FI82336C - Method for determining coefficients in a transverse equator - Google Patents

Description

1 82336

Method for determining transverse equalizer coefficients

The invention relates to a method according to the preamble of claim 1 for determining the initial values of the coefficients of a transverse equalizer in a receiver of a communication system.

In synchronous communication systems, the data to be transmitted is in the form of a bit sequence. In a transmitter (e.g. 10 modems), the bits are converted into signaling symbols, which are then sent to a communication channel at a certain signaling rate a 1 / T, where T is the symbol interval. The symbols received at the receiver (e.g., modem) are detected and converted back into a data bit sequence. The signal transmitted in the communication channel-15 deteriorates due to various sources of interference. These include e.g. linear distortion (amplitude and delay distortion) and noise.

To limit this problem, the system may be provided with an adaptive equalizer, e.g. a transverse filter with variable pin coefficients and a pin spacing T equal to or less (fractional equalizer) than the signal symbol spacing Τ '.

The article "Rapid Training of a VoiceBand Data-Modem Receiver Employing an Equalizer with Fractional-T 25 Spaced Coefficients", IEEE Transactions on Communications, Vol. COM-35, pp. 869-876, October 1987, discloses one method of to calculate the initial values of the transverse equalizer coefficients.

In this known method, the data transmitted to the transmission channel is preceded by a predetermined cyclic symbol sequence, called a training sequence. The channel transfer function H (k) is first estimated by calculating the DFT or discrete Fourier transform R (k) of one or more periods of the received training signal and dividing it by the DFT S (k) of the transmitted training sequence. The equalizer transfer function C (k) is obtained from the ratio C (k) * A (k) / H (k), where A (k) is the reference spectrum, i.e. the desired corrected transfer function (common transfer function of the transfer channel and the equalizer). The coefficients of the equalizer are obtained from C (k) by the inverse DFT.

5 For the fractional equalizer (T <T *), however, there are an infinite number of solutions, so one must choose the appropriate one using one of the criteria.

In the above-mentioned article, the appropriate equalizer spectrum is selected so that the gain of the white noise at the input of the equalizer is minimized (cf. Equation 16 of the article). However, in the case of a high signal-to-noise ratio and a short equalizer, this is not a good solution, because then most of the residual error of the equalizer is caused by the folding of the impulse response of the equalizer. 15 In addition, in many applications, such as multipoint networks using a poll, it is advantageous to minimize the length of the training sequence. On the other hand, the equalizer's ability to correct transmission channel distortion deteriorates as the training sequence shortens.

The object of the invention is to provide a method for determining the coefficient of a transverse equalizer, in which the criterion used takes into account the folding of the impulse response of the equalizer and which allows the equalizer to be initialized using a shorter training period than before.

This is achieved by a method according to the invention, which is characterized by the features set out in claim 1.

The invention is based on the fact that the rapidly decaying equalizer impulse response results in the folding of the equalizer impulse response 30 being minimized. Thus, it could also be said that the amount of folding of the impulse response of the equalizer is minimized using a reference spectrum A (k) optimized for the respective estimated transmission channel.

According to one embodiment of the invention, the reference spectrum is optimized and the appropriate equalizer spectrum is selected by estimating the transmission channel group delay and selecting the reference spectrum or equalizer spectrum so that the resulting equalizer uses the frequencies with the least estimated group delay distortion. As a result, the equalizer has a faster attenuating impulse response than would be obtained using a fixed reference spectrum. The folding problem is thus significantly alleviated, making it possible to use a shorter training period. This, in turn, results in an increase in the efficiency of the transmission system and a shorter start-up time of the 10 equalizers.

The invention will now be explained in more detail by means of examples with reference to the accompanying figure, which shows a typical telephone channel amplitude spectrum and a group delay function.

The general construction and operation of the transfer system and transverse equalizer are known to those skilled in the art and are referred to, for example, in the aforementioned article and U.S. Patent No. 4,152,649. The invention is applicable to the equalizers disclosed therein or other suitable ones.

The basic principles of the method used to determine the transverse equalizer coefficients are also described in the above article. However, in order to facilitate an understanding of the invention, the basic principles of the method will be described below before describing the actual inventive part.

It is assumed that the baseband equivalent impulse response of the transmission channel of the communication system must be corrected using a transverse equalizer whose pin spacing 30 is KT / L S T, where T is the symbol range of the signal and K and L are small integers. Before transmitting the data, the transmitter transmits a training signal s (t) = Σ s (i) δ (t-iT) (1) 35 i where the sequence s (i) is periodic with the period M = KN / L and 4 82336 N is the number of pin coefficients of the equalizer. The transmitted signal passes through the channel and is sampled at the receiver at the sampling frequency L / T. The received signal samples are 5 x (n) = Σ s (i) y (nT / Lr-iT) e32BAfnT / L + w (n) (2) i where x is the sampling phase, w (n) represents the summed 10 complex noise and is unknown constant frequency offset. Other channel non-idealities (phase jitter, amplitude jitter, nonlinearities, etc.) are assumed to be insignificant or included in the noise term w (n).

At the receiver, the incoming signal is continuously monitored to detect a cyclic training signal, and the carrier frequency offset estimate is calculated as in the above article. As soon as the presence of a cyclic training signal is detected, one period r (n) of the received signal is separated, where n = 0, 1, ...., LM-1, and is used to calculate the pin coefficients of the equalizer. The sequence r (n) is obtained by copying the LM sample from the equalizer delay line and removing the phase rotation induced by the carrier frequency shift. The samples received may also be averaged over several periods to reduce the effect of noise and other channel non-idealities at the expense of increased teaching time.

To completely correct the received cyclic sequence r (n), the pin coefficients c (i) of the equalizer are chosen to satisfy the equation 30 N = 1 Σ c (i) r [(Ln-Ki) „„ d LM] = s (n), n = 0.1 ,. . . , M-1 (3) i = 0 35 where modLM means the modulo LM operation. At the frequency level, this can be expressed as ti 5 82336 L-l Σ C [(k + iM) eodl |] R (k + iM) = LS (k), k = 0.1,. . . , M-1 (4) i-0 5 where C (k), R (k) and S (k) are discrete Fourier transforms of the impulse responses of the equalizer, the received sequence and the training sequence, respectively. Equation (4) can also be expressed by reference spectrum A (k) 10 C (k „odN) R (k) = A (k) S (kBodM), k-0,1 ..... LM-1 (5) This equation is equivalent to Equation (4) if the reference spectrum A (k) satisfies the Nyqvist criterion.

15 L-l Σ A (k + Mi) - 1, k = 0.1, ..., M-1 (6) i = 0

The reference spectrum A (k) refers to the desired spectrum of the 20 corrected channels before sampling at the symbol frequency.

Calculating the equalizer spectrum of the inter-T equalizer is. simple, because then there is at most one solution to Equation (4) or (5). The spectrum of the equalizer is obtained from 25 C (k) = S (k) / R (k), k-0,1 ..... N-1 (7) if R (k) differs from zero by all values of k.

For the fractional equalizer, calculating the spectrum is more difficult -30 because Equation (4) gives only M equations and C (k) the number of variables N> M. It can be seen from Equation (5) that an infinite number of solutions can be found for the fractional equalizer unless there are L spectral zeros in the spectrum of the received signal at 1 / T Hz intervals. From the infinite number of possible solutions resulting from Equation (4), one must choose the appropriate one according to some criteria.

6 82336

Ideally, a reference spectrum A (k) should be found that gives the optimal N-length equalizer for the channel impulse response. This is usually not possible because it requires information about the channel transfer function at kai-5 wedge frequencies and the reference spectrum of the optimal N-length equalizer does not necessarily meet the Nyqvist criterion. Therefore, some less optimal solution must be used.

Depending on the reference spectrum, an equalizer is obtained which is a more or less folded version of the "imagined" infinitely long equalizer. However, an infinitely long equalizer is not calculated at any stage. In theory, an infinitely long equalizer could be computed by increasing the period of the training sequence to infinity.

15 In the method of the above article, the reference spectrum is selected so that the noise gain is minimized. However, this is not a good choice in the case of a high signal-to-noise ratio and / or a short equalizer.

According to the invention, the wetting of the impulse response of the equalizer is minimized by the criterion Nl J = Σ f (k) | C (k) | 2 (8) k = 0 25 where f (k) is a weight function that emphasizes more frequencies that are difficult for folding , and fewer frequencies, which are easy in this regard.

The weight function f (k) is chosen so that the resulting infinitely long equalizer impulse response is attenuated as quickly as possible. That is, the variation in the group delay of the equalizer spectrum is minimized at frequencies at which the channel amplitude function is significant. At the same time, sharp changes in the amplitude of the equalizer amp-35 spectrum are avoided, as they also result in a slowly attenuated equalizer impulse response.

Il 7 82336

When the reference spectrum is assumed to have a linear phase, the equalizer group delay function necessarily becomes a mirror image of the channel group delay. Therefore, in a preferred embodiment 5 of the method according to the invention, the amplitude of the equalizer is minimized at those frequencies at which the channel delay of the channel deviates much from the average and at the same time the amplitude spectrum of the equalizer is kept as uniform as possible.

This is achieved when the weight function F (k) is chosen to be, for example, F (k) = | x (k) -xava | n + Fo (9) where x (k) is the estimated group delay of the channel at frequency k xava is the average group delay and n ä 1. The spectral uniformity of the equalizer 15 is guaranteed by adding a positive constant Fo to the squared group delay difference. As a result of this weighting function, the equalizer mainly uses frequencies at which the group delay is close to the mean, and amplifies fewer frequencies at which the group delay differs much from the mean. 20 The weight function F (k) can also be another function of the group delay difference.

For example, in the figure showing the amplitude spectrum D and the group delay E of a typical badly distorted telephone channel, the frequencies A and B overlap when the equalizer output signal is sampled at 1 / T intervals. In this case, it is advisable to make the spectrum of the equalizer such that it mainly uses frequency B, because at frequency A the group delay of the channel deviates much more from the average.

For the above weight function F (k), the channel group delay function must be determined. When the channel transfer function H (f) is written in the complex exponential form H (f) = | H (f) | eJ '(f) 35 where 0 (f) is a continuous phase response, the channel group delay function β 82336 is th0 (f ) x (f) = - 2udf 5

In the method according to the invention, the group delay of a channel is estimated by calculating the phase of the channel transfer function H (k) = R (k) / S (k) and calculating the group delay function from it by means of numerical derivation.

10 When the phase function of H (k) is calculated using a conventional arctan operation, all the values obtained are between -π and π. From these phase baseline samples, continuous phase function samples are formed by adding an appropriate multiple of 2it to the baseline samples. The correct multiple of 2n 15 can be determined if the samples are so close together that discontinuities can be detected.

In the case of a very short equalizer and a severely distorted channel, the channel group delay variation of the channel may be greater than the time length of the equalizer. That is, the phase difference between two adjacent frequencies of the transfer function H (k) of the channel 20 van may be greater than n, making it impossible to determine which multiple of 2n should be added to the base value of the phase.

In the method according to the invention this is solved by assuming that there can be no sudden changes in the channel group delay between two adjacent frequency points, whereby 2τι: η the correct multiple for a phase function it to the common known group delay characteristics of the transmission channel. For example, in the case of a speech link channel, it is known that the group delay function should be a generally parabolic function (see figure). The calculation of the group delay function is preferably started at a DC frequency or other frequency at which the group delay 9 82336 is assumed to be small, and then proceeding separately towards each edge of the band.

The above examples are intended to illustrate the invention only. The details of the method according to the invention may vary within the scope of the appended claims.

Claims (8)

A method for determining initial values for the coefficients of a fractional-type transversal equalizer in a data transmission system, comprising a transmission channel, the method including the following step a) transmitting a predetermined periodic data sequence, whose discrete Fourier transform is S (k), through the transmission channel, b) calculating the discrete Fourier transform R (k) for a period in the periodic sequence passed through the transmission channel, c) determining the relationship C (k) = A (k) S (k) / R (k), where A (k) is a reference spectrum, and d) determining the values of the coefficients in the equator by calculating the inverse C (k) inverse discrete Fourier transform, characterized in that in point (c), such a reference spectrum is chosen 20 A (k), which gives the equalizer a decreasing pulse response as quickly as possible. 2. A method according to claim 1, characterized in that the reference spectrum A (k) is chosen by means of the group run time estimated for the transmission channel, such that the amplifier amplitude is reduced at the frequencies at which the group run time for the equalizer is cumbersome. in the amplitude of the equator's spectrum there are no rapid changes. Method according to Claim 1 or 2, characterized in that the reference spectrum A (k) is chosen so that the equalizer uses more the frequencies at which the group duration estimated for the transmission channel is close to the average group duration time and less amplifies the frequencies. at which the group maturity differs significantly from the mean. ti 13 82336 4. A method according to claim 2 or 3, characterized in that the determination of the group duration of the transmission channel comprises calculation of the phase in the transmission function estimated for the transmission channel and calculation of the group duration from the phase by means of numerical derivation. A method according to claim 4, characterized in that the determination of the transmission time of the transmission channel comprises the following steps: a) calculating the phase of the transfer function of the transmission channel with an arctane operation which gives the phase values between -π and n, b) forming of a continuous phase function from the calculated phase values by adding an appropriate 2n integer multiple to each original phase value and calculating the group runtime values of the transmission channel using numerical derivation from the values of the continuous phase function: the one that results in a group maturity value is selected, which, with the 20 preceding frequency points, calculated the group maturity values best following the group maturity function adopted for the transmission channel. 6. A method according to claim 5, characterized in that as the correct 2n's multiple 25, it is selected which results in a group maturity value, which at least deviates from the group maturity value calculated from the 1 preceding frequency point. 7. A method according to claim 5 or 6, characterized in that the calculation of the group run time starts from a frequency at which the group run time of the transmission channel is assumed to be the least. Method according to Claim 7, characterized in that as the correct 2ti's multiple, the one that results in a group maturity value is chosen, which is the larger value that at least deviates from the group maturity value calculated in the previous release point.