FR2647609A1 - METHOD FOR DETERMINING THE INITIAL VALUES OF THE COEFFICIENTS OF A NON-RECURSIVE EQUALIZER - Google Patents

Abstract

The invention relates to a method for determining the coefficient of a non-recursive equalizer used in the receiver of a data transmission system by sending over the transmission channel a sequence of known periodic data, by calculating the known Fourier transform Ck of the equalizer using the sequence of data received, either directly or through the discrete Fourier transform Uk of the channel, and by calculating the equalizer coefficients by an inverse discrete Fourier transform of said discrete Fourier transform Ck of the equalizer. In order that the coefficients can be calculated using a shorter synchronization sequence, the method is characterized in that the number of spectral components of the discrete Fourier transform of the equalizer or the channel is increased by interpolation of components intermediate between the original spectral components before said calculation of the inverse discrete Fourier transform.

Description

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  METHOD FOR DETERMINING THE INITIAL VALUES OF COEFFI-

CIENTS OF A NON-RECURSIVE EQUALIZER.

  The invention relates to a method for determining the coefficient of a non-recursive equalizer used in the receiver of a data transmission system.

  sending on the transmission channel a sequence of

  known periodic methods, by calculating the discrete Fourier transform C (k) of the equalizer by means of the received data sequence, either directly or via the discrete Fourier transform U (k), and calculating the coefficients of the equalizer by an inverse discrete Fourier transform with respect to said discrete Fourier transform C (k) of the equalizer to determine the initial values of said coefficient. In a synchronous data transmission system, the data to be transmitted is in the form of a series of bits. In the transmitter (for example a modem), the bits are converted into signaling symbols which are then transmitted on the transmission channel at a given signaling rate 1 / T, where T is the interval between the symbols. In the receiver (eg a modem), the received symbols are detected and converted back into a series of data bits. The transmission path degrades the transmitted signal due to various sources of interference, including linear distortion (distortion of amplitude and

propagation time) and noise.

  To alleviate this problem, the system may be provided with an adaptive equalizer, for example a digital cross-sectional filter with variable sensing coefficients and an equal or lower sensing interval T '(fractional-space equalizer) at the interval T between signal symbols. A first method for calculating the initial values of the coefficients of the fractional-space non-recursive equalizer is presented in Rapid Training of a Voiceband Data-Modem Receiver Employing an Equalizer with Fractional-T Spaced Coefficients, IEEE Transactions on

  Communications, Vol. COM-35, p. 869-876, Oct. 1987.

  In this prior art method, the data transmitted on a transmission path is preceded by a periodic sequence of symbols called synchronization sequence, in which each period contains N symbols. The transfer function U (k) of the channel is estimated first by calculating the discrete Fourier transform (DFT) R (k) of at least one period of the received synchronization signal and then dividing it by the DFT S (k) the transmitted synchronization sequence. The transfer function C (k) of the equalizer is obtained from the ratio C (k) = B (k) S (k) / R (k), where B (k) is the reference spectrum, c ' that is, the desired transfer function of the system (the common transfer function of the transmission channel and the equalizer). The coefficients of the equalizer are obtained by the inverse DFT of Clk). Thus, the time space or the propagation time of the equalizer is equal to the length NT

of the synchronization sequence.

  An important problem to be overcome by the initial equalization is the inter-symbol interference caused by the distortion of the delay, ie the group delay. The delay distortion means that the data transmission channel delays the different frequencies to a different degree. In a telephone connection, the propagation delay as a function of frequency forms a typically parabolic function in which the propagation time increases from the medium

  from the frequency band to its edges.

  The time space of the impulse response in a path causing a distortion of the propagation time is substantially equal to its maximum difference in propagation time between the different frequencies. The equalization of this type of channel usually requires an equalizer having an equal impulse response duration or, preferably, greater than the duration of the response.

impulse of the way.

  The smooth running of the method described above requires that at least 1.5 to 3 periods of a periodic synchronization sequence be sent, since an increase in the number of periods facilitates the limitation of other defects affecting the signals, for example the noise, frequency shift and phase jitter. The required length of the synchronization sequence is therefore 2 to 3 times the

  maximum distortion of the propagation time.

  In many cases, the equalizer coefficients should be calculated only when the program is triggered. Since this does not happen very often, the extra bit caused by the synchronization sequence

  is insignificant compared to the total duration of the program.

  In other cases, especially when interrogating multipoint networks, the data emlssion consists of short messages. Since each message must be preceded by a synchronization sequence and the transmission quality of the system can be defined as the ratio of the time required to send a message to the time the channel is busy, it is obvious that it is extremely important. to limit as much as possible the length

of the synchronization sequence.

  The method described above for calculating the coefficients of an equalizer results in a cyclic equalizer having a period length NT. If the length of the period of the synchronization sequence is reduced to be shorter than the duration of the impulse response of the channel, which results in a staircase effect of the equalizer periods in the field of the time. This greatly reduces the performance of the equalizer. A corresponding phenomenon can occur in connection with a difficult transmission path whose duration

  the impulse response is greater than NT.

  The object of the invention is to provide a method by which equalizer coefficients can be calculated using a very short periodic synchronization sequence. The invention also aims to provide a method which, despite the short synchronization sequence, can calculate the coefficients of an equalizer so that the interference between

the symbols are very small.

  The object of the invention is also to provide a method which performs calculations quickly and efficiently so that it can be performed with a processing unit of

digital signals.

  These objectives are achieved by means of a method according to the invention, calculating by interpolation of the intermediate components between the original spectral components of the spectrum of the channel or the equalizer after the determination of the channel's TFDD. or equalizer, then calculating the inverse DFT of the interpolated spectrum obtained from the equalizer, so as to obtain an equalizer having a greater length

  as the length of the synchronization sequence.

  Concretely, this means that the duration of a single period of the synchronization sequence can be shortened to almost half of the original value without

  adversely affect the performance of the equalizer.

  On the other hand, if the length of the synchronization sequence is not shortened, the length of the equalizer that results is twice as large as before, so that it can be used for the equalization of

  distortions caused even by a difficult path.

  The invention will now be described in more detail by way of embodiments with reference to the drawings, in which: Figure 1 shows a timing sequence consisting of a pulse sent at intervals of NT; Figure 2 shows a real part of a response of a channel received in a receiver for the pulse sequence of Figure 1 when the impulse response of the channel is longer than NT; FIGS. 3 and 4 show phase and group delay characteristics for the channel, and FIGS. 5 and 6 show the propagation time characteristics of the real part of the impulse response calculated by the basic method of the channel. equalizer; Figure 7 shows the amplitude spectrum of the calculated equalizer, when the interval between the spectral components is 1 / NT; Figure 8 shows the amplitude spectrum of the channel of Figure 7 when spectral components have been interpolated therein at 1/2 NI intervals; Figure 9 shows the real cyclic part of the impulse response of an equalizer, calculated from the interpolated spectrum; and Figure 10 shows an equalized group delay characteristic, corresponding to the spectrum

interpolated from Figure 9.

  In the method according to the invention, the coefficients of a non-recursive equalizer used in the receiver of a data transmission system are calculated by determining the discrete Fourier transform of the impulse response of the equalizer with the aid of a synchronization sequence sent on the channel, directly or via the DFT of the channel. The coefficients of the equalizer are obtained by the inverse of the DFT from the DFT of the equalizer. The novelty of the process lies in the processing of the DFT or the spectrum of the equalizer or the

  way before calculating the coefficients.

  The general structure and operation of the transmission system itself and the non-recursive equalizer are obvious to those familiar with the technique, and

  see the aforementioned article and the description of the

  U.S. Patent No. 4,152,649. The invention can be implemented in equalizers presented in the article and in

  the patent description, or in other equalizers

  appropriate. The principles of the basic method for determining the coefficients of the non-recursive equalizer are also presented in the aforementioned article. To facilitate the understanding of the invention, the basic principles of

  process will be described below before the description of the

principle of the invention.

  Assuming that the impulse response equivalent to the baseband of a transmission channel in a data transmission system must be equalized by a non-recursive equalizer having a (M / K) -T pickup spacing less than or equal to 1 interval T between signal symbols, the number of sensing coefficients in the non-equalizer

recursive being NK / M.

  Prior to the transmission of data, the transmitter sends a periodic sequence s (t) of synchronization with a period length of NT. The transmitted signal is propagated by the way and

  is sampled at the sampling rate (M / K) -T.

  At the receiver, the presence of a periodic synchronization sequence is constantly monitored

  in the arrival signal, and a period r (n), n = 0, 1 ...

  NK / M, is extracted from the periodic sequence of

received synchronization.

  By calculating the DFT of the received samples or the period r (n), the DFT of the frequency characteristic L (k) of the channel can be determined U (k) = R (k) / S (k) (1) at uniformly spaced 1 / NT frequency points, where R (k) is the DFT of the received timing sequence, and S (k)

  is the DFT of the transmitted synchronization sequence.

  The DFT or the frequency characteristic C (k) of the equalizer can now be obtained by calculating the ratio C (k) = B (k) / U (k) = B (k). S (k) / R (k) (2) Finally, the coefficients of capture of the equalizer are obtained by calculating the inverse DFT of C (k). The propagation time or time space of the impulse response of the obtained equalizer is equal to the length NT of period

of the synchronization sequence.

  However, in the context of the invention, the exact way in which the DFT of the channel or equalizer is calculated for the interpolation according to the invention does not present a

capital importance.

  In the remainder of the present description, the method of

  The base will be represented in a graphical form, assuming for simplicity that the pulses are sent at intervals of N symbols, as shown in Figure 1. If the duration of the impulse response of the channel is less than NT, the response impulse u (t) of the channel is obtained directly in the receiver. The equalizer can then be calculated directly from the transformation

  discrete Fourier U (k) of the impulse response u (k).

  The impulse response of the equalizer can therefore be fully placed in NT propagation time, so that it can equalize even arbitrary non-periodic data. With a very difficult path, the impulse response of the channel may be longer than NI, whereby the responses of the successive periods (in this case, pulses) of the synchronization sequence undergo the staircase effect in the receiver, As shown in FIG. 2, the channel can have, for example, the phase characteristic shown in FIG. 3 and the group delay characteristic shown in FIG. the group delay characteristic of the equalizer resulting from the basic method are shown in FIGS. 5 and 6. The impulse response of this type of equalizer can not be entirely shifted in the

  NT propagation time limits.

  In the method according to the invention, the channel U D (k) and / or the equalizer EFT (C) are firstly determined either by the known basic method or

  also, by one of its variants.

  Then, an intermediate component, for example, is determined by interpolation between the original spectral components of the DFT of the channel or equalizer, the interval between the spectral components of the interpolated DFT (spectrum) being 1 / 2NT, as shown on the

Figures 7 and 8.

  Finally, if the spectrum to be interpolated is the spectrum C (k) of the equalizer, the capture coefficients of the equalizer, now of number 2N, are calculated using the inverse DFT of the spectrum C '(k) interpolated from the equalizer. Space

  time of the equalizer obtained is thus 2 NT, that is,

  twice as long as without interpolation, as well as the "dynamics" of the propagation delay, ie the equalizer is able to process the propagation delays of

  the track in limits of 0 to 2 NT.

  On the other hand, if the spectrum to be interpolated is the spectrum U (k) of the channel, the new spectrum C '(k) = B (k) / U' (k) of the equalizer is calculated first, the capture coefficients are then calculated from the spectrum of

  the equalizer, as described above.

  Various interpolation techniques will be discussed below.

  after. The channel and equalizer spectrum is complex, so it is also necessary to define real and imaginary parts for the intermediate components. The simplest way would be to interpolate the real and imaginary parts of the intermediate components directly from the real and imaginary parts of the original spectral components. In this way we obtain an equalizer with a length of 2 NT, while the result can be more or less defective, depending on the modalities of the interpolation, and it is also often impossible to deduce the correct

  phase of the intermediate component.

  In the preferred embodiment of the invention, the amplitude A (k) and the phase P (k) of the spectral components of the spectrum of the channel or of the equalizer are firstly determined, and the phases of the intermediate components are deduced from the phase function, or the amplitude and phase of the intermediate components are interpolated to

using the amplitude function.

  The amplitudes of the intermediate components can be determined directly from the amplitudes of each pair of original contiguous components of the original spectrum of the equalizer or the channel (see Figure 7), interpolating for example according to the approximation following: A (k + i) = A (k) + A (k + 1) A (k + I) 2> However, the calculation of the phase of the intermediate components is not uniformly unambiguous because the phase values of the spectral components calculated by an operation on arc tangents are between n and -n and contain discontinuity points. A continuous phase function can be formed from the calculated phase values by adding to each of the phase values an appropriate multiple of 2n if the samples are close enough to each other for the discontinuity points to be observed. With a very short equalizer and a high distortion path, the variation in the group delay of the channel can be greater than the time space of the equalizer. This means that the phase difference between two contiguous frequency points may be greater than 2n, which makes it impossible to determine the multiple of 2n to be added to the calculated phase value. In Figure 3, for example, it can not be known with certainty whether the correct value of the phase of the intermediate component, interpolated from the original phases P1 and P2, is Px or Pv. This results in distortion

  and a staircase effect of the impulse response.

  In the preferred embodiment of the invention, the group delay characteristic of the channel is calculated from the phases of the original components. The group delay G (f) is generally determined as follows: dP (f) G (f) 2Tdf (6) where P (f) is the phase of the spectrum of the channel. With discrete frequency points, the value of G (k) at different frequency points can be approximated P (k) -P (k-1) P (k) -P (k-1) G (k) k 2n [f (k) -f (k-1)] 2 N (7) When calculating the group delay of the channel, ambiguous points can be determined, because the behavior of the group delay of the channel way is known with a predetermined accuracy. For example, the propagation time of a telephone link as a function of frequency forms a parabolic function which increases from the middle of the frequency band towards the edges and - IL contains no point of sudden change. In addition, the path is causal, which means that it can not exist

negative propagation times.

  By using this channel information, an unambiguous group delay function G (k) can be formed, according to the invention, using equation (7) from the discrete Fourier transform. U (k) of the channel assuming that the group delay can not modify more than one predetermined maximum value between two predetermined frequency points. By adding the multiple of 2n to the values after the points of discontinuity and choosing the value that best coincides with the curve of the assumed delay function, the propagation time, as well as the phase of the original components, can to be determined with maximum probability. In Figure 10, for example, it is known that the correct group delay curve should form an extension D shown in phantom, and not a portion E of propagation time represented by a solid line, so that the value of propagation time

  interpolated between Gi and G2 must be Gx instead of Gy.

  The calculation of the group delay function preferably begins at a DC frequency or some other frequency at which the group delay is assumed to be short, then

  advancing separately to both edges of the band.

  If the DFT to be interpolated is the DFT of the equalizer, the phase P (k) of the intermediate components can then be deduced directly, or it can be interpolated at each discrete frequency point, for example according to the approximation hereinafter. P (i) = Pfo) + P (1) PO

2

  = P (k) + P (k + 1) -P (k-) P (k +) = P (k) + () k = 1, 2 ... (NK / 2M) -1

P (0) -P (NK / M)

  P (i) = P (0) P) - (N / M) Pal,) = P (k) + Pk - P (k +) k = -1, -2, ..., - (NK / 2M ) + 1 Then the real and imaginary parts of the interpolated spectrum C '(k) = 1 / U' (k) of the equalizer are calculated re [C '(k +)] = A (k +) cos [R k +) ] Im [C '(k +)] = A (k +) sin [P (k + i)] The capture coefficients of the equalizer, now 2N, are obtained in a conventional way by calculating the inverse DFT interpolated spectrum C '(k) of the equalizer. The equalizer obtained has, for example, a length

  of 2NT, as shown in Figure 9.

  In the example above, the length of the equalizer and the number of coefficients have been doubled; in general, the number of coefficients can be increased x times, x being 0. The method according to the invention requires only a small computation capacity and is therefore easy to implement, even in existing non-recursive performers, in

  modifying the coefficient calculation program.

  Although only a few preferred interpolation modalities have been described above, it is also possible to use other interpolation modalities without departing

of the scope of the invention.

Claims (9)

claims   A method for determining the coefficient of a non-recursive equalizer used in the receiver of a data transmission system by sending on the transmission path a sequence of known periodic data, by calculating the discrete Fourier transform C (k) of the equalizer using the received data sequence, either directly or via the discrete Fourier transform U (k), and calculating the equalizer coefficients by an inverse discrete Fourier transform by relative to said discrete Fourier transform C (k) of the equalizer, characterized in that the number of spectral components of the discrete Fourier transform of the equalizer or the channel is increased by interpolation of the intermediate components between the spectral components of origin before said calculation of the   inverse discrete Fourier transformation.   2. Method according to claim 1, characterized in that the number of spectral components is doubled by the interpolation of a single intermediate component between   each pair of spectral components of contiguous origin.   3. Method according to claim 1 or 2, characterized in that the real and imaginary parts of the intermediate components are interpolated from the real parts   and imaginary original components.   4. Method according to claim 1 or 2, characterized in that it comprises the calculation of the phase of the original components and the determination of the phase of the components.   intermediate according to the phase of the original components.   5. Method according to claim 4, characterized in that it comprises the calculation of the amplitude and phase of the original components, the calculation of the amplitude and the phase of the intermediate components by interpolation from the components. of origin, and the calculation of the real and imaginary parts of the intermediate   from interpolated amplitudes and phases.   6. Method according to claim 4, characterized in that it comprises the calculation of the amplitude and phase of the original components, the calculation of the amplitude of the intermediate components by interpolation from the original components, calculating the group delay values of the channel using the original phase values, calculating the phases of the intermediate components using said group delay values, and determining the parts real and imaginary intermediate components to   from the amplitudes and phases calculated for them.   7. Method according to claim 6, characterized in that the determination of the group delay of the transmission channel comprises a) calculating the phase of the transfer function of the transmission channel by an operation on tangents d arc giving phase values between -a and n; and b) forming a continuous phase function from the calculated phase values by adding an appropriate integer multiple of 2n to each of the original phase values and calculating channel delay values of the channel digital bypass transmission from the values of the continuous phase function, the appropriate multiple of 2n being chosen so that the value obtained for the group delay, as well as the group delay values calculated at the previous frequency points best coincides with the assumed function of the transmission path for the time of group spread.   Method according to claim 6 or 7, characterized in that, in the calculation of the group delay values, a value located in predetermined limit values -6 relative to a preceding frequency point, or very close to said limits, is chosen at ambiguous points such as points of discontinuity or points of sudden changes.   9. Method according to claim 7, characterized in that the appropriate multiple of 2n is chosen so that the obtained value of group delay deviates at least from the group delay value.   calculated in the previous frequency spectrum.