WO2005039081A1

WO2005039081A1 - Method for transmitting signals in a communications system

Info

Publication number: WO2005039081A1
Application number: PCT/EP2004/052556
Authority: WO
Inventors: Martin Piekov; Pavol Svac
Original assignee: Siemens Aktiengesellschaft
Priority date: 2003-10-15
Filing date: 2004-10-15
Publication date: 2005-04-28
Also published as: EP1673887A1; KR101090987B1; KR20060107781A; CN1894877A; CN1894877B

Abstract

According to the invention, a method for transmitting signals in a communications system is proposed, wherein code sets comprising a number of two-shift complete complementary code pairs are assigned for communication between stations of the communications system, and wherein the assigned code sets are mutually orthogonal and possess ideal autocorrelation functions. The inventive method is characterized in that a code length is defined as L=2n, the order of the code sets is defined as N=2r, and the cardinality P of the code sets is defined as : (I) wherein r and n are positive integer numbers.

Description

Method for transmitting signals in a communications system

The invention relates to a method for transmitting signals in a communications system, and to a station of such a communications system.

In radio communications systems, signals are exchanged be- t een terminals and base stations via a so called radio interface or air interface. Such terminals are mobile or stationary user terminals (UE - user equipments), whereas base stations (NB - Node B) provide access to a land based communications network. Examples of well known radio communica- tions systems are second generation digital mobile radio com^¬ munication systems like GSM (Global System for Mobile Communication) , which is based on TDMA (Time Division Multiple Access) and provides data rates of up to 100 kbit/s, and third generation digital mobile radio communications systems like UMTS (Universal Mobile Telecommunication System) , which is based on CDMA (Code Division Multiple Access) and provides data rates of up to 2 Mbit/s.

For even higher data rates and a larger number of users than provided by the above systems, it is proposed for future radio communications systems to rely on so called multicarrier CDMA (MC-CDMA) techniques, wherein a number of separated frequency bands (carriers) are used in parallel for transmission of signals to/from user terminals. One approach for an imple- mentation of a MC-CDMA system is discussed in [1], which is based on an offset stacked spreading technique using complete complementary codes . H.H. Chen et al. introduced in [1] a MC-CDMA architecture based on so called orthogonal complementary codes, the origin of which can be traced back to the 1960s, when Golay [2,3,4] and Turyn [5] first studied pairs of binary complementary codes. Compared to conventional CDMA systems, the proposal of [1] achieve a spreading efficiency, which is defined as the amount of information bit(s) conveyed by each chip, of very close to one, it offers MAI-free operation in both up- and downlink transmissions in A GN (average white Gaussian noise) channels, which can significantly reduce co-channel interfer^¬ ence resulting in a capacity reduction of a CDMA system, it offers a high bandwidth efficiency due to the usage of an offset stacked spreading modulation scheme, and it enables multirate signal transmissions, which greatly simplify rate- matching algorithms used for multimedia services.

The proposed MC-CDMA architecture relies on so called complete complementary (CC) codes which are based on N-shift cross-orthogonal sequences known from [6] . CC codes of order N consist of N flocks each containing N element codes with a code length of L = N _f wherein N = 2 f_or n e N _

Such codes only exist for code length L = 4 . Another drawback is due to the structure of these codes. Each flock consists of a fixed number of elements which is equal ^"v^ . Since all elements comprise auto-complementary sets, it is thus necessary to receive all elements for a correct detection of a particular flock. The number of elements within a flock determines a number of allocated resources, i.e. the number of used frequencies (carriers) in case of a MC-CDMA system. In case it is necessary to vary the number of allocated resources, it would also be necessary to change the code length. As each user employs a distinct flock as its signature code, the number of flocks or, in other words, the number of users supported by the system equals ^ . In case of higher capacity requirements, e.g. because of a larger number of users, it would be necessary to use CC codes of a greater length.

C.-C. Tseng et al introduced in [7] mutually orthogonal com^¬ plementary sets of sequences, each complementary set thereby consisting of N sequences with a length L = N _{# n} comparison to CC codes, the same number of sequences within a flock can be achieved at shorter code length. On the other hand, the number of sequences in a particular complementary set is also fixed and dependent on the code length. Therefore, in case of a necessity to change the number of allocated resources, for example the number of frequencies bands (carriers) , it would be again necessary to change the code length. In addition, for a correct detection it would still be necessary to receive all sequences within one complementary set.

It is therefore an object of the invention to provide code sets to enable the support of a larger number of users and greater flexibility for ressource allocation especially in MC-CDMA based communications systems. This object is ad- dressed by the inventive features of the independent claims.

The invention relies on offset stacked spreading techniques and defines a new class of complete complementary codes which enables a more flexible variation of the number of users and data rates in e.g. MC-CDMA based communication systems in comparison to codes known in the art. The invention may be understood more readily, and various other aspects and features of the invention may become apparent from consideration of the following description and the figures as shown in the accompanying drawing sheets, wherein:

FIG 1 shows a block diagram of a radio communications network,

FIG 2 shows a synthesis of a quadruplet of mutually or^¬ thogonal couples of VT-SACC sets, FIG 3 shows a ID VT-SCC code of code length L,

FIG 4 shows a ID VT-SCC code of code length L=4 and the sum of autocorrelation between two sets,

FIG 5 shows the sum of autocorrelations for a VT-SACC set with code length of L=4 and cardinality of 8, FIG 6 sum of autocorrelations for the following VT-SACC set with code length of L=4 and cardinality of 4, FIG 7 two tables comparing properties of codes known in the art with codes according to the invention.

FIG 1 shows the basic structure of a radio communications system based on the well known UMTS-standard. Such a system consists of a central mobile switching center (MSC) which is connected to the public switched telephone network PSTN and other MSCs. Connected to a MSC is a plurality of base station controllers RNC (Radio Network Controller) , which inter alia coordinate the sharing of radio resources provided by base stations NB (Node-B) . Base stations NB transmit in downlink DL and receive in uplink UL signals respectively to or from a number of user equipments UE situated within the area C cov- ered by the base station NB. As an example, code sets Y1...Y4, which will be explained in detail in the following, are used for communication between the base station NB and the user equipments UE1...UE4. In the following, the synthesis of variable two-shift complete complementary (VT-SCC) codes according to the invention is discussed.

Variable two-shift autocomplementary code (VT-SACC) sets form the basis of one dimensional (ID) variable two-shift complete complementary (ID VT-SCC) codes. Such VT-SACC sets consist of a variable number of two-shift complementary code (T-SCC) pairs of code length L = 2 , with n e natural numbers, each consisting of two two-shift complementary (T-SC) code elements, wherein the term complementary means that the sum of aperiodic auto-correlation (AAC) functions of T-SC code elements of a certain T-SCC pair is an impulse of magnitude 2 _and sidelobe levels of zero. Since every second shift of the AAC function of each T-SC code element is zero, the term two-shift is used in combination with the term complementary.

The smallest unit of VT-SACC sets are T-SC code elements that create T-SCC pairs. In the following, two methods for generating such sequences are discussed. The first method is based on a synthesis from Reed-Muller codes, whereas the second one uses a system of multi-variable polynomial equations for the synthesis .

Synthesis of VT-SACC sets from Reed-Muller codes

In [8], existing relations between Golay complementary pairs and common binary Reed-Muller codes are disclosed. In this paper it was proven to be possible to generate all Golay sequences using RM(l ,n) codes and coset leaders with needed properties. In addition it was also proven that a set of ^z "^• «!

Golay sequences can be represented as 2 distinct cosets of

RM(l ,n) , each containing codewords.

Considering binary sequences of length 2" over •^■ ' > , and °

being an all-ones sequence. For ^{l ~} ' '^•••'^rt let ' be 2' 2 n-ι -.-..^--_^-...---._^^ -.-._j--..-,-. -,._. -.ii_^. _^^wv.!.-,^ ,_w.„_r-^-ι.>_j zeros

followed by ones. Then °' ''^'"' " form the rows of a generator matrix for the first-order Reed-Muller code RM(l , n) .

The codeword

is a binary Golay sequence of code length - 2 for any

permut .at.i.on ^Λ _π of {^l1,2,...,/» '}and, f_or any coeff_*i■ci■en_>t.s c,' ^e{^l0>l} ' .

The first term of (1) determines the quadratic coset leader and the second term determines a component from Reed-Muller code RM(l ,n) . (1) shows how the "^• binary Golay sequences n\ can be explicitly represented as 2 distinct cosets of RM (l ,n) .

In order to obtain T-SC code elements over {^l0,1} , i.t is necessary to modify (1) . It is clear that formula (1) provides also a way for an analytical determination of maximum cardinality of VT-SACC set. As T-SC code elements are a subset of Golay sequences, their cardinality will be smaller than that of Golay sequences. In addition, components from RM(l ,n) must be the same also for T-SC code elements. Therefore, the only distinction may come from the quadratic coset leaders .

From the theory of factor groups, it is well known that coset leader is a representative of the coset with the minimum weight, it thus represents properties of the whole coset. In order to determine the properties of the coset, it is sufficient to analyse the properties of coset leader which is gen- erating this coset. In other words, coset leaders used for generating of T-SC code elements must fulfill the properties of T-SC code elements.

The first part of (1)

∑nn--l\ ,=1 X π ^■{( ,ι,)),^•x π(ι+!) (2)

generates 2 coset leaders, which are added to the set of RM (l ,n) codes. Coset leaders, which meet properties of T-SC X code elements, generate cosets of T-SC code elements. Let " be J- concatenated copies of the sequences consisting of zeros and ones, and consider following coset leaders consisting of following RM(l ,n) codewords

(00...11) n = 2k + \

X_kX_t θ . ⁾χ_lx_n ®... ® x_mx_n = k e Z⁺ (00...00) n = 2k (3)

After correlation analysis it can be seen that this coset leader representative does not provide properties of T-SC code elements and therefore, its coset will not have proper^¬ ties of T-SC code elements as well. Thus, if quadratic coset X leader defined by (3) comprise more than one " in its notation, it will not have the property of T-SC code elements. Therefore, such a coset leader must be excluded from the set of coset leaders for generating T-SC code elements. rή As mentioned above, there are 2 distinct coset leaders. In (n-2)(n-\)\ this set there are 2 coset leaders comprising more x than one ", and therefore, must be subtracted form the set (n-\)\ of all distinct coset leaders. Doing so, ^; coset leaders are obtained for generating T-SC code elements. With this, it is possible to determine the number of all distinct T-SC code elements or, in other words, the maximum cardinality of the

VT-SACC set of particular code length L = 2 .

As a theorem, let L - 2 e the code length of T-SC code elements, then the cardinality of a set consisting of all T-SC

code elements of code length L is *- '' .

T-SC code elements generated with the above approach are coupled to form T-SCC pairs using two possible ways. The first one is based on an evaluation of similarities of elements within one sequence for all possible separations, followed by a comparison with another sequence, as disclosed in [4] . The second way, which is based on correlation properties, is, however, more popular. A couple of T-SC code elements of the

same code length L ⁼ 2 , with n £ natural numbers, comprises T-SCC pairs if AAC functions of both T-SC code elements add up to an impulse of magnitude 21.

According to a first example, for ^{n =} ^ there are three choices of coset representatives, namely x,x₂ +x₂x₃ =00010010 x,x₃ +x₂x₃ =00010100 _and x, 'x₂ ^z+x,'x₃ ^J =00000110. „The f _firs ,t one is chosen and_^ ad_^ded_^.to y c,χ, the encoded value ' of four further data bits (cⁱ' c²' c3' c ^{A )} _{ιn orc}j_er to generate a Golay complementary code set of code length N=8 and a cardinality of 16. This set would fulfill the above given conditions of a VT-SACC set. In addition, the first coset also generates T-SC code elements of code length L=8. The second coset comprises the last row

of generator matrix ³ twice and therefore, its AAC does not fulfill the given conditions for T-SC code elements. As for the last coset, its AAC meets the property of T-SC code elements and therefore, it generates cosets of T-SC code elements.

Since a ID VT-SCC code is defined over {^l±¹} > and T-SC code

elements generated from RM(l ,n) are defined over {^lo>ι '} , their

amplitudes {^l0,1} to {^l±1 '} are converted by using following rule: ^→~. _ancj 1—>1^ without losing any generality.

Synthesis of VT-SACC sets based on a system of multi-variable polynomial equations According to the second method, the generation of T-SC code elements is based on a reformulation of the definition of T- SC code elements in terms of a system of multi-variable polynomial equations, for which a systematic solution approach is known from [9] .

It is assumed that all T-SC code elements of code length L should be found. Let

3L l≤i≤ m,(Xι,...,x_L) ( :

be the following set of polynomials.

l≤i≤L m. 31 j^Xk^Xk+> (<-!) L + \≤i≤ (5)

Then x is a T-SC code element if and only if (^XI^>X2^>---^>XL) is a 31 m, = 0; 1 < < — solution of the system 2 over complex numbers. From equation (5) it can be seen that the first part of polynomial set defines only values for polynomial coefficients. The next part expresses the main feature of T-SC code elements, according to which every second shift in an AAC function is zero. One way to solve such polynomial equations is to transform the given equations into a special form called Grobner bases. The following second example summarises results derived with Grδbner bases technique for T-SC code elements of code length =8.

Let ⁵2 be the set ^^±1J, then any code ^{ϊ =} (*ι^«—^>**) i_{s a T}__Sc code element if and only if

6 ~ ~*0"*2 ^**4

As mentioned above, coupling of T-SC code elements into T-SCC pairs can be carried out by either using original Golay defi- nitions [4] or autocorrelation definitions.

The unique feature of providing a variability results directly from the structure of the VT-SACC sets. Since T-SC code elements coupled into T-SCC pairs comprise of VT-SACC sets by adding or removing one or more T-SCC pairs, the cardinality of VT-SACC sets could be varied without losing ideal autocorrelation properties. The number of T-SCC pairs may be

= 2"^+](n -\) ' .

Synthesis of a quadruplet of mutually orthogonal couples of VT-SACC sets

In the following, the synthesis of mutually orthogonal cou- pies of VT-SACC sets creating a quadruplet of VT-SACC sets will be described. Based on this quadruplet of mutually or- thogonal couples of VT-SACC sets, the synthesis of ID VT-SCC codes will subsequently be discussed.

^:X = [ k;^>l- ≤ k ^■- ≤ p-]^j j__{s a} VT-SACC set which is either generated from RM(l ,n) or from the system of multi-variable polynomial ^fχ„ equations described above. Furthermore, ^k denotes a reverse operation (i.e. multiplication with -1) of the sequence ^εΪL ^k . With this, further VT-SAC sets

[(*)mod4]+l-g _ |-[(_£)mod4]+l_ ._{1 1} *'^{~ " J} can be obtained from X^Λ by us- ing the following recursive formula disclosed in [7] :

£=[(.-l)mod4]+l with c_γ [(fi)mod4]+l _γ

The sets and ^Λ are mutually orthogonal and have the properties of T-SCC code elements. The upper limit of "

i .s 2"^+,(»-l) '! , with « = log ^b ₂ ²Z

Formula (6) consists of four independent operations, i.e. reordering, negating and reversing elements in a sequence. It can be shown that using this formula, more than three times will cause replication of former sets. This is depicted in I E

FIG 2. The left upper index ^ε for <* ' >' is therefore de-

fined over an interval of ' .

Each circle in FIG 2 represents a distinct VT-SACC set, and connections between particular circles represent the property of mutual orthogonality. In the given example of FIG 2, cir- ' Y ² Y ⁴ Y cle ^Λ is linked to circles ^Λ and ^Λ , but not linked to 3 \ γ circle ^Λ . This means, that the set ^Λ is mutually orthogo-

nal to sets ^{2 Λ} Y and ^{4 Λ} Y , but not to set ^{3 Λ} Y . This is due to ε r _ _[(ε)mod4]+2 „ Ϊ E (1, L the property of (6), where Λ = — A f_or ^\ ' . As each circle is linked to only two neighboring circles, only couples of VT-SACC sets from the quadruplet of VT-SACC sets are mutually orthogonal.

In the following third example, ^Λ is a VT-SACC set of code length L=4 and maximum cardinality of p=8 obtained by (5) . By applying the formula (6), a quadruplet of mutually orthogonal couples of VT-SACC sets is generated. As can be seen from the first two rows of the sets, the first row of the first set iγ ^Λ is reverted and negated to form the second row of the following set. Subsequently, the second row of the second set is only reverted to form the first row of the third set. Then again, the first row of the third set is reverted and negated to form the second row of the fourth set.

Synthesis of ID VT-SCC codes

In the following, the synthesis of one dimensional VT-SCC codes is discussed. For this purpose, a VT-SACC set 'X = [%;l < k ≤ p] from a quadruplet of mutually orthogonal couples of VT-SACC sets, written in the following matrix rep- resentation, is assumed:

Transforming the above matrix into a vector form leads to:

^ε X wherein each ^k is a T-SC code element of code length L Furthermore, a LxL orthogonal matrix is assumed, which is generated from a set of complementary sets according to [7], written in following form:

This matrix is used for an orthogonalisation of the quadru^¬ plet of mutually orthogonal couples of VT-SACC sets. This leads to a matrix:

wherein Y; for l≤i≤L are sub-matrices of the dimension pxL defined as

for l≤k≤p (11)

is a ID VT-SCC code.

The sub-matrices ' are VT-SACC sets of dimension " ,

written into a pL*L matrix representing a ID VT-SCC code. An examplary ID VT-SCC code of code length L is depicted in Y

FIG 3. Each circle in FIG 3 denotes a VT-SACC set '. Links between individual circles represent the property of ID VT- SCC codes. It can be seen, that each circle or set is linked to any other circle, and that thus, all VT-SACC sets comprising a ID VT-SCC code are mutually orthogonal.

In a fourth example is based on X, X, X and X from the third example, and the following orthogonal matrix

which is the first set from complementary sets created by Theorem 12 from [9] .

Y -Y

With this, ID VT-SCC codes could be derived from (11):

FIG 4 depicts properties of ID VT-SCC codes, wherein circles represent particular sets Y _t and links between them their complete complementary property, i.e. any _αand Y_b , with a ≠ b , are mutually orthogonal.

The cardinality of VT-SACC sets from ID VT-SCC codes depends on the code length and the code order. Assuming that L = 2 is the code length and ^{ι ~} the order of the code, with ^r≤", the variability of the cardinality p of VT-SACC sets comprising a ID VT-SCC code is a function of upper right indexes n and r of the code length and the order, respectively. It can be varied in discrete steps defined by following formula:

This inventive variable cardinality p is not known for already existing sets of sequences with complementary principle, which is restricted to a certain code length and order. But (12) still covers the proposed solution of [6], for which r=n=l . Systems employing such ID VT-SCC code can thus benefit form this variable cardinality, which is linked to variability in allocating resources according to requirements of the system.

Thus, according to the invention, a synthesis of a new class of CC codes is introduced, i.e. the ID variable two-shift complete complementary (ID VT-SCC) codes which are suitable for MC-CDMA systems using offset stacked spreading. These codes are based on Golay complementary pairs over {±l}. The unique property of enabling a high degree of variability lead to remarkable improvements in systems based on MC-CDMA employing offset stacked spreading techniques.

The variability of the complementary code class according to the invention lie in the following properties and ways of the new synthesis.

Variable two-shift autocomplementary code (VT-SACC) sets (flocks) consist of a variable number of two-shift complemen- tary code (T-SCC) pairs of length 1 = 2". A T-SCC pair consists of two two-shift complementary (T-SC) code elements such that the sum of their aperiodic auto-correlation (AAC) functions is an impulse of magnitude 21 and sidelobe level of zero. In addition every second shift in the AAC function of each T-SC code element within a T-SCC pair must equal zero except for zero shift. The AAC function of VT-SACC set is defined as the sum of AAC functions of each element in a set. Since elements are coupled into T-SCC pairs, the AAC function of VT-SACC set is defined as an impulse of magnitude —.21

and sidelobe level of zero, where — is a number of T-SCC 2 pairs with code elements of length L .

If compared to complementary codes known in the art which are based on a fixed number of code elements within a set or flock, by adding or removing T-SCC pairs to/from a VT-SACC set, it is possible to vary the cardinality of VT-SACC set. The possible number of T-SCC pairs is within a range of

(1,—j, with p = 2"^+].(n - \)\ . As can be seen, the upper limit of

VT-SACC set cardinality with T-SC code elements of length

L - 2" greatly exceeds the cardinality of the former complementary sets or flocks, especially for longer code lengths. This variability can be essential to adapt the di- versity of allocated system resources according to system's requirement. Another important advantage of having such cardinality, is a greater processing gain (PG) in comparison to complementary codes known in the art, i.e. 2"⁺¹(2«-l)! times greater compared to CC codes, and 2(π-l)! times greater co - pared to complementary sets. By chosing the number of T-SCC pairs in a VT-SACC set, the sum of autocorrelation peaks of the set can be controlled and thus, a lower bit error rates (BER) achieved in hostile radio channels in comparison to known complementary codes.

As discussed above, using VT-SACC sets as building blocks for a synthesis of a new ID variable two-shift complete complementary (ID VT-SCC) code, one can take an advantage of their unique variable property. ID VT-SCC code consists of k VT- SACC sets, which are mutually orthogonal. The number k of the mutually orthogonal VT-SACC sets comprising ID VT-SCC code can vary within an interval (2,Lj , wherein L is the code length of the T-SC code elements in a VT-SACC set. In case of a MC-CDMA system based on offset stacked spreading tech- niques, the number of mutually orthogonal VT-SACC sets corresponds to the number of supported user equipments UE. Since all VT-SACC sets within ID VT-SCC code are mutually orthogo^¬ nal, the number of supported user equipments UE may be varied in the range of (\,L,} . If compared to CC codes proposed in [6], ID VT-SCC codes employ 41 times more VT-SACC sets (flocks) , which leads to a support of I times more user equipments in MC-CDMA systems based on offset stacked spreading techniques.

In the following, some further examples are given. Firstly, a Two-Shift Complementary Code (T-SCC) pair is regarded. A T- SCC pair consists of two T-SC code elements x = (x_t ,x₂,...,x_L ) and y = (y_\ ,y₂ ,---,y_L) i both of length L = 2" for x_l ,y_l <≡{±l} such that:

∑(xk^Xk+i +ykyk+i) = ^2Lδ i] , for δ[i] = \ [ ' ,° '^"eZ, • [ 0 otherwise

and additionally: j

∑^xk^xk+(L-2i) ^{= ()} and ∑JTC+(L-2i) = ° ^f°r *eZ and i ≠ - k k ²

The complementary property between two T-SC code elements x and y is denoted as x«y. An example are the following elements : x = ( +) y = (- - + -),

wherein {+,-} corresponds to {+1,-1}.

Secondly, a Variable Two-Shift Auto-Complementary Code (VT- SACC) set is regarded. A VT-SACC set is a set X

comprising — T-SCC pairs such that X_j ~ x_j+γ for j,γ e N and

j=l...p .

The AAC function of said VT-SACC set can be defined as

The sum of autocorrelations for the following VT-SACC set with code length of L=4 and cardinality of 8 is shown in FIG 5.

Changing the number of pairs from 4 to 2 within the same VT- SACC set acording to the following set, the processing gain also changes from 32 to 16, as shown in FIG 6.

FIG 5 and 6 demonstrate typical examples of the variability of the VT-SACC set according to the invention. The variable number of T-SC code elements within a VT-SACC set causes changes in the peak value of the AAC functions. For FIG 6, the number of T-SCC pairs within a VT-SACC set with T-SC code

elements of length 4 can be derived from the range ^N ' .

Thirdly, a one Dimensional Variable Two-Shift Complete Complementary (ID VT-SCC) code of order L is regarded. A ID VT- SCC code Y of order L consists of L VT-SACC sets

Y =tø Ϊ2 - YL )

with a property that any two VT-SACC sets Y_aand Y_b for α ≠ b are mutually orthogonal. More precisely:

In other words, the sum of aperiodic cross-correlation (ACC) functions between particular T-SC code elements of both VT- SACC sets is equal zero for any possible shift.

The mutually orthogonal property of a general ID VT-SCC code of order L is depicted in FIG 3. As discussed above, each circle denotes a VT-SACC set Y_t , and links between individual circles represent mutually orthogonal properties between any two VT-SACC sets.

Taking the example of FIG 4, wherein a ID VT-SCC code of or- der L=4 is used, the ACC function between the exemplary sets Yi and Y₂ is zero for all shifts.

In FIG 7, two tables for comparison of the above described codes and sets according to the invention with classes of complementary codes known in the art. Table 1 shows a com^¬ parison in cardinality for different classes of complementary codes, wherein the last row discloses the cardinality of VT- SCC codes according to the invention. As can be seen from the table, the usage of VT-SCC codes enables the support of a much higher number of user equipments when using the same code length. Table 2 shows a comparison in processing gain PG for different classes of complementary codes. Again, is can be clearly seen that using VT-SCC codes substantially enhances the processing gain when using a same code length.

The application of codes/sets according to the invention in above discussed MC-CDMA-systems ensures that, even if signals on one of number of used carriers (which corresponds to the cardinality) are not received, because of ideal autocorrelation functions of the code sets, the received signals can be detected with a low BER due to a prominent peak arising from a high processing gain and substantially reduced side lobes. Usage of codes known in the art would in such a case, lead to an occurrence of multiple side lobes, which would cause even more difficulties for the receiver to detect the received signals .

References

[1]H.H. Chen, J.F. Yeh, N. Suehiro, "A multicarrier CDMA architecture based on orthogonal complementary codes for new generations of wideband wireless communications, ", IEEE Comm. Magazine, no.10, pp.126-135, Oct. 2001.

[2_.M.J.E. Golay, "Multislit spectrometry, " J. Opt. Soc. Amer., vol. 39, pp. 437-444, June 1949.

[3]M.J.E. Golay, "Static multislit spectrometry and its application to the panoramic display of infrared spectra," J. Opt. Soc. Amer., vol. 41, pp. 468-472, July 1951. [4_.M.J.E. Golay, "Complementary sequences," IEEE Trans. Inform. Theory, vol. IT-7, pp.82-87, Apr. 1961.

[5]R. Turyn, "Ambiguity functions of complementary sequences," IEEE Trans. Inform. Theory, vol. IT-9, pp.46-47, Jan. 1963.

[6]N. Suehiro, M. Hatori, "N-shift cross-orthogonal sequences," IEEE Trans. Inform. Theory, vol. IT-34, no.l, pp.143- 146, Jan. 1988.

[7]C.-C. Tseng and C.L. Liu, "Complementary sets of sequences," IEEE Trans. Inform. Theory, vol. IT-18, pp.644-652, Sept. 1972.

[8]J.A. Davis and J. Jedvab, "Peak-to-mean power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes," Elec. Lett., 33, pp. 267-268, 1997. [9]R. Urbanke and A.S. Krishnakumar, "Compact description of Golay sequences and their extensions ", 34th Allerton Conf. on Communication, Control, and Computing, Monticello, USA, Oct. 1996.

Claims

1. Method for transmitting signals in a communications system, wherein code sets comprising a number of two-shift complete complementary code pairs are assigned for communication between stations (NB, UE1, UE2, UE3, UE4) of the communications sys^¬ tem, wherein the assigned code sets are mutually orthogonal and possess ideal autocorrelation functions, characterised in that a code length is defined as L = 2ⁿ, a maximum number of code sets to be assigned is defined as N = 2^r, and -l

wherein r and n are positive integer numbers.

2. Method according to claim 1, wherein said correlation functions are calculated as being the sum of individual correlation functions of each code word used, and wherein the cross correlation function between any two code sets is identical to zero for arbitrary shifts and the auto^¬ correlation function equals zero, except for zero shifts.

3. Method according to claim 1 or 2, wherein the communications system employs MC-CDMA techniques.

4. Station of a communication system, with means for transmitting and/or receiving signals employing code sets according to claim 1.

5. Station according to claim 4, that is realised as a base station (NB) or a user equipment (UE) .