CN1234221C - Coding method of multiuser bidimension combined complementary spread spectrum code used for radio communication - Google Patents

Abstract

The present invention relates to a coding method of multi-user two dimensional combined complementary spread spectrum codes used for wireless communication. When spread spectrum coding operation is carried out in multi-carrier code division multiple access communication, two complementary codes of which the length is two are set as a seed code pair, the length of the seed code pair is extended to M, and the seed code pair is arrayed to become a 2*M matrix; the matrix is transposed to obtain an M*2 transposed matrix which is extended to obtain an M*N fundamental row vector matrix; the number of users is set to be seven; when P is greater than one, P M*N' extended row vector matrixes are repeatedly generated, and an M*N'*P fundamental user matrix is obtained after stacking operation; when the number C of subcarriers in multiple carriers is greater than the length M of the extended seed codes, the M*N'*P fundamental user matrix is extended to obtain a C*N'*P multi-user two-dimensional combined spread spectrum code matrix. The method of the present invention has the advantages that the correlation functions of the spread spectrum codes in a multi-carrier system form zero correlation windows, the signal-to-noise ratio is increased, the transmission rate and the utilization rate of bandwidth are increased, the peak-to-average power ratio of multi-carrier signals is decreased, and the equipment cost is reduced.

Description

Be used for the coding method of the complementary spreading code of multi-user's two dimension associating of radio communication

Technical field the present invention relates to a kind of coding method that is used for the complementary spreading code of multi-user's two dimension associating of radio communication, belongs to wireless communication technology field.

There is a very big benefit in the existing MC-CDMA of background technology (hereinafter to be referred as MC-CDMA) system, it is exactly the transmission means that system adopts multicarrier, to be the data that serial sends originally, at first carry out serial to parallel conversion, convert parallel data to and be redistributed to each transmission simultaneously above carrier wave.Significant benefit of such system is exactly that the transfer rate of system is very high because adopted a large amount of subcarriers.In order further to improve the availability of frequency spectrum, generally adopt OFDM (hereinafter to be referred as OFDM) signal.Simultaneously on each subcarrier, adopt spread spectrum coding, improve the signal to noise ratio of system.If spreading code simultaneously as address code usefulness, can also further be distinguished the user.This has just formed MC-CDMA (MC-CDMA) system.

But said system is because bottom has adopted ofdm signal, so introduced the shortcoming of ofdm signal inevitably, is exactly that peak equal (PAR) is bigger than very.The peak-to-average force ratio of signal is meant the ratio of the peak power and the average power of transmission signals, if this ratio is very big, will cause serious consequence to follow-up signal amplifier.Amplifier has a linear dynamic range in work, if signal peak-to-average ratio is too big, then saturation distortion will take place.

Summary of the invention the objective of the invention is to propose a kind of coding method that is used for the complementary spreading code of multi-user's two dimension associating of radio communication, the spreading code that makes each carrier wave in the CDMA multiple carrier is as the row vector, form the two-dimensional matrix of a spreading code, two-dimensional encoded matrix is carried out special processing, make and two-dimensional encodedly not only on each subcarrier, have spread spectrum function, and can directly suppress the peak value of multi-carrier signal and the ratio of average, an and cover coding, under the prerequisite that does not increase system complexity, can realize the function of spread spectrum, multiple access, inhibition peak-to-average force ratio.

The coding method of the complementary spreading code of multi-user's two dimension associating that is used for radio communication that the present invention proposes comprises the steps:

When (1) carrying out spread spectrum coding in MC-CDMA communication, it is right for kind of subcode to establish length and be two mutual-complementing codes of 2, and this kind subcode is to being (--,-+), (+,--), (+-,--), (++,-+), (--,+-), (-+, ++), (+-, ++), any one in (++ ,+-);

(2) selected kind of subcode is right extended length is to M, M=2 ^m, m is a positive integer;

(3) with above-mentioned length be the mutual-complementing code of M to being arranged in the matrix of 2 * M, with this matrix transpose, obtain the transposed matrix of M * 2, with this transposed matrix expansion, obtain the basic row vector matrix of M * N, wherein N=2 ⁿ, n is a positive integer;

(4) establish the user and have P, P=2 ^P, p is a positive integer, when P=1, then carries out following step (5), when P greater than 1 the time, then repeat to generate P M * N ⁿExpansion row vector matrix, obtain M * N after piling up ⁿThe elemental user matrix of * P;

(5) as the sub-carrier number C in the multicarrier greater than above-mentioned expansion seed code length M the time, to M * N ⁿThe elemental user matrix of * P is expanded, and obtains C * N ⁿMulti-user's two dimension associating spreading code matrix of * P, wherein C=2 ^cM, c are positive integers.

The method that in the said method transposed matrix is expanded to the basic row vector matrix is: establish transposed matrix for by M length being 2 the vectorial matrix of forming of row, this M capable vector respectively is labeled as (C ₁, C ₂, C ₃..., C _M), it is carried out following expansion:

$(C_1\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,}{C}_2(-\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1}),C_3\stackrel{\&OverBar;}{C_4},C_4(-\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="C200310123848.500171.png"\; state="\{\{state\}\}">C</figure-callout>}}_3}),...,C_{M-1}\stackrel{\&OverBar;}{C_M},C_M(-\stackrel{\&OverBar;}{C_{M-1}}))$

Wherein, C ₁C ₂Expression cascade row vector C ₁And C ₂, C represents the inverted order with C, and-C represents C is got opposite sign, and the length of the row vector after the expansion is 4, repeats (n-1) inferior operation, obtains the basic row vector matrix of a M * N.

Said method with the method that the expansion of elemental user matrix generates multi-user's two dimension associating mutual-complementing code matrix is: rewrite i user's expansion row vector matrix as follows:

${\mathrm{\&Delta;}}^i\left(0\right)=\left[\begin{array}{c}{\mathrm{\&Delta;}}_1^i\left(0\right)\\ {\mathrm{\&Delta;}}_2^i\left(0\right)\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{\&Delta;}}_{N^n}^i\left(0\right)\end{array}\right]={\mathrm{\&Delta;}}^{i^T}$

Wherein, Δ _i ^j(O) be 1 * Metzler matrix, 1≤j≤N ⁿ, n is a positive integer,

Above-mentioned matrix is carried out iteration k time, obtain i user's two dimension associating mutual-complementing code matrix

1≤k≤c wherein, symbol " ο " expression is carried out cascade with two matrixes, c is a positive integer.

The coding method of the complementary spreading code of multi-user's two dimension associating that is used for radio communication that the present invention proposes, not only can make the correlation function of spreading code in the multicarrier system form zero correlation zone, improve signal to noise ratio, increase transmission rate and bandwidth availability ratio, can also reduce simultaneously the peak-to-average force ratio (it is following to be limited to 3dB) of multi-carrier signal, reduce the cost of follow-up radio frequency signal amplifiers greatly.Reduce the peak-to-average force ratio value, just reduced the linear dynamic range of required amplifier, reduced cost.

Finish code Design of the present invention, what at first relate to is exactly the selection of sign indicating number type.Up to the present, the spreading code that has had is a lot, as the simplest m sign indicating number, and Gold sign indicating number, mutual-complementing code or the like.In these sign indicating numbers, have only mutual-complementing code to have spread spectrum and two kinds of functions of restriction peak-to-average force ratio simultaneously.And generating mode is simple relatively.Therefore, the present invention has selected mutual-complementing code as the basic code type, generates " the complementary spreading code of two dimension associating ".When " two dimension associating complementary spreading code " of the present invention is applied in the actual MC-CDMA system, the two-dimensional encoded matrix that is generated, the sign indicating number of each row is corresponding to a carrier wave.The number of row vector and the number of carrier wave equate.All capable vectors are to be changed by one group of row vector the most basic to generate.The row vector that this group is the most basic is exactly a complementary code character in fact.The number of basic row vector, the number of users decision by system generally equals number of users.Such as, there are 1024 subcarriers in system, and encoder matrix just has 1024 row so.If 4 of system users just generate preceding 4 of encoder matrix earlier and go, be referred to as the basic row vector.Other the 5th row is all derived out by this 4 row basic row vector to the row vector of the 1024th row.But derive come what may, should guarantee that all column vector is of mutual-complementing code centering, does not promptly destroy the mutual-complementing code character of column vector.Like this, just can reach the effect that limits peak-to-average force ratio.Therefore, gained of the present invention is encoded into the shape of a two-dimensional matrix.On the row and column both direction, coding all forms the mutual-complementing code structure.

Description of drawings

Fig. 1 adopts one of the subscriber-coded matrix of list that the inventive method generates for example, wherein "+" expression 1, and "-" expression-1, row, column is mutual-complementing code, and code length is 16, basic row vector 4 row, sub-carrier number is 4, f ₁～f ₄Be corresponding subcarrier;

Fig. 2 be of the multi-user coding matrix that generates of the inventive method 4 encoder matrixs among the figure belong to user 1～user 4 from top to bottom successively for example, code length is 16, basic row vector 4 row, sub-carrier number is 4.

Fig. 3 is the functional image of " aperiodic auto-correlation and " that is encoded to single user's basic row vector of example with Fig. 1, and the encoder matrix in the upper left corner is user 1 a spreading code among the figure, and the left side is user 1 a matched filter banks.

Fig. 4 be with Fig. 2 be encoded to the example multi-user's basic row vector between " aperiodic cross-correlation and " functional image, the encoder matrix in the upper left corner is user 2 a spreading code among the figure, the left side is user 1 a matched filter banks.

Fig. 5 is the single user's two-dimensional expansion spreading code matrix schematic diagram that is encoded to example with Fig. 1.

Fig. 6 is the image (preceding 4 classify example as with what the encoder matrix among Fig. 5 began from the right, figure (a) is followed successively by the 1st to the 4th Fourier transform that is listed as that begins from the right to figure (d)) of the inverse Fourier transform of column vector among the present invention.

Fig. 7 is the comparison diagram of the code signal among not code signal and the present invention.Wherein figure (a) is code signal not, and figure (b) is the signal after encoding through the complementary spreading code of two dimension associating.

Fig. 8 is the schematic diagram of the two-dimensional encoded matrix displacement of the user among the present invention stack.

Fig. 9 is the generative process schematic diagram of the two-dimension code among the present invention.

Figure 10 is a MC-CDMA system transmitter full figure of the present invention.

Embodiment

The coding method of the complementary spreading code of multi-user's two dimension associating that is used for radio communication that the present invention proposes, when at first carrying out spread spectrum coding in MC-CDMA communication, it is right for kind of subcode to establish length and be two mutual-complementing codes of 2, this kind subcode to be (--,-+), (+,--), (+-,--), (++,-+), (--,+-), (-+, ++), (+-, ++), any one in (++ ,+-); The extended length that selected kind of subcode is right is to M, M=2 ^m, m is a positive integer; The mutual-complementing code that with length is M with this matrix transpose, obtains the transposed matrix of M * 2 to being arranged in the matrix of 2 * M, with this transposed matrix expansion, obtains the basic row vector matrix of M * N, wherein N=2 ⁿ, n is a positive integer; If the user has P, P=2 ^P, p is a positive integer, when P greater than 1 the time, then repeat to generate P M * N ⁿExpansion row vector matrix, obtain M * N after piling up ⁿThe elemental user matrix of * P; As the sub-carrier number C in the multicarrier greater than above-mentioned expansion seed code length M the time, to M * N ⁿThe elemental user matrix of * P is expanded, and obtains C * N ⁿMulti-user's two dimension associating spreading code matrix of * P.

The method that in the said method transposed matrix is expanded to the basic row vector matrix is: establish transposed matrix for by M length being 2 the vectorial matrix of forming of row, this M capable vector respectively is labeled as (C ₁, C ₂, C ₃..., C _M), it is carried out following expansion:

$(C_1\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,}{C}_2(-\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1}),C_3\stackrel{\&OverBar;}{C_4},C_4(-\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="C200310123848.500171.png"\; state="\{\{state\}\}">C</figure-callout>}}_3}),...,C_{M-1}\stackrel{\&OverBar;}{C_M},C_M(-\stackrel{\&OverBar;}{C_{M-1}}))$

Wherein, C ₁C ₂Expression cascade row vector C ₁And C ₂, C represents the inverted order with C, and-C represents C is got opposite sign, and the length of the row vector after the expansion is 4, repeats (n-1) inferior operation, obtains the basic row vector matrix of a M * N.

Said method with the method that the expansion of elemental user matrix generates multi-user's two dimension associating mutual-complementing code matrix is: rewrite i user's expansion row vector matrix as follows:

${\mathrm{\&Delta;}}^i\left(0\right)=\left[\begin{array}{c}{\mathrm{\&Delta;}}_1^i\left(0\right)\\ {\mathrm{\&Delta;}}_2^i\left(0\right)\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{\&Delta;}}_{N^n}^i\left(0\right)\end{array}\right]={\mathrm{\&Delta;}}^{i^T}$

Wherein, Δ _i ^j(0) is 1 * Metzler matrix, 1≤j≤N ⁿ, n is a positive integer,

Above-mentioned matrix is carried out iteration k time, obtain i user's two dimension associating mutual-complementing code matrix

1≤k≤c

Wherein, symbol " ο " expression is carried out cascade with two matrixes.

Introduce content of the present invention in detail below in conjunction with accompanying drawing.

Seeing also Fig. 1, is the example of a single user " the complementary spreading code of two dimension associating ".4 subcarriers of system, so two-dimension code also has only 4 row, length is 16.Simple in order to represent, with "+" expression " 1 ", with "-" expression " 1 ".The present invention is with specific algorithm, according to number of users, and the multipath transmisstion maximum delay, data transmission rate, the error rates etc. produce corresponding two-dimension code.Every row and every row all are mutual-complementing codes.Every capable spreading code correspondence sends above the subcarrier at one.

Seeing also Fig. 2, is the example of one group of multi-user " the complementary spreading code of two dimension associating ".4 users of system, each user's two-dimension code is quadrature each other, thus can send simultaneously, and use identical carrier wave (4 users' first provisional capital sends at first carrier, and second row sends at second carrier wave, and the like).Receiver one side, user's matched filter can be removed the interference of other yards fully by the orthogonality of sign indicating number.

Referring to Fig. 3 and Fig. 4, be respectively the two-dimensional spread-spectrum sign indicating number non-periodic autocorrelation function image of user 1 in 4 custom systems shown in Figure 2 and 2 couples of users' 1 of user two-dimensional spread-spectrum sign indicating number cross correlation image aperiodic.As can be seen, user's two-dimension code itself when passing through the matched filter of oneself, forms desirable spike impulse function, other user's two-dimension code, even enter this user's matched filter, output then can be desirable full null function.This has illustrated that in fact other users' signal can not influence this user's signal fully.

Referring to Fig. 5, be that the derive line number that forms of the vector of basic row as shown in Figure 1 that utilizes the inventive method to produce is 32 two-dimension code, be used for carrier number and be 32 situation.Original basic row vector is 4 row, can derive to 32 row by algorithm, and the mutual-complementing code character of row and column is constant.If multi-user's situation, multi-user's coding can be derived according to basic row vector separately simultaneously forms.

Referring to Fig. 6, be the example of two-dimensional encoded inverse Fourier transform image shown in Figure 5, with explanation with the encode peak-to-average force ratio of back signal of the inventive method.Enumerated from the right number the inverse Fourier transform of the coding of the 1st, 2,3,4 row respectively.Also gone out in one-period the average of signal after the conversion among the figure with the asterisk table, as we can see from the figure, the roughly limited situation of the peak-to-average force ratio of signal, strict mathematical computations shows that the peak-to-average force ratio of signal is limited to below the 3dB.

Referring to Fig. 7, be prior art encoded signal and with the comparison diagram of the inventive method coding back signal.The left side is an encoded signal, and the right is a code signal.Can find out significantly that the peak-to-average force ratio of encoded signal is very big, and the peak-to-average force ratio of code signal diminishes significantly.

As shown in Figure 8, illustrate that the method with the displacement stack sends the present invention's coding to improve the situation of user's data transfer rate.Can be shifted the figure place of stack by the decision of the maximum multipath time delay of system.The rule of concrete displacement is: whenever stagger one, just stack once.Be subscriber-coded displacement shown in Figure 12 times among the figure, 2 times situation superposes.Having formed an amplitude at last is many-valued coding, when such coding passes through user 1 matched filter, can form 3 desirable impulses.Like this, user's transmission rate has been enhanced 3 times.If original transmission rate is 1Mbps, then the transmission rate of the coding after the employing displacement stack is enhanced and is 3Mbps.

The correlation of mutual-complementing code by all code words in the complementary code character relevant after again addition produce, so in fact the designed two-dimension code of the present invention can be divided into the plurality of sub piece from top to bottom, each piece all be one by one group of matrix of forming of mutual-complementing code completely, promptly form by the basic row vector matrix and the matrix of deriving thereof.The encoder matrix that each piece is such will be modulated 1 Bit data.That is to say that in multicarrier system, user data is through behind the serial to parallel conversion, the number of parallel data should be the number of coded sub-blocks, and should not be the number of carrier wave.Such as, basic row vector matrix 4 row, just the code word number is 4 in the mutual-complementing code code character, carrier number 1024, then coded sub-blocks is exactly 256.User data should be 256 channel parallel datas behind serial to parallel conversion like this.

The generation method that has " the complementary spreading code of two dimension associating " of above-mentioned character among brief description the present invention.

See also Fig. 9, the method for generation had 5 steps:

The first step, preseting length are that two mutual-complementing codes of 2 are kind of a subcode.Such kind subcode comprises (--,-+) altogether, (+,--), (+-,--), (++,-+), (--,+-), (+, ++), (+-, ++), (++ ,+-).For example, can select kind of subcode is S ₁=(++) S ₂=(+-).

Second step is with S ₁And S ₂Extended length to M (M=2 ^m, m is a positive integer), for example, make S ₁=(++) S ₂=(+-), M=2 ³=8.It is expanded to S ' ₁=(++-+---+), S ' ₂=(+----+--).("+": 1; "-" :-1) S ' ₁And S ' ₂Can be considered to new S ₁And S ₂Proceed following algorithm.

The 3rd step is with S=(S ₁, S ₂) be expressed as the form of 2 * Metzler matrix, then S ^T=(S ₁, S ₂) ^TBe M * 2 matrixes, with S ^TContinue to expand to M * N matrix, be labeled as S ' .N=2 ⁿ, n is a positive integer.

Can be with S ^TRegard M length as and be the matrix that 2 sign indicating number is formed.With this M code labeling is (C ₁, C ₂, C ₃..., C _M)..With expanding of this M sign indicating number by as follows

$(C_1\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">C</figure-callout>}}_2,}{C}_2(-\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1}),C_3\stackrel{\&OverBar;}{C_4},C_4(-\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="C200310123848.500171.png"\; state="\{\{state\}\}">C</figure-callout>}}_3}),...,C_{M-1}\stackrel{\&OverBar;}{C_M},C_M(-\stackrel{\&OverBar;}{C_{M-1}}))$

Like this, Ma length becomes 2 ²=4. through (n-1) inferior similar operation, just obtained as what is desired the matrix S of a M * N '. for example, if M=N=2 ³=8, and continue to use second the step in S ₁' and S ₂'. obtain S ^TAnd S ' is as follows:

$S^T=\left[\begin{array}{cc}+& +\\ +& -\\ -& -\\ +& -\\ -& -\\ -& +\\ -& -\\ +& -\end{array}\right]$ $S^{\&prime;}=\left[\begin{array}{cccccccc}+& +& -& +& -& -& -& +\\ +& -& -& -& -& +& -& -\\ -& -& -& +& +& +& -& +\\ +& -& +& +& -& +& +& +\\ -& -& +& -& +& +& +& -\\ -& +& +& +& +& -& +& +\\ -& -& -& +& +& +& -& +\\ +& -& +& +& -& +& +& +\end{array}\right]=\mathrm{\&Delta;}$

Because matrix S ' very important effect is arranged in algorithm defines Δ=S '.

In the 4th step, the algorithm in this step in two kinds of situation

Situation one: if having only a user in the system, and code length N satisfies the requirement of sub-carrier number purpose, and algorithm directly entered for the 5th step.

Situation two: if a plurality of users are arranged in the system, the such matrix allocation of basic row vector matrix Δ that then must produce a plurality of similar unique users is given these users, is labeled as Δ ¹, Δ ²..., Δ ^P, establish P=M=N=2 ^m

Provide two kinds of building methods and generate M * N ⁿ, the matrix Δ ¹, Δ ²..., Δ ^P

Structure 1: look for earlier the orthogonal matrix A of a M dimension arbitrarily, its element constitutes by 1 and-1,

$A=\left[\begin{array}{c}{A}_1\\ {\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ A_M\end{array}\right]=\left[\begin{array}{cccc}{a}_{\mathrm{1,1}}& a_{\mathrm{1,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{1,M}\\ a_{\mathrm{2,1}}& a_{\mathrm{2,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{2,M}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ a_{M,1}& a_{M,2}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{M,M}\end{array}\right]$ $\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_{j,i}{a}_{k,j}=0$ (j≠k)

And then look for a similar orthogonal matrix BB=[b _{I, j}] b _{I, j}=1 or-1

Afterwards, derive M * M by matrix A and B ²Matrix C is as follows

$C=\left[\begin{array}{c}{C}_1\\ {\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ C_M\end{array}\right]=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,1}}{A}_1& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">A</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,M}{\mathrm{<figure-callout\; id="2"\; label="A\; M\; b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">A</figure-callout>}}_M& \\ b_{}{}_{\mathrm{2,1}}{A}_1& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">A</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,M}{A}_M\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ b_{M,1}{A}_1& b_{M,2}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">A</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& b_{M,M}{A}_M\end{array}\right]=\left[\begin{array}{cccccc}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">c</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">c</figure-callout>}}_{\mathrm{1,2}}& {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">\; <figure-callout\; id="3"\; label="c"\; filenames="C200310123848.500171.png"\; state="\{\{state\}\}">c</figure-callout>\; </figure-callout>}}_{\mathrm{1,3}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,M^2-1}& {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,M^2}\\ {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">c</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">c</figure-callout>}}_{2,2}& {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">\; <figure-callout\; id="3"\; label="c"\; filenames="C200310123848.500171.png"\; state="\{\{state\}\}">c</figure-callout>\; </figure-callout>}}_{\mathrm{2,3}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">c</figure-callout>}}_{2,M^2-1}& {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">c</figure-callout>}}_{2,{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ c_{M,1}& c_{M,2}& c_{M,3}& \&CenterDot;\&CenterDot;\&CenterDot;& c_{M,M^2-1}& c_{M,{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}\end{array}\right]$

Wherein, c _{I, j}=1 or-1.

Now, use M * N matrix Δ that above-mentioned the 3rd step obtains, its rewriting is as follows:

Δ＝[δ _i，j] δ _i，j＝i?or?-1

Wherein, N=M=2 ⁿ, Δ is a M * N matrix.

C and Δ obtain the following sign indicating number E of family by a kind of computing of following similar " matrix direct product " _{I, j}(i=1,2 ..., M; J=1,2 ..., N).

E _i，j＝(c _i，1δ _j，1?c _i，2δ _j，2，…，c _i，Nδ _j，N，

c _i，N-1δ _j，1?c _i，N+2δ _j，2，…，c _i，2Nδ _j，N

…

…

$\left.\begin{array}{cccc}{c}_{i,N^2-N+1}{\mathrm{\&delta;}}_{j,1}& c_{i,N^2-N+2}{\mathrm{\&delta;}}_{j,2}& \&CenterDot;\&CenterDot;\&CenterDot;& c_{i,{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}{\mathrm{\&delta;}}_{j,N}\end{array}\right)$

Can obtain by proof

Δi＝[E _i，1，E _i，2，…，E _i，N] ^T，1≤i≤P＝N＝M

So far, obtained distributing to P M * N of P user ²The matrix Δ ¹, Δ ²..., Δ ^PIf continue to adopt alternative manner, the dimension of this P matrix can be expanded to M * N ⁿ

Structure 2: suppose N=M=P, set an element and be any M orthogonal dimension matrix A of 1 or-1,

$A=\left[\begin{array}{c}{A}_1\\ {\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ A_M\end{array}\right]=\left[\begin{array}{cccc}{a}_{\mathrm{1,1}}& a_{\mathrm{1,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{1,M}\\ a_{\mathrm{2,1}}& a_{\mathrm{2,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{2,M}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ a_{M,1}& a_{M,2}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{M,M}\end{array}\right]$ $\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_{j,i}{a}_{k,j}=0$ (j≠k)

Directly use the M * N matrix Δ that obtains in above-mentioned the 3rd step, be rewritten as Δ=[δ _{I, j}] δ _{I, j}=1 or-1

By " Kronecker of matrix is long-pending ", obtain M ²* N matrix D is as follows

$D=\left[\begin{array}{c}{D}_1\\ {\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">D</figure-callout>}}_2\\ \&CenterDot;\\ \&CenterDot;\\ D_M\end{array}\right]A\&CircleTimes;\mathrm{\&Delta;}=\left[\begin{array}{cccc}{a}_{\mathrm{1,1}}\mathrm{\&Delta;}& a_{\mathrm{1,2}}\mathrm{\&Delta;}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{1,N}\mathrm{\&Delta;}\\ a_{2,1}\mathrm{\&Delta;}& a_{2,2}\mathrm{\&Delta;}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{2,N}\mathrm{\&Delta;}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ a_{M,1}\mathrm{\&Delta;}& a_{M,2}\mathrm{\&Delta;}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{M,N}\mathrm{\&Delta;}\end{array}\right]$

Set the orthogonal matrix B of the similar A of another one again

$B=\left[\begin{array}{c}{B}_1\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">B</figure-callout>}}_2\\ \&CenterDot;\\ \&CenterDot;\\ B_M\end{array}\right]=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,\mathrm{<figure-callout\; id="2"\; label="N\; b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">N</figure-callout>}}& \\ b_{}{}_{2,1}& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>\; </figure-callout>}}_{2,2}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,N}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ b_{M,1}& b_{M,2}& \&CenterDot;\&CenterDot;\&CenterDot;& b_{M,N}\end{array}\right]$ b _i，j＝1?or?-1

Each capable being together in series one by one of B is obtained the matrix that length is M * N:

$\tilde{B}=({\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">B</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">B</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="B"\; filenames="C200310123848.500171.png"\; state="\{\{state\}\}">B</figure-callout>}}_3...B_M)=({\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}...{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,\mathrm{<figure-callout\; id="2"\; label="N\; b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">N</figure-callout>}}{b}_{}{}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>\; </figure-callout>}}_{\mathrm{2,2}}...,b_{M,1}{b}_{M,2}...,b_{M,N})$

To above-mentioned M ²D in the * N matrix D _iBe rewritten as:

$D_i=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{1,1}}^i& {\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{1,2}}^i& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,\mathrm{MN}}^i\\ {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,1}^i& {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,\mathrm{MN}}^i\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ d_{M,1}^i& d_{M,2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& d_{M,\mathrm{NM}}^i\end{array}\right]$

So obtain

$=\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{1,1}}^i& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{1,2}}^i& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="N\; d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">N</figure-callout>}}{d}_{}^{}{}_{1,N}^i& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,N+1}^i& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">d</figure-callout>}}_{1,N+2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& b_{M,\mathrm{<figure-callout\; id="1"\; label="N\; d"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">N</figure-callout>}}{d}_{}^{}{}_{1,\mathrm{MN}}^i\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,1}^i& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,\mathrm{<figure-callout\; id="2"\; label="N\; d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">N</figure-callout>}}{d}_{}^{}{}_{2,N}^i& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,N+1}^i& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">d</figure-callout>}}_{2,N+2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& b_{M,\mathrm{<figure-callout\; id="2"\; label="N\; d"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">N</figure-callout>}}{d}_{}^{}{}_{2,\mathrm{NM}}^i\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,1}}{d}_{M,1}^i& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{1,2}}{d}_{M,2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C200310123848.500111.png,C200310123848.500121.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,N}{d}_{M,N}^i& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,1}}{d}_{M,N+1}^i& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="C200310123848.500171.png,C200310123848.500191.png"\; state="\{\{state\}\}">b</figure-callout>}}_{\mathrm{2,2}}{d}_{M,N+2}^i& \&CenterDot;\&CenterDot;\&CenterDot;& b_{M,N}{d}_{M,\mathrm{MN}}^i\end{array}\right]$

Because M=N, so produce P M * N ²The matrix Δ ¹, Δ ²..., Δ ^PIt is such that erect image is said in structure one, can expand Δ ¹, Δ ²..., Δ ^PDimension to M * N ⁿ

The 5th step: as the number C of subcarrier the time greater than M, must be with the matrix Δ ¹, Δ ²..., Δ ^PProceed expansion, make the row number of vectors become C by original M, satisfy C=2cM, c is a positive integer.Be labeled as Δ ¹', Δ ²' ..., Δ ^P'.

Extended method is as follows.

Rewrite the expansion row vector matrix Δ of user i ⁱAs follows

${\mathrm{\&Delta;}}^i\left(0\right)=\left[\begin{array}{c}{\mathrm{\&Delta;}}_1^i\left(0\right)\\ {\mathrm{\&Delta;}}_2^i\left(0\right)\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{\&Delta;}}_{N^n}^i\left(0\right)\end{array}\right]={\mathrm{\&Delta;}}^{i^T}$

Wherein, Δ _i ^j(0) is 1 * Metzler matrix, 1≤j≤N ⁿ, n is a positive integer.Wherein use " (k) " expression iterations, use Δ _i ^j(k) two dimension of the user i that obtains after expression iteration k time is united complementary spreading code matrix,

1≤k≤c

Wherein, symbol " ο " carries out cascade with two sign indicating numbers.

So far, generated " the complementary spreading code of two dimension associating " that the present invention needs.

Such coding in the MC-CDMA of reality system, will be modulated user data by coded sub-blocks.

Shown in Figure 10 is an application example of the inventive method, is the transmitter full figure of system, wherein (d ₁, d ₂..., d _k) be user data, at first through a precoder, the main effect of precoder is such: behind the original user data modulation two-dimension code, will destroy the complementary structure of two-dimension code, just can not play the effect of restriction peak-to-average force ratio.In order to keep the mutual-complementing code characteristic of modulation back two-dimension code, can add precoder.Such as, user's data is carried out the Walsh coding.Certainly, can keep the precoding of two-dimension code complementary type to also have a lot.

The serial data of precoder output enters serial-parallel converter, becomes and line output, and the number of parallel data equates with the number of coded sub-blocks, the coded sub-blocks Δ among the figure ₁, Δ ₂..., Δ _KExpression, parallel data b ₁, b ₂..., b _KMultiply each other with corresponding coded sub-blocks, the final two-dimension code of gained will send above the subcarrier at each respectively.

Figure 10 shows that the system transmitter schematic diagram, system receiver structure and transmitter architecture are opposite.

Figure 10 shows that single user structure, in the time of the multi-user, as long as the final two-dimension code of each user is sent on identical subcarrier.Satisfying under the situation of system requirements, the interference between the user is zero.

Spreading code obtained by the method for the present invention becomes the shape of two-dimensional matrix, by being made up of the pulse of polarity.Each row vector of encoder matrix all is a mutual-complementing code, and each column vector also is a mutual-complementing code.Each row coding, corresponding one road carrier wave.Encoder matrix is parallel transmission on multicarrier.In multicarrier transmission systems, the row vector of encoder matrix uses as spreading code, can utilize all advantages of mutual-complementing code spread spectrum.Column vector then can be utilized the characteristics of mutual-complementing code reduction multi-carrier signal peak equal ratio, limits the peak-to-average force ratio of multi-carrier signal.This encoding scheme has been finished above-mentioned two functions simultaneously.

The coding that the inventive method generated is not limited to that only to comprise amplitude be 1 and-1 dual code, and comprises amplitude and phase place is many-valued multi-element code.This two-dimension code can be shifted and send after the stack, and two-dimensional encoded notion is not limited to mutual-complementing code, can also be generalized to other codings, for example the column vector of encoder matrix is extended to wood and reins in sign indicating number (Reed-Muller).

Claims (3)

1, a kind of coding method that is used for the complementary spreading code of multi-user's two dimension associating of radio communication is characterized in that this method comprises the steps:

When (1) carrying out spread spectrum coding in MC-CDMA communication, it is right for kind of subcode to establish length and be two mutual-complementing codes of 2, and this kind subcode is to being (--,-+), (+,--), (+-,--), (++,-+), (--,+-), (-+, ++), (+-, ++), any one in (++ ,+-);

(2) selected kind of subcode is right extended length is to M, M=2 ^m, m is a positive integer;

(3) with above-mentioned length be the mutual-complementing code of M to being arranged in the matrix of 2 * M, with this matrix transpose, obtain the transposed matrix of M * 2, with this transposed matrix expansion, obtain the basic row vector matrix of M * N, wherein N=2 ⁿ, n is a positive integer;

(4) establish the user and have P, P=2 ^P, p is a positive integer, when P=1, then carries out following step (5), when P greater than 1 the time, then repeat to generate P M * N ⁿExpansion row vector matrix, obtain M * N after piling up ⁿThe elemental user matrix of * P;

(5) as the sub-carrier number C in the multicarrier greater than above-mentioned expansion seed code length M the time, to M * N ⁿThe elemental user matrix of * P is expanded, and obtains C * N ⁿMulti-user's two dimension associating spreading code matrix of * P, wherein C=2 ^cM, c are positive integers.

2, the method described in claim 1 is characterized in that the method that in the step (3) transposed matrix is expanded to the basic row vector matrix is: establish transposed matrix for by M length being 2 the vectorial matrix of forming of row, this M capable vector respectively is labeled as (C ₁, C ₂, C ₃..., C _M, it is carried out following expansion:

$(C_1\stackrel{\&OverBar;}{C_2},C_2(-\stackrel{\&OverBar;}{C_1}),C_3\stackrel{\&OverBar;}{C_4},C_R(-\stackrel{\&OverBar;}{C_3}),...,C_{M-1}{C}_M(-\stackrel{\&OverBar;}{C_{M-1}}))$

Wherein, C ₁C ₂Expression cascade row vector C ₁And C ₂, C represents the inverted order with C, and-C represents C is got opposite sign, and the length of the row vector after the expansion is 4, repeats (n1) inferior operation, obtains the basic row vector matrix of a M * N.

3, the method described in claim 1 is characterized in that the method that in the step (5) expansion of elemental user matrix is generated multi-user's two dimension associating mutual-complementing code matrix is: rewrite i user's expansion row vector matrix as follows:

${\mathrm{\&Delta;}}^i\left(0\right)=\left[\begin{array}{c}{{\mathrm{\&Delta;}}^i}_1\left(0\right)\\ {{\mathrm{\&Delta;}}^i}_2\left(0\right)\\ \&CenterDot;\\ \&CenterDot;\\ {{\mathrm{\&Delta;}}^i}_{N^n}\left(0\right)\end{array}\right]={\mathrm{\&Delta;}}^{i^T}$

Wherein, Δ ⁱ _j(0) is 1 * Metzler matrix, 1≤j≤N ⁿ, n is a positive integer,

Above-mentioned matrix is carried out iteration k time, obtain i user's two dimension associating mutual-complementing code matrix

Wherein, symbol " ο " expression is carried out cascade with two matrixes, and c is a positive integer.

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