CN103023836B - The generation method of three value zero cross-correlation region sequences and device - Google Patents

Abstract

The invention discloses the generation method of three value zero cross-correlation region sequences and device, belong to communication system signal and set juice technical field.The present invention is based on the long-pending arrangement set with block interleaved computing acquisition with three different in width zero cross-correlation districts of displacement Kronecker of DFT sequence matrix.The three value zero cross-correlation region sequence set generated are divided into multiple sequence set, and each sequence set is divided into again multiple sequence subgroup, and the sequence in sequence subgroup, between sequence subgroup and between sequence set has different in width zero cross-correlation district.Arrangement set and its each sequence set all reach the theoretical boundary of sequential design, can provide, for code division multiple address communication system, the address code sequence suppressing intersymbol interference, it is also possible to for ofdm communication system time/frequency synchronize and channel estimation etc. provide needed for training sequence and reference signal.

Description

The generation method of three value zero cross-correlation region sequences and device

Technical field

The invention belongs to communication system signal design field, be specifically related to a kind of generation method of three value zero cross-correlation region sequence collection suitable in wireless communication system AF panel.

Background technology

As sequential design and most important two factors in application, correlated performance and mutually restricting between both sequence number, contradiction each other.How they are carried out the balance of the best, be always up the problem that people are concerned about and endeavour research.There is by sacrificing certain sequence number the zero-correlation zone sequence of the desirable correlated performance in local, it is possible to the code division multiple access system for near-synchronous suppresses intersymbol interference effectively.But, as a class unique sequence (such as gold sequence and Walsh-Hadamard orthogonal sequence etc.), Welch circle has illustrated such sequence can not obtain completely desirably cycle and aperiodic dependency.Although complementary series can have completely desirably dependency, but the sequence number in such arrangement set is extremely limited, and namely the number of complementary series is not more than in each complementary series the number of subsequence.

Optimizing compromise in order to obtain between correlated performance and sequence number, it is a kind of effective method that arrangement set carries out careful packet.Tradition zero-correlation zone sequence is grouped, the arrangement set then obtained will have the zero correlation block (X.H.Tang of multiple different in width, P.Z.Fan, andJ.Lindner, MultiplebinaryZCZsequencesetswithgoodcross-correlationpr opertybasedoncomplementarysequencesets, IEEETrans.Inf.Theory, vol.56, no.8, pp.4038-4045, Aug.2010).Although owing to the reason of unique sequence limits the acquisition of desirable correlated performance, but this arrangement set has had correlated performance more better than single zero-correlation zone sequence set under the premise of identical sequence number.The tectonic ideology of packet is applied to complementary series, then can also obtain greater number of sequence (A.RathinakumarandA.K.Chaturvedi, Anewframeworkforconstructingmutuallyorthogonalcomplement arysetsandZCZsequences, IEEETrans.onInf.Theory, vol.52, no.8, pp.3817-3826, Aug.2006).For having the complementary series of zero correlation block, i.e. Z-complementary series (P.Z.Fan, W.N.YuanandY.F.Tu, Z-complementarybinarysequences, IEEESignalProcess.Lett., vol.14, no.8, pp.509-512, Aug.2007), the zero correlation block of multiple different in width is produced, it is also possible to effectively increase the available sequences number in arrangement set, and desirable correlated performance can be kept between some particular sequence by packet transaction.

If $U={\left\{U_i\right\}}_{i=0}^{M-1}={\left\{{\left\{U_{i,r}\right\}}_{r=0}^{N-1}\right\}}_{i=0}^{M-1}={\left\{{\left\{{\left(U_{i,r}\left(l\right)\right)}_{l=0}^{L-1}\right\}}_{r=0}^{N-1}\right\}}_{i=0}^{M-1}$ Being a Z-complementary series set, sequence number is M, and subsequence number is N, and sub-sequence length is L, then meet|τ|≤Z_C-l, i ≠ j and $\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_{U_{i,r},U_{i,r}}\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{E}_{U_{i,r}},\mathrm{\&tau;}=0\\ \mathrm{0,1}\&le;\left|\mathrm{\&tau;}\right|\&le;Z_A-1\end{array}\right.,$ WhereinRepresent U_{I, r}Power,For cross-correlation function aperiodic, meet ${\mathrm{\&psi;}}_{U_{i,r},U_{j,r}}\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}\underset{l=0}{\overset{L-1-\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}{U}_{i,r}\left(l\right)\&CenterDot;{U_{j,r}}^{*}(l+\mathrm{\&tau;}),0\&le;\mathrm{\&tau;}\&le;L-1\\ \underset{l=0}{\overset{L-1+\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}{U}_{i,r}(l-\mathrm{\&tau;})\&CenterDot;{U_{j,r}}^{*}\left(l\right),1-L\&le;\mathrm{\&tau;}<0\\ 0,\left|\mathrm{\&tau;}\right|\&GreaterEqual;L\end{array}\right.,$ Symbol * represents complex conjugate.As i=j,Become non-periodic autocorrelation function.Z_AAnd Z_CRepresent the monolateral zero auto-correlation sector width of Z-complementary series set U and monolateral zero cross-correlation sector width respectively.Any one Z-complementary seriesEach subsequence can be regarded as unique sequence form, then multiple unique sequencesBetween intertexture can be expressed as U_{I, 0}⊙U_{I, 1}⊙…⊙U_{I, N-1}=(U_{I, 0}(0), U_{I, 1}(0) ..., U_{I, N-1}(0), U_{I, 0}(1), U_{I, 1}(1) ..., U_{I, N-1}(1) ..., U_{I, 0}(L-1), U_{I, 1}(L-1) ..., U_{I, N-1}(L-1))。

Visible, Z-complementary series remains the attribute that conventional complementary sequence is made up of multiple subsequences, and therefore when processing gain is identical with sequence number, such sequence will have more excellent performance than unique sequence.If application packet set juice method, then can obtain the Z-complementary sequence set with multiple different zero correlation blocks further, and can obtain between some sequence the desirable cycle and aperiodic correlated performance.Chinese patent CN102291197 gives the generation method of orthogonal complement sequence sets between group, to some extent solves the deficiency of conventional complementary sequence number.But, such sequence only has two value zero cross-correlation districts, therefore can be subject to certain restrictions in the design of sequential parameter and the practical application of sequence.

Summary of the invention

It is an object of the invention to the optimization compromise obtaining between correlated performance and sequence number according to system actual demand, power system capacity limitation problem is solved under the premise ensureing certain systematic function, long-pending and the intertexture computing by the displacement Kronecker of discrete Fourier transform (DFT) sequence matrix, it is provided that a kind of generation method of arrangement set with three value zero cross-correlation districts and device.

According to first aspect, generation method and the device of the three value zero cross-correlation region sequences of the present invention include:

The selected DFT sequence order of matrix number of actual requirement based on power system capacity and processing gain, then this DFT sequence matrix and himself carry out displacement Kronecker amass, then carry out direct Kronecker with the new sequence matrix obtained for coefficient and former DFT sequence matrix to amass and block interleaved computing, finally obtained sequence matrix is carried out packet numbering, thus obtaining the zero correlation block of three different in width between each sequence subgroup between each sequence set and in sequence set.

According to second aspect, the generation method of the three value zero cross-correlation region sequences of the present invention and device, comprise the following steps:

A) according to actual requirements such as the power system capacity of wireless communication system, processing gain and zero correlation block width, it is determined that DFT sequence matrixExponent number N, whereinEvery a line in this matrix is considered as a unique sequence, and line n sequence can be expressed as

B) DFT sequence matrix F is amassed with the Kronecker himself carrying out shifting, obtain a N²×N²The coefficient matrix of dimension $E=\left[E^{\left(0\right)}\right|E^{\left(1\right)}|...|E^{(N-1)}],$ M-th submatrix $E^{\left(m\right)}={\left[E_{\mathrm{gN}+r,s}^{\left(m\right)}\right]}_{g,r,s=0}^{N-1}$ Dimension be N²× N, wherein 4 footmark variablees meet m, g, r, s=0,1 ..., N-1.The element of the gN+r row s row of this submatrixWherein ()_NRepresent modulo-N arithmetic；

C) to coefficient matrix E=[E⁽⁰⁾E⁽¹⁾|…|E^(N-1)] and DFT sequence matrixIt is made directly Kronecker to amass, it is thus achieved that a dimension is N³×N³Sequence matrix

D) successively by N³×N³In dimension every a line of sequence matrix D, the N number of element of continuous print regards a unique sequence as, then altogether comprise N in every a line²Individual unique sequence；

E) the N of a line every in sequence matrix D²Individual unique sequence forms one group of sequence according to N continuous, then every a line comprises N group sequence, often organizes and comprises the unique sequence that N number of length is N；

F) sequence in a line every in sequence matrix D same group is interleaved computing, then after computing, every a line comprises N number of unique sequence, and the length of each unique sequence is N², the sequence matrix obtained is three value zero cross-correlation region sequence matrix (arrangement set) C.

According to above-mentioned generation step, the three value zero cross-correlation region sequence set C obtained have the feature that

1) arrangement set C comprises N altogether³Individual Z-complementary series, each Z-complementary series comprises N number of subsequence, and the length of each subsequence is N², therefore the processing gain of this sequence sets is N³；

2) N that arrangement set C comprises³Individual Z-complementary series is divided evenly into N number of sequence set, and each sequence set is divided evenly into N number of sequence subgroup, comprises N number of Z-complementary series in each sequence subgroup；

3) C is made_{G, r, n}Represent in three value zero cross-correlation region sequence set C in the g sequence set the n-th Z-complementary series, then C in the r sequence subgroup_{G, r, n}Corresponding to step F) in gN+rN+n line order row in the sequence matrix C that obtains, wherein g, r, n=0,1 ..., N-1；

4) all N³Individual Z-complementary series all has the monolateral zero auto-correlation district that width is N；

5) in different sequence set, monolateral zero cross-correlation sector width between sequence is 1, namely mutually orthogonal；

6) in same sequence set in different sequence subgroups monolateral zero cross-correlation sector width between sequence equal to the length N of subsequence², namely there is desirable cross-correlation performance；

7) the monolateral zero cross-correlation sector width between the sequence in same sequence subgroup is N, and this value is equal with monolateral zero auto-correlation sector width；

8) three value zero cross-correlation region sequence set C and whole N number of sequence set thereof all reach the theoretical circles of sequential design, and namely they are all desirable.

The above-mentioned steps A of the present invention)-F) produced by as characterized above 1)-8) and three value zero cross-correlation region sequence set C have 1, N, N²Zero cross-correlation district of three different in width, it is possible to the address code sequence suppressing intersymbol interference is provided for code division multiple address communication system, it is also possible to for ofdm communication system time/frequency synchronize and channel estimating etc. provide needed for training sequence and reference signal.

Accompanying drawing explanation

Fig. 1 is the installation drawing that the present invention generates three value zero cross-correlation region sequences；

Fig. 2 is the schematic diagram that the present invention generates the N rank DFT sequence matrix F of module 2 in installation drawing 1；

Fig. 3 is the schematic diagram long-pending for displacement Kronecker that the present invention generates module 4 in installation drawing 1；

Fig. 4 be the present invention generate the direct Kronecker of module 5 in installation drawing 1 long-pending schematic diagram；

Fig. 5 is the schematic diagram that the present invention generates the intertexture computing of module 7 in installation drawing 1；

Fig. 6 is Z-complementary series C in the three value zero cross-correlation region sequence set that the present invention generates in example 1_0,0,0Normalization non-periodic autocorrelation function Distribution value figure, non-periodic autocorrelation function has the monolateral zero auto-correlation district that width is N=2；

Fig. 7 is two Z-complementary series C in the three value zero cross-correlation region sequence set that the present invention generates in example 1_0,0,0And C_0,0,1Between normalization cross-correlation function value aperiodic scattergram, cross-correlation function aperiodic in sequence subgroup has the monolateral zero cross-correlation district that width is N=2；

Fig. 8 is two Z-complementary series C in the three value zero cross-correlation region sequence set that the present invention generates in example 1_0,0,0And C_0,1,0Between normalization cross-correlation function value aperiodic scattergram, cross-correlation function aperiodic between different sequence subgroups in same sequence set is equal to 0 in any displacement, has cross-correlation performance desirable aperiodic between display the two sequence；

Fig. 9 is two Z-complementary series C in the three value zero cross-correlation region sequence set that the present invention generates in example 1_0,0,0And C_1,1,1Between normalization cross-correlation function value aperiodic scattergram, between different sequence set aperiodic cross-correlation function in zero shift equal to 0, mutually orthogonal between display the two sequence, namely between group, sequence is orthogonal.

Detailed description of the invention

Below in conjunction with drawings and Examples, technical scheme is further described below:

Example 1

The present embodiment according to system requirements, design a number of users and processing gain be equal to 8 three value zero cross-correlation region sequence set C.Then can determine that the exponent number of DFT sequence matrix F is N=2, the sequence number of set C is 8, and subsequence number is 2, and sub-sequence length is 4.

The flow process shown in installation drawing 1 is generated, first selected 2 rank DFT sequence matrixes according to the present invention $F=\left[\begin{array}{c}{F}_0\\ F_1\end{array}\right]=\left[\begin{array}{cc}{F}_{\mathrm{0,0}}& F_{\mathrm{0,1}}\\ F_{\mathrm{1,0}}& F_{\mathrm{1,1}}\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],$ And F is circulated up displacement according to each row, obtain shift sequence matrix $F^{\&prime;}=\left[\begin{array}{c}{F}_1\\ F_0\end{array}\right]=\left[\begin{array}{cc}{F}_{\mathrm{1,0}}& F_{\mathrm{1,1}}\\ F_{\mathrm{0,0}}& F_{\mathrm{0,1}}\end{array}\right]=\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right].$ Herein, because F only has two row, so only upward displacement is once.

According to Fig. 3, DFT sequence matrix F and its shift sequence matrix F ' are carried out displacement Kronecker and amasss, it is thus achieved that the coefficient matrix E=[E of 4 × 4⁽⁰⁾|e⁽¹⁾], wherein $E^{\left(0\right)}=\left[\begin{array}{cc}{E}_{\mathrm{0,0}}^{\left(0\right)}& E_{\mathrm{0,1}}^{\left(0\right)}\\ E_{\mathrm{1,0}}^{\left(0\right)}& E_{\mathrm{1,1}}^{\left(0\right)}\\ E_{\mathrm{2,0}}^{\left(0\right)}& E_{\mathrm{2,1}}^{\left(0\right)}\\ E_{\mathrm{3,0}}^{\left(0\right)}& E_{\mathrm{3,1}}^{\left(0\right)}\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& -1\\ 1& 1\\ 1& -1\end{array}\right],$ $E^{\left(1\right)}=\left[\begin{array}{cc}{E}_{\mathrm{0,0}}^{\left(1\right)}& E_{\mathrm{0,1}}^{\left(1\right)}\\ E_{\mathrm{1,0}}^{\left(1\right)}& E_{\mathrm{1,1}}^{\left(1\right)}\\ E_{\mathrm{2,0}}^{\left(1\right)}& E_{\mathrm{2,1}}^{\left(1\right)}\\ E_{\mathrm{3,0}}^{\left(1\right)}& E_{\mathrm{3,1}}^{\left(1\right)}\end{array}\right]=\left[\begin{array}{cc}1& -1\\ 1& 1\\ -1& 1\\ -1& -1\end{array}\right].$

Then, according to Fig. 4, coefficient matrix E and DFT sequence matrix F carried out direct Kronecker and amass, obtain 8 × 8 sequence matrix as follows,

$D=E\&CircleTimes;F=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& -1& -1\\ 1& -1& 1& -1& 1& -1& -1& 1\\ 1& 1& -1& -1& 1& 1& 1& 1\\ 1& -1& -1& 1& 1& -1& 1& -1\\ 1& 1& 1& 1& -1& -1& 1& 1\\ 1& -1& 1& -1& -1& 1& 1& -1\\ 1& 1& -1& -1& -1& -1& -1& -1\\ 1& -1& -1& 1& -1& 1& -1& 1\end{array}\right].$

Finally, according to Fig. 5, sequence matrix D is carried out block interleaved computing, obtains three value zero cross-correlation region sequence matrixes as follows,

$C=\left[\begin{array}{c}{C}_{\mathrm{0,0,0}}\\ C_{\mathrm{0,0,1}}\\ C_{\mathrm{0,1,0}}\\ C_{\mathrm{0,1,1}}\\ C_{\mathrm{1,0,0}}\\ C_{\mathrm{1,0,1}}\\ C_{\mathrm{1,1,0}}\\ C_{\mathrm{1,1,1}}\end{array}\right]=\left[\begin{array}{ccccccccc}1& 1& 1& 1& ;& 1& -1& 1& -1\\ 1& 1& -1& -1& ;& 1& -1& -1& 1\\ 1& -1& 1& -1& ;& 1& 1& 1& 1\\ 1& -1& -1& 1& ;& 1& 1& -1& -1\\ 1& 1& 1& 1& ;& -1& 1& -1& 1\\ 1& 1& -1& -1& ;& -1& 1& 1& -1\\ 1& -1& 1& -1& ;& -1& -1& -1& -1\\ 1& -1& -1& 1& ;& -1& -1& 1& 1\end{array}\right].$

Visible, three value zero cross-correlation region sequence set (sequence matrix) C obtained comprise 2 sequence set altogether, each sequence set comprises 2 sequence subgroups, comprises 2 Z-complementary seriess in each sequence subgroup, and each Z-complementary series is made up of 2 sub-sequences.Therefore, set C comprises 8 Z-complementary seriess altogether, and processing gain is equal to 8.

Fig. 6-Fig. 9 give successively aperiodic in auto-correlation aperiodic of three value zero cross-correlation region sequence set C that the present embodiment generates, sequence subgroup cross-correlation, in same sequence set between different sequence subgroups aperiodic cross-correlation and different sequence set between aperiodic cross-correlation distribution situation.This four width figure demonstrates the three value zero cross-correlation region sequences that the present invention generates and is integrated between different sequences to include the monolateral zero cross-correlation district { 1 of 3 different in width, 2,4}, namely the monolateral zero cross-correlation sector width between sequence set is 1, monolateral zero cross-correlation sector width in sequence subgroup is 2, and in same sequence set, the monolateral zero cross-correlation sector width between different sequence subgroups is 4.

8 processing gains that the three value zero cross-correlation region sequence set C that the present embodiment generates comprise be all 8 Z-complementary series between mutually orthogonal, therefore set C reached theoretical circles.Two sequence set C in set C₀And C₁All comprising 4 processing gains is all the Z-complementary series of 8, and the minimum monolateral zero correlation block width within sequence set is 2, then two sequence set C₀And C₁Also theoretical circles have all been reached.

Although above the present invention being described in detail, but the invention is not restricted to this, those skilled in the art of the present technique can carry out various amendment according to principles of the invention.Therefore, all amendments made according to the principle of the invention, all should be understood to fall into protection scope of the present invention.

Claims (1)

1. the generation method of a value zero cross-correlation region sequence, it is characterised in that:

Wherein based on the selected DFT sequence order of matrix number of the actual requirement of power system capacity and processing gain, then this DFT sequence matrix and himself carry out displacement Kronecker amass, then carry out direct Kronecker with the new sequence matrix obtained for coefficient and former DFT sequence matrix to amass and block interleaved computing, finally obtained sequence matrix is carried out packet numbering, thus obtaining the zero correlation block of three different in width between each sequence subgroup between each sequence set and in sequence set；

Comprise the following steps:

A) actual requirement according to the power system capacity of wireless communication system, processing gain and zero correlation block width, it is determined that DFT sequence matrixExponent number N, whereinEvery a line in this matrix is considered as a unique sequence, and line n sequence can be expressed as

B) DFT sequence matrix F is amassed with the Kronecker himself carrying out shifting, obtain a N²×N²Coefficient matrix E=[the E of dimension⁽⁰⁾|E⁽¹⁾|…|E^(N-1)], m-th submatrixDimension be N²× N, wherein 4 footmark variablees meet m, g, r, s=0,1 ..., N-1, the element of the gN+r row s row of this submatrixWherein ()_NRepresent modulo-N arithmetic；

C) to coefficient matrix E=[E⁽⁰⁾|E⁽¹⁾|…|E^(N-1)] and DFT sequence matrixIt is made directly Kronecker to amass, it is thus achieved that a dimension is N³×N³Sequence matrix

D) successively by N³×N³In dimension every a line of sequence matrix D, the N number of element of continuous print regards a unique sequence as, then altogether comprise N in every a line²Individual unique sequence；

E) the N of a line every in sequence matrix D²Individual unique sequence forms one group of sequence according to N continuous, then every a line comprises N group sequence, often organizes and comprises the unique sequence that N number of length is N；

F) sequence in a line every in sequence matrix D same group is interleaved computing, then now every a line comprises N number of unique sequence, and the length of each unique sequence is N², the sequence matrix obtained after computing is three value zero cross-correlation region sequence Matrix C.