FI82337C - Procedure for determining basic values for a transverse coefficient of coefficients - Google Patents

Description

! 82337

Method for determining the initial values of the 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 transversal fingerprint when received by a communication system.

In synchronous communication systems, the data to be transmitted is in the form of a bit sequence. At the transmitter (e.g., the mo-10 demem), the bits are converted into signaling symbols, which are then transmitted to the communication channel at a certain signaling rate of 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 equipped with an adaptive equalizer, e.g. a digital transverse filter with variable pin coefficients and a pin spacing Τ 'equal to or smaller (fractional equalizer) than the signal symbol spacing T.

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 periodic symbol sequence, called a training sequence, in which each period contains N symbols. The channel transfer function U (k) is first estimated by calculating the DFT or disk-35 reet 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 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, i.e. the desired transfer function of the system (transfer channel and common transfer function of the equalizer). The coefficients of the coefficient 5 are obtained from C (k) by the inverse DFTz. The time range or delay of the equalizer is then equal to the length NT of the training sequence.

The main problem that the initial correction must overcome is the interference between the 10 symbols caused by the delay distortion, i.e. the group delay. Delay distortion means that the communication channel delays different frequencies by a different amount. In a telephone connection, the delay as a function of frequency typically forms a parabolic function in which the delay increases as the channel moves from the center to the edges of the frequency band. The channel that causes the delay distortion has a pulse response duration that is approximately equal to its maximum travel time difference between the different frequencies. In general, repairing such a channel requires an equalizer having a pulse response length equal to, or preferably greater than, the length of the channel impulse response.

The successful operation of the method described above requires the transmission of at least 1.5-3 periods of a periodic training sequence, as increasing the number of periods makes it easier to reduce other signal-induced signal disturbances, such as noise, frequency shift, and phase jitter. The required length of the training sequence is thus 2-3 times the maximum possible delay distortion.

In many applications, the equalizer coefficients only need to be calculated at the beginning of the transmission. Since this occurs quite rarely, the overhead caused by the training sequence is insignificant compared to the total transfer time. In other applications, especially in multi-point networks using polling, the data transmission consists of short messages. Since each message must be preceded by a training sequence and the efficiency of the system can be defined as the ratio of the time required to transmit the message to the time the channel is busy, it is clear that it is extremely important to minimize the length of the training sequence.

The above method of calculating the equalizer coefficients results in a cyclic equalizer with a period length of NT. If the period length of the training sequence is shortened to less than the length of the channel impulse response, the folding of the equalizer periods in the time plane results. This significantly degrades the performance of the equalizer. A similar phenomenon 10 may occur in the case of a difficult transmission channel with a pulse response length greater than NT.

The object of the invention is to provide a method by which the coefficients of an equalizer can be calculated using a very short periodic training sequence.

Another object of the invention is to provide a method which, despite the short training sequence, is able to calculate the equalizer coefficients so as to achieve a large reduction in the interaction of the symbols.

Yet another object of the invention is to provide a method that is computationally fast and efficient so as to be suitable for implementation with a digital signal processor.

This is achieved by the method according to the invention, after determining the channel or equalizer DFTt by calculating the interpolation of intermediate components between the original spectral components of the channel or equalizer spectrum, whereby the inverse DFT of the interpolated equalizer spectrum thus obtained gives a equalizer longer than the training sequence length.

30 In practice, this means that the length of a training sequence can be reduced to almost half ai-. . without compromising the performance of the equalizer.

On the other hand, if the length of the period of the training sequence is not shortened, a twice longer cor-35 is obtained, which can effectively correct the distortions caused by even the most difficult channel 4 82337.

The invention will now be described in more detail by means of embodiments with reference to the drawings, in which Fig. 1 shows a training sequence consisting of a pulse transmitted every 5 NT, Fig. 2 shows the real part of the channel response to the pulse train of Fig. 1 when the channel impulse response is longer than NT. Fig. 4 shows channel phase and group-10 delay responses and Figs. 5 and 6 show group delay responses of the real part of the impulse response calculated by the equalizer basic method, Fig. 7 shows the calculated equalizer amplitude spectrum when the spectral component spacing is 1 / NT, Fig. 8 shows the channel amplitude spectrum of Fig. 7 , after interpolating the intermediate components at 1 / 2NT intervals, Fig. 9 shows the real part of the cyclic impulse response of the equalizer calculated from the interpolated spectrum, and Fig. 10 is a corrected group delay response corresponding to the interpolated spectrum of Fig. 9.

In the method according to the invention, the coefficients of the transverse equalizer used in the receiver of the communication system are determined by determining the discrete Fourier transform of the equalizer impulse response 25 either directly or via the channel DFT by means of a training sequence transmitted through the channel. The equalizer coefficients are obtained by inverse DFT from the equalizer DFT. The novelty of the method according to the invention is directed to the processing of the DFT or spectrum of the equalizer or channel before calculating the coefficients.

The general construction and operation of the transfer system and transverse equalizer itself 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.

5,82337

The principles of the basic 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.

The basic method

It is assumed that the baseband equivalent impulse response of the transmission channel of the communication system must be left-10 using a transverse equalizer whose pin spacing (M / K) · T is less than or equal to the signal symbol spacing T and whose number of pin coefficients is NK / M.

Initially, before transmitting the actual data, a periodic training sequence s (t) with a period pi-15 of NT is transmitted. The transmitted signal passes through the channel and is sampled at a sampling frequency (Μ / Κ) · Τ.

The incoming signal at the receiver is continuously monitored to detect a periodic training sequence, and one period r (n) is collected from the received periodic training sequence 20, where n = 0.1, ..., NK / M.

By calculating the DFT of the received samples, i.e. the period r (n), the channel DFT, i.e. the frequency response U (k) U (k) - R (k) / S (k) (1) can be determined at 25 equally spaced frequency points 1 / NT, where R (k) is the received training period DFT and S (k) the transmitted training period DFT.

The DFT of the equalizer, i.e. the frequency response C (k), can now be obtained by calculating the ratio C (k) = B (k) / U (k) - B (k). S (k) / R (k) (2)

Finally, the pin coefficients of the equalizer are obtained by calculating the inverse DFT of 35 C (k). An equalizer is obtained whose impulse response delay, i.e. the time length, is equal to the length NT of the training sequence period.

However, the exact way in which the DFT of the channel or equalizer is calculated for interpolation according to the invention is not essential to the invention.

The basic method is illustrated below graphically by assuming, for simplicity, that the period of the training sequence s (t) consists of a pulse and that the pulses are transmitted at N symbol intervals, as shown in Fig. 1.

If the length of the channel impulse response is less than NT, the channel impulse response u (t) is obtained directly at the receiver. From the discrete Fourier transform U (k) of the impulse response u (k), a equalizer can then be calculated directly, the impulse response of which is generally completely within the delay NT, so that it is also able to correct random non-periodic data.

In the case of a very difficult channel, the channel impulse response may be longer than NT, with the responses of successive periods (in this case pulses) of the training sequence being folded at the receiver, as illustrated in Figure 2. In this case, the channel can have, for example, the phase response shown in Fig. 3 and the group delay response shown in Fig. 4. The impulse response and the group delay response of the equalizer resulting from the basic method are shown in Figures 5 and 6. The impulse response of such an equalizer cannot be shifted so that it is completely within the delay NT.

Method according to the invention

In the method according to the invention, the DFT U (k) of the 30 channels and / or the DFT C (k) of the equalizer is first determined either according to a known basic method or alternatively one of its variants.

Next, for example, one intermediate component is determined by interpolating between the original spectral components of the channel or equalizer DFT 35, wherein the spacing of the spectral components of the interpolated 7 82337 DFT (spectrum) is 1 / 2NT, as illustrated in Figures 7 and 8.

If the spectrum to be interpolated was the equalizer spectrum C (k), finally the inverse DFT of the interpolated equalizer spectrum C '(k) calculates the equalizer pin coefficients, which are now 2N pieces. The time length of the resulting equalizer is thus 2NT, i.e. twice as long as without interpolation, as is the "dynamics" of the delay, i.e. the equalizer can handle channel delays in the range 0-2NT. 10 If the spectrum to be interpolated was the channel spectrum U (k), first calculate a new equalizer spectrum C '(k) = B (k) / U' (k), from which the pin coefficients can then be calculated as described above.

The following is a discussion of different interpolation-15 techniques. The spectrum of the channel and the equalizer is complex, so the real and imaginary parts must also be determined 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, a 2NT length equalizer is obtained, but depending on the interpolation method, the result may be more or less erroneous and, in addition, it is usually impossible to deduce the correct phase of the intermediate component.

Thus, in a preferred embodiment of the invention, the amplitude A (k) and phase P (k) of the spectral components of the channel or equalizer spectrum are first determined and the phases of the intermediate components are deduced by the phase function or the amplitude and phase of the intermediate components are interpolated by the amplitude function.

30 The amplitudes of the intermediate components can be determined directly from the amplitudes of the two adjacent original components of the original equalizer or channel spectrum (cf. Fig. 7) by interpolating, for example, according to the following approximation 8 82337 A (k) + A (k + 1) A (k +%) = - (5) 2 However, the phase calculation of the intermediate components 5 is less unambiguous, since the phase values of the spectral components calculated by the arctan operation are between n and -n, including points of discontinuity. From the calculated phase values, it is possible to form a continuous phase function by adding to each phase value a suitable multiple of 2π: η if the 10 samples are so close to each other 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 15 between two adjacent frequency points may be greater than 2ti, which generally makes it impossible to determine which multiple of 2ix should be added to the calculated phase value. For example, in Figure 3, it is not possible to say with certainty whether the phase of the interpolated intermediate component Px and P2 is the correct value of Px or Py. This results in a distorted and folded equalizer impulse response.

In a preferred embodiment of the invention, the channel group delay response of the channel is calculated from the phases of the original components. The group delay G (f) is generally defined as 25 dP (f) G (f) --- (6) 2ndf where P (f) is the phase of the channel spectrum. In the case of discrete frequency-30 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) * - * -. NT (7) 2u [f (k) -f (k-1)] 2it 35

When calculating the channel group delay, ambiguities can be resolved because the channel group delay behavior 9,82337 is known with a certain accuracy. For example, the delay of a telephone connection as a function of frequency constitutes a parabolic function that increases from the center of the frequency band toward the edges and does not include abrupt points of change. In addition, channel 5 is causal, which means that negative delays are impossible.

Utilizing these known channel facts, according to the invention, formula (7) can be used to form an unambiguous group delay function G (k) from the channel discrete Fourier transform U (k), assuming that the group delay between two known frequency points cannot change more than a certain maximum value. By adding a multiple of 2ix to the values after the discontinuity and selecting the value that best follows the curve of the assumed delay function, the delay of the original components and the phase can be determined with the highest probability. For example, in Fig. 10 it is known that the correct graph of the group delay must form an extension D drawn with a broken line and not the delay portion E shown by a solid line, so the delay value interpolated between Gx and G2 must also be Gx and not Gy.

The calculation of the group delay function is preferably started at a DC frequency or other frequency at which the group delay is assumed to be small, and then proceeding separately towards each edge of the band 25.

If the DFT to be interpolated is the DFT of the equalizer, the phase P (k) of the intermediate components can now be directly deduced or can be interpolated at each discrete frequency point, for example according to the following approximation.

30 P (1) -P (0) P (%) = P (0) + - 2 35 P (k + 1) -P (k-%) P (k + ^ «P (k) + -, k = l, 2,. .., (NK / 2M) -1 3 10 82337 P (O) -P (ΝΚ / Μ) P (-½) = P (0) - - 2 5 P (kl) -P ( k +%) P (k - ^ = P (k) + ----, k — 1, -2,. .., - (NK / 2M) +1 3 10 Then calculate the C 'of the interpolated equalizer spectrum ( k) = 1 / U '(k) real and imaginary parts re [C' (k +%)] = A (k + ^ * cos [P (k +%)] 15

Im [C '(k +%)] = A (k + ^. Sin [P (k +%)]

The pin coefficients of the equalizer, which now number 2N, are obtained in a conventional manner by calculating the inverse DFT of the interpolated equalizer spectrum C '(k). The result is a equalizer with a length of 2NT, as illustrated, for example, in Fig. 14.

As an example above, the length of the equalizer and the number of coefficients were doubled, but in general the number of coefficients 25 can be increased x-fold, where x> 0.

The method according to the invention requires only a small computational power and can thus be easily implemented in already existing transverse correctors by changing the coefficient calculation program.

Although a few preferred interpolation methods have been described above, other interpolation methods may be used without departing from the scope of the invention. The description and related figures are therefore intended to illustrate the invention only. The details of the method 35 according to the invention may vary within the scope of the appended claims.

Claims (9)

11 82337 A method for determining a coefficient of a transverse equalizer to be used in a receiver of a communication system by transmitting a known periodic data sequence through a transmission channel, calculating a discrete Fourier transform C (k) of the equalizer either directly or via a channel discrete Fourier transform U (k); calculating the equalizer coefficients by inverse discrete Fourier transform from said equalizer discrete Fourier transform C (k), characterized in that the number of spectral components of the equalizer or channel discrete Fourier transform is increased by interpolating the intermediate spectral components between said original inverse components before said inverse Calculation of the Fourier transform. Method according to Claim 1, characterized in that the number of spectral components is doubled by interpolating one intermediate component in each case between two adjacent original spectral components. Method according to Claim 1 or 2, characterized in that the real and imaginary parts of the intermediate components are interpolated from the real and imaginary parts of the original components. A method according to claim 1 or 2, characterized in that it comprises calculating the phase of the original components and solving the phase of the intermediate components on the basis of step 30 of the original components. A method according to claim 4, characterized in that the method comprises calculating the amplitude and phase of the original components, calculating the amplitude and phase of the intermediate components by interpolation, and calculating the real and imaginary portions of the intermediate components from the interpolated amplitudes and phases. A method according to claim 4, characterized in that the method comprises calculating the amplitude and phase of the original 5 components, calculating the amplitude of the intermediate components by interpolating from the originals, calculating channel group delay values using the original phase values, calculating intermediate component phases using said group delay values and intermediate components. and determining the imaginary parts from the amplitudes and phases calculated for them. A method according to claim 6, characterized in that determining the group delay of the transmission channel comprises the steps of: a) calculating the phase of the transmission channel transmission function by an arctan operation giving phase values between -n and n, b) generating a continuous phase function from the calculated phase values by adding an appropriate 2it an integer multiple of 20 for each initial phase value and numerical derivation of the transmission channel group delay values from the values of the continuous phase function, wherein the correct multiple of 2n is selected to give the group delay value that best follows the group delay value calculated at the previous frequency points. Method according to Claim 6 or 7, characterized in that when calculating the group delay values at ambiguous points, such as discontinuity points or sudden change points, the value which is within or closest to certain limit values with respect to the previous frequency point is resolved. Method according to Claim 7, characterized in that the correct multiple of 2n is chosen to be that which results in a group delay value which deviates least from the group delay value calculated in the previous frequency spectrum. i3 82337