CN101662304B - Method for designing zero correlation zone sequence on quadrature amplitude modulation constellation - Google Patents

Abstract

The invention discloses a method for designing a zero correlation zone sequence on a quadrature amplitude modulation constellation, belonging to the technical field of digital communication and mainly solving the problems that the prior zero correlation sequence family has few sequences, the transmission bits during each sequence period is very little and the zero correlation interval of the sequence is very small. The method comprises the following steps: constructing a 4-phasezero correlation zone sequence family by adopting a recursive mode through utilizing 4*4 order 4-phase compound Hadamard matrix; dividing the 4-zero-phase zero correlation zone sequence family into disjoint sequence sets, wherein each sequence set includes equal sequences; and constructing the zero correlation zone sequence family on the quadrature amplitude modulation constellation according to the disjoint sequence sets. With the method, the constructed sequence family has the advantages of large number of sequences, large transmission bits during each sequence period and large zero correlation interval; and the method can be applied to the fields of medium and large capacity digital microwave communication, wire television network high speed data transmission and satellite communication.

Description

Zero-correlation zone sequence method for designing on the quadrature amplitude modulation constellation

Technical field

This programme belongs to digital communication technology field, relates to the structure of the zero correlation sequence cluster on the quadrature amplitude modulation constellation, in can be applicable to, the field such as large capacity digital microwave communication, cable TV network high speed data transfer, satellite communication.

Background technology

Code division multiple access (Code Division Multiple Access, CDMA) is a major technique of 3-G (Generation Three mobile communication system).This technology is given the address code of different uniquenesses of user assignment, be a kind of allow different users at one time, the communication mode of working simultaneously on the same frequency spectrum.Code division multiple access has overcome the shortcoming of time division multiple access and frequency division multiple access, and the number of users of holding increases substantially.CDMA technology began for military communication in the forties in 20th century, began for cellular mobile communication and satellite communication system to the latter stage seventies.1993, the CDMA technology standard that the U.S. second generation cellular mobile communication standard I S-95 that the TIA of American Communications Association determines has adopted Qualcomm company to work out.CDMA technology also obtains using more and more widely in many fields such as transfer of data, satellite communication and remote-control romote-sensing, space communications except being applied to the mobile communication at present.

In cdma communication system, the correlation criterion of sequence is the engineening instruments of weighing sequences Design.People wish that the sequence of using in the cdma communication system should have desirable correlation properties, thereby the multiple access of eliminating cdma communication system disturbs (MAI), so that the performance of system reaches best.Particularly, the sequence that is applied to cdma communication system should have following correlation properties:

(1) auto-correlation function of each sequence is an impulse function, and namely except zero time delay, its value should be zero everywhere.

(2) cross-correlation function value of every pair of sequence is zero everywhere.

Described article one character is to being very important such as telemetry system, radar system and spread spectrum communication system.And concerning the system of a plurality of targets of while remote measurement, a plurality of terminal recognition system and code division multiple address communication system, second character is then even more important.Regrettably, no matter binary, polynary or sequence of complex numbers, theoretical circles show: the Spread Spectrum Sequence Set with this desirable correlation properties is non-existent.In order to solve the contradiction of desirable correlation properties and theoretical circles, also for the minimizing system to spreading code design with to the requirement of synchronization accuracy, people have proposed quasi-synchronous CDMA (QS-CDMA) system, and its synchronous error can be controlled within several chip period as required.The initial sequence of using all is traditional orthogonal sequence (Wash code) in the QS-CDMA system, and synchronous error is controlled in the chip.Along with going deep into gradually of zero correlation block (Zero Correlation Zone, ZCZ) sequencing theory, people recognize that can surpass the restriction of a chip and reach several chips maximum relative time delay in the QS-CDMA system.Therefore the ZCZ sequence also becomes the frequency expansion sequence of desirable QS-CDMA communication system, and the quality of ZCZ sequences Design is the problem that is directly connected to QS-CDMA systematic function quality.

With reference to Fig. 1, the principle that the ZCZ sequence is used for the QS-CDMA communication system is as follows: at first, each user is sent in the system through the data after the chnnel coding; Then, respectively with coming these data are carried out spread spectrum for the ZCZ sequence of each user assignment; Then, respectively these spread spectrum data are modulated, and the signal after will modulating is sent in the channel after merging and is transmitted; Afterwards, carry out demodulation at receiving terminal; At last, utilize respectively again the ZCZ sequence distribute to each user to carry out despreading, because the ZCZ sequence has desirable correlation properties in certain interval, for the quasi-synchronous CDMA system, just recovered the data that each user does not pass through channel decoding.

At present, for the research of ZCZ sequence sets, many achievements have been obtained.The people such as Fan Pingzhi have proposed the concept of zero correlation block (ZCZ) sequence sets, and aperiodic the orthogonal complement sequence ZCZ sequence sets has been constructed on the basis.Hayashi has used any a pair of Hadamard matrix construction binary ZCZ sequence sets.Although binary ZCZ sequence sets is compared easier realization on hardware with polynary sequence sets, the theoretical circles of binary ZCZ sequence sets only can reach half of polynary ZCZ sequence sets theoretical circles.Li Daoben has proposed a kind of building method of LA sequence, and this is actually a kind of ternary ZCZ sequence under strange correlation function meaning of Periodic correlation, aperiodic correlation function and cycle.Matsufuji has constructed ternary and polynary ZCZ sequence based on complete sequence.But there are following problems in present existing ZCZ sequence:

1, the sequence number in the sequence cluster has directly limited user's quantity in the cdma communication system very little.

2, the transferable bit information of each sequence period directly affects the information transfer rate of user in the cdma communication system very little.

3, too little between the zero correlation block of sequence, namely the interval of anti-multiple access interference is too little.

Summary of the invention

The object of the invention is to the deficiency for existence in the present zero-correlation zone sequence design, the building method of the zero correlation sequence cluster on a kind of quadrature amplitude modulation constellation has been proposed, with size between the zero correlation block of the number that increases sequence in the sequence cluster, information bit that each sequence period was transmitted and sequence, improve the communication performance of quasi-synchronous CDMA system.

Realize that the object of the invention technical scheme is: at first, utilize mutually Hadamard matrix again of 4 * 4 rank 4-, construct a kind of 4-phase zero-correlation zone sequence bunch; Then, this sequence cluster is divided into disjoint arrangement set, each arrangement set comprises the sequence of same number; At last, according to the zero-correlation zone sequence on the incompatible structure quadrature amplitude modulation of the sequence sets that the obtains constellation bunch.Concrete constitution step comprises:

(1) utilizes mutually Hadamard matrix again of 4 * 4 rank 4-, adopt the mode of recurrence to obtain 4-phase zero-correlation zone sequence bunch: S={s _p(t) | 1≤p≤2 ^N+2, 1≤t≤2 ²ⁿ⁺², n 〉=1,2 wherein ^N+2Be the quantity of sequence, 2 ²ⁿ⁺²Be the length of sequence, s _p(t) be among the S p sequence in the value at position t place;

(2) a 4-phase zero-correlation zone sequence bunch S is divided into Individual disjoint arrangement set: { g _q, 0≤q＜Q}, wherein $g_q=\left\{s_{p_i}^q\left(t\right)\right|1\≤i\≤m,1\≤t\≤2^{2n+2}\},$ The sequence number of m for comprising in each arrangement set, Be p among the sequence cluster S _iIndividual sequence is in the value at position t place;

(3) according to { g _q, 0≤q＜Q} obtains the zero-correlation zone sequence bunch on the quadrature amplitude modulation constellation:

${\mathrm{CQ}}_{M^2}=\left\{s(g_q,{\mathrm{\κ}}_q,t)\right|{\mathrm{\κ}}_q\∈Z_4^m,1\≤q\≤Q,1\≤t\≤2^{2n+2}\},$

Wherein $s(g_q,{\mathrm{\κ}}_q,t)=\sqrt{2j}\left(\underset{k=0}{\overset{m-1}{\mathrm{\Σ}}}{2}^k{s}_{n_k}^q\left(t\right)j^{{\mathrm{\κ}}_k^q}\right),$ κ _qBe 4 yuan of vectors of m dimension, κ _KqBe vectorial κ _qThe value at k place, middle position, j is imaginary unit,

Be p among the sequence cluster S _kIndividual sequence is in the value at position t place, 2 ²ⁿ⁺²Be sequence length.

The constellation point of described quadrature amplitude modulation constellation has M ²Individual, M=2 wherein ^m, m is set g _qThe number of middle sequence.

Described 4 * 4 rank 4-answer the Hadamard matrix mutually

$H\left(0\right)=\begin{array}{c}\end{array}\left(\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -j& 1\\ 1& -j& j& -1\\ 1& -1& -1& 1\end{array}\right),$ J wherein ²=-1.

Zero-correlation zone sequence on the described quadrature amplitude modulation constellation bunch ${\mathrm{CQ}}_{M^2}=\left\{s(g_q,{\mathrm{\κ}}_q,t)\right|{\mathrm{\κ}}_q\∈Z_4^m,1\≤q\≤Q,1\≤t\≤2^{2n+2}\}$ Sequence quantity be

The zero correlation siding-to-siding block length is 2 ⁿ-1.

Zero correlation sequence cluster on the designed quadrature modulation constellation of the present invention has following advantage:

1. the quantity of sequence is large, can increase power system capacity, has guaranteed that user's quantity can satisfy actual demand in the cdma communication system;

2. transferable bit information is more in a sequence period, be conducive to high speed data modulations, improved user in the cdma communication system the rate of information throughput;

3. the variable size of employed quadrature modulation constellation can be used in the cdma system transfer of data of variable bit rate in the reverse link;

4. larger between the zero correlation block of sequence, guaranteed the interval that has larger anti-multiple access to disturb in the cdma communication system;

5. the length of sequence is large, has increased the anti-attack ability of signal;

6. owing to adopted quadrature amplitude modulation, same user's modulation signal corresponding to different pieces of information bit has large Euclidean distance, can increase the reliability of communication.

Description of drawings

The quasi-synchronous CDMA system block diagram that Fig. 1 is traditional;

Fig. 2 the present invention constructs zero-correlation zone sequence flow chart on the quadrature amplitude modulation constellation;

Accurate synchronously QAM-CDMA system block diagram among Fig. 3 the present invention.

Embodiment

With reference to Fig. 2, the step that the present invention constructs zero-correlation zone sequence on the quadrature amplitude modulation constellation is as follows:

Step 1 is chosen 4 * 4 rank 4-and is answered mutually the Hadamard matrix.

Among the present invention selected 4 * 4 rank 4-mutually again the Hadamard matrix be:

$H^{\′}\left(0\right)=\begin{array}{c}\end{array}\left(\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -j& 1\\ 1& -j& j& -1\\ 1& -1& -1& 1\end{array}\right),$ J wherein ²=-1.

Step 2, structure 4-phase zero-correlation zone sequence bunch S.

4 * 4 rank 4-that utilize step 1 to choose answer the Hadamard matrix mutually, adopt the mode of recurrence to obtain 4-phase zero-correlation zone sequence bunch S, and concrete constitution step is as follows:

(2.1) according to (2 ^k* 4) * (2 ^k* 4) rank matrix H ' (k), structure (2 ^K+1* 4) * (2 ^K+1* 4) rank matrix H ' (k+1);

With (2 ^k* 4) * (2 ^k* 4) rank matrix H ' (k) be designated as:

$H^{\′}\left(k\right)=\left(\begin{array}{cccccc}{a}_{11}\left(k\right)& a_{12}\left(k\right)& \·& \·& \·& a_{1(2^k\×4)}\left(k\right)\\ a_{21}\left(k\right)& a_{22}\left(k\right)& \·& \·& \·& a_{2(2^k\×4)}\left(k\right)\\ \·& \·& & & & \·\\ \·& \·& \·& \·& \·& \·\\ \·& \·& & & & \·\\ a_{(2^k\×4)1}\left(k\right)& a_{(2^k\×4)2}\left(k\right)& \·& \·& \·& a_{(2^k\×4)(2^k\×4)}\left(k\right)\end{array}\right);$

0≤k≤n-1 wherein, n 〉=1;

(k) construct H ' extended matrix (k) according to H ': $H(k+1)=\left(\begin{array}{cc}{A}_{11}\left(k\right)& A_{12}\left(k\right)\\ A_{21}\left(k\right)& A_{22}\left(k\right)\end{array}\right),$ Wherein

A ₁₂(k)＝A ₂₁(k)，A ₁₁(k)＝A ₂₂(k)，

$A_{11}\left(k\right)=\left(\begin{array}{cccccc}{a}_{11}\left(k\right)a_{11}\left(k\right)& a_{12}\left(k\right)a_{12}\left(k\right)& \·& \·& \·& a_{1(2^k\×4)}\left(k\right)a_{1(2^k\×4)}\left(k\right)\\ a_{21}\left(k\right)a_{21}\left(k\right)& a_{22}\left(k\right)a_{22}\left(k\right)& \·& \·& \·& a_{2(2^k\×4)}\left(k\right)a_{2(2^k\×4)}\left(k\right)\\ \·& \·& & & & \·\\ \·& \·& \·& \·& \·& \·\\ \·& \·& & & & \·\\ a_{(2^k\×4)1}\left(k\right)a_{(2^k\×4)1}\left(k\right)& a_{(2^k\×4)2}\left(k\right)a_{(2^k\×4)2}\left(k\right)& \·& \·& \·& a_{(2^k\×4)(2^k\×4)}\left(k\right)a_{(2^k\×4)(2^k\×4)}\left(k\right)\end{array}\right);$

$A_{12}\left(k\right)=\left(\begin{array}{cccccc}\left({-a}_{11}\left(k\right)\right)a_{11}\left(k\right)& \left({-a}_{12}\left(k\right)\right)a_{12}\left(k\right)& \·& \·& \·& \left({-a}_{1(2^k\×4)}\left(i\right)\right)a_{1(2^k\×4)}\left(k\right)\\ \left({-a}_{21}\left(k\right)\right)a_{21}\left(k\right)& \left({-a}_{22}\left(k\right)\right)a_{22}\left(k\right)& \·& \·& \·& \left({-a}_{2(2^k\×4)}\left(i\right)\right)a_{2(2^k\×4)}\left(k\right)\\ \·& \·& & & & \·\\ \·& \·& \·& \·& \·& \·\\ \·& \·& & & & \·\\ \left({-a}_{(2^k\×4)1}\left(k\right)\right)a_{(2^k\×4)1}\left(k\right)& \left({-a}_{(2^k\×4)2}\left(k\right)\right)a_{(2^k\×4)2}\left(k\right)& \·& \·& \·& \left({-a}_{(2^k\×4)(2^k\×4)}\left(k\right)\right)a_{(2^k\×4)(2^k\×4)}\left(k\right)\end{array}\right)$

Note: a _Ij(k+1)=a _Ij(k) a _Ij(k), 1≤i, j≤2 ^k* 4,

$a_{(i+2^k\×4)(j+2^k\×4)}(k+1)=a_{\mathrm{ij}}\left(k\right)a_{\mathrm{ij}}\left(k\right),1\≤i,j\≤2^k\×4,$

$a_{(i+2^k\×4)j}(k+1)=\left({-a}_{\mathrm{ij}}\left(k\right)\right)a_{\mathrm{ij}}\left(k\right),1\≤i,j\≤2^k\×4,$

$a_{i(j+2^k\×4)}(k+1)=\left({-a}_{\mathrm{ij}}\left(k\right)\right)a_{\mathrm{ij}}\left(k\right),1\≤i,j\≤2^k\×4,$

Extended matrix H (k+1) is expressed as one (2 ^K+1* 4) * (2 ^K+1* 4) matrix H ' (k+1) be:

$H^{\′}(k+1)=\left(\begin{array}{cccccc}{a}_{11}(k+1)& a_{12}(k+1)& \·& \·& \·& a_{1(2^{k+1}\×4)}(k+1)\\ a_{21}(k+1)& a_{22}(k+1)& \·& \·& \·& a_{2(2^{k+1}\×4)}(k+1)\\ \·& \·& & & & \·\\ \·& \·& \·& \·& \·& \·\\ \·& \·& & & & \·\\ a_{(2^{k+1}\×4)1}(k+1)& a_{(2^{k+1}\×4)2}(k+1)& \·& \·& \·& a_{(2^{k+1}\×4)(2^{k+1}\×4)}(k+1)\end{array}\right);$

(2.2) according to 4 * 4 rank 4-that choose in the step 1 Hadamard matrix H ' (0) again mutually, adopt the method in the step (2.1), generator matrix H ' (1) recursively, H ' (2) ..., H ' (n) finally obtains (2 ⁿ* 4) * (2 ⁿ* 4) matrix H on rank ' (n), wherein, n 〉=1;

For example, for n=1, the matrix H that finally obtains ' (1) is:

$H^{\′}\left(1\right)=\left(\begin{array}{cccccccc}11& 11& 11& 11& (-1)1& (-1)1& (-1)1& (-1)1\\ 11& \mathrm{jj}& (-j)(-j)& (-1)(-1)& (-1)1& (-j)j& j(-j)& 1(-1)\\ 11& (-j)(-j)& \mathrm{jj}& (-1)(-1)& (-1)1& j(-j)& (-j)j& 1(-1)\\ 11& (-1)(-1)& (-1)(-1)& 11& (-1)1& 1(-1)& 1(-1)& (-1)1\\ (-1)1& (-1)1& (-1)1& (-1)1& 11& 11& 11& 11\\ (-1)1& (-j)j& j(-j)& 1(-1)& 11& \mathrm{jj}& (-j)(-j)& (-1)(-1)\\ (-1)1& j(-j)& (-j)j& 1(-1)& 11& (-j)(-j)& \mathrm{jj}& (-1)(-1)\\ (-1)1& 1(-1)& 1(-1)& (-1)1& 11& (-1)(-1)& (-1)(-1)& 11\end{array}\right)$

(2.3) with (2 ⁿ* 4) * (2 ⁿ* 4) the capable vector of rank matrix H ' (n) is regarded sequence as, obtains 4-phase zero-correlation zone sequence bunch, and its parameter is: sequence length is 2 ²ⁿ⁺², sequence quantity is 2 ^N+2, the zero correlation siding-to-siding block length is 2 ⁿ-1.

Step 3 is divided into a 4-phase zero-correlation zone sequence bunch S

Individual non-intersect+arrangement set.

From S, choose arbitrarily m not identical sequence composition sequence set g ₁, again from remaining 2 ^N+2Choose arbitrarily m not identical sequence composition sequence set g in-m the sequence ₂, the rest may be inferred, until the not enough m of remaining sequence number is individual among the S, marks off at most

Individual arrangement set, disjoint arrangement set that note marks off is { g _q, 1≤q≤Q}.

Step 4 is according to { g _q, 1≤q≤Q}, the zero-correlation zone sequence on the quadrature amplitude modulation constellation that obtains bunch is:

${\mathrm{CQ}}_{M^2}=\left\{s(g_q,{\mathrm{\κ}}_q,t)\right|{\mathrm{\κ}}_q\∈Z_4^m,1\≤q\≤Q,1\≤t\≤2^{2n+2}\},$

Wherein $s(g_q,{\mathrm{\κ}}_q,t)=\sqrt{2j}\left(\underset{k=0}{\overset{m-1}{\mathrm{\Σ}}}{2}^k{s}_{p_k}^q\left(t\right)j^{{\mathrm{\κ}}_k^q}\right),$ κ _qBe 4 yuan of vectors of m dimension, κ _k ^qBe vectorial κ _qThe value at k place, middle position, j is imaginary unit,

Be p among the sequence cluster S _kIndividual sequence is in the value at position t place.

In the present invention,

Be the zero-correlation zone sequence on the cluster quadrature amplitude modulation constellation, this sequence cluster has following properties: sequence period is 2 ²ⁿ⁺²Sequence cluster Can offer Individual user; Each user can transmit the 2m bit information at each sequence period; Be 2 between the zero correlation block of sequence ⁿ-1.This sequence cluster can be used in the quasi-synchronous CDMA system.

Designed sequence among the present invention is the zero-correlation zone sequence on the quadrature amplitude modulation constellation.Quadrature amplitude modulation be with two independently baseband digital signal two mutually orthogonal same frequency carrier waves are carried out suppressed-carrier double side band modulation, utilize the character of this modulated signal frequency spectrum quadrature in same bandwidth to realize the digital information transmission that two-way is parallel, it is the very high modulation system of a kind of frequency efficiency.

The constellation point composition set of quadrature amplitude modulation constellation a+bj|-N+1≤a, and b≤N-1, a, b odd}, wherein, N ²The size of set also is the number of the constellation point of this quadrature amplitude modulation constellation for this reason.Work as N=2 ⁿThe time, this quadrature amplitude modulation constellation is described to:

$\left\{\sqrt{2j}\left(\underset{k=0}{\overset{n-1}{\mathrm{\Σ}}}{2}^k{i}^{a_k}\right)\right|\∈Z_4\}$ Wherein

Expression 1+j.

The number of constellation points of the quadrature amplitude modulation constellation that uses in the present invention, is M ², M=2 wherein ^m, m is { g _q, the number of the sequence that each element comprises among 1≤q≤Q}.

Effect of the present invention can further specify by following test:

In traditional accurate synchro system, the design of ZCZ sequence and modulation system are irrelevant, and the zero-correlation zone sequence on the quadrature amplitude constellation among the present invention has also related to the content of modulation, and traditional quasi-synchronous CDMA system block diagram is inapplicable.

This tests the synchronous QAM-CDMA system block diagram of employed standard as shown in Figure 3.Process of the test is as follows:

(a) each user is sent in the system through the data of chnnel coding, the data of sending into are continuous 4 yuan of vectors of m dimension;

(b) respectively with for the zero correlation sequence on the quadrature amplitude of each user assignment the data of sending into system being carried out spread spectrum and quadrature amplitude modulation;

(c) transmit sending in the channel after the signal merging of each user through spread spectrum and after modulating;

(d) utilize the zero-correlation zone sequence on the quadrature amplitude modulation constellation of distributing to each user to carry out respectively to the received signal the demodulation expansion;

(e) obtain the data that each user does not pass through channel decoding.

Result of the test shows: in the synchronous QAM-CDMA of standard system, zero-correlation zone sequence on the quadrature amplitude modulation constellation that designs in the application of the invention, the number of users that system can hold is more, the data bit that each sequence period can transmit is more and variable, the noise robustness of system is better, and the anti-attack ability of system is stronger.

Claims (5)

1. the zero-correlation zone sequence method for designing on the quadrature amplitude modulation constellation comprises the steps:

(1) utilizes mutually Hadamard matrix again of 4 * 4 rank 4-, adopt the mode of recurrence to obtain 4-phase zero-correlation zone sequence bunch: S={s _p(t) | 1≤p≤2 ^N+2, 1≤t≤2 ²ⁿ⁺², n 〉=1,2 wherein ^N+2Be the quantity of sequence, 2 ²ⁿ⁺²Be the length of sequence, s _p(t) be among the S p sequence in the value at position t place;

(2) a 4-phase zero-correlation zone sequence bunch S is divided into

Individual disjoint arrangement set:

{ g _q, 0≤q＜Q}, wherein

The sequence number of m for comprising in each arrangement set,

Be p among the sequence cluster S _iIndividual sequence is in the value at position t place;

(3) according to { g _q, 0≤q＜Q} obtains the zero-correlation zone sequence bunch on the quadrature amplitude modulation constellation:

Wherein

к _qBe 4 yuan of vectors of m dimension,

Be vectorial к _qThe value at i place, middle position, j is imaginary unit, Be p among the sequence cluster S _iIndividual sequence is in the value at position t place, 2 ²ⁿ⁺²Be sequence length, M=2 ^m

2. sequences Design method according to claim 1, the constellation point of wherein said quadrature amplitude modulation constellation has M ²Individual, M=2 wherein ^m

3. sequences Design method according to claim 1, wherein said 4 * 4 rank 4-mutually again the Hadamard matrix be:

J wherein ²=-1.

4. sequences Design method according to claim 1, the described mutually Hadamard matrix again of 4 * 4 rank 4-that utilizes of step (1) wherein adopts the mode of recurrence to obtain 4-phase zero-correlation zone sequence bunch, carries out as follows:

(4.1) select 4 * 4 rank 4-to answer mutually Hadamard matrix H ' (0):

(4.2) according to (2 ^k* 4) * (2 ^k* 4) rank matrix H ' (k) is come structural matrix (2 ^K+1* 4) * (2 ^K+1* 4) rank matrix H ' (k+1), 0≤k≤n-1 wherein, n 〉=1;

(2 ^k* 4) * (2 ^k* 4) rank matrix H ' (k) be expressed as:

(k) construct H ' extended matrix (k) according to H ':

Wherein

A ₁₂(k)＝A ₂₁(k)，A ₁₁(k)＝A ₂₂(k)，

Note: a _lf (k+1)=a _lf (k) a _lf 1 (k) ,≤ l, f≤2 ^k* 4,

Extended matrix H (k+1) is expressed as one (2 ^K+1* 4) * (2 ^K+1* 4) matrix H ' (k+1):

(4.3) according to step (4.2), generator matrix H ' (1) recursively, H ' (2) ..., H ' (n) finally obtains (2 ⁿ* 4) * (2 ⁿ* 4) matrix H on rank ' (n), wherein, n 〉=1;

(4.4) with (2 ⁿ* 4) * (2 ⁿ* 4) the capable vector of rank matrix H ' (n) is regarded sequence as, obtains 4-phase zero-correlation zone sequence bunch, and its parameter is: sequence length is 2 ²ⁿ⁺², sequence quantity is 2 ^N+2, the zero correlation siding-to-siding block length is 2 ⁿ-1.

5. sequences Design method according to claim 1, the zero-correlation zone sequence on the wherein said quadrature amplitude modulation constellation bunch Sequence quantity be

The zero correlation siding-to-siding block length is 2 ⁿ-1.

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