EP1386439A2 - Method for transmitting data and transmitter and receiver device therefor - Google Patents

Abstract

In order to transmit data flows via channels which respectively have several inputs and outputs, said data flows (d[n]) are respectively modulated at the channel inputs in a given manner to form transmission signals (s[n]), and corresponding data flows (d[n]) are derived at the channel outputs from the reception signals (x[n]) by equalization of distortion. A given matrix modulation structure (Mk) is imposed upon the data flows (d[n]) at the channel inputs and the equalization of distortion is carried out for the reception signals (x[n]) at the channel outputs on the basis of said known given matrix modulation.

Description

 Method for transmitting data streams and transmitting and receiving device therefor

The invention relates to a method for transmitting data streams via a channel with a plurality of inputs and outputs, the data streams at the channel inputs being modulated into transmit signals in a predetermined manner and corresponding data streams being derived from the received signals at the channel outputs by equalization. A preferred application is in the field of mobile radio or mobile telephone systems.

Furthermore, the invention relates to a transmitting device and to a receiving device for carrying out this method.

One of the goals of third and fourth generation mobile radio systems is to provide broadband data services to users who may be moving at high speeds. Real-time multimedia services, such as Video conferencing requires data rates in the order of 2 to 20 Mb / s. Current standards, such as GSM, however, only support data rates that are two to three orders of magnitude lower.

Other applications that rely on high data rates are modern office applications. For example, Wireless network connections from portable computers (laptops) Data rates in the order of 10 to 100 Mb / s.

With portable devices, however, not only is the required data rate essential, but also the power consumption, which is reflected in the battery life.

It is known that the spectral efficiency (ie the data rate that can be transmitted per frequency bandwidth) while the transmission power remains the same by using several transmit and receive antennas (the channels considered here, each with several inputs and outputs, are also called "multi-input / multi-output "channels or MIMO channels for short) can be increased very strongly. For example, the spectral efficiency can be increased by using k antennas on the transmitter and receiver side by a factor that is greater than the number k.

The majority of the currently known methods now assume this that the channel is memory-free (ie instantly mixing) and that the channel is perfectly known to the receiver. In practice, however, the channel is not known a priori to the receiver, so that the channel can be estimated with the aid of so-called training symbols known from the receiver, which are transmitted, for example, in a middle, etc. As a rule, however, the number of training symbols that are used for channel estimation according to the prior art increases linearly with the number of transmit / receive antenna pairs. For example, in the GSM system that is widely used today, 26 training symbols (ie approximately 22%) of the data burst are used per data burst with a length of 142 symbols. Now, however, the GSM system has been designed for just one pair of transmit / receive antennas, and it is obvious that complex MIMO channel systems can then lead to situations in which half of the data burst has to be assigned training symbols , Considerations for this can be found, for example, in T. Marzetta, "BLAST training: Estimating Channel characteristics for high-capacity space-time wireless", Proc.7th Allerton Conf. Commun. , Contr., Conαput., Sept. 1999.

The currently known methods for transmission via MIMO channels can be roughly divided into three groups: (1) the group of the so-called space-time block codes (space-time block codes); see. e.g. S. M. Alamouti, "A simple trans it diversity technique for wireless communications", IEEE J. Sel.Areas Comm. , vol. 16, pp. 1451-1458, Oct. 1998; (2) the group of so-called space-time trellis codes (space-time trellis codes), cf. e.g. V. Tarokh et al. , "Space-time codes for high data rate wireless communications", IEEE Trans. Inf. Theory, vol. 44, pp. 744-765, March 1998; and (3) a group of methods which do not fit into the two aforementioned groups, such as methods of the so-called unitary space-time codes, cf. e.g. B. Hochwald et al. , "Systematic design of unitary space-time constellations", IEEE Trans. Infor. heory, vol. 46, no. 6, pp. 1962-1973, 2000.

Space-time block codes (1st group) are easy to decode, but they have the major disadvantage that they can no longer reach the channel capacity for more than one receiving antenna. They also assume ideal channel knowledge on the receiver side.

Space-time trellis codes (2nd group) represent a direct extension of the known coding methods for a send / receive catch antenna pair on MIMO channels. In principle, they are suitable for making full use of the channel capacity of a MIMO channel, but have the disadvantage that the decoding complexity increases exponentially with the number of transmit antennas. For this reason, the literature mainly contains simulations for up to just three pairs of transmit / receive antennas. These methods also assume ideal channel knowledge at the receiver end, which, however, leads, as mentioned, to high training symbol portions in the data bursts.

The procedures of the third group are naturally difficult to summarize. Of particular interest here are those methods that do not require any channel knowledge on the receiver side. The method of unitary space-time codes (see Hochwald et al.) And the similar differential space-time modulation (see e.g. BLHughes, "Differential space-time modulation", IEEE Trans. Inf. Theory, vol. 46, pp. 2567-2578, Nov. 2000) belong to these processes. With this unitary space-time modulation or the differential form of it, the data are characterized solely by their belonging to a certain subspace. However, both of these methods have the disadvantage that they have a decoding complexity that increases exponentially with the number of transmitting antennas and with the transmission rate. In addition, the application of these methods is limited to instantly mixing channels.

It is an object of the invention to provide a method of the type mentioned at the outset, and a transmitting and receiving device therefor, it not being necessary to explicitly estimate the channel and in which only little bandwidth is lost because the channel is not known.

To achieve this object, the invention provides a method as defined in claim 1 and a transmitting device and a receiving device as defined in claims 11 and 15, respectively. Advantageous refinements and developments are specified in the subclaims.

In the technique according to the invention, no explicit estimation of the channel is necessary, since it is robust to an unknown channel; implicitly some bandwidth is lost due to the unknown channel also in the technique according to the invention ren, because the matrix modulation structure inserted on the transmitter side must contain a certain redundancy. The extent of this redundancy can, however, be easily adapted to requirements during operation.

Furthermore, the technique according to the invention can also be used for MIMO channels with memory in addition to instantly mixing channels. A channel "with memory" has an impulse response length ("memory length"), which is denoted by L, with such a channel causing a mixture of symbols, e.g. sent from time n-L to time n is received. In contrast, in the case of a channel without memory (which in the MIMO case is also referred to as an instantly mixing channel), the symbols received at time n only depend on symbols sent at the same time n. The physical cause of a channel's memory can e.g. Multipath propagation, i.e. the existence of several transmission paths of different lengths from sender to receiver. The method according to the invention also enables relatively simple decoding and has no restriction with regard to the number of receiving antennas.

The method according to the invention is a matrix modulation method for MIMO channels, which is robust against unknown channels, i.e. the method works regardless of whether the channel is known or not. At the same time, the method can also be classified as blind and deterministic since, as just mentioned, the channel does not have to be known and no statistics need to be estimated for the purpose of demodulation or equalization. With the technology according to the invention it can also be achieved that the demodulation complexity only increases linearly with the number of transmit antennas.

In the following, as is common in the literature on deterministic blind methods, the noise is neglected. However, simulations showed that the present method is extremely robust against additive channel noise.

The method is based on the fact that the signal to be transmitted is forced on the transmitter side by a known matrix structure chosen for the respective application, which can be shown to be strong enough to hold the data to reconstruct the recipient without errors, solely on the basis of the known structure. It is expedient if each data stream to be written as a diagonal data matrix is multiplied by its own predetermined modulation matrix, all modulation matrices preferably having full rank and the columns of the individual modulation matrices corresponding to one another being linearly independent. Furthermore, the conditions should be met that the number of channel inputs is greater than the number of data streams and that the length of the respective send or receive signal block of the condition

N> J- -: is enough

where M _{τ is} the number of channel inputs and

K is the number of data streams. If the minimum block length N given thereby falls below, the present method could break down.

With a view to an additional reduction in the computing effort in the case of received signal demodulation (equalization), an approximation method is advantageously used in which the equalization of the received signals is carried out in iterative form by alternately projecting transmit signal matrices onto two signal spaces, starting from a predetermined start value of which the one signal space represents the modulation structure property and the other signal space represents a subspace property according to the condition that the row space of the received signal matrix lies in the row space of the transmit signal matrix, where appropriate these row spaces are equal to one another, the sought transmission signal matrix is obtained as an intersection of the two signal spaces. If, then, when moving from one iteration step to the next, the difference between the transmission signals obtained, i.e. Transmission signal matrices, below a predetermined maximum value, the so-called convergence or stop criterion, the transmission signal is obtained with the desired accuracy.

It is also advantageous if, in order to take into account a memory of the respective transmission channel, a length of the transmit signal length that is longer than the length of the received signal block. nalblocks is taken as a basis. This takes into account the fact that in such a case more input symbols have an influence on the block of output symbols.

In the case of a channel with memory, it is also advantageous for the calculations if the individual matrices are used as matrices with a block-toeplitz structure or block-Hankel structure.

To determine the transmission signal, it is also possible to proceed in such a way that the line space of the received signal matrix is calculated and from this the line space of the transmission signal matrix, e.g. by singular value decomposition. The generating matrix of the transmission signal matrix is expediently determined from its line space with resolution of the matrix ambiguity. On the other hand, with a view to high computing efficiency, the transmission signal matrix can be derived in a uniform step from the line space of the received signal matrix, forcing a block-toeplitz structure and a matrix modulation structure.

The invention is explained in more detail below on the basis of preferred exemplary embodiments with reference to the accompanying drawings. Show it:

1 schematically shows a transmission device with a MIMO channel;

2 shows in a flowchart the determination of equalized signals in an iterative process; 3 and 3A and 4 and 4A in corresponding diagrams and associated detailed diagrams alternative equalization methods; and FIGS. 5 and 6 in diagrams the received signal quality for an instantaneously mixing channel (FIG. 5) or for a MIMO channel with memory (FIG. 6) when using different parameters. *

1 schematically shows a transmission device 1 with a MIMO channel 2, where • K data streams _h [] to be transmitted in parallel are supplied with & = 1, _" *, ÜT; these data streams d _k [n] are shown in FIG a modulator 3 according to a matrix modulation method the desired matrix modulation Structure imprinted, resulting in 4 M antenna input signals S _jf c [«j (with k = 1, _" , Mη) on M _τ transmit antennas. These signals Sk [n] are transmitted via MIMO channel 2 (with the transmission matrix H) and Received on the receiver side by Λ antennas 5. The receive signals [ϊ] (with M _% ) are then processed in a demodulator (equalizer) 6 to estimated values d ^ [rύ äer data signals ä _k [].

First, the case of so-called instantly mixing MIMO channels, ie MIMO channels without memory, should be considered. (However, this restriction will be dropped later.) It is possible to arrange a vector / matrix value input / output relationship x [n] = Hs [n] ⁽ D

specify. The transmit vector is given as s [n] = [sι [»]» "S _τ lijf ^r and the receive vector as x [» | = [xι [n] • ' ^, % M _n [ϊlψ'. The unknown (ax Λ # τ) channel matrix H contains, as the (i, j) th entry hi, that channel coefficient which describes the transmission from the jth transmitting antenna 4 to the ith receiving antenna 5.

In the following it is assumed that only one transmit or receive signal block of length N is considered. This assumption is common and is in no way restrictive, since on the one hand the block length N can be chosen arbitrarily and on the other hand blocks can be strung together.

The transmitter-side matrix modulator 3 (essentially a computer) generates a transmission signal block (a transmission signal matrix) S = [s [ü]>_" « s [iV ~ "l]) from the K data streams d ^«] to be transmitted Size M ^ x N according to the following regulation:

K

S = ^ M _Ä D _A. (2)

In it are the K data matrices D _& diagonal JVxJV matrices of the form D _fc = diag {<έ * [0], •• ■, <{JV-3]} and M _& the so-called modulation matrices of size Mi XN, of which there are K also exists.

N successive receive signal vectors become analog combined into a received signal block (a received signal matrix) X = [x [ö] _" * x [JV-l]]. If the forced modulation structure - according to the above relationship (2) - is combined with the input / output relationship (1), you get a common matrix input / output relationship for modulator 3 and channel 4 as follows:

K = HS = Hj M _fe D _& , (3) fe = l

In the following it is assumed that the receiver (5, 6) knows the forced structure, ie, all K modulation matrices Mj., But that both the channel H and the data sequences d _k {n] are unknown.

The methods described in detail below also assume that the i-th columns (with i = 1 ₃ - ... j \ f) of all modulation matrices M _& (k = 1, _' « _' , K) are linearly independent , So if the £ th column of the fifth modulation matrix is called ϊEig [$], it means that • • * <] f]} for any ϊ £ - [1.2. _' »• _j Λ ^" } must be a set of linearly independent vectors.

In addition, K ^f <K <ang {H} is defined, where K * denotes the number of active data streams and K the maximum number of data streams (see (2)). It was found experimentally that if real-value data streams are used, the less restrictive condition K '<K <2R @ jttg {H} should be fulfilled. This is obvious since complex-valued vectors have twice as many degrees of freedom as real-valued ones.

N> 1 _j ^T T _f is to further the apply, and the modulation matrices ^¬ Lfc should fulfill the condition described in the following: With {ι [t], '• *, bMτ-. _K lMl i ^rd denotes an arbitrary base that spans that space that is orthogonal to that of the vectors {-Bi [i] _j m ₂ [i | _' • _' g-jt] is space. Now a matrix W is formed, the first (K ^f Mγ - K ^f K) columns of the so-called Kronecker product possible combinations (r, holds. The second (I Mψ - K * K) columns of the matrix W are formed by all possible combinations of m ^ S] ® b _# [2]. Continue in the same way up to the combinations m ^ / f] Θ b _s fiVj- driving, one obtains an MXN (K ^f M - K'K) matrix W. It can be shown that the rank of W must be M _ηp - 1 in order to obtain a matrix _modulation structure that is strong enough to To enable error-free reconstruction on the receiver side. The rank of ^" depends only on the Tt matrices M ^ and on the parameters K * and Λ ^r . For example, you can see that the matrix must be horizontal to meet the rank requirement, which in turn means the one mentioned above inequality

N>^" M ^ ~ 11 _Af ^T - _K.

Accordingly, it was investigated for some cases how one can systematically generate modulation atrices that meet the ranking condition just described. However, this does not harm the applicability of the method. It was found experimentally that randomly chosen modulation matrices, which have the necessary dimensions given above, met the rank condition and brought the desired results with every simulation carried out.

Under the conditions described above, the structure of 8 (see equation (2)) enforced on the transmit side in the matrix modulator 3 is in any case strong enough to enable a reconstruction (demodulation) of the data sequences that is unambiguous apart from a common constant factor to allow d ^ [n] from the reception matrix X. Expressed mathematically, this means that the reception matrix (where K * <K, as mentioned, is the number of active data streams, ie it is taken into account that the receiver (5, 6) could expect more data streams than it actually receives from the transmitter (3, 4)) not as can be represented, with the exception of a constant factor ΕL ≠ Η. and / or D _Ä jέD _A is. This also means that if the recipient succeeds, matrices H and

D _ß , with fc = l, «« *. If, so that

K κ> fi∑MÄ _^ -H∑ _f cD *, (4) fe = ι fc = ι

it follows that H ^# H = eI (here I denotes the unit matrix and H # the pseudo inverse of H; see also GH Golub et al., Matrix Computations. Baltimore: Johns Hopkins University Press, 3 ed., 1996) and further cD _Λ ,

D & = {k ≤ K '(5) l o,

where c € C (di the set of all complex numbers) is an unknown constant factor. The fact that almost all blind methods can only be demodulated (equalized) down to an unknown constant factor is not a limitation, since the constant factor is either like differential modulation (see JG Proakis, Digital Communications. New York : McGraw-Hill, 3 ^rd ed., 1995) is not used or can easily be estimated with the help of additional knowledge, such as knowledge of the symbol alphabet used.

In the following, two different methods for demodulation (equalization) are presented, e.g. an exact method, which has the disadvantage, however, that it is relatively computationally complex - especially for large values of M, Mi and FC - and an iterative method, which is considerably more computationally efficient than the exact method.

To simplify the description of the methods, it is first assumed that H has full rank and that the same number or more receiving antennas as transmitting antennas are used, i.e. Λ '2.. Changes that are necessary for a singular channel matrix H or -ig <d are noted separately.

For the exact demodulation method, the above equation (3) is first column by column

K x [»] = H $ ^ <k [n] m * [nI, n = 0, -, - Vl, ⁽ 6 ⁾

rewritten, where m * [ft] denotes the nth column of the modulation matrix M _& . If this equation (6) is multiplied by the pseudo inverse H * of the channel matrix H from the left, the result is

This set of ΛT linear equations can be used as a matrix vector product

Qy = 0 ⁽ 7 ⁾

to sum up. Here the matrix is of size MN x (M _T M _Α «J-KN) by .PJ .P4

Q

: 0 ^{• "•} ■

given, the (px MιM) matrix X _q [n] by

X _fl [n]

0 x ^r M

and the (Mi x K) matrix Mq [n] is given by M _g [κ] = [mi [»], - • •, m _if [«]]. Furthermore, the vector y, which in particular also contains the data signal quantities sought, is through

given, where d [n] = [ι [»], --- _J ώf [«] 'and © is; the respective transposed vector is designated with the index "T"; furthermore by (H #) _<s5 - the (i, j) -th element of the pseudo inverses of the matrix H is designated.

As already mentioned, equation (7) only applies to the noise-free case. However, since noise is always present in practice, equation (7) can only be solved approximately, for example with the method of minimum squares (LS). The LS solution of (7), namely yLg , as known per se, is given by the right singular vector for the smallest singular value of the matrix.

However, the calculation of the singular vector sought is relatively computationally complex for large _τ or N due to the resulting large dimensions of the matrix. In these cases, the next iterative procedure presented is significantly computationally efficient. more focused.

As explained, for a given received signal block X = HS and for known modulation matrices M ^, the transmission signal matrix S = ^ * ₁ M ^ D ^ and thus also the K data matrices D _{& are} uniquely determined (apart from a scalar factor). It can be shown that for a given receive signal block X, the matrix S has already been reconstructed unambiguously (except for an unknown factor) if one finds a matrix that simultaneously fulfills the following two properties:

1. S has the desired modulation structure, ie, S = ∑J ιMfcD _f t, with diagonal matrices D ^; and

2. the line space of S is equal to the line space of X.

The second property follows from X = HS, since it is assumed that the channel matrix H has full rank.

Since both of the properties listed implicitly define linear spaces, the reconstruction can also be formulated as follows: You are looking for a matrix S that fits both in a space Λ according to the modulation structure property and in a space B according to the subspace property (property no . 2) lies. So you're looking for S € «AnB. Since both Λ and S are linear subspaces of C ^{τxJ *} ( ^ie the set of all complex-valued matrices with M _τ rows and N columns) and therefore also convex, the algorithm of continuous projections onto convex sets (projections onto convex sets, so-called POCS method, see PLCombettes, "The foundations of set theoretic estimation", Proc.IEEE, vol. 81, pp. 181-208, Feb. 1993) an element of the intersection S 6 _* . (1 and thus calculate the desired S.

According to FIG. 2, a computationally efficient iterative method is used for the calculation, which, starting from a starting value S ^(0), projects alternately onto the two spaces Λ and ß (see blocks 10 and 11 in FIG. 2) until it is clear a further projection no longer results in a significant change, ie until the estimated value converges, s. Query step 12 in Figure 2); 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 projection method is inherently teratur (see above) under the name "projections onto convex sets", also known as POCS. The value of the stop criterion should be determined according to the circumstances and objectives. The detailed procedure is as follows.

1. Projection on Λ-. The projection on Λ results in , _where ]; 5 _e i can be shown that the diagonal elements of the matrices D / through

given are. Here S ^ " ^* ^ is the result of the previous iteration (ie the previous projection on B), and the matrices Mjjj" of size M x N are defined in such a way that (m ^ j »]) ² ', i.e. the transpose of the nth column of MJJ, "equal to the fe-th row of the (K x Mi) matrix [ι [» J • •• mjr [ 'Y] is *. (Math ^¬ are seen matically so {mι [ n], and {m £ Mj ** 'jmκM} reciprocal bases of an Ä "-dimensional subspace of & ^iτ .) In the event that the vectors m ₁ [n], -.«, mjg'J | are orthonormal, Mj applies = M, where M is the complex conjugate of M _Ä .

2. Projection on ß: The projection on S results in S ⁽ * 1 ₌ BW, whereby it can be shown that the matrix B ^(l1

BW = SP- ¹ 3X *

is. Here S ^ " ¹ ^ is the result of the previous iteration (ie the projection onto -4.) And # is the pseudo inverse of X, which only has to be calculated once before the iterative process begins.

It can be shown that the convergence of the method is given in the present case. This ensures that for a given received signal block X and a ge ^¬ passed modulation structure (s. Equation 2) the input data streams di] are determined up to a common scalar factor.

The rate of convergence (but not the convergence itself) depends on the starting point S ^ of the iterations. An advantage The method is that in the semi-blind case, ie in the event that a certain number of the transmitted data is known (see, for example, the midamble for existing standards such as GSM or UMTS), the data known a priori can be used to calculate a good starting value and thus to accelerated convergence and higher computing efficiency can be used. Another method to increase the convergence speed of the method is the so-called relaxation, cf. the PLCombettes document mentioned above. Furthermore, knowledge of the broadcast symbol alphabet used can be used to accelerate convergence, especially towards the end of the iteration; see. e.g. S. Talwar et al. "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 for algorithms that use a finite symbol alphabet. However, this last approach to accelerating convergence has the disadvantage that convergence can no longer be guaranteed.

For large values of N and / or Λ, the POCS-based method explained above is considerably more computationally efficient than the method presented before.

If the channel matrix H becomes singular or M, Mrp, the matrices Bflg "which contain the dual bases must be recalculated in each iteration step, with the columns of the matrices now being replaced by the columns of the matrices M ^ calculation must be taken as a basis in order to reconstruct the data exactly in the case of noiselessness. However, simulations have shown that, in particular at low SNR, the original method without the changes just mentioned causes only slightly higher reconstruction errors than the modified method.

The matrix modulation method described can also be used without changes in order to transmit the FC-independent data streams <4-Mι via a MIMO channel 2 with memory. In this case, however, some additions are necessary for demodulation and equalization, which are described below.

For a MIMO channel 2 with memory, the input / output relationship is

where the (R X Mp) matrices H [m] are the channel's matrix-valued impulse response and (L-1) represents the channel's maximum delay.

The transmitter-side matrix modulation is still in shape

K

k = &,

however, the transmission signal block length (with the reception block length N remaining the same) is increased to N + Ll in order to take into account the memory of channel 2. It follows that the send matrix S = [s [-, £ + l]>_" s [A ^r > ~ l]] now has the size Λf _τ x (N + L - 1) and accordingly the diagonal data matrices D _ifeϊ ^s dia {dA [-L + l], '", rfft [JV-l]} have ^{the size} (N + i ~ l) x {N + -l).

It is again possible to matrice the input / output relationship (see equation 9) by arranging the receive vectors x [n], the channel impulse response Η. [M) and the transmit vectors sj »} into a single matrix-valued input / output relationship

X = HS ⁽¹⁰⁾

summarize. Here X is the output matrix that is created from the received signals; Kanal 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 blind equalization.

A possible arrangement that is assumed in the following is, for example, the following: The entire matrix-valued impulse response is combined to H '= [H [ö] • • • H [L— 1]], which ultimately results in a channel block matrix Η the size

Mjp M (L + p - 1), in which H 'p times, shifted by positions, is stacked (the stacking parameter p is in the Literature also referred to as smoothing parameters), as

0 H 'n H'

H '0

can be defined, cf. also e.g. A.J. van der Veen et al. , '' A supspace approach to blind space-time signal processing for wireless communication Systems ", IEEE Trans. Signal Processing, vol. 45, pp. 173-190, Jan. 1997; and H.Liu et al.," Closed form blind "symbol estimation in digital communications", IEEE Trans. Signal Processing, vol. 43, pp. 2714-2723, Nov. 1995. Other arrangements are also conceivable, for example, by interchanging the order of the rows or columns of the individual matrices arise, but are equivalent to the above arrangement.

Next, a transmit block matrix of size _τ (£ + $> - 1) X (N - p + 1), namely

S [ΛΓ-I] -2] -1] N-2]

L shL + 1] st-ü + 2] .. ^, s [JV-X-p + l]

Are defined . These block matrix S has a block Toeplitz structure and is of the columns of the matrix S = [s [- 1] - L + 1] ""<s [N] riert gene ^¬ why this matrix S-generating than the Matrix of S is called. Finally, with the output vector x [«] the following receive block Toeplitz matrix of size Mjφ X (N - p + 1), namely x [2] x (jV _ p] _x jv - p + 1]

X xfr - 1]] x [JV - 2] xfJV - 1].

. 3A, this step is illustrated the formation of the receiving or from ^¬ transition matrix X at block 16 in FIG. 3, with the results shown in Fig. 2 Detail steps according to Fig. It then follows three-stage method for demodulation, wherein according to block 17 the row space of the reception matrix X is first calculated. The sizes of the individual matrices depend on parameters such as the channel impulse response length L, the number of transmit and receive antennas 4, 5, the block length N and the smoothing factor p. Under the condition that these parameters are chosen in such a way that standing and S is lying (formally, ff> ^ ^ _> ^m t M »> M and ^' N> M _∑ L + (JW ^" τ + l) {p — 1) apply), and that Η also has full rank is the space that is spanned by the rows of the receive matrix X (the row space of X), equal to the row space of S. So the row space of the send- Block matrix S can be calculated, for example, by means of a singular value decomposition of the reception matrix X. This step could, however, also be approximated by other methods known per se, which are less computationally expensive than the singular value decomposition. D and V according to the relationship A = TJDV, where U and V have orthogonal columns or rows, ie TJ ^ff U = I and V ^H V = I, where I is the unit matrix of the corresponding dimension and D is a diagonal matrix.) the calculation of the line space of the reception matrix x X takes place according to block 18 in FIG. 3, the calculation of the generating matrix of S -. It is known that the matrix itself can be reconstructed from the row space of a lying Toeplitz matrix or Hankel matrix down to a multiplicative factor. 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 horizontal block toeplitz matrix which, as mentioned, is determined by the generating matrix S. The given equalization problem can therefore also be formulated as the calculation of the generating matrix S from the reception matrix X.

In H.Liu et al., "Multiuser blind channel estimation and εpatial channel pre-equalization", Proc. IEEE ICASSP-95, (Detroit (MI)), pp. 1756-1759, May 1995; as well as in the aforementioned document by AJvan der Veen et al. two methods are described, such as S-up to a matrix ambiguity (i.e. SA = AS with unknown invertible px T matrix H) can be calculated from a block Toeplitz matrix. Furthermore, the one from E. Moulines et al. , "Subspace methods for the blind identification of multichannel FIR filters", IEEE Trans. Signal Processing, vol. 32, no. 2, pp. 516-525, 1995 known methods can be used accordingly to solve the present problem. Common to all methods, however, is that either the matrix X or a matrix whose row space spans the space orthogonal to the row space of X must be stacked in a "supermatrix" in order to be able to conclude from this supermatrix by a singular value decomposition. However, since the computational complexity of a singular value decomposition increases with the third power of the dimensions of the matrix to be decomposed, these methods are rather computationally complex, which is why an alternative (namely the so-called direct factorization, see FIG. 4) is proposed below.

. In the scheme of Figure 3 now follows in accordance with step 19, the resolution of the Matrixambiguität, the calculation of the generating matrix S that is, from A - ^Since the remaining Matrixambiguität entirely analogous to an instantaneous mixing channel X = HS

(cf. equation (3)), the ambiguity can be resolved with the demodulation methods for the instantaneously mixing channel, which were described above, in order to obtain the data dJ- + 1], <[- £ + 2], • ••, <[Λ ^r —1] ki ^{s aυ} -f to reconstruct an unknown common constant factor. Accordingly, the resolution of the matrix ambiguity (block 19 in FIG. 3) is drawn out in detail in FIG. 3A with blocks 10, 11 and 12 which correspond to those of FIG. 2.

A direct factorization can also be used for demodulation (equalization), as shown schematically in FIG. 4, which is also based on the aforementioned POCS method, but which calculates the generating matrix S and resolves the matrix ambiguity in a step 20 (FIG 4) united and therefore 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 options, possible relaxation, possible use of a priori knowledge, the possibility of subchannels of different lengths, etc. In addition, the advantages just mentioned are not only limited in their impact on direct factorization the resolution of the matrix limited, but advantageous for the entire step 20.

As mentioned, the calculation of the generating matrix A except for an ambiguity 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 ~ T ^ M _f cD _f c with diagonal matrices D _& ;

2. the row space of the matrix S is equal to the row space of X.

In other words, S € Äfl B, where Λ is the linear subspace of all Block-Toeplitz matrices with the generating matrix S (where the matrices M * are given and the matrices O _{k are} diagonal). Furthermore, B denotes the linear subspace of all matrices whose row space lies in the row space of X (ie all matrices of the form with any Mι {L -jr - 1) x p-matrix B). This formulation again leads to a POCS method for calculating S, in which the iterated version of S is alternately projected onto Λ and B:

1. Projection onto Λ: (see block 21 in FIG. 4A): since a so-called linearly structured matrix (cf. JACadzow, "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 Λ can be accomplished by the following two steps:

In the first step (block 24 in FIG. 4A) the block Toeplitz structure is enforced: Let S ^ "" ^ be the result of the previous iteration (ie the projection onto B). From the matrix 5 "" ¹⁾ , which has no block Toeplitz structure, a K x (N + L - l) "pseudo-generating matrix" S ^ "^ is calculated as follows. The first of the Mi lines from S " ^{* 1} ^ is calculated by averaging correspondingly shifted and padded versions of the first, ( _τ + l) -th, (2M _τ -l} -th, etc. lines of S ^ ~ ^. Man So take the first row of S ^ "^, move it one position to the right and then add it to the (Mτ + 1) ~ line of« SC "" ¹⁾ , adding zeros if necessary. The result will be again shifted one position to the right and added to the (2 _τ + l) th line of S ^ "^, etc. Finally, the jth element of the resulting line vector of length N + Ll is replaced by the jth element of {1,, •• -, _τ , M _τ , •>_'3 M _τ , pl, _' ««, l) divided to get the first line of S ^ ^{™ 1} ^. The second line of S ^ ^" " ¹⁾ is calculated in a similar way, whereby now the second, (r + 2) -th, (2 r + 2) -th, etc. line of S ^ " ¹⁾ are used. All M rows of S ^ " ¹ ^ are calculated in this way.

In the second step (cf. block 25 in FIG. 4A), the modulation structure is enforced. Doing so formed, it can be shown that the diagonal elements of the diagonal matrix DW by

given are. Finally, the Block-Toeplitz matrix ß® is formed, which is generated by S ^.

2. Projection onto β (see block 22 in FIG. 4A): The projection onto B can be written by tS "s = B ^ '- Y, it being possible to show that

Here S ^ ~ ¹ ^ is the result of the previous iteration (i.e. 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, the convergence (see block 23 in Fig. 4A, corresponding to block 12 in Fig. 2) of the POCS algorithm to an intersection of the two spaces is guaranteed, i.e. S ^ € Af. It can be shown that S ^ = cS with e € <C.

The speed of convergence and thus the computational efficiency of the process strongly depends on the initialization S®>. In the semi-blind case, known input data <4D * _I ] _J * " ₃ <a] could be used to generate a matrix S ^, where

D ^α5 POCS algorithm would then be initialized with B ^ = XS *. Furthermore, the convergence can be accelerated again using the methods described above.

Finally, some practical studies or simulation results relating to the invention will be presented with reference to FIGS. 5 and 6.

A number of Mj = 4 transmit antennas was chosen, and JFf = 3 uncoded QPSK data signals d _f cjn] were used as a basis. The modulation matrices M _k with the block length N = 200 were constructed as follows: All matrix entries were chosen randomly as a realization of Gauss' independently distributed identically random variables, and then the corresponding columns of all M ^. orthonormalized (that is, random modulation matrices were chosen whose corresponding columns were orthonormal intermatricially). The channel impulse responses were generated randomly for each simulation run, and the received signals x [n] were disturbed by white Gaussian noise with variance Λ ³ and observed over an interval of length N = 200.

First, three instantly mixing MIMO channels with _R = 4, M _R = 6 and M _R = 8 receiving antennas were considered as an example, see. curves 30, 31 and 32 in Fig. 5; 5 shows the normalized mean square error (MSE) as a function of the signal-to-noise ratio (SNR). The MSE value was defined as ∑ ∑ Wa Wl ∑L∑ 4WP averaged over all isolation runs, where <[n] is the estimated value of «M that was achieved with the corresponding method, and where c is the least - squares "estimate for the unknown factor c. The number of simulation runs over which averaging varied between 200 and 10,000, depending on the SNR. The SNR was as

J ü Εi _k i ∑S was defined and was the same for every simulation run that was averaged. The simulation results show that an increasing number of receiving antennas, corresponding to a higher reception diversity, achieves better results.

A MIMO channel with memory (with M _R = 6 receiving antennas and with an impulse response length of L = 3) was then examined, see. Fig. 2. Fig. 6 shows that normalized mean square error (MSE) as a function of the signal Signal-to-noise ratio (SNR), which was determined with the multi-step method (curve 33), and the one (see curve 34) that was achieved with direct factorization (smoothing factor p = 5). The simulation results show that, especially for low SNR values, the direct factorization achieves much better results than the multi-step method. This poorer performance of the multi-step method should be due to the fact that in the second step an assignment of singular vectors to a useful signal or Noise signal space is required, in which errors easily occur, especially in the case of low SNR. This assignment is not necessary for direct factorization.

The technology according to the invention is thus suitable for transmitting large amounts of data with low transmission power without loss of capacity through training symbols via MIMO channels. It has the advantage of being robust against an unknown MIMO channel thanks to a matrix modulation structure that was deliberately introduced on the transmitter side, and furthermore to separate the MIMO channel into several "virtual" channels with one input and one output that can be used independently of one another. As a result, this method can be combined with conventional channel coding (for each virtual channel separately), which is to be decoded much more computationally efficiently than channel codes designed for MIMO systems, which also means the use of a large number of transmitting and receiving antennas 4, 5, at relative low computing effort compared to a system designed according to the state of the art, allowed. Furthermore, it is conceivable to combine the method with a coding method which uses known dependencies between the individual virtual channels generated on the transmitter side during decoding (so-called turbo decoding).

Claims

Claims:

1. Method for transmitting data streams via channels with several inputs and outputs each, the data streams (d [n]) at the channel inputs being modulated in a predetermined manner to transmit signals (s [n]) and at the channel Outputs are derived from the received signals (x [n]) by equalization corresponding data streams (d [n]), characterized in that a predetermined matrix modulation structure (Mk) at the channel inputs of the data streams (d [n]) is forced and the equalization of the received signals (x [n]) is carried out at the channel outputs on the basis of this known predetermined matrix modulation.

2. The method according to claim 1, characterized in that each of data streams to be transmitted d%] of length N as a diagonal N x N data matrix D _{& of} the form D _fc = diag {fe [0], • • ■, d * [ N — 1]} is written and multiplied by a respective modulation matrix M _f t of size _τ x A ^r , where M _∑ indicates the number of channel inputs.

3. The method according to claim 1 or 2, characterized in that each data stream (d [n]) to be written as a diagonal data matrix (D _k ) is multiplied by its own predetermined modulation matrix (Mk), the modulation matrices (Mk) preferably having full rank and the corresponding columns of the individual modulation matrices (Mk) are linearly independent.

4. The method according to claim 2 or 3, characterized in that the number (MT) of the channel inputs is greater than the number (K) of the data streams (d [n]).

5. The method according to any one of claims 2 to 4, characterized labeled in ^¬ characterized in that the length (N) of the respective transmission and reception signal block (x [n]) of the condition

N> [|| Ξ] is enough where MT is the number of channel inputs and K is the number of data streams.

6. The method according to any one of claims 1 to 5, characterized in that the equalization of the received signals (x [n]) in iterative form by alternately projecting transmission signal matrices (S), starting from a predetermined starting value, onto two signal spaces (A , B) is carried out, of which one signal space (A) represents the modulation structure property and the other signal space (B) represents a subspace property according to the condition that the line space of the received signal matrix (X) in the line space of the transmission signal Matrix (S) lies, where appropriate these line spaces are identical to one another, the sought transmission signal matrix (S) being obtained as the intersection of the two signal spaces (A, B).

7. The method according to any one of claims 1 to 6, characterized in that in order to take into account a memory of the respective transmission channel an increased length (N + Ll) of the transmission signal block is used as a basis, where L is the impulse response length of the Channel is.

8. The method according to claim 7, characterized in that the individual matrices are used as matrices with a block-toeplitz structure or block-Hankel structure.

9. The method according to any one of claims 6 to 8, characterized in that the row space of the received signal matrix is calculated and from this the row space of the transmit signal matrix, e.g. by singular value decomposition.

10. The method according to claim 9, characterized in that the generating matrix of the transmission signal matrix is determined from its row space with resolution of the matrix ambiguity.

11. The method according to claim 9, characterized in that the transmit signal matrix is derived from the line space of the received signal matrix in a uniform step by forcing a block toeplitz structure and a matrix modulation structure becomes .

12. Transmitting device for performing the method according to one of claims 1 to 11, with one of several data stream inputs (di _j * * * _j diζ) and several transmission signal outputs {, § ₁ , • • ». _fτ ) _having modulator (3), which is set up to force supplied data streams (d [n]) the predetermined matrix modulation structure (Mk).

13. Transmitting device according to claim 12, characterized in that the modulator (3) is set up to transmit each data stream d _k [n] of length N as a diagonal N x N data matrix D _{fc of} the form D _ft = iag {<[ 0] -. •, cfef-V-1]} to write, and with a respective fe-th modulation multiply matrix _M of size M x N, wherein M _Σ indicates the number of channel inputs.

14. Transmitting device according to claim 12 or 13, characterized in that the modulator (3) is set up to multiply each data stream (d [n]) to be written as a diagonal data matrix (Dk) by its own predetermined modulation matrix (Mk), the modulation matrices (Mk) preferably have full rank and the corresponding columns of the individual modulation matrices (Mk) are linearly independent.

15. Transmitting device according to claim 13 or 14, characterized in that the number (M _τ ) of the channel inputs is greater than the number (K) of the data streams (d [n]).

16. Transmitting device according to one of claims 13 to 15, characterized in that the length (N) of the respective transmission or reception signal block (x [n]) of the condition

N> \ ^ is enough

where M is the number of channel inputs and K is the number of data streams.

17. receiving device for carrying out the method according to ne of claims 1 to 11, with a multiple received signal inputs (jp ^ .. «« _? XM ^) and a plurality of data signal outputs ß, _" *, g *} demodulator (6), which is set up, an equalization of to carry out received signals (x [n]) fed to its inputs on the basis of the predetermined matrix modulation (Mk).

18. Receiving device according to claim 17, characterized in that the demodulator (6) is set up to equalize the received signals (x [n]) in iterative form by alternating projection of transmit signal matrices (S), starting from a predetermined starting value perform two signal spaces (A, B), of which one signal space {A) represents the modulation structure property and the other signal space {B) represents a subspace property according to the condition that the line space of the received signal matrix (X) in the line space the transmit signal matrix (S), where appropriate these line spaces are identical to one another, the sought transmit signal matrix (S) being obtained as an intersection of the two signal spaces {A, B).

19. Receiving device according to claim 17, characterized in that the demodulator (6) is set up to calculate the line space of the received signal matrix and from this the line space of the transmitted signal matrix, e.g. by singular value decomposition.

20. Receiving device according to claim 19, characterized in that the generating matrix of the transmission signal matrix is determined from its row space with resolution of the matrix ambiguity.

21. The receiving device as claimed in claim 19, characterized in that the transmit signal matrix is derived from the line space of the received signal matrix in a uniform step, forcing a block toeplitz structure and a matrix modulation structure.