WO2002041593A1

WO2002041593A1 - Method and device for blindly equalizing signals transmitted over time-variant transmission channels

Info

Publication number: WO2002041593A1
Application number: PCT/AT2001/000360
Authority: WO
Inventors: Harold ARTÉS; Franz Hlawatsch
Original assignee: Innovationsagentur Gesellschaft M.B.H.
Priority date: 2000-11-20
Filing date: 2001-11-15
Publication date: 2002-05-23
Also published as: AU2002223245A1; ATA19522000A; AT410870B; WO2002041593A8

Abstract

In order to blindly equalize signals transmitted over time-variant transmission channels, the respective time-variant transmission channel is modeled by diversifying it with a finite number of time-invariant subchannels. Two corresponding signal spaces (A', B') are derived from the received signals (x[n]) based on the diversity of the respective time-variant channel both in the time direction as well as in the frequency direction, and the equalized signal (s[n]) is derived from the intersection of these signal spaces.

Description

Method and device for blind equalization of signals transmitted over time-variant transmission channels

The invention relates to a method for blind equalization of signals transmitted via time-variant transmission channels, the respective time-variant transmission channel being modeled by diversification with a finite number of time-variant sub-channels.

Furthermore, the invention relates to a device for equalizing signals transmitted over time-variant transmission channels, with a receiving circuit and with a computer, the respective time-variant transmission channel being modeled by diversification with a finite number of time-variant sub-channels.

Transmission channels (hereinafter referred to as channels) generally add distortions to a transmitted signal, which the receiver receiving the signal must equalize in order to be able to detect the information transmitted with the signal. In the case of linear channels (to which special reference is made below), the distortions consist on the one hand of intersymbol interference and, on the other hand, of double (frequency) shifts. In order to equalize these distortions, it is usually assumed that the channel is known (for example, the channel is estimated using training symbols). In contrast, so-called blind methods equalize the received signal without knowing the channel and the transmitted symbols.

In mobile radio (in mobile telephony), the mobile radio channel is inherently a time-changing, ie time-variant channel due to the movement of the mobile station (ie the moving user) and the movement of some spreaders. (In the following, the usual abbreviation "LTV" (for "linear time-varying" - linear time-variant) is to be used for time-variant. Although the mobile radio channel is still largely time-variant today for reasons of simplicity ("LTI" - "linear time- invariant "-) channel, ^'is modeled not changing channel, but it shall be with increasing data rates and thus also with increasing transmission bandwidths in the future of advantage to channel his ^nature' that is, as one over short periods of linear time-invariant according to the time-variant In contrast to time-varying channels, 1 1 ιH o cd -H oil so W 1 - g ----------- -. H> c- φ 4J 4J oo CQ -bs -El d ω -

Φ CQ AI ü Φ φ ß o T Oil P N SH Φ H ß SH d CQ 4J SH <CQ cd Φ d SH: cd φ SH

-H Oil TJ cd Φ & Φ H ß CQ TJ> υ TJ N U 4-1 α. P 4-J CQ 4-J

-ß 4-1 TJ d d υ Φ SH d Φ

: cd P X N cd

TJ Oil Oil -§ ß φ M d N o Oil CQ Oil Φ S φ ß Φ p p CQ

CQ CQ: cd PO cd φ -d SH _^ . CD

TJ 5 -d SH ^ -— -. d

T Φ? - d cd J N CQ Φ m

4J 4-1 φ J CQ d

SH -b ---. P Dl o CQ o • H TJ d H d 4H φ

^• ä Φ Φ TJ

4J H SH 4-> SH d H d -b Φ P • rH Φ CQ cd -b φ N cd 4J

M rH cd N SH -H d rH cd d EH 4-> ß ß 4-1 d Φ -b d a cd Φ -H d 0 d g, 4-J, -d o g φ

1: tti P cd 1 K

H 4H H. 4H S cd EH J-> O ß SH Φ CQ SH ß J ß CQ Φ 4H o φ cd φ -b ß> rH T

K g cd Φ

Φ ra 4-1 d ffi Φ ω

SH ß φ SH -rH φ -b • H, Φ Φ φ -d 4J ra

TJ Φ .-. TJ N υ • H H cd

Oil g φ m

Φ • rH d Φ, 0

Oil Φ 4-1 0 & 4H ß CQ> g cd cd ß

: cd: ß cd: 0 d 4-1 cd vA • Oil 4-1 X cd -P

4-> SH SH W Φ φ -b. -. O: - =! φ s rH

-H ^• H & 4H -ddo

TJ Oil - - 4-1 φ φ -bdd ^• rt ^• H ε cd Oil cd g Φ TJ ^) d CQ m 4-1 CQ

-H ---. P ß ^"" CQ.

O Φ CQ -d P SH H ß

O -b rH Φ Φ o cd a -d φ oil g ß> A

5 d NH II N - υ

Practice: Upper Saddle River, New Jersey: Prentice Hall, 1996; or JG Proakis, Digital Communications. New York: McGraw-Hill, 3 ^d ed, 1995. A disadvantage of this known method is that a considerable part of the transmission capacity to be sacrificed for the training symbols must, as these training symbols are sent with the data.. The faster the channel changes, the more training symbols have to be transmitted, and the more transmission capacity is lost in conventional systems.

In contrast, the so-called blind methods for equalization do not use explicit knowledge about the channel, but rather knowledge about certain generally valid mathematical structures of the channel. Training symbols are generally not required for these methods, and the full transmission capacity can therefore be used for the transmission of data. Although the computing power required for blind methods is higher than that for the conventional methods using training symbols, the enormously high costs of the mobile radio operators for rights of use for their frequency bands justify the additional computing effort of blind methods in future systems with regard to the then possible higher bandwidth efficiency , With GSM mobile telephony e.g. 116 data symbols and 26 training symbols were sent per data burst, which corresponds to a loss of approx. 22% in transmission capacity.

From H. Liu and GB Giannakis, "Deterministic approaches for blind equalization of time-varying Channels with antenna arrays", IEEE Trans. Signal Processing, vol.46, pp. 3003-3013, Nov. 1998, direct and indirect deterministic methods are known to carry out a blind signal equalization. The direct method is conceptually a modification of a method designed for LTI channels (cf. G.Xu, H.Liu, L.Tong, and T.Kailath, "A least-squares approach to blind channel identification", IEEE Trans Signal Processing, ol. 43, pp. 2982-2993, Dec. 1995). A disadvantage of this known direct method is that an equation system would have to be solved, the size of which is exponential with the product of the number of Doppler shifts and the channel length plus. Smoothing factor increases. In the indirect method, an atrix-valued impulse response characteristic of the channel is concluded via the column space of a reception or output matrix obtained from the received signals (with Matrix ambiguity). Then equalization (again with matrix ambiguity). Finally, the matrix ambiguity is removed. However, this process is very computationally complex; furthermore, there is no way to incorporate a priori knowledge, for example "semi" blind initialization, and there is no way to equalize channels with different subchannel lengths; finally, this method delivers relatively poor results, since on the one hand the column space of the output matrix has comparatively little structure and on the other hand the method for removing the matrix ambiguity is associated with relatively large errors.

The aim of the invention is now to enable efficient blind equalization of time-variant transmission channels with relatively little computational effort, with different sub-channel lengths and several users on one channel also being possible.

To achieve this object, the invention provides a method or a device as defined in independent claims 1 and 15.

Advantageous embodiments and further developments are specified in the subclaims.

With the invention it is possible to transmit data in a computer-efficient manner without loss of capacity through training symbols via time-variant channels and to obtain them in an equalized form. It is also advantageous that a deterministic method is available with which the received signal can be equalized without redundancy in the transmitted signal. Although the invention is intended in particular for use in equalization without the use of training symbols, it can also be used in conventional systems using training symbols, in particular when the conventional equalization techniques, for example due to an excessive time variance of the transmission channel at a high speed of the mobile station, can no longer equalize a transmission channel. The training symbols common from these known techniques can be used in the context of the invention for the "semi" -blind initialization of the equalization calculation in order to increase the computing efficiency, ie to shorten the computing time, and to increase the quality of the equalization. Furthermore, it is advantageously possible to use the invention even in a multi-user case. that, ie in the case of sending several user signals on one and the same channel, different modulation structures being used as a basis for the different user signals in order to separate the user signals. In this way, several users can be clearly and error-free separated from each other, even if they transmit on the same frequency and interfere with each other.

In the context of the invention, it is also not necessary to estimate Doppler shift frequencies, and qualitatively better results are achieved in the equalization compared to the prior art, specifically with improved computing efficiency. With regard to the diversification in the frequency direction, at least one of the signal spaces takes into account a modulation structure that indicates a relationship between the signal input values. In general, a Doppler shift diversity in the signals to be equalized is taken into account with a signal space.

In order to further increase the computer efficiency, it is advantageous if only active subchannels are used in the derivation of the two signal spaces, associated values being used for Doppler shifts and for the lengths of subchannel impulse responses.

For the calculation of the equalized signal values, it has also proven to be advantageous if a received matrix with a Hankel or Toeplitz structure is formed from the received signals on the basis of the temporal and frequency diversity of the respective time-variant channel, and its line space is determined. It is also advantageous if an input matrix with a Toeplitz or Hankel structure, which is representative of the equalized signal, is derived from the reception matrix and a matrix-value impulse response for all subchannels. It is also advantageous if the line space of the input atrix (s) is calculated from the line space of the receive matrix (x), for example by singular value decomposition of the receive matrix. Furthermore, it is advantageous if the generating matrix of the input matrix is determined from its row space while resolving the matrix ambiguity. On the other hand, in order to achieve particularly short computer times, it has proven to be advantageous if the input matrix is forced out of the row space of the reception matrix while forcing a block-toeplitz structure and a modulation structure is derived. For a quick calculation, it is also advantageous if, starting from the row space of the reception matrix, the input matrix is determined by iterative projection onto the two signal spaces.

In the technique according to the invention, different subchannel lengths that belong to different Doppler shifts can also be taken into account, wherein a respective modulation matrix can be defined to take into account different subchannel lengths.

Within the scope of the invention, the model parameters on which the calculations are based can also be determined from the scattering function, and previously given knowledge relating to a discrete symbol alphabet can be used in order to further shorten the computer time required for the various calculations.

The invention is explained in more detail below on the basis of particularly preferred exemplary embodiments, to which, however, it should not be restricted, and with reference to the drawing. Show it:

Fig.l is a schematic representation of a signal transmission with temporal variance with a moving receiver (mobile phone) and moving spreader (vehicle);

2 shows a schematic representation of a model with time-variant channels with several antennas;

3 shows a model multi-channel representation, with a number of time-invariant channels as a replacement for a time-variant transmission channel;

4 shows a somewhat modified multi-channel model in order to take into account the several time-variant channels according to FIG.

5 shows the determination of the equalized signals in a flowchart;

5A in an associated flowchart a part of the diagram according to FIG. 5 in more detail; FIGS. 6 and 6A in the flow diagrams corresponding to FIGS. 5 and 5A show a modified procedure when determining the equalized signals;

7 shows a scheme derived from FIG. 2 with a plurality of time-variant channels, this scheme being applicable to the case of several users, so that DxM time-variant channels are given; - 1 -

8 shows a model corresponding to FIG. 3 with time-invariant channels, but for the multi-user case according to FIG. 7; 9 and 9A show a flow chart corresponding to the diagrams according to FIGS. 5 and 5A or 6 and 6A, but now for the multi-user case according to FIGS. 7 and 8;

10 in a diagram in which the mean square error (MSE) of the equalization is plotted against the signal-to-noise ratio (SNR), a comparison of a method according to the prior art with the inventive technology in the equalization of time-variant channels transmitted signals;

11 shows, in a diagram similar to FIG. 10, a comparison of the equalization technology according to the invention in a multi-user case with a single-user case according to the prior art; and FIGS. 12A and 12B are scatter points for two users after the equalization, FIG. 12A illustrating one user and FIG. 12B the other user.

A mobile radio transmission for mobile telephones is schematically illustrated in FIG. 1, with a mobile telephone 1 and a spreader given by a moving vehicle 2 moving relatively quickly, as an example. The signals transmitted by radio are received via several signal paths, corresponding to the respective reflections, for example on buildings 3 or on moving vehicle 2. At 4, a rectification device is generally illustrated in FIG. 1, in which channels corresponding to corresponding antenna elements 5ι to 5 _M , each with a filter 6ι .. 6 _M , modulator 7ι to 7 _M (which converts to the baseband accomplished) and analog / digital converter 8 _M , a computer 9 is connected to carry out the corresponding equalization as explained in more detail below and finally to output an equalized received signal at 10.

In Figure 2 the transmission with the given M transmission channels lli is shown schematically to 11 _M at which the transmitted signal S [N] is applied, wherein the respective received signals on the outputs of the individual channels lli to 11 _M xι [n] to x _m [n] is present. The individual transmission channels lli to 11 _M are known. Channel impulse responses h [n, m] is characterized, is, as indicated in the present case corresponding to such through a total of M impulse responses in Fig.2 at 12ι to 12 _M.

Each of these M transmission channels 11 is shown in FIG models a number N _D of subchannels so that instead of having to perform the calculation of a time-variant channel, a number of time-variant subchannels can be calculated.

The present method is a blind, deterministic (i.e. no statistics need to be estimated) method for equalizing time-variant channels. In the following, the noise is neglected, as is usual in the literature. However, simulations showed that the present method is extremely robust against additive channel noise.

The method is based on the fact that a horizontal Toeplitz or Hankel matrix is uniquely determined by its row space (except for a scalar factor). A Toeplitz matrix is a matrix whose entries are constant along the diagonal, e.g. Tl 2.51;

[o 12 a Hankel matrix is a matrix whose entries are along the

Anti-diagonals are constant, e.g. 1 2 31

2 3 4j the row space of a matrix is the space that is spanned by the rows of the matrix, cf. also G.H. Golub and C.F. Van Loan, Matrix Computations. Baltimore: Johns Hopkins University Press, 3rd ed., 1996.

Similarly, a horizontal block toeplitz matrix or block Hankel matrix is uniquely determined by its row space except for a multiplication from the right by a block diagonal matrix (this ambiguity is referred to below as matrix ambiguity). A Block-Toeplitz or Block-Hankel matrix is defined exactly like a Toeplitz or Hankel matrix, except that the entries are not scalars, but matrices again.

For all blind methods that are based on so-called subspace methods, several observations of the transmitted signal are required, for example several .receiving antennas or one receiving antenna with subsequent oversampling or a combination of the two possibilities. 2 shows schematically M time-variant channels with M associated reception sequences xi [n], with i = 1, ---, M. The single time-variant channel generally does not have the structure required for blind equalization. Practically all existing mobile radio channels can, however, be represented in an equivalent way as a multi-channel LTI model. Fig.3 shows schematically the multi-channel LTI model used here, which models a single time-variant channel according to FIG. 2, ie there are then a total of M such multi-channel LTI models in order to model the M time-variant channels from FIG. 2; this is illustrated schematically with supplementary channel representations in dashed lines in FIG. From this equivalent representation it can be seen that this class of time-variant channels then has a structure that is suitable for blind equalization.

The multichannel representation arises in the present case from a discretization of a continuous time-variant channel with the additional assumption that only one reception signal block of finite length is considered at a time. This assumption is common and is in no way restrictive, since the block length can be chosen arbitrarily and blocks can be strung together. An advantage of this special method in contrast to the prior art (where Doppler shifts around continuous frequencies are used) is that the individual Doppler frequencies do not have to be additionally estimated. It only needs to know whether a subchannel is available at a particular Doppler frequency or not, that is, it is assumed that the Doppler shifts are ^'on a grid, and it is then necessary to examine the halftone dots are "active". The given “modulation structure” is indicated schematically in FIG. 3 at 13, while the channel impulse responses are again illustrated at 12. The individual time-invariant channels 14ι ... 14 _N are reassembled at 15.

The information regarding active subchannels (i.e. where there is a subchannel at a Doppler frequency) can be extracted from the spreading function of the channel if the channel can be assumed to be stationary with independent spreaders (WSSUS). However, the method presented here also works without restriction with the model according to the prior art.

In the following it is assumed that K of the N _D subchannels 14ι ... l4 _N in FIG. 3 are active. These K subchannels correspond to K Doppler shifts l * G [0, N _D - 1] with k = 1,2, ---. K. It follows that only the associated subchannel impulse responses hi k [m]

(with m = 0.1 ... L - 1) are not equal to zero, but this means no restriction, since the case K = N _{D is also} permitted. The input / output relationship for the i-th observation is now where h < ⁱ⁾ [m]

whereS [J] = ∑ ^ -jh ln, m] c - **, v, and where

The relevant model parameters are the "active" Doppler shift indices l and the lengths of the corresponding subchannel impulse responses hilc [m]. As already mentioned, these can

Parameters for WSSUS channels can be easily determined from the channel's spreading function. Since the spreading function changes only slowly over time, it is much easier to estimate than the channel itself.

For physical reasons (e.g. the antennas are usually relatively close together) it can be assumed that all M channels have the same channel model parameters. If this assumption does not apply to a specific application, the method can easily be adapted to this case. Furthermore, it is assumed for the time being that all K LTI subchannels h J [m] have the same length L. (This assumption will be dropped later.)

It is possible to matrix all M input / output relationships of the multi-channel LTI model by arranging the individual receive values x [n], the channel impulse responses h [n, m] and the transmit values s [n] into a single matrix-valued input / output relationship

X = HS (3)

summarize. Here X is the output matrix that is created from the received signals; H the channel matrix obtained from the channel impulse responses; and § the input matrix containing the transmitted signals to be determined. The arrangement is chosen so that the individual matrices have the block-toeplitz structure or block-Hankel structure desired for the blind equalization.

A possible arrangement, which is assumed below, is, for example, the following: When defining a matrix-value impulse response for all subchannels as

The total impulse response is then H = [H [0] ... H [L-1]], with which the channel matrix H with the size Mu x K (L + ul), in which H u times, each by K Positions shifted, stacked (the stacking parameter u is also referred to in the literature as a smoothing parameter), as

can be defined.

However, other arrangements are also conceivable, e.g. by swapping the order of the rows or columns of the individual matrices, but are equivalent to the above arrangement.

Next a vector is defined, which is modulated

Versions of the input signal include: s [n] = [sι [n] ... sι [n]] ^τ ; and the following block Toeplitz input matrix of size K (L + ul) x (N-u + l) is formed: s [ul] s [u] • • • s [Nl] s [o-2] s [-l] • • • s [N-2]

s [- + l] s [-L + 2] ^{■ ■ ■} s [NL- u + 1]

Finally, an output vector x [n] = [i [n] ... x _M [n]] ^{τ is} defined and thus a block Hankel output matrix x of size

Mu x (N-u + 1) shaped: x [0] x [l] • • • x [Nt - l] x [Nu] _{χ = ^} x [l] x [2] • • • x [Nu ] x [iV- «+ l]

x [ul] x [u] ^■ • • x [N-2] x [Nl]

This step of forming the receive or output matrix x with block 16 is illustrated in FIG. This is followed by the calculation of the row space of the receive matrix X at 17. The sizes of the individual matrices depend on parameters such as the impulse response length, the number of Doppler shifts, the smoothing factor and the number of observations (oversampling factor or number M of receiving antennas). On the condition that these parameters are chosen in such a way that

K (-l)

H is standing and S is lying (so formally, u>

MK with M> K, and N> KL + (K + 1) (u-1) apply), and that H also has full rank is the space that is spanned by the rows of the reception matrix s (the row space of X) , equal to the line space of S. The row space of the input matrix S can thus be calculated, for example, by means of a singular value decomposition of the reception matrix x. However, this step could also be approximated by other methods known per se, which are less computationally expensive than the singular value decomposition. (A singular value decomposition divides a matrix A into three matrices U, D and V, so that A = UDV, where U and V have orthogonal columns or rows (ie U ^H U = I and W ^H = I, where I is the unit matrix correspondingly Dimension is) and D is a diagonal matrix.)

After the row space of the reception matrix x has been calculated, the generating matrix of S is calculated in accordance with block 18 in FIG. 5: It is known that the matrix itself can be reconstructed down to a multiplicative factor from the row space of a lying Toeplitz matrix or Hankel matrix alone. However, if the matrix is a block Toeplitz matrix, the matrix itself can generally only be determined from its row space except for one matrix ambiguity, since the block rows generally have no structure.

The input matrix s is a block-toeplitz matrix, which is uniquely determined or "generated" by its elements s [-L + l], s [-L + 2], ..., s [N-l]. That is why the matrix

S = [s [-L + l] s [- +2] - s [N-l]]

the size K x (N + L-l) also called the generating matrix of s. The given equalization problem can therefore also be formulated as the calculation of the generating matrix S from the matrix x.

In AJ van der Veen, S. Talwar, and A. Paulraj, "A subspace approach to blind space-time signal processing for wireless communication communication systems ", IEEE Trans. Signal Processing, vol.45, pp.173-190, Jan. 1997; and H. Liu and G. Xu," Multiuser blind Channel estimation and spatial Channel pre-equalization ", Proc. IEEE ICASSP -95, (Detroit (MI), pp. 1756-1759, May 1995, two methods are described, such as S up to a matrix ambiguity (ie S _A = AS with unknown invertible KxK matrix A) from a block Toeplitz matrix Furthermore, this could also be from E. Moulines, P.Duhamel, JF Cardoso, and S. Mayrargue, "Subspace methods for the blind identification of multichannel FIR filters", ^' IEEE Trans. Signal Processing, vol.43, no.2, pp.516-525, 1995, known methods for solving the present problem can be used accordingly, but all methods have in common that either the matrix § or a matrix whose row space is orthogonal to the row space of

S spanned into a "supermatrix". must be stacked in order to be able to conclude from this supermatrix on S _A by a singular value decomposition. Since the computational effort of a singular value decomposition increases with the third power of the dimensions of the matrix to be decomposed, these methods are extremely computationally complex, which is why an alternative (namely the so-called direct factorization) is proposed below.

For the sake of simplicity, the one from H.Liu and G.Xu, "Multiuser blind Channel estimation and spatial Channel pre-equalization", Proc. IEEE ICASSP-95, (Detroit (MI)), pp.1756-1759, May 1995. First, a matrix V is defined, the row space of which is orthogonal to the row space of x; ie VX = o, where o is a matrix whose elements are identical to zero. From VX ^H = o follows VS = o, which in turn is due to the block-toeplitz structure of

S implies that N-u + 1 consecutive entries of the generating matrix S are orthogonal to V. This gives:.

M ^V £ ^ 0] S "= 0 mitt - = i ... _{L + u} _ _{2) (5)} x times (--- + t.-2-t) times where o the size (Nutl-Mu ) x 1. From equation (5) it follows again that

in which

is.

In order to determine the generating matrix S except for a matrix ambiguity (ie SA) with the help of equation (6), a singular value decomposition of v is carried out and SA is set equal to the K right singular vectors, which belong to the K smallest singular values.

Due to the construction using the singular value decomposition, the rows of S _{A are} orthonormal. For typical sizes of Ma ^¬ trizen H and S, this step is, as mentioned above, but relatively computationally intensive.

5, step 19 now follows the resolution of the matrix ambiguity. Due to the modulation structure of the present multi-channel LTI model, the individual block rows of the matrix S have a well-defined relationship, which makes it possible to resolve the matrix ambiguity remaining from the last calculation step, i.e. from SA to conclude the desired generating matrix S. In H.Liu and GBGiannakis, "Deterministic approaches for blind equalization of time-varying Channels with antenna arrays", IEEE Trans. Signal Processing, vol.46, pp.3003-3013, Nov. 1998, there is a method for elimination the matrix ambiguity presented, but this is practically very difficult to implement due to the particularly high computing effort.

In the present method, the resolution of the matrix ambiguity is based on the fact that the generating matrix S of the sought transmission matrix S is completely described by its belonging to two linear spaces.

The first linear space A 'takes into account the modulation structure, that is, the relationship between the input values Si [n]

(namely si [n] = s [n] _& i ^2π . ^k . This modulation structure of the

N nerating matrix S with the size Kx (NtLl) can be characterized by the following matrix notation: S = M (no) D. (7)

Here, the "modulation matrix" M (n ₀ ) of size Kx (NtLl) is complete

N

M (no)

_W -nolκ _ _w - ("* + N + L- _l ) l _κ

given, where * = e ^j2π -. Furthermore, the diagonal input matrix D containing the transmission data is of the size (N + L- l) x (N + Ll) as D = diag {ε [-L + l], s [-L + 2], .. ., s [Nl]} defined. The definition of the modulation matrix M (no) allows an unknown time shift no, which could occur in practice.

The second linear space B 'is the row space of the generating matrix S, which is equal to the row space of SA. It follows that the matrix S sought must lie in the intersection of the two spaces, i.e. S -≡A'nB ', where A' represents the linear subspace of all matrices with the modulation structure M (no) D, given M (no) and diagonal D, and B 'represents the linear subspace of all matrices whose row space in the row space is from SA lies, ie the subspace of all matrices of the form BSA with any KxK matrix B.

For calculation - cf. FIG. 5A - a computationally efficient iterative method is used, which, starting from a starting value, projects alternately onto the two spaces A 'and B' (see blocks 20 and 21 in FIG. 5A) until a further projection occurs no longer results in a significant change, ie until the estimated value converges (see query step 22 in FIG. 5A); the convergence is checked with a so-called stop criterion - if the change in another iteration is smaller than the stop criterion, the process is terminated. This mathematical pro ection process is known per se in the literature under the name "projections onto convex sets", also called "POCS", see p. PLCombettes, "The foundations of set theoretical 'estimation", Proc. IEEE, vol .81, pp.181-208, Feb. 1993. The value of the stop criterion has to be determined according to the circumstances and objectives. - Pro ection on A ': The projection on A' results in S ^(v> = M (n ₀ ) D ^(vl , whereby it can be shown that the diagonal elements of D ^(v> by

given are. Here s ^{(v_1) is} the result of the previous iteration (ie from the projection onto B '). - Projection on B ': The projection on B' results in

where it can be shown that

BW = - s ^ - ^ s *.

Here s ^{(v_1) is} the result of the previous iteration (ie the projection on A '), and S is the pseudo inverse of SA. Since SA is a horizontal matrix with orthonormal lines, S * = S * applies.

It can be shown ^'that in the present case, the convergence of the method is given. This ensures that, for a given generator,

and for given Doppler shifts l _k the input data s [-L + l], s [-L + 2], ..., s [N- 1] are uniquely determined except for a scalar factor. This applies even under the condition that the time difference o is unknown. The convergence can be done with a so-called relaxation (e.g. PLCombettes, "The foundations of set theoretic estimation", Proc., IEEE, vol .81, pp.181-208, Feb. 1993; or S. Hein, "A fast block -based non-linear decoding algorithm for ΣΔ modulators ", IEEE Trans. Signal Processing, vol. 43, pp. 1360-1367, June 1995) can be significantly accelerated, which in turn further reduces the computing effort of the method.

Furthermore, the present method for resolving the matrix ambiguity can be used without changes even if the Doppler shifts are not on a grid (grid) (for example with a model as described in H.Liu and GBGinakis, "Deterministic approaches for blind equalization of time-varying channels with antenna arrays ", IEEE Trans. Signal Processing, vol.46, pp.3003-3013, Nov. 1998).

It can even be shown that the resolution of the matrix ambiguity still works when the active ones Dopplerver shifts l are unknown. In this case, the input data s [n] can be determined except for a multiplication by ce ^{3 π} -, where 1 e [0, N-1]. This unknown "residual modulation" can also be resolved if s [n] is a symbol sequence with a known finite symbol alphabet.

Another advantage of the present method for resolving the matrix ambiguity is the simple usability of a priori knowledge. For example, Knowledge of a specific symbol alphabet used by the sender (i.e. the elements of the matrix S may only take values from a certain known set of values) can be used to further accelerate the convergence (however, the convergence cannot be guaranteed in this case). Furthermore, the method can be initialized semi-blind by a suitable choice of the starting point of the iterations, which also accelerates the convergence.

Although the above steps of modeling, the calculation of the row space of the reception matrix and the calculation of the generators of the input matrix are known in principle, their application to the equalization of time-variant channels and the compilation of these steps are not yet known; then the described method for eliminating the matrix ambiguity is not yet known.

The method explained above for blind equalization of time-variant channels can also be adapted for different sub-channel lengths. For this purpose, known methods for LTI channels (see H.Liu and G.Xu, "Closed form blind symbol estimation in digital communications," IEEE Trans. Signal Processing, vol. 3, pp. 2714-2723, Nov. 1995 ; or AJ van der Veen, S. Talwar, and A. Paulra, "A subspace approach to blind space-time signal processing for wireless communication Systems", IEEE Trans. Signal Processing, vol. 45, pp. 173-190, Jan 1997) adapted.

In the event that the K active subchannels have different lengths, it is assumed on the basis of physical considerations that the corresponding active subchannels of the M channels (cf. the above relationship (2) - ie h ^" [m] with different i, but the same k - have impulse responses of identical length.

In particular, it is assumed that P groups of active sub- channels exist, whereby the pth group consists of K _p subchannels with identical length L _p and with Doppler shifts 1 ^ (k = 1, 2, ... K _P ). (It should be noted that Σ ^ _{= 1} K _P = K.)

The problem why the original method has to be adapted is that the matrix H of size MuxK (Ltul) (contrary to the prerequisites in this case will not have full rank. However, in order to work around this problem, the relationship (3) by X = ∑ _{p = 1} H _p S _p , where the matrices H _p of size MuxK _p (L _p + ul) have full rank. The generating S _p of S _p can be as

can be written (see above relationship (7)). Here the K _p x (N + L _p -l) modulation matrix is through

_W - ⁿ ° ^l l ^P ... _W7 - (no-f-iV + L „-l) -ω

Mp (n ₀ ) = ww; ^{{no +)} ... w- ^{0 + N + L} '' - ⁾ )

the diagonal matrix containing the input values is D _p = diag {s [-L _P + l], s [-L _P +2], ..., s [Nl]} of the size (N + L _P -l ) x (N + L _p -l) defined. As with the calculation of the generating matrix of S explained above, the methods known per se from H.Liu and G.Xu, "Multiuser blind channel estimation and spatial channel pre-equalization", can now be used in Proc. IEEE ICASSP-95, (Detroit (MI)), pp.1756-1759, May 1995; or AJ van der Veen, S. Talwar, and A. Paulraj, "A subspace approach to blind space-time signal processing for wireless co munication Systems", IEEE Trans. Signal Processing, vol. 45, pp.173-190, Jan. 1997, can be used to determine S _A , _P = A _P S _P (with unknown A _p ) from X. It can be shown that S _{P is} clearly determined down to a scalar factor by S _A , _P (this fact still applies to an unknown time shift no). The POCS method described above can be used to calculate S _p and thus also the input values s [-L _p + l], ..., s [Nl]. Although such a calculation is theoretically sufficient, with additive channel noise it will be advantageous to calculate several or even all p estimates of s [-L _p + l], ..., s [Nl] and the corresponding results to mittein.

For blind equalization of LTV channels, direct factorization can also be carried out (see also FIGS. 6, 6A), which is also based on the POCS method, but which calculates the generating matrix of S and resolves the matrix ambiguity in one step 23 (Fig. 6) united and thus more computationally efficient than the above procedure. At the same time, however, this modified method retains the advantages of the first method, such as semi-blind initialization option, possible relaxation, possible use of a priori knowledge, the possibility of subchannels of different lengths, etc. In addition, this modified method is to a certain extent particularly robust against unknown different ones Subkanallängen.

As mentioned, the calculation of the generating matrix SA apart from an authenticity is computationally complex. This step can be avoided if one recognizes that the input matrix S is uniquely determined except for a scalar factor by the following two properties:

1. S is a block Toeplitz matrix and its generator has a modulation structure, ie S = M (n ₀ ) D with a diagonal matrix D;

2. The row space of the input matrix S lies in the row space of the output matrix X.

In other words, S eA'nB ', where A' is the linear subspace of all Block-Toeplitz matrices with a generating matrix M (n ₀ ) D, where M (n ₀ ) is given with any fixed n ₀ , D is a diagonal matrix and B 'represents the linear subspace which consists of all matrices whose row space lies in the row space of X (ie from all matrices of the form BX with any K (L + ul) x Mu matrix B). This formulation leads again to a POCS method for calculating S in which the iterated version of S is alternately projected onto A 'and B'. Projection onto A '(step 20 in FIG. 6A): Since S is a so-called linearly structured matrix (cf. JA Cadzow, "Signal enhancement - A composite property mapping algorithm", IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 49-62, Jan. 1988), it can be shown that the projection onto A 'can be accomplished by the following two steps:

Step 24 (Fig. 6A): Enforce the block toeplitz structure. It εeis ^{<v ~ 1)} the result of the previous iteration (i.e. the Projection on B '). From the matrix S ^(-1) , which has no block Toeplitz structure, a Kx (N + Ll) "pseudo-generating matrix" S ^(v_1> is calculated as follows: The first of the K rows of S ^{( v} is calculated by averaging appropriately shifted and padded versions of the first, (Ktl) -th, (2K + l) -th, etc. lines of S ^(v-1) , so it becomes the first row Taken from S, shifted one position to the right and then added to the (Kl) th line of S ^v_1, adding zeros if necessary. The result is shifted one position again • to the right and to (2K + l) - th row of S, etc. Finally, the jth element of the resulting row vector of length N + Ll is replaced by the jth element of (1,2, ..., K, K, ..., K, K -1, ..., 1) divided to get the first row of S. The second row of S is calculated in a similar way, with the second, (K + 2) -th, (2K + 2) - te, etc. line of S. In this way, all K lines calculated from S ^lv_1) .

Step 25 (Fig. 6A): Enforce the modulation structure. Now S ^(v) = M (no) D ^{(v) is} formed, whereby it can be shown that the diagonal elements of the diagonal matrix D ^(vl by

given are. Finally, the block-toeplitz matrix § ^(> , which is generated by S ^<v) , is formed.

- Projection on B '(step 21 in Fig. 6A): The projection on B' 'can be written kkaannnn dduurrcchh § = B, whereby it can be shown that

_B () _{= g} (-l) _i #.

Here it is ^{(v_1 |} the result of the previous iteration (ie the projection onto A '). It should be noted that the pseudo inverse X only has to be calculated once at the beginning of the iterative procedure.

Again, convergence of the POCS method to an intersection of the two spaces is guaranteed, ie S ^(∞) e AnB (see PLCombettes,

"The foundations of set theoretical estimation," Proc. IEEE, vol. 81, 3). It can be shown that therefore

The speed of convergence and thus the computational The efficiency of the procedure strongly depends on the initialization §. In the semi-blind case, known input data s [ni], ..., ε [n∑] could be used to generate a matrix S with a generating matrix S ⁽⁰⁾ -M (n ₀ ) D ⁽⁰⁾ , where

D ^{! 0 |} = diag {0, ..., 0, s [nι], ..., s [n ₂ J, 0, ..., 0}; the POCS method would then be initialized with B ^<0> = XS ^{(0) #} .

Furthermore, the convergence can be accelerated again with relaxation.

The modification described here to increase the computing efficiency can also be modified in the case of unequal subchannel lengths (as described above).

The method described above with all its possible modifications can also be used to equalize the corresponding time-variant channels when several users are being transmitted at the same time. It can be shown that if the channels meet certain conditions, the users can be correctly separated in the absence of noise; i.e. that in this case several users can use the same frequency at the same time without interfering with each other. If the requirement for the channels is not met, the users can still be separated if a finite signal alphabet is used for transmission, as is customary in practice.

In the following it is assumed that D users are to be transmitted simultaneously, cf. 7, from which I derive DM time-variant channels 11, and the associated model from FIG. 8 with DXND time-variant channels 14, derived from FIG. 3. The method explained above must do something for this can be changed to allow D users. In the following, only the changes for each step will be explained individually.

As far as modeling is concerned, FIG. 7 schematically illustrates the case where D users are simultaneously transmitting data. Furthermore, M observations of the transmitted signals are assumed. Accordingly, FIG. 7 shows schematically DxM time-variant channels with M associated reception sequences i [n], with i = 1, ..., M.

The individual LTV channels are again represented by multi-channel LTI models, see FIG. 8, which shows the multi-channel LTI model used here, which shows the time-variant channels from the Users modeled into an antenna, ie there are a total of M

Multi-channel LTI models before., According to the DxM time-variant channels

Fig. 7 to model.

In the following it is assumed that the dth user K _{d of} the Na subchannels in FIG. 8 are active. These Ka channels correspond

Ka Doppler shifts 1 _k e [0, N _D -l] with k = 1, 2, ..., Ka. It follows that only the subchannel impulse responses h [m] with 1 = 1 'are non-zero. The above input / output relationship (2) is thus by

replaced, where h ⁽ⁱ '^d> [n, m] represents the LTV impulse response of the channel, which maps s ^(d) [n] to x ^(il [n]. Furthermore, h ^ ^1,0 ' [m] analogous to the above explanations, the 1st subchannel of the multi-channel LTI model of h ⁽ⁱ - ^d) [n, m]. In addition, s' ^ [n] = s ^ldl [n] e ^{j2πlnN is} used, which results in the modulation structure results. the relevant model parameters are again the "active" Doppler shift indexes 1 ^ and the lengths of the corresponding sub-channel impulse responses [m]. the consequence of the differences of two successive Doppler shift indexes _1, for a given d (wherein the

Doppler shift indices 1 (a _k ) k are assumed to be in ascending order), that is, the sequence

is called the Doppler profile of user d below. Again, it is assumed that all M channels assigned to a particular user have the same channel model parameters. To simplify the illustration, it is also assumed that the LTI subchannels [m] have impulse responses of identical length. However, the multi-user case can be extended to different subchannel lengths in the same way as the single-user case.

To remain compliant with the method described above, K is defined as the total number of all subchannels per observation, ie K = Σ ° _{= 1} K _d .

Again, it is possible to change all of the input / output relationships of the Multi-channel LTI model by arranging the individual receive values, the channel impulse responses and the send values in matrices to form a single matrix-valued input / output relationship identical to equation (3):

X = H S,

see. also block 16 in Fig. 9.

In principle, the same definitions for X, H and s are available, but due to the D users the

Change entries in these matrices as described below. For example, the impulse response becomes contrary to the equation

Are defined. The input vector is modified in such a way that it contains the modulated input data of all users, s [n]

= [sι 1.1 [n] [n] ... si

D, l [n] ... siD.K _D [n]] ^τ . Because of the changed

The definition of K also means that the expressions for the dimensions of the individual matrices and the expressions for the conditions that must be set for identifiability remain unchanged from those from Section 2.

The row space of the reception matrix X (see block 17 in FIG. 9) is calculated in the same way as described above.

The procedure for calculating the generating matrix S _κ of S (see block 18 in FIG. 9) is also the same as that described above.

As far as the resolution of the matrix ambiguity is concerned (see block 26 in FIG. 9), in contrast to the single-user case there is no longer a well-defined relationship between all inputs.

(ά) output signals s [n], but only between the sub-channel input signals that come from one and the same user, that is, between those K _d signals s. [n] that have the same d. However, it can be shown that if the Doppler profiles of the individual users are different, the users can be separated due to this fact alone. ^■ If two or more user channels with identical double If you use a user profile, a method can be used to separate these users, which takes advantage of the properties of a discrete symbol alphabet (see, for example, S. Talwar, M.Viberg, and A. Paulraj, "Blind Separation of synchronous co-channel digital Signals using an antenna array - Part I: Algorithms, "IEEE Trans. Signal Processing, vol. 44, pp. 1184-1197, May, .1996; or AJ van der Veen, S. Talwar, and A. Paulraj," A subspace approach to blind space -time signal processing for wireless communication systems, "IEEE Trans. Signal Procesεing, vol.45, pp.173-190, Jan. 1997; or J.Laurila, K.Kopsa, R. Schürhuber, and E. Bonek," Semiblind Separation and detection of co-channel signals, "in Proc. IEEE Int. Conf. Commun. (ICC), (Vancouver BC, Canada), pp. 17-22, June 1999). In this case, however, convergence can no longer be guaranteed; however, semi-blind initialization is useful to practically ensure convergence (see J. Laurila, K. Kopsa, R. Schürhuber, and E. Bonek, "Semi-blind Separation and detection of co-channel signals," in Proc. IEEE Int .Conf .Commun. (ICC), (Vancouver BC, Canada), pp. 17-22, June 1999).

In contrast to the procedure described above, the modulation structure of the generators S changes as follows due to the presence of D users:

S = [(MιDι) ^τ ... (M _D D _D π ^τ .

Here again so-called modulation matrices Ma (with different sizes Kax (N + Ll), their elements

/ N) and the (N + Ll) x (N + Ll) diagonal

Input matrices Da = diag {s ^(d) [- +1], s ^(a) [-L + 2], ..., s ^(d) [Nl]} are used. (For the sake of simplicity, an unknown time shift by n ₀ is now disregarded here.)

As already mentioned above, it can be shown that under the condition that all D users use channels with different Doppler profiles, the users can be separated apart from one scalar factor per user. In other words, the generating S is clearly determined by the following two properties (apart from the scalar factors):

1. S has the modulation structure [(MιDι.) ^Τ ... (M _D D _D ) ^T ], where M _{d are} given and all Da are diagonal;

2. The line space of S lies in the line space of S _A. So S e A 'n B', s. Block 26 in FIG. 9, where A 'is the linear subspace of all matrices of the form [(MιDι) ^τ ... (MDD _D ) ^T ] ^T with given dimensions and diagonal Da and B' denotes the linear space of all matrices whose Row space lies in the row space of S _A , ie the linear space of all matrices of the form BS _A with any KxK matrix B.

The POCS method can be used again for the equalization, which projects alternately on A 'and B', ε. blocks 20, 21 in Fig. 9A. Due to the slightly changed modulation structure, the projection onto A 'changes slightly as follows: First, S ^(v> = [(MiD ⁽ ^) ^{τ •••} (M _D D ⁽ ^) ^τ ] is set, whereby it can be shown that the diagonal elements of thereby

given are. Here will

used, and S ^(v is that

Result of the previous iteration (i.e. the projection onto B ').

The projection on B 'does not change.

This POCS method will again converge to a point at the intersection of A 'and B', ie S ^> e A 'nB'. This

Convergence is independent of whether all users have different Doppler profiles or not. If all users have different Doppler profiles, a separation of the users according to the described POCS procedure is guaranteed; however, if two or more users have identical Doppler profiles, the users within the group of users with identical Doppler profiles are mixed and must e.g. with methods that take advantage of a finite signal alphabet. This is shown schematically at 27 in FIG.

Again, all modifications such as different subchannel lengths, direct factorization, semi-blind initialization or relaxation can be used to accelerate the convergence.

Of. It is also possible to approximately separate several users with identical Doppler profiles, but different Doppler line profiles, in order to accelerate a subsequent separation using other methods.

Finally, there are some practical studies or simulation results relating to the invention compared to the prior art (H.Liu and GB Giannakis, "Deterministic approaches for blind equalization of time-varying channels with antenna arrays", IEEE Trans. Signal Processing, vol.46, pp. 3003- 3013, Nov. 1998) on the basis of FIGS. 10 to 12.

For a first simulation of the equalization according to the invention, a number of M = 5 observations i [n] was chosen, which were disturbed by additive white Gaussian noise with a variance σ ² . Furthermore, the block length was chosen to be N = 115, and each of the five channels contained K = 3 subchannels with active Doppler shifts lk = 0, 1, 2 and identical subchannel filter lengths L = 5. The impulse responses of the subchannels became random for each simulation run selected.

FIG. 10 compares the mean square error (MSE) of the equalization with direct factorization (see FIG. 6) with that MSE value which was achieved by the "indirect" method according to the prior art as a function of the signal-to-noise ratio SNR. The MSE value was 11 sc's' I [ ² / |. s 11 ^{2 defined} averaged over all simulation runs, where s = [s [-L + 1] s [-L + 2] ... s [N- l]] ^τ , s is the estimated value of ε, which corresponds to the corresponding one Method was achieved, and c is the least-squares estimate for the unknown factor c. The SNR ratio is called 11 [x [0] ... x [Nl]] | | _p / (NMσ ² ) defines, where Irllp represents the Frobeniuε norm. The same SNR value was used for each simulation run.

U = 6 for the direct factorization and u = 7 for the indirect method according to the prior art were chosen as smoothing factors; in both cases this was the minimum possible value for u. The direct factorization was carried out with (see curves 30, 31 in FIG. 10) and without relaxation (ε. Curve 32 in FIG. 10) and with different convergence criteria. Furthermore, a semi-blind initialization with 13 known symbols was simulated (curve 33 in Fig. 10). This is contrasted by curve 34 representing the known method.

The simulation results show that the present equalization - direct factorization - performs much better (in terms of MSE, but also in terms of computing effort) than the indirect method according to the prior art.

In another investigation, the multi-user case explained above with reference to FIGS. 7 to 9 with D = 2 users o so I c- ooo H <HU α. 4

4

^• •

•

-

O -

O

Claims

Patentanεprüche

1. Method for blind equalization of signals transmitted via time-variant transmission channels, the respective time-variant transmission channel being modeled by diversification with a finite number of time-invariant subchannels, characterized in that the received signals (x [n]) are based on the diversity of the respective one time-variant channel, both in the temporal direction and in the frequency direction, two corresponding signal spaces (A ', B') are derived and the equalized signal (s [n]) is derived from the intersection of these two signal spaces.

2. The method according to claim 1, characterized in that at least with one (A ') of the signal spaces (A', B ') indicating a relationship between signal input values (sin [n])

Modulation structure is taken into account.

3. The method according to claim 1 or 2, characterized in that with a signal space (A ') a Doppler shift diversity (lk) is taken into account in the signals to be equalized.

4. The method according to any one of claims 1 to 3, characterized in that only active subchannels are used in the derivation of the two signal spaces (A ', B'), associated values for Doppler shifts (lk) and for the lengths of subchannel impulse responses (hι _k ) can be used.

5. The method according to any one of claims 1 to 4, characterized in that from the received signals based on the temporal and frequency diversity of the respective time-variant channel, a reception matrix (x) with Hankel or Toeplitz structure is formed and the line space is determined.

6. The method according to claim 5, characterized in that the reception matrix (x) and a matrix-valued impulse response (H) for all subchannels are derived from an input matrix (s) representative of the equalized signal and having a Toeplitz or Hankel structure.

Method according to claim 6, characterized in that the row space of the input matrix (s) from the row space of the receive matrix (x), e.g. by singular value decomposition of the reception matrix.

8. The method according to claim 7, characterized in that the generating matrix (S) of the input matrix (s) is determined from its row space while resolving the matrix ambiguity.

9. The method according to claim 7, characterized in that the input matrix (s) is derived from the row space of the reception matrix (x) in a uniform step, forcing a block toeplitz structure and a modulation structure.

10. The method according to claim 8 or 9, characterized in that starting from the row space of the reception matrix (x), the input matrix (s) is determined by iterative projection onto the two signal spaces (A ', B').

11. The method according to any one of claims 4 to 10, characterized in that different values are taken into account for the subchannel lengths belonging to the different Doppler shifts.

12. The method according to claim 11, characterized in that a respective modulation matrix (M _p ) is defined to take into account different subchannel lengths.

13. The method according to any one of claims 1 to 12, characterized in that in the case of the transmission of several user signals on the same channel for the different user signals different modulation structures are used as a basis to separate the user signals.

14. The method according to any one of claims 1 to 13, characterized in that an initialization is carried out with a known transmission signal sequence.

15. Device for equalizing transmission over time-variant signals transmitted signals, with a receiving circuit and with a computer, the respective time-variant transmission channel being modeled by diversification with a finite number of time-invariant subchannels, characterized in that the computer is set up to derive from the received signals (x [n]) To derive two corresponding signal spaces (A ', B') based on the diversity of the respective time-variant channel both in the temporal direction and in the frequency direction and to derive the equalized signal (s [n]) from the intersection of these two signal spaces.

16. Device according to claim 15, characterized in that the computer is set up to take into account a modulation structure indicating a relationship between signal input values (sι _n [n]) with at least one signal space (A ').

17. The device according to claim 16, characterized in that the computer is set up to take into account a Doppler shift diversity (lk) in the signals to be equalized with a signal space (A ').

18. Device according to claim 17, characterized in that the computer is set up to use only active subchannels with the derivation of the two signal spaces (A ', B'), associated values for Doppler shifts (lk) and for the lengths of subchannel Impulse responses (hι _k ) are used.

19. Device according to claim 18, characterized in that the computer is set up to form a reception matrix (x) with a Hankel or Toeplitz structure from the received signals based on the temporal and frequency diversity of the respective time-variant channel and to form its line space determine.

20. Device according to claim 19, characterized in that the computer is set up with the E pfangεmatrix (x) and a matrix-valued impulse response (H) for all subchannels a representative for the equalized signal input matrix (s) with Toeplitz or Hankel Structure.

21. Device according to claim 20, characterized in that the line space of the input matrix (s) is calculated from the line space of the reception matrix (x), for example by singular value decomposition of the reception matrix.

22. Device according to claim 21, characterized in that the computer is set up to determine the generating matrix (S) of the input matrix (s) from their row space while resolving the matrix ambiguity.

23. Device according to claim 22, characterized in that the computer is set up to derive the input matrix (s) by forcing a block toeplitz structure and a modulation structure in a uniform step from the row space of the receive matrix (x).

24. Device according to claim 23, characterized in that the computer is set up to determine the input matrix (s) from the row space of the reception matrix (x) by iterative projection onto the two signal spaces (A ', B').

25. Device according to claim 24, characterized in that the computer is set up to take into account different values for the subchannel lengths belonging to the different Doppler shifts.

26. Device according to claim 25, characterized in that the computer is set up to define a respective modulation matrix (M _p ) to take into account different subchannel lengths.

27. Device according to claim 26, characterized in that the computer is set up to be different for the different user signals in the case of the transmission of several user signals on one and the same channel

Modulation structures are used to separate the user signals.

28. Device according to claim 27, characterized in that the computer is set up to carry out an initialization with a known transmission signal sequence.