WO2002051084A1

WO2002051084A1 - Method for adaptive adjustment of a coefficient of an equaliser

Info

Publication number: WO2002051084A1
Application number: PCT/IB2000/002027
Authority: WO
Inventors: Gerhard Peter Herbig; Thomas Gebauer
Original assignee: Marconi Communications Gmbh
Priority date: 2000-12-20
Filing date: 2000-12-20
Publication date: 2002-06-27
Also published as: AU2001223900A1

Abstract

The coefficients (w(0), w(1)) of an equaliser are adapted according to an error correction algorithm, in such a way that intersymbol interference is minimised. In order to prevent coefficient migration in adaptive equalisation, the coefficients (w(0), w(1)) that were determined using the error correction algorithm are modified with a correction term (kt(0), kt(1)), in such a way that the transfer function of the equaliser adopts a valid value for one or more selected frequencies outside of the useful signal frequency band.

Description

Method for adaptively adjusting the coefficients of an equalizer

State of the art

The present invention relates to a method for adaptively setting the coefficients of an equalizer, the coefficients being adapted according to an error correction algorithm in such a way that intersymbol interference is minimized.

If digital signals are to be transmitted over channels with time-variant channel distortions, adaptive equalizers are necessary in the receiver, which have to adapt automatically 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.

In the case of the simply sampled equalizers (baud-spaced equalizer), 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 can be obtained with an oversampled equalizer (fractionally-spaced equalizer), the simplest version of which processes exactly two samples per symbol cycle at the input. Even with an oversampled equalizer, only one is always output

Sample value calculated per symbol cycle because only one transmit 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. The consequence of this is that 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 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 generally used and the Least Mean Square Algorithm (LMSA) is used during the tracking phase, i.e. during the actual continuous operation of the receiver. The two algorithms mentioned are e.g. in K.D. Kammeyer,

News transmission, BG Teubner Verlag, Stuttgart, 1992, pp. 313-316, 510-512 and in JG 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 known from point-to-point radio links, lead to failures of the equalizer 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 in R. D. Giltin, H. C. Meadors, S. B. Weinstein: The Tap Leakage Algorithm: An Algorithm for the Stahle 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 by which the Coefficient hiking 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 the coefficients determined with the aid of the error correction algorithm are changed by a correction term so that the

Transmission func ion of the equalizer outside the Nu zsignalfrequenzbandes for one or more selected frequencies assumes an unchanged fixed value. 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 unwanted

Coefficient hiking 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 further developments of the invention emerge from the subclaims. So a simple 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 Derivation from it can be set to 0 or another fixed value at the selected frequency (s).

drawing

The invention will now be explained in more detail using an exemplary embodiment. FIG. 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,

3 shows a transfer function of the equalizer with a first correction and FIG. 4 shows a transfer function of the equalizer with a second correction.

Description of an embodiment

The adaptive transversal equalizer shown in FIG. 1 has a delay chain, of which the first two delay elements V0 and VI can be seen. A digital input signal x is present at input 1 of the delay chain and has been distorted on the transmission path from a transmitter to a receiver in which the adaptive equalizer is located. In the individual delay elements VO, 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 formed in this way in the equalizer with the coefficients w (0), w (l), ... w (n) weighted signal symbols y (0), y (l), ... y (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 most likely transmission symbols based on 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. The decision maker ES also creates an

Error signal e, which depends on the storage between the respective symbol of the Ξummierer output signal y and the estimated send bol 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, an adder AO, AI follows, in which the change value for the coefficient w (0), w (l) output by the correlator K0, Kl follows

Correction term kt (0), kt (l) is added. 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.

Each of the adders AO, AI is followed by a coefficient register KRO, KR1, in which all change values, including the correction terms for the Coefficients w (0), w (l) is 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

If the radio system is active, 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 of the Quadrature phase branch is switched to the in-phase branch.

The following explains how the processor PZ the

Correction terms kt (k) with k = 0.1, ..., n are generated. As already said, the correction terms kt (k) for the coefficients w (k) are intended to prevent the so-called coefficient hiking. 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 CD = -2π / T to ω = + 2π / T can affect. The undesired coefficient wandering can be recognized by an amplification of the spectral ranges not used by the useful signal, which are grayed out 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, the transfer function remains within the

Useful signal frequency band completely unaffected by this, so that the actual equalization is not impaired.

The following applies to the transfer function E (ω) of the equalizer: E (ω) = ∑ (i (k) ₊ jw _q (k)) e-3ωkτ / 2

= Ei (ω) + jE _q (ω)

= ∑W _j _ (k) cos ω ^ - + ∑w _q (k) sin ωk ^ -

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

Here, w _i (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 =. In order to reduce the transfer function outside the useful frequency band, the algorithm running in the processor PZ should form a zero or another fixed value of the transfer function at at least one specific frequency co ₀ <± π / T. The target function of the algorithm is thus:

| E) | = | E _; ) | ² + | E,) | [2)

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. This results in - for the amount of the transfer function.

| £) f = ∑w (*) costö ₀ A ^; + 2 (3)

and for your gradient:

(4)

T r

= 2 cos ω _J0o k, κ: ——2_ _| ww ((kk)) ccooss ωω ₀₀ kk —— ++ 22 ssimn ωω ₀₀ kk ——2_ _J w ^ ("k)] sin ω ₀ k

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

w „ ₊ , (k) = wχk) -a-sign [j (k)] (5)

w „(/ c) is the coefficient previously formed one time _cycle , and w _{ιl +]} (k) is the current one by adding the

Correction terms kt (k) = -a ■

coefficient resulting from the coefficient w _lt (k). Incidentally, for the sake of clarity, equation (5) does not take into account the change value for the coefficient w _n (fc) formed in the correlators KO, Kl according to, for example, the known CMA or LMSA algorithm.

In equation (5) is

T T

J (k) = W _c -COsω ₀ k - + W _s -s ω _o k— (6)

Here were the abbreviations

EW _c = T w (k) cos ω ₀ k—

(7) E

W _s = Yw (i) smω ₀ Λ: 2

used. Since only a very slight influence on the coefficients is desired (small), the Algorithm in practical operation to be simplified to a Signumform. 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 those frequencies 0) ₀ which allow a simple and periodic calculation of the trigonometric functions. The following frequencies are possible:

2π 3π, 4π ^ω _A => ^ω _B = ^ r and ω _c = - - (8)

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

2π 1. Case: ω. ~ - -

The following applies to this particularly simple case:

E sin «, k— = smkπ = 0 ^A 2

(9)

E cosω _A k - - coskπ = (-1) ^{A '}

and therefore

= 2 (~ l) ∑M> ik) (Xγ (10)

The complete algorithm for adapting the coefficients is therefore according to equation (5): w „ _{+ I} (k) = w„ (k) - 2a ^■ sign [(- l) ^k ∑ w (k) (- l) ^k (11) with

J _A = 2 (-lγ - ∑wχk) {- ϊ) ^k ; i2)

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).

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

L5 in comparison to the uncorrected transfer function shown in FIG. 1 has occurred.

4π

2nd case: ω. 3E

20 In this case:

T sϊnω _c k sin — kπ = 3 (z ^k )

(13) cosω _c k - cos-kπ = 'R (z ^k )

25

With the table:

applies:

^W c = ∑ ^W W cos ω _c k - = ∑ w (3k) - 0.5 ^ [w {3k + 1) + w (3k - 1)] (14)

T

W _s = ∑ w (k) sin ώ? _c k - = _Λ / Ö / 75 V [(3t +) - w (3 £ -)] (15)

2 '

Additional abbreviations are introduced to calculate the correction terms:

10

_ W = Σw (3k-l)

W _d = ∑w (3k)

15 ^w + x∑ ^{w k + l} ) (16)

WD = W ₊₁ -W_ _x

WS = W _^ . + w

30

So:

J _c {3k - 1) = - _Λ / Ö / 5 ^■ W _s - 0.5 ■ W _c = - (-3WD ^■ -2WχWS)

25 J _c (3k) = W _c (17)

J _c (3 / c + 1) = +70/75 • W _s - 0.5 ^• W _c = - (+ 3FE - 2PF ₀ + FFS ')

While in the 1st case r A according to equation (12) for everyone

30 coefficients W (k) applies, must in the second case for three different coefficient groups w (3k-l), w (3k) and w (3k + l) can be distinguished.

A very efficient correction of the coefficients 5 results when the 1st and 2nd cases are combined:

X »( ^k ) = ^w _n ( ^k ) ~ _A ^■ sign [j _A (k)] - a _c ^■ sign [J _c (k)] ( ¹⁸ )

- _] _0 As Figure 4 shows, the adaptive correction causes the

Coefficients _w (fcΛ according to equation (18) greatly reduce the spectral ranges outside the useful signal spectrum.

_5 Instead of, as shown in Figures 3 and 4, by the

Correction To force zeros in the transfer function, the transfer function can also be set to a constant value (e.g. 1) at certain frequencies.

20

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 ones can also be used

25 frequencies can 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 (D) so that the transfer function (E (ω)) of the equalizer or a first and / or higher derivative 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

Derivation 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.