Pulse or digital communications – Equalizers
Reexamination Certificate
1999-09-28
2002-08-20
Tse, Young T. (Department: 2634)
Pulse or digital communications
Equalizers
C375S232000, C375S346000
Reexamination Certificate
active
06438161
ABSTRACT:
TECHNICAL FIELD
This invention relates to a method of designing an equaliser, and more particularly to systems for transmission and reception of signals over channels which require equalisers for shortening the duration of the impulse response of the overall system. The invention is particularly related to multicarrier data transmission over severely distorting channels. Throughout this specification, the British-variant spelling of the term “equaliser” is used in lieu of the term equalizer, although the two terms mean the same thing.
BACKGROUND ART
FIG. 1
of the accompanying drawings depicts a basic diagram of a discrete multitone (DMT) data transmission system. A block of serial input data (information bits) is collected in a serial-to-parallel (S/P) converter and then passed through an encoder which groups them into a number of sub-blocks and subsequently maps the bits belonging to each sub-block to real and imaginary parts of a complex number. The complex numbers generated in this way are considered as DFT (direct Fourier transform) values of a time domain signal. An inverse DFT transformer (usually implemented using an inverse fast Fourier transform (IFFT) algorithm) is then used to convert the mentioned frequency domain complex-valued numbers to the time-domain. These time-domain numbers are treated as a sequence of amplitude modulated pulses which after band-limiting are transmitted over the channel. Up-conversion to a higher frequency band may be also necessary, depending on the communication channel.
In the receiver, the received signal is frame synchronised and sampled at proper time instants. A block of samples are collected and passed through a DFT transformer (usually implemented using a fast Fourier transform (FFT) algorithm) to recover back the original frequency domain complex-valued numbers which were generated at the encoder output in the transmitter. The decoding process in the receiver follows the reverse of the encoder at the transmitter, thus the original information bits are recovered.
The IFFT and FFT blocks in the DMT transmission system, in fact, are modulator and demodulator blocks, respectively, operating on all subcarriers in parallel. More detailed discussions on the concepts related to DMT transmission systems could be found in the literature (see E. A. Lee and D. G. Messerschmitt,
Digital Communication
. Kluwer Academic Publishers, 1994, and J. G. Proakis,
Digital Communications
. McGraw-Hill, 3rd Ed., 1995, for example).
The block diagram of
FIG. 1
of the accompanying drawings ignores possible distortion that may be introduced by the channel. In DMT transmission systems, channel distortion is taken care of in a very special way, known as cyclic prefix.
FIG. 2
of the accompanying drawings shows a block-diagram representation of this process. It can be shown that if the duration of the impulse response of the channel is less than or equal to L data samples, by appending the last L samples of each data block at the output of the IFFT unit in the transmitter to the beginning of that data block, sending this extended block over the channel and subsequently, at the receiver, using the last N samples of the extended block as input to the FFT unit, the resulting set of frequency domain samples at the FFT output will be similar to the complex-valued numbers at the input to the IFFT unit in the transmitter within some complex-valued constant coefficients. The process involving the extraction of the latter coefficients is known as frequency-domain equalisation. This type of equalisation is not the subject of the present invention. In this invention, we are concerned with another aspect of the DMT signals equalisation which is widely known as time-domain equalisation. This is explained next.
We note that the use of L prefix samples in each block of transmitted signal with N samples per block, in its original form, effectively reduces the data rate of the system by a factor N/(N+L). It is thus very important to keep L as small as possible. Since in most of the practical applications, one has very little or no control over existing channels, a feasible solution to reduce L is to add an equaliser at the receiver and choose the parameters of this equaliser such that the cascade of the channel and equaliser results in a shortened impulse response. This is known as impulse response truncation or shortening.
Falconer and Magee have given a solution to the problem of equaliser design for impulse response shortening in the context of single carrier data transmission systems. Their solution involves the following steps:
1. An L-by-L matrix, Q, which is given in terms of the channel impulse response and the autocorrelation coefficients of channel noise, is evaluated;
2. the eigenvector, q, of the matrix Q which corresponds to its minimum eigenvalue is obtained; and
3. the elements of the vector q are considered as the samples of the desired response at the equaliser output and the equaliser coefficients are obtained accordingly.
For more details on this procedure the reader should refer to D. D. Falconer and F. R. Magee, Jr., “Adaptive channel memory truncation for maximum likelihood sequence estimation”, Bell Syst. Tech. J., vol. 52, No. 9, pp. 1541-1562, November 1973.
The above procedure is rather involved because of involvement of an eigenproblem. Thus, search for finding other alternative solutions which can be used to obtain the equaliser coefficients by a less involved procedure is of great practical interest.
Jacky Chow and John M. Cioffi have proposed such a method (U.S. Pat. No. 5,285,474, Feb. 8, 1994). This method involves a process of pole-zero modelling through a sequence of operations consisting of FFT, IFFT and some other intermediate operations. These operations, although relatively simple and regular, do not guarantee convergence of the equaliser coefficients to their optimum values, although a somewhat suboptimal solution may be achieved, if the system parameters are properly initialised. Nafie and Gatherer of Texas Instruments in a paper presented in ICC'97 (see list of references), have given an example of subscriber lines and shown that the results obtained by the method of Chow and Cioffi can be very far from the optimal solution that could be obtained from Falconer and Magee solution. They have also proposed a new scheme which works better than the method of Chow and Cioffi. However, their scheme also results in a solution which remains relatively far from the optimum, although it gives results somewhat better than those obtained by Chow and Cioffi's method. Only for relatively low signal-to-noise ratio (SNR) cases, the solutions provided by the method of Chow and Cioffi and also that of Nafie and Gatherer appear to be acceptable, however for moderate and high SNR's they fail to give acceptable results.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a completely different approach for designing impulse shortening equalisers. We have in particular examined our method on Asymmetric Digital Subscriber Line (ADSL) channels and have found that to be very useful and practical in this context. Nevertheless, the use of the methodology reported in this patent to other communication channels, wherever applicable, may be readily implemented by a person skilled in the art.
Accordingly, one aspect of the present invention provides a method of designing an equaliser having a target response suited to a particular subclass of communication channels to shorten the duration of the impulse response of the overall transmission system, a class of channels being divided into a number of subclasses, each subclass having a fixed set of parameters selected to achieve the target response of the equaliser for that particular subclass of channel, the method comprising the steps of:
recognizing the subclass of the channel;
and identifying the fixed set of parameters for the equaliser to achieve the target response by reference to a look-up table based on the subclass of the channel.
Preferably, the further step of
Chakraborty Mrityunjoy
Farhang-Boroujeny Behrouz
Wang Baoli
ipsolon llp
National Univ. of Singapore
Tse Young T.
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