WO2003081822A1

WO2003081822A1 - A coding method to create mismatched spread spectrum sequence with zero correlation window

Info

Publication number: WO2003081822A1
Application number: PCT/CN2002/000194
Authority: WO
Inventors: Shaojun Xu; Yan Gao; Daoben Li
Original assignee: Linkair Communications,Inc.
Priority date: 2002-03-22
Filing date: 2002-03-22
Publication date: 2003-10-02
Also published as: AU2002249062A1; CN1613220A

Abstract

The present invention provide a coding method to create general spread spectrum sequence with zero correlation window, wherein general spread spectrum sequence with zero correlation window include binary codes at least in complex field. The present invention is to solve the problems remains in prior art, including the fatal near-far effects in traditional CDMA radio communications and leads to many new codes which have a much wider range of available lengths and window widths of zero correlations. All codes constructed by the method are close to the theoretical bound.

Description

A Coding Method to

Create Mismatched Spread Spectrum Sequence

With Zero Correlation Window

Field of the invention The present invention relates to the field of telecommunications, and more particularly to a coding method to create mismatched spread spectrum sequence with zero correlation window.

Background of the invention

The growing popularity of personal communication services coupled with the scarcity of radio bandwidth resources has resulted in the ever-increasing demand for higher spectral efficiency in wireless communications. Traditional multiple access control (MAC) schemes such as FDMA, TDMA already can't satisfy such demand because of low spectral efficiency. More and more people think that CDMA will become the main MAC scheme in the next generation wireless communication because of its high spectral efficiency. The difference between CDMA and other MAC schemes is: CDMA capacity is a soft- capacity and it lies in the interference level, i.e. any technique to reduce interference can directly increase the CDMA system capacity. Otherwise, system capacity of other MAC schemes is a hard-capacity and it is decided before design.

Now that CDMA system capacity lies in the system interference level, how to reduce the system interference is the most important to increase the CDMA system capacity. There are many techniques to reduce interference in CDMA system such as Multiple User Detection (MUD), Adaptive Antenna Array, Power Control and so on. In fact the interference a user receives from other users, and the interference between two users stem from imperfect correlation between two spread spectrum codes specific to two users. So it is necessary to find a code group with good Auto-Correlation Function (ACF) and Cross-Correlation Function (CCF) for CDMA system.

To avoid the interference in CDMA system, we hope to find a code group with ideal ACF and ideal CCF. Unfortunately ACF and CCF of a code group are bounded by Welch bound. According to Welch bound, ACF and CCF can not be decreased simultaneously. So it is impossible to find a code group with ideal ACF and ideal CCF.

But in many applications, it is not necessary to construct such code group with ideal ACF and ideal CCF in all time shifts. And it is enough for a synchronized CDMA system to ensure the ideal ACF and ideal CCF within maximum time spread of the channel. For example, if the maximum time spread of the channel is Δ , it is enough that ACF and CCF are ideal within [- Δ , Δ ]. In 1997, Prof. Li Daoben found an approach to construct a spread spectrum multiple access code with zero correlation window (ZCW). And his work has been granted a patent (patent application number is PCT/CN00/00028). Given the code length, the size of LS code set is much greater than before, and it has great worth in CDMA applications.

Summary of the invention

The objective of the present invention is to provide a coding method to create mismatched spread spectrum sequence with zero correlation window, the new coding method to create a series of mismatched spread spectrum multiple access codes that have the "Zero Correlation Window" in their auto-correlation functions and cross-correlation functions. Due to the creation of the "zero correlation window", the fatal near- far effects in traditional CDMA radio communications is avoided. The space of mismatched codes with ZCW is much larger than that of matched codes. Matched code space is only one of its subset, which provides more flexibility to choose MAC sequence for us. A new mismatched spread spectrum sequence with ZCW is proposed in the present invention. In principle matched filtering operation is the optimum operation. In CDMA system, if one sequence (MA code) is employed to spread, then the same sequence should be employed to dispread, such sequences are called the matched sequences. When the dispread sequence is different from the spread one, it is called a mismatched one. The expansion method to create such mismatched ZCW sequences is also introduced in the invention.

The mismatched ZCW sequences greatly enrich the ZCW sequence space. Matched

ZCW sequences such as LS code are only one of its subsets, which provides us more flexibility to choose MAC sequences for us.

The present invention provide a coding method to create mismatched spread spectrum sequence with zero correlation window, wherein mismatched spread spectrum sequence with zero correlation window include:

Mismatched codes have the "Zero Correlation Window" in their auto-correlation functions and cross-correlation functions; the space of mismatched codes with ZCW is much larger than that of matched codes, matched code space is only one of its subset; wherein said the mismatched codes with zero correlation window can be constructed from binary field at least.

Wherein said the mismatched codes with zero correlation window can be constructed from expanding the said code length and family size of basically complementary orthogonal code group.

Wherein said the mismatched codes with zero correlation window can be constructed from ternary field; more codes and codes with higher efficiency can be obtained. we can also construct the mismatched codes with zero correlation window from complex field; more codes and codes with higher efficiency can be obtained, wherein said the method includes the following steps:

Selecting a basically complementary orthogonal mismatched code (Cl, SI) and (Cl ^' ,

SI ' ) with code length N, where the aperiodic auto-correlation functions of code C and code S oppose each other but also complement each other except at the origin. (Cl, SI) is the local code which is applied at transmitter, and (Cl ' , SI ' ) is the mismatched code which is applied at receiver; selecting another complementary orthogonal mismatched code (C2, S2) and(C2 ^' ,S2 ' ) which is uncorrelated with the code (Cl, SI) and (Cl ^' , SI ^' ), i.e. the mismatched aperiodic cross-correlation functions of code C and code S between two codes sum to zero at all ime shifts;

It can be proved that code (Cl,Sl) , (C1',S1') and code

(Sϊ^* -Cl^* ) are uncorrelated with each other, where ' ^~ ' denotes reversing operation, '*' denotes the complex conjugate operation; selecting any orthogonal matrix, H_MxM which has M rows and M columns. The new codes can be constructed as following: the local code group:

(H_MxM ® Cl, H_MxM ® S\) [H_MXM ® C2, H_MxM ® S2) the mismatched code group:

H_MxM ® CΪ, H_MxM ® SΪ H_MxM ® C2', H_MxM ® S2' where ' ® ' denotes the Kronecker product;

The auto-correlation functions or cross-correlation functions of the expanded code group will form a zero correlation window around the origin with the size of window equal or greater than 2N-1 (double side). wherein said expanding the said code length and family size of basically uncorrelated complementary orthogonal code group include:

The expansion method is superior to the binary generation tree; if code length of the original uncorrelated complementary orthogonal code group is N, the binary generation tree only generates the expanded code groups with code length 2ⁿN, wherein n is nonnegative integer;

However orthogonal matrix expansion can generate code groups with code length MN, wherein M is any positive integer; because there exist original uncorrelated complementary orthogonal code pair with any positive integer N, we can construct such mismatched complementary codes with zero correlation windows (2M, MN, 2N-1), wherein M, N are any positive integer and 2M denotes family of access codes, MN denotes code length of access codes and 2N-1 denotes the window width of zero correlation;

More mismatched ZCW codes can be obtained if equivalent transformations are applied to the said codes. wherein said the method includes the following steps:

( C\ \ ( CV SIN ^ \ C2 v2 ' C2' 92' ^{s a} P^a^^r °^ ^uncorrelated mismatched complementary

orthogonal code group with code length Ν, and the binary orthogonal matrix H + +

2x2 + - is adopted; wherein "+" denotes +1 and "-" denotes -1; the expanded code group is:

H ^■ 2_Mx2 ® CV H 2x2 ®SV) H_2x2 ® C2' H_M 2x2 ® S2' J

when Ν=4, a pair of uncorrelated mismatched complementary orthogonal code group is: local code group: l SI '+ + + +, - + + +^Λ C2 S2 + + + -, - + + - mismatched code group:

according to the said expansion method, the expanded local group:

the expanded mismatched group is: ^fcv cv Sr Sr '+ -- + + - - +, ^■ + + + - + + + cv -cv Sr -Sr + - - + - + + -, ^■ + + + +

C2' C2' S2' S2' + + + - + + + -, -

C2' -C2' S2' -S2'_j + + + +, - + + + + , the width of zero correlation windows will be 7; the equivalent transformation can be applied to generate basically mismatched orthogonal complementary code group.

The aim of present invention is to solve the problems remains in prior art.including the the fatal near-far effects in traditional CDMA radio communications. The mismatched ZCW sequences greatly enrich the ZCW sequence space. Matched ZCW sequences such as LS code are only one of its subset, which provides us more flexibility to choose MAC sequence for us..

Detail of the invention

The present invention will be detailedly described with reference to the preferred embodiments and the drawings.

The present invention is to provide a new coding method to create a series of mismatched spread spectrum multiple access codes that have the "Zero Correlation Window" in their auto-correlation functions and cross-correlation functions. The mismatched codes have the following properties: i They have the "Zero Correlation Window" in their auto-correlation functions and cross-correlation functions. ii The space of mismatched codes with ZCW is much larger than that of matched codes.

Matched code space is only one of its subset. iii In binary field, we can construct the matched codes with ZCW (-N, N) only when N is equal to some given values such as 0, 1, 3, 7 etc. But the mismatched codes can be found when N is equal to some other values, which greatly enriches the code space with ZCW property. Thus we can select proper N according to the maximum time dispersion of the channel. iv we can also construct the mismatched codes with zero correlation window from ternary field or complex field. More codes and codes with higher efficiency can be obtained. Given a mismatched complementary orthogonal code with code length N=5: Cl = (+ - + - +), Sl = (- + ), Cl' = ( ), Sl' = (- + ), wherein '+' denotes '1 ' and '-' denotes '-1'. It is true that the mismatched aperiodic auto-correlation of code (Cl,Sl) and (C1',S1') is equal to zero except at the origin, i.e. code C and code S are mismatched complementary orthogonal. Now define:

The mismatched auto-correlation function of code C is: R_cl(τ) = ∑ c, (*^')c'^*ι (t + r), ι^'=0 wherein r is the time shift.

The mismatched auto-correlation function of code S is: R., (r) = ∑ s_λ (i)s''ι (i + τ),

wherein τ is the time shift.

And the mismatched auto-correlation function of code 1 is: R, (r) = R,, (r)+ R., (τ) Table 1 is for the mismatched auto-correlation values of code 1.

Table 1: Mismatched Auto-Correlation of Code 1

According to the forementioned construction method for uncorrelated mismatched complementary orthogonal code from a known code, we can obtain another uncorrelated mismatched complementary orthogonal code.

(C2,S2)= (S1'\-C1'^*)= ( +- + + + + +)

( ₊-, - + - + -)

We define:

The mismatched cross-correlation function between code 1 and code 2 are:

R , (r) = ^N'∑ c_x (ι (i + τ), R . (r) = "∑ ' 5, (i " ₂ (i + r)

^C1 ^C2 ,=0 ^*SI ^J- (=0

R_n(τ) = R_CιC2 (τ)₊ R_SιS. (τ)

Table 2 is for the mismatched auto-correlation values of code 2.

Table 3 is for the mismatched cross-correlation values between code 1 and code 2. Table 2: Mismatched Auto-Correlation of Code 2.

Table 3: Mismatched Cross-Correlation between Code 1 and Code 2.

There is only one basic form for the mismatched complementary orthogonal code with family size of access code 2 and each code length 5. Other forms can be derived from reordering of Cl and C2, SI and S2, swapping C and S, rotation, order reverse, and alternative negation etc. It should be noted that only the operation of code C with code C and code S with code S should take place when making the operation of correlation or matching filtering. Code C and code S will not encounter on operation.

Now we define the efficiency of the mismatched complementary orthogonal code:

Let ξ, = (C,.,S, ), ξ = (C;,S;), then the efficiency of code i is:

^{ηi =} \(_ξi,_ξi)\ - \(_ξ;,_ξ;)\

The efficiency of the code group above is: η_x - r\ = 16%

Given any orthogonal matrix, the expanded code group with longer length can be derived from the original mismatched complementary orthogonal code. Suppose the orthogonal is H_2x2 = + + + - , then we can achieve new code group with access number 4 and

code length 10.

'Cl Cl SI SI + - + - + + - + -+, - + + Cl - l SI - SI + - + - + - + - + -, - + + - + + +

C2 C2 S2 S2 + + -, + + + + + + + + -1- +

C2 - C2 S2 - S2 + - + + + -+, + + + + + • - + + - + + +

Table 4 is for the mismatched correlation of the new expanded code group.

The size of zero correlation window of new expanded code group is equal to 9. And the efficiency of new code group is: ι = 7₂ = ?7₃ = ^ = 16%

We can conclude that the expansion method doesn't change the efficiency. And the width of zero correlation window of the new expanded code group is 2N-1=9.

If we extend binary mismatched complementary orthogonal codes to ternary mismatched complementary orthogonal codes, higher efficiency will be achieved. The following example is given:

The original mismatched complementary orthogonal code group is:

Cl SI + +0 + -, + +0 - + cv Sr + +0 + -, + +0 - +^' C2 S2 + -0 + +, + -0 - - C2' S2' + -0 + +, +-0 - -

The expansion matrix is:

^2x2 = I ₊ _ The expanded code group is:

'Cl Cl SI (++0 + - + +O+- ++0--r + -rO-+^Λ

Cl - l SI + +0 + 0-+, ++0- + --0 + - C2 C2 S2 + -0 + + + -0 + +, +-0-- + -0-- C2 -C2 S2

■+-0 + + -+0--, +-0 +0 + +

'cr cr Sr Sr ( + +0 + - + +0 + -, + +0- + + +0-+ cr -cv Sr -Sr + +0 + 0-+, ++0- + --0 + -

C2' Cϊ S2' S2' + -0 + + + -0 + +, +-0-- + -0 —

C2' -Cl' S2' -ST + -0 + + - +0 - -, + -0 +0 + +

Table 5 is for mismatched correlation of the original code group. Table 6 is for mismatched correlation of the expanded code group.

The efficiency of the original code group is: η_t = η₂ = 100%

The efficiency of the expanded code group is: η_i =η₁=η₃=η = 100% In fact it is also an example of matched complementary orthogonal codes with zero correlation window. The width of zero correlation window of the new expanded code group is 2N-1=9.

If we extend binary or ternary code group to complex code group, we can obtain more mismatched code groups with zero correlation window. Table 7 is for the original mismatched complementary orthogonal code groups with various code lengths, and table 8 is for the orthogonal expansion matrices of various dimensions.

Table 7: Original Mismatched Complementary Orthogonal Code Groups

Table 8: Orthogonal Expansion Matrices H MxM

The aim of present invention is to solve the problems remains in prior art,including the the fatal near-far effects in traditional CDMA radio communications. The mismatched ZCW sequences greatly enrich the ZCW sequence space. Matched ZCW sequences such as LS code are only one of its subset, which provides us more flexibility to choose MAC sequence for us..

Although the invention has been described in detail with reference only to a preferred embodiment, those skilled in the art will appreciate that various modifications can be made without departing from the invention. Accordingly, the invention is define only by the following claims, which are intended to embrace all equivalents thereof.

Claims

1. A coding method to create general spread spectrum sequence with zero correlation window, wherein general spread spectrum sequence with zero correlation window include binary codes at least in complex field.

2. A method of claim 1, wherein said general spread spectrum with zero correlation window sequence include ternary codes in complex field.

3. A method of claim 1, wherein said general spread spectrum sequence with zero correlation window include poly-phase codes in complex field.

4. A method of claim 1, wherein said general spread spectrum sequence with zero correlation window include any other ZCW codes in complex field.

5. A method of claim 1, wherein said general spread spectrum sequence with zero correlation window include binary codes , ternary codes , poly-phase codes and any other ZCW codes in complex field.

6. A method of claim 1, wherein said binary codes include : In binary field, family size of LS code is only 2", wherein n is a positive integer; because there exist orthogonal matrices H_{12 2}, we can construct binary ZCW codes with family size 12*2; so said method will provide wider range of family size of binary ZCW codes.

7. A method of claim 2, wherein said ternary codes include : In binary field, there only possibly exist complementary codes for N=2^a10^b26^c, so the width of zero correlation windows of binary codes only takes 1, 2, 4, 8, ^{• ••}; but there exist ternary complementary orthogonal codes with zero correlation windows for any positive N, so ternary complementary codes with any ZCW length can be constructed; furthermore, there exist binary orthogonal matrices H_M*_M only when M is equal to 2,4,8,12, ^{• • •}, while there exist ternary matrices H_{M *M} for any positive M; said method leads to many new codes which have a much wider range of available lengths and window widths of zero correlations, thus we can select proper ZCW length and family size of complementary codes according to the channel condition and system demand.

8. A method of claim 3, wherein said poly-phase codes include : In binary field, there only possibly exist complementary codes for N=2^a10^b26^c,so the width of zero correlation windows of binary codes only takes 1, 2, 4, 8, ^{• ••}; but there exist poly-phase complementary orthogonal codes with zero correlation windows for any positive N, so poly-phase complementary codes with any ZCW length can be constructed; furthermore, there exist binary orthogonal matrices H_M*_M only when M is equal to 2,4,8,12, ^{• • •}, while there exist poly-phase matrices H_M*_M for any positive M; said method leads to many new codes which have a much wider range of available lengths and window widths of zero correlations, thus we can select proper ZCW length and family size of complementary codes according to the channel condition and system demand.

9. A method of claim 1, wherein said the method includes the following steps: Selecting a complementary orthogonal code (Cl, SI) with code length N, where the aperiodic auto-correlation functions of code C and code S oppose each other but also complement each other except at the origin; selecting another complementary orthogonal mismatched code (C2, S2) which is uncorrelated with the code (Cl, SI), i.e. their aperiodic cross-correlation functions of code C and code S between two codes sum to zero at all time shifts;

It can be proved that code (Cl,Sl) and code IS1 ,-Cl^* j are uncorrelated with each other, where ' ^ denotes reversing operation, '*' denotes the complex conjugate operation; selecting any orthogonal matrix, H_MxM which has M rows and M columns, the new codes can be constructed:

H_MxM ® Cl, H_MxM ® Sl) H_MxM ® C2, H_MxM ® S2) where ' ® ' denotes the Kronecker product; the auto-correlation functions or cross-correlation functions of the expanded code group will form a zero correlation window around the origin with the size of window -^ N.

10. A method of claim 2, wherein said the method includes the following steps:

( Cl Sl^ If Lπ« e_l ^{ιs a} P^a"" ° uncorrelated complementary orthogonal codes with code

f+ + 0 length N, and the ternary orthogonal matrix H 3x3 + - 0 is adopted, wherein "+" denotes 0 0 +

+1, "0" denotes 0 and "-" denotes -1; the expanded code group is

when N=5, a pair of ternary uncorrelated complementary orthogonal codesis: Cl SI + + + -0, + - + +0 C2 S2 + + - +0, + 0 according to the said expansion method, the expanded code group:

' l l 0 SI SI 0 (+ + + -0++ + -000000, + - + +0 + - + +000000^1 Cl - Cl 0 SI - SI 0 ++ +-0 +000000, +-++0-+--000000

0 0 l 0 0 SI 0000000000+++-0, 0000000000+-++0 C2 C2 0 S2 S2 0 ++-+0++-+000000, + 0+ 000000 C2 - C2 0 S2 - S2 0 ++-+0—+-000000, + 0-+++000000

0 0 C20 0 S2 0000000000 + + - +0, 0000000000 + 0 he width of zero correlation window will be N=5; family size of the expanded code group is 6; the equivalent transformation can be applied to generate basically ternary complementary ZCW code group.

11. A method of claim 3 or 4, wherein said the method includes the following steps: The original uncorreated complementary orthogonal quadri-phase code pair is:

The expansion matrix is:

0 0

#2x2 = 0 2

The expanded code group is:

(Cl Cl SI SI (010010, 002002 l - Cl SI - SI 010230, 002220 C2 C2 S2 S2 200200, 212212 C2 - C2 S2 - S2 200022,212030

It can be verified that the zero correlation window width of expanded code group is 3, and family size of expanded code group is 4;

If the orthogonal matrix H_MxM is defined:

a ZCW code group (2M, 3M, 3) is obtained;

The proposed ZCW codes are expanded by an orthogonal matrix Η_M._M from a pair of uncorrelated complementary orthogonal codes with code length N; the new expanded code group is the Kronecker product of the uncorrelated complementary orthogonal code pair and orthogonal expansion matrix, The expanded code group can be denoted by (K, L, W)= (2M, MN, N), wherein M, N are any positive integer;

The proposed code groups satisfy: K=2L/W, but the family size of access codes of code group is not limited to K=2 ^(M+1) any more, and code length are also not only 2^MN; said method leads to many new codes which have a much wider range of available lengths and window widths of zero correlations; said method can construct complementary codes with any even family size K, zero correlation window width W and code length L which satisfy K=2L/W; said method is also available for generalized complementary codes, such complementary code triads and complementary quads etc.

12. A method of claim 1 or 2 or 3 or 4 or 5, equivalent transformations don't change the

ZCW properties of proposed complementary ZCW codes.

13. A method of claim 1 or 2 or 3 or 4 or 5, all codes presented in said method are close to the theoretical bound.