EP1576752A1 - Improvements in or relating to spreading codes for quasisynchronous code division multiple access systems - Google Patents
Improvements in or relating to spreading codes for quasisynchronous code division multiple access systemsInfo
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- EP1576752A1 EP1576752A1 EP03780406A EP03780406A EP1576752A1 EP 1576752 A1 EP1576752 A1 EP 1576752A1 EP 03780406 A EP03780406 A EP 03780406A EP 03780406 A EP03780406 A EP 03780406A EP 1576752 A1 EP1576752 A1 EP 1576752A1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/707—Spread spectrum techniques using direct sequence modulation
- H04B1/7073—Synchronisation aspects
- H04B1/7075—Synchronisation aspects with code phase acquisition
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04J—MULTIPLEX COMMUNICATION
- H04J13/00—Code division multiplex systems
- H04J13/10—Code generation
- H04J13/12—Generation of orthogonal codes
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B2201/00—Indexing scheme relating to details of transmission systems not covered by a single group of H04B3/00 - H04B13/00
- H04B2201/69—Orthogonal indexing scheme relating to spread spectrum techniques in general
- H04B2201/707—Orthogonal indexing scheme relating to spread spectrum techniques in general relating to direct sequence modulation
- H04B2201/7097—Direct sequence modulation interference
- H04B2201/709709—Methods of preventing interference
Definitions
- the present invention relates to improvements in or relating to spreading codes for quasisynchronous code division multiple access systems, and is more particularly concerned with the optimisation of code assignment for such systems.
- This "synchronisation” can be achieved, for example, by providing each user of the system with a global positioning system (GPS) receiver and triggering the user bit epochs by a GPS clock. The relative delays of received signals can then be held to within a few chips.
- GPS global positioning system
- the candidate spreading codes are m -length sequences, the small Kasami set, the Gold codes and the large Kasami set. These terms are well known in the relevant technical field and no further discussion will be given here. These codes correspond to periodic binary sequences.
- a method of generating codes for a multiplicity of cliques in which the properties within the cliques are orthogonal or pseudo orthogonal and the cross-correlation of pairs selected from different cliques exhibit pseudo orthogonal properties within specific time windows.
- 'clique' is meant a fully connected subset of constraints as will be readily understood by a person of ordinary skill in the art.
- the pairs may be selected from different cliques are such that both elements of each pair are in the small Kasami set.
- the pairs selected from different cliques are such that one element of each pair is in the small Kasami set and the other element of each pair is a Gold code.
- the pairs selected from different cliques are such that each element of each pair is generated by a simplex code.
- the small Kasami set has good cross-correlation properties and it is possible to use several different phases of the same sequence for different users.
- the small Kasami set contains an m-length sequence, and is embedded within the large Kasami set which also contains a set of Gold codes. Whilst it may be thought that the small Kasami set is too small to be useful in a system with many users, this assumption ignores the following:-
- the small Kasami set contains an m -length sequence and some of the most important pairs of transmitters can be assigned different phases of this sequence. Should the small Kasami set prove inadequate, some transmitters can be assigned Gold codes, and the correlation of a small Kasami code-Gold code pair is no worse than that of a Gold code pair. Such an assignment is made to a pair where the interference potential is relatively limited.
- ⁇ x y ⁇ is generally required to be small for all ⁇ . In quasisynchronous systems, it may be simply required that, for any user codes x and , then ⁇ x y ⁇ ) is small for 0 ⁇
- the correlation functions can also be defined in the same way when the periods of the sequences are divisors of p .
- the correlation functions can also be defined over windows of length w ⁇ p . In this case the definitions are:
- K_ ( «) ⁇ -., « ⁇ w, u ⁇ Tw,u® T 2 w...,u® T " 2 ⁇ 2 > ⁇ ,
- the small Kasami set is contained within the large Kasami set, which also includes Gold codes.
- These Gold codes can be expressed as:
- the assignment of spreading codes in CDMA systems appears to have received almost no attention. There appear to be two basic reasons for this. The first reason is concerned with the need for code re-use. In many circumstances, particularly with long spreading codes, the number of codes available may be sufficiently large that code assignment is not a critical problem. An example of this is the long (scrambling) codes proposed for cells in UMTS mobile telephone systems. Code re-use is clearly more critical when the small Kasami set is used. The second reason is concerned with the assignment of codes so that constraints on the codes assigned to pairs of transmitters are satisfied. This does not generally arise when codes are used for which the maximum correlation between all pairs of codes is the same. This does not hold for the codes described here.
- Electromagnetic Compatibility Vol. 43, No. 2, pages210 to 218, 2001 can be modified for spreading code assignment. If f(t,) denote the code assigned to a transmitter t, . Pairs of transmitters t,,t 2 have one of the following:
- the frequency domains (or sets of available frequencies) in the frequency assignment algorithms are replaced by codewords which are equally spaced phases (separated by at least 2-- max +1 cyclic shifts) of the various sequences.
- the cost function is simply a (weighted) sum of the number of constraint violations. Although it is not possible to give a theoretical estimate of the reduction of the ' multiple access interference in the system without making many assumptions, the assignment of the best code pairs to the most critical interfering pairs should ensure that the overall reduction is substantial.
- X. D. Lin and K. H. Chang have proposed a construction for spreading sequences for QS-CDMA ("Optimal PN sequence design for quasisynchronous CDMA communication systems", IEEE Trans.
- ⁇ xA ⁇ > where ⁇ m (d) is the cross-correlation function of certain seed sequences u, v .
- ⁇ x y -1 for the chosen pair of vectors X,Y , but it is easy to see that if m > 3 , this cannot be the case for every pair.
- ⁇ be a primitive element of the Galois field, GF(2"), and
- Tr n '](x) _" l "' ⁇ x ⁇ 2" " be the trace function from GF(2") to GE(2 m ), then the properties of the trace function are as described in MacWilliams and Sloane referenced above.
- the sequence X e of length 2"-l for a balanced seed vector can be constructed from a (2 m -l)xT array with columns labelled 0, 1, ..., T- ⁇ as follows:- If s, - ⁇ , then the tth column is a column of zeros. If -., ⁇ ⁇ , then the / th column is the transpose of (e Sj , e ⁇ +1 , ..., c , +2 *»_ 2mod(2 *. ) ) a d thus ' s a cyclic shift of e .
- ⁇ e ( e s 0 s e S ⁇ ⁇ > — ⁇ > e ⁇ ⁇ . t • > e ⁇ ⁇ > • •• ⁇ > e !2(7 ._ l) > e *--. ⁇ > •• • ⁇ > e ⁇ i ,
- ⁇ ef (0) -1 for any pair of seed vectors. It is also required that all the vectors must be cyclically distinct.
- a simplex code is the dual of a Hamming code as discussed by F. J.
- MacWilliams and N. J. A. Sloane in "The theory of error-correcting codes", Amsterdam, Elsevier 1996, 9 th Edition. It is a linear code with a generator matrix with columns formed from the set of all distinct, non-zero (0, 1) vectors of length m in some order. The code has parameters (2 m -1, m, 2 (m_1) ) . Thus a simplex code is an equidistant code and all 2"' -l non-zero codewords have weight 2"' "1 . It follows that if these 2"' -l non-zero codewords are used as seed vectors, then ⁇ ef (0) -l for any pair.
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- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Mobile Radio Communication Systems (AREA)
Abstract
Described herein is a method of generating spreading codes which ensures that the cross-correlation is -1 for all pairs of sequences within the relevant time delays.
Description
IMPROVEMENTS IN OR RELATING TO SPREADING CODES FOR QUASISYNCHRONOUS CODE DIVISION MULTIPLE ACCESS SYSTEMS
The present invention relates to improvements in or relating to spreading codes for quasisynchronous code division multiple access systems, and is more particularly concerned with the optimisation of code assignment for such systems.
It is well known to use asynchronous code division multiple access (CDMA) systems in communications systems and to make use of spreading codes which have correlation properties close to the best possible achievable properties. However, the demand for high traffic levels in modern communications systems imposes ever more stringent requirements on such systems, for example, the minimisation of multi-user interference. At the same time, the so-called quasisynchronous CDMA (QS-CDMA) systems are becoming more practical. In QS-CDMA systems, the chips of the information symbols of the users should be nearly synchronised, normally to within a small number of chips, referred to as the synchronisation uncertainty rmax . This "synchronisation" can be achieved, for example, by providing each user of the system with a global positioning system (GPS) receiver and triggering the user bit epochs by a GPS clock. The relative delays of received signals can then be held to within a few chips.
Among the candidate spreading codes are m -length sequences, the small Kasami set, the Gold codes and the large Kasami set. These terms are well known in the relevant technical field and no further discussion will be given here. These codes correspond to periodic binary sequences.
When the CDMA system is completely asynchronous, a separate, cyclically distinct periodic sequence is assigned to each user and it is possible to assign many users to different phases of the same sequence provided that the phases are separated by at least 2rmax +l cyclic shifts and a suitable synchronisation mechanism is provided. If T is the left cyclic shift operator on code vectors, u is a periodic sequence of period p , then there are exactly p
sequences (or binary code vectors) u,T(u),T2 (u),....,Tp~] (u) . These sequences are cyclic shifts of u and are known as the different phases of u . However, large sets of m -length sequences with good correlation properties do no exist.
Moreover, as the spectrum is a fixed asset which is continuously subject to requests which increases its packing density, it is necessary to find a solution which overcomes these problems. One solution is to utilise higher frequencies but this is not practical as constraints are imposed by the propagation of the higher frequencies. Furthermore, there is a requirement for compatibility to be maintained using existing carriers in some systems. It is therefore an object of the present invention to provide an improved quasisynchronous code division multiple access system which overcomes the problems mentioned above.
In accordance with one aspect of the present invention, there is provided a method of generating codes for a multiplicity of cliques in which the properties within the cliques are orthogonal or pseudo orthogonal and the cross-correlation of pairs selected from different cliques exhibit pseudo orthogonal properties within specific time windows.
By the term 'clique' is meant a fully connected subset of constraints as will be readily understood by a person of ordinary skill in the art. The pairs may be selected from different cliques are such that both elements of each pair are in the small Kasami set.
Alternatively, the pairs selected from different cliques are such that one element of each pair is in the small Kasami set and the other element of each pair is a Gold code. As a further alternative, the pairs selected from different cliques are such that each element of each pair is generated by a simplex code.
In one embodiment of the present invention, it has been noted that the small Kasami set has good cross-correlation properties and it is possible to use several different phases of the same sequence for different users. Moreover, the small Kasami set contains an m-length sequence, and is embedded within
the large Kasami set which also contains a set of Gold codes. Whilst it may be thought that the small Kasami set is too small to be useful in a system with many users, this assumption ignores the following:-
1. The possibility of re-using codes for transmitters with no potential for interference.
2. The possibility of assigning as many as phases of the
same sequence to different users.
3. The possibility of assigning the small Kasami set so that the best correlation properties belong to the more critically important pairs of transmitters with respect to multiple access interference. Indeed, the small Kasami set contains an m -length sequence and some of the most important pairs of transmitters can be assigned different phases of this sequence. Should the small Kasami set prove inadequate, some transmitters can be assigned Gold codes, and the correlation of a small Kasami code-Gold code pair is no worse than that of a Gold code pair. Such an assignment is made to a pair where the interference potential is relatively limited.
It is therefore proposed that careful assignment of code pairs in a quasisynchronous code division multiple access (QS-CDMA) system can be utilised to maximise both re-use of the code pairs and take advantage of the benefits of the small Kasami set whilst, at the same time, ensuring that the number of available user codes is adequate.
An essential features for the codes used in accordance with the present invention is that the codes must have certain correlation properties. In this way, given a (0,1) binary vector, it is usual in correlation calculations to consider it as a (+1 ,-1) vector, using the mapping 0- (+1), 1-»(-1). Let χ = {x0,xλ,...,xpy, y = {y0,y] ,...,yp_;} be vectors with entries +1 ,-1 , then the autocorrelation function on x is defined by:
Clearly if τ ≡ Omodj. then θx(τ) = p . If τ ≠ Omoάp then θx(τ) is generally required to be small. In quasisynchronous systems, it may be simply required that, for any user code x , then θx(τ) is small for 0 < Id < rmax .
In a similar way, the cross-correlation function on x, y is defined to be
where θx y{τ) is generally required to be small for all τ . In quasisynchronous systems, it may be simply required that, for any user codes x and , then θx y{τ) is small for 0 < |r| < rmax .
The correlation functions can also be defined in the same way when the periods of the sequences are divisors of p . The correlation functions can also be defined over windows of length w < p . In this case the definitions are:
and w-l θXty(τ,k)= ∑xl+ky„k+T modp
;=0
If we define c, = max;.≠ , max0≤r≤p_I|'-?Λ>..(r)|, c2 = maxx
and cmax = max(c,,c2). Then, according to the disclosure by L. R. Welch in "Lower bounds on the maximum cross correlation of signals", IEEE Trans. Inform. Theory, Vol. lT-20, No. 3, pages 397 to 399, May 1974, asymptotically cmax > Jp (and indeed the result is accurate even when the number of sequences is fairly small). This is subsequently referred to as the 'Welch bound'.
In a similar way, over a window of length w , the lower bound is Vw .
Ideally, very small values of iJL are required. The problem may be particularly p difficult for small p or small w . It should be noted that these bounds do not apply in the quasisynchronous case. Codes in the small Kasami set provide the requisite correlation properties. For the small Kasami set, let m be an even integer and let u denote an m -sequence of period N = 2"' -l , generated by a primitive binary polynomial h(x) of degree m . If we define s(m) =2^ +1 and consider the sequence w obtained by taking every s(m)'ih bit of u . The sequence w is of period s(m)=2^+ι and is generated by the polynomial h'(χ) of degree ϋ whose
2 roots are the s(m)'ih powers of the roots of h(χ) . This is discussed by D. V. Sarwate and M. B. Pursley in "Crosscorrelation properties of pseudorandom sequences", Proc. IEEE, Vol. 68, No. 5, pages 593 to 619, 1980.
Now consider the sequences generated by the polynomial h(x)h'(x) of degree ---!- . Any sequence of period 2m-ι generated is a sequence of the small
2
Kasami set
K_ («) = {-.,«© w, u θ Tw,u® T2w...,u® T "2~2 >},
where θ denotes mod2 addition of the corresponding vectors.
Further, for the code vectors corresponding to the phases of these sequences, CmΑ =s(m)=2% +\- Thus, in the case of m being even, a set of 2m'2 sequences which meet the 'Welch bound' asymptotically is known. This proposal offers a method to use a small set in a system with a large number of users.
The small Kasami set is contained within the large Kasami set, which also includes Gold codes. These Gold codes can be expressed as:
G(u, V) = {«, v, u θ v, u ® Tv, u θ T7v..., u θ T "2 ~2 v} ,
Cmax = m) where w, are m -sequences generated by a preferred pair of primitive polynomials as described in the disclosure by D. V. Sarwate and M. B. Pursley
referenced above. In this large Kasami set, cmax •= t(m) = 1 + 2 IL— 2 J I. cmax = s(m) only holds if the code vectors are chosen as phases of sequences from the small Kasami set. Similarly, the small Kasami set contains the m -sequence u , and if the code vectors are chosen to be phases of this sequence, then cmax = 1.
The assignment of spreading codes in CDMA systems appears to have received almost no attention. There appear to be two basic reasons for this. The first reason is concerned with the need for code re-use. In many circumstances, particularly with long spreading codes, the number of codes available may be sufficiently large that code assignment is not a critical problem. An example of this is the long (scrambling) codes proposed for cells in UMTS mobile telephone systems. Code re-use is clearly more critical when the small Kasami set is used. The second reason is concerned with the assignment of codes so that constraints on the codes assigned to pairs of transmitters are satisfied. This does not generally arise when codes are used for which the maximum correlation between all pairs of codes is the same. This does not hold for the codes described here.
The algorithms described by R. K. Taplin, D. H. Smith and S. Hurley in "Frequency assignment with complex cosite constraints", IEEE Trans. On
Electromagnetic Compatibility, Vol. 43, No. 2, pages210 to 218, 2001 can be modified for spreading code assignment. If f(t,) denote the code assigned to a transmitter t, . Pairs of transmitters t,,t2 have one of the following:
1. No constraint, in which case they can be assigned the same code;
2. A constraint \θf{h)J^(τ)\ ≤ \ (θ < r < rmax), in which case both t, and t2 must be assigned codes which are different phases (separated by at least 2rmax +1 cyclic shifts) of the m -length sequence within the small Kasami set;
3. A constraint
≤ s(m) (° ≤ r ≤ rma . in which case both /, and t, must be assigned codes which are different phases (separated by at least 2rma +1 cyclic shifts) of sequences within the small Kasami set;
4. A constraint |ø/(rι)ι (,2)(r)| < t(m) (0 < τ < rmax ) , in which case both t, and t2 must be assigned codes which are different phases (separated by at least 2rmax + 1 cyclic shifts) of sequences within the large Kasami set.
One way to derive these constraints might be to carry out signal-to- interference (SIR) calculations for the unspread signals in the same way as is done for frequency division multiple access (FDMA) systems. Three different thresholds γχ ≥ γ_ ≥ γ3 could be set for a "satisfactory" SIR. Then at a worst case receiver the appropriate constraint is set as follows:
1. If SIR ≥ γ no constraint is necessary;
2. If γλ > SIR ≥ γ_ constraint 4) above is used;
3. If γ_ > SIR ≥ γ3 constraint 3) above is used;
4. If χ3 > SIR constraint 2) above is used.
Care must be taken in the choice of the thresholds to ensure that there are not too many of the stronger constraints for the number of codes available. The frequency domains (or sets of available frequencies) in the frequency assignment algorithms are replaced by codewords which are equally spaced phases (separated by at least 2--max +1 cyclic shifts) of the various sequences.
The cost function is simply a (weighted) sum of the number of constraint violations. Although it is not possible to give a theoretical estimate of the reduction of the'multiple access interference in the system without making many assumptions, the assignment of the best code pairs to the most critical interfering pairs should ensure that the overall reduction is substantial.
In another embodiment of the present invention, a construction for spreading sequences based on simplex codes is proposed in which Θx r(0) = -1 is guaranteed. X. D. Lin and K. H. Chang have proposed a construction for spreading sequences for QS-CDMA ("Optimal PN sequence design for quasisynchronous CDMA communication systems", IEEE Trans.
Communications, Vol. 45, No. 2, pages 221 to 226, February 1997) in which the cross-correlation has a construction with Θ^ y(r) = -1 for all values in the range except possibly τ = 0.
Lin and Chang referenced above modified the construction of the GMW- sequences proposed by R. A. Scholtz and L. R. Welch in "GMW sequences",
IEEE Trans. Information Theory, Vol. IT-30, No.3, pages 549 to 553, May 1984
to create a family of cyclically distinct sequences of length N = 2" - 1
with
~ xAτ>
where θm (d) is the cross-correlation function of certain seed sequences u, v . In Lin and Chang's examples Θx y = -1 for the chosen pair of vectors X,Y , but it is easy to see that if m > 3 , this cannot be the case for every pair.
Let cmaλ -= max- \ ΘXJ (τ) \ where 0 <) r |< T = 2rmax +1 . Then as noted by
X. H. Tang, P. Z. Fang and S. Matsufuji in "Lower bounds on correlation of spreading sequence set with low or zero correlation zone", Electronic Letters, Vol. 36, No. 6, pages 210 to 218, March 2000, a modified 'Welch bound' for
This can be found by applying the inner product theorem discussed by Welch in "Lower bounds on the maximum cross correlation of signals" referenced above, to the set of vectors
--W-
SτaΛ(C, } (mapped to vectors with elements from {-1,+1} and adjusted for norm N ).
Thus, for the parameters considered by Lin and Chang, cma will significantly exceed 1 if u exceeds 2"'-l where m>3. By restricting the choice of seed sequences in Lin and Chang's construction to a set of 2m-l cyclically distinct seed sequences with ΘUV(Q) = -1 to ensure that exactly 2"' -1 cyclically distinct sequences are obtained with Θxγ(τ) = -l for
0<|r|<r = 2rmax+l and ΘΛ, (r) = -l for 0<|r |<r = 2rraax +1.
Thus for sequences of odd length, the best cross-correlation possible is achieved, and according to inequality (1) above, the number of sequences is maximised for the given value of τms , and the value of rmax is maximised for the given number of sequences.
Let α be a primitive element of the Galois field, GF(2"), and
Trn'](x) = _"l"'~xχ2"" be the trace function from GF(2") to GE(2m), then the properties of the trace function are as described in MacWilliams and Sloane referenced above. The trace function is used to define a shift sequence S *= (s0, -?-,..., *-•_„_,) .
Specifically, for k = 0, 1, 2, ..., 2" - , if sk is defined by
s /e{0,l,...,2m -2
The sequence Xe of length 2"-l for a balanced seed vector, that is, with 2"'"1 1's and e = (e0,e,,..., e_m__) , can be constructed from a (2m-l)xT array with columns labelled 0, 1, ..., T-\ as follows:-
If s, - ∞ , then the tth column is a column of zeros. If -., ≠ ∞ , then the / th column is the transpose of (eSj, eΛ +1, ..., c, +2*»_2mod(2*. )) a d thus 's a cyclic shift of e . The array is shown below with the convention e∞ = 0 :-
e_ e. ... e.
<25„+2'"-2modC2'"-l) s,+2",-2mod(2'"-l) ""
Then Xe is obtained by scanning the rows of the array, starting in the top left hand corner to provide
χ e = (es0 s e Sχ ■> —■> eχτ.t •> e τ ■> • •• ■> e !2(7._l) > e*--. ■> •• •■> eχi,
In a similar way, for a second balanced seed vector / , the sequence below can be constructed :-
If the seed vectors are restricted to be codewords of a simplex code, then Θ . .. (0) = -l for any pair Xe, Xf of sequences. Clearly, it is necessary for
Θef (0) = -1 for any pair of seed vectors. It is also required that all the vectors must be cyclically distinct. A simplex code is the dual of a Hamming code as discussed by F. J.
MacWilliams and N. J. A. Sloane in "The theory of error-correcting codes", Amsterdam, Elsevier 1996, 9th Edition. It is a linear code with a generator matrix with columns formed from the set of all distinct, non-zero (0, 1) vectors of length m in some order. The code has parameters (2m -1, m, 2(m_1)) . Thus a simplex code is an equidistant code and all 2"' -l non-zero codewords have weight 2"'"1 . It follows that if these 2"' -l non-zero codewords are used as seed vectors, then θef (0) = -l for any pair. However, there is no guarantee that the code vectors are cyclically distinct. In fact, m -length sequences are simplex codes with a single cycle of non-zero codewords.
Cyclically distinct seed sequences e are necessary if the sequences Xe are to be cyclically distinct. Clearly, if Sγ(e) = e , then SγT(Xe) = Xe . On the other hand, if SrT(Xe) = Xe, it will follow that Sr(e) = e by considering the positions congruent to OmodE . It is not possible that ST(Xe) = Xe with τ ≠ γT as the cross-correlation of the two sequences is -1.
Given a simplex code, it is possible to find an equivalent simplex code that has the maximum number of cyclically distinct codewords by using a hillclimbing algorithm or a metaheuristic which finds the equivalent simplex code in a very small number of iterations. An equivalent simplex code is a code with the columns of the generator matrix permuted. If m = 3 , there are at most 5 balanced vectors of length 7. Thus the algorithm cannot find 7 cyclically distinct codewords in an equivalent simplex code, but does find 5 very quickly. In the cases where ..- = 4- 5, 6, 7, 8 , the maximum number 2m -l of cyclically distinct code vectors in an equivalent code are found in a very small number of iterations.
The periodic odd correlation properties of a QS-CDMA system are as important as the even correlation properties as discussed by D. V. Sarwate and M. B. Pursley in "Crosscorrelation properties of pseudorandom sequences", Proc IEEE, Vol. 68, No.5, pages 593 to 619, May 1980. Lin and Chang point out that the absolute value of the periodic odd correlation function | Θ( (τ) \ is bounded according to the inequality:
| Θ . (r) | < | ΘAT (r) | +2 M
The same result holds for the more restricted class of sequences described above and shows that the odd correlation is small for small τ . However, the bound on the odd correlation is correspondingly smaller when r = 0.
Although the invention has been described with reference to binary vectors, it will readily be appreciated that the invention can also be applied to polyphase or multi-dimensional vectors.
Moreover, although the invention has been described with reference to QS-CDMA systems, it has wider applicability.
Claims
1. A method of generating codes for a multiplicity of cliques in which the properties within the cliques are orthogonal or pseudo orthogonal and the cross-correlation of pairs selected from different cliques exhibit pseudo orthogonal properties within specific time windows.
2. A method according to claim 1 , wherein the pairs selected from different cliques are such that both elements of each pair are in the small Kasami set.
3. A method according to claim 1 , wherein the pairs selected from different cliques are such that one element of each pair is in the small Kasami set and the other element of each pair is a Gold code.
4. A method according to claim 1 , wherein the pairs selected from different cliques are such that each element of each pair is generated by a simplex code.
5. A method of generating codes for a multiplicity of cliques substantially as hereinbefore described.
Applications Claiming Priority (5)
Application Number | Priority Date | Filing Date | Title |
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GBGB0230260.2A GB0230260D0 (en) | 2002-12-23 | 2002-12-23 | Improvements in or relating to spreading codes for quasisynchronous code division multiple access systems |
GB0230260 | 2002-12-23 | ||
GB0303141A GB0303141D0 (en) | 2003-02-10 | 2003-02-10 | Improvements in or relating to spreading codes for quasisynchronous code division multiple access systems |
GB0303141 | 2003-02-10 | ||
PCT/GB2003/005512 WO2004057784A1 (en) | 2002-12-23 | 2003-12-18 | Improvements in or relating to spreading codes for quasisynchronous code division multiple access systems |
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US6091760A (en) * | 1998-06-29 | 2000-07-18 | L-3 Communications Corporation | Non-recursively generated orthogonal PN codes for variable rate CDMA |
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2003
- 2003-12-18 EP EP03780406A patent/EP1576752A1/en not_active Withdrawn
- 2003-12-18 WO PCT/GB2003/005512 patent/WO2004057784A1/en not_active Application Discontinuation
- 2003-12-18 AU AU2003288567A patent/AU2003288567A1/en not_active Abandoned
Non-Patent Citations (1)
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WO2004057784A1 (en) | 2004-07-08 |
AU2003288567A1 (en) | 2004-07-14 |
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