EP1203475A1

EP1203475A1 - Method for the adaptive adjustment of an equaliser coefficient

Info

Publication number: EP1203475A1
Application number: EP00962164A
Authority: EP
Inventors: Gerhard Herbig; Thomas Gebauer
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 1999-07-23
Filing date: 2000-07-20
Publication date: 2002-05-08
Also published as: WO2001008364A1; DE19934672A1

Abstract

According to the present invention, the coefficients (w(0) and (w(1) of an equaliser are adapted using an error correction algorithm in order to minimise interference between symbols. The purpose of the invention is to prevent a coefficient migration during adaptive equalising. To this end, the coefficients (w(0) and (w(1) determined using the error correction algorithm are modified using a correction term (kt(0), kt(1)) so that the equaliser transmission function has a favourable value outside the utility signal frequency range for one or more preselected frequencies.

Description

Method for adaptively adjusting the coefficients of an equalizer

State of the art

The present invention relates to a method for adaptively adjusting the coefficients of an equalizer, the coefficients according to a

Error correction algorithm are adapted so that intersymbol interference is minimized.

If digital signals via channels with time variations

Channel distortions are to be transmitted, adaptive equalizers are necessary in the receiver, which must automatically adapt to the channel distortions in order to compensate for them. Channel distortions occur, for example, on radio transmission channels in point-to-point directional radio links due to multipath propagation. A distinction is made between single-sampled and oversampled equalizers. With the simply sampled equalizers (baud-spaced equalizers) there is exactly one sample value at both the input and the output of each symbol clock. Since the sampling condition is already violated at the input of the equalizer in this case, such equalizers are only of limited performance. Much better results are obtained with an oversampled equalizer (fractionally-spaced equalizer), their simplest execution processes exactly two samples per symbol cycle at the input. Even with an over-sampled equalizer, only one sample value is calculated per symbol cycle at the output, because only one transmission symbol can be detected per symbol cycle. Since conventional error correction algorithms for adaptive adjustment of the equalizer coefficients can only evaluate the simply sampled output signal, important information for complete control over all possible coefficient settings is missing in the case of oversampled equalizers. As a result, this type of equalizer tends to an undesirable "coefficient shift", which can no longer be controlled with the usual algorithms. Coefficient shift means that due to rounding errors in the calculation of the

Coefficients very slow changes in the adapted correction values for the coefficient values occur in one direction. The following known algorithms are generally used to adapt the equalizer coefficients via sampled equalizers:

During the acquisition phase, as long as the transmitter has not yet been recognized, the control loop for

Carrier phase synchronization is not yet engaged, the Constant Modulus Algorithm (CMA) is usually used and during the tracking phase

Continuous operation of the recipient, the Least Mean Square

Algorithm (LMSA) is used. The two mentioned

Algorithms are e.g. in K.D. Kammeyer, Messaging, B.G. Teubner Verlag, Stuttgart,

1992, pp. 313-316, 510-512 and in J.G. Proakis, digital

Communications, McGraw-Hill, 1989, pp. 561-569, 587-593. Coefficient hiking is observed in particular in the CMA algorithm as a result of quantization errors, since it is particularly difficult with the CMA algorithm, which is a higher-order algorithm, to completely avoid offset errors as a result of quantization operations. In the LMSA algorithm, the lack of control capability, particularly in the case of dynamic transmission channels, leads to inadequate adaptation of the equalizer coefficients to the channel changes. Channels with multi-path reception, as is known from point-to-point radio links, cause the equalizer to fail even with minor distortions, although its basic performance would be able to equalize these channels.

A countermeasure against the phenomenon of

The tap-leakage algorithm (TLA), which is a variant of the LMSA algorithm, forms coefficient hiking in an oversampled equalizer. The tap leakage algorithm is described by R. D. Giltin, H. C. Meadors, S. B.

Weinstein: The Tap-Leakage Algorithm: An Algorithm for the Stable Operation of a Digitally Implemented, Fractionally Spaced Adaptive Equalizer, BSDJ No. 8, VOL. 61, October 1982, pages 1817 to 1839. According to the TLA algorithm, smaller amounts are subtracted from the amount of the coefficients in order to reverse the coefficient shift. This measure not only avoids coefficient wandering, but it also leads to a deterioration in the equalization result, i. H. the intersymbol interference increases again.

The invention is therefore based on the object of specifying a method of the type mentioned at the beginning with which the coefficient shift can be prevented without deteriorating the equalization quality. Advantages of the invention

The above object is achieved with the features of claim 1 in that with the help of

Error correction algorithm determined coefficients are changed by a correction term so that the transfer function of the equalizer outside the useful signal frequency band assumes an unchanged fixed value for one or more selected frequencies. Instead of the transfer function itself, a first and / or a higher derivative of the transfer function outside the useful signal frequency band can be set to a fixed value for one or more selected frequencies. With this method, increases in the transfer function of the equalizer on both sides of the groove signal frequency band, which are due to the undesired coefficient wandering, are largely reduced. This prevents dynamic fading events on the transmission link from causing the equalizer to fail if e.g. B. a certain coefficient setting can no longer be adapted quickly enough.

Advantageous developments of the invention emerge from the subclaims. Thus, the simplest possible calculation of correction terms for the coefficients is possible if the transfer function or the first and / or a higher derivative of the transfer function at the frequency 2π / T and / or the frequency 3π / T and / or the

Frequency 4π / 3T is set to a fixed value, where π / T is the corner frequency of the useful signal frequency band. The transfer function or a first and / or higher derivative of it can be selected at the one (s) Frequency (s) can be set to the value 0 or another fixed value.

drawing

The invention will now be explained in more detail using an exemplary embodiment. Show it:

1 shows a circuit diagram of an adaptive equalizer, FIG. 2 shows a transfer function of the equalizer without the correction according to the invention,

Figure 3 shows a transfer function of the equalizer with a first correction and

Figure 4 shows a transfer function of the equalizer with a second correction.

Description of an embodiment

The adaptive transversal shown in FIG.

Equalizer has a delay chain, of which the first two delay elements V0 and VI can be seen. At input 1 of the delay chain there is a digital input signal x which is on the transmission path from a transmitter to a receiver in which the adaptive

Equalizer located, has been distorted. In the individual delay elements V0, VI, the input signal x is delayed by T / 2, where T is the symbol clock of the input signal x. The symbols of the distorted input signal x are tapped from the delay chain in front of the individual delay elements and are each fed to a multiplier MO, Ml in which the symbol is weighted with a coefficient w (0), w (l). All signal symbols y (0), y (l), ... y (n) thus formed in the equalizer and weighted with the coefficients w (0), w (l), ... w (n) are combined by an adder to form an output signal y. The output signal y is fed to a decision maker ES, which decides for each symbol of the output signal y which of the possible transmission symbols it comes closest to, ie the decision maker ES estimates the transmission symbols most likely to be transmitted on the basis of the symbols of the summer output signal y. The estimated transmission symbols a can thus be tapped at the output 2 of the decision maker ES. In addition, the decision maker ES also generates an error signal e, which depends on the storage between the respective symbol of the summer output signal y and the estimated transmission symbol a.

The error signal e is fed to correlators K0, Kl, which are responsible for the formation of the coefficients w (0), w (l). Namely, the correlators K0, Kl determine according to a known error correction algorithm, e.g. B. according to the LMSA algorithm already mentioned at the beginning, from the error signal e and the tapped off symbols from the delay chain of the distorted input signal x adaptive change values for the coefficients w (0), w (l). Following each correlator K0, Kl is an adder A0, AI, in which a correction term kt (0), kt (l) is added to the change value for the coefficient w (0), w (l) output by the correlator K0, Kl becomes. The correction terms kt (0), kt (l) are formed in a processor (PZ) according to an algorithm described in more detail below. These correction terms kt (0), kt (l) aim to avoid the “coefficient wandering” mentioned at the beginning.

The individual adders A0, AI are each followed by a coefficient register KR0, KR1, in which all change values, including the correction terms for the coefficients w (0), w (l), are integrated, from which the current coefficient w (0), w (l) arises. FIG. 1 shows an adaptive equalizer for a real digital input signal x. In a digital radio relay system, however, QAM signals are usually transmitted. Accordingly, four such adaptive equalizers would have to be provided for a QAM receiver, namely one in the in-phase branch, one in the quadrature-phase branch and, to compensate for crosstalk, an adaptive equalizer that goes from the in-phase branch to the quadrature-phase branch and one from the quadrature phase Branch is switched to the in-phase branch.

The following explains how the processor PZ generates the correction terms kt (k) with k = 0.1, ..., n. As already said, the correction terms kt (k) for the coefficients w (k) are intended to prevent the so-called coefficient wandering. FIG. 2 shows a transfer function E (ω) of an equalizer, the useful signal frequency band having its corner frequencies at ω = ± π / T, but the equalizer having the spectrum in the range from ω = -2π / T to ω = + 2π / T can influence. The undesired coefficient wandering can be recognized by an amplification of the spectral ranges not used by the useful signal, which are shaded gray in FIG. 2. The correction term kt (k) directly influences the transfer function of the equalizer, so that the increases outside the useful signal frequency band are reduced, and as a result there is no longer any coefficient wandering. At the same time, however, the transmission function within the useful signal frequency band remains completely unaffected, so that the actual equalization is not impaired.

The following applies to the transfer function E (ω) of the equalizer:

E (ω) = ∑ (w _± (k) + jw „(k)) ei ^ωkτ = E _i (ω) + jE _q (ω)

= ∑ w _i (k) cos ωk - + ∑ w _q (k) sin ωk ^ -

+ j (- ∑ w _i (k) sin ωk— + ∑ w _g (k) cos ωk ^ ⁾ (1)

Here w ^ _ (k) and w _q (k) are the kth in-phase and quadrature-phase coefficients.

The summation ∑ extends over all coefficients from k = 0 to k = n. In order to reduce the transfer function outside the useful frequency band, the algorithm running in the processor PZ is intended to be a zero or at least at a certain frequency ω ₀ <± π / T form another fixed value of the transfer function. The target function of the algorithm is thus:

Since, in the case of a complex equalizer for QAM signals, all of the associated four partial equalizers are to be set independently of one another in terms of their transmission function in the above sense, the distinction between w and w for the in-phase branch and the quadrature-phase branch can be omitted. This results in the amount of the transfer function:

and for your gradient:

(4) TTTT

= 2cos ω ₀ k— w (&) cos ω _Q k— + 2sin ω ₀ k - w (£) sinω ₀ & - 2 2 2 2

The algorithm for correcting the coefficients w (k) is then formed as follows:

w „ ₊ , (*) = w _B (*) - α-« gw [(*)] (5)

w _n (k) is the coefficient formed one time before, and w _{n + l} (k) is the current one by adding the correction term kt (k) = -a • sign [j (k)] to the coefficient w _n (k) resulting coefficient. Incidentally, for the sake of clarity, equation (5) does not take into account the change value for the coefficient w _n (k) formed in the correlators KO, Kl according to, for example, the known CMA or LMSA algorithm.

In equation (5) is

ow (k)

T T

J (k) = W _c ■ cosω ₀ k - W _s ^■ sin ω ₀ k - 16)

Here were the abbreviations

W _c = w (k) cos ω _Q k

(7)

T ^w s = ∑w (k) sinω ₀ k-

used. Since only a very slight influence on the coefficients is desired (small α), the

Algorithm in practical operation for a Signumform be simplified. The effectiveness factor α for the correction term kt (k) is set to a suitable value by field simulation.

The algorithm should be able to be implemented with little effort. One must therefore restrict oneself to frequencies ω _Q which allow a simple and periodic calculation of the trigonometric functions. The following frequencies are possible:

2π 3π. Λπ ω - _a tt. = - ηri, 'ω _n JD = —T and ω _r = - "2T (8]

The two simplest cases ω _A and ω _{c will} now be dealt with.

2π

Case ω _Λ = ^■

The following applies to this particularly simple case;

smω, k— = sinÄTT = 0

^A 2

(9)

T cosω _A k— = - -. k COS ÄTΓ = (-1)

and therefore :

The complete algorithm for adapting the coefficients is therefore according to equation (5):

w _{n + i} (k) = w _n (k) - 2a - sign [(- \) ^k ∑w (k) (- l) ^k ] (n) with J _A = 2 (-l) ^k ∑w „(k) (- \) ^k (12)

Since the average coefficients are preferably involved in the undesired portions in the transfer function, the algorithm according to equation (11) can be limited to an interval in the order of magnitude k e [-4, 4]. Of course, all coefficients must be taken into account in equation (12).

10

The result of this algorithm is shown in FIG. 3, in which it can be seen that there is already a certain reduction in the transfer function outside the useful signal frequency band compared to the uncorrected one in FIG. 1

L5 transfer function shown has occurred.

2nd Case:

In this case:

20

7 ^* 2 sinω _r ck— ₂ = sin - ₃ for = 3 (z *)

(13)

T 2 cos ω _r k - = cos - kπ = 5R (z *) ^c 2 3

25 r - e ' ² " ³ » «""'

With the table:

applies: W _c = ∑w (k) cosω _c k- = ∑w (3k) -0.5∑ [w (3k + \) + w (3k-l)] (14)

Additional abbreviations are introduced to calculate the correction terms:

W ₀ = ∑w (3k)

W ₊ = ∑w (3k + \) ⁽ 16 ⁾

WD = W _+] -W_ _l

WS = W _^ + W

So:

J _c (3k -1) - -VÖ75 • W _s -0.5 -W = - (-3WD - 2W _ϋ + WS)

J _c (3k) = W _c ⁽ 17 ⁾

J _c (3k +1) = +70/75 • W _s -0.5 -W _c = - (+ 3WD - 2W ₀ + WS)

While in the 1st case j according to equation (12) applies to all coefficients W (k), in the 2nd case j for three different groups of coefficients w (3k-l), w (3k) and w (3k + l) must be distinguished , The coefficients can be corrected very efficiently if the 1st and 2nd cases are combined:

w „ ₊₁ (k) = w _n (k) - a _A ^■ sign [j _A (k)} - a _c ^■ sign [j ₍ . (k)] (18)

As FIG. 4 shows, the adaptive correction of the coefficients _w according to equation (18), a sharp decrease in the spectral ranges outside the useful signal spectrum.

Instead of forcing zeros in the transfer function by the correction, as shown in Figures 3 and 4, the transfer function can also be set to a constant value (e.g. 1) at certain frequencies.

Instead of setting the transfer function of the equalizer to a constant value even at certain frequencies, a first and / or higher derivative of the transfer function for one or more selected frequencies can also be set to a constant value.

Claims

Expectations

1. A method for adaptively adjusting the coefficients of an equalizer, the coefficients (w (0), w (l)) being defined according to an error correction algorithm in such a way that the intersymbol interference is minimized, characterized in that the using the

Error correction algorithm determined coefficients (w (0), w (l)) are changed by a correction term (k (0), k (l)) so that the transfer function (E (ω)) of the equalizer or a first and / or higher Derivation of the

Transfer function outside the useful signal frequency band assumes an unchanged fixed value for one or more selected frequencies.

2. The method according to claim 1, characterized in that the coefficients (w (0), w (l)) are changed so that the transfer function (E (ω)) or a first and / or higher derivative of the transfer function at the frequency 2π / T and / or the frequency 3π / T and / or the frequency 4π / 3T assumes a fixed value, where π / T is the basic frequency of the useful signal frequency band.

3. The method according to any one of claims 1 or 2, characterized in that the transfer function (E (ω)) or a first and / or higher derivative of the

Transfer function at the selected frequency (s) is set to the value 0 or another constant value.