WO2007131384A1

WO2007131384A1 - A grouping time, space, frequency multiaddress coding method

Info

Publication number: WO2007131384A1
Application number: PCT/CN2006/000947
Authority: WO
Inventors: Daoben Li
Original assignee: Daoben Li
Priority date: 2006-05-12
Filing date: 2006-05-12
Publication date: 2007-11-22
Also published as: IL195258A0; CN101438524B; CN101438524A

Abstract

A grouping time, space, frequency multiaddress coding method for using the low correlation random variables or constants such as time, space and frequency etc as the coding elements, includes following steps to accomplish the coding: selecting basic perfect complementary orthogonal code pairs mate; selecting basic time, space, frequency codes expanding matrix; constructing basic perfect complementary orthogonal code pair group mate; spreading the code length and the code number in the basic perfect complementary orthogonal code pair group mate according to the spanning tree method; transforming the spanning tree. The invention make the CDMA or other communication systems using this address codes have higher frequency spectrum efficiency and larger capacity, and at the same time have stronger antifading ability, that is higher implied diversity multiplicity and higher transmission reliability, lower receiving threshold SNR, so that it need smaller transmitting power to accomplish higher reliability and higher transmission rate of the project's real requirements.

Description

Method for grouping time, space and frequency multi-address coding

The present invention relates to the field of code division multiple access (CDMA) wireless mobile digital communication, and particularly relates to a multi-address block coding method with high spectral efficiency, high anti-fading capability and high transmission reliability, which is specifically a grouping time, Space, frequency multi-address coding method. Background technique

Increasing the capacity and frequency of the system "Efficiency and improving the transmission reliability of the system are the most important basic tasks in any wireless communication system, especially in mobile digital wireless communication systems.

The so-called spectrum efficiency refers to the maximum total transmission rate supported by the system per unit bandwidth in a cell (cel l) or sector (sector) given a system bandwidth. The unit of measurement is bps/Hz/cel l (sector), the so-called transmission reliability refers to the ability of the system to resist fading.

As is well known, wireless channels, especially mobile wireless channels, are typical random time-varying channels, which have random dispers in the time domain, the frequency domain, and the spatial angular domain. These spreads will cause severe fading of the received signal in the corresponding frequency domain, time domain and spatial domain. Fading will seriously deteriorate the transmission reliability and spectral efficiency of the wireless communication system.

The only means of combating fading is diversity, and the basic measure of the ability of a wireless communication system to resist fading is the diversity multiplicity. Diversity can be divided into two categories: apparent divers i ty and hidden divers ty. The explicit diversity technique has no need to elaborate as its name suggests. Hidden diversity technology is a signal design technique. For example, in spread spectrum wireless communication systems and code division multiple access (CDMA) systems, a spread spectrum signal design technique is used, which has a certain resistance against channel time spread. The ability to frequency selective fading. The essence of diversity is that the transmitted message is "sorted" in the "subchannel" of the uncorrelated or independent fading, and at the receiving end, the output of the "subchannel" is "set". Unified demodulation of the information they share. The number of uncorrelated or independent fading "subchannels" available, referred to as the "order of uncorrelated diversities", the higher the diversity number, the higher the transmission reliability of the system. In general, when the basic parameters of the channel and the communication system are determined, the maximum irrelevant or independent diversity multiplicity, that is, the maximum transmission reliability that the system can achieve is also determined.

For a wireless communication system, there are three basic parameters: system bandwidth B (Hz); symbol duration T _M (seconds s) or symbol rate 1/T _M (symbols per second sps) and available geospatial range Surrounding R (m ² M ² ). For a channel, there are three basic parameters: the effective time spread of the channel △ (seconds s), or the effective correlation bandwidth of the channel 0-丄 (Hz); effective frequency dispersion of the channel

Δ

Quantity (Hz), or the effective correlation time of the channel (seconds); and the effective geographic phase of the channel

F

Off space (m ² M ^Z ). After the above basic parameters are determined, the uncorrelated maximum hidden diversity weights that the system can achieve are: |5Δ + 1Ι;

Here the symbol Lvl represents the smallest integer of · because the diversity multiplicity must be an integer.

And the total diversity of the system can reach = . is the product of the three.

In general, improve the system's hidden frequency diversity multiplicity and implicit time diversity multiplicity and improvement system

1

The spectrum efficiency of the system is contradictory. Since the channel is given once, 0=丄, ^丄 is determined,

Δ F

Increasing means increasing the frequency resource B occupied by the system. The increase means increasing the time resource T _M occupied by the system. Both of them improve the spectrum efficiency of the system, and only the system space diversity is the exception.

As with any other multiple access technique, in a Code Division Multiple Access (CDMA) system, users of different addresses have their own unique address codes for mutual identification. The best address codes can still be well distinguished after channel transmission, without mutual interference, ie they should always maintain orthogonality. Unfortunately, any wireless channel, especially a mobile wireless channel, is not a time-invariant non-diffusion system. They all have random angular spreads (which produce spatially selective fading); random frequency spreads (which produce temporally selective fading) and random temporal spreads (which produce frequency selective fading). Fading not only seriously degrades system performance, but also greatly reduces system capacity and reduces system spectral efficiency. In particular, the time spread of the channel (caused by multipath propagation) causes adjacent symbols to overlap each other to cause mutual interference, so that inter-symbol interference (ISI) occurs between the front and rear symbols of the user signal of the same address, but different Address user Multiple access interference (MAI) will also occur between the signals. This is because when the relative delay between address signals is not zero, the orthogonality between any orthogonal codes will generally be corrupted.

In order to make the inter-symbol interference USI) zero, the autocorrelation function of each address code should be an impulse function, that is, the autocorrelation function value should be zero for various relative delays except the origin; in order to make the multiple access interference (MAI) ) is zero, the value of the cross-correlation function between each address code should also be zero for various relative delays.

The value of the autocorrelation function origin (the relative delay is zero) is the main peak of the correlation function, and the autocorrelation or cross-correlation function other than the origin is the peak of the autocorrelation or cross-correlation function. The peak of the autocorrelation and cross-correlation of the ideal address code should be zero. Unfortunately, both theoretical and ubiquitous searches have shown that there are no multi-address code groups in the real world where the peak is zero. In particular, the theoretical Welch bounds point out that the peak of the autocorrelation function and the peak of the cross-correlation function are a pair of contradictions. When one is reduced, the other must increase, and vice versa.

The PCT patent application, the application number is PCT/CN00/0028, the inventor of the present invention, the disclosure of which is incorporated herein by reference. The method ensures that the address code encoded by it is within a specific window (- Δ , Δ ), and the autocorrelation function and cross-correlation function of each address code in the complementary sense have no peak. Thus, as long as Δ is larger than the maximum time spread of the channel (maximum multipath broadening) plus timing error, inter-symbol interference (ISI) and multiple access interference (MAI) do not occur in any two-way synchronous wireless communication system.

It has been proved that the large area synchronous code division multiple access (LAS-CDMA) mobile communication system established by the above invention has higher system capacity and spectrum efficiency than any other similar communication system. However, people always hope that the hurdles will go further. These hopes are combined in the following two main points:

1) Under the given window width (- Δ, △), can the number of address codes be more, or vice versa, can the window be wider under the same number of address codes?

2) Can the address code itself have stronger implicit diversity capability and higher transmission reliability? For requirement one, if the inventor's symbol is used, it is assumed that the orthogonal complementary code group with zero correlation window is {C _ft , S _ft }, l ≤ k ≤ K, and the code length of ^ is N, the required zero correlation is required. The width of the window is (- Δ , △ ). The theory has proved that the number K of codes should satisfy the following infinitive:

That is, after the code length N and the zero window size Δ are given, regardless of which coding element is used, including the random element used in the present invention, the maximum number of possible address codes K has been determined, and it is impossible to have more address codes. The number of address codes provided by the inventor is very close to the theoretical world, and basically does not exist. There is room for improvement.

But from the needs of engineering, people do have the above hopes. So the only way out is to relax some of the constraints of the code. If one or some of the constraints are relaxed, the individual unimportant indicators or complexity of the system are only slightly affected, but when the overall system such as capacity, spectrum efficiency, etc. is significantly improved, then this can be considered. Coding under new constraints with relaxation.

The fatal shortcoming of the traditional code division multiple access system is the "far-and-far effect", which is caused by the unsatisfactory cross-correlation properties of the address codes. Because the main peak of a long-distance weak signal is overwhelmed by the peak of a close-range strong signal, it is known that only the main peak is a useful signal. In order to overcome the fatal effect of the "far effect", the traditional CDMA system is strict and fast. The power control technique tries to make the signal of each address user reach the receiver at the same intensity in any case, but it has been proved that the effect of this method is very limited; the theoretically best method is to ensure that each address code is mutually The correlation function has no peaks under the working environment conditions. This is the method adopted by the LAS-CDMA system. Both theory and practice have proved that this method is indeed the best. Therefore, the requirement for a "zero correlation window" for the cross-correlation function cannot be relaxed. So can you relax the requirements of the autocorrelation function? The answer is yes, because they will only cause mutual interference between the symbols before and after, and will not cause interference to other signals, so it will not cause "far-and-far effect. When self-interference has little effect on the performance of the receiver, both theory and practice have proved that when the diversity multiplicity is high, the peak of the autocorrelation function of e- ¹ (about 0.37) or even higher, The loss caused by the performance of the receiver is almost negligible. Therefore, we can relax the limitation of the peak of the autocorrelation function in the window. Further, we can set a set of autocorrelation and cross-correlation functions that are not ideal in the window. All are handed over to an address user, and they are treated as "self-correlation". This ensures that there is a "zero correlation window" in the cross-correlation function between each address code group.

It is an object of the present invention to provide a packet time, space, and frequency multiple address encoding method. There is a "zero correlation window" for the cross-correlation function between the group and group of the encoded address code. Each group of address codes consists of several codes. The autocorrelation and cross-correlation functions of each code in the group are not required to have a "zero correlation window" feature. By virtue of the method of the present invention, the present invention can provide more address codes under the same "window" width. On the contrary, under the condition that the number of address codes is the same, the present invention can provide a wider "window", thereby creating conditions for more greatly improving the capacity and spectral efficiency of the system.

Another important object of the present invention is to make the encoded address code have a transmission reliability of 4 inches at the same time. That is, it has a very high degree of hidden diversity, and while increasing the number of hidden diversity, the frequency efficiency of the system will not increase but will remain unchanged or remain unchanged.

Since the present invention requires each address user to use a set of codes, although the autocorrelation function and the cross-correlation function between the codes in the group are not ideal, since the codes in the group are used by the same user, the channel fading characteristics are completely consistent. At the same time, the number of codes in the group is a fixed finite number, which will facilitate the multi-code joint detection and solve the complexity of joint detection in the traditional CDMA system.

The technical solution of the present invention is:

A packet coding method for multiple address codes, using weakly correlated random variables or constants such as time, space, frequency, etc. as coding elements, characterized in that the method comprises the following steps:

Select the basic perfect orthogonal complementary code dual;

Select a basic time, space, frequency coding extension matrix;

Forming a substantially perfect orthogonal complementary code group couple;

According to the spanning tree method, the length of the code and the number of codes in the basic perfect orthogonal complementary code group are extended;

Transform the spanning tree.

The selection of the substantially perfect orthogonal complementary code dual also includes the following specific steps:

According to the width of the required zero correlation window, the number of codes in the code group, etc., determine the length of the basic perfect positive interaction complement dual;

According to the relationship]\^ ^ ><2'_; / = 0,1,2,..., determine the perfect complementary code of a peas 33⁄4⁄4 according to the shortest code length determined by the above steps, and the requirements of the project implementation, arbitrarily selected one The code length is the shortest code length N. (^ code, C ₁₂ ,...C _1W( J;

According to the requirement of complete complementarity of the autocorrelation function, mathematically solve the simultaneous equations to solve the fully complementary ^ code, = [ _pl S" ₁₂ ,...S _1W| , ]; Solving the shortest basic complementary code pair ( , S, ), and solving another pair of shortest basic complementary code pairs ( , s ₂ ) that are completely orthogonally complementary thereto;

The code length is N. The perfect orthogonal complementary code dual forms the required length N = N ₀ x 2 ^l ( = 0,1,2,...) Perfect orthogonal complementary code dual.

According to the width of the required zero correlation window, the number of codes in the code group, etc., determine the length N of the basic perfect positive interactive complement dual;

According to the relationship N = N ₀₁ X Ν ₀₁ χ 2 ^M ; I = 0, 1, 2, ... determines the length N ₀₁ , N of the two shortest basic perfect complementary codes. ₂ ;

According to the shortest code length determined by the above steps, and the requirements of engineering implementation, arbitrarily select a code length to the shortest code length N. Code,

According to the requirement of complete complementarity of the autocorrelation function, mathematically solve the simultaneous equations to solve the fully complementary ^ code, ₇ = [5 _{11 5} 5 ₁₂ ,...5 _{1 ϋ} ]; repeat the above steps Rubber, solve two pairs (C , ^' ) and (0: , S ); according to the shortest basic complementary code pair solved by the above steps _; ), solve another pair of shortest basic complements that are completely orthogonally complementary Code pair ( , s ₂ );

The code length is N. The perfect orthogonal complementary code dual forms the required length N = N. Perfect orthogonal complementary code dual for X 2' {1 = 0,1,2,...).

By connecting the short code in the following steps, you can get the new perfect orthogonal complementary code dual that doubles the length:

C j ⁼ C c 2 , S 1 — S js 2

You can also use the following steps to obtain a new perfect orthogonal complementary code dual that doubles the length: the parity bits of the c (Sj ) code are composed of ( ₇ ) and ( s ₂ ) respectively; the parity bits of the c ₂ (s ₂ ) code are respectively

<^ _/ ( _/ ) and (^ (^).

By connecting the short code in the following steps, you can get the new perfect orthogonal complementary code dual that doubles the length: You can also use the following steps to get a new perfect orthogonal complementary code dual that doubles in length:

(The parity bits of the ^ code are respectively composed of and ^; S, the parity bits of the code are respectively composed of έ and ^; the parity bits of the code are respectively composed of and ^; the parity bits of the code are composed of (5 ₂ and ^ respectively). Using the steps described, a new perfect orthogonal complementary code pair of the desired length Ν can be obtained. The selection of the basic time, space, and frequency coding extension matrix further includes the following specific steps: According to the size of the required zero correlation window Δ, Determine the number of columns of the extended matrix from the relationship Δ≥Λ3⁄4 - 1

L, where: Ν is the length of the perfect perfect orthogonal complement dual, L is the number of columns of the extended matrix, and the unit of Δ is calculated by the number of chips;

According to the engineering requirements such as available time, frequency, space size and system complexity, select the number of basic weakly correlated random variables (coding elements);

Determine the number of codes in each group of address codes according to system complexity and requirements for improving spectral efficiency

Μ, Μ is the number of rows of the expansion matrix;

The basic coding extension matrix is constructed according to the available time, frequency, spatially weakly related random variables (coded elements), the number of rows of the required extension matrix Μ and the number of columns L.

The basic coding extension matrix constructed only needs to satisfy the following basic conditions:

Arrange as many weakly correlated random elements as possible in each row vector, or arrange only constant elements; the extended matrix should be a row full rank matrix, that is, each row vector should be linearly independent;

The aperiodic and periodic autocorrelation functions of each row vector should have as small a pay peak as possible; the aperiodic and periodic cross-correlation functions between the row vectors should have as small a pay peak as possible.

The constructed basic coding extension matrix can be a random matrix, a constant matrix, or even a constant.

The number of weakly correlated random elements in each row vector is the hidden diversity of the corresponding wireless communication system.

The autocorrelation function of the corresponding code in the window in the group is affected by the autocorrelation function of each row vector Good or bad.

The quality of the cross-correlation function in the window between the corresponding codes in the group is determined by the quality of the cross-correlation function between the row vectors.

The basic perfect orthogonal complementary code group is generated by the basic perfect orthogonal complementary code dual and the basic time, space, and frequency coding extension matrix.

The expanded group address codes have hidden diversity numbers corresponding to the types and numbers of random variables. Meanwhile, the cross-correlation function between different code group address codes has a zero correlation window near the origin, and the window width is perfect. The basic length of the orthogonal complementary code group is determined.

Extending the basic perfect orthogonal complementary code group is performed according to the relationship of the spanning tree, which is determined by the generated code group.

The transform spanning tree may be a location for exchanging spanning tree C code and S code.

The transform spanning tree may be a negation of one of the C code or the S code in the spanning tree, or both.

The transform spanning tree may be using a reverse sequence, that is, the C and S codes are taken at the same time as the reverse sequence. The transform spanning tree may be the polarity of the interleaved code bits.

The transform spanning tree may be a uniform rotational transform of each code bit in a complex plane.

The transform spanning tree may be arranged by synchronizing the C code with each column in the S code in a spanning tree, wherein the columns are in units of codes in the substantially perfect orthogonal complementary code group.

The address code is in units of groups, each group has a fixed number of codes, and the mutual function between each group of address codes has a zero correlation window.

The address code has a high hidden diversity number, and the effective diversity weight is equal to the number of random variables such as weak correlation time, space and frequency in the coding element and the channel time spread amount in chips in the window. product. ,

The address code is in units of groups, and each group has a plurality of codes, and the cross-correlation function of the codes between the groups has a zero correlation window characteristic. The autocorrelation function of each code in the address code group and the cross-correlation function between codes do not require certain ideals, and there is no requirement that a zero correlation window exists.

The size of the cross-correlation zero correlation window between each address code group can be adjusted.

The adjustment method may be to adjust the length of the pair of substantially orthogonal complementary codes.

The adjustment method may be to adjust the number of columns of the basic time, space, and frequency extension matrix.

The adjustment method may be to adjust the number of zero elements between the code generation tree coding extension matrix.

The number of codes in each address code group can be adjusted by adjusting the number of lines of the basic time, space, and frequency code extension matrix.

In the zero correlation window, the autocorrelation function of each code of each address code group is mainly determined by the autocorrelation property of each row of the selected basic time, space and frequency coding extension matrix. The cross correlation function between codes in the group is mainly determined by the selected one. The cross-correlation properties between the corresponding rows of the time, space, and frequency extension matrices.

In the window of the gate, the autocorrelation and cross-correlation properties of each Λί^ horse include the autocorrelation and cross-correlation properties of each address code in the group, which are determined by the duality of the basic orthogonal complementary code and the structure of the corresponding spanning tree.

The time, space, and frequency coding extension matrix may be an arbitrary matrix.

The time, space, and frequency coding extension matrix includes: time, space, time, frequency, time, space, frequency, and even a constant matrix or constant.

The present invention provides a new packet multi-address coding technique that uses time, frequency, space and other related random variables as coding elements. The basic features of this coding technique are as follows:

1) The address code is in units of groups, each group has a fixed number of codes, and the cross-correlation function between each group of address codes has a "zero correlation window" characteristic, and the condition that the window width is the same or wider and the address code length is slightly longer Next, compared with the multi-address code invented by Li Daben in PCT/CN00/0028, the number of sets of address codes provided by the present invention is the same as the number of codes thereof, but since there are a plurality of codes in the group, the code provided by the present invention The total number has increased substantially, and vice versa. Therefore, the wireless communication system using the present invention as an address code will have higher system capacity and higher spectral efficiency.

2) Since the elements of the address code are weakly related random variables such as time, frequency or space, the encoded address code also has a high hidden diversity number, which can greatly improve the transmission reliability of the system. - its _ effective diversity multiplicity is equal to the product of the weak correlation time, space, frequency and other random variables in the coding element and the product of the channel time spread in the "window", for example, the address code element is used. Two-frequency, There are four fading random variables in the two spaces. The time spread of the channel has three chip widths. The actual system using the address code will have 4 X 3=12 re-diversity effect, and the transmission reliability is very close to the non-fading constant ginseng. Gaussian channel.

3) The encoded address code is in "group", each group has several codes, and the cross-correlation function of the code between the groups has a "zero correlation window" feature, if the "window" width is wider than the actual channel time Diffusion plus system timing error, while each user in the system uses a set of codes, the corresponding wireless communication system will not have "far-and-far effect", and the system capacity and spectrum efficiency are greatly improved.

4) The autocorrelation function of each code in the address code "group" and the cross-correlation function between codes are not necessarily ideal, and there is no need to have a "zero correlation window" port. This will require the use of multi-code (multi-user) joint detection techniques in practice to reduce the effects of intra-group interference, but since the codes in the group are generally used by the same user, the channel fading characteristics are identical and the group The number of internal codes is generally small, which brings convenience to the application of multi-code joint detection, multi-code interference cancellation, multi-code channel equalization and other technologies.

5) Cross-correlation between each address code group The size of the "zero correlation window" port can be adjusted by the following main means:

a) adjusting the length of the dual of the basic orthogonal complementary code;

b) adjusting the number of columns of the basic time, space and frequency coding extension matrix;

c) Adjust the number of "zero" elements between the code spanning tree coding extension matrix.

6) The number of codes in each address code group can be adjusted by adjusting the number of lines of the basic time, space and frequency coding extension matrix.

7) In the "window", the autocorrelation function of each code in each address code group is mainly determined by the autocorrelation property of each row corresponding to the selected basic time, space and frequency coding extension matrix, and the cross-correlation function between the codes in the group is mainly Determines the cross-correlation properties between the corresponding rows of the selected time, space, and frequency extension matrices. Therefore, it is important to choose an extension matrix with good correlation between each line and autocorrelation and inter-row correlation.

8) In the "window,", the autocorrelation and cross-correlation properties of each address code (including the group) are determined by the basic orthogonal complementary code dual and the corresponding spanning tree structure.

9) Time, space, and frequency coding extension matrix, which can be any matrix, such as time and space; time and frequency; time, space, frequency and even constant matrix. The only difference is the type of diversity and whether it is there. DRAWINGS

1 is a basic code generation tree; 'FIG. 2 is a diagram of a specific embodiment of a code generation tree; Figure 3a is an original arrangement diagram of column transformations in a spanning tree;

Figure 3b shows the transformation of the column transformation in the spanning tree. The new alignment diagram after the 3 columns. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, specific embodiments of the present invention will be described with reference to the accompanying drawings:

The basic coding steps of the present invention are as follows:

step one:

The choice of Basic perfect complementary orthogonal code pairs mate.

This step can be subdivided as follows:

1) Determine the length N of the basic perfect orthogonal complementary code pair according to the width of the required "zero correlation window" port, the number of codes in the code group, and so on.

2) According to the relationship

First determine the length N of the shortest perfect complementary code. . For example, N=12 is required, then N. =3, 1 = 2.

3) or according to the relationship

N = N ₀₁ xN ₀₂ x2 ^{, +1} ; / = 0,1,2,...

First determine the length of the two shortest basic perfect complementary codes ₀₁ , N _02o, for example, N = 30, then N ₀₁ = 3, N ₀₂ = 5 (/ =.).

4) According to the minimum code length determined by 2) or 3), and the requirements of engineering implementation, arbitrarily select a code with a code length of the shortest code length ^, c _; =[c„,c ₁₂ ,...c _Wo ] ₀

5) According to the requirement of complete complementarity of the autocorrelation function, mathematically solve the simultaneous equations to solve the code that is completely complementary with the autocorrelation function, ^s i - ί ιι' ₂ "Ί _ο J.

The elements of Sj are solved by the following simultaneous equations

c!i · c _w . =—S _u . s _]Nfi

C'l , c _iw . One, +C ₁₂ -c _lNa = -(s _u +S _n - S _lNo )

c _u ' c _No — ₂ +c _n - _1Wo _! +c ₁₃ -c _lN(i = -(S _n - s _}Na _2 +s _n - s _Wo ^ +s _l3 - s _Wo ) W

Cu .C ₁₂ + C _]2 - C _]3 + + C _w ',一'' C _W( , = - (5",] .S ₁₂ +S _N - S ₁₃ + S _W _ _} - S _]NA )

The code solved by the above simultaneous equations generally has many solutions, and one can be selected as one. Example 1: If + +— , where + means +1; - means -1, there are many possible solutions, such as:

+ 0 +; - 0 -; + j +; + - +; a j one; - - - Temple.

Example 2: If the possible ₇ solution has

V2-1, 1, -^J—; V2+1, 1, -^—; , -^, -丄, etc., here a

V2-1 V2 + 1 a ² -1 a

Any number that is not equal to +1 or -1.

Example 3:

One solution for

1, 4, 0, 0, - 1 and so on.

If the primary selection (^ value is not appropriate, then ^ may have no solution; sometimes although there is a solution, but it is not convenient for engineering application, at this time, need to re-adjust (^ value, until we take (^ and ^ The value is satisfactory.

6) If 3), because there are two shortest lengths N _Q1 , N „ ₂ , repeat 4) 5 ), and solve two pairs ( C , S ) and ( C ₂ ^r , S ).

Where C = C _u C _n ..., C _lNm '; S, ' = s _u s _n ..., s _]Nn 'C2' ⁼ C ₂ i , C ₂₂ ,..., C _{2W() 2} , S ₂ ' = S ₂ , S ₂₂ ,..., S _2Nm and solve the length as follows

_.Completely complementary code pair ( , S _} ), where Ci ⁼ [Qi '[C ₂₁ , C ₂₂ ,..., C _2NOI ], C ₁₂ , [C ₂₁ , C ₂₂ ,..., C _2N ^ ],..., _1Woi '[C ₂₁ ',C ₂₂ C _2Wo2 ],

Si

']'···»

C!w',, [^2^,,;, ''^2N _m -l ,··', S ₂₂ ,,S ₂₁ '],-5^ [ _{2NB2 2NM} _ C ₂₂ ',C _2] ' ],

~ ']]

They are all 2N in length. , x N ₀₂ .

Mathematically noted as: 4 Sj'®S ₂ ' Where ® is the Kroneckzer product; indicates the reverse sequence; - indicates the non-sequence, ie the element value is inverted.

7) According to 5) 6) The shortest basic complementary code pair solved (The Shortest Basic

Complementary Code pair ) ( c ₁ , _/ ), solves another pair of shortest basic complement code pairs ( , S ₂ ) that are completely orthogonally complementary. { ( , S, ); ( C ₂ , S ₂ ) } is called Perfect Complete Orthogonal Complementary code pairs mate, that is, in a complementary sense, each of them The autocorrelation function and the cross-correlation function between the two pairs are ideal.

The theory and the pass search have proved that for any complementary code pair ( , ) only in a complementary code pair (4, s ₂ ) with its mate, and they satisfy the following relationship:

Here: the underline indicates the reverse sequence, that is, the order of the order is reversed (from the tail to the head); the upper line "is a non-sequence, that is, the element values are all inverted (negative) values; * represents a complex conjugate;

k is an arbitrary complex constant.

For example: ^ C, =+ + -; S, = + j +; Let & = 1 get C ₂ = + -j +; s ₂ =+ - -.

Table 1: Autocorrelation function of S, ) Α(τ)^^( _τ ) + ^(τ) Relative scale value τ -2 -1 0 1 2

0 0 6 0 0

+ + -; Sj = + j +

Table 2: Autocorrelation function of ( C ₂ , s ₂ ) R ₂ (x)AR (x) + R _Si (x) Relative scale value τ -2 -1 0 1 2

0 0 6 0 0 C ₂ =+ -j +; s ₂ =+ - -

Table 3: Cross-correlation function of ( , S° _; ) with (<^, S ₂ )

C, =+ + ―, Sj =+ j +; C ₂ = + -j +, s ₂ = + one

Tables 1 through 3 list the autocorrelation and cross-correlation function values in their complementary senses, respectively, and they are all ideal.

8) The code length is N. The perfect orthogonal complementary code pairs mate form a perfect orthogonal complementary code pair of the required length N = N ₀ χ 2' (/ = 0, 1, 2, . . . ).

If ( , ^ ; ) and ( , S ₂ ) are a perfect orthogonal complementary code dual, we can use the following four methods to double the length, and the two new pairs after the length is doubled, still Is a perfect orthogonal complementary code dual.

Method 1: Connect the short codes in the following way

C - C j C , ^ j ⁼⁼ ^ ] ^

C ₂ = Cj ₂ ; S ₂ = Sj S ₂

Method 2: (^ (The parity of the code is composed of ^^ ;! and ^^ respectively; the parity of the c ₂ (s ₂ ) code is composed of ( _; ) and ₂ ( ) respectively. For example: If C° ₇ - [C„C ₁₂ ... C _1W .1 S, = [5 _U 5 ₁₂ ... 5 _1W J;

Method 3: Connect the short code by the fan method:

C ₂ = C ₂ S ₂ ; S ₂ = C ₂ S ₂

Method 4: The parity bits of the code are respectively composed of and ^; S, the parity of the code is respectively (^ and

^ Composition; (The parity bits of the ^ code are respectively composed of (^ and ^; the parity bits of the S ₂ code are respectively composed of and ^.

There are many other equivalent methods, which are not described here.

Using the above method in succession, a perfect orthogonal complementary code pair of the desired length N can be finally formed. Step 2: Selection of basic time, space, frequency code expansion matr ix

The basic time, space and frequency coding extension matrix is an important part of extending the "zero correlation window" coding between basic codes into the "zero correlation window" coding between code groups. Since the introduction of the extension matrix is under the same "window" width condition, the available code number provided by the present invention will be greatly improved. On the contrary, the invention can provide a wider "zero correlation" under the same available code number. Window" mouth.

If the order of the expansion matrix is M x L, where M represents the number of rows of the extended matrix, and L represents the number of columns of the extended matrix. Generally, the larger the M x L, the higher the spectral efficiency of the formed address code. At the same time, the higher the number of hidden diversity of the corresponding communication system, the higher the transmission reliability, and the smaller the transmission power required by the system, but the complexity of the system also increases.

The number of rows of the extension matrix M is equal to the number of codes in each code group. The larger the M, the higher the spectral efficiency of the system, but the higher the system complexity.

The number of columns L of the expansion matrix is related to the width of the "zero correlation window" of the cross-correlation function between the formed address code group and the group. The larger L is, the wider the "window" is. L is generally greater than or equal to the multiplicity of the system's implicit diversity, that is, the number of random variables such as time, space, and frequency that are actually associated with weak fading. These random variables are elements in the extended matrix. In traditional system design, people Unrelated diversity is often required, which will result in the requirement that the coding elements should have irrelevant or independent fading. However, the number of random elements with irrelevant fading or independent fading that are available under the constraints of a certain "space" that can be handled, such as geospatial size, processing time, and system usable bandwidth, will be limited. Both theory and practice have shown that the requirements for the correlation of random elements used can be appropriately relaxed. Professor Li Daoben proposed the _e- ' criterion in his book, that is, the correlation is zero and the correlation is as high as e-' (about 0.37). There is almost no difference in performance. According to the experimental results, the correlation can even be relaxed to 0. 5 left Right, so that a higher degree of hidden diversity can be achieved within a given "space" range, but further relaxation of the correlation is not desirable, although this can result in a higher apparent implicit diversity multiplicity, but The really effective diversity multiplier improvement is very limited. Therefore, the relaxation of relevance must be moderate.

Step 2 can be subdivided as follows:

1) According to the required "zero correlation window" port Δ size, by relationship

A ≥ NL - determines the number of columns L of the extended matrix.

Here: N is the length of the perfect perfect orthogonal complementary code pair;

L is the number of columns of the expansion matrix; the unit of Δ is calculated in chips.

2) According to the engineering requirements such as "space, size and system complexity" of available time, frequency and space, select the number of basic "weak" related random variables (coding elements).

3) According to the complexity of the system and the requirements for improving the spectrum efficiency, determine the number of codes in each "group" address code, M, which is the number of rows of the extended matrix.

4) The number of available time, frequency, space weakly correlated random variables (coding elements), the number of rows of the required expansion matrix M and the number of columns L, construct a basic coding extension matrix. The matrix only needs to meet the following four basic conditions:

a) arrange as many "weak" related random elements as possible in each row vector;

b) the extension matrix should be a row full rank matrix, ie each row vector should be linearly independent;

c) The aperiodic and periodic autocorrelation function of each row vector should have a peak that is as small as possible. For example, the absolute value is not greater than e- ¹ or even 0.5.

d) The aperiodic and periodic cross-correlation functions between the vector lines should have as many "small" peaks as possible. For example, the absolute value is not greater than or even 0.5.

among them: '

a) the number of "weak" related random elements in each row vector, that is, the implicit diversity of the corresponding wireless communication system;

b) The quality of the autocorrelation function of each row vector will determine whether the autocorrelation function of the corresponding code in the group is "window,";

c) The quality of the cross-correlation function between the vector lines will determine the quality of the cross-correlation function in the "window" between the corresponding codes in the group. Several practical basic time, space, and frequency coding extension matrices are given below.

a) The number of rows and columns of the coded extension matrix is M=L=2, and the number of random variables is 2. The basic coding extension matrix is «1. This is an orthogonal matrix, where two spatial or polarization or frequency diversity random variables, or even two constants, have no requirement for their correlation. When their correlation is 1 (ie, a constant matrix), the implicit diversity gain disappears, but it is still beneficial for improving system capacity and spectral efficiency.

b) The number of columns of the coding extension matrix is L=2, the number of rows is M=4, and the number of random variables is 4.

There are two basic forms of this extension matrix:

Basic coding extension matrix

The matrix has two upper and lower sub-blocks, wherein β, , ₂ in the upper sub-block are two spatial or polarization diversity random variables but the carrier frequency is y; and ₀₁ and _{2 in the lower} sub-block are also two spatial or polarization diversity random variables. , just change the carrier frequency to / ₂ . There is no requirement for the correlation distance between the two _antennas of ^ £7 ₂ , even A and fl ₂ are two constants (including _fll = « ₂ ), but there is no spatial diversity or polarization diversity gain at this time. Should be different from / ₂ , but without the requirement of uncorrelated fading, this coding extension matrix can also be extended to multi-carrier situations, ie

Where Λ is "a carrier of related fading.

The address code group formed by the multi-carrier coding extension matrix described above has the capability of at most two hidden spaces or polarization diversity, and multiple carriers are used to increase the capacity and spectral efficiency of the system. Basic extension matrix two is

The matrix has two sub-blocks above and below, where / ₂ is a two-frequency diversity random variable in the upper sub-block but uses an antenna, and /, / ₂ in the lower sub-block are also two frequency diversity random variables, just using an antenna. ₂ . There is no requirement for the distance between the two carrier frequencies of /, Λ, even if the two are equal, but there is no frequency diversity gain at this time. There should be an appropriate distance between and ^, but there is no independent fading requirement. This coding matrix can also be generalized to multiple antennas, ie

Where _βι , « ₂ ,..., „ are the “antennas that produce spatially selective fading.

The address code group formed by the above multi-antenna coding extension matrix two has the capability of at most two hidden frequency diversity, and multiple antennas are used to increase the capacity and spectral efficiency of the system. Obviously, the above two coding extension matrices can also be used in combination.

c) The number of rows and columns of the coded extension matrix is M=L-4, and the number of random variables is 4. The basic coding extension matrix is

This is also an orthogonal matrix, where ^, ^, ^ can be any spatial, frequency, polarization diversity random variable or a new diversity random variable generated by their combination, or any constant.

There are many more basic coding extension matrices that can be applied, as long as they meet the aforementioned Four basic conditions, even a constant matrix can be applied, but it should be noted that the constant coding extension matrix is only useful for improving the system spectrum efficiency and increasing the system capacity, and not only does it have any effect on improving the system transmission reliability, but even The opposite effect.

The "zero correlation window" multi-address coding method of Li Daoben in PCT/CN00/0028 is only a special case when the extension matrix is 1 X 1 matrix (constant) in the present invention.

Step three:

The composition of Basic perfect complementary orthogonal code pair group mate.

The basic perfect orthogonal complementary code group is generated by the basic perfect complementary orthogonal code pair mate and the basic time, space and frequency coding extension matrix. The generation method is as follows:

Let the basic perfect orthogonal complementary code pair be ((,, s _} ), ( c ₂ , s ₂ ); the basic coding extension matrix is A, where: (^ -[Cu ^.Cw], S _; =[S _U 5 ₁₂ ... 5 _1A ,];

The basic perfect orthogonal complementary code group, as the name suggests, has two sets of codes, each group has M pairs of codes, and the code length is NL + Ll. The cross-correlation function between each code pair in any group and any code pair in another group is ideal in a complementary sense, that is, there is no peak at all, and each code pair in the group is autocorrelation or cross-correlation. Functions are not guaranteed to have ideal characteristics. The basic perfect orthogonal complementary code group even formed by the basic perfect orthogonal complementary code dual and the basic coding extension matrix is denoted by ( Cj, S _} ); ( C ₂ , S ₂ ) ₀ where: ( 0 Α, 0; S _;

i = 1,2

Here: ® means Kronecker product

0 means Mx (L-l) zero matrix.

which is,

C ₂ =[C _2] A,C ₂₂ A,...,C2 _N A,0], S, = [S ₂ A,S ₂₂ A,...,S _2N A,0] _o

They are all Mx ( NL + L-\ ) order matrices, where the 0 matrix is used to isolate the two generating units in the spanning tree, in the worst case possible "caused, and the maximum protection is set. The interval can be shortened or even cancelled according to the actual situation. The 0 matrix can also be placed at the end of each code group and placed at the head.

For example 1: If the basic orthogonal complementary code is dual

C, =-+ , s ₇ = one by one, they are all code lengths, it is 4 columns

An orthogonal matrix of M = L = 2. Then the generated substantially perfect orthogonal complementary code group is

, a ₂ a, a ₂ aa ₂ aa ₂ 0

C

—C _u — a ₂ a, a ₂ a ₂ α a ₂ a _x 0

Since L-2, only one 0 is inserted here. It can be very easy to face, from the standpoint of the single complement, the autocorrelation and cross-correlation functions of the two pairs of codes in the code group ( C _; , ) or ( S ₂ ) are not ideal (both peaks appear) ), but the sum of the two pairs of code autocorrelation functions in the group is still ideal (see Table ⁴ , Table 5), which is a more general complement. The most important feature of this kind of extended coding is that, in a simple complementary sense, the cross-correlation functions between pairs of codes of different code groups are completely ideal (see Table 6).

Table 4: (C _} , S,) Autocorrelation and cross-correlation functions of code groups

Note: Shadow numbers do not appear in the spanning tree structure code

Table 5: Autocorrelation and cross-correlation functions of (C ₂ , S ₂ ) code groups

Correlation function relative position τ -4 -3 -2 0 1 2 3 4

. - _{α Ω} -432 ₁

S ₂ ) Cross-correlation function of each code between different code groups

21 ", 0 's ₂₁ ' α ₂ , α ₂ 0—

22. α ₂ α _χ α ₂ α _λ 0 β22. ₂ «1 α ₂ α _λ 0

In this example, L = 2, N = 2, so the unilateral "window" port width Δ ≥ 3 between the spread spectrum address code groups formed by "■,, (see below).

For another example 2: If the substantially perfect orthogonal complementary code pair is ( , S _} ), ( C ₂ , S ₂ ), where: ;= + + , i ₇ = + -; C ₂ =-+, =- _. They are all vectors of code length N=2.

The basic coding extension matrix A is:

j Basic perfect orthogonal complementary code group is:

Since L=4, three zeros are inserted here. Similarly, the autocorrelation and cross-correlation functions of the four pairs of codes in the code group ( ) and ( C ₂ , S ₂ ) are also not ideal (both have six peaks). (See Table 7 and Table 8), but the cross-correlation functions between pairs of codes in different code groups are completely ideal (Table 9).

In this example, L = 4, N = 2, so the unilateral "window" port width Δ ≥ 7 between the spread spectrum address code groups formed by ' 艮,, (see below).

Table 7: (C,, autocorrelation and cross-correlation function of code groups

C

(Table 7 below)

Relative to each other, relative shift 1 -10 -9 -8 -6 -5 -4 -3 -2 -1 0 1 2

4{α _χ α ₂ +α ₂ α^ 4(α,α ₂ +

^a _x a _t

A)

4

One 43⁄4 a 4 («!3⁄4 (3⁄4« ₄ — " _{3 4} -4 ₃

4 4ο ₂ α ₃ + - α ₂ α ₄ )

- 4( ₂ . ₄ 4 _{3 4} — α ₂ α ₃ -4(ο ₂ α ₄

-4α,α ₄

Λ _Η (τ) + Λ ₁₂ (τ) 16(«ι +%

0 0 0 0

+ Λ _Ι3 (τ) + Λ ₁₄ (τ) + ² +β)

One 4 (.," ₄ 4(" ₂ ² - A 4 _{2 3}

4 ₁ 43⁄43⁄4

4(α ₂ α ₃

4 (. ₂ ² - α' ² ) 4 ₃ ² - ₄ ² ) 4 one. ι ) J

-Aai 8 α ₄

4a - ² 83⁄43⁄4 -4a:

4 (.,. ₂ - 4( ₂ α ₃

-4α,α ₂ 4 , ² — ί3⁄4 ² ) 4(. ₄ ² —. ₃ ² ) -4α _{3 4}

4(«, +a ₂ a ₄ 4(. ₂ a ₃

, ₃ ,"(τ) 0 0 0 - ^4α Λ 4a _A a.: A) +. + )

Note: Shadow numbers do not appear in the spanning tree structure code

)

Correlation function of related number functions from Table 8: Autocorrelation and cross-correlation function of CC ₂ , S ₂ ) code groups

α _{ α _ζ α ₃ α _χ α _ζ α ₃ α ₄ 000 α ₂ α _ι α^α ₃ α ₂ α _χ α _Α α _ι ^

_{4 3} α ₂ α _] ά _{4 3} α ₂ α 000

Table 9: ( , 5,), (C ₂ , cross-correlation function of codes between different code groups

Relative shift τ -10 -9 -8 -7 -6 -4 -3 -2 8 9 10

R, τ) ο 0

R

23 τ)

24 τ)

R τ)

R, 22 τ)

R 23

R τ)

R. τ)

R, 22 τ)

R τ)

R 24

R,

R τ)

R τ) Note: The shadow number appears small in the spanning tree structure code Step four:

According to the spanning tree method, the length and number of codes of the basic perfect orthogonal complementary code group are expanded. After the extended group address codes, if the elements of the basic coding extension matrix are composed of "weak" correlation diversity random variables, it will have an implicit diversity multiplicity corresponding to the type and number of random variables, and different code group addresses. The cross-correlation function between codes has a "zero correlation window" near the origin, and its "window" port width is determined by the basic length of the perfect orthogonal complementary code pair.

If ( c,, S, ) and ( c ₂ , s ₂ ) are a substantially perfect orthogonal complementary code pair, the basic operation of code length and code number expansion is,

Newly generated (c, c ₂ , s, s ₂ ) and ( , s, s ₂ ) and ( c^ , S ₂ S, ) and ( c ₂ ,

S ₂ S, ) is a new perfect orthogonal complementary code group couple with two code lengths doubled, but the cross-correlation function between the code groups is no longer perfect, but only has the "zero correlation window" characteristic, and the above is continuously implemented. By expanding the operation, the tree structure diagram of Fig. 1 is formed.

At the root of the tree, the initial 0 stage, we have only one perfect orthogonal complementary code pair, and there are two sets of codes. In the first stage, we can get two perfect orthogonal complementary code pairs, which have four sets of codes, and the code length is 2^2 times of the initial stage. The cross-correlation function in the even is ideal, but even and even There is a "zero correlation window" between the cross-correlation functions. 'In the second stage, we can get four code groups and even a total of eight sets of codes, the code length is ²² = 4 times of the initial stage, ... so continuous expansion, in general, in the extended stage / stage, we can Get 2' code groups even a total of 2 ^w group code, the code length is 2 初始 in the initial stage. In each stage of the expansion, each code group is a perfect orthogonal complementary code pair, and the cross-correlation function of each code is ideal, but there is a "zero correlation window" in the cross-correlation function of each code. The width of the unilateral "window" port is not less than the basic code length of the two even "roots". For example, in Figure 1, the unilateral "window" of the cross-correlation function between codes in 1 ₂ and 11 ₂ The width is not narrower than the basic length of the ^ medium code minus one, because it is the common "root" of 1 ₂ and 11 ₂ . Similarly, the unilateral "window" mouth width of the cross-correlation function between codes in III ₂ and IV ₂ is not narrower than the basic length of the 11-coded code minus 1, because 11, is the common "root" of 111 ₂ and IV ₂ . However ΠΙ ₂ or ₁₂ and in IV _2-sided among the cross-correlation function code "window" opening width can not be less than I. That is, the basic code length of the initial root is decremented by one, because the initial roots are their common "roots". The so-called "basic code length" It refers to the length of the code that is not included in the last 0 element, and the 0 element in the middle part should be calculated within the basic code length.

It should be particularly noted that the basic coding extension matrix used in the present invention may be a random matrix. It is only possible for users of different addresses to use the same extension matrix at the base station, but for address users at different mobile stations, when the basic coding matrix is a random matrix, it is no longer possible to use the same coding extension matrix. In the case where the extension matrix is not the same matrix, can it still guarantee the "zero correlation window" characteristic of the cross-correlation function between the code groups? The answer is yes. Both theory and practice have proved that as long as the spreading matrix used by the address code of each address user is a homomorphic matrix (Homomorphi c matr i ces ), the "zero correlation window" between the address code groups generated by the spanning tree and other properties They will all be preserved without being destroyed. The so-called homomorphic matrix (Homomorphi c ma tri ces ) means that the structure of the matrix is completely identical and the elements in the matrix are not required to be the same, such as " ¹ "

a 2 «3 (-

Therefore, at each stage of the graph generation tree, different "rows", ie, code extension matrices in different code groups, may be the same matrix (for example, applied in a base station), or may be a homogeneous matrix (for example, on a mobile basis). In the station application, but in any case must guarantee the same "row", that is, the code extension matrix in the same group is the same matrix.

Figure 2 is an example of a specific code spanning tree. Only two phase trees are drawn for simplicity. The basic orthogonal complementary code pair used in the figure is

C; = + + , S, = + -;

, = -+ , S, = - -.

, a.

The basic coding extension matrix is ₌ "rows" in Figure 2, that is, the coding extension matrices in different code groups have all been represented by isomorphic matrices ₍ after applying the isomorphic coding extension matrix, let us use the foregoing example 1 ie Figure 2 Code generation tree to illustrate, In the first stage, two even (c^S, ), (c ₂ , s ₂ ) and ( , S3 ), ( c ₄ , s ₄ ) are generated, as described above, ( ^S, ), ( C ₂ , S ₂ ) and ( C;, ), ( c ₄ , s ₄ ) should be perfectly orthogonal complementary code pairs, that is, cross-correlation functions of codes between different code groups in each even Should be ideal, but the cross-correlation function between different even codes should have a "zero correlation window" feature. Tables 10 through 13 show the autocorrelation and cross-correlation functions of different code groups, while Table 14 shows the cross-correlation functions of codes between different code groups. Since the length of the basic perfect complementary code dual is N=2 in this example, and the number of columns of the coding extension matrix is L=2, the width of the unilateral "window" should not be narrower than NL - 1 = 2 x 2- 1 = 3 codes. Slice width.

(Table 10 to Table 14 are as follows)

Table 10: Autocorrelation and cross-correlation function of the ( ,,,,) code group in the first stage of Figure 2

Table 11: Relative shift of the autocorrelation and cross-correlation function of the (C ₂ , S ₂ ) code group in the first stage of Figure 2 τ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 From 0 0 0 0 0 0 0 8 8bA 8^b ₂ 0 0 0 0 0 0 0 0 Phase i? ₂₂ ( ) 0 0 0 0 0 0 0 0 — 8ό[6 ₂ 0 0 0 0 0 0 0 0 off

The letter R _2] (X) + R ₂₂ (T) 0 0 0 0 0 0 0 0 0 16(έ, ² +ό ₂ ² ) 0 0 0 0 0 0 0 0 0 Cross-correlation 0 0 0 0 0 0 0 0 a 86, ² 0 8ό ₂ ² 0 0 0 0 0 0 0 0

Table 12: Relative shift of the autocorrelation and cross-correlation function of the ( , ) code group in the first stage of Figure 2 τ -9 -8 -6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 White 0 0 0 0 0 0 0 0 8c _t c ₂ 8(c _t ² +c ₂ ² ) Sc^c ₂ 0 0 0 0 0 0 0 0 Phase 0 0 0 0 0 0 0 -8c, c ₂ 0 0 0 0 0 0 0 0 off

R _3l (x) + R ₃₂ (x) 0 0 0 0 0 0 0 0 0 16(c, ² +c ₂ ² ) 0 0 0 0 0 0 0 0 0 Cross correlation

0 0 0 0 0 0 0 0 0 8c ₂ ² 0 0 0 0 0 0 0 0 function

Table 13: In the first stage of Figure 2 ( ₄ , S ₄ code group autocorrelation and cross-correlation function relative shift τ - 9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 from 0 0 0 0 0 0 0 0 8 ( , ² + ₂ ² ) 0 0 0 0 0 0 0 0 Phase 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Ό 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Cross correlation

^41,42 W 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 function

Table 14: Cross-correlation function of codes between different code groups in the first stage of Figure 2.

Compare Table 1 with the coding method in PCT/CN00/0028, even if it is only used so simple The single code extension matrix, under the same cross-correlation function "window" condition, the number of address codes provided by the present invention doubles, of course, we sacrifice the "zero correlation window" feature between the address codes in the group, The code length also increases a little (by 25%). The reason for the increase in code length is that the two generating units must be isolated in the spanning tree so that they do not interfere with each other. After adopting a more complex coding extension matrix, the spectrum efficiency and the "window" width of the wireless communication system using the address coding technique of the present invention are further improved.

In summary, the basic perfect complement code set in the initial "root" in the spanning tree completely determines the nature of the sets of address codes that are extended by the spanning tree. Such as:

1) In the spanning tree / (/ = 0, 1, 2, ...) phase, a total of 2 (' ⁺¹⁾ group codes are generated; there are M codes in each group, where M is the row of the coding extension matrix The length of each group of codes is ( + £ -1) χ 2' , where Ν is the length of the pair of basic orthogonal complementary codes, and L is the number of columns of the coding extension matrix.

2) The cross-correlation function between different code group address codes not only has a "zero correlation window" near the origin, but also a series of "zero correlation windows" outside the origin. The width and origin of these "zero correlation windows" The nearby "zero correlation window" is the same, that is, not less than twice the basic length of their common "root" minus one. There may be some correlation peaks between the "zero correlation windows", the number of peaks is not more than twice the number of columns (L) of the code extension matrix minus one (ie 2L-1).

3) The address code itself has a hidden diversity multiplicity equal to the number of weakly correlated random variables in the corresponding row of the coding extension matrix, and the maximum value is the number of columns L of the coding extension matrix. The actual coefficient has the largest hidden diversity multiplicity equal to the product of L and the amount of time spread of the actual channel in chips.

Step 5: Spanning Tree Transformation

Figure 1 shows only one of the most basic spanning trees. There are many types of spanning trees, but they are mathematically equivalent. Transforming the spanning tree can produce a large number of address code group variants. These transformations bring a lot of convenience to the engineering, because there are often many new and even wonderful properties between the code groups generated before and after the transformation, which can be adapted. Different engineering needs, such as networking needs, switching needs and even the need to expand capacity. Some of the main changes are listed below:

1. Exchange the location of the C code and the S code in the spanning tree;

2. Invert one of the C code or the S code in the spanning tree, or both.

3. Using the reverse sequence, the C and S codes are taken at the same time as the reverse sequence;

4. Interleaving the polarity of each code bit, such as keeping the odd digital bits unchanged, the even digital bits being inverted, or vice versa keeping the even digital bits unchanged, and the odd digital bits are inverted;

5. Perform a uniform rotation transformation on each code point in the complex plane. For example, a C code is ς ς Q ς , If each position is rotated by 72 degrees, that is, the rotation of one hook is turned into a bit rotation of 144 degrees, that is, even rotation

C ^{( +21ff)} ; If fi is rotated 216 degrees, that is, the rotation for three weeks is changed to C, e C ₂ e ^{J1⁄22+2, ff)} ,

; If each bit rotates 288 degrees, the change around the hook is C ₂ e ^M ^ C ( ⁺² ' ^ff ), C, e ^M ^ C ( ⁺⁷² °). Among them. , ξ „ ξ ₂ , ξ ₃ is any initial angle, the S code corresponding to the c code should also be the same rotation transformation, but the initial angle can be different from the C code. The above describes the whole cycle rotation, the non-integer cycle rotation It’s actually feasible, just keep it

The C code and the corresponding S code are rotated in the same way. After the rotation transformation, the correlation function "zero window, the position and the position of the peak will not change, but the polarity and magnitude of the relevant peak are related to the rotation angle.

6. In the spanning tree, re-arrange the C code with each "column" in the S code. The "column" here is the code in the basic perfect orthogonal complementary code group. For example, Figure 1 basically has four columns of C code and S code in the third stage of the tree. If C and S 2 are interchanged with the second and third columns, a new code group is obtained. 3b is shown.

In one case, if the C ( S ) code of a certain stage in the spanning tree has a P "column", the permutation transformation may have P !

Above we have only listed a few basic transformations, and there are many transformations that can be performed separately, continuously, or even jointly. Since there are so many types of transformations, the number of code groups that can be used in engineering before and after the transformation will be very large, which is an important feature of the wireless communication system using the present invention.

In engineering practice, the wireless communication system using the present invention must ensure that the C code can only be operated with the C code (including itself and others), and the S code must be associated with the S code (including itself and others). C code and S code are generally not allowed to meet. Therefore, special isolation measures should be adopted in engineering. For example, under certain propagation conditions, if two propagating polarized electromagnetic waves have synchronous fading, C and S codes can be used. Modulated separately on two mutually orthogonal polarized waves (horizontal and vertical polarized waves, left-handed and right-handed polarized waves); as another example, when the channel is fading over two or more codes for a long time When it is unchanged, the C and S codes can be placed in two time slots that do not overlap after transmission, and so on. In short, in order to ensure complementarity, the C and S codes must be synchronously faded during transmission and the two are not allowed to "meet,". These are the two most basic requirements. Of course, the information symbols on the C code and the S code must also be the same. .

One of the important features of the present invention is that the system's frequency effect is improved while increasing the system's hidden diversity. The rate will not only decrease, but will increase! This is mainly due to the use of "packet" coding techniques and the concept of related diversity. The so-called correlation diversity, as the name suggests, means that the fading between "subchannels" is related, that is, allowing partial overlap between "subchannels", so that when given channel "space" and system parameters, the possible diversity "heavy" The number will increase. Generally speaking, the performance of correlation diversity is inferior to uncorrelated diversity under the same diversity "heavy" number, but both theory and experiment have proved that as long as the correlation coefficient is not large, such as less than e-'s 0.37 Even 0.5. 5, this performance loss is negligible. For example, if the correlation coefficient is defined as 0.5, the relative diversity "heavy" number can be doubled relative to the irrelevant diversity. However, it is not advisable to excessively reduce the requirement for correlation to increase the apparent diversity number, because on the one hand, this will greatly increase the system complexity, and the actual effective diversity "heavy" number will increase less and less. Therefore, this practice must be moderate.

The present invention provides a multiple address coding technique in Code Division Multiple Access (CDMA) and other wireless communication systems. Unlike traditional address coding techniques, where each address code element (chip) is a fixed binary value (+ or -), a multivariate value, or a complex value. The address code elements (chips) used in the present invention are not necessarily fixed values but may be random variables or, more specifically, fading variables that produce random fluctuations after transmission over different "subchannels". Since fading exists only in three types of time, frequency and space, the address coding of the present invention is also referred to as time, space and frequency address coding.

The effect of the present invention is that there is a "zero correlation window" between the groups and groups of the encoded address codes, and each group of address codes is composed of several codes, and the autocorrelation and cross-correlation functions of the codes in the group are not It is required to have a "zero correlation window" characteristic. By virtue of the method of the present invention, the present invention can provide more address codes under the same conditions of "window, width". Conversely, under the same number of address codes, the present invention can provide a wider "window", thereby creating conditions for a greater increase in system capacity and spectral efficiency. The invention makes the encoded address code have high transmission reliability at the same time, that is, has a high hidden diversity multiplicity, and while increasing the hidden diversity multiplicity, the spectral efficiency of the system is not lowered but is increased or maintained. change. Since the present invention requires each address user to use a set of codes, although the autocorrelation function and the cross-correlation function between the codes in the group are not ideal, since the codes in the group are used by the same user, the channel fading characteristics are completely consistent. At the same time, the number of codes in the group is a fixed finite number, which will facilitate the multi-code joint detection and solve the complexity of joint detection in the traditional CDMA system.

The above specific embodiments are merely illustrative of the invention and are not intended to limit the invention.

Claims

Rights request

A packet encoding method for multiple address codes, which uses weakly correlated random variables or constants such as time, space, frequency, etc. as encoding elements, wherein the method comprises the following steps:

Select the basic perfect orthogonal complementary code dual;

Select a basic time, space, frequency coding extension matrix;

Forming a substantially perfect orthogonal complementary code group couple;

Transform generates *t.

2. The method of claim 1 wherein said selecting substantially perfect orthogonal complementary code duals further comprises the following specific steps:

According to the relationship N = N. X2'_; / ₌ 0,1,2".., determines the 3⁄4 of a perfect complementary code for the peas

According to the shortest code length determined by the above steps, and the requirements of the engineering implementation, an arbitrary code length is selected as the shortest code length N. (^code, C,=[c _n ,C _n ,...C _Wo ]

According to the requirement of complete complementarity of the autocorrelation function, mathematically solve the simultaneous equations to solve the code that is completely complementary to έ, ^ =[n...s _w . According to the shortest basic complementary code pair ( , s _} ) solved by the above steps, another pair of shortest basic complementary code pairs ( ₂ , s ₂ ) which are completely orthogonally complementary thereto are solved;

The code length is N. The perfect orthogonal complementary code dual forms the perfect orthogonal complementary code dual of the required length N = N ₀ x2 ^l (= 0, 1, 2, ...).

3. The method according to claim 1, wherein said selecting the substantially perfect orthogonal complementary code dual comprises the following specific steps:

According to the relationship ^^ ^ ^'; 〖 = 0,1,2,... determines the length of the two shortest basic perfect complementary codes, N ₀₂ ;

According to the shortest code length determined by the above steps, and the requirements of the project implementation, arbitrarily select a code length The shortest code length is N. C ₇ code, Cj

According to the requirement of complete complementarity of the autocorrelation function, mathematically solve the simultaneous equations to solve the problem with complete complementation _; code, ^ ^[Su, .,.^]; Repeat the above steps to solve two pairs ( C°/, ') and (c, έ ₂ ');

According to the shortest basic complementary code pair (<^, s _} ) solved by the above steps, another pairs of shortest basic complementary code pairs ( , s ₂ ) complementary to which they are completely orthogonally complementary are obtained;

The code length is N. The perfect orthogonal complementary code dual forms the perfect orthogonal complementary code dual of the required length N = 7^x2' (/ = 0,1,2,...).

4. The method according to claim 1 or 3, characterized in that the short code is concatenated according to the following steps, and a new perfect orthogonal complementary code dual that doubles in length can be obtained:

C ~ C j c 2, S ― S j s 2

5. A method according to claim 2 or 3, characterized in that the new perfect orthogonal complementary code pair is doubled in length by the following steps:

c _; (s _} ) The parity bits of the code are composed of ( _; ) and ₂ ) respectively; the parity bits of the c ₂ (s ₂ ) code are respectively

<^( ) and (5 ₂ 0^) are composed.

6. The method according to claim 2 or 3, characterized in that the short code is concatenated according to the following steps, and a new perfectly orthogonal complementary code pair doubled in length can be obtained:

C ₂ — C ₂ S _{2 2} = C ₂ 5^.

7. The method according to claim 2 or 3, characterized in that the following step is further used to obtain a new perfect orthogonal complementary code dual that is doubled in length:

C _; the parity bits of the code are respectively composed of and ^; S, the parity bits of the code are respectively composed of and ^;

(The parity of ₂ codes is composed of ^ and ^; the parity of the code is composed of ^ and ^ respectively.

8. Method according to claim 4 or 5 or 6 or 7, characterized in that the successive use of said steps results in a new perfect orthogonal complementary code pair of the desired length N.

9. The method according to claim 1, wherein said selecting a basic time, The spatial and frequency coding extension matrix also includes the following specific steps:

According to the size of the required zero correlation window ,, the number of columns L of the extension matrix is determined by the relationship Δ ≥ Λ 3⁄4 - 1 , where: Ν is the length of the perfect perfect orthogonal complementary code, L is the number of columns of the extended matrix, △ The unit is calculated in chips;

According to the complexity of the system and the requirements for improving the spectral efficiency, the number of codes in each group of address codes is determined, and Μ is the number of rows of the extended matrix;

10. The method according to claim 9, wherein the constructed basic coding extension matrix only needs to satisfy the following basic conditions:

The aperiodic and periodic autocorrelation functions of each row vector should have as small a pay peak as possible;

The aperiodic and periodic cross-correlation functions between the row vectors should have as small a pay peak as possible.

11. The method according to claim 9, wherein the constructed basic coding extension matrix may be a random matrix or a constant matrix, or even a constant.

12. Method according to claim 9 or 10, characterized in that the number of weakly related random elements in each row vector is the implicit diversity of the corresponding wireless communication system.

13. A method according to claim 9 or 10, characterized in that the quality of the autocorrelation function of the corresponding code in the window within the group is determined by the quality of the autocorrelation function of each row vector.

14. A method according to claim 9 or 10, characterized in that the quality of the cross-correlation function within the window between corresponding codes within the group is determined by the quality of the cross-correlation function between the rows of vectors.

15. The method of claim 1 wherein the substantially perfect orthogonal complementary code set is generated from a substantially perfect orthogonal complementary code dual and a basic time, spatial, frequency coded spreading matrix.

The method according to claim 1, wherein each of the expanded group address codes has an implicit diversity multiplicity corresponding to the type and number of random variables, and at the same time, cross-correlation between different code group address codes The function has a zero correlation window near the origin, and its window width is determined by the basic length of the perfect orthogonal complementary code pair.

17. The method of claim 1 'characterized by extending substantially perfect orthogonal complementarity The code group is performed according to the relationship of the spanning tree, wherein the properties of each group of address codes extended by the spanning tree are completely determined by the basic perfect complementary code group in the initial root in the spanning tree.

18. The method according to claim 1, wherein the transform spanning tree is a location for exchanging a spanning tree C code and an S code.

The method according to claim 1, wherein the transform spanning tree is performed by inverting one of a C code or an S code in a spanning tree, or both.

The method according to claim 1, wherein the transform spanning tree may be a reverse sequence, that is, the C and S codes are simultaneously taken in reverse sequence.

21. The method of claim 1, wherein the transform spanning tree is a polarity of interleaving code bits.

The method according to claim 1, wherein the transform spanning tree is configured to perform a uniform rotation transformation on each code bit in a complex plane.

The method according to claim 1, wherein the transform spanning tree is that the C code is synchronized with each column in the S code in a spanning tree, wherein the columns are substantially perfectly orthogonal The code in the complementary code group is a unit.

The method according to claim 1, wherein the address code is in units of groups, each group has a fixed number of codes, and the cross-correlation function between each group of address codes has a zero correlation window.

The method according to claim 1, wherein the address code has a high implicit diversity multiplicity, and the effective diversity multiplicity is equal to the number of random variables such as weak correlation time, space, frequency, etc. in the coding element. The product of the amount of channel time spread in units of chips within the window.

The method according to claim 1, wherein the address code is in units of groups, each of which has a plurality of codes, and the cross-correlation function of the codes between the groups has a zero correlation window characteristic.

27. The method according to claim 1, wherein the autocorrelation function of each code in the address code group and the cross-correlation function between codes do not require a certain ideal, and there is no requirement that a zero correlation window exists.

28. The method of claim 1 wherein the size of the cross-correlation zero correlation window between each address code group is adjustable.

The method according to claim 28, wherein the adjusting method is to adjust a length of a pair of substantially orthogonal complementary codes.

30. The method according to claim 28, wherein the adjusting method may be to adjust the number of columns of the basic time, space and frequency spreading matrix.

The method according to claim 28, wherein the adjusting method may be: adjusting a number of zero elements between the code generation tree coding extension matrix.

32. The method of claim 1 wherein the number of codes in each address code group is adjustable by adjusting the number of lines of the basic time, space, and frequency coded spreading matrix.

33. The method according to claim 1, wherein in the zero correlation window, the autocorrelation function of each code in each address code group is mainly determined by the autocorrelation of each row of the selected basic time, space and frequency coding extension matrix. Characteristic, the cross-correlation function between codes in a group mainly depends on the cross-correlation property between the corresponding rows of the selected time, space and frequency extension matrix.

34. The method according to claim 1, wherein, in addition to the zero correlation window, the autocorrelation and cross-correlation properties of each address code include autocorrelation and cross-correlation properties of each address code in the group, and are determined to be substantially positive. Complement the complementary code pair and the structure of the corresponding spanning tree.

The method according to claim 1, wherein the time, space and frequency coding extension matrix may be an arbitrary matrix.

36. The method according to claim 35, wherein the time, space and frequency coding extension matrix comprises: time and space; time and frequency; time, space, frequency, even constant matrix or constant.