PARAMETRIC GENERATING METHOD FOR ZCZ SEQUENCE SET

Abstract

A parametric generating method for a zero correlation zone sequence set, includes: determining a ZCZ sequence set to be generated; determining a limited symbol set; determining an initial non-periodic orthogonal complementary sequence set; constructing a discrete Fourier transformation matrix by using elements in the limited symbol set; constructing a coefficient matrix based on the number of sequences and the number of iterations in the sequence set; using the columns of the coefficient matrix respectively as the coefficients of each sequence in the ZCZ sequence set, iteratively generating ZCZ sequence sets by using a method of zero filling the tails of weighting coefficients; and traversing the coefficient matrix, and selecting a ZCZ sequence set meeting the criteria or an optimal ZCZ sequence set according to requirements.

Claims

1. A parametric generating method for a ZCZ sequence set, comprising the following steps: (1) determining a ZCZ sequence set to be generated; (2) determining a limited symbol set according to the types of symbols contained in the required sequence; (3) determining an initial non-periodic orthogonal complementary sequence set according to the ZCZ sequence set to be generated and the limited symbol set; (4) constructing a discrete Fourier transformation matrix by using elements in the limited symbol set based on the size of the ZCZ sequence set; (5) constructing a unitary matrix by using the elements in the limited symbol set based on the size of the ZCZ sequence set and the number of iterations; (6) constructing a coefficient matrix composed of any elements in the limited symbol set based on the number of the ZCZ sequence sets and the number of iterations; and (7) using the columns of the coefficient matrix respectively as the coefficients of each sequence in the ZCZ sequence set, finally generating different ZCZ sequence sets by using a method of zero filling the tails of weighted coefficients in two iterative combination modes.

2. The parametric generating method for the ZCZ sequence set of claim 1, wherein in step 1, the ZCZ sequence set to be generated is determined as Z(N, Q, Z), N represents the length of a ZCZ sequence, Q represents the number of ZCZ sequences, Z represents the length of a zero correlation zone, and they meet the following relation:
N=Q.sup.KL  (formula 1) wherein K≧2 represents the number of iterations, and L represents an initial sequence length; and in step 2, the limited symbol set M={e.sup.j2πθ/Q}.sub.θ=0.sup.Q-1 is determined.

3. The parametric generating method for the ZCZ sequence set of claim 2, wherein the initial sequence length L is determined, a non-periodic orthogonal complementary sequence set consisting of symbols in the limited symbol set M= and having a length L is generated to serve as an initial sequence set Ã.sup.(0)={ã.sub.p,q.sup.(0)}.sub.p,q=1.sup.Q, which is represented by a matrix as follows: $\begin{array}{cc}{\tilde{A}}^{\left(0\right)}=\left[\begin{array}{ccc}{\tilde{a}}_{1,1}^{\left(0\right)}& \mathrm{.Math.}& {\tilde{a}}_{1,Q}^{\left(0\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ {\tilde{a}}_{Q,1}^{\left(0\right)}& \mathrm{.Math.}& {\tilde{a}}_{Q,Q}^{\left(0\right)}\end{array}\right]& \left(\mathrm{formula}.Math..Math.2\right)\end{array}$ wherein Ã.sup.(0) represents a matrix expression form of the set Ã.sup.(0), and {ã.sub.1,q.sup.(0), ã.sub.2,q.sup.(0), . . . , ã.sub.Q,q.sup.(0)} represents a non-periodic orthogonal complementary sequence set, and q=1, 2, . . . , Q; the DFT matrix is constructed by using the elements in the limited symbol set M according to the size Q of the sequence set, wherein the size of the DFT matrix is Q×Q, that is $\begin{array}{cc}{F}_Q=\left[\begin{array}{ccc}{f}_{1,1}& \mathrm{.Math.}& f_{Q,1}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ f_{1,Q}& \mathrm{.Math.}& f_{Q,Q}\end{array}\right]=\left[\begin{array}{cccc}1& 1& \mathrm{.Math.}& 1\\ 1& {\omega }_Q^1& \mathrm{.Math.}& {\omega }_Q^{Q-1}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 1& {\omega }_Q^{Q-1}& \mathrm{.Math.}& {\omega }_Q^{\left(Q-1\right).Math.\left(Q-1\right)}\end{array}\right]& \left(\mathrm{formula}.Math..Math.3\right)\end{array}$ wherein ω.sub.Q.sup.mn=e.sup.−j2πmn/Q; K−2 Q×Q unitary matrices G.sub.Q.sup.(k), k=1, 2, . . . , K−2 are constructed by using the elements in the limited symbol set M according to the size Q of the sequence set, that is $\begin{array}{cc}{G}_Q^{\left(k\right)}=\left[\begin{array}{ccc}{g}_{1,1}^{\left(k\right)}& \mathrm{.Math.}& g_{Q,1}^{\left(k\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ g_{1,Q}^{\left(k\right)}& \mathrm{.Math.}& g_{Q,Q}^{\left(k\right)}\end{array}\right]& \left(\mathrm{formula}.Math..Math.4\right)\end{array}$ a Q×K coefficient matrix W is constructed by using the elements in the limited symbol set M according to the number Q of the sequence sets and the number K of iterations, and the matrix W is expressed as $\begin{array}{cc}W=\left[\begin{array}{ccc}{w}_{1,1}& \mathrm{.Math.}& w_{1,K}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ w_{Q,1}& \mathrm{.Math.}& w_{Q,K}\end{array}\right].& \left(\mathrm{formula}.Math..Math.5\right)\end{array}$

4. The parametric generating method for the ZCZ sequence set of claim 3, wherein (41) the elements on the k.sup.th column of the coefficient matrix W are used as the coefficients of each row of Ã.sup.(k), and the result is represented by B.sup.(k), that is $\begin{array}{cc}.Math.\left(\mathrm{formula}.Math..Math.6\right)& \\ \begin{array}{c}{B}^{\left(k\right)}=.Math.\left[\begin{array}{ccc}{B}_1^{\left(k\right)}& \mathrm{.Math.}& B_Q^{\left(k\right)}\end{array}\right]=\left[\begin{array}{ccc}{b}_{1,1}^{\left(k\right)}& \mathrm{.Math.}& b_{1,Q}^{\left(k\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ b_{Q,1}^{\left(k\right)}& \mathrm{.Math.}& b_{Q,Q}^{\left(k\right)}\end{array}\right]\\ =.Math.\left[\begin{array}{cccc}{w}_{1,k}.Math.I_{Q^{k-1}.Math.L}& 0_{Q^{k-1}.Math.L}& \mathrm{.Math.}& 0_{Q^{k-1}.Math.L}\\ 0_{Q^{k-1}.Math.L}& w_{2,k}.Math.I_{Q^{k-1}.Math.L}& \mathrm{.Math.}& 0_{Q^{k-1}.Math.L}\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 0_{Q^{k-1}.Math.L}& 0_{Q^{k-1}.Math.L}& \mathrm{.Math.}& w_{Q,k}.Math.I_{Q^{k-1}.Math.L}\end{array}\right]\left[\begin{array}{ccc}{\tilde{a}}_{1,1}^{\left(k-1\right)}& \mathrm{.Math.}& {\tilde{a}}_{1,Q}^{\left(k-1\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ {\tilde{a}}_{Q,1}^{\left(k-1\right)}& \mathrm{.Math.}& {\tilde{a}}_{Q,Q}^{\left(k-1\right)}\end{array}\right]\end{array}& \end{array}$ wherein the superscript (k) represents the k.sup.th iteration, and B.sub.q.sup.(k)=[b.sub.1,q.sup.(k), . . . , b.sub.Q,q.sup.(k)].sup.T, q=1, . . . , Q, I.sub.L and 0.sub.L respectively represent a unit matrix with a size L×L and an all-zero matrix; and (42) the non-periodic orthogonal complementary sequence set is generated, that is
Ã.sup.(k)=D.sub.g{tilde over (B)}.sup.(k)  (formula 7)
or
Ã.sup.(k)=D.sub.f{tilde over (B)}.sup.(k)  (formula 8) wherein D.sub.g=Diag(g.sub.1,1.sup.(k)I.sub.Q.sub.k-1.sub.L, . . . , g.sub.1,Q.sup.(k)I.sub.Q.sub.k-1.sub.L, . . . g.sub.Q,1.sup.(k)I.sub.Q.sub.k-1.sub.L, . . . , g.sub.Q,Q.sup.(k)I.sub.Q.sub.k-1.sub.L) D.sub.f=Diag(f.sub.1,1I.sub.Q.sub.k-1.sub.L, . . . , f.sub.1,QI.sub.Q.sub.k-1.sub.L, . . . f.sub.Q,1I.sub.Q.sub.k-1.sub.L, . . . , f.sub.Q,QI.sub.Q.sub.k-1.sub.L), Diag (υ) represents generation of a diagonal matrix with elements of the vector υ as diagonal elements, {tilde over (B)}.sup.(k)=1B.sup.(k), 1 represents a Q-dimensional all-1 column vector, represents a Kronecker product of the matrix, and Ã.sup.(k) represents the matrix of the non-periodic orthogonal complementary sequence set of the k.sup.th iteration.

5. The parametric generating method for the ZCZ sequence set of claim 4, wherein when K=2, step (511) is executed; when K=3, steps (510) and (511) are executed; or step (513) is executed, when K>3, steps (510) and (511) are executed, or steps (512) and (513) are executed; (510) k=1, 2, . . . , K−2 is set, and an iterative operation is carried out on steps (41) and (42) by adopting the formula (7) to obtain the matrix Ã.sup.(K-2); (511) k=K−1, K is set, and the iterative operation is carried out on steps (41) and (42) by adopting the formula (8) to obtain the matrix B.sup.(K); the matrix B.sup.(K) is the resulting ZCZ sequence set, wherein B.sub.q.sup.(K), q=1, 2, . . . , Q, and Q is a ZCZ sequence; the length of the zero correlation zone in the Z(N, Q, Z) is:
Z=(Q−1)Q.sup.K-2L,K≧2  (formula 9); (512) k=1, 2, . . . , K−3 is set, and the iterative operation is carried out on steps (41) and (42) by adopting the formula (7) to obtain the matrix Ã.sup.(K-3); and (513) k=K−2, K−1, K is set, and the iterative operation is carried out on steps (41) and (42) by adopting the formula (8) to obtain the matrix B.sup.(k); the matrix B.sup.(k) is the resulting ZCZ sequence set; and similarly, the length of the zero correlation zone in the obtained ZCZ sequence set Z(N, Q, Z) is:
Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L,K≧3  (formula 10).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. 1 is a block diagram of generation of a ZCZ sequence set;

[0016] FIG. 2 is a periodic autocorrelation result of a Z (128, 4, 28) sequence set with a maximum sidelobe value;

[0017] FIG. 3 is a periodic cross-correlation result of a Z (128, 4, 28) sequence set with a maximum peak value;

[0018] FIG. 4 is a periodic autocorrelation result of a Z (256, 4, 56) sequence set with a maximum sidelobe value;

[0019] FIG. 5 is a periodic cross-correlation result of a Z (256, 4, 56) sequence set with a maximum peak value;

[0020] FIG. 6 is a periodic autocorrelation result of a Z (512, 4, 112) sequence set with a maximum sidelobe value;

[0021] FIG. 7 is a periodic cross-correlation result of a Z (512, 4, 112) sequence set with a maximum peak value.

DETAILED DESCRIPTION

[0022] The present invention will be further illustrated in combination with the specific embodiments. It should be understood that these embodiments are merely used for illustrating the present invention rather than limiting the scope of the present invention, and after reading the present invention, various equivalent modifications made by those skilled in the art to the present invention shall all fall within the scope defined by the appended claims of the present application.

[0023] A parametric generating method for a ZCZ sequence set is provided, and a plurality of sequence sets with more flexible relations between the length of a sequence and the number of sequences in the sets can be generated by the method.

[0024] As shown in FIG. 1, in the present invention, using a non-periodic orthogonal complementary sequence set as an initial sequence set, the ZCZ sequence set is generated by using a method of zero filling the tails of weighted coefficients. The specific implementation is as follows:

[0025] (1) a ZCZ sequence set to be generated is determined as Z(N, Q, Z), wherein N represents the length of a ZCZ sequence, Q represents the number of ZCZ sequences, Z represents the length of a zero correlation zone, and they meet the following relation:

N=Q.sup.kL  (formula 1)

[0026] wherein K≧2 represents the number of iterations, and L represents an initial sequence length.

[0027] (2) A limited symbol set M={e.sup.j2πθ/Q}.sub.θ=0.sup.Q-1 is determined, for example, the limited symbol set is a two-phase {+1, −1} in the case of Q=2, and is a four-phase {+1, −1, +j, −j} in the case of Q=4 and the like, wherein j represents an imaginary unit, that is j.sup.2=−1.

[0028] (3) The initial sequence length L is determined according to the formula (1), a non-periodic orthogonal complementary sequence set consisting of symbols in the limited symbol set M= and having a length L is generated to serve as an initial sequence set Ã.sup.(0)={ã.sub.p,q.sup.(0)}.sub.p,q=1.sup.Q, ã.sub.p,q.sup.(0) represents a column vector having the length L in the p.sup.th sequence in the q.sup.th non-periodic orthogonal complementary sequence set in Ã.sup.(0), which is represented by a matrix as follows:

[00001]$\begin{array}{cc}{\tilde{A}}^{\left(0\right)}=\left[\begin{array}{ccc}{\tilde{a}}_{1,1}^{\left(0\right)}& \mathrm{.Math.}& {\tilde{a}}_{1,Q}^{\left(0\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ {\tilde{a}}_{Q,1}^{\left(0\right)}& \mathrm{.Math.}& {\tilde{a}}_{Q,Q}^{\left(0\right)}\end{array}\right]& \left(\mathrm{formula}.Math..Math.2\right)\end{array}$

[0029] wherein Ã.sup.(0) represents a matrix expression form of the set Ã.sup.(0), {ã.sub.1,q.sup.(0), ã.sub.2,q.sup.(0), . . . , ã.sub.Q,q.sup.(0)} represents a non-periodic orthogonal complementary sequence set, and q=1, 2, . . . , Q.

[0030] (4) A DFT matrix is constructed by using elements in the limited symbol set M according to the size Q of the ZCZ sequence set, wherein the size of the DFT matrix is Q×Q, that is

[00002]$\begin{array}{cc}{F}_Q=\left[\begin{array}{ccc}{f}_{1,1}& \mathrm{.Math.}& f_{Q,1}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ f_{1,Q}& \mathrm{.Math.}& f_{Q,Q}\end{array}\right]=\left[\begin{array}{cccc}1& 1& \mathrm{.Math.}& 1\\ 1& {\omega }_Q^1& \mathrm{.Math.}& {\omega }_Q^{Q-1}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 1& {\omega }_Q^{Q-1}& \mathrm{.Math.}& {\omega }_Q^{\left(Q-1\right).Math.\left(Q-1\right)}\end{array}\right]& \left(\mathrm{formula}.Math..Math.3\right)\end{array}$

[0031] wherein ω.sub.Q.sup.mn=e.sup.−j2πmn/Q.

[0032] (5) K−2 Q×Q unitary matrixes G.sub.Q.sup.(k), k=1, 2, . . . , K−2 are constructed by using the elements in the limited symbol set M according to the size Q of the sequence set, that is

[00003]$\begin{array}{cc}{G}_Q^{\left(k\right)}=\left[\begin{array}{ccc}{g}_{1,1}^{\left(k\right)}& \mathrm{.Math.}& g_{Q,1}^{\left(k\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ g_{1,Q}^{\left(k\right)}& \mathrm{.Math.}& g_{Q,Q}^{\left(k\right)}\end{array}\right].& \left(\mathrm{formula}.Math..Math.4\right)\end{array}$

[0033] (6) A Q×K coefficient matrix is constructed by using the elements in the limited symbol set M according to the number Q of the sequence sets and the number K of iterations, and the matrix W is expressed as

[00004]$\begin{array}{cc}W=\left[\begin{array}{ccc}{w}_{11}& \mathrm{.Math.}& w_{1.Math.K}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ w_{Q.Math..Math.1}& \mathrm{.Math.}& w_{\mathrm{QK}}\end{array}\right].& \left(\mathrm{formula}.Math..Math.5\right)\end{array}$

[0034] (7) The elements on the k.sup.th column of the coefficient matrix W are used as the coefficients of each row of Ã.sup.(k), and the result is represented by B.sup.(k), that is

[00005]$\begin{array}{cc}\begin{array}{c}{B}^{\left(k\right)}=.Math.\left[B_1^{\left(k\right)}.Math..Math.\mathrm{.Math.}.Math..Math.B_Q^{\left(k\right)}\right]=\left[\begin{array}{ccc}{b}_{1,1}^{\left(k\right)}& \mathrm{.Math.}& b_{1,Q}^{\left(k\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ b_{Q,1}^{\left(k\right)}& \mathrm{.Math.}& b_{Q,Q}^{\left(k\right)}\end{array}\right]\\ =.Math.\left[\begin{array}{cccc}{w}_{1,k}.Math.I_{Q^{k-1}.Math.L}& 0_{Q^{k-1}.Math.L}& \mathrm{.Math.}& 0_{Q^{k-1}.Math.L}\\ 0_{Q^{k-1}.Math.L}& w_{2,k}.Math.I_{Q^{k-1}.Math.L}& \mathrm{.Math.}& 0_{Q^{k-1}.Math.L}\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 0_{Q^{k-1}.Math.L}& 0_{Q^{k-1}.Math.L}& \mathrm{.Math.}& w_{Q,k}.Math.I_{Q^{k-1}.Math.L}\end{array}\right]\hspace{1em}\\ .Math.\left[\begin{array}{ccc}{\tilde{a}}_{1,1}^{\left(k-1\right)}& \mathrm{.Math.}& {\tilde{a}}_{1,Q}^{\left(k-1\right)}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ {\tilde{a}}_{Q,1}^{\left(k-1\right)}& \mathrm{.Math.}& {\tilde{a}}_{Q,Q}^{\left(k-1\right)}\end{array}\right]\end{array}\hspace{1em}& \left(\mathrm{formula}.Math..Math.6\right)\end{array}$

[0035] wherein the superscript (k) represents the k.sup.th iteration, and B.sub.q.sup.(k)=[b.sub.1,q.sup.(k), . . . , b.sub.Q,q.sup.(k)].sup.T, q=1, . . . , Q, I.sub.L and 0.sub.L respectively represent a unit matrix with a size L×L and an all-zero matrix.

[0036] (8) The non-periodic orthogonal complementary sequence set is generated, that is

Ã.sup.(k)=D.sub.g{tilde over (B)}.sup.(k)  (formula 7)

or

Ã.sup.(k)=D.sub.f{tilde over (B)}.sup.(k)  (formula 8)

[0037] wherein D.sub.g=Diag(g.sub.1,1.sup.(k)I.sub.Q.sub.k-1.sub.L, . . . , g.sub.1,Q.sup.(k)I.sub.Q.sub.k-1.sub.L, . . . g.sub.Q,1.sup.(k)I.sub.Q.sub.k-1.sub.L, . . . , g.sub.Q,Q.sup.(k)I.sub.Q.sub.k-1.sub.L)

[0038] D.sub.f=Diag(f.sub.1,1I.sub.Q.sub.k-1.sub.L, . . . , f.sub.1,QI.sub.Q.sub.k-1.sub.L, . . . f.sub.Q,1I.sub.Q.sub.k-1.sub.L, . . . , f.sub.Q,QI.sub.Q.sub.k-1.sub.L), Diag (v) represents generation of a diagonal matrix with elements of the vector v as diagonal elements, {tilde over (B)}.sup.(k)=1B.sup.(k), 1 represents a Q-dimensional all-1 column vector, represents a Kronecker product of the matrix, and Ã.sup.(k) represents the matrix of the non-periodic orthogonal complementary sequence set of the k.sup.th iteration.

[0039] (9) when K=2, step (11) is executed; when K=3, steps (10) and (11) are executed; or step (13) is executed, when K>3, steps (10) and (11) are executed, or steps (12) and (13) are executed.

[0040] (10) k=1, 2, . . . , K−2 is set, and an iterative operation is carried out on steps (7) and (8) by adopting the formula (7) to obtain the matrix Ã.sup.(K-2).

[0041] (11) k=K−1,K is set, and the iterative operation is carried out on steps (7) and (8) by adopting the formula (8) to obtain the matrix B.sup.(k). The matrix B.sup.(k) is the resulting ZCZ sequence set, wherein B.sub.q.sup.(K), and q=1, 2, . . . ,Q is a ZCZ sequence. The length of the zero correlation zone in the Z(N, Q, Z) is:

Z=(Q−1)Q.sup.K-2L,K≧2  (formula 9).

[0042] (12) k=1, 2, . . . , K−3 is set, and the iterative operation is carried out on steps (7) and (8) by adopting the formula (7) to obtain the matrix Ã.sup.(K-3).

[0043] (13) k=K−2, K−1, K is set, and the iterative operation is carried out on steps (7) and (8) by adopting the formula (8) to obtain the matrix B.sup.(K). The matrix B.sup.(K) is the resulting ZCZ sequence set, wherein B.sup.(K), and q=1, 2, . . . ,Q is a ZCZ sequence. The length of the zero correlation zone in the obtained ZCZ sequence set Z(N, Q, Z) is:

Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L,K≧3  (formula 10).

[0044] It is set that a Z (128, 4, 28) sequence set is generated, the number K of iterations is 3, the limited symbol set M={+1, +j, −1, j}, j represents the imaginary unit, that is j.sup.2=−1. The initial sequence set of the non-periodic orthogonal complementary sequence set is selected as follows:

[00006]$\begin{array}{cc}{\tilde{A}}^{\left(0\right)}=\left[\begin{array}{cccc}{\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T\\ {\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T& {\left(+1,+1\right)}^T& {\left(+1,-1\right)}^T\\ {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T\\ {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T& {\left(+1,-1\right)}^T& {\left(+1,+1\right)}^T\end{array}\right].& \left(\mathrm{formula}.Math..Math.11\right)\end{array}$

[0045] The DFT matrix with a size 4×4 is as follows:

[00007]$\begin{array}{cc}{F}_4=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right].& \left(\mathrm{formula}.Math..Math.12\right)\end{array}$

[0046] The unitary matrix G.sub.4.sup.(1) is as follows:

[00008]$\begin{array}{cc}{G}_4^{\left(1\right)}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right].& \left(\mathrm{formula}.Math..Math.13\right)\end{array}$

[0047] The coefficient matrix is

[00009]$\begin{array}{cc}W=\left[\begin{array}{ccc}j& j& 1\\ 1& -j& -1\\ -j& -j& 1\\ -j& j& 1\end{array}\right].& \left(\mathrm{formula}.Math..Math.14\right)\end{array}$

[0048] The obtained ZCZ sequence set is as shown in table 1, wherein 0, 1, 2, and 3 respectively represent +1, +j, −1, and −j.

TABLE-US-00001 TABLE 1 examples of the ZCZ sequence set (N = 128, Q = 4, K = 3) Z (128, 4, 28) B.sub.1.sup.(3) 00112020222220132211022000220213 00112020111113020033200211331320 00112020000002312211022022002031 00112020333331200033200233113102 B.sub.2.sup.(3) 02132222202022112013002202200011 02132222131311000231220013311122 02132222020200332013002220022233 02132222313133220231220031133300 B.sub.3.sup.(3) 00332002220020312233020200000231 00332002113313200011202011111302 00332002002202132233020222222013 00332002331131020011202033333120 B.sub.4.sup.(3) 02312200200222332031000002020033 02312200133111220213222213131100 02312200022000112031000020202211 02312200311333000213222231313322

[0049] Table 1 provides the Z (128, 4, 28) sequence set, the maximum sidelobe of normalized periodic autocorrelation is 0.3536, and the maximum peak value of normalized periodic cross-correlation is 0.3536.

[0050] FIG. 2 provides a periodic autocorrelation result of the sequence set with a maximum sidelobe value, the zero correlation zone is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L=28, and the maximum sidelobe of normalized periodic autocorrelation is 0.3536. FIG. 3 provides a periodic cross-correlation result of the sequence set with a maximum peak value, the zero correlation zone is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L=28, and the maximum peak value of normalized periodic cross-correlation is 0.3536.

[0051] If a Z (256, 4, 56) sequence set needs to be generated, then the number K of iterations is 4, the limited symbol set M={+1, +j, −1, −j}. The initial sequence set of the non-periodic orthogonal complementary sequence set is as follows:

[00010]$\begin{array}{cc}{\tilde{A}}^{\left(0\right)}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right].& \left(\mathrm{formula}.Math..Math.1\right)\end{array}$

[0052] The DFT matrix with the size 4×4 is as follows:

[00011]$\begin{array}{cc}{F}_4=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right].& \left(\mathrm{formula}.Math..Math.2\right)\end{array}$

[0053] The unitary matrix G.sub.4.sup.(k), k=1, 2 is as follows:

[00012]$\begin{array}{cc}{G}_4^{\left(k\right)}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],k=1,2.& \left(\mathrm{formula}.Math..Math.3\right)\end{array}$

[0054] The coefficient matrix is

[00013]$\begin{array}{cc}W=\left[\begin{array}{cccc}1& -1& -j& -j\\ -1& j& -j& -j\\ -j& -1& -j& 1\\ j& -j& -1& j\end{array}\right].& \left(\mathrm{formula}.Math..Math.4\right)\end{array}$

[0055] FIG. 4 provides a periodic autocorrelation result of the Z (256, 4, 56) sequence set, with a maximum sidelobe value, the zero correlation zone is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L=56, and the maximum sidelobe of normalized periodic autocorrelation is 0.1976.

[0056] FIG. 5 provides a periodic cross-correlation result of the Z (256, 4, 56) sequence set with a maximum peak value, the zero correlation zone is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L=56, and the maximum peak value of normalized periodic cross-correlation is 0.3125.

[0057] If a Z (512, 4, 112) sequence set needs to be generated, then the number K of iterations is 4, the limited symbol set M={+1, +j, −1, −j}, and the initial sequence set of the non-periodic orthogonal complementary sequence set is as follows:

[00014]$\begin{array}{cc}{\tilde{A}}^{\left(0\right)}=\left[\begin{array}{cccc}{\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T\\ {\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T& {\left(+1,+1\right)}^T& {\left(+1,-1\right)}^T\\ {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T& {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T\\ {\left(-1,+1\right)}^T& {\left(-1,-1\right)}^T& {\left(+1,-1\right)}^T& {\left(+1,+1\right)}^T\end{array}\right].& \left(\mathrm{formula}.Math..Math.5\right)\end{array}$

[0058] The DFT matrix with the size 4×4 is as follows:

[00015]$\begin{array}{cc}{F}_4=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right].& \left(\mathrm{formula}.Math..Math.6\right)\end{array}$

[0059] The unitary matrix G.sub.4.sup.(k), k=1, 2 is as follows:

[00016]$\begin{array}{cc}{G}_4^{\left(k\right)}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],k=1,2.& \left(\mathrm{formula}.Math..Math.7\right)\end{array}$

[0060] The coefficient matrix is

[00017]$\begin{array}{cc}W=\left[\begin{array}{cccc}1& -j& -j& -j\\ j& -j& j& -j\\ j& j& -j& -1\\ -j& -j& 1& -j\end{array}\right].& \left(\mathrm{formula}.Math..Math.8\right)\end{array}$

[0061] FIG. 6 provides a periodic autocorrelation result of the Z (512, 4, 112) sequence set with a maximum sidelobe value, the zero correlation zone is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L=112, and the maximum sidelobe of normalized periodic autocorrelation is 0.2275.

[0062] FIG. 7 provides a periodic cross-correlation result of the Z (512, 4, 112) sequence set with a maximum peak value, the zero correlation zone is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L=112, and the maximum peak value of normalized periodic cross-correlation is 0.2275.

[0063] The present invention provides a Z (N, Q, Z) sequence set generation method, sequence sets with more flexible relations between the length N of a sequence and the number Q of sequences in the sets can be generated by the method, namely it is required that N=Q.sup.KL is satisfied, the zero correlation zone in the first iterative combination of the ZCZ sequence set is Z=(Q−1)Q.sup.K-2L, K≧2, the zero correlation zone in the second iterative combination is Z=[(Q−1)Q+(Q−2)]Q.sup.K-3L, K≧3, and the sequence elements belong to the characteristics of the limited symbol set; and moreover, different unitary matrixes can be selected for each iteration step, and the coefficients are randomly or exhaustively transversed to obtain the ZCZ sequence set having specific properties.