DE10115261A1 - Operating digital mobile radio network involves using orthogonal space-time block transmission codes with maximum diversity for given number of transmission antennas - Google Patents

Abstract

The method involves using orthogonal space-time block transmission codes with maximum diversity n x m for a given number of n transmission antennas, whereby a transmitting station has n (n=2,3,4..) transmission antennas and a set of 2l information bit vectors to be transmitted by the station is formed on a set of 2l space-time symbols using a defined function, whereby each symbol corresponds to a unitary matrix. Independent claims are also included for the following: a base station, a mobile station and a computer program product.

Description

The present invention relates to a method for Operating a digital cellular network using of space-time block codes (ST codes = "space-time block Codes ") according to the preamble of claim 1.

Such methods according to the preamble of claim 1 are z. B. in "Space-Time Codes for High Data Rate Wirelesss Communication: Performance Criterion and Code Construction " by V. Tarokh et. al. in IEEE Transactions on Information Theory, vol. 44, no.2 March 1998, pages 744-765 or in "Space-Time Block Codes from Orthogonal Designs", IEEE Transactions on Information Theory, vol. 45, no.5, July 1999, pages 1456-1467 by V. Tarokh et. al. described.

The use of the space-time block codes described there there is the following physical problem in cellular networks based on: Strong attenuation due to the transmission path or Distortion of a signal from a transmitting station (e.g. a fixed base station in a cellular network) wirelessly sent out signal makes it for a receiving one Station (e.g. a mobile station in a cellular network) very much difficult to get the originally transmitted signal correctly to recognize. This is especially true when the receiving mobile station in a wireless multipath Receiving environment ("multipath wireless environment"), where they z. B. due to multiple reflections of the original broadcast signal on the walls of surrounding Buildings only have several strongly weakened "echoes" of the original transmission signal. To remedy this too create is for a certain "diversity" of the received Signal to worry. This is done by the receiving station additionally one or more less strongly weakened "images" of the transmitted signal to provide. The so-called "Diversity" is a measure for the recipient obtained number of the statistically independent "images" of the broadcast signals broadcast by the broadcaster.

In practice this required diversity is e.g. B. achieved in that sender and / or receiver side several spatially spaced apart from each other or differently polarized transmission resp. Receiving antennas are used that each have an "image" transmit or receive a signal to be transmitted. "Image" does not necessarily mean that two or more exactly identical copies of the same signal be sent out.

Rather, especially with the known spatial Time block codes at a given time from the different transmitting antennas different signals are sent out, each through a special Coding algorithm from the information bits of the original signal. With every receiving antenna then goes to a given (later due to the signal delay) Time the sum of the changes due to the transmission route Send signals from which on the receiver side below With the help of MLD estimation algorithms ("maximum likelihood detection ") in turn reconstructs such information bits with as high a probability as possible Information bits correspond to the original signal.

For a better understanding of the underlying problem of the present invention is to FIGS. 1 and 2 taken.

Fig. 1 shows schematically a conventional single-antenna single-antenna radio transmission link between a transmitter Tx and a receiver Rx in a digital cellular network. In the transmitter information bits are fed, the z. B. consist of a sequence of ones and zeros. It is assumed that a bit vector (1,0,1) of length l = 3 is fed in and consists of the number sequence 1-0-1. Depending on the coding method used, this bit vector is transformed uniquely (ie reversibly unambiguously) into a symbol vector of lengths at the transmitter end. As symbolized in FIG. 1 by different shades of gray, the numbers appearing in the symbol vector can differ from 1 and 0; B. signals corresponding to the real part and imaginary part are sent out of phase by 90 °.

In Fig. 1, the case n = l = 3 is shown, ie each single bit is encoded into a single symbol (BPSK modulation - Binary Phase Shift Keying, in QPSK - Quadrature Phase Shift Keying would n = l / 2 shall apply).

A symbol vector comprising several individual symbols is then broadcast by an antenna in the transmitter Tx and by a Receiver Rx received. There the symbol vector becomes the length n = 3 by an inverse transformation to the original Bit vector (here (1,0,1)) of length l = 3 reconstructed.

Fig. 2 illustrates schematically a radio transmission link between a transmitting system with n = 3 transmit antennas Tx1, Tx2, Tx3 and one receiver Rx in a digital mobile radio network, as per se already known space-time block codes are used. In this case, a bit vector of length l = 3 is fed to a space-time block coding device (ST coder = space time coder). This maps an incoming bit vector onto an n × n matrix.

Here, n corresponds to the number of transmitting antennas that are used in the transmission system. In a given time slot j, an antenna i sends a signal which corresponds to the matrix element C _{ijk of} a 3 × 3 matrix C _k which has been encoded by the ST coder from the incoming bit vector of length l = 3. k is an index that distinguishes individual matrices, which in turn correspond to one-to-one k different bit vectors. These relationships are explained in more detail below.

As a result of the signals emitted via the three transmitting antennas Tx1, Tx2 and Tx3, signals corresponding to the matrix elements C _1jk , C _2jk , C _{3jk arrive at the receiving antenna Rx at a receiving time corresponding to the transmitting time slot j (later due to the delay time} ). _{At the receiver end, a space-time block matrix C k is} reconstructed from the sum of the incoming signals in a space-time block decoder (ST decoder) using MLD algorithms and converted into the corresponding original bit vector (here ( 1,0,1)) translated back.

The general problem with this is that the Diversity in the mobile station of a digital one Cellular network through the use of several transmitting antennas at the base station to maximize. There shouldn't be any special prior knowledge of the time-varying downlink channel (from a base station to a mobile station) are assumed.

For the case of linear space-time block codes with two antennas the result is known (it is optimal in the sense that it provides a doubling of the diversity for two antennas) and it is part of the UMTS standard (3GPP TS 25.211 V3.4.0: Physical channels and mapping of transport channels onto physical channels (FDD) (1999 edition), September 2000) become. This well-known space-time block code scheme is fulfilled the "rate 1" requirement.

A space-time block code scheme with "rate 1" is clearly stated a system in which just as many information bits can be effectively transmitted from a transmitter to a receiver per considered time segment as in the reference system shown in FIG a transmitting and a receiving antenna. In other words: a "rate 1" ST code has an unchanged transmission rate compared to a basic system with only one transmitting and one receiving antenna. This is e.g. B. a system in which a block of two code words is transmitted to the receiver simultaneously in two successive time windows over two different transmission channels; the receiver thus receives just as much information per unit of time as if two corresponding individual bits had been transmitted over a single transmission channel in two consecutive time windows. Thus z. B. in the W-CDMA mode of the UMTS standard for future mobile radio systems (see e.g. www. 3GPP.org) ^{to transmit the standard mapping of four bits to 2 4} = 16 ST symbols in two time steps via two transmitting antennas. A system with "rate 1" for outer blocks behaves in exactly the same way as the basic system with only one transmitting and one receiving antenna. This property is crucial for upgrading a basic system to a system with several transmitting antennas and space-time block codes.

The space-time block code used in W-CDMA mode corresponds to the so-called Alamouti code. That’s what it’s about very easy to deal with on the receiver side reconstructing code to increase diversity in one digital cellular network with a sending station with two (n = 2) transmitting antennas. The Alamouti code is e.g. B. in "A simple Transmitter Diversity Scheme for Wireless Communications ", IEEE J. Select Areas Commun, vol. 16, pp. 1451-1458, Oct. 1998 by S. M. Alamouti or in both of the above Publications by V. Tarokh et. al. described.

About the diversity in a cellular network in the future both in the "uplink" direction (from a mobile station to a Base station) as well as in the "downlink" direction (from a Base station to a mobile station) should be increased further the number of antennas per sector of a base station is greater be than two. So it is obvious to use space-time codes to look for which are applicable in the case of three, four or more transmitting antennas. An increase in diversity Constant transmission power leads to an increase the reception quality. Or viewed differently: through the Increase in diversity can be maintained at the same time Reception quality the transmission power can be reduced. the then in a transmitter not exhausted transmission power can then in turn used to attract more participants supply.

Furthermore, the performance of a space-time block Codes also through the spaces between the code words influenced. Considerations on this are already in both of them mentioned articles by V. Tarokh et. al. contain.

In the transmission shown schematically in FIG. 2, the matrix shown with the elements c _{ijk corresponds to} a code word with the number k. The "distance" between code words, ie the "distance" between two matrices C _k1 and C _k2 is ultimately a measure of the quality of a transmission code, ie for the probability that from a sequence of code words received by the receiver distorted due to the transmission path, the originally transmitted code words are reconstructed as clearly as possible. From this point of view, the known space-time block codes for the case of two transmitting antennas can still be improved.

In the case of three, four or more antennas (n <2), in "Space-time Block Codes from Orthogonal Designs", IEEE Transactions on Information Theory, vol. 45, no.5, July 1999, pages 1456-1467 by V. Tarokh et. al. has been shown that linear codes with "rate 1" and complex symbols are not can exist.

In one given at Globecom 2000 in December 2000 Presentation on "Complex Space-Time Block Codes for Four Tx Antennas "by Olav Tirkkonen and Ari Hottinen became the case examined with n = 4 transmitting antennas and complex-valued spatial Time block codes given at a rate of 3/4.

Thus, the search for space-time codes, especially for a number n <2 of transmitting antennas, has currently taken two approaches:

• 1. In "Space-time Block Codes from Orthogonal Designs", IEEE Transactions on Information Theory, vol. 45, no.5, July 1999, pages 1456-1467 by V. Tarokh et. al. are linear Space-time codes with a rate less than one for more than two Transmitting antennas have been constructed. The space-time Symbols Linear combinations of the original signals. These Constructions are not open to external coding because they do not have the "rate 1" property. Thus can they are not simply additional features in an existing one Mobile radio system can be integrated without space-time coding.
• 2. By combining space-time codes with external ones Error correction codes are space-time convolution codes ("space- time trellis codes "). The mixing of However, it does space-time mappings with external codings again impossible to use space-time codes as a simple one feature to be added into an existing system integrate. In such a case, they must also be tried and tested external coding techniques such as turbo codes (see C. Berron, A. Glavieux and P. Thitimajshima: "Near Shannon limit error correcting codes and decoding: turbo codes "in Proc. IEEE ICC, Geneva, May 1993, pp. 1064-1070)) or convolutional codes be changed.

This shows the problem that the digital code words to be transmitted between the sending and receiving stations in a digital cellular network should be optimized for the case of two or more transmitting antennas under the following aspects:

• 1. If possible, there should be a "rate 1" code.
  This is an imperative for mobile radio networks already on the market to be able to be converted to use the new space-time block codes with as little conversion effort as possible. When using "rate 1" when converting from a conventional single- antenna-single-antenna system shown in FIG. 1 to a multi-antenna-single-antenna system shown in FIG The assemblies required for the bit vector to be fed in ( not shown in FIGS. 1 and 2) and the assemblies (also not shown) required on the receiver side for further processing of the reconstructed bit vectors output by the receiving unit are not exchanged. "Rate 1" codes thus guarantee "downward compatibility" of digital mobile radio stations operated with multiple antenna systems and corresponding space-time block codes with other existing system components and thus remove a decisive investment barrier which the practical introduction of "Rate ≠ 1 "Systems, since with these the assemblies for generating bit vectors on the transmitter side and for reconstructing bit vectors on the receiver side would have to be exchanged.
  Due to the introduction of space-time block codes with "rate 1" it is possible to leave the other parameters of a transmission code scheme (such as channel coding, interleaving, service multiplexing, etc.) unchanged.
• 2. The code should be simple to construct and on the transmitter side be easy to reconstruct on the receiver side.
• 3. The code words should be as "large as possible" have each other. That is, a set of code words should do so be built up that noisy from the receiver side and / or distorted received signals, which respectively times the original signal emitted by the transmitter one that goes along with the increasing distance "Fading factor" describing intensity attenuation ("Fading value") plus noise (thermal noise at Receiver input amplifier plus interference noise due to interference signals from other users of the cellular network) persist, even with relatively strong disturbances as error-free as possible than those sent by the transmitter Have signals reconstructed (i.e. without confusion between individual code words).
• 4. The space-time block code used is intended to ensure diversity maximize, d. H. for two transmitting antennas, the theoretical maximum degree of diversity of 2, for three Transmitting antennas the theoretical maximum degree of diversity of 3 can be achieved, etc.
• 5. The space-time block code used should be complex-valued Enable broadcast symbols to e.g. B. can be used with UMTS be where a QPSK modulation (Quadrature Phase Shift Keying) is used. Due to complex-valued symbols there are also 8-PSK (8-Phase Shift Keying) or M-QAM (M-fold Quadrature Amplitude modulation) possible.

The object of the present invention is to provide the known Method for operating a digital cellular network according to the preamble of claim 1 by using alternative Space-time block codes with regard to the above Criteria 1. to 5. to be optimized as far as possible. This should especially space-time block codes with "rate 1" and maximum broadcast diversity in the case of three or more Transmitting antennas (n <2) are provided. It should but especially distance-optimized space-time block Codes for the case n ≧ 2 are provided.

This task is in its most general form solved according to the invention by the measures of claim 1.

The measures of claim 1 are in the further Description based on the knowledge that for the Case of known methods of operating Cellular networks according to the preamble of claim 1 spatial Time block codes can be formed that consist of unitary n × n matrices according to the characteristic features of claim 1 can be constructed.

Especially in the case of n <2, i.e. three or more Transmitting antennas, is made in accordance with the present invention demonstrated that space-time block codes for cellular systems with n transmitting antennas and m receiving antennas with a complex ST modulation scheme with the degree of diversity n × m and the "rate 1" basically exist as they are from unitary n × n matrices according to the characterizing part of claim 1 can be constructed.

The further independent method claims 3 and 8 relate to the method according to the preamble of claim 1, with those in the case of two or more (n ≧ 2) transmitting antennas optimized space-time block codes with a complex ST- Modulation scheme with the degree of diversity n × m and "Rate 1" can be determined numerically in which the code symbols largest possible "distance" in the sense of a specified Have metric.

The other independent material claims relate to basic and Mobile stations in a digital cellular network in which Look-up tables that are used in the Method used matrix elements of code words contain, are stored, as well as computer program products, in which appropriate look-up tables are implemented are.

The dependent claims relate to advantageous ones Embodiments of the present invention.

According to the present invention, in particular Measures to construct space-time block codes with a "rate 1", specified for three, four or more antennas, with which a maximum diversity enhancement is achieved.

This is viewed as a significant theoretical and practical breakthrough and is based on two changes from prior art approaches:

• 1. Non-linear codes are used. This is not a problem because the number of code words in space-time blocks is 2 ⁿ for BPSK (BPSK = binary phase shift keying; digital frequency modulation technology for sending data over a coaxial cable network: this type of modulation is less efficient but also less susceptible to noise than similar modulation techniques, such as QPSK = quadrature phase shift keying) and 4 ⁿ for QPSK modulation. This means that even for n = 4 in the case of using a QPSK modulation, only 256 code words are used, which can easily be stored in a table.
• 2. Neither the radiated energy per antenna and Time unit still the over all antennas to a given one Time averaged energy is kept constant. In particular with W-CDMA this is not critical, since larger ones Variations in emanation energy in one too normal system due to the superposition of different User signals can occur. The additional Fluctuations in performance caused by use In contrast, new space-time codes are introduced negligible.

Figure description

Fig. 1 shows schematically a radio transmission path and a corresponding symbol vector encoding and - decoding for a known Einantennen- single-antenna device in a digital mobile radio network;

Fig. 2 illustrates schematically a radio transmission path and a corresponding symbol encoding and decoding for a known space-time block coding in a multi-antenna single-antenna device in a digital mobile radio network;

Fig. 3 shows in table form an explicit example of a BPSK-compliant coding of eight bit vectors in the matrix elements of eight complex-valued unitary matrices (ST symbols), the space-time block coding when performing a method according to the invention for n = 3 transmit antennas are used as a basis;

FIG. 4 illustrates the distances between eight ST symbols for the case of space-time block coding discussed in connection with FIG. 3; FIG.

For the case n = 2 transmitting antennas, FIG. 5 shows the comparison in the code spectrum for a distance-optimized space-time block code constructed according to the invention for the case SU (2) and a space-time code constructed according to the known Alamouti scheme which is not distance-optimized;

Fig. 6 is for the case n = 3 transmit antennas, a code spectrum for a distance according to the invention constructed optimized space-time code for the case of SU (3) and QPSK modulation when using a minimum standard;

Fig. 7 shows a code range for n by means of numerical optimization method according to the invention constructed space-time block codes in the event = 3 transmit antennas and BPSK modulation using different standards;

Fig. 8 is a BPSK shows simulation for two and three antennas using an L _min codes;

Fig. 9 shows the spectrum of minimum eigenvalues in various inventive codes from n = 3 transmit antennas and BPSK modulation; and

Fig. 10 for n = 3 transmit antennas using an L shows a BPSK simulation _-1 codes.

For a better understanding of the present invention initially provided constructive evidence that complex space-time block codes with maximum diversity are not only if n = 2 transmitting antennas exist (e.g. shown by the well-known Alamouti scheme), but that also for the case with n <2 transmitting antennas complex space-time Block with maximum diversity exist.

The mathematical structure underlying the present invention is relatively complicated. In practice, however, the application of the present invention is reduced to the use of a look-up table for space-time code words which are stored in a receiver and transmitter. Fig. 3 shows an example of such a look-up table. Their structure and how they are used will be explained in more detail below. These tables can then be used without having to have an in-depth understanding of how they were derived.

The mathematical one used in the present application Notation is e.g. B. explains in Simon Barry, "Representation of Finite and Compact Groups ", Graduate Studies in Mathematics, Volume 10, American Mathematical Society or in Bronstein, Semendjajew: "Taschenbuch der Mathematik", p. 155, Verlag Harm Deutsch, Thun and Frankfurt / Main, ISBN 3 87144 492 8.

According to the invention, a conceptually new approach to space time codes given. First the transmitter settings described. Then a standard multiple entry Multiple output fading channel described. Finally the Describes the acquisition process for space-time symbols. Building on this, there is constructive evidence for the Existence of space-time codes with maximum diversity for Mobile radio systems with n ≧ 2 transmitting antennas are given. This Proof covers the cases with complex-valued and real valuable space-time symbols.

Although the proof of existence is constructive, it does not provide any optimal space-time codes, d. H. a space-time code with optimized "distances" between the code words. That's why will also be practical methods of constructing Codes given based on numerical optimization. Ultimately, the results will get through Simulations confirmed.

Channel

First there are n transmitting antennas and one receiving antenna accepted.

(An extension to n transmitting antennas and m receiving antennas looks like this:
In the case of m <1 receiving antennas, the codes and detection methods described below are carried out separately for all m receiving antennas. The results are then combined in the sense of a "maximum ratio combining" method. Such a "maximum ratio combining" method is z. B. Proakis, M. Salehi: Communication Systems Engineering, Prentice Hall, 1994, ISBN: 0-13-306625-5.
This then results in a maximum degree of diversity of n × m.
In particular, the optimization of the transmitter side is not influenced by the expansion to m <1 receiving antennas. You can see that z. B. from equation (8) in Tarokh et. al., "Space-Time Codes for high data wireless communication: performance criterion and code construction". There it is shown that the falsification probability between two sequences is the same as the product of the falsification probabilities for only one receiving antenna and that all product components are of the same size.
Accordingly, the minimization of a product component leads to the minimization of the entire product. This means that the number of receiving antennas has no influence on the optimality of the transmission symbols.
In this respect, all of the transmission methods described below can be used unchanged for any number of receiving antennas.)

Space-time block coding ("block ST modulation") is described as mapping a total of 2 ^l different bit vectors ∈ B ^l (each comprising l bits ∈ {0,1}) onto a set of 2 ^l space-time -Symbols C () ∈ U (n), which are described as unitary n × n matrices by the figure:

STM: B ^l → U (n)
→ C () (1)

The modulation rate is R = 1 if the l input bits are in n symbols are arranged, each symbol from l / n Bits (e.g. l / n = 1 for BPSK and l / n = 2 for QPSK).

Thus, the mapping of bit vectors _k to the symbols transmitted in n time steps via an antenna (see. Fig. 1) is replaced by the mapping of bit vectors _k to a set of space-time symbols (space-time symbols ST), the are transmitted via n antennas in n time steps. Thus, the use of these space-time codes for outer transmission blocks, such as. B. a channel coder, without influence ("transparent).

At the transmitter, the matrix elements c _{ijk of} the 2 ^l unitary n × n matrices C _{k are} treated as space-time variables in the following sense: If a bit vector _k to be transmitted has the unitary n × n matrix C _k as an ST symbol, then a the matrix element c _ijk (with row index i = 1,..., n, column index j = 1,..., n) emitted by the i-th antenna in time window j. With this structure, the transmission time for a complete ST symbol is thus n time units.

Since all matrices C _{k are} unitary, ie

the rows and columns of C _{k are} orthonormal. This implies that the (time-averaged) power emitted by each antenna is identical. Furthermore, the total symbol energy (summed over all antennas) is constant in each time slot. Note that the transmit power E _{b is} automatically normalized and independent of n due to the fact that the C _{k are} unitary.

Channel model

In the following, a fading channel with a simple Rayleigh or Rice distribution is assumed. Transmission paths (from each antenna) are subject to e.g. B. an independent Rayleigh fading in each channel state α _ij and it is assumed that the channel does not change significantly during the transmission period of an ST symbol (this corresponds to n time slots). The signal-to-noise ratio in each channel is the same, namely

γ _b = E _b / N ₀ .

recipient

With the above-described modulation and channel model, the receiver will receive a signal at a delayed reception time corresponding to the transmission time j, which is derived from the summation of all matrix elements c _ijk , j = const., For a specific one in a matrix column (fixed transmission time j) Code word C _k , each weighted with a channel state-specific fading factor, with noise also to be taken into account. This means that when a code symbol C _k , which corresponds to a bit vector _k , is transmitted, the signal (the receive vector) is present on the receiver side at a delayed reception time

at. (In other words: the channel state characterized by α does not depend on the transmitted space-time symbol C _k and is constant for all n time slots.

In the following, the index k is for the sake of simplicity omitted.

If one writes the receive vector as = (r ₁ ,..., R _n ) ^T and the channel state vector as = (α ₁ ,..., Α _n ) ∈ C ^n, this can be written in matrix form as:

() = C () +, (2)

where describes the normally distributed noise vector. Thus, from the recipient's point of view, the receive symbols () are not fixed, but are also stochastically distributed variables (ie they are dependent on the channel status!). Thus, the overall modulation is a mapping of the bits on the n-dimensional complex number level:

For a good code, this mapping must of course be uniquely reversible for each channel state ≠ 0. This defines the set of ST symbols

Boundary conditions. In fact, for any two symbols C ( _i ) and C ( _j ), _i ≠ _j, the Euclidean distance must not be zero, i.e. it must be:

for every state vector that is not equal to Is zero vector.

In particular, the following must apply:

for all ≠ 0 (zero vector).

If this condition is met, a unique solution of the existing linear equation system must be given, ie

where the determinate is equal to the product of the eigenvalues of

is.

Minimizing equation (4) for all under the condition that ∥∥ = 1 gives an eigenvalue equation for the matrix C ( _i ) - C ( _j ).

Thus, the minimum distance (which is determined by the "worst case" channel "with the greatest signal distortion) for a given pair of ST codes is equal to the minimum eigenvalue λ _min of C ( _i ) - C ( _j ). Λ _min must be positive, so that there is reversibility.

The following statements are equivalent:
The eigenvalues λ _min of C ( _i ) - C ( _j ) are non-zero for any pair of ST symbols.

For all i, j (i ≠ j) the rank of C ( _i ) - C ( _j ) is equal to n. For all i, j (i ≠ j) the determinant det (C ( _i ) - C ( _j ) ) do not disappear.

In view of equation (2), an optimal MLD (= minimum likelihood detector) detector minimizes the distance to all possible channel symbols _j = C ( _j ), an estimated value for the channel status information (e.g. by pilot sequences) being used:

A logarithmic probability value ("soft symbol") for the bit vector can be derived from the distance ∥ - C ( _{j) ∥.} If the mapping of the bits in symbols (Gray Code or similar) is fixed (e.g. by pilot sequences), an LLR value (log likelihood ratio = logarithmic probability ratio) could also be used

can be determined for each bit.

Existence of space-time symbols (ST symbols) with a maximum rank

The question is whether for every number n of antennas there is a set of 2 ^l ST symbols (matrices C _k ) with the property that they have a maximum rank. That is, it is

for all pairs of C _i , C _j .

For unitary n × n matrices it holds that their rank in each case is equal to n. The crucial question for that ST codes considered according to the invention is now whether all Differences of the selected matrices have full rank (s).

If we can construct a set of matrices C = {C _i } in such a way that they form a group in the sense of the usual matrix multiplication, things simplify:

Lemma 1

If C = {C _i } a group. If C ₁ = 1 is the identity matrix of the group, then we have

proof

Because of the group property is

Hence C _j -1 | i = C _k ∈ C and it holds

In addition, use was made of the fact that | det (C) | = 1.

example 1

The Alamouti scheme is based on

In fact, the Alamouti scheme consists of a subset of the cube group with order o = 24. Eight of the group elements are not used, although they result in the same d _min = 1. Thus, in principle, ld (24) <4 bits could be transmitted in this scheme without any loss of information. (However, the symbols not transmitted have a bad crest factor, e.g. C = 1).

From the aforementioned publication "Space Time Codes for High Data Wireless Communication: Performanve Criterion and Code Construction "by V. Tarokh is known that the Rank n of n × n constructed as space-time block symbols Code matrices is equal to the degree of diversity. It follows also that the rank of the difference between two n × n code matrices is at most n. This knowledge is now shown in the following exploited.

Complex symbols Theorem 2

For any l and n ≧ 2 there exists a complex-valued ST Modulation scheme with a degree of diversity of n.

Proof: by explicit construction

Note that in this case the ST code

consists of a subset of all possible unitary n × n matrices. Based on the spectral theorem given in Simon, Barry: Representations of Finite and Compact Groups, 1996, Graduate Studies in Mathematics, American Mathematical Society, ISBN 0-8218-0453- 7, any unitary Matric C can be written as:

where V is unitary and λ _i = exp (jβ _i ) (in the argument of the function exp, j is the imaginary unit). Choose now

where q _{i is} an arbitrary odd integer. Then C ^2l = 1, and {C _k } _{k = 0. . . ^l -1} is an (Abelian) group, with a generator

for any fixed V. The eigenvalues of C _k are

By construction with k = 0. . . 2 ^l - 1 they are clearly different from 1. Proceeding from this, it must be shown that

d _min = min _{k ≠ 0} | det (1 - C _k ) ≠ 0.

Since | det (V) | = 1, the following applies:

Note that the key to the above proof is on it was based on the fact that it is always possible to unitary a set Construct matrices whose eigenvalues are all different of 1 are.

Equation (7) thus provides the basis for a method for the construction of complex-valued unitary n × n code matrices C _k , which can serve as symbol words for space-time block codes for any number of n ≧ 2 transmitting antennas, whereby these space- Time block codes provide a maximum diversity n, since the rank of the complex-valued unitary n × n code matrices C _{k is} equal to n.

If you calculate a group of code matrices according to the above equation (7), you get a list of 2 ^l unitary n × n matrices with complex-valued matrix elements, which can be based on a non-linear space-time block code with which one of the in Fig. 2 schematically shown radio transmission link can be operated in a digital cellular network. This knowledge is based on the technical teaching of claim 1.

For the case n = 3 transmit antennas and BPSK modulation, ie number of transmit antennas n = length of symbol words l, an explicit example of such a list of code matrices C _{k is given} in the look-up table in FIG. 3 for the sake of clarity.

In the look-up table shown in FIG. _{1, the bits b i} ∈ {0,1} are ^{mapped to 2 3} = 8 bit vectors. These are explicitly the eight possible bit vectors (0,0,0) formed by permutations; (0,0,1); (0,1,1); (0,1,0); (1,1,0); (1,1,1); (1,0,1); (1,0,0).

These eight bit vectors are uniquely (reversibly unambiguous) assigned to one of eight code matrices C _k = C (:;: k). The code matrices in Table 1 are unitary complex-valued 3 × 3 code matrices, the matrix elements of which have been calculated according to equation (7).

If one uses the assignment made by way of example in FIG. 3 between the eight bit vectors and the eight code matrices C _k z. B. in a digital mobile radio system shown in Fig. 2 and if there, for example, a bit vector (1,0,1) arrives at the ST coder, it sends out one column of the code matrix C ₇ in three successive time slots, namely as follows: that the complex-valued matrix element c ₁₁₇ = 0.0000 + 0.6442i = is transmitted via the antenna 1 in time slot 1, the complex-valued matrix element c ₂₁₇ = -0.2175-0.0412i, etc., to _{The complex-valued matrix element C 337} = 0.0000-0.5065i is transmitted via the antenna 3 in the time slot 3 (i has been used for the imaginary unit in FIG. 3).

_{On the receiver side, the complete code matrix C 7 is then} reconstructed from the signals received by a receiving antenna Rx, as already explained above, by means of an MLD detector, and the original bit vector (1,0,1) is assigned to it in an inverse mapping.

For practical use, only the matrices calculated according to equation (7) with the respective bit vector assignment need to be stored in a look-up table in the form of the table shown in FIG Decoder.

The ST coder at the transmitter end can be in a base station of a digital cellular network, and the ST decoder at the receiving end in the mobile station of one of a digital cellular network. In principle, however, it can also be reversed.

The look-up tables can be found as computer program products in machine-readable form e.g. B. be saved on diskette, or in the form of on the internet or the Machine-readable transmittable radio transmission links Files must be saved and, if necessary, in appropriate Memory of ST encoder on the transmitter side or ST decoders on the receiver side in the base stations or Mobile stations fed into a digital cellular network will.

Real symbols

For real-valued symbols the equation above applies (7) leading design evidence exploited property, that it is always possible to assign a set of unitary matrices construct whose eigenvalues are all different from 1, no longer to.

Real ST codes

If the ST code matrices are restricted to real-valued matrix elements C _ijk , a maximum rank (and thus a maximum diversity order of the ST codes) can only be constructed for the case of even antennas.

Theorem 3

Real-valued ST codes of order 2n + 1 have a non- maximum order of diversity.

proof

Any O ∈ SO (2n + 1) can be written as

O = VDV ^-1 (8)

(see Simon, Barry: Representations of Finite and Compact Groups, 1996, Graduate Studies in Mathematics, American Mathematical Society, ISBN 0-8218-0453-7),
where V is orthogonal and

(For matrices with detO = -1 the proof is essential identical).

Consider now det (O ₁ - O ₂ ) = det (1 - O ₂ O -1 | 1) = det (1 - O _{21 ), where O 21} ∈ SO (2n + 1) again applies due to the group structure. Thus O ₂₁ again has the structure according to equation (8) and the determinate det (O ₁ - O ₂ ) vanishes.

The reason why SO (2n + 1) is not a maximum order of diversity delivers, is thus based on the fact that every orthogonal Matrix with odd dimension (at least) an eigenvalue which is equal to 1.

For an even number of antennas, the additional 1 at position (n, n) of D does not appear, and one Code construction similar to the unitary case is possible.

ST symbol optimization

Although the theorem for complex-valued ST modulation is constructive, it does not provide an optimal ST code. The asymptotic symbol error is of the form

creating an optimal diversity order for large

occurs. However, the constant c is not minimal.

Therefore, the following practical procedures for coding Construction based on optimization considerations presented. The results are confirmed by simulations been.

The following sections outline construction techniques indicated for "good" unitary ST codes, i. H. such ST codes, in which the spacing between the code symbols is optimized are.

optimization

The idea is to find a suitable parameterization for a set of unitary U (n) matrices, and then numerically minimize a suitable metric that represents the distances between the code words. Since the distance measure d _ev = min {eigenvalues of C ( _i ) - C ( _j )} is not differentiable, we choose

Here, _k stands for the parameters of the k-th code matrix C _k .

As a target functional

for global extreme value formation we can use the L _q norm of all mutual code distances. Eg q → -∞ yields the minimal norm (a large negative q can be used for a numerical optimization); the case with q = -1 can be interpreted as an electrical potential. In fact, due to the compactness of U (n), the problem is comparable to minimizing the electrical energy of 2 ^{l of} like-charged particles moving on a sphere. Positive values for q do not make sense because they do not exclude distances that could become zero (i.e. two particles sitting in the same place do not generate infinite energy, so they would not repel each other).

The case of group SU (2)

This case corresponds to n = 2 transmitting antennas.

For this case one can explicitly construct the energy function explained above, since according to Simon Barry, "Representation of Finite and Compact Groups", Graduate Studies in Mathematics, Volume 10, American Mathematical Society, every unitary matrix C can be parameterized as

where _{i are} the well-known Pauli spin matrices:

and here j the imaginary Unity is.

The real-valued parameters β are subject to the restriction

In fact, this ensures that SU (2) is isomorphic to a 3-sphere (a sphere in four dimensions). It's easy to show that

is, that's why we define

as a measure of the distance between two code matrices.

Note that d _{ij is} really a metric in the case of SU (2).

We use d = Σ _{i <j} d _ij as the complete distance. A 3-sphere is easily parameterized by three angles:

The gradient is:

Optimization method based on that of the steepest Relegation gives quick results for a reasonable l.

The resulting code spectrum for QPSK (l = 4) is compared in FIG. 5 with the code spectrum for the Alamouti scheme. As you can see, the minimum distance in this approach is greater than that in the case of the Alamouti scheme. Thus, in the asymptotic borderline case, it is to be expected that this non-linear code shows a higher coding gain (same bit error rate with a lower signal-to-noise ratio).

SU (3) and an implicit numerical gradient method

For cases with more than two transmitting antennas, that is SU (n), n <2, does the explicit computation of determinants very extensive. For gradient methods (e.g. the conjugate gradient method, see W. Press, B. Flannery, S. Tenkolsky, W. Vetterling: "Numerical recipes in C ", Cambridge University Press, ISBN 0-521-35465-X) it is however sufficient to calculate the local gradient.

We define the L _m distance of the i-th matrix to all others as:

If the i-th code matrix is varied by an infinitesimal (unitary) rotation

thus results for the gradient

whereby

The σ _{i are} the corresponding Hermite standard spin matrices. For higher-dimensional spaces (n <2) these are z. B. in the book "Gauge theory of elementary particle physics" by Ta-Pei Cheng and Ling-Fong Li.

A variation with a step size δ is then applied to the ith code word according to

A steepest descent algorithm then works as follows:

• 1. 1.) Generate a random set of 2 ^l unitary n × n matrices S _k , k = 1.. .2 ^l as starting matrices (this can be done according to equation (7)).
• 2. 2.) Calculate the gradient vectors according to equation (10).
• 3. 3.) "Rotate the matrices according to equation (11), iterate then according to step 2.)

Of course, a conjugate gradient method can be used be constructed in the appropriate way, and there are also stochastic gradient methods to find the global extreme value generator possible.

An example for 3 antennas and a QPSK modulation which ^{delivers 2 6} = 64 ST matrices is shown in FIG . Fig. 6 shows a spectrum for SU (3), three transmit antennas, and QPSK modulation using a minimum standard. If the same method is used for SU (3) but for a BPSK modulation and different standards (min, L _-1 , L _-2 ) are used, the spectra shown in FIG. 7 are obtained.

It seems remarkable that it is possible eight Finding code matrices in SU (3) which are all the same show mutual distance. This corresponds to a Thetrahedra in ordinary three-dimensional space.

Fig. 4 shows a two-dimensional illustration of this case. The eight bit vectors (0,0,0); (0,0,1); (0,1,1); (0,1,0); (1,1,0); (1,1,1); (1,0,1); (1,0,0) are mapped onto eight code matrices (for example the code matrices explicitly specified in the table in FIG. 3) which are optimally spaced from one another.

Fig. 8 shows a spectrum of n = 3 antennas and BPSK using various optimization criteria.

In addition to the numerical ones discussed above Optimization procedures are still further approaches for a Code optimization, i.e. the explicit construction of ST Symbols in the form of unitary n × n matrices with each optimized distances to each other:

Construction of hyperspheres

Construct a (hyper) sphere with a given radius around a given code symbol (e.g. a unitary n × n matrix C _k ), find a second code symbol on the sphere around this first code symbol, and construct a third symbol as an intersection the (hyper) balls and the first and second code symbols. Then iteratively construct further code symbols as intersections of further (hyper) spheres around the code words already found.

In the case that the code words are unitary n × n matrices with n ≧ 2, a "sphere" with radius r around a code word is given by S _r = {C '| det (C' - C) = r}.

It can be constructed by

where λ _{i are} the eigenvalues of j.

For example, in SU (2) one finds that

Thus, such a sphere can be parameterized as C '= Cexp (j) with a constraint on the sum of the squared β's.

A sphere with radius 1 is z. B. given by

If you use this idea, you can actually do that Construct Alamouti scheme (by constructing two Spheres with radius 1 around elements 1 and -1 (the center from SU (2),. . . Z (SU (2)).

This provides the formula for the code words

where b _i ∈ {0,1} are the bits and σ _{i are} the Hermite standard spin matrices.

Explicit calculation leads back to what is already known Alamouti scheme, so what the correctness of the approach of the Construction over hyperballs occupied.

As the example of the Alamouti scheme in connection with FIG. 5 shows, a local optimum can be found with the hypersphere method, but a global optimum is not necessarily found.

However, for n <2 the eigenvalues of j (analytically) very extensive.

Therefore, for n <2, a different parameterization appears to be more successful here:

If one keeps the eigenvalues λ _i = const., A sphere around the code symbol C with results

C '= CVDV.

V can be parameterized as V = exp (j).

Unitary representations of finite groups

Another code construction method is based on the Use of finite groups. For this, be back to Simon Barry, "Representation of Finite and Compact Groups", Graduate Studies in Mathematics, Volume 10, American Mathematical Society referenced.

The connection of two elements in a finite group leads again to an element of the group, since according to a group axiom the group is closed. In addition, the multiplication of two unitary matrices also yields a unitary matrix. Accordingly, there are numerous representations of finite groups in which a unitary matrix is assigned to each group element. If such a representation of a finite group is chosen, the number of group elements being greater than 2 ^l , then good starting values are obtained for the above-mentioned optimization methods.

For this purpose one tries to find the unitary representations of finite groups (with dimension n), for which o (G) ≧ 2 ^l . There is no guarantee that this will lead to optimal results.

Some simulation results

Simulations have been carried out for the cases with n = 2 and n = 3 antennas, where (currently) only BPSK was used. Theoretical limits for antenna diversity can be derived in closed form (cf., for example, J Proakis, M. Salehi: "Communications Systems Engineering", Prentice Hall Int., ISBN 0-13-300625-5, 1994). These can be seen as solid lines in FIG. 9. Simulation results are shown along with 70% confidence intervals.

As can be seen from FIG. 10, the theoretical limit for high E _b / N _{0 is reached} in the case of three antennas for the L _min code. This is based on the fact that L _{min is} really the maximum possible smallest distance.

Practically only contribute to a good signal-to-noise ratio the errors at the smallest distances contribute.

However, if the signal-to-noise ratio is low, Ratio the properties of the code and can even worse than with a diversity of two antennas. In fact, ST codes can be higher than schema Modulation (which makes the symbol space is expanded). It is of course not possible increase the number of symbols without changing the spacing in to shrink into a compact space. For QPSK (with 64 ST Symbols) make this problem even more important.

For the L _-1 code, the performance is better in the areas with a low signal-to-noise ratio. For this code (which has two different distances in the minimum eigenvalue norm) Gray coding was used in order to avoid multiple-bit errors in the event of a symbol error. As can be seen in the spectrum below, every code matrix has exactly two nearest neighbors. All other code words have a greater distance. As can be seen, the code is close to the theoretical limit for E _b / N ₀ <4 dB and exceeds the L _min code in the range with low E _b / N ₀ .

Claims (11)

1. Method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n × m for a given number of n transmitting antennas and m (m = 2, 3, 4...) Receiving antennas, one transmitting station of (... n = 2, 3, 4) mobile radio network with n transmitting antennas is provided, and from this transmitting station to be transmitted set of 2 ^l Informationsbitvektoren = (b1, b2,... b _l) ∈ B ^l with l bits b _i ∈ {0,1} through a one-to-one mapping STM: B ^l → U (n)
→ C ()
to a set of 2 ^l space-time symbols (ST code symbols) C _k , k = 0, 2,. . ., 2 ^l - 1, where each code symbol C _k corresponds to a unitary n × n matrix and the matrix elements C _ijk of each of the 2 ^l code symbols C _k are interpreted as space-time variables so that when a certain one of the 2 ^l Code symbols C _k for each of its matrix elements c _ijk a corresponding signal is emitted by the transmitting antenna 1 in a time interval j via a fading channel assigned to the transmitting antenna i, so that at each of m receiving antennas of a receiving station located within the range of the transmitting station the radiated in the time interval j and the matrix elements c _ijk , i = 1,. . ., n of the code symbol C _k corresponding signals are received, and due to the orthogonal structure of the space-time block transmission code and by decoupling the signals emitted by the n transmitting antennas and corresponding to the matrix elements c ijk, a corresponding information _{bit vector} ^{∈ B l to be transmitted} by the reverse mapping
STM ^-1 : U (n) → B ^l
C () →
is decoded,
characterized by
_{that the matrix elements c ijk} corresponding to the signals to be transmitted are the elements of 2 ^l unitary n × n matrices C _k , k = 0, 2,. . ., 2 ^l - 1, which are constructed according to the following regulation:
where V is any unitary complex-valued n × n matrix,
c _{ijk are} the complex-valued matrix elements of C _k ,
j is the imaginary unit,
q _i , i = 1,. . ., n any odd whole numbers,
and k = 0, 1,. . ., 2 ^l - 1. 2. The method according to claim 1, characterized in that n is an even number and the c _{ijk are} real-valued. 3. Method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n × m for a given number of n transmitting antennas and m (m = 2, 3, 4...) Receiving antennas, one transmitting Station of the cellular network is provided with n (n = 2, 3, 4 ^{...) Transmitting antennas, and a set of 2 l} information bit vectors to be transmitted by this transmitting station = (b1, b2,... B _l ) ∈ B ^l with l bits b _i ∈ {0,1} through a one-to-one mapping STM: B ^l → U (n)
→ C ()
to a set of 2 ^l space-time symbols (ST code symbols) C _k , k = 0, 2,. . ., 2 ^l - 1, where each code symbol C _k corresponds to a unitary n × n matrix and the matrix elements C _ijk of each of the 2 ^l code symbols C _k are interpreted as space-time variables so that when a certain one of the 2 ^l Code symbols C _k for each of its matrix elements c _ijk a corresponding signal is emitted from the transmitting antenna i in a time interval j via a fading channel assigned to the transmitting antenna i, so that at each of m receiving antennas of a receiving station located within the range of the transmitting station the radiated in the time interval j and the matrix elements c _ijk , i = 1,. . ., n of the code symbol C _k corresponding signals are received, and due to the orthogonal structure of the space-time block transmission code and by decoupling the signals emitted by the n transmitting antennas and corresponding to the matrix elements c ijk, a corresponding information _{bit vector} ^{∈ B l to be transmitted} by the reverse mapping
STM ^-1 : U (n) → B ^l
C () →
is decoded
characterized,
_{that the matrix elements c ijk} corresponding to the signals to be transmitted are the elements of 2 ^l unitary n × n matrices C _k , k = 0, 2,. . ., 2 ^l - 1, which are numerically optimized according to the following rule:

• a) it is an initial set of 2 ^l unitary n × n output matrices S _k , k = 0, 2,. . ., 2 ^l - 1 generated numerically at random;
• b) these output matrices S _k , k = 0, 2,. . ., 2 ^l - 1 have been parameterized;
• c) It is the size as a measure of the distance between two starting matrices
  has been chosen, where _{i stands} for the parameters of the i-th output matrix;
• d) through numerical variation of the parameters _i is the objective functional
  been minimized;
• e) the n × n matrices, for whose parameter _i the objective functional
  has been numerically minimized have been chosen as final n × n matrices (code symbols C _k ) and their matrix elements have been chosen as the matrix elements C _ijk corresponding to the signals to be transmitted.

4. The method according to claim 3, characterized in that n = 2 and

• a) that every matrix S _{k of} the initial set of unitary n × n output matrices as
  has been parameterized,
  where for the σ _i applies:
  and j is the imaginary unit,
  and the real-valued parameters β are subject to the following restriction:
  
• b) that
  has been chosen as the distance measure between two matrices A _i , A _j;
• c) that the parameter vectors _i as
  have been parameterized,
• d) that the gradient
  for all matrices of the initial set of n × n matrices have been numerically minimized by iteration,
• e) that the n × n matrices corresponding to the minimized gradients have been selected as the final n × n matrices (code symbols C _k ) and their matrix elements have been selected as the matrix elements c _ijk corresponding to the signals to be transmitted.

5. The method according to claim 3, characterized in that

• a) that an initial set of 2 ^l unitary n × n output matrices S _k , k = 0, 2,. . ., 2 ^l - 1 was generated numerically at random;
• b) that the L _m distance of the ith output matrix to all others has been defined as:
  
• c) that the gradient
  have been calculated, where
  and σ _{i are} the corresponding standard Hermite spin matrices;
• d) that the ith output matrix S _i by an infinitesimal (unitary) rotation
  has been varied;
• e) that by iterative calculation the gradients
  have been calculated until these have been minimized.
• f) that the n × n matrices corresponding to the minimized gradients have been selected as the final n × n matrices (code symbols C _k ) and that their matrix elements have been selected as the matrix elements c _ijk corresponding to the signals to be transmitted.

6. The method according to any one of claims 3 to 5, characterized in that
that the output matrices S _k have been calculated according to the following scheme:
where V is any unitary complex-valued n × n matrix,
s _{ijk are} the, in the general case, complex-valued matrix elements of s _k ,
q _i , i = 1,. . ., n any odd whole numbers,
and k = 0, 1,. . ., 2 ^l - 1. 7. The method according to any one of claims 3 to 5, characterized in that a mapping of a finite group G with dimension n and the order o (G) ≧ 2 ^{l has been determined} on unitary n × n matrices, which are then used as output matrices S. _k have been used. 8. Method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n × m for a given number of n transmitting antennas and m (m = 2, 3, 4...) Receiving antennas, one transmitting Station of the cellular network is provided with n (n = 2, 3, 4...) Transmitting antennas, and a set of 2 ^l information bit vectors to be transmitted by this transmitting station = (b ₁ , b ₂ , _{... B l} ) ∈ B ^l with l bits b _i ∈ {0,1} through a one-to-one mapping STM: B ^l → U (n)
→ C ()
to a set of 2 ^l space-time symbols (ST code symbols) C _k , k = 0, 2,. . ., 2 ^l - 1, where each code symbol C _k corresponds to a unitary n × n matrix and the matrix elements c _ijk of each of the 2 ^l code symbols C _k are interpreted as space-time variables so that when a certain one of the 2 ^l Code symbols C _k for each of its matrix elements c _ijk a corresponding signal is emitted from the transmitting antenna i in a time interval j via a fading channel assigned to the transmitting antenna i, so that at each of m receiving antennas of a receiving station located within the range of the transmitting station the radiated in the time interval j and the matrix elements c _ijk i = 1,. . ., n of the code symbol C _k are received, and due to the orthogonal structure of the space-time block transmission _{code and by decoupling the signals emitted by the n transmitting antennas, corresponding to the matrix elements c ijk, a corresponding information bit vector} ∈ B to be transmitted ^l by the reverse image
SMT ^-1 : U (n) → B ^l
C () →
is decoded,
characterized,
_{that the matrix elements c ijk} corresponding to the signals to be transmitted are the elements of 2 ^l unitary n × n matrices C _k , k = 0, 2,. . ., 2 ^l - 1, which are constructed according to the following regulation:

• _{a) A "hypersphere" with radius r has been constructed numerically around any first code symbol C 1} represented by a unitary n × n matrix, ie the set of all code symbols has been determined for which the following applies:
  S _r = {C '| det (C'-C ₁ ) = r}, which is obtained by calculating
  has happened, where λ _{i are} the eigenvalues of j;
• _{b) a second code symbol C 2} , represented by a unitary n × n matrix, has been selected on this hypersphere, around which a hypersphere has in turn been constructed in a manner analogous to step a);
• c) the intersection of the two hyperspheres around the code symbols C ₁ , C ₂ has resulted in at least one further code symbol C ₃ , around which further hyperspheres have been iteratively constructed in the manner indicated in step a) until a complete set of 2 ^l _{constructed in this way, code symbols C k} each represented by a unitary n × n matrix has been constructed.

9. Base station, which can be used in a method according to one of the preceding claims 1 to 8 in a digital cellular network, and which contains a memory in which the assignment of individual bit vectors to be transmitted to space-time block symbols is stored in the form of assignment tables which contain the _{matrix elements c ijk} used in one of the methods according to claims 1 to 8. 10. Mobile station, which can be used in a method according to one of the preceding claims 1 to 8 in a digital mobile radio network, and which contains a memory in which the assignment of individual bit vectors to be transmitted to space-time block symbols is stored in the form of assignment tables which contain the _{matrix elements c ijk} used in one of the methods according to claims 1 to 8. 11. Computer program product stored on a computer-readable medium, wherein the computer program product machine-readable program means for reading into the Assignment tables contained in the computer program product a memory of a base station or a mobile station in a digital cellular network, and wherein the Allocation tables show the allocation of individual items to be transferred Bit vectors to space-time block symbols for use in a method according to any one of claims 1 to 8.