DE102005005695B4 - Code sequence and radio station - Google Patents

Abstract

A method for transmitting data between at least two radio stations, comprising a Hadamard matrix of length n, derived from one according to a law of formation for constructing a Hadamard matrix of length n from a Hadamard matrix of length n / 2, - a code matrix different from the one Hadamardmatrix at least differs in that it is designed with the following steps: (a) a code sequence is described by a line of the code matrix, (b) the code sequence is used to transmit the data by spreading or adding the data when transmitting with the code sequence Reception with the code sequence are correlated.

Description

The invention relates to both code sequences and radio stations, in particular mobile stations or base stations, which are set up to use code sequences accordingly.

The rapid technological development in the field of mobile radio communication has led in recent years to the development and standardization of the so-called third generation of mobile radio systems, in particular the Universal Mobile Telecommunications System (UMTS), which among other things aims to provide users of mobile stations, such as mobile phones, to provide increased data rates.

Especially in the last few months, a so-called Enhanced-Up-Link is a focus of these development and standardization activities. With this Enhanced-Up-Link increased data rates are to be made available for the connection from a mobile station to a base station. To establish such an enhanced-up link, the Enhanced Up Link Dedicated Channel Hybrid (ARQ Indicator Channel) and E-RGCH (Enhanced Up Link Dedicated Channel Relative Grant Channel) signaling channels are in the direction of the base station provided to the mobile station.

With the E-HICH an "ACK: Acknowledge" or a "NACK: Not-Acknowlegde" is signaled to the mobile station, depending on whether a packet was received correctly by the base station or not.

The E-RGCH signals to the mobile station whether it is allowed to transmit at a higher, equal or lower data rate.

The data, in particular data bits, which are sent via said signaling channels, in particular via the same radio channel, to different mobile stations are spread for subscriber separation with a code sequence, also called a signature sequence.

For example, since different data are transmitted to different mobile stations within the same radio channel, it is necessary to impose different code sequences on the various data so as to allow the mobile stations to separate the data received over that radio channel and only those to a mobile station Mobile station directed data further processing.

While the Enhanced-Up-Link channel relates to data transmission from the mobile station to the base station, said signaling channels, E-HICH and E-RGCH, describe the direction from the base station to various mobile stations.

See also:

R1-041421, "E-HICH / E-RGCH Signature Sequences", Ericsson, and R1-041177, "Downlink Control Signaling", Ericsson - all from 3GPP, 3 ^rd Generation Partnership Program as well
EP 1 055 996 A2 and MASAHIKO MIYAMOTO: A Construction of Hadamard Matrices. In: JOURNAL or COMBINATORIAL THEORY, 1991, 86-108. - ISSN 0097-3165 / 91, and Wikipedia: Hadamard matrix

It is now the goal of global development efforts to provide a set of code sequences or signature sequences that enable efficient implementation of these signaling channels.

The invention is therefore based on the problem to provide a technical teaching that allows efficient implementation of said signaling channels. In particular, it is an object of the invention to provide code sequences which enable efficient implementation of said signaling channels.

This object is solved by the features of the independent claims. Advantageous and advantageous developments of the invention are defined by the features of the dependent claims.

The invention is based initially on the idea to use code sequences that are orthogonal to each other. This has the advantage that a receiver (for example a mobile station) which correlates with its code sequence to a received signal sequence which is not intended for it, ideally receives no correlation signal. Therefore, in a first step, the use of code sequences which form the lines of a Hadamard matrix proves to be advantageous, since the lines of a Hadamard matrix are mutually orthogonal.

Hadamard matrices are defined in particular as matrices with elements of size 1 whose rows are mutually orthogonal and whose columns are mutually orthogonal. In the context of the application, however, the term "Hadamardmatrix" is intended to include all matrices with elements of size more generally 1 describe whose lines are mutually orthogonal.

However, investigations based on the invention have shown that the use of the lines of a Hadamard matrix as code sequences for imprinting on data, in particular data bits, in the named application does not lead to the desired results.

Elaborate research and thought led to the realization that frequency errors, in particular the difference of the transmission frequency and the reception frequency due to a Doppler shift, reduce or worsen the orthogonality of the code sequences in practical application. This reduction or deterioration of the orthogonality of code sequences due to a frequency error turned out to be particularly strong just when the lines of known Hadamard matrices are used as code sequences.

minimal ist, wobei das Maximum für alle möglichen Paare s und e, wobei s ungleich e ist, gebildet wird, wobei C(s,i) das Element der Codematrix in Zeile s und Spalte i ist, und wobei die Summe über alle Spalten der Codematrix ausgeführt wird.An essential aspect of the invention is therefore the recognition to use for the realization of the above signaling channels code sequences whose orthogonality to each other is not affected as possible even in the presence of a frequency error. The invention is therefore also a set of code sequences, in particular the length 40 , for which the code sequences are orthogonal to each other and the maximum of $$e={\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^j=}{\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">j</figure-callout>}2\pi fTi}}$$

is minimal, with the maximum being formed for all possible pairs s and e, where s is not equal to e, where C (s, i) is the element of the code matrix in line s and column i, and where the sum over all columns of the Code matrix is executed.

• - Bilden einer Hadamardmatrix der Länge n;
• - Vertauschen von Spalten der Hadamardmatrix.

Also within the scope of the invention is a code sequence which is described by a line of a code matrix, the code matrix being obtainable by the following steps:

• Forming a Hadamard matrix of length n;
• - Swap columns of the Hadamard matrix.

Elaborate simulations with simulation tools created especially for this purpose showed that code sequences described by the lines of a code matrix formed in this way preserve their orthogonality with each other as well as possible in the event of a frequency error, and thus the mobile stations have good separability of signals that are spread based with such code sequences allow.

• - Gruppierung der Spalten in Spalten der ersten Hälfte (0,1,2, ..., n/2-1) und in Spalten der zweiten Hälfte (n/2, n/2+1, ..., n-1);
• - Gruppierung der Spalten in Spalten mit gerader Nummer (0,2,4, ...n-2) und in Spalten mit ungerader Nummer (1,3,5, ..., n-1) ;
• - Vertauschen der Spalten der Hadamardmatrix derart, dass die Gruppe der Spalten der ersten Hälfte die Spalten mit gerader Nummer (0, 2, 4, ..., n-2) der geänderten Codematrix bilden, und dass die Gruppe der Spalten der zweiten Hälfte die Spalten mit ungerader Nummer (1, 3, 5, ..., n-1) der geänderten Codematrix bilden.

A further improvement results from the use of code sequences taken from a code matrix which can be obtained by the following steps:

• - Grouping of columns in columns of the first half ( 0 . 1 . 2 , ..., n / 2-1 ) and in columns of the second half ( n / 2 . n / 2 + 1 , ..., n-1 );
• - Grouping of columns in even-numbered columns ( 0 . 2 . 4 , ... n-2 ) and in odd-numbered columns ( 1 . 3 . 5 , ..., n-1 );
• Interchanging the columns of the Hadamard matrix such that the group of the columns of the first half contains the even-numbered columns ( 0 . 2 . 4 , ..., n-2 ) of the changed code matrix, and that the group of the columns of the second half form the odd-numbered columns ( 1 . 3 . 5 , ..., n-1 ) form the modified code matrix.

For example, for a matrix with 8 columns, the columns would be in the order ( 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 ) in the order ( 0 . 4 . 1 . 5 . 2 . 6 . 3 . 7 ) are reversed. 4 shows with the example of a matrix 8th Columns the permutation or column swap achieved by this operation.

This operation is referred to as "combing" in the context of this invention. It is similar in some ways to a so-called Pharaoh mixture, called in England also Weber mixture. The cards are divided into two equal stacks. Then the two cards are mixed together, taking turns a card from one and the other stack is used. (Please refer Martin Gardner: head or number? Paradox and mathematical puzzle, 1978, Spektrum der Wissenschaft Verlagsgesellschaft mbH & Co., Weinheim, page 144-145 ). Strictly speaking, a pharaoh mixture differs slightly from the operation of combing: Typically, you start by mixing with the top two cards of the two stacks, building up the new, mixed stack. This brings these two cards at the bottom of the new stack. The pharaoh mixture is thus a combing combined with a reversal of the order of the cards. However, as discussed below, the frequency error characteristics do not change as the consequences are reversed.

• - Nummerierung der n Spalten der Hadamardmatrix von 0 bis n-1;
• - Gruppierung der Spalten in Spalten mit gerader Nummer (1,2,4, ...n-2) und in Spalten mit ungerader Nummer (1,3,5, ..., n-1);
• - Vertauschen der Spalten der Hadamardmatrix derart, dass die Gruppe der Spalten mit gerader Nummer die ersten n/2 Spalten der Codematrix bilden, und dass die Gruppe der Spalten mit ungerader Nummer die letzten n/2 Spalten der Codematrix bilden.

The combing inverse operation (here called "de-combing") is the following operation:

• Numbering of the n columns of the Hadamard matrix from 0 to n-1 ;
• - Grouping of columns in even-numbered columns ( 1 . 2 . 4 , ... n-2 ) and in odd-numbered columns ( 1 . 3 . 5 , ..., n-1 );
• Swapping the columns of the Hadamard matrix such that the group of even-numbered columns form the first n / 2 columns of the code matrix, and that the group of odd-numbered columns form the last n / 2 columns of the code matrix.

This type of column interchange can also lead to improved code matrices.

Elaborate simulations with simulation tools made especially for this purpose finally gave the following code matrix:

Verwendet man als Codefolgen zur Separierung von zu übertragenden Daten Zeilen aus dieser Codematrix, so ist also gewährleistet, dass die übertragenen Daten auch beim Vorliegen eines Frequenzfehlers empfangsseitig besonders gut zu separieren sind. Dis gilt insbesondere dann, wenn die Daten über die oben genannten Signalisierungskanäle von einer Basisstation an verschiedene Mobilstationen gesendet werden. This code matrix has maximum secondary correlations of 2.7 at a frequency error of 200 Hz compared to a value of 8.3 achieved using a conventional code matrix. This means a suppression for the reception of broadcasts for other mobile stations of about 9.5 dB. The maximum side correlation results from the worst sequence pair (code string pairs) of the code matrix, where a sequence of one row corresponds to the code matrix. If we denote the elements of the matrix with x (i, k), where i is the row index and k is the column index, then the secondary correlation values NC of two rows (code sequences) a and b (a ≠ b) are calculated by means of their scalar product, taking the frequency error into account follows: $$\begin{array}{l}\text{NC}\left(\text{a}\text{, b}\right)=\text{Section}\left(\mathrm{\Sigma }\text{x}\left(\text{a}\text{, k}\right)\text{x}\left(\text{b}\text{, k}\right)\text{exp}\left(\text{j}*2*\mathrm{\pi }*\text{K}*\text{T}*\text{f}\right)\right)\\ \text{k}\end{array}$$

If one uses lines from this code matrix as code sequences for the separation of data to be transmitted, then it is ensured that the transmitted data are to be separated particularly well in the presence of a frequency error at the receiving end. Dis is especially true when the data is sent via the above signaling channels from one base station to different mobile stations.

Within the scope of the invention, of course, radio stations, in particular base stations and mobile stations, which are suitably set up to use code sequences according to the invention, in particular for the realization or transmission of the above-mentioned signaling channels. In this case, the data bits to be transmitted via these signaling channels can be multiplied (spread) by the transmitter side for better separability with the code sequences according to the invention. On the receiver side, to better separate the received signals, the receiver can correlate a code sequence according to the invention with the received signals, i. Form correlation sums and process them accordingly. The formation of the correlation sums, for example, as described below, by the calculation of the received signal E. One way of further processing is then, for example, to compare the signal strength with a threshold. If this is exceeded, the receiver knows that its assigned sequence (code sequence) has been received and evaluates the information. Using the example of the UMTS E-HICH channel, the information content of the received signal is an ACK or NACK of the base station to the mobile station in response to a data packet transmitted from the mobile station to the base station on the E-DCH. The information ACK or NACK can be signaled by the sign of the received signal E.

• 1 eine vereinfachte Darstellung einer Up-Link- bzw. Down-Link-Verbindung;
• 2 eine Code-Matrix;
• 3 ein Simulationsergebnis;
• 4 eine Darstellung der Spaltenvertauschungsoperation des Verkämmens für das Beispiel einer Matrix mit 8 Spalten;
• 5 eine Darstellung der Spaltenvertauschungsoperation Blockinversion für das Beispiel einer Matrix mit 8 Spalten;
• 6 eine Darstellung der Spaltenvertauschungsoperation Blockverschiebung für das Beispiel einer Matrix mit 8 Spalten;
• 7 eine Darstellung der Spaltenvertauschungsoperation des Block Verkämmens für das Beispiel einer Matrix mit 8 Spalten;
• 8 eine Darstellung der Spaltenvertauschungsoperation des Block Entkämmens für das Beispiel einer Matrix mit 8 Spalten;
• 9 eine Darstellung einer einfachen Spaltenvertauschungsoperation für das Beispiel einer Matrix mit 8 Spalten;
• 10 eine Code-Matrix;
• 11 ein Simulationsergebnis.

In the following, embodiments of the invention will be described in more detail with reference to figures. Showing:

• 1 a simplified representation of an up-link or down-link connection;
• 2 a code matrix;
• 3 a simulation result;
• 4 a representation of the column interchange operation of the combing for the example of a matrix with 8th Columns;
• 5 a representation of the column swap operation block inversion for the example of a matrix with 8th Columns;
• 6 a representation of the column swap operation block shift for the example of a matrix with 8th Columns;
• 7 a representation of the column interchange operation of the block combing for the example of a matrix with 8th Columns;
• 8th a representation of the column interchange operation of the block combing for the example of a matrix with 8th Columns;
• 9 a representation of a simple column interchange operation for the example of a matrix with 8th Columns;
• 10 a code matrix;
• 11 a simulation result.

1 shows two (enhanced uplink) data channels EU0 and EU1 from two mobile stations MS0 and MS1 to a base station BS of a UMTS system.

In order to establish or maintain such an enhanced-up link, the signaling channels E-HICH0 and E-HICH1 (Enhanced Up Link Dedicated Channel Hybrid ARQ Indicator Channel) and E-RGCHO and E-RGCH1 (Enhanced Up Link Dedicated Channel Relative Grant Channel) in the direction from the base station BS to the mobile stations MS0, MS1.

To the from the base station BS to the mobile stations MS0 . MS1 Within a radio channel (same time and frequency resource) realized signaling channels receiver side for the various mobile stations MS0 . MS1 To make separable, the data bits to be transmitted via these signaling channels on the transmission side (base station side) different code sequences are impressed.

The radio stations (mobile stations, base stations) are hardware-technically, for example by suitable receiving and / or transmitting devices or by suitable processor devices, and / or software so arranged that for the transmission of data code sequences according to the invention are used, in particular data to be transmitted multiplied by a code sequence according to the invention be (spread) or received signals are correlated with a code sequence according to the invention.

In addition to the spreading with the described code sequences, a further spreading with so-called OVSF (Orthogonal Variable Spreading Factor) sequences can be carried out, since the UMTS is a CDMA system. However, this spreading takes place only at the symbol level, ie a very short time interval, so that this spread has only a negligible influence on the frequency error characteristics and is therefore mentioned here only for the sake of completeness.

• - Bilden einer Hadamardmatrix der Länge n;
• - Vertauschen von Spalten der Hadamardmatrix.

For example, a base station has a transmitting device for transmitting data to different subscribers and a processor device which is set up such that data directed to different subscribers are impressed on different code sequences, the code sequences being taken from a code matrix by the following steps available is:

• Forming a Hadamard matrix of length n;
• - Swap columns of the Hadamard matrix.

• - Gruppierung der Spalten in Spalten der ersten Hälfte (1,2, ..., n/2-1) und in Spalten der zweiten Hälfte (n/2, n/2+1, ..., n-1) mit ungerader Nummer (1,3,5, ..., n-1);
• - Gruppierung der Spalten in Spalten mit gerader Nummer (0,2,4, ...n-2) und in Spalten mit ungerader Nummer (1,3,5, ..., n-1);
• - Vertauschen der Spalten der Hadamardmatrix derart, dass die Gruppe der Spalten der ersten Hälfte die Spalten mit gerader Nummer (0,2,4, ...n-2) der Codematrix bilden, und dass die Gruppe der Spalten der zweiten Hälfte die Spalten mit ungerader Nummer (1,3,5, ..., n-1) der Codematrix bilden.

According to one embodiment, the code sequences are taken from a code matrix which is obtainable by the following steps (combing):

• - Grouping of columns in columns of the first half ( 1 . 2 , ..., n / 2-1 ) and in columns of the second half ( n / 2 . n / 2 + 1 , ..., n-1 ) with an odd number ( 1 . 3 . 5 , ..., n-1 );
• - Grouping of columns in even-numbered columns ( 0 . 2 . 4 , ... n-2 ) and in odd-numbered columns ( 1 . 3 . 5 , ..., n-1 );
• Interchanging the columns of the Hadamard matrix such that the group of the columns of the first half contains the even-numbered columns ( 0 . 2 . 4 , ... n-2 ) of the code matrix, and that the group of columns of the second half are the odd-numbered columns ( 1 . 3 . 5 , ..., n-1 ) form the code matrix.

• - Nummerierung der n Spalten der Hadamardmatrix von 0 bis n-1;
• - Gruppierung der Spalten in Spalten mit gerader Nummer (0,2,4, ...n-2) und in Spalten mit ungerader Nummer (1,3,5, ..., n-1) ;
• - Vertauschen der Spalten der Hadamardmatrix derart, dass die Gruppe der Spalten mit gerader Nummer die ersten n/2 Spalten der Codematrix bilden, und dass die Gruppe der Spalten mit ungerader Nummer die letzten n/2 Spalten der Codematrix bilden.

According to another embodiment variant, the code sequences are taken from a code matrix obtainable by the following steps (decombining):

• Numbering of the n columns of the Hadamard matrix from 0 to n-1 ;
• - Grouping of columns in even-numbered columns ( 0 . 2 . 4 , ... n-2 ) and in odd-numbered columns ( 1 . 3 . 5 , ..., n-1 );
• Swapping the columns of the Hadamard matrix such that the group of even-numbered columns is the first n / 2 Form columns of the code matrix, and that the group of odd-numbered columns is the last one n / 2 Form columns of the code matrix.

For example, a mobile station has a receiving device for receiving a received signal sequence and a processor device which is set up in such a way that the received signal sequence is correspondingly correlated with one of the above-mentioned code sequences.

For better separability because of these code sequences should be mutually orthogonal. This means that a receiver (such as a mobile station) that correlates to one line (code train) will not receive a signal if another line (code train) has been sent:

dabei stellt C(s,i) das i-te Element der sendeseitig verwendeten Codefolge dar und C(e,i) das i-te Element der empfangsseitig verwendeten Codefolge. The received signal E is when the transmitter transmits the sequence (code sequences) s and the receiver correlates to the sequence (code sequence) e: $$e={\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)=0}$$

where C (s, i) represents the i-th element of the code sequence used on the transmitting side, and C (e, i) represents the i-th element of the code sequence used at the receiving end.

Thus, because the lines of the Hadamard matrix used for the code sequences are orthogonal to each other, transmissions for other users based on the code sequence s do not interfere with the transmissions for a given user who expects data based on the code sequence e. However, this perfect orthogonality is lost if the signals have a frequency error. Then: $$e={\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^j=}{\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^j}\ne 0$$

Where f denotes the value of the frequency error, t (i) = Ti is the time at which the i-th bit is transmitted, T is the duration of one bit. As usual in signal processing, the calculation is complex. Here, it is assumed that the i-th symbol is transmitted at the time T times i. Strictly speaking, this is only the case if the bits are transmitted serially in succession. It is also possible, for example, to transmit two bits in parallel at the same time, for example by using a so-called IQ multiplex method, ie in a complex transmission signal the one bit is transmitted as a real part and the other as an imaginary part. In this case, two bits each are transmitted at the same time, so that t (i) = (int ( i / 2 ) * 2 + 0.5) * T is. int () denotes the integer part here. However, the difference between these two cases is only 0.5T and is generally negligible so that this fineness will not be discussed further below. An equivalent formulation is that the two bits i and i + 1 of the symbol ( i / 2 ) are sent at the time i * T. The difference between the two nomenclatures is only an offset of 0.5 * T. This offset is irrelevant; it would only shift the transmission of all symbols, but the problem is invariant with respect to a time shift.

Thus, transmissions affect each other, ie when data is sent to a mobile station on the basis of the code sequence s, this interferes with the reception at the mobile station, which expects data on the basis of the code sequence e.
This disturbance is minimized by the present invention.

It would be optimal if one could find sets (code matrices) of orthogonal sequences (code sequences) which have good properties even in the presence of a frequency error. In particular, in the worst case, the above influence should be as small as possible for the worst pair of sequences. The aim of the invention is therefore also to provide a method for generating such sequences and the use of these sequences for purposes of transmission.

Square matrices with n orthogonal lines are also called Hadamard matrices. The following education law for the construction of a Hadamard matrix of length 2n from a matrix of length n is well known and widely used: $$C_{2n}=\left[\begin{array}{cc}{C}_n& C_n\\ C_n& -C_n\end{array}\right]$$

Starting from the Hadamardmatrix H2 the length 2 can be used to create matrices whose length is a power of two: $${\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">H</figure-callout>}}_2=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$$

Furthermore, Hadamard matrices are of length 20 known, which make up with this rule matrices of length 40 . 80 . 160 ... generate it.

It turns out, however, that matrices generated by this rule are of length 2n have a particularly bad property in the presence of frequency errors, ie the loss of orthogonality is particularly large. The influence on the lines k and n + k (where k <n) is particularly large. This is because two such lines are identical in the first n elements, whereas in the last n elements they have opposite signs. The correlation contribution of the first half will thus only be corrected in the second half. However, as the frequency error increases with time, this correction is already comparatively strongly falsified by the already relatively strong influence of the frequency error.

It turns out that, given a certain exchange of columns of a Hadamard matrix, the orthogonality properties (without frequency errors) do not change, but the column interchange has an influence on the orthogonality properties in the case of frequency errors. It is therefore possible to optimize the orthogonality properties in frequency errors suitable column interchanges feasible.

A column interchange that has been found to be particularly advantageous in simulations is the following (the algorithm is described here for the convention that the columns are counted starting with 0 (not 1), but can of course also be adapted to other numbering conventions):

From the matrix C _2n one selects the columns 0 to n-1 and put them on the even columns (columns 0 . 2 . 4 , ... 2n-2 ). The columns n to 2n-1 put one on the odd columns (columns 1 . 3 . 5 , ... 2n-1 ). The order within even or odd columns is preserved. So you use the following permutation: 0 . n . 1 . n + 1 . 2 . n + 2 , ..., n-3 . 2n-3 . n-2 . 2n-2 . n-1 . 2n-1 ,

The just-shown column interchange is equivalent to the following alternative construction principle (by the way, this design principle also leads to an equivalent interchanging of lines.) However, interchanging lines are irrelevant to the problem to be solved.)

Dadurch erhält man eine Matrix mit der doppelten Länge.A Hadamard matrix of length 2n is generated by taking all elements of the Hadamard matrix of length 2n replaced by the elementary 2's Hadamard matrix, multiplied by the value of the element. ie one replaces in the matrix $$1\text{by}\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]\text{and -}1\text{by}\left[\begin{array}{cc}-1& -1\\ -1& 1\end{array}\right]$$

This gives a matrix of twice the length.

• - Generierung einer Hadamardmatrix C20 oder C20' der Länge 20 als eine sog. Williamson-Matrix; diese kann generiert werden als: $$C_{20}={\left[\begin{array}{llll}A\hfill & A\hfill & C\hfill & D\hfill \\ -C\hfill & -D\hfill & A\hfill & A\hfill \\ -A\hfill & A\hfill & D\hfill & -C\hfill \\ -D\hfill & C\hfill & -A\hfill & A\hfill \end{array}\right]}_{\text{oder auch als:}}{C}_{20}=\left[\begin{array}{llll}-A\hfill & -A\hfill & D\hfill & C\hfill \\ A\hfill & -A\hfill & -C\hfill & D\hfill \\ -D\hfill & C\hfill & -A\hfill & A\hfill \\ -C\hfill & -D\hfill & -A\hfill & -A\hfill \end{array}\right]$$
  

Wobei A bzw. C jeweils 5 mal 5 Matrizen sind mit Zeilen die aus den zyklische Vertauschungen der Folgen [-1 1 1 1 1] bzw. [1 -1 1 1 -1] bestehen und D=2I-C wobei I die 5 mal 5 Einheitsmatrix darstellt, damit enthält D die zyklischen Vertauschungen der Folge [1 1 -1 -1 1]. The following construction method proved particularly advantageous for a code matrix:

• - Generation of a Hadamard matrix C20 or C20 'of length 20 as a so-called Williamson matrix; this can be generated as: $$C_{20}={\left[\begin{array}{llll}A\hfill & A\hfill & C\hfill & D\hfill \\ -C\hfill & -D\hfill & A\hfill & A\hfill \\ -A\hfill & A\hfill & D\hfill & -C\hfill \\ -D\hfill & C\hfill & -A\hfill & A\hfill \end{array}\right]}_{\text{or as:}}{C}_{20}=\left[\begin{array}{llll}-A\hfill & -A\hfill & D\hfill & C\hfill \\ A\hfill & -A\hfill & -C\hfill & D\hfill \\ -D\hfill & C\hfill & -A\hfill & A\hfill \\ -C\hfill & -D\hfill & -A\hfill & -A\hfill \end{array}\right]$$
  

Where A and C are each 5 times 5 matrices with lines consisting of the cyclic permutations of the sequences [-1 1 1 1 1] and [1 -1 1 1 -1] and D = 2I-C where I is the 5th times 5 unit matrix, thus D contains the cyclic permutations of the sequence [1 1 -1 -1 1].

In general, a Williamson matrix in the sense of this invention consists of blocks of elementary matrices, the elementary matrices containing lines with cyclic permutation.

The Williamson matrix C20 is thus the following matrix, with the individual blocks of 5 highlighted: -1 1 1 1 1 -1 1 1 1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 -1 1 1 1 1 -1 1 1 1 -1 1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 1 1 1 -1 1 1 1 -1 1 -1 1 -1 1 1 1 -1 1 1 1 -1 1 1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 1 1 1 1 1 1 -1 1 1 1 1 -1 -1 1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 1 1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 -1 1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 1 1 1 1 -1 1 -1 -1 1 1 1 -1 -1 1 -1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 1 1 1 1 -1

Another way to generate a Williamson matrix is the design rule: $$C_{20}^{\text{'}}=\left[\begin{array}{llll}-A\hfill & -A\hfill & D\hfill & C\hfill \\ A\hfill & -A\hfill & -c\hfill & D\hfill \\ -D\hfill & C\hfill & -A\hfill & A\hfill \\ -C\hfill & -D\hfill & -A\hfill & -A\hfill \end{array}\right]$$

• - Generierung einer Hadamardmatrix der Länge 40 aus einer dieser soeben beschriebenen Williamson-Matrizen der Länge 20 nach dem genannten Bildungsgesetz;
• - Nummerierung der 40 Spalten der Hadamardmatrix von 0 bis 39;
• - Gruppierung der Spalten in Spalten der ersten Hälfte (0,1,2, ..., 19) und in Spalten der zweiten Hälfte (20, 21, 22, ..., 39);
• - Vertauschen der Spalten der Hadamardmatrix derart, dass die Gruppe der Spalten der ersten Hälfte die Spalten mit gerader Nummer (0,2,4, ..., 38) der Codematrix bilden, und dass die Gruppe der Spalten der zweiten Hälfte die Spalten mit ungerader Nummer (1,3,5, ..., 39) der Codematrix bilden.
• - Vertauschen der Spalten 12 und 37.

This leads to the following matrix C20 '(C' ₂₀ ): 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1

• - Generation of a Hadamard matrix of length 40 from one of these just described Williamson matrices of length 20 according to the aforementioned education law;
• - Numbering of 40 Columns of the Hadamard matrix of 0 to 39 ;
• - Grouping of columns in columns of the first half ( 0 . 1 . 2 , ..., 19 ) and in columns of the second half ( 20 . 21 . 22 , ..., 39 );
• Interchanging the columns of the Hadamard matrix such that the group of the columns of the first half contains the even-numbered columns ( 0 . 2 . 4 , ..., 38 ) of the code matrix, and that the group of columns of the second half are the odd-numbered columns ( 1 . 3 . 5 , ..., 39 ) form the code matrix.
• - Swapping the columns 12 and 37 ,

Furthermore, you can already column interchanges with the Hadamardmatrix of length 20 then generate the 40's Hadamard matrix from it and then do more column interchanges on the 40's Hadamard matrix. This has the advantage of starting with a better 20's Hadamard matrix, which also results in a better 40's Hadamard matrix, so that this procedure will result in a better solution faster than if you were to do column interchanges only on the 40's Hadamard matrix.

• - Auf der 20er Hadamardmatrix vertausche die Spalten (5,6), (0,4), (6,9), (0,1) (Hinweis: Da die Spalte 0 zweimal vertauscht wird, entspricht das einer zyklische Vertauschung der Spalten (1, 4, 0); die Permutation gegenüber der ursprünglichen 20er Hadamardmatrix ist dann (1, 4, 2, 3, 0, 8, 9, 7, 5, 6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19);
  • - Generiere dann nach einer der oben genannten Vorschriften die 40er Hadamardmatrix, und vertausche dann die Spalten (1, 10), (3, 4) .

In a computer-aided search, the following column interchanges were found to be particularly favorable:

• - On the 20's Hadamard matrix, swap the columns ( 5 . 6 ) 0 . 4 ) 6 . 9 ) 0 . 1 ) (Note: because the column 0 is exchanged twice, this corresponds to a cyclic permutation of the columns ( 1 . 4 . 0 ); the permutation over the original 20's Hadamard matrix is then ( 1 . 4 . 2 . 3 . 0 . 8th . 9 . 7 . 5 . 6 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 . 19 );
  • Then generate the 40's Hadamard matrix according to one of the above instructions, and then replace the columns ( 1 . 10 ) 3 . 4 ).

This gives the in 2 illustrated improved matrix. The maximum of the sub-correlations in this matrix is 3.9, which is to be compared with the value of the original matrix of 8.3. This means suppression for receiving transmissions for other mobile stations of 6.54dB.

• - Auf der 20er Hadamardmatrix vertausche die Spalten (6,9), (10,13), (0,3), (16,19), (0,1), (18,19), (5,7), (12,14), (1,2), (17,18)
  • - Generiere dann nach einer der oben genannten Vorschriften die 40er Hadamardmatrix, und vertausche dann die Spalten (6,9), (11,14), (6,10), (14,16), (3,4), (13,14), (2,3), (17,18).

Another, even better, optimization is available through the following operations:

• - On the 20's Hadamard matrix, swap the columns ( 6 . 9 ) 10 . 13 ) 0 . 3 ) 16 . 19 ) 0 ,1), ( 18 . 19 ) 5 . 7 ) 12 . 14 ) 1 . 2 ) 17 . 18 )
  • Then generate the 40's Hadamard matrix according to one of the above instructions, and then replace the columns ( 6 . 9 ) 11 . 14 ) 6 . 10 ) 14 . 16 ) 3 . 4 ) 13 . 14 ) 2 . 3 ) 17 . 18 ).

The maximum of the secondary correlations in this matrix is 3.7406.

• - C und D seien Hadamardmatrizen,
• - $C_{20}=\left[\begin{array}{cc}{D}_n& C_n\\ C_n& -D_n\end{array}\right].$
  

A development of the invention further provides the following steps for forming an advantageous code matrix:

• - C and D are Hadamard matrices,
• - $C_{20}=\left[\begin{array}{cc}{D}_n& C_n\\ C_n& -D_n\end{array}\right],$
  

• - C und D seien Hadamardmatrizen,
• - bilde eine Codematrix gemäß: $D_{2n}=\left[\begin{array}{cc}{D}_n& D_n\\ C_n& -C_n\end{array}\right].$
  

A development of the invention provides the following steps for the formation of an advantageous code matrix:

• - C and D are Hadamard matrices,
• - form a code matrix according to: $D_{2n}=\left[\begin{array}{cc}{D}_n& D_n\\ C_n& -C_n\end{array}\right],$
  

These code matrices can be further optimized by the above-mentioned column interchange steps, in particular combing.

In 3 the distribution of correlations in frequency errors is given for the prior art (UMTS) and the presented method with the improved column swap (opt) shown above (group even and odd columns), which is equivalent to the method of alternative generation of the matrix (FIG. but without the above-mentioned further column exchanges). The frequency error was assumed to be 200 Hz. The size of the cross-correlations is plotted on the y-axis, they are sorted by size. The x-axis thus corresponds to the number of the pair for which the cross correlation was calculated, this number being assigned to a pair so that the pairs are sorted according to the amount of their cross-correlation.

As you can see, arise according to the prior art 40 Secondary lines with a value greater than 8th , After the improvement, the maximum is only approx. 6 and is also reached less often.

It can be shown that the sum of the squares of all secondary lines is constant. If, therefore, the maxima are lowered, the values are inevitably increased for smaller secondary lines. But it is essentially the maxima that determine the performance of the system. This is because an error occurs just when a reception value is corrupted by the interference of the cross-correlation. This is mainly caused by the large secondary maxima, less by the small ones. Thus, the increase of the smaller secondary lines (cross-correlations) is not only inevitable but also harmless.

So far, code matrices have been described, which result from a Hadamard matrix by way of column interchanging operations. In particular, the column swapping operations were performed before and / or after doubling the length of an output Hadamard matrix.

The most common column swapping operations have been described as "combing", "combing out" and "simple column exchanges".

In addition, the following studies showed that the following column-interchanging operations are feasible and can lead to better code matrices with regard to the above-mentioned criteria:

"Block inversion": You can reverse the order for a block of columns, that is, a set of consecutive columns. From a column arrangement 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 obtained by block inversion of the block of columns 3 to 6 the permutation 0 . 1 . 2 . 6 . 5 . 4 . 3 . 7 , This example is in 5 shown. This is also a good operation: the contribution of a block to the total correlation remains the same in this operation, but the sign is reversed. As a result, it may be possible for the value of the correlation to be better compensated for by the negative contribution of the inverted block, ie the contributions of the remaining columns are better compensated.

Wird ein Block von Spalten um k Spalten verschoben, so ändert sich sein Beitrag zur Gesamtkorrelation um den Betrag e^J2π∫Tk. Das Vorzeichen von k entspricht dabei der Richtung der Verschiebung. Das bedeutet eine Drehung des Beitrages des Blocks im komplexen Zahlenraum. Durch das Blockverschieben kann man erreichen, dass die Gesamtkorrelationssumme kleiner wird, wenn man erreicht, dass durch die Verdrehung der Beiträge der verschobenen Blöcke (explizit und durch Verdrängung implizit verschobene Blöcke) sich die Beiträge besser aufheben, da die Beiträge, bildlich gesprochen wie ein Taschenmesser zusammengeklappt werden."Block shift": You can move a block of columns so that this block is in a different position. From a column arrangement 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 obtained by moving the block of columns 5 to 6 to the place 1 the permutation 0 . 5 . 6 . 1 . 2 . 3 . 4 . 7 ( 6 ). This is also a good operation: the contribution of a block to the total correlation remains the same in this operation (considering the amount as a complex value), but by shifting the complex value is rotated by an amount equal to the frequency error of the shift. As a side effect, moving a block also moves other blocks of columns because the moved block displaces or displaces other columns at its new location. The contribution to the correlation of these implicitly shifted columns also changes. As already shown, the correlation sum is given by: $$e={\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*{\mathrm{<figure-callout\; id="2"\; label="e\; J"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^{J^{}}=}{\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*{\mathrm{<figure-callout\; id="2"\; label="e\; J"\; filenames="DE102005005695B4\_0022.png,DE102005005695B4\_0023.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^{J^{}}\ne 0}$$

If a block of columns is shifted by k columns, its contribution to the total ^correlation changes by the amount e ^J2π∫Tk . The sign of k corresponds to the direction of the shift. This means a rotation of the contribution of the block in the complex number space. By shifting the block, one can achieve that the total correlation sum becomes smaller, if one achieves that by the rotation of the contributions of the shifted blocks (explicitly and displacementally implicitly displaced blocks) the contributions cancel one another better, since the contributions, metaphorically like a penknife be folded.

For the sake of completeness, the column interchanging operations "combing", "combing out" and "simple column interchanging" will be described again here, whereby it is additionally described here that the combing and decongesting does not necessarily have to refer to the entire matrix, but instead can only refer to sub-blocks:

"Combing" and "combing out": as already stated, combing is a valuable operation to influence the correlation sum. In the above, combing was performed for the entire matrix, that is, for all columns of the matrix. However, it can also be applied to only one subarea: one chooses a block of columns and performs the operation only on this subarea. From a column arrangement 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 obtained by combing the block of columns 0 to 5 the permutation 0 . 3 . 1 . 4 . 2 . 5 . 6 . 7 , This example is in 7 shown.

From a column arrangement 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 obtained by de-combing the block of columns 0 to 5 the permutation 0 . 2 . 4 . 1 . 3 . 5 . 6 . 7 , This example is in 8th shown.

"Simple column swap": Here, two columns of the matrix are swapped. From a column arrangement 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 obtained by swapping the columns 2 and 5 the permutation 0 . 1 . 5 . 3 . 4 . 2 . 6 . 7 , This example is in 9 shown.

The "combing out" is thus the operation "inverse" for "combing", whereas the inverse to a "block shift" is again a "block shift". "Block inversion" and "simple column swap" are each inverted to themselves.

It has now been found that based on these column swap operations, code matrices can be generated that are even better in terms of the above criteria.

In particular, by a "simulated annealing" method based on these column interchange operations, it has been found that code matrices having a maximum of the correlation sums of 3 . 0 can be generated.

With the so-called "simulated annealing" method, a vanishingly small number of code matrices with a maximum of the correlation sums of under 3 . 0 being found.

If one compares this maximum from below 3 with the maximum of non-optimized code sequences of 8th . 26 , this corresponds to a reduction of the maxima by a factor of over 2 . 75 , This corresponds to a reduction of the interference power by almost 9dB. Such a strong reduction of the correlation maxima was not to be expected.

A particularly preferred example of such a optimized code matrix is in 10 and again shown below:

durch Anwenden der folgenden Permutation:

• 28, 21, 26, 37, 24, 11, 19, 32, 34, 14, 6, 23, 31, 16, 20, 15, 2, 25, 18, 12, 39, 8, 7, 22, 33, 36, 29, 35, 27, 17, 3, 13, 5, 10, 38, 0, 30, 1, 4, 9.

This code matrix is obtainable from the 40s matrix C _'40 by the following law of formation of the above-mentioned matrix C' is formed _20: $$C{\text{'}}_{40}=\left[\begin{array}{cc}C{\text{'}}_{20}& C{\text{'}}_{20}\\ C{\text{'}}_{20}& -C{\text{'}}_{20}\end{array}\right].$$

by applying the following permutation:

• 28 . 21 . 26 . 37 . 24 . 11 . 19 . 32 . 34 . 14 . 6 . 23 . 31 . 16 . 20 . 15 . 2 . 25 . 18 . 12 . 39 . 8th . 7 . 22 . 33 . 36 . 29 . 35 . 27 . 17 . 3 . 13 . 5 . 10 . 38 . 0 . 30 . 1 . 4 . 9 ,

That is, column no. 28 of the original matrix C _'40 is the column number. 0 set, the column no. 21 the original matrix to the column no. 1 etc. The columns are each again from 0 to 39 numbered.

This is equivalent to applying the following permutation: 29 . 22 . 27 . 38 . 25 . 12 . 20 . 33 . 35 . 15 . 7 . 24 . 32 . 17 . 21 . 16 . 3 . 26 . 19 . 13 . 40 . 9 . 8th . 23 . 34 . 37 . 30 . 36 . 28 . 18 . 4 . 14 . 6 . 11 . 39 . 1 . 31 . 2 . 5 . 10 , That is, the 29te column of the original matrix C _'40 is set to the first column, the 22nd column of the original matrix in this case be the second, and so the columns of each 1 to 40 numbered.

The resulting matrix has maximum secondary correlations of 200 Hz with a frequency error of 2 . 7 what with the value of the original matrix of 8th . 3 is to be compared. This means a suppression for the reception of broadcasts for other mobile stations of about 9.5 dB.

As in 11 , in addition to the 3 shows two further distributions, shown, the distribution (ann.) of the correlation sums when using such a optimized code matrix (see claim 9) is now fairly balanced and contains in particular no peak at the maximum. The distribution approximates the theoretical ideal course (Theo.), In which all secondary lines have the same value. In this case, every correlation sum would have the value 1 . 53 , However, this ideal case is practically unattainable because of the large number of theoretically possible correlation pairs. The optimization can, however, achieve a value that comes very close to this value for practical application.

• - Vertauschen von Zeilen der Matrix;
• - Umkehren der Reihenfolge der Spalten der gesamten Matrix;
• - Multiplizieren von Zeilen mit einem konstanten Wert, insbesondere mit -1;
• - Multiplizieren von Spalten mit einem konstanten Wert, insbesondere mit -1-, etc.

It should be noted that although column invocations have an influence on the behavior in the presence of a frequency error, but there are also other operations that have no influence on it and also do not affect the orthogonality properties. Therefore, a code matrix according to the invention can be converted with these operations into various other matrices, which likewise have the properties according to the invention. These operations include:

• - swapping lines of the matrix;
• - reversing the order of the columns of the entire matrix;
• - multiplying rows by a constant value, in particular -1;
• - Multiplying columns with a constant value, especially with -1-, etc.

For this reason, code matrices which result from the use of one or more of these operations of code matrices according to the invention and their use according to the invention are, of course, likewise within the scope of the invention.

Claims (12)

A method for transmitting data between at least two radio stations, comprising: - a Hadamard matrix of length n, derived from one according to a law of formation for constructing a Hadamard matrix of length n from a Hadamard matrix of length n / 2; a code matrix which differs from the Hadamard matrix at least in that it is formed in this way

comprising the following steps: (a) a code sequence is described by a line of the code matrix; (b) the code sequence is used to transmit the data by spreading the data on transmission with the code string or correlating in reception with the code string. Method according to Claim 1 in which the code matrix is formed as follows: numbering of the n columns of the Hadamard matrix from 0 to n-1; - Grouping of the columns in even-numbered columns (0,2,4, ... n-2) and in odd-numbered columns (1,3,5, ..., n-1); Swapping the columns of the Hadamard matrix such that the group of even-numbered columns form the first n / 2 columns of the code matrix, and that the group of odd-numbered columns form the last n / 2 columns of the code matrix. Method according to one of Claims 1 or 2 in which the Hadamard matrix is based on an interlated Hadamard matrix of length n / 2, which results from an interchange of columns from an output Hadamard matrix of length n / 2. Method according to one of the preceding claims, in which the columns of the Hadamard matrix have been multiply interchanged within the framework of a simulated annealing method. Method according to one of the preceding claims, in which the columns of the Hadamard matrix have been reversed several times until the maximum amount of $$e={\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*e^{j2\pi ft\left(i\right)}=}{\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*e^{j2\pi fTi}}$$

which is formed for all possible pairs s and e with s not equal to e, where C (s, i) is the element of the code matrix in line s and column i, the sum is made over all columns of the code matrix, and the matrix is size 40 has, f has the value 200 Hz and T has the value 16.66 microseconds, is less than 3. Method according to one of the preceding claims, in which lines of the code matrix form a plurality of code sequences which are code sequences orthogonal to one another, and the maximum amount of $$e={\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*e^{j2\pi ft\left(i\right)}=}{\displaystyle \underset{i}{\Sigma }C\left(s.i\right)C\left(e.i\right)*e^{j2\pi fTi}}$$

which is formed for all possible pairs s and e with s not equal to e, where C (s, i) is the element of the code matrix in line s and column i and the sum is performed over all columns of the code matrix is less than the maximum amount formed over the elements of the Hadamard matrix. Method according to one of the preceding claims, in which n = 40. Method according to the preceding claim, wherein the Hadamard matrix C _'40 of the length 40 of an output matrix C' ₂₀ of the length 20 of the Education Act $$C{\text{'}}_{40}=\left[\begin{array}{cc}C{\text{'}}_{20}& C{\text{'}}_{20}\\ C{\text{'}}_{20}& -C{\text{'}}_{20}\end{array}\right]$$

and the code matrix differs from this Hadamard matrix in that the columns are reversed as follows: Column of Column of Hadamard matrix C _'40 code matrix 29 1 22 2 27 3 38 4 25 5 12 6 20 7 33 8th 35 9 15 10 7 11 24 12 32 13 17 14 21 15 16 16 3 17 26 18 19 19 13 20 40 21 9 22 8th 23 23 24 34 25 37 26 30 27 36 28 28 29 18 30 4 31 14 32 6 33 11 34 39 35 1 36 31 37 2 38 5 39 10 40 Method according to the preceding claim, in which the output matrix C _'20 is formed as follows: 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 Method according to one of the preceding method claims, in which the code matrix moves from the Hadamard matrix by carrying out at least one further operation on the code matrix Claim 1 which does not affect the orthogonality properties. Method according to the preceding claim, in which the further operation is formed by at least one of the following steps: - swapping lines of the matrix; - reversing the order of the columns of the entire matrix; - multiplying rows by a constant value, in particular -1; Multiplying columns by a constant value, especially -1. 12 base station with a transmitting device for transmitting data to different subscriber stations, in particular mobile stations, and a processor device which is set up such that data directed to different subscriber stations, in particular mobile stations, different code sequences are impressed, wherein the code sequences of one of the code matrices are taken, which are described in one of the method claims. 13. A mobile station having a receiving device for receiving a received signal sequence, and a processor device, which is set up such that the received signal sequence is correlated with a code sequence according to one of the method claims.

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