Parametric generating method for ZCZ sequence set
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.
1. A parametric generating method for a ZCZ sequence set, comprising the following steps:
(1) determining a zero correlation zone (ZCZ) sequence set to be generated, wherein the ZCZ sequence set to be generated is determined as Z(N, Q, Z), N represents a length of the ZCZ sequence, Q represents a number of the ZCZ sequences, Z represents a length of a zero correlation zone, and they meet the following relation:
N=Q K L (formula 1)
wherein K≥2 represents a number of iterations, and L represents an initial sequence length;
(2) determining a limited symbol set according to the types of symbols contained in the ZCZ 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 (DFT) 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 2, the limited symbol set M={e j2πθ/Q } θ=0 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 à (0) ={ã p,q (0) } p,q=1 Q , which is represented by a matrix as follows:
A
~
(
0
)
=
[
a
~
1
,
1
(
0
)
…
a
~
1
,
Q
(
0
)
⋮
⋱
⋮
a
~
Q
,
1
(
0
)
…
a
~
Q
,
Q
(
0
)
]
(
formula
2
)
wherein à (0) represents a matrix expression form of the set à (0) , and {ã 1,q (0) , ã 2,q (0) , . . . , ã Q,q (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
F
Q
=
[
f
1
,
1
…
f
Q
,
1
⋮
⋱
⋮
f
1
,
Q
…
f
Q
,
Q
]
=
[
1
1
…
1
1
ω
Q
1
…
ω
Q
Q
-
1
⋮
⋮
…
⋮
1
ω
Q
Q
-
1
…
ω
Q
(
Q
-
1
)
(
Q
-
1
)
]
(
formula
3
)
wherein ω Q mn =e −j2πmn/Q ;
K−2 Q×Q unitary matrices G Q (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
G
Q
(
k
)
=
[
g
1
,
1
(
k
)
…
g
Q
,
1
(
k
)
⋮
⋱
⋮
g
1
,
Q
(
k
)
…
g
Q
,
Q
(
k
)
]
(
formula
4
)
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
W
=
[
w
1
,
1
…
w
1
,
K
⋮
⋱
⋮
w
Q
,
1
…
w
Q
,
K
]
.
(
formula
5
)
4. The parametric generating method for the ZCZ sequence set of claim 3 , wherein ( 41 ) the elements on the k th column of the coefficient matrix W are used as the coefficients of each row of à (k) , and the result is represented by B (k) , that is
(
formula
6
)
B
(
k
)
=
[
B
1
(
k
)
…
B
Q
(
k
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]
=
[
b
1
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1
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k
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b
1
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k
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⋱
⋮
b
Q
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1
(
k
)
…
b
Q
,
Q
(
k
)
]
=
[
w
1
,
k
I
Q
k
-
1
L
0
Q
k
-
1
L
…
0
Q
k
-
1
L
0
Q
k
-
1
L
w
2
,
k
I
Q
k
-
1
L
…
0
Q
k
-
1
L
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Q
k
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1
L
0
Q
k
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1
L
…
w
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k
I
Q
k
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1
L
]
[
a
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1
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1
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k
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…
a
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1
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Q
(
k
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1
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a
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,
1
(
k
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1
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…
a
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Q
,
Q
(
k
-
1
)
]
wherein the superscript (k) represents the k th iteration, and B q (k) =[b 1,q (k) , . . . , b Q,q (k) ] T , q=1, . . . , Q, I L and 0 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
à (k) =D g {tilde over (B)} (k) (formula 7)
or
à (k) =D f {tilde over (B)} (k) (formula 8)
wherein D g =Diag(g 1,1 (k) I Q k-1 L , . . . , g 1,Q (k) I Q k-1 L , . . . g Q,1 (k) I Q k-1 L , . . . , g Q,Q (k) I Q k-1 L )
D f =Diag(f 1,1 I Q k-1 L , . . . , f 1,Q I Q k-1 L , . . . g Q,1 I Q k-1 L , . . . , f Q,Q I Q k-1 L ), Diag(ν) represents generation of a diagonal matrix with elements of the vector ν as diagonal elements, {tilde over (B)} (k) =1⊗B (k) , 1 represents a Q-dimensional all-1 column vector, ⊗ represents a Kronecker product of the matrix, and à (k) represents the matrix of the non-periodic orthogonal complementary sequence set of the k 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 à (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 (K) ; the matrix B (K) is the resulting ZCZ sequence set, wherein B q (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 K-2 L,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 à (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 (k) ; the matrix B (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 K-3 L,K≥ 3 (formula 10).