CN104485977B - A kind of parameterized ZCZ arrangement set inserts value generation method - Google Patents

Abstract

The invention discloses a kind of parameterized ZCZ arrangement set and insert value generation method, include the steps of determining that required generation ZCZ arrangement set；Determine limited assemble of symbol；Determine orthogonal complement arrangement set initial aperiodic；Utilize the element structure Discrete Fourier transform in limited assemble of symbol；According to the sequence bar number in arrangement set and iterations, construct coefficient matrix；Initiation sequence is utilized the interpolation method grey iterative generation ZCZ arrangement set of weight coefficient；Traversal coefficient matrix, selects to meet condition or optimal ZCZ arrangement set as required.The zero correlation section length of the ZCZ arrangement set that the present invention generates is close to theoretical circles, and can generate out of phase ZCZ arrangement set as required.Further, it is also possible to change unitary matrice and coefficient matrix during generating, the optimal ZCZ arrangement set of character needed for random or exhaustive search.

Description

A kind of parameterized ZCZ arrangement set inserts value generation method

Technical field

The present invention provides a kind of parameterized ZCZ (zero correlation block, Zero Correlation Zone, ZCZ) arrangement set Insert value generation method, belong to signal processing and communication technical field.

Background technology

Along with the high speed development of WLAN (Wireless Local Access Network, WLAN) technology, various The wlan device of various kinds such as smart mobile phone, panel computer etc. just emerge in multitude, and people are at the transmission number of various indoor wireless networks The most day by day increase according to the requirement of rate.In following short-distance wireless communication system, support that higher data transfer rate becomes current channel radio The huge challenge of letter technology.Traditional view is thought, increasing bandwidth is considered as the most most effective of raising transmission data rate Means.

With multiple-input and multiple-output (Multiple-Input and Multiple-Output, MIMO) single carrier (Single Carrier, SC) technology is that the wireless communication technology of representative is developing progressively as hot topic, by utilizing Spatial Dimension so that being On the basis of system obtains higher throughput and more reliable transmission, carry out same the most quickly and accurately Step and time domain channel are estimated to have become one of core research contents.Use and there is the sequence of preferable correlation properties as pilot tone sequence Row, utilize unique non-zero peak value of preferable correlated series, can realize exact time synchronization；Utilize zero correlation block, multipath can be eliminated Interference, it is achieved optimum time domain channel is estimated.It addition, the element of pilot frequency sequence belongs to limited assemble of symbol can reduce receiver together The complexity that step and channel are estimated.Theoretical it was demonstrated that be provided simultaneously with preferable auto-correlation and the arrangement set of preferable cross correlation Not existing, therefore, have auto-correlation and the cross-correlation of sufficient length zero correlation block between design multiple antennas, autocorrelation sidelobe is relatively low, Cross-correlation peak value is relatively low, and sequential element belongs to the pilot frequency sequence set of limited assemble of symbol and becomes key point.

ZCZ arrangement set, i.e. in set, arbitrary sequence has certain length zero correlation block autocorrelation performance, the most different sequences There is between row equal length zero correlation block cross correlation.The ZCZ arrangement set sequence that the generating mode of the present invention is generated Relation between length and sequence bar number is flexible, and zero correlation section length approximation theory circle can according to different Demand Design not yet Same ZCZ arrangement set.

Summary of the invention

Goal of the invention: challenge present in prior art, the present invention provides a kind of parameterized ZCZ arrangement set to insert Value generation method.

Technical scheme: a kind of parameterized ZCZ arrangement set inserts value generation method, comprises the steps:

(1) required generation ZCZ arrangement set is determinedIncluding sequence length N, sequence bar number Q, zero correlation block Length Z and iterations K-2, K ＞ 2 and be integer；

(2) comprise the kind of symbol according to required sequence, determine limited assemble of symbol；

(3) according to required generation ZCZ arrangement set and limited assemble of symbol, the initiation sequence of orthogonal complement aperiodic is determined SetWhereinFor initiation sequence；

(4) according to ZCZ arrangement set size Q, limited assemble of symbol is utilizedIn element structure discrete Fourier transform (Discrete Fourier Transform, DFT) matrix F_Q；

(5) according to ZCZ arrangement set size Q and iterations K-2, limited assemble of symbol is utilizedIn element structure Q × Q unitary matriceK=1,2 ..., K-2；

(6) according to ZCZ arrangement set bar number Q and iterations K-2, structure is by the arbitrary element structure in limited assemble of symbol The coefficient matrix W become, matrix element is w_qk；

(7) to initiation sequenceCarry out interpolation, i.e. after each element of initiation sequence, fill out Q^K-2-1 zero, obtain a length of Q^K-2The arrangement set of LL is initiation sequence length；

(8) to sequenceCyclic shift is also multiplied by coefficient w_qk, recycle matrixCarry out piecemeal unitary transformation, obtainWherein k=1,2 ..., K-2；

(9) step (8) iteration K-2 time altogether, obtains matrix

(10) utilizeAnd F_Q, generate ZCZ arrangement set.Each step of iteration is arbitrarily chosen unitary matrice, random or Person's exhaustive traversal coefficient matrix, can generate the ZCZ arrangement set with different autocorrelation sidelobe and cross-correlation peak value, choose and return One changes autocorrelation sidelobe less than threshold value T_a, normalized crosscorrelation peak value is less than threshold value T_cZCZ arrangement set, 0 ＜ T_a＜ 1,0 ＜ T_c＜ 1 is for meeting the value set by application demand performance.

Beneficial effect: compared with prior art, the present invention provide parameterized ZCZ arrangement set insert value generation method, There is the auto-correlation of sufficient length zero correlation block and the arrangement set of cross-correlation, i.e. ZCZ arrangement set, be to be applied to multiple antennas One of key of excellent targeting sequencing design.The method of the generation ZCZ arrangement set used by the present invention: generate ZCZ arrangement set Zero correlation section length is close to theoretical circles, and sufficiently long zero correlation block can eliminate multi-path jamming, it is achieved optimum time domain channel is estimated；And And out of phase ZCZ arrangement set can be generated as required, increase the choice in wireless communications application；Additionally, also Can change unitary matrice and coefficient matrix during generating, random or exhaustive search normalized autocorrelation secondary lobe is less than threshold value T_a, normalized crosscorrelation peak value is less than threshold value T_cZCZ arrangement set, improve time synchronized apply in degree of accuracy；It addition, All elements in the ZCZ arrangement set generated belongs to limited assemble of symbol, it is simple to design high-speed correlator, reduces receiver Complexity.

Accompanying drawing explanation

Fig. 1 is the block diagram generating ZCZ arrangement set；

Fig. 2 isThe cycle autocorrelation result that the side lobe levels of arrangement set is maximum；

Fig. 3 isThe cycle cross correlation results that the peak value of arrangement set is maximum；

Fig. 4 isThe cycle autocorrelation result that the side lobe levels of arrangement set is maximum；

Fig. 5 isThe cycle cross correlation results that the peak value of arrangement set is maximum.

Detailed description of the invention

Below in conjunction with specific embodiment, it is further elucidated with the present invention, it should be understood that these embodiments are merely to illustrate the present invention Rather than restriction the scope of the present invention, after having read the present invention, the those skilled in the art's various equivalences to the present invention The amendment of form all falls within the application claims limited range.

Parameterized ZCZ arrangement set inserts value generation method, utilize the method can with formation sequence length and set in sequence The row bar the most multiple arrangement set of number both sides relation.

As it is shown in figure 1, the present invention utilizes orthogonal complement arrangement set aperiodic to be initiation sequence set, use weight coefficient Interpolation method, generate ZCZ arrangement set.Specific embodiments is as follows:

(1) determine that the required ZCZ arrangement set that generates isN is ZCZ sequence length, and Q is ZCZ sequence bar number, Z is the length of zero correlation block, and they meet following relation:

N=Q^KL (formula 1)

Wherein, K-2 is iterations, K ＞ 2 and be integer, and L is initiation sequence length.

(2) limited assemble of symbol is determinedDuring such as Q=2For two-phase set {+1 ,-1}, Q=4 TimeIt is that {+1 ,-1 ,+j ,-j} etc., j is imaginary unit, i.e. j in four phase set²=-1；

(3) determine length L of initiation sequence according to (formula 1), generate by limited assemble of symbolIn symbol composition and length For L aperiodic orthogonal complement arrangement set as initiation sequence set ${\tilde{a}}_{p,q}^{\left(0\right)}={(a_{p,q,1}^{\left(0\right)},...,a_{p,q,L}^{\left(0\right)})}^T$ RepresentPth sequence in middle q-th orthogonal complement aperiodic arrangement set and be the column vector of a length of L,Be one aperiodic orthogonal complement arrangement set, q=1,2 ..., Q, be expressed as follows with matrix:

(formula 2)

Wherein,Represent arrangement setMatrix representation forms.

(4) according to arrangement set size Q, limited assemble of symbol is utilizedIn element structure DFT matrix, this DFT matrix Size is Q × Q, i.e.

(formula 3)

Wherein,M=0 ..., Q-1, n=0 ..., Q-1.

(5) according to ZCZ arrangement set size Q, find out matrix element and belong to limited assemble of symbolK-2 identical or Different Q × Q unitary matriceK=1,2 ..., K-2, i.e.

(formula 4)

(6) according to ZCZ arrangement set bar number Q and iterations K-2, the coefficient matrix W of structure Q × (K-2), matrix W Element can be setIn arbitrary element, i.e.Matrix W is expressed as

(formula 5)

(7) at initiation sequenceEach element after insert Q^K-2-1 zero, obtain length Q^K-2The sequence of L

Set

(8) setFor in arrangement setAll sequencesMatrix representation forms, it may be assumed that

(formula 6)

To sequenceCyclic shift is also multiplied by coefficient w_qk, recycle matrixCarry out piecemeal unitary transformation, obtainThat is:

(formula 7)

Wherein,Represent a size of Q^K-2L×Q^K-2The unit matrix of L, Φ^(k)=blkdiag{w_1,kΠ^(1,k),…,w_Q,k Π^(Q,k), blkdiag{ } represent block diagonal matrix,e_nRepresent a length of Q^K-2L and Nth elements is the unit vector of 1, and C=circ{c} represents the circular matrix that first row element is c.

(9) utilizing (formula 7), iteration K-2 time, obtains matrix altogether

(10) utilizeGenerate required ZCZ arrangement set, i.e.

(formula 8)

Wherein, $D_f=\mathrm{Diag}(f_{\mathrm{1,1}}{I}_{Q^{K-2}L},...,f_{1,Q}{I}_{Q^{K-2}L},...f_{Q,1}{I}_{Q^{K-2}L},...,f_{Q,Q}{I}_{Q^{K-2}L}),$ Diag(υ) Represent the generation element with the vector υ diagonal matrix as diagonal element,1 represents that Q ties up complete 1 column vector, The Kronecker of representing matrix amasss, matrixTotal Q row,Q=1 ... Q be N=QKL length row to Amount,For required ZCZ arrangement set.

(11) gained ZCZ arrangement setMiddle zero correlation section length is:

Z=(Q-1) Q^K-2L (formula 9)

Especially, when Middle zero correlation section length is:

Z=(Q-1) Q^K-2L+(Q-2)Q^K-3(formula 10)

(12) each step of iteration is arbitrarily chosen unitary matrice G_Q, random or exhaustive traversal coefficient matrix W, can generate There is the ZCZ arrangement set of different autocorrelation sidelobe and cross-correlation peak value, choose normalized autocorrelation secondary lobe less than threshold value T_a, return One changes cross-correlation peak value less than threshold value T_cZCZ arrangement set, 0 ＜ T_a＜ 1,0 ＜ T_c＜ 1 is for meeting set by application demand performance Fixed value.

Instantiation illustrates:

GenerateArrangement set, iterations K=4, limited assemble of symbol Aperiodic, the initiation sequence set of orthogonal complement arrangement set was as follows:

(formula 15)

The DFT matrix of a size of 4 × 4 is as follows:

$F_4=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right]$ (formula 16)

Unitary matriceK=1,2 is as follows:

$G_4^{\left(k\right)}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],k=\mathrm{1,2}$ (formula 17)

Coefficient matrix:

$W=\left[\begin{array}{cc}-1& 1\\ -1& -1\\ j& -1\\ -1& -1\end{array}\right]$ (formula 18)

Obtaining ZCZ arrangement set, as shown in table 1, wherein 0,1,2,3 represents+1 ,+j ,-1 ,-j respectively.

Table 1, ZCZ arrangement set example (N=256, Q=4, K=4)

Table 1 be normalization period auto-correlation maximum secondary lobe be 0.1976, normalization period cross-correlation peak-peak is 0.3125Arrangement set.

Fig. 2 givesThe cycle autocorrelation result that the side lobe levels of arrangement set is maximum, meets zero correlation block For Z=(Q-1) Q^K-2L+(Q-2)Q^K-3=56 and normalization period auto-correlation maximum secondary lobe be 0.1976.

Fig. 3 givesThe cycle cross correlation results that the peak value of arrangement set is maximum, meeting zero correlation block is Z=(Q-1) Q^K-2L+(Q-2)Q^K-3=56 and normalization period cross-correlation peak-peak be 0.3125.

GenerateArrangement set, K=4, iterations K-2=2, limited assemble of symbol Aperiodic, the initiation sequence set of orthogonal complement arrangement set was as follows:

(formula 19)

The DFT matrix of a size of 4 × 4 is as follows:

$F_4=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right]$ (formula 20)

Unitary matriceK=1,2 is as follows:

$G_4^{\left(k\right)}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],k=\mathrm{1,2}$ (formula 21)

Coefficient matrix:

$W=\left[\begin{array}{cc}-1& 1\\ -1& -1\\ j& -1\\ -1& -1\end{array}\right]$ (formula 22)

Fig. 4 givesThe cycle autocorrelation result that the side lobe levels of arrangement set is maximum, meets zero correlation District is Z=(Q-1) Q^K-2L+(Q-2)Q^K-3=104 and normalization period auto-correlation maximum secondary lobe be 0.2275.

Fig. 5 givesThe cycle cross correlation results that the peak value of arrangement set is maximum, meets zero correlation block For Z=(Q-1) Q^K-2L+(Q-2)Q^K-3=104 and normalization period cross-correlation peak-peak be 0.2670.

The invention provides oneArrangement set generates method, utilizes the method can be with formation sequence length N With sequence bar number Q both sides relation arrangement set the most flexibly in set, i.e. it is required to meet N=Q^KL, this ZCZ arrangement set zero Correlation zone length is Z=(Q-1) Q^K-2L,Time, zero correlation section length is Z=(Q-1) Q^K-2L+(Q-2)Q^K-3, And sequential element belongs to the feature of limited assemble of symbol；And, each step of iteration can be chosen different unitary matrice, with Machine or exhaustive traversal coefficient obtain the ZCZ arrangement set with special properties.

Claims (5)

1. a parameterized ZCZ arrangement set inserts value generation method, it is characterised in that comprise the steps:

(1) required generation ZCZ arrangement set is determinedIncluding sequence length N, sequence bar number Q, the length of zero correlation block Degree Z and iterations K-2, K ＞ 2 and be integer, L is initiation sequence length；And they meet following relation:

N=Q^KL (formula 1)；

(2) comprise the kind of symbol according to required sequence, determine limited assemble of symbol

(3) according to required generation ZCZ arrangement set and limited assemble of symbol, the initiation sequence set of orthogonal complement aperiodic is determinedWhereinFor initiation sequence,RepresentMiddle q-th aperiodic Pth sequence in orthogonal complement arrangement set and be the column vector of a length of L,It it is a non-week Phase orthogonal complement arrangement set, q=1,2 ..., Q；

(4) according to ZCZ arrangement set size Q, limited assemble of symbol is utilizedIn element structure Discrete Fourier transform F_Q；

(5) according to ZCZ arrangement set size Q and iterations K-2, limited assemble of symbol is utilizedIn element structure Q × Q tenth of the twelve Earthly Branches MatrixK=1,2 ..., K-2；

(6) according to ZCZ arrangement set bar number Q and iterations K-2, structure is made up of the arbitrary element in limited assemble of symbol Coefficient matrix W, matrix element is w_qk,

(7) to initiation sequenceCarry out interpolation, i.e. after each element of initiation sequence, fill out Q^K-2-1 zero, obtain a length of Q^K-2L Arrangement set

(8) to sequenceCyclic shift is also multiplied by coefficient w_qk, recycle matrixCarry out piecemeal unitary transformation, obtainIts Middle k=1,2 ..., K-2；

(9) step (8) iteration K-2 time altogether, obtains matrix

(10) utilizeAnd F_Q, generate ZCZ arrangement set；Each step of iteration is arbitrarily chosen unitary matrice, random or poor Lift traversal coefficient matrix, the ZCZ arrangement set with different autocorrelation sidelobe and cross-correlation peak value can be generated, choose normalization Autocorrelation sidelobe is less than threshold value T_a, normalized crosscorrelation peak value is less than threshold value T_cZCZ arrangement set, 0 ＜ T_a＜ 1,0 ＜ T_c＜ 1 For meeting the value set by application demand performance.

Parameterized ZCZ arrangement set the most according to claim 1 inserts value generation method, it is characterised in that: step (4) In, matrix F_QSize is Q × Q, i.e.

Wherein,

Parameterized ZCZ arrangement set the most according to claim 1 inserts value generation method, it is characterised in that: in step 6, Matrix W is expressed as

Parameterized ZCZ arrangement set the most according to claim 1 inserts value generation method, it is characterised in that:

Wherein,Represent a size of Q^K-2L×Q^K-2The unit matrix of L, Φ^(k)=blkdiag{w_1,kΠ^(1,k),...,w_Q,k Π^(Q,k), blkdiag{ } represent block diagonal matrix,e_nRepresent a length of Q^K-2L and Nth elements is the unit vector of 1, and C=circ{c} represents the circular matrix that first row element is c.

Parameterized ZCZ arrangement set the most according to claim 1 inserts value generation method, it is characterised in that: utilizeGenerate required ZCZ arrangement set, i.e.

Wherein,Diag (υ) table Show the generation element with the vector υ diagonal matrix as diagonal element,1 represents that Q ties up complete 1 column vector,Represent Existence and unigueness, matrixTotal Q row,Q=1 ... Q is N=Q^KThe column vector of L length,For required ZCZ arrangement set.