DE2416058B2 - Method and circuit arrangements for equalizing a quadrature-modulated data signal - Google Patents

Description

(49;

öyk ■. the

(50;

the ίο

15th

The invention relates to a method for equalizing a quadrature-modulated data signal which is transmitted via a linear Distortion causing transmission medium is received, according to the generic terms of Claims I and 11 as well as soundings for carrying out these processes.

When data signal elements are transmitted over a transmission medium such as e.g. B. transmitted a telephone line , each individual data element generates time components without any suppression or compensation one or more subsequent data elements can interfere if their spacing is a critical value falls below. Incorrect evaluations of the data elements on the receiving side are then the result. Such disturbances, which are also referred to as inter-symbol overlays, are in the properties of the transmission medium itself. They are increased by the added noise that comes from external, often difficult to control sources of noise.

In view of the existing efforts to further increase the data transmission rate, the problem of linear distortions through the transmission medium is becoming more and more important. In order to solve the emerging difficulties, it has long been proposed to provide a correction device for the received signals before the data evaluation at the receiving end. Such a correction device is intended to compensate for the linear distortions contributed by the transmission medium. Devices of this type have entered the literature under the name of equalizers.

Right from the start, equalizers were designed as networks whose amplitude-frequency response and phase-frequency response were able to compensate for the corresponding frequency responses of the transmission medium , whereby when combining such networks with the given transmission media, relatively constant amplitude-frequency responses and relatively linear phase responses are achieved. Let achieve frequency responses . Such arrangements are in use for relatively low data transmission rates up to 2400 baud. However, they have proven to be insufficient at higher transmission speeds.

Significant improvements have been achieved through the use of transversal or recursive filtering techniques. Such an equalizer was designed for the low band signal, i.e. for use at a point in the transmission system at which the carrier-modulated signal transmitted is already demodulated again Lucky in "The Bell System Technical Journal" of April 1965, pages 547 to 588, and of February 1966, pages 255 to 286, with the titles "Automatic Equalization for Digital Communication" and "Techniques for Adaptive Equalization of Digital Communication Systems" pointed out. For an application with non-linear modulation (phase modulation) the CCITT article No. 171 from December 1971 of the study group Sp.A. to be named. In the latter case, the demodulation is carried out with the aid of two carriers arranged in quadrature; the equalization is carried out separately for the two channel signals formed in this way, it being possible for these channel signals to act on one another.

The main disadvantage of these techniques is that the demodulation on the receiving side of the carrier is precise must be recovered. On the other hand, such demodulation makes the use of digital methods impossible on the receiving side.

As a result, numerous proposals have been made to use the receiving-side equalizer directly in the to operate the received frequency band. For this purpose, the work of Lucky and Rudin with the title “An Automatic Equalizer for General Purpose Communication Channels” and by Rudin with the title “A Continously Adaptive Equalizer for General Purpose Communication Channels "in" The Bell System Technical Journal "of November 1967, pages 2179 to 2208, and of July / August 1969, pages 1865 to 1884. pointed out. The technique described there consists essentially in the fact that the data signals are constantly on Test signal is superimposed, resulting in a duplicate of this test signal in the receiver: that in turn is compared with the received test signal in order to provide a measure of error for setting the equalizer define. Such a technique, which is also relatively expensive because of the required interpretation of the Circuit has the disadvantage that it increases the noise level. The test signal works for the actual data signal recoverable as an interfering signal and vice versa.

In the German patent specification 22 64 124 entitled "Entzerrer für den Datenempfang" it is proposed to let the equalizer work in the transmission channel, but to transpose the equalized signal into a different frequency range in which an error signal can then easily be defined. Such a technology with frequency conversion is somewhat more complex, but it is advantageous if digital technology is to be used.

For the special case of phase modulation, in the German Offenlegungsschrift 23 17 597 describes a method and a circuit arrangement for transmission systems operating with phase modulation, a transversal equalizer is used in the transmission channel.

However, all these equalization techniques in the transmission channel have the same disadvantage. The taps on the delay lines used in transversal equalizers must be arranged at time intervals which are smaller than the time interval between two successive data elements in order to meet the known Nyquist criterion. This leads to various conclusions: Firstly, the number of taps required overall for the given equalization quality increases. Second, brings the correlation between the signals to the

individual taps cause certain most unstable Equalizer with it if the equalizer is to work with setting options. The instabilities result relatively long setting times of up to a few seconds and also a certain drift of the Equalizer coefficients after the equalization optimum is already easy.

French patent 20 94 CMl describes another technique for phase modulation: two transversal filters are used which use the same delay line but two groups of attenuators. The signal from the output of the transmission line is fed to the delay line after translation into a higher frequency range. The first group of attenuators works directly with the removed at taps of the delay line signals, the second group of attenuators I whereas with these signals to a 90 ° phase rotation in their Fig. Is a block diagram of a trägermodulierenden Datenübertragup "ssystems,

F i g. 2 the block diagram of a receiver for after Fig. I transmitted signals without significant line distortions.

J shows the block diagram of such a receiver with an equalizer to compensate for linear distortions contributed by the transmission channel,

ίο Fig.4 the circuit diagram of a first embodiment the filter part of the equalizer,

5 shows the circuit diagram of a broad exemplary embodiment the filter part of the equalizer and

F i g. 6 circuits for setting the filter part of the r> Equalizer.

For a second feasible approach, FIG. 7 again the filter part of the equalizer, F i g. 8 the details of this filter part and FIG. 9 the circuits for adjusting the filter part.

■ ι ι uii-sti / i if iutiuiif ^ "

L / V.H Ul-IIIl. IV.

is working. The output signal of the equalizer then results from the summation of the output signals of the both groups of attenuators. The equalized signal is given a reference amplitude Times compared in order to gain an error signal. The setting of the first attenuator group takes place due to a correlation between the error signal and the directly to the Signals obtained tapped. A correlation is used for setting the second group of attenuators between the error signal and the signals rotated by 90 °.

This technique, in which delay line taps can be used, the spacing of which corresponds to the Interval between two successive data elements on the transmission line however, other disadvantages. The use of a Hilber transformer on each tap of the delay line difficult to perform when digital techniques are to be used. The complexity the necessary structure excludes an economic usability of this route. Further makes the frequency tramming behind the equalizer a fully digital circuit design is impossible. The transposed analog signal should be sampled at a very high frequency and the large number of taps to be attached to the delay line make one such Execution unthinkable.

The object of the present invention, the bypass all the aforementioned drawbacks and to create a beneficial hold equalization method quadrature modulated data signals using digital techniques and without performing frequency modulation or transposition above; the equalization carried out should take place in the transmission frequency band and use a delay line whose tap spacing corresponds to the time interval between the individual information elements on the transmission medium; a high setting speed and a stable mode of operation should be achievable.

The solution to this problem is characterized in claims 1 and 11. Advantageous configurations and circuits for carrying out this Methods are described in the subclaims.

Embodiments of the invention are shown in the drawings and are described below explained in more detail It shows

Equalizer for carrier-modulating data transmission, a signal / ft ) being generated from a signal φ) received via a line using a Hilbert transformation from φ). The signals φ) and φ) are fed to two filters with the transmission paths h \ (t) and h ₂ (t) . This results in the two components y (t) and y (t) of the equalized signal:

The character 0 always stands for a convolution.

The equalization is made adjustable by generating two error signals 6y and 6y from these components y (t) and fft} With these signals, the filter processes Ai ^ and hi (t) are set so that the error occurring at the equalizer output reaches a minimum.

The signals y (t) and y (t) are sampled at characteristic times and the following polar coordinates are determined from them:

'.' » - iv» + ) "k
'Λ ·. = arc tu -

From this and from previously specified values ρί and ^ the error polar coordinates result:

** Q \ ⁼ 'Jk - ¹ Jk ΛΦί = <1> k - $

The Cartesian coordinates of the error signal t5y * and öyt are determined from these error polar coordinates, with the aid of which the filter curves h \ (t) and h ^ t) are set.

In the case of the other possible solution, the received signal φ) is from the transmission medium

two filters with the filter passages h; (t) and H ₂ (I) are supplied in parallel. -This results in / -two filtered signals, which are determined by the following
presses werc * e <i can:

g g

Convocations excluded

to avoid is known
Equation must be fulfilled:

that the following

constant

In it is:

Θ is again the convolution symbol.

These two signals are each fed to a phase shifter, which provides signals p \ (i) and p \ (t) in quadrature from the filtered signals / white and also in quadrature pi (t) and pi (t) . The signals p \ (l% ßxft), p2 (t) and p> (t) are algebraically combined to generate the two components y (i) and y (t) of the equalized signal:

Si Π =

V (M = p ₂ (/)

The equalization rate is adjustable again due to the generation of two field signals <\\ and by from y (t) and y (tX, with which the filter rates h, (:) and hi (t) are again set so (Ι; ^{| Γ (} Meh result in a minimum error at the equalizer output ;.

When considering the two solution paths so far and also in the following for equivalent terms the same signs have been set. This to the conceptual correspondence of the two related Clearly highlight possible solutions.

Fi g. As already mentioned, FIG. 1 shows the block diagram of a conventional data transmission system. In multiple phase-modulating transmission systems, the data to be transmitted are encoded in the encoder 1 in the form of sequences of discrete amplitude and phase levels ¹ "" and $ " . In this description, the symbol means - a discrete signal value. Sequences of such discrete signal values become modulation of a carrier signal S (i) with the carrier frequency / ö is used in a modulator 2 in order to provide a signal s (t) of the following form to be transmitted:

sit) = X » _m SU - nT) ■ cos (2.-7./n '

'K

ίο

T stands for the time interval between two successive effects on the carrier signal, that is to say for the interval between two successive data elements on the line. Tis the reciprocal of the data transfer rate on the line and is usually expressed in baud. To improve understanding it should be pointed out that the transfer rate is defined as the number of actions on the carrier per second. With a phase-modulating transmission system, the following speed of! 200 baud is given if 1200 phase shifts of the carrier are carried out per second.

To avoid unwanted superimpositions between the individual data elements on the transmission line

S (M,

"df

S (O is the spectrum of the signal S (l), ie the Fourier transform of S (t) m \ lj = / -Π.

In the following it is assumed that the signal S (i) c \ .t occupies a limited frequency band, i.e.:

Sif) = 0 with \ f> J _n

The signal received at the end of the transmission line 3 is referred to as r (i). If the transmission line were ideal, then φ} = s (t). In the receiver 4, the transmitted data could be recovered by measuring the instantaneous amplitudes and phases of the signal φ) at times kT , where k is an integer.

F i g. Fig. 2 illustrates such a receiver using digital circuitry. The signal φ) from the transmission line 3 is transmitted through the lower branch in Fig. 2 is fed to a block 6, a phase shifter which rotates all frequency components contained in the frequency spectrum of the signal φ) by 90 °. The block 6 carries out the required Hilbert transformation and is thus referred to as a Hilbert filter. As is generally known, the transformation H (t) is carried out in such a filter with a phase shift of -; r / 2sign / '.

The output signal φ) of the block 6 is thus the Hilbert transformation of the signal φ). It should be mentioned at this point that the same thing was achieved instead of a 90 'phase shifter in the lower branch. if a + 45 ° phase shifter is provided in the upper branch and a -45 ° phase shifter in the lower branch. This applies to the entire following part of the description without repeatedly referring to it in detail.

Under the assumption given by equation (3), the signal φ) can be written:

The signals rft) and φ), which may be referred to as the fundamental phase signal and the quadrature signal, are sampled every T seconds, as shown in FIG. 2 is indicated in order to obtain the sample values x> and Xk .

Under the assumption made in accordance with equation (2), the signals at the output of the sampling devices be written as:

x _k = r {kT) = O ₁ cos (2.τ / _ο ί.Τ + $ _k )

x _k = r (kT) = o _k sin

$ _k )

These signals xt and x * are fed to a coordinate converter 7 which converts Cartesian coordinates into polar coordinates. The following is generated:

0 _k = arc tg -

^x k

This means:

Assuming that neither noise nor distortion were present, S '(t) = S (t), B (t) = 0 and \ b (t) \ = 0. The ideal case would be:

This means:

= e * cos (2ji / _n fcT +

Qk ⁼ Qk

2nf ₃ kT

(4)

The values Qt and Φ * obtained are used in the decoder 5 according to FIG. 1 is decoded in order to recover the transmitted data, with the elimination of the term 2nfokT. Such a separation does not cause any difficulties, since k is decisive, which on the other hand is the ordinal number of the corresponding sample in the sampling sequence and also corresponds to the ordinal number of the data element transmitted via the line be effected.

So far, the overall arrangement has been considered for the case of an ideal transmission line for which r (t) = s (t) applies. In practice, however, this can never be achieved. Thus, the most frequently occurring distortion properties of the transmission lines must now be considered, in particular those of telephone lines. In order to make the considerations as understandable as possible, a complex analytical expression should be used for the signals; in the following, the symbol 11 should each stand for a complex variable.

The complex signal received on the line can be written:

(6)

This equation (6) is another possibility, to express the statement of equation (4).

In order to keep the linear distortion influences as low as possible and to approximate the ideal condition \ xt | = | a * | To achieve this, an equalizer, as shown by block 8 in FIG. 3, must be provided. The task of this equalizer is to form the following complex signal based on the input signal \ xt \

IyJ = λ

Here, \ yt \ should be as good as possible with | a * | to match. yt-Xk and pk- & t should be as small as possible. 2, the phase and amplitude information are to be subjected to a coordinate conversion, whereby

Qk = M + H and

Φ »= arc tg - result.

Ir (Ol =

Here \ b (t) \ stands for the noise.

and

_ For this purpose, the invention makes use of the complex equivalent of an equalization filter ». Such a complex filter uses (2 / V + 1) complex coefficients. which may be referred to as | o | - Ci + jdi.

The transmission path of a real transversal filter may be designated with the coefficients ei may

a "\ - \ φ (ί- ~ nT) \ + 16 (0 | as A _t fr>, the transmission path of another real _{/ f} . filter with dir as a coefficient may be called

als Azftjl The signals φ) and! ft) are fed to the complex equalizer 8, which forms the complex equalized signal:

Q _n sin (2nf _o t + $ J

with S '(t) £ S (t) and 6 »(ί) φ 0

The two aforementioned conditions leave the linear amplitude and phase distortion of the transmission line; recognize. However, it should be pointed out that there are also other distortions which, however, should not be taken into account for reasons of clarity of the description.

When the signals r (t) and r (t) are sampled according to FIG. 2 obtained signals can be written in complex form as follows:

kl = **

In it are:
yd) -

(7)

® stands as a symbol for knowledge.

Sampling value sequences with yt and ft are then obtained by sampling the signals jf /) and # y.

Exemplary embodiments for the first approach

In the arrangements shown in FIGS. 4 to 6, the real filters are transversal filters with (2 / * / + 1) taps on two delay lines with the time intervals T.

In this case, equations (7) can be used at

Introduction of the coefficients Q and d / are written as;

Adders 12 and 15 are added in an adder 17 and the following sampling sequence is obtained:

y (t) = Σ t ^c '■ Ki - IT) - d, r (l - / T)]

2N

(8th)

c, -Ht-IT) + drrlt-

IO

4 shows a first embodiment of an equalizer according to the invention according to the first approach. The analog signal φ) from the transmission line is sampled at a frequency -

Atf where M is chosen so that -ψ is higher than that Nyquist frequency, e.g. B. twice as high as the highest Frequency of the spectrum of the transmitted signal. The samples obtained in this way are used a second time

sampled with a frequency ψ and thereby a sampling sequence x * ared; parallel to this, the first scanning sequence with M is fed to a Hilbert filter 9 ^M

This is implemented digitally in a conventional manner as a transversal filter. It works as before called a 90 ° phase shift of all frequencies of the spectrum of the input signal. The initial

signal of the filter 9 is also with- =; scanned and

a scanning sequence itt is generated in the process

Dip samples xt are fed to a digital delay line 10 ζ Β. a shift register with (2 / V + 1) taps with the time interval T. Two groups of multipliers Mi to Mis and Mi to M \ n are connected to the individual taps. The removable at the individual taps of signals by the coefficients q> to cw or as up dtu multiplies the outputs of the multipliers M an adder 11 is supplied with the outputs of multipliers M ¹ whereas a second adder 12 to be supplied.

In the same way, the sample values x »are fed to a delay line 13 which is to consist of a similar shift register with taps.

Two groups of multipliers Mi to Mi / twnd Mt to Minund are connected to the individual taps. The thus coefficients 4> to dm are input to each multiplier M * and corresponding to the coefficients <b to cui in the multipliers ΛΛ the AusgaJijrtiignale multiplier rW are input to an adder 14 and the outputs of the ss multiplier M * to an adder, 13th

The outputs of the adders 11 and 14 become subtracted in an adder 16 and thereby obtained at the output of the adder 16 the following sequence of operations;

2.V

y _k = j) (Cj'Xt-j + rfj'Xt-j) 1 = 0

The samples y * and j> i are the two components of the complex equalized signal | y * J. According to FIG. 3 these samples are converted and while the polar coordinates ρ * and Φ * are generated by the Contain phase and amplitude information from which, by means of decoding, the transmitted Data are recoverable.

According to FIG. 5, a second embodiment of the first approach, the received

Signal φ) also sampled at the frequency ^ Die

Samples x * obtained in this way are transmitted to a digital delay line 18, e.g. B. again fed to a shift register. In parallel, the sampled values Xk are fed to a feeder 19, which uses them to generate the sampled values jf *, which are input to a digital delay line 20. It should be noted that in this exemplary embodiment M samples Xk and it occur per period.

The delay lines 18 and 20 have (2 / V + 1) taps at a time interval T. Multipliers M ₀ to Mw receive the tapped signals from the individual taps of the delay line 18 and multiply them by the coefficients ca to Cw. The output signals of the multipliers Me to Min are added in an adder 21. The multipliers M ₀ 'to MSn receive the tapped signals from the delay line 20 and multiply these signals by the coefficients da to <Am. The output signals of the multipliers M { to Mis are added in an adder 22.

Finally, the output signals of the two adders 21 and 22 are added by means of an adder 23 The output signal of the adder 21 is subtracted by the output signal of the adder 22 reduced

The output of the adder 23 gives the sample value sequence / tab:

60

Xk-i and jf * _, are the signals tapped on the taps / delay lines 10 and 13.

Furthermore, the output signals of the

1-0

jct-i and Stk-t correspond to the signals taken from the / taps of the delay lines 18 and 20.

The sequence of the sampling values pt is generated in that the sampling values yt are fed to a second Hilbert filter 24, which outputs the following values:

Since ΓA / samples »and ^ * are present per period, with a subsequent offload operation the

Corresponding Weffepäfe >> iiftd % for the recovery of the phase and amplitude information

sampled at a frequency ~.

Compared to the example according to FIG. 4, this / broad embodiment according to FIG. 5 only requires half as much Multiplier. Furthermore, at the output of the

Equalizer output samples y _k and y _t per period TM; this can be important for certain cases which are not part of the subject matter of the invention; z. B, to regain synchronization.

The way in which the equalizers according to FIGS. 4 and 5 can be made adjustable, ie how the coefficients \ ci \ = ci + jd / can be found in such a way that the function of the equalizer is constantly optimal, will now be described will.

In a known way, the equalization is considered to be optimal viewed when the root mean square

Replacing the expressions on the left with the following values results in:

⁵ J-

öc, dV

10 From this the following conditions for the Derive setting coefficients:

i IkI-UJP

dv ^tm)

15th

a minimum reached The horizontal line should indicate that an average over time is being considered; mark the two vertical lines, that the modulus of the complex term between the two is meant

Introducing the error signals Oy * and 6y _k , which are given by

25th

30th

V = Jr

The minimum of the function Vwi-tf is reached when the (4 / V + 2) components of the gradient V become 0. These are:

de,

de,

dV Ö (iy _k ) d {

wr ^dy * '~ w * ^yh ~

It should be noted that

d {y _k )

de,

identical to Xt-i being the signal at the / -th tap of the delay line 10 of Figure 4 or 18 g in accordance with Fi. 5 corresponds to this sample value, the only term of dyt-yk- * k dependent on C / being the term a · Xk-i , which results from the multiplication at the / -th tap. This result should not be derived in detail; it is evident from the generation of # in accordance with FIG. 4 or 5. Analogous to this are identical:

50

55

60

Ί5

U ₁

Here the exponents (m) and (m + \) stand for successive steps and μ for a scale parameter.

F i g. FIG. 6 shows an exemplary embodiment for the circuits for determining the setting coefficients ei and d / in accordance with the above analysis.

The samples yu and pt correspond to FIG. 4 and 5 are fed to a Kootfiinatenkonverter 25 for generating ρ * and Φ *, the phase and amplitude information of the received signal at the points in time. The information Qt is compared in a comparator 26 with discrete amplitude levels 3Ό. These reference amplitudes can either be determined in advance in a known manner or obtained during a test period before the actual data transmission or can be derived from the received data itself. The comparator 26 outputs the level JJt which, among a large number of levels ^ _n, is that which comes from the received amplitude information ρ * at the next & wn. It also outputs relative amplitude error information:

45

(H *> ■ - m.t.x,

nit ög _k = g _k -g _k

In a similar way, the phase information Φι is used in the comparator 27 with different discrete phase values $ _n which are used for the transmission? ^r the, compared. These discrete phase values can also either be specified in advance or derived from received data. The comparator 27 outputs a phase value $ _t which, under “Vvalues, is the one that comes closest to the received phase information Φ *. The comparator 27 also outputs phase error information tök * = $ k— Φ *”.

The values JJi and Φ * from the comparators 26 and 27 are then decoded for the purpose of outputting the data The circuits required for this are not shown in detail The error information OQt / Qk and O ¹ Pk are fed to a coordinate converter 28 to provide the error information in Cartesian coordinates:

These error signals are then multiplied by the values of the non-equalized signals Xk and xt which emerge one after the other from the delay lines 10 and 13 according to FIG. 4 or 18 and 20 according to FIG. Fig. 6 shows only the multiplication for the A-th tap; however, it is clear that (2Λ / + 1) similar circuits are required. Only the operation on the tap / is described, with / between 0 and 2A / for the: Obtaining the setting signals of the individual handles.

In accordance with equation (A) already given above, the signals "5" are multiplied by the signals Xk-i and Xk-i , which are taken from the taps on the delay lines 10 and 13 or 18 and 20. These multiplications are done in multiply! Pj and Pf In the same way, the signals ö? K are multiplied by the signals Xk-i and x _k -i , which are taken from the Ath taps of the delay lines 10 and 13 or 18 and 20. This takes place in the multipliers Qj and Qi

Two adders 29 and 30 form the products from the Siinjuncni

Accordingly, the two equations (7) already mentioned can be written as follows:

10

(in adder 29) (in adder 30)

+ MO ® KO

It is known that mathematically a convolution operation is both commutative and associative With this the equations (8) can be written as:

t) = MO ® KO - [MO ®

KO = CMO ® KO] ®g (0 + MO® Kt)

15th

25th

In this way, the two components of the function “grad V” for the Aten taps of the delay lines 10 and 13 or 18 and 20 are formed.

It now remains to determine the coefficients C / and di in accordance with the specified equation (B).

The κ at the outputs of the adders 29 and 30 output values are accumulated in ascending or count-down counters 31 and 32, respectively, when the content of a counter a predetermined positive value + / or a negative value - γ reached, causes each subsequent threshold circuit 33 or 34 the addition of a correction value + p \ when the counter reaches -y, or -ß when the counter reaches + γ. This is how the actual coefficients c and d are formed. The associated counter is deleted in parallel with an addition of + ß or -ß.

In this way, the counters 31 and 32 enable the output signals of the adders 29 and 30 to be averaged over time. The ratio β / γ is the scale factor denoted by μ in the equations (B) already given. The values β and γ, both positive, must meet two opposing requirements: the ratio β / γ must be sufficiently small to ensure the convergence of the algorithm given in equations (B); on the other hand, a quick adjustment of the equalization requires that this ratio should be as large as possible. A good compromise is to choose β to be large at the beginning and then to reduce it as it approaches the optimum.

Embodiment for the second approach

With the introduction of the designation g (t) for the transmission path of the Hilbert filter 6 (Fig. 2), M can be written:

The equalization according to this second approach is based on this knowledge and in particular on the Equations (9). For a description of the details, reference should be made to FIGS. 7 to 3.

Fig. 7 shows the general structure as a block diagram. The signal φ) from the transmission line is fed in parallel to the two filters 49 and 5tf, which have the transmission paths h \ (t) and hi (t) . Thus, these two filters emit the following signals:

Pi (O = MO® KO
P ₂ (O = MO® KO

Signal p \ (t) is fed to a Hilbert filter 51 with the transmission path g (t) and on the other hand to the input of a summer 52. The output signal ß \ (t) of Hilbert filter 51 is fed to the input of another summer 53. The signal p ^ t) is a second Hilbert filter 54 with the transmission path g (t) and on the other hand to the second input of the adder 53. The output signal ßi {t) of the Hilbert filter 54 is fed to the input of the adder 52 with a minus sign

The following signals are therefore present at the outputs of the summers 52 and 53:

y (0 = Pi (0 - PAt) = MO ® KO - CMO ® KO] ® E (O W) = Pi (0 + P ₂ (O = lh (0 ® KO] ® 8 (0 + MO ® KO

This is in accordance with equation (9).

F i g. 8 shows the details of the example according to the second approach. The signal φ) from the transmission line is sampled at a repetition frequency γ , where -L is the transmission repetition frequency. and M

a positive ». Number is such that the number of per Modulation period Γ sampled values define the signal with sufficient accuracy. The one with the repetition rate

- = sampled values should be referred to as η .

/ denotes the successive samples of the signal t'i). It will be seen in the following that only one value sampled per period Γ is used for data evaluation. The index k is used to denote this particular value. The values r are fed to the input of a delay line 48 which consists of 2Λ / delay elements depending on the duration. These delay elements are denoted by Oi to Ü2m \, their

however, only four are shown in FIG. In practice, this delay line can again be a shift register. (2 / V + 1) taps are provided between the individual elements and at the input and output of the delay line. The signals picked up by the individual taps are fed, on the one hand, to a first group of binary multipliers Mi to MfN and, on the other hand, to a second group of binary multipliers Mo * to MiJv. In these multipliers, the signals are multiplied by the factors cn to CiN or by the factors dt to din . The output signals of the multipliers Mf to Mfn are algebraically added in a summer 55 and the sample values pi are added as the output signal of the filter with the coefficients cy (which the filter 49 with the 1> transmission path h \ (t) according to FIG. 7) corresponds, submitted. In the same way, the output signals of the multipliers M * are algebraically added in a summer 56 !? ¹ " ¹ » nd Hahei provides the sampled values th. Of the output signal de: with the filter operating with the factors di (which corresponds to the filter 50 with the transmission path hj (t) according to FIG. 4).

The sample values p 1 are fed to a Hilbert filter 57 (corresponding to filter 51 in FIG. 4) in order to generate sample values pt, a signal phase-rotated by π / 2 with respect to the signal consisting of the sample values pi. The sampled values pi are also fed to a Hilbert filter 58 (corresponding to the Hilbert filter 54 in FIG. 4) in order to form the sampled values p 1 of a signal which is phase shifted by .τ / 2 with respect to the signal with the sampled values pi . The summers 59 and 60 give algebraic combinations of the py

Signals pu ^ u P2, and p2, ab: -γτ

The symbols used in this equation have the same meaning as in the one described first solution.

The error signals are now defined as follows:

This results in:

The equalizer works optimally when the function V reaches a minimum. The similar mathematical gradient observation applies here as in the first solution approach. The minimum of the function V is reached when the (4 / V + 2) components of the vector gradient V, ie '] ^V and' ^. at 0 </ <2 / V assume the size 0.

The expansion γ- and st gives:

<V

⁼ "■ S,

- -r f% ' χ

de,

dd,

dd,

i = Pm + Pu-

These are the sample values of the components of the equalized signal.

tin clock with a repetition rate of approximately

- is used to make up pairs of values y * y, respectively

select a suitable pair of values yi « y * from which the data can be retrieved with the aid of conventional technology, which itself is not part of the subject matter of the present invention. F i g. 9 shows a circuit arrangement for this.

In the exemplary embodiment described, the equalization is adaptable due to the setting of the factors c / and di. The transmission paths h \ (t) and Iy ₂ (O can thus be changed so that the error at the output of the equalizer reaches a minimum. The factors c; and d; are determined on the basis of two error signals ε </ and it, the for their part can be defined from the two components of the equalized signal.

The generation of the error signals ε * and 6 * and the method of determining the factors C; and dt shall now be understood with reference to FIG. 9 will be explained in more detail.

The root mean square is again used as the error function:

50

55

60 The minimum of the function V is reached when all of these expressions become 0 for all /.

Two remarks should now be made: The term

^ i is identical to α_ι d. H. with the signal at the Aten

Tapping of the equalizer delay line, since the only term of β * => ϊ - «t that depends on ο, is the term ο- ric-i , which by multiplication in the multiplier Mf (Fig. 8) from the signal / · * _ / is obtained with the coefficient cy. This result, which is not to be derived mathematically at this point in order not to unnecessarily lengthen the description, results directly from the generation of yt , which can be seen from FIG. 8 to

is seen. - Similarly, the term - = 4- is also identical

»« Ι

with / ϊ-α because the only term of £ * = / * - oCt that depends on di is the term d / ■ r * _ / obtained by multiplying the signal r ^. / by the coefficient di'wn multiplier MJ * ( Fig. 8) is obtained.

On the other hand, due to the known properties of the Hilbert transformation (Bedrosian's theorem) the time integral of the product of two functions is equal to the time integral of the product of Hilbert transformations of these two functions. This will:

65 (10)

^8V _ ■> - ^ fL

337 * " dd,

The change algorithm can be derived directly from this. Using the Rekiirsinns formula can be written:

f | - ^c l ~

(ID

10

For μ and the exponents (m) and (7n + 1) the same applies as for the first solution approach.

Fig. 9 shows the construction of the circuitry for determining the coefficients c / and d / in accordance with the above investigation. ii

M samples y 1 and y 1 per information period T are subjected to a second sampling process, and

with a repetition frequency ψ, with only one pair each of samples v *. yi, is used per information period. The selection of the pair of values to be used is made by means of the clock generator used, which itself is not part of the subject matter of the present invention. The sample values selected in this way are sent to a coordinate converter 61 for generating the polar coordinates pt and Φ *. the phase and amplitude information of the received signal. The information ρ »is compared in a comparator 62 with the various discrete amplitude _{levels O n} which are used in the transmission jo under consideration. These level values can either be specified in advance or extracted from received data using known technology. The comparator 62 supplies the amplitude level ρϊ. which comes closest to the received amplitude information ρ * ü from the JT _n. The comparator also supplies relative amplitude error information dgi / Ok mhdot "Qk -pi-

Similarly, the phase information Φ * is compared in a comparator 63 with the various discrete phase values $ which are used in the transmission. The discrete comparison values can also either be specified in advance or determined by extraction from received data. The comparator 63 supplies the phase value Φ ** of all values $ ″, which comes closest to the received phase information Φΐι. It also supplies phase error information kk $ k

The values Ji and Φ ** from comparators 62 and 63 are then decoded to recover the transmitted data. The necessary circuitry for this are not shown The error information φ * / ρ * and <# * are assigned to a coordinate converter 64 Access to provide the error information in Cartesian coordinates:

dpi

= y _k ■ - £ - - y _k ■ 6 <P _k ?

bot

Qk

will. F i g. 9 shows the multipliers for the / th tap only; however, again it is clear that (2N + 1) similar multipliers are required. The operation for tapping at / is described. The corresponding must be carried out for all taps from 0 to 2Λ /:

According to the above equation (10), the signals ε * and £ * with the signal r * _ / at / -th tap the equalizer delay line (Fig. 8) is multiplied in multipliers 65 and 66. This results in the following product signals:

r _k ■ r, _, (in multiplier 65) f _k r _k -i (in multiplier 66)

50

55

60

These error signals are then multiplied by the values of the non-equalized signal η which are tapped from the delay line 48 according to FIG

65 These are the two components of a degree V function for the / -th tap of the equalizer delay line.

What remains is the determination of the coefficients Ci and di in accordance with the recursion formulas mentioned (11).

The values from the output of the multipliers 65 and 66 are accumulated in two counters 67 and 68 which count up and down. If the content of one of these counters reaches a predetermined positive value + γ or negative value -γ , which are each defined by means of a threshold circuit 69 Drier 70, a correction + β is added if the counter reading has reached -γ , or a correction -β added when the count has reached the value + γ . This addition of + β or - β takes place in each case to the determined coefficient c or d. On the other hand, when one of the thresholds is reached, the corresponding determining counter is deleted.

The two determining counters 67 and 68 determine the time average of the output signal of the multipliers 65 and 66. The ratio β / γ is again the scale parameter μ in equations (11). For the compromise with regard to the ratio β to γ , what has been said for the first approach applies again.

General for both solutions

A total of three exemplary embodiments have been explained above in the description of two possible solutions. To increase the understanding of the actual invention, some points that do not belong to the subject matter of the invention were not taken into account. For example! the synchronization problems were not explained. Of course, all the operations described above must be carefully synchronized. The defined period T as the time base is the reciprocal of the transmission rate of the information elements on the transmission line. This following speed is predetermined in the transmitter, but its recognition in the receiver at the other end of the transmission line brings with it some problems that arise from the line distortions. Several solutions to this problem are known in the art and consist essentially in the fact that a local clock is used in the receiver, the fundamental frequency of which is the same as that of the clock in the transmitter; the frequency and phase of the local receiver clock must be carefully and constantly based on the received

ί j L:

Data signals are readjusted. A local clock T ' is thus used which corresponds as closely as possible to the clock T in the transmitter. Strictly speaking, the value T used in the description should therefore be replaced by this receiver clock value Γ. However, this does not affect the basic idea and the execution of the functions.

There are also details of the coordinate converter has not been described since such circuits are well known in the art. It becomes that z. For example, reference is made to the work by J. E. Voider, which is published in the "IRE Transactions on Electronic Computers" in September 1959 under the title "The CORDIC Trigonometry Computing Technique", pages 3JO bis 334, was published. Another technique for extracting the phase was used in the German Offenlegungsschrift 22 58 383 entitled "Digital phase detector" has already been described.

i ^ ic VorSiciicilucn Efiäüici UMgCM were unier

Referring to scanning signals performed. If all the operations used are to proceed in a digital manner, it is clear that the individual samples can be encoded as n-digit binary numbers, where η depends on the degree of accuracy required

According to the state of equalization technology, it would also be possible to only display the signs of the error signals to use instead of the complete signal values. The following algorithm would be used to determine the coefficients:

The second approach is according to FIG. 7 for a phase modulating transmission system with eight

Phases at a repetition rate ~ of IbOO band

π has been implemented in practice. The selected Hilbert feeders are transversal filters with seven taps. The received signal is tested with a repetition frequency of 14,400 Hz (M = 9) and uic cMi / .ciiicM Abiasiwerie are coded with i 2 bits each.

> o The delay line of the equalization filter is designed with nine taps (W = 4). The following values are selected for the values β and; ·: y = 0.5; 0 = 0.01 for the first 100 periods T, 0.005 for the next 100 periods and 0.0025 afterwards. There is a setting time

.'5 of 500 ms is achieved on average if all coefficients cv and di are set to 0 at the beginning, except for the coefficient c \ which is set to 1.

For this purpose fi sheet of drawings

Claims (1)

Patent claims: 1. Method for equalizing a quadrature modulated Data signal received over a linear distortion-inducing transmission medium is characterized by the following process steps: a) The received via the transmission medium (3) distorted signal φ) is subjected to a transformation, while the quadrature signal φ) of the signal φ) generated in a conventional manner b) These signals φ) and / ft / become two signals by means of filtering - / I ₂ (Z) ®Ht) and 25th ^15th formed, where ® tConvolutionsoperatconen the signals r (t) and φ) with two filter transmissions ^M gungikgSngen / h / W and / b ^ f / denotes and these filter transmission paths by means of assigned false signal values; dj »and öyt are set, which can either be specified empirically or are determined manually or automatically from the actual properties of the signals y (t) and y (t) following the convolution operations in relation to nominal reference values. c) The signal values of y (t) and y (t) as the respective ^M cartesian vector coordinates of the equalized signal can be used to derive the individual transmitted data elements according to the state of the TecLnft. 2. The method according to claim 1 for the formation of the two signals y (t) and jffjt characterized by dip the following process steps: a) The signal φ) is a first filter having the transfer passage h \ (t) and a second ** filter with the transmission gear h _t (t) and the quadrature signal φ) a third filter to the transmission gear hi (t) as well as a «) Fourth filter with the transmission path h \ (l) supplied b) By subtracting the output signal of the third filter from the output signal of the first. The filter becomes the signal y (t) and, by adding the output signals of the second and fourth filters, the signal jfi / gebÜJet. 3. The method according to claim 1 for forming the two signals, iff / and yft), characterized by the following method steps: a) The signal φ) is fed to a first filter with the transmission path h \ (t) and the quadrature signal / ff / is fed to a second filter with the transmission path ^ (/ j. b) By subtracting the output signal of the second filter from the output signal of the first Filter, the signal ^ is formed. c) This signal y (t) is subjected to a transformation and thereby formed the quadrature signal y (t). 4. The method according to any one of claims 1 to 3, characterized by the following process steps: 50 a) Corresponding polar coordinate values eft) and Φ (ή are derived from the Cartesian vector coordinates of y (t) and y (t) b) At predetermined clock times, the polar coordinate values g (t) and Φ (ΐ) are compared with reference values and amplitude error signal values 6g and phase error signal values 6Φ are derived c) These error signal values öq and δΦ, given in the form of polar coordinate values, are converted into Cartesian error signal values (Jy and 6y d) Adjustment of the transmission paths h \ (t) and hrft) by means of these error signal values oy and 6y so that minimum root mean square values dyt + lSp result. 5. Circuit arrangement for performing the method according to one of the preceding claims, marked by a) a phase shifter (9.191 to which the received distorted signal φ) is fed from the transmission medium (3) and which derives the quadrature signal / ff / from it in a manner known per se, b) a filter arrangement (10-11 / 12 and 13-14 / 15; or 18-21 and 20-22) to which the signals φ) and φ) are fed and from which the equalized signal or this signal and its quadrature signal forms, c) Adjusting elements (M) in the intended filter arrangements (10-11 / 12 and 13-14 / 15; or 18-21 and 20-22), their control inputs (c ., d .. ./ empirically specified or manual or automatically determined error signal values dy _k or dft are supplied. β circuit arrangement according to claim 5, characterized by a) a first filter (10-11) with the transmission path ht (t) and a second filter (10-12) with the transmission path tn (t), to which the signal / fr / is fed, b) a third filter (13-14) with the transfer path hi (t) and a fourth filter (13-15) with the transfer path h \ (t), to which the quadrature signal / ff / is fed, c) a first summer (16) to which the output signal of the first filter (10-11) and subtractively the output signal of the third filter (13-14) and the from this forms the signal jf / J, d) a second summer (17). the that Output signal of the second filter (10-12) and additively the output signal of the fourth Filters (13-15) are fed and from this forms the quadrature signal> f //. 7. Circuit arrangement according to claim 5, characterized by a) a first filler (18-21) with the transfer path h \ (t), to which the signal φ) is fed, b) a second filter (20-22) with the transmission path hjft), to which the quadrature signal φ) is fed, c) a summer (23) to which the output signal of the first filter (18-21) and subtractively the output signal of the second filter (20-22) are fed and which forms the signal y (t) therefrom, d) a second phase shifter (24), which is supplied with the output signal y (t) of this summer (23) and which forms therefrom the quadrature signal y (t) 8. Circuit arrangement according spoke 6, characterized by a) a first signal sampling device (M / T) between the receiving end of the transmission medium (3) and the input of said arrangement of riters, phase shifters and summers, which samples the received distorted signal / fy with the repetition frequency M / T , where MT is equal to Is the repetition frequency of the transmitted data elements and M / T is at least twice as large as the highest frequency in the received signal spectrum, b) a second signal sampling device {MT) in series with the first signal sampling device (M / T), which samples the samples of the signal φ) and its quadrature signal φ) at the repetition frequency MT of the transmitted data elements and thereby forms the samples x> and Xk, which are fed to the filters provided, c) the filters provided (10-11, 10-12, 13-14, 13-15) are used as transversal filters tapped delay lines (10, 13), the taps of which have a temporal Show distance. 9. Circuit arrangement according to claim 7, characterized by a) a signal sampling device (M / T) between the receiving end of the transmission medium (3) and the input of said arrangement of filters, phase shifters and summers, which samples the received distorted signal / frj at the repetition frequency M / T , where MT is equal to Repetition frequency of the transmitted data elements and M / T is at least twice as large as the highest frequency in the received signal spectrum. b) a second signal sampling device either in series with the first signal sampling device (M / T) at the input of the arrangement of filters, phase shifters and summers, which the samples of the signal / friend whose quadrature signal φ) with the repetition frequency IT of the transmitted data elements samples and thereby forms the samples Xi, and .v * and feeds them to the filters provided, or at the output _h -, the arrangement of filters, phase shifters and summers, whereby it samples the output signal of this arrangement with the sampling rate / I / Tdii, and where in In both cases, the sampling values y * and S'k of the signals y (t) and y (;) are removable at the output, c) the filters (18-21, 20-22) provided are transversal filters with tapped delay lines (18, 20 ), the taps of which have a time interval T. 10. Circuit arrangement according to one of claims 8 or 9, characterized by the following features for the automatic setting of the transfer fermentation h \ (t) and hi (t): a) a first coordinate converter (25) to which the samples y * and y * from the adders (16, 17) or from the summer (23) and from the second phase shifter (24) behind the output of the provided filter and the Cartesian coordinate form-polar coordinates from these sampled values other = arc tg - derives, b) two comparators (26,27), with the help of which the polar coordinate values ρ * and Φ * derived in this way with predetermined or previously determined reference values (5 * and $ t with formation of error signal values ÖQk / gt with OQk = Qk- ^ i and δΦk = Φk - Φk are compared, c) a second Koordiriaienkonverter (28) to which the Output error signal values <5ρ * / ρ * and <? Φ * of the comparators (26, 27) are fed and these error signal values in Cartesian Error signal values <5y * and <5.y * converts, d) Adjusting elements (Ml ... 2M M _0. in) of the first filter (10-11, 18-21) and possibly adjusting elements (Mi ... 2At, l of the fourth filter (13-15), to which the error signal values < 5y * and which set the transmission path h \ (t) on the basis of this, e) Adjusting elements (Mi ... ₂ / v, Mi ... ₂ n) of the second filter (10-12, 20-22) and possibly adjusting elements (Mo ... 2N) of the third filter (13-14) to which the error signal values dfa are fed and which set the transmission path hi (t) on the basis of these. 11. Method for equalizing a quadrature mode 1 data signal that is transmitted via a transmission medium that causes linear distortion is received, characterized by the following procedural steps: a) The distorted signal φ) received via the transmission medium (3) becomes two signals and / ': (/) = / i, i /) ®r (ll
formed, where (S) convolution operations of the signal / fij with two filter transmission paths h \ (t) and hi (t) and these filter transmission paths are set by means of assigned error signal values <) y _k and oy _k , which can either be specified empirically or manually or automatically from the actual properties of the signals y (t) and yft) can be determined following the convolution operations in relation to desired reference values. in b) From these signals p \ (t) and pi (t) , their two quadrature signals ß \ (t) and ßi (i) are derived by a transformation in a manner known per se. c) The four signals P- (I), P ₁ (I). p ₂ (t) and p :( ') : · are algebraically combined to form the signals and i'C) = PiC) + d) The signal wcrtc of y (l) and y (l) as the respective Cartesian square coordinates of the equalized signal can be used to derive the individual transmitted data elements in accordance with the state of the art. m 12. The method according to claim 11, characterized through the following process steps: a) Comparison of the signals y (t) and $ (t) at given cycle times with reference values and deriving two error signal values dy and Oy, b) Setting the transmission path h \ (t) with oy so that the error signal value oy tends towards 0, -to and the transmission path h? (t) m \ l dyso that the error signal value oy also tends towards 0. 13. Circuit arrangement for performing the method according to one of the aforementioned claims -r, before 11 or 12, indicated by a) a first filter (49; 48 / Mo ... 2 \) with the transmission path h \ (t), to which the received distorted signal r (t) from the transmission medium 5 »(3) is fed and a first filtered one Signal whistle generated, b) a second filter (50; 48 / Mo * ... 2n) with the transmission path h ^ t% to which the received distorted signal φ) is fed and which generates a second filtered signal P ₂ (I) therefrom, c) a first phase shifter (51; 57) to which the first filtered signal p \ (t) is fed and which forms its quadrature signal piffj therefrom in a manner known per se, d) a second phase shifter (54; 58) to which the second filtered signal checks) is fed and which therefrom, in a manner known per se, checks its quadrature signal, b5 e) a first adder (52; 60) to which the first filtered signal p \ (t) and the quadrature signal subtractively pi (t) of the second filtered signal pi (t) are fed and the resulting signal > (0 "Pi (O- Pi 0 'educates. f) a / wide summer (53; 59) to which the quadrature signal p \ (i) of the first filtered signal p \ (l) and additively the second filtered signal pi (t) are fed and to which the signal is derived therefrom Y (O-P <(0 + P2 (0 forms. g) Adjustment elements (M) in the filters provided (49, 50). whose control inputs (c ... d ...) are empirically specified or manually determined automatically determined error signal values Λι, or dft are supplied. Ί4. Circuit arrangement according to claim ι j marked by a) a signal scanning device (M / 7) / wipes the F.mpfangsendc of the transmission mechanism (i) and the F.input of the first and / wide filter _V 49; 48 / M ₀ *, v; 50; 48 / Mon * iv). which samples the received distorted signal φ) with a repetition frequency M / T , where 1 / T is the same , ttr is the l-olge frequency of the transmitted data elements and M / T is at least twice as large as the highest frequency in the received signal spectrum; b) the first and / or second filter (49; 48 / M * : ».;">0; 48 / Mo *. ^ contain a tapped delay line (48). The taps of which have a time interval of 7 ". 15. Circuit arrangement according to one of claims 13 or 14, characterized by the features mentioned next for the automatic setting of the transmission gears h] (l) and h -> (t) -. a) a (second) signal sampling device (1/7 ^, to which the formed signals y (0 and y (t) are fed and which from them samples samples yic and y ~ k with the repetition frequency of the transmitted data elements, b) a first coordinate converter (61) to which the sample values yt and yt formed in this way are fed in Cartesian coordinate form and to which polar coordinate values are derived therefrom and < _lk = arctg - derives, c) two comparators (62,63) with whose help the polar coordinate values ρ * and Φ * derived in this way with predetermined or previously determined reference values §i and $ t while forming error signal values OOk / Qk with OQk = Qi-Qt and <5Φ * = Φί— $ t are compared, d) a second coordinate converter (64) to which the output error signal values ogt / gt and 5Φ * from are fed to the comparators (62,63)
converting these into Cartesian error signal values
and often converts, e) Adjustment elements (Μξ in) of the first filter
48-55), to which the error signal values e
are fed and due to this
Set transmission path / !! ^. !) EinsiellgliederfA / o * .2 / vJ of the second filter
⁷ JS-56) to which the error signal values
are fed and due to this
Set transfer gear /) ₂ (7,). and «In