis, it can be proved that the DHT-based FEQ and the DFT-based FEQ have identical subchannel signal-to-noise ratios (SNRs).
Although the present invention has been described with reference to the preferred embodiments, it will be understood that the invention is not limited to the details described thereof. Various substitutions and modifications have been suggested in the foregoing description, and others will occur to those of ordinary skill in the art. Therefore, all such substitutions and modifications are intended to be embraced within the scope of the invention as defined in the appended claims.
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Number | Date | Country | |
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20070201574 A1 | Aug 2007 | US |