JP2002522963A - Dynamic sampling of transmission channels - Google Patents

Abstract

SUMMARY OF THE INVENTION The present invention relates to a training sequence (TS) and a method for sampling a transmission channel which is subject to a temporal variation (d) from a received signal (s) corresponding to this sequence. By the measurement matrix (M) constructed from the considered training sequence (TS). The method includes steps for generating an impulse dynamic response of this channel by a least-squares technique, such as a combination of a static response (r) having a component of (d + 1) and a temporal shift (r '). Including.

Description

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a transmission channel sampling method. In other words, the present invention proposes a method for estimating the impulse response of a transmission channel.

In a transmission system, a transmitter transmits a signal in a transmission channel toward a receiver, particularly by radio waves. Since the transmitted signal is subject to variations in the amplitude and phase of the transmission channel, the signal received by the receiver is not the same. Signal variations are essentially due to what those skilled in the art refer to as intersymbol interference. This interference can result from the modulation rules used for transmission. It also depends on the propagation of multiple propagation paths in the channel.

[0003] In fact, the different propagation paths utilized by the transmitted signal thus lead to various delays at the level of the receiver, and the received signal generally results from a large number of reflections in the channel. ing. The impulse response of the channel represents the total of these variations experienced by the emitted signal. Thus, the fundamental feature representing the transmission between the transmitter and the receiver is problematic there.

[0004] The impulse response of the channel is used in particular by equalizers, which just do the job of correcting intersymbol interference in the receiver. A conventional way of performing this impulse response estimation consists in placing in the emitted signal a training sequence formed from the recognized codes. This sequence is selected according to the temporal variation of the channel and the modulation rule, where the variation is for a transmitted code utilizing the longest channel of the channel for the same code utilizing the shortest channel. Should be understood as a delay. Temporal variation is usually expressed as a number of times, or "code times," separating two consecutively transmitted codes.

[0005] Known techniques speculate that the impulse response of the channel remains constant for a relatively short time. However, this is not the case when the relative speed of the receiver to the transmitter is relatively large. This is also not the case when the conditions of propagation between these two devices change rapidly, for example when a moving object temporarily blocks at least one of the propagation paths of the channel.

Thus, the present invention is directed to a transmission channel sampling method having significantly improved performance in a mobile environment.

According to the present invention, a sampling of a transmission channel which is affected by a temporal variation d from a training sequence and a received signal corresponding to this sequence is performed, which is constructed from the training sequence taking this temporal variation into account. According to the measurement matrix. This method generates the impulse dynamic response of this channel by a least-squares technique, such as the combination of a static response r with a component of (d + 1) and a temporal and thus time-dependent deviation r ′. Including the stage.

For the most straightforward implementation of the method, the received signal is given by the equation s = M. r + TM. r
'+ N, where T is a time matrix representing time and n represents received noise, and the temporal shift also includes a (d + 1) component.

[0009] However, this method may require relatively complicated calculations. This is even more so because of large time variations.

Thus, according to another implementation of the method, the static response r is given by the equation s = M. r + n (
Where n represents the received noise).

Furthermore, according to a first application, the method comprises the step of determining an eigenvector r ₀ coupled to the largest eigenvalue of the covariance of the static response r, wherein the temporal shift r ′ is The value of the product of the coefficient α ₀ and this eigenvector is represented by the following equation: r + α ₀ TM. r ₀ +
n.

Conveniently, the shift coefficient substitutes the variance σ ^2, which is calculated by the equation σ ² / (σ ² + N ₀ ), where N ₀ represents the module of the received noise. For weighting.

It can be expected that the module of the received noise is equal to the minimum of the eigenvalues of the covariance of the static response.

It can also be expected that the module of the received noise is obtained by energy normalization of the instantaneous noise.

According to a second application, the method comprises the step of calculating a plurality of eigenvectors r of the covariance of the static response. _i And the received signal is

[0016]

(Equation 2)

(Where α _i is a shift coefficient substituted into the eigenvector r _i ).

On the other hand, the present invention contemplates the case where the relative speed of the receiver to the transmitter is large. In this case, the received signal s is given by the equation s = M. r + TM. r ′ + ／ (T ² M.r
") + N, where T is a time matrix representing time and n represents received noise.

As before, the static response is given by the equation s = M. r + n, where n represents received noise.

The method also includes eigenvector r ₀ coupled to the largest eigenvalue of the covariance of the static response.
, And the received signal is given by the equation s = M.r + β ₀ TM.r ₀ + ／ (β ₁ T ² M.r ₀ ) + n (where β ₀ and β ₁ are shift coefficients) Is).

The present invention will now appear in greater detail in the following description, with which examples are proposed by way of illustration, with reference to the accompanying drawings, in which:

Elements common to the figures have been assigned a single reference symbol.

The present invention is shown as applied to GSM. This system has the advantage of being well known to those skilled in the art. Thus, the introduction employed with concern for clarity is at issue here, but in no event should the admission be made that the invention is limited to this sole system.

The system relies on a training sequence TS formed from 26 codes a ₀ to a ₂₅ taking the values +1 or −1. These codes emitted by the transmitter are known to the receiver and therefore, by any means, in the term "training sequence", any bits known a priori of this receiver Summarize the sequence.

The sequence of codes s received by the receiver, corresponding to the training sequence TS transmitted by the transmitter, is also formed from the 26 codes s ₀ to s ₂₅ .

For the rappel, the estimation technique relies on a measurement matrix M consisting of a training sequence TS of length n. This matrix includes (nd) rows and (d + 1) columns, where d always represents the time variation of the channel. The element that appears in the i-th row and j-th column is the training sequence

[0027]

(Equation 3)

Is the (d + ij) -th code.

The training sequence consists of the operators. ^{Where t} represents the intersection, the matrix M ^t M has been chosen to be reversible.

Conventionally, when the impulse response is considered to be time-independent, the time variation of the channel having a value of 4 in the case of GSM is denoted by d, and the estimation of this response is performed in the form of a vector having five components. Take. If we take the least squares technique, this vector is (M ^t M) ⁻¹ M ^t . Worth s.

According to the present invention, and referring to FIG. 1, the impulse dynamic response is represented by the equation s = M. r + TM. r ′ + n (1) (where n represents the additive noise in the transmission channel and T is a matrix representing the time to receive different codes, this time being the code time

[0032]

(Equation 4)

(Represented by .times..times..times..times..times..times..times.).

In fact, T is an element of dimension 22 in which the element appearing at the ith row and ith column represents the time corresponding to the (d + i) th code of the training sequence, ie, a _{(d + i−1)} . A diagonal matrix, where the time origin is arbitrarily fixed between the fifteenth and sixteenth codes.

Assuming that M ′ = TM, equation (1) is equivalent to the following two equations M ^t . s = ^MtM . r + ^MtM '. r ′ + M ^tn M ′ ^t . s = ^M'tM . r + M ' ^t M'. It is represented by r ′ + M ′ ^t n.

The system of equations can be solved in the form of a matrix in the least squares direction.

[0037]

(Equation 5)

Therefore, the impulse dynamic response CIR is calculated from the five components of the static response r and the time shift r
'Is shown as a vector with ten components formed by the five components. The result is that relatively complex calculations are required compared to conventional methods.

To limit this complexity, according to a first application of the invention, the dynamic response is limited to six components. Of which, there are five components for the static response and one for the temporal shift.

Referring to FIG. 2, a static response r is first calculated by any one of the known techniques.
When taking the least squares method, this static response is obtained as follows. r = (M ^t M) ⁻¹ M ^t . s

On the other hand, a smoothing matrix L is constructed by smoothing the different responses obtained for successively transmitted training sequences, which makes it possible to estimate the covariance combined with this static response. To get it. Here, smoothing is understood in a very general sense. That is, any operation that can mediate a smoothing or static response.

The first example of smoothing consists of averaging the matrix rr ^h over the period assumed to contain m training sequences, and the operator. ^h is Hermitian transformation

[0043]

(Equation 6)

Represents

A second example of smoothing consists in realizing, in the received i-th training sequence, the smoothing matrix obtained in the (i−1) -th training sequence by a multiplication factor λ, this factor Is generally the smoothing omission factor (fact
eur d'ubli) and ranges from 0 to 1. ^{_{L i (rr h) = λr}} i r i h; (1-λ) L i-1 (rr h)

The initialization can be done by any means, in particular by the first estimate r obtained, or by the average obtained above when the number of training sequences is small.

At this time, an eigenvector r ₀ combined with the maximum eigenvalue of the matrix L (rr ^h ) is obtained.

U ₀ = M. r ₀ and repeat the same convention as before, the received signal is of the form s = M. r + α ₀ T. Suppose u ₀ + n (2).

The temporal shift corresponds to the term α ₀ r ₀ .

Let I be an identity matrix and introduce a transformation operator A. A = I−M (M ^t M) ⁻¹ M ^t

Equation (2) then becomes the following equation: s = α ₀ AT. u ₀ + A. n.

U ′ ₀ = T. Let u _0, and the solution of this equation in the least squares direction be the coefficient α ₀
Estimate of

[0053]

(Equation 7)

Is shown.

[0055]

(Equation 8)

This estimation is not circuitous and the module of additive or received noise is N ₀ And the estimation error is

[0057]

(Equation 9)

A variance having a value of

Therefore, the additional noise N ₀ should be estimated.

The first solution consists in substituting a predetermined value for N ₀ below which reflects a threshold value at which the additional noise is unlikely to fall. This value can be determined by measuring the signal-to-noise ratio or by the performance of the receiver,
This is an example.

A second solution consists in considering that the (minimum) last eigenvalue of the smoothing matrix L is equal to N ₀ .

A third solution, perhaps the most sophisticated, consists of directly estimating the additive noise from the received signal. In fact, s = M. r + α ₀ T. u ₀ + n

Considering that the vectors s and n have 22 components,

[0064]

(Equation 10)

Therefore, additional noise is obtained by energy normalization of instantaneous noise.

Of course, the estimation of the additional noise N ₀ may be mediated or smoothed.

Conventionally, the estimation coefficient

[0068]

[Equation 11]

Reducing the variance of

[0070]

(Equation 12)

It is possible if one accepts means for adding a weight to this coefficient in order to obtain

[0072]

(Equation 13)

When the transmission channel is stationary, the variance σ ² also goes to zero.

[0074]

[Equation 14]

Note that goes to zero.

Referring to FIG. 3, according to a second application of the present invention, there are seven components, of which five components for static response and two for temporal shift. Adopt the impulse dynamic response having.

As before, the static response r is calculated by any one of the known techniques.

At this time, the first eigenvector r ₀ combined with the maximum eigenvalue of the smoothing matrix L
And a second eigenvector r ₁ coupled to the eigenvalues immediately below the matrix L is also determined.

U ₀ = M. r ₀ , u ₁ = M. r ₁ and repeat the same convention as before, the received signal is of the form s = M. r + α ₀ T. u ₀ + α ₁ T. Suppose u ₁ + n (3).

The temporal shift corresponds to the term α ₀ r ₀ + α ₁ r ₁ .

The conversion operator A is repeated. A = I−M (M ^t M) ⁻¹ M ^t

Equation (3) is then given by the following equation: s = α ₀ AT. u ₀ + α ₁ AT. u ₁ + A. n.

U ′ ₀ = T. u ₀ and u ′ ₁ = T. Solving this equation in the least-squares direction, with u ₁ , gives estimates of the coefficients α ₀ and α ₁ ( ₀ and ( ₁

[0084]

(Equation 15)

Of course, in order to estimate the impulse dynamic response by an arbitrary number (q + 1) of eigenvectors of the smoothing matrix L, if this number (q + 1) is smaller than the dimension of this matrix, the above-described method will be used first. And for the second application.

At this time, the eigenvector u ₁ is set so that the received signal is expressed as follows:
Are assigned to α _i , u ₁ = M. r ₁ and u ′ ₁ = T. u ₁ .

[0087]

(Equation 16)

The temporal shift is

[0089]

[Equation 17]

Corresponds to the term

At this time, the element g _ij appearing in the i-th row and the j-th column is

[0092]

(Equation 18)

It is necessary to determine a new matrix G having the value of

The solution is thus as follows.

[0095]

[Equation 19]

According to a third application of the invention, the received signal s is given by the equation s = M. r + TM. As represented by r ′ + ／ (T ² M.r ″) + n, the impulse dynamic response is described by the combination of the static response r and the temporal second-order shift.

According to this application, which is particularly well suited for high velocities, the impulse dynamic response has five components of the static response r and ten components of the temporal shift (5 for r ′ and r for r ′). 5 ") as a vector with 15 components.

To limit the computational complexity required, five components are always preserved for the static response, and two components for the temporal shift, one for r ′ and one for r ′. It is convenient to take one for r "and only seven components for the dynamic response.

Referring to FIG. 4, as before, the static response r is first calculated by any one of the known techniques.

At this time, an eigenvector r ₀ combined with the maximum eigenvalue of the smoothing matrix L is obtained.

Repeating the same convention as above, the received signal is of the form s = M. r + β ₀ T. It is assumed that u ₀ + （(β ₁ T ² .u ₀ ) + n (4).

Assuming that u ″ ₀ = １ ／ (T ² .u ₀ ), equation (4) is then represented by the following equation: s = Mr + β ₀ u ′ ₀ + β ₁ u ″ ₀ + n

The solution of this equation in the least squares direction is done in the following way.

(Equation 20)

Those skilled in the art will use the impulse dynamic response of the present invention, for example, in an equalizer, as if the prior art impulse response was a problem. In fact, for the code received at the referenced instant, it is sufficient to calculate the exact dynamic response at this instant from any one of the general formulas appearing above.

The present invention is not limited to the embodiments described above. In particular, any means can be replaced by means of equal value.

[Brief description of the drawings]

FIG. 1 is a basic diagram of the method according to the invention.

FIG. 2 is a basic diagram of a first application example of the present invention.

FIG. 3 is a basic diagram of a second application example of the present invention.

FIG. 4 is a basic diagram of a third application example of the present invention.

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Ben Ratchad, Nidoham France F-75017 Paris, Lyubaron, 32F term (reference) 5K029 AA03 CC01 HH05 HH13 KK21 KK31 5K046 AA05 EE06 EE19 EE47 EF05 EF13

Claims (11)

[Claims] 1. A method of sampling a transmission channel which is subject to a temporal variation d from a training sequence (TS) and a received signal (s) corresponding to this sequence, wherein a measurement matrix (M) determines the temporal variation. Impulse dynamics of this channel by a least squares technique, such as a combination of a static response (r) with a (d + 1) component and a temporal shift (r '), constructed from the considered training sequence (TS) A method comprising generating a response (CIR). 2. The received signal (s) is given by the equation s = M. r + TM. r ′ + n, where T is a time matrix representing time and n represents received noise, wherein the temporal shift (r ′) also includes a (d + 1) component. The method according to claim 1, wherein 3. The static response (r) is given by the equation s = M. The method of claim 1, constructed by r + n, where n represents received noise. 4. Estimating an eigenvector (r ₀ ) coupled to the largest eigenvalue of the covariance of the static response (r), wherein the temporal shift (r ′) is determined by a shift coefficient α ₀ and the eigenvector (R ₀ ), the received signal (s) is given by the equation s = M. r + α ₀ T
M. The method according to claim 3, characterized in that it is determined by r ₀ + n. 5. The deviation coefficient (α ₀ ) is obtained by substituting the variance σ ² into the equation σ ² / (σ ² +
N ₀₎ (where, N ₀ The method according to claim 4, characterized in that it comprises a step for providing weights to the coefficients by representing) the module of the received noise. 6. The reception noise module (N ₀ ) includes: a static response (r).
6. The method according to claim 5, wherein the eigenvalues of the covariances are selected equal to the minimum. 7. The method according to claim 5, wherein the module of received noise (N ₀ ) is obtained by energy normalization of instantaneous noise. 8. include determining a plurality of eigenvectors of the covariance said static response (r) (r _i), the received signal (s) is ## EQU1 ## 4. The method of claim 3, wherein α _i is determined by: where α _i is the shift coefficient substituted for the eigenvector r _i . 9. The reception signal (s) is expressed by the equation s = M. r + TM. r '+ 1/2
^{(T 2 M.r ") + n} ( where, T is the time matrix representing time, and n represents a received noise) The method according to claim 1, characterized in that determined by. 10. The static response (r) is given by the equation s = M. 10. The method of claim 9, wherein the method is constructed by r + n, where n represents received noise. 11. The eigenvector coupled to the largest eigenvalue of the covariance of the static response (r).
Kutor (r₀), Wherein the received signal is given by the formula: s = Mr + β₀TM.r ₀ +1/2 (β₁T^TwoM. r₀) + N (where β₀And β₁Is the deviation coefficient)
11. The method of claim 10, wherein the method is determined.