GB2236036A

GB2236036A - Fine-tuning of a transversal equalizer

Info

Publication number: GB2236036A
Application number: GB9017904A
Authority: GB
Inventors: Risto Kari
Original assignee: Nokia Data Systems Oy
Current assignee: ICL Personal Systems Oy
Priority date: 1989-08-24
Filing date: 1990-08-15
Publication date: 1991-03-20
Anticipated expiration: 2010-08-15
Also published as: FR2653622B1; SE9002672D0; FI83010C; FI83010B; GB9017904D0; FR2653622A1; DE4021641A1; SE512377C2; SE9002672L; GB2236036B; FI893987A0

Abstract

The invention relates to a method for the fine-tuning of a transversal equalizer used in the receiver of a data communication system by means of a short, non-periodic signal sequence contained in the received signal immediately after the determination of the initial values of the equalizer coefficients on the basis of a received training sequence. The time required for the fine-tuning and the used signal sequence can be substantially reduced when only pan of the frequency components of the equalizer transfer function are subjected to fine-tuning while the rest maintain the values they had before the fine-tuning. <IMAGE>

Description

P6507GB A method for the fine-tuning of a transversal equalizer used in

the receiver of a data communication system The invention relates to a method for the finetuning of a transversal equalizer used in the receiver of a data communication system by means of a short, non-periodic signal sequence contained in the received signal.

In a synchronous data communication system, the data to be transmitted is in the form of a sequence of bits. In the transmitter (such as a modem) the bits are converted into signalling symbols which are then transmitted over the communication channel at a given signalling rate 1/T, where T is the symbol interval. In the receiver (such as a modem), the received symbols are detected and again converted into a sequence of data bits. The communication channel degrades the transmitted signal by various sources of interference, including linear distortion (amplitude and delay distortion) and noise. To alleviate this problem, the system may be provided with an adaptive equalizer, such as a digital transversal filter with variable tap coefficients and a tap interval T' equal to or smaller than (fractionally-spaced equalizer) the symbol interval T of the signal. In a typical method for the calculation of the initial values of the coefficients of this kind of transversal equalizer, the data transmitted over a communication channel is preceded by a known periodic sequence of symbols called a training sequence. The transfer function H(k) of the channel is estimated by first calculating the discrete Fourier transform (DFT) R(k) of at least one period of the received training signal and then dividing it with the DFT S(k) of the 2 transmitted training sequence. The transfer function C(k) of the equalizer is obtained from the ratio C(k) = A(k)/H(k), where A(k) is the reference spectrum, that is, the desired equalizer transfer function (the common transfer function of the communication channel and the equalizer). The equalizer coefficients are obtained by inverse DFT of C(k). This kind of method is described e.g. in FI Patent Application 891186 and in Rapid Training of a Voiceband DataModem Receiver Employing an Equalizer with Fractlonal-T Spaced Co effi-ci-ents, IEEE Transactions on Communications, Vol. COM-35, p. 869-876, Oct. 1987.

A method utilizing a periodic training signal gives as a solution an aliased version of an equalizer of indefinite length. In theory, this aliased equalizer may appropriately equalize the channel at a plurality of uniformly spaced discrete frequencies, whereas intermediate frequencies cannot be appropriately equalized as the channel transfer function is not known at these frequencies.

As soon as the equalizer coefficients have been calculated and the initialization of the other operations of the receiver has been completed, the receiver is ready for operation and the equalized samples for the carrier follower and detector can be calculated at a rate 1/T. At this point, there may be several symbols of the training sequence left before an arbitrary data signal appears in the output of the equalizer. This period of time can be utilized for the fine-tuning of the equalizer, because the training sequence is known by the receiver. It is also possible to transmit a few signalling symbols at a low bit rate between the training sequence and a subsequent arbitrary data signal. As a consequence, the signal occurring in the delay line of the 3 equalizer during the last symbols of the training sequence is no longer cyclic. So it would be possible to train the equalizer during a f ew symbol intervals by means of a partly arbitrary signal which would provide information about the channel at the abovementioned intermediate frequencies as well.

Previously it has been suggested to use a stochastic gradient algorithm for updating tap coeff icients in f ine-tuning (cf. the article mentioned above). In general, however, a short training sequence is aimed at, so that only a few symbols are available for fine-tuning and the improvement achieved by the gradient algorithm is rather small. A more accurate finetuning by means of a gradient algorithm is achieved only by increasing the length of the training sequence. If the signal sequence to be used in the fine-tuning is formed merely by increasing the number of periods in the original periodic training sequence, the gradient algorithm converges slightly more rapidly than with an arbitrary data signal, but not necessarily in the right direction. This is because with a cyclic training sequence the gradient algorithm tends to change the equalizer coefficients so as to optimize cyclic equalization and minimize noise amplification. Therefore the signal sequence to be used should be nonperiodic.

If the receiver should have a very rapid startup, the length of the training sequence cannot be increased. Instead, the converging rate of the gradient algorithm has to be increased in one way or another or a completely new technique has to be f ound for fine tuning the equalizer. The number of operations required by the fine-tuning method should not be much greater than that required for updating the equalizer 4 coefficients during data transmission.

The object of the present invention is to provide a new fine-tuning method which avoids the abovedescribed problems.

This is achieved by means of a method according to the invention which is characterized in that only part of the frequency components of the equalizer transfer function are subjected to fine-tuning while the rest maintain the values they had before the fine-tuning.

It is assumed in the invention that the aliased equalizer achieved by me. ?lns of the basic method is sufficiently good at N discrete frequencies at which the properties of the channel were estimated by means of the training sequence. So the transfer function of the equalizer can be kept constant during the finetuning at most of these frequencies, so that the number of adjustable parameters and, accordingly, the number of operations required for updating the equalizer can be reduced - considerably. For instance, it is thereby possible to fine-tune the equalizer many times by using one and the same received signal sequence. This signal sequence may now be rather short, because the number of adjustable parameters (frequency components) is smaller than the number of equalizer taps. In practice, the fine-tuning may utilize the non- eriodic signal sequence formed by a few known symbols at the end of the training sequence. Decrease in the number of adjustable equalizer parameters does not, however, necessarily affect the converging rate of one iteration cycle, because all the frequencies of the transfer function of the equalizer converge substantially independently of each other.

The fine-tuning method of the invention, in which the equalizer transfer function is locked partly, also enables the use of non-iterative methods, because the number of adjustable parameters is low, so that the criterion of minimum square error can be applied.

The invention will now be described in greater detail by means of examples with reference to the attached figure, which illustrates the transfer function of one particular equalizer.

The general structure and operation of the communication system and the transversal equalizer are obvious to one skilled n that art, see the abovementioned article and FI Patent Application 891186. The invention can be applied in equalizers described in them or in other equalizers.

The principles of the method used for the determination of the coefficients of the transversal equalizer are also discussed in the above -mentioned_ article and FI Patent Application 891186.

Prior to the data transmission, the transmitter sends a periodic training signal. The transmitted signal propagates through the data communication channel. At the receiver, the incoming signal is monitored continuously for the presence of the periodic training signal. When the presence of the training signal is observed, one period r(n) is extracted from the received signal and used for the calculation of the equalizer tap coefficients. The sequence r(n) is obtained by copying from the delay line of the equalizer, as described in the abovementioned article, for instance.

The discrete Fourier transform of the T/2spaced equalizer is calculated by means of the prior art cyclic basic method

6 C(k) = A(k)D(<k>M)/R(k), k = 0, 1 N-1 (1) where D(k) and R(k) are the discrete Fourier transforms of the transmitted training sequence and the received training sequence, respectively, N = 2M is the number of the equalizer coefficients with a T/2spaced equalizer, M is the number of symbols per one period of the training sequence, and <>M means the modulo-Moperation. The previously defined reference spectrum A(k) satisfies the Nyquist criterion, that is A(k)+A(k+M) = 1, k = 0,1,...,M-1, (2) where k and k + M are a frequency pair (e. g. the frequencies A and B in the attached figure) which will be aliased at the same frequency in the equalizer output (frequency A in the figure). The reference spectrum A(k) can be assumed to be real with all values of k.

As described above, a non-periodic signal having a length of several symbols is available at the end of the training signal sequence bef ore the proper data. Transmitted symbols corresponding to the non-periodic signal are either accurately known (training sequence) or can be detected reliably by means of an equalizer obtained by the above-mentioned prior art method (signalling symbols possibly following the periodic training sequence at a low transmission rate). In the preferred embodiment of the invention, the equalizer is fine-tuned by means of this received nonperiodic sequence so as to minimize the errors and distortions caused by the communication channel in this particular signal.

In the preferred embodiment of the invention, 7 the transfer function of the equalizer is kept constant during the f ine- tuning at frequencies where A(k) is 0 or 1 (preferably all the other frequencies except those f alling within the Nyquist ramps). For the other frequencies the transfer function of the equalizer is determined by f ine-tuning the reference spectrum by varying the spectral components in pairs.

When the transfer function of the equalizer is kept constant at part of the frequencies, the equalizer impulse response can be expressed Nú_1 c(i) = C,(i)+E[xqc,(i)+(1-X,)cqt(:!)], i=0,1.... N, (3) q= where cf(i) is the impulse response corresponding to the locked frequencies of the equalizer transfer function and Nf is the number of fine-tuning parameters. The end portion of the equation is formed by the pairs of the impulse responses cq(i) and cq'(i), where q 0, 1,_,Nf-1, each impulse response pair corresponding to a pair of two fre quencies which are aliased at the same f requency in the equalizer output and which are obtained as in verse discrete Fourier transforms of the ratios D(k)/R(k) and D(k+M)/R(k+M) with predetermined values of k. These impulse response pairs are weighted by real number coefficients x q and (1-xq) which with each value of q correspond to A(k) and A(k+M) with some value of k. Equalization at intermediate f re quencies can be affected by varying the weighting coefficients of these frequency pairs without affect ing the cyclic equalization of the equalizer.

Since the transfer function of the equalizer can be kept constant at most frequencies during the 8 fine-tuning, the number of adjustable equalizer parameters will be relatively low. For instance, if the period of the training sequence is 24T and the extra channel band width is 20%, the number of tap coefficients in a T/2-spaced equalizer is 48 whereas the fine-tuning of the equalizer requires only 5 real parameters. As used in the attached figure, the extra band width of 20% refers to the frequency range falling outside the frequency range between -T/2 and T/2.

Many iterative and non-iterative methods and algorithms can be used for fine tuning an equalizer locked partly in the manner of the invention. One way is to use a stochastic gradient algorithm used widely in updating equalizer coefficients. The error function of the average square sum between the transmitted signal sequence and the corresponding sequence appearing in the equalizer output can be applied as an error criterion, for instance. The converging rate of the gradient algorithm, however, is so low that it requires too many iteration cycles to achieve sufficient equalization, especially with severely distorted channels.

In the preferred embodiment of the invention, a non-iterative algorithm is used in place of a gradient algorithm. The non-iterative algorithm solves the fine-tuning parameters or weighting coefficients at one step. The use of non-iterative algorithms in the method of the present invention is practical and possible because the number of the parameters to be solved is very small and the parameters are real.

In the preferred embodiment of the invention, a non-iterative algorithm is used in which the error function of the minimum square sum is applied as a 9 performance criterion ni N-1 12, J, E 1 E d(n)-c,(i)r(2n-i) (4) n=n, i=o where r(n) is the sequence of samples taken from the received signal at a sampling rate 2/T and d(n) is the sequence of the transmitted symbols. When applying this criterion, the equalizer coefficients are solved in such a way that the power of the difference sequence between the transmitted signal sequence d(n) and the received sequence r(n) appearing in the equalizer output is minimized within a predetermined control time interval. The summing limits no and nj are selected so that the errors are calculated by using the non-periodic portion of the received training sequence. When part of the equalizer transfer function is kept constant during the fine-tuning, the error criterion can be expressed ni Nf- 1 1 2, J,, = E id(n)-y(n)- E x q z 9 (n) (5) n=n, q=0 where y(n) and zq(n) are the output sequences of Nf+1 fixed transversal filters, N-1 Nf_1 y(n) = E [cf(i) + E c q 1 (i)] r (2n-i) (6) i=0 q=0 N-1 Z,,(n) E EcqM-C,'(i)]r(2n-i), q=0,1...,Nf-1 (7) i=o Eq. (5) can be rewritten in matrix form ni T J. E id(n)-y(n)_X n Z. 1 2 (8) n=n, T n where X n ={X 0 ' Xl, X.,f_,.n} is a vertical vector formed T by fine-tuning parameters, and Z, = Z,(n), zl(n),..., Z.._,(n). If the equalizer parameters xq are assumed to be real, the gradient of Eq. (8) relative to the term Xn is ni Nf_1 G, Wn/2dX,, = E Re{z q (n)Ey(n)+ E xPzP(n)-d(n)]} (9) n=n, P= Aj-B,, where the elements of the matrices A, and B, are obtained from the equations n.

apqn = E Re{z.(n)zP(n)}, p,q=0,1,...,Nf-1 (10) n=no ni bn q = E Re{z,,(n)[d(n)-y(n)1}, q=0,1,...Nf-l. (11) n=n, The fine-tuning parameters xq., which minimize the error criterion 8, are obtained by setting the gradient to zero and by solving the resulting Nf linear equations. The solution is in the matrix form X = An- 1Bn. (12) 11 In practice, Eq. (12) can be replaced with the equation X = (An+aI)-1Bno, (13) where a is a small positive constant which is added to the diagonal of the matrix to ensure that the inverting matrix is not singular. The constant also reduces the noise increasing effect of the resulting equalizer.

Since the real gradient of the error function is now known relative to the fine-tuning parameters, the equalizer can also be fine-tuned by using a deterministic gradient algorithm Xm+1 = Xm-a[(An+I)Xm-Bn] (14) where a is a step size parameter.

After the parameters xq have been solved, they are introduced into Eq. (3), which gives the equalizer impulse response.

The method of the present invention can be easily realized programmatically in existing transversal equalizers when the setting of the initial values of the equalizer takes place by first determining the channel and equalizer frequency responses at N discrete frequency points.

The above examples are only intended to illustrate the invention. In its details, the method of the invention may vary within the attached claims.

12

Claims

Claims:

1. A method for the fine-tuning of a transversal equalizer used in the receiver of a data communication system by means of a short, non-periodic signal sequence contained in the received signal immediately after the determination of the initial values of the equalizer coefficients on the basis of a received training sequence, characteri z e d in that only part of the frequency components of the equalizer transfer function are subjected to fine-tuning while the rest maintain the values they had before the fine-tuning.

2. A method according to claim 1, c h a r a c t e r 1 z e d in that the frequency components of the equalizer transfer function corresponding to reference spectrum frequency components having a value 1 or 0 are maintained unchanged during the_ fine-tuning.

3. A method according to claim 1 or 2, c h a ra c t e r i z e d in that the equalizer transfer function frequency components to be fine-tuned are divided into groups of two frequency components aliasing at the same frequency in the equalizer output, and that one frequency component in each group is weighted by a weighting coefficient x and the other by a weighting coefficient (1-x).

4. A method according to claim 1, 2 or 3, c h a r a c t e r i z e d in that the equalizer transfer function frequency components to be finetuned are equalized in a direction in which the error between the transmitted signal sequence and the corresponding sequence appearing in the output of the equalizer is minimized.

5. A method according to claim 4, c h a r a c 13 t e r i z e d in that the error function of the minimum square sum between the transmitted signal sequence and the corresponding version appearing in the equalizer output Is applied as an error criterion.

6. A method according to claim 4, c h a r a c t e r i z e d in that the error function of the average square sum between the transmitted signal sequence and the corresponding version appearing in the equalizer output is applied as an error criterion.

7. A method according to claim 6, c h a r a c t e r i z e d in that the fine-tuning is carried out once or several times in succession iteratively by means of the same signal sequence.

8. A method according to claim 1 and substantially as hereinbefore described.

9. Any novel feature or combination of features described herein.

Published 1991 at The Patent Office. State House, 66171 High Holborn, London WC I R 47P. Further copies may be obtained from Sales Branch. Unit 6, Nine Mile Point Cwmfelinfach. Cross Keys, Nrt NPI 7HZ. Printed by Multiplex techniques lid, St Mary Cray. Kent.