EP1084547A1

EP1084547A1 - Method for fine synchronisation on a signal received from a transmission channel

Info

Publication number: EP1084547A1
Application number: EP99914586A
Authority: EP
Inventors: Jean-Louis Dornstetter; Nidham Ben Rached
Original assignee: Nortel Matra Cellular SCA
Current assignee: Nortel Networks France SAS
Priority date: 1998-04-10
Filing date: 1999-04-09
Publication date: 2001-03-21
Also published as: WO1999053645A8; FR2777408A1; WO1999053645A1; CA2328293A1; CN1300488A; FR2777408B1

Abstract

The invention concerns a method for fine synchronisation on a reception signal (S) corresponding to a reference signal (TS) transmitted in a transmission channel, comprising the following steps: selecting a signal source producing a characterisation signal (X) following its passage in the transmission channel; establishing a characterisation matrix (L) to estimate the characterisation signal (X) covariance; identifying characteristic modal values which are the highest characteristic values (μi) of said characterisation matrix (L); computing the source signal correlation function c(t) with the sum of characteristic vectors (vi) associated with the characteristic modal values; searching said correlation function c(t) first maximum.

Description

Fine synchronization method on a signal received from a transmission channel

The present invention relates to a method of fine synchronization on a reception signal corresponding to a reference signal transmitted in a transmission channel.

In a transmission system, in particular by radio waves, a transmitter transmits a reference signal in a transmission channel intended for a receiver. One of the first operations that the receiver must perform is synchronization on the reception signal. This problem is well known to those skilled in the art and it is therefore not necessary to recall here the different techniques which are used to obtain this synchronization. When the signals are digital, it is customary to evaluate the synchronization difference by means of a time unit, the bit time, which is the time difference separating two successive bits of a signal. However, it appears that the solutions available in the state of the art do not make it possible to acquire a much more precise synchronization than bit time.

This precision may prove to be insufficient in certain cases. In fact, it is synchronization which gives the signal journey time in the transmission channel or, in other words, the transmission time between the transmitter and the receiver. This is important because, in a duplex radiocommunication system where a base station is in communication with a terminal, each piece of equipment being provided with a transceiver, the terminal must operate so that the signal it transmits arrives at a precise instant with reference to the time base of the base station. To do this, it is of course necessary for the terminal to know the time it takes for this signal to reach the base station. On the other hand, this transmission time directly reflects the distance between the transmitter and the receiver. We understands that the accuracy of this distance is fundamental when it comes to locating the terminal by locating its relative position with respect to one or more base stations. The general problem of locating a terminal is a very current concern because of its applications, among which we will cite, for example, strategies for cell change ("handover") in cellular networks. We will also mention the area of security, whether it is necessary to locate the origin of an emergency call or the position of a stolen vehicle equipped with the terminal.

The present invention thus relates to a synchronization method whose precision is much greater than the bit time.

According to the invention, the fine synchronization method on a reception signal corresponding to a reference signal transmitted in a transmission channel comprises the following steps: - selection of a source signal producing a characterization signal following its passage through the transmission channel,

- establishment of a characterization matrix to estimate the covariance of the characterization signal, - identification of the dominant eigenvalues which are the highest eigenvalues of this characterization matrix,

- calculation of the correlation function of the source signal with the sum of the eigenvectors associated with the dominant eigenvalues,

- search for the first maximum of this correlation function.

When the time increment adopted for the calculation of the correlation function is chosen to be sufficiently small, in any case much less than a bit time, this method makes it possible to obtain very good precision. According to a first option, the number of these dominant eigenvalues is predetermined. Typically, this number represents around 20 to 30% of the dimension of the characterization matrix. According to a second option, the ratio of the sum of the dominant eigenvalues to the sum of all the eigenvalues is greater than or equal to a predetermined number. Here, the number chosen will often be greater than 90%, 95% for example. According to a third option, the method further comprising a step of estimating the additive noise in the transmission channel, the dominant eigenvalues are such that their sum is less than or equal to the sum of all the eigenvalues minus the additive noise. In addition, the estimation of the additive noise is carried out by normalizing the instantaneous noise which is evaluated by means of the reception signal, the reference signal and an estimation of the impulse response of the transmission channel. Advantageously, by noting A to the transmission matrix associated with the reference signal, the expression of the instantaneous noise is as follows: N _Q = S - AX

In addition, whatever option is chosen, the characterization matrix results from a smoothing operation.

According to a preferred embodiment, the characterization signal is an estimate of the impulse response of the transmission channel.

It can also be provided that the characterization signal is the reception signal.

The present invention will now appear in more detail in the context of the description which follows, where illustrative examples are provided, this with reference to the appended figures which represent: FIG. 1, a first alternative embodiment of the invention, and

- Figure 2, a second variant.

The elements common to the two figures are assigned a single reference.

The receiver has already acquired coarse synchronization on the reception signal, of the order of bit time, using any of the solutions available.

This reception signal corresponds to a reference signal produced by the transmitter and known to the receiver. This reference signal can be known a priori, that is to say that it is a learning sequence formed from identified symbols. It can also be known a posteriori by means of techniques generically referred to as the blind survey. In this case, during the synchronization procedure, the receiver regenerates the series of symbols forming the reference signal from the reception signal.

It is first of all necessary to characterize the transmission between the transmitter and the receiver. To this end, a source signal is selected which, produced by the transmitter, gives to the receiver, after transmission in the channel, a characterization signal.

Naturally, if the source signal is the reference signal, this characterization signal is the reception signal itself. However, this is not always the optimal solution as regards the complexity and performance of the process of the invention.

Another solution consists in retaining a modulated pulse as the source signal, the characterization signal then becoming the impulse response of the transmission channel.

For example, the GSM digital cellular radio system uses a learning sequence of 26 symbols, the impulse response being generally estimated with 5 coefficients since it is admitted that the dispersion of the channel is worth 4.

In this case, the reception signal has a maximum dimension of 22 which is significantly larger than that of the impulse response.

We will therefore successively examine two alternative embodiments of the invention, starting with the case where the source signal is a modulated pulse with reference to FIG. 1. The estimation of the impulse response does not pose any difficulties in itself because of numerous methods make it possible to achieve this, for example the so-called least squares criterion method which is described in particular in patent applications FR 2696604 and EP 0564849. In terms of recall, this technique uses a measurement matrix A constructed at from the training sequence TS of length n. This matrix includes (n-d) rows and (d + 1) columns, d representing the dispersion of the channel. The element appearing in the ith line and in the jth column is the (d + i- j) th symbol of the training sequence, that is to note a ^ the th symbol of a TS sequence of 26 symbols:

The learning sequence is chosen such that the matrix A ^ A is invertible where the operator represents the transposition.

In the reception signal S, the first four symbols S _Q to S3 are not taken into account because these also depend on unknown symbols transmitted before the learning sequence, since the dispersion of the channel is worth 4. By an abuse of language one will henceforth define the reception signal as a vector S having for components the symbols received, S4, S5, s_, ..., S25. Consequently, the estimation of the impulse response X takes the following form:

X = (A ^t A) ^-1 A ^t . The next step of the method of the invention consists in establishing a statistic of this impulse response. By statistic, we mean a set of data reflecting the average value of this response over an analysis period.

We therefore construct a smoothing matrix of the different estimates X obtained during the analysis period to obtain an estimate of the covariance associated with this impulse response. Here, we mean smoothing in a very general sense, that is to say any operation making it possible to smooth or average the impulse response over the analysis period.

A first example of smoothing consists in carrying out the average of the matrix XX ⁿ over the analysis period assumed to include m learning sequences:

L (XX ^h ) = -Yxx ^h

The operator .h represents the Hermitian transformation or complex conjugation transposition. A second smoothing example consists in updating, after receipt of the ith training sequence, the smoothing matrix Li_ι (XX ⁿ ) obtained in the (il) th training sequence by means of a multiplicative coefficient α, this factor being generally known as smoothing forget factor and being between 0 and 1:

Li (XX ^h ) = αXiXi ^h + (l-α) Li _! (XX ^h ) Initialization can be done by any means, in particular by means of the first estimate X obtained or by an average obtained as above for a low number of training sequences. For the sake of simplification, the smoothing matrix L (XX ⁿ ) which is in fact a statistical characterization matrix, will henceforth be denoted L.

The method then comprises a step of searching for the pairs (eigenvalue, eigenvector) of the characterization matrix.

This step will not be more detailed as well known to one skilled in the art.

The eigenvalues λ ^ are now classified, in descending order. Indeed, the sum of these values corresponds to the energy of the characterization signal X composed partly of a useful signal which is the image of the source signal and partly of the additive noise N of the transmission channel. It follows that the dominant eigenvalues, those which are the highest, represent the useful signal, while the weakest eigenvalues represent the noise.

According to a first option, the method consists in retaining a predetermined number of dominant eigenvalues. For example, for an impulse response to

5 coefficients, we retain the first two eigenvalues λi and λ2 "

According to a second option, it is considered that the useful signal has an energy which is a predetermined fraction f of the energy of the characterization signal. Thus by noting λi the eigenvalues for i varying from 1 to p, there will be d dominant eigenvalues, d being obtained as follows:

d d + 1

Σ λ. Σ λ.

—— <f and ——> f

P P

Σ λ. ∑ λ. i = 1 i = 1

The fraction f can be set a priori, to a value of 95% for example. This fraction can also be derived the signal-to-noise ratio of the reception signal obtained elsewhere.

According to a third option of the method, undoubtedly the most efficient, the additive noise N is estimated directly from the reception signal and from the measurement matrix A. In fact, by noting N _Q the noise vector affecting the reception signal, it follows that: S = AX + N ₀ Taking into account that the vectors S and NQ have 22 components, the additive noise N can be expressed in the following way:

N = (-) (S - AX) ^h (S - AX)

Naturally, this estimate of the additive noise can be averaged in smoothness. By taking up the previous notations and normalizing the energies, it follows that:

P P

∑ λ. > N and ∑ λ. <N i = d i = d + 1

The dominant eigenvalues are therefore obtained from a direct estimate of the noise.

Whatever the option previously selected, the next step of the method consists in calculating the correlation function of the source signal with the sum of the eigenvectors VJ_ associated with the dominant eigenvalues λj_. The source signal is oversampled with respect to the bit time and it will therefore be noted g (t) where t which represents the time is a discrete variable whose quantization step is, for example, 1/32 bit time. It is represented by a vector of the same dimension as the characterization signal, ie 5 in the example adopted. The correlation function c (t) is calculated for example for t varying from -1 to +1 bit time by means of the following expression: dc (t) = ∑ g (t) .v _± i = 1

The point appearing between the source signal g (t) and the eigenvector v ^ classically represents the scalar product. The last step of the process consists in finding the value t ₀ of t closest to zero which corresponds to the first relative maximum of the correlation function c (t).

It is this particular value tg which gives the desired synchronization difference with respect to the reception signal.

Furthermore, we can consider the following complementary function c '(t): c' (t) = ∑ g (t). _Vi i = d + 1

It should be noted that the particular value to mentioned above can also be obtained by looking for the value of t closest to zero which corresponds to the first relative minimum of the complementary formation c '(t).

These two methods to obtain 1 * synchronization difference to are therefore equivalent.

With reference to FIG. 2, let us now consider a second variant of the invention according to which the characterization signal is the reception signal S, so that the source signal is now the reference signal, ie in the case of GSM, the modulated TS training sequence GMSK (for "Gaussian Minimum Shift Keying").

The statistics of the characterization signal are therefore estimated by means of a characterization matrix which is now obtained by smoothing the various occurrences of the reception signal S. Here again, the term smoothing is considered in a very general sense.

The characterization matrix L therefore takes the following form: h 1 ^m V.

L (SS ⁿ ) = - Y SS ⁿ or, m -?

Li (SS ⁿ ) = αS S ⁿ + (l-α) Li_ι (SS ⁿ )

We then look for the p 'eigenvalues λ'j. of this matrix and, as in the first variant, we identify the dominant eigenvalues.

We now calculate the correlation function f (t) of the modulated learning sequence and of the sum of the eigenvectors v '_ associated with the dominant eigenvalues

A. dd. Again, the learning sequence g '(t) is oversampled and is represented by a vector of

22 components. The correlation function therefore becomes:

d 'f (t) = ∑ g'ttJ.v i = 1 As before, we can define a new complementary function f' (t):

P 'f' (t) = ∑ g '(t) .v'. i = d '+ l The process ends in the same way by looking for the first maximum of the correlation function f (t) or the first minimum of the complementary function f (t).

The invention can thus be implemented in different ways, the essential point being to have a source signal and the result of its transmission, namely the characterization signal.

Claims

1) Method of fine synchronization on a reception signal (S) corresponding to a reference signal (TS) transmitted in a transmission channel, characterized in that it comprises the following steps:

- selection of a source signal producing a characterization signal (X, S) following its passage through said transmission channel,

- establishment of a characterization matrix (L) to estimate the covariance of said characterization signal (X,

S),

- identification of the dominant eigenvalues which are the highest eigenvalues (λ ^, λ '_) of this characterization matrix (L), - calculation of the correlation function (c (t), f (t)) of said source signal with the sum of the eigenvectors (v ^, v '^) associated with said dominant eigenvalues,

- search for the first maximum of this correlation function (c (t), f (t)). 2) Method according to claim 1, characterized in that the number (d, d ') of said dominant eigenvalues (λi, λ' is predetermined.

3) Method according to claim 1 characterized in that the ratio of the sum of said dominant eigenvalues to the sum of all eigenvalues is greater than or equal to a predetermined number.

4) Method according to claim 1 characterized in that, further comprising a step of estimating the additive noise (N) in the transmission channel, said dominant eigenvalues are such that their sum is less than or equal to the sum of all the eigenvalues minus said additive noise (N).

5) Method according to claim 4, characterized in that the estimation of the additive noise (N) is carried out by normalizing the instantaneous noise (N _Q ) which is evaluated by means of said reception signal (S), of said reference signal (TS) and an estimate of the impulse response (X) of the transmission channel.

6) Method according to claim 5 characterized in that, by noting A the transmission matrix associated with said reference signal (TS), the expression of instantaneous noise (NQ) is as follows: N _Q = S - AX

7) Method according to claim 6, characterized in that said additive noise (N) is more average.

8) Method according to any one of claims 1 to 7, characterized in that said characterization matrix (L) results from a smoothing operation.

9) Method according to any one of the preceding claims, characterized in that the said characterization signal is an estimate of the impulse response (X) of the transmission channel.

10) Method according to any one of claims 1 to 8, characterized in that said characterization signal is said reception signal (S).