Signal sampling and recovery method and apparatus applicable to OvXDM system, and OvXDM system
The present application discloses a signal sampling and recovery method and apparatus applicable to an OvXDM system, and the OvXDM system. The method includes: constructing, based on design parameters, an observation matrix Φ that is irrelevant to an original signal y, wherein the observation matrix Φ is a two-dimensional M*S matrix, S is a length of the original signal y, and M is smaller than S; compressing the original signal y based on a formula Y cs =ΦY, to obtain a M*1 compressed signal Y cs , wherein Y is a S*1 column vector that is obtained according to the original signal y; and reconstructing the compressed signal Y cs based on a predetermined algorithm, so as to recover the original signal y. The present application implements accurate recovery of the original signal at a reduced sampling rate, thereby reducing hardware requirements of the system and improving feasibility of the technical solution.
1. A signal sampling and recovery method applicable to an Overlapped X Division Multiplexing (OvXDM) system, comprising:
constructing, based on design parameters, an observation matrix Φ that is irrelevant to an original signal y, wherein the observation matrix Φ is a two-dimensional M*S matrix, S is a length of the original signal y, and M is smaller than S, and M/S is greater than 0.1;
compressing the original signal y based on a formula Y cs =ΦY, to obtain a M*1 compressed signal Y cs , wherein Y is a S*1 column vector that is obtained according to the original signal y; and
reconstructing the compressed signal Y cs based on a predetermined algorithm, so as to recover the original signal y.
2. The signal sampling and recovery method applicable to an OvXDM system according to claim 1 , wherein a value of M is selected based on a sparsity of the original signal y.
3. The signal sampling and recovery method applicable to an OvXDM system according to claim 1 , wherein the step of reconstructing the compressed signal Y cs based on a predetermined algorithm, to recover the original signal y comprises:
transforming a S*S diagonal matrix to a sparse domain of the original signal y, to obtain an orthogonal transformation matrix Ψ;
calculating a recovery matrix T based on a formula T=ΦΨ′, wherein Ψ′ is a transposed matrix of Ψ;
setting a margin r n , an incremental matrix Aug_t, a 1*S to-be-reconstructed signal hat_Y in the sparse domain, and a total number N of iteration times, wherein N is a nonnegative integer, an initial value of the margin r 0 is equal to Y cs , and an initial value of the incremental matrix Aug_t is an empty matrix;
starting to perform an iterative calculation, wherein each iterative calculation comprises steps of:
calculating an inner product g n of the margin and each column of the recovery matrix T, to obtain S inner products, wherein g n =T′r n−1 ;
obtaining an index k that is corresponding to an element, having a maximum absolute value, in the S inner products, wherein k meets
k
=
arg
max
i
∈
(
1
,
S
)
g
n
[
i
]
;
storing data of the k th column of the recovery matrix T in the incremental matrix Aug_t to extend the incremental matrix Aug_t, and resetting the data of the k th column of the recovery matrix T to zero; wherein when the incremental matrix Aug_t is extended each time, data corresponding to the (n−1) th iteration times is reserved, and data corresponding to the n th iteration times is added to the end of the incremental matrix, and n is the current iteration times;
calculating an approximate signal Ŷ of the original signal y in the sparse domain, to obtain a formula Ŷ=(Aug_t′ Aug_t) −1 Aug_t′*Y cs ; wherein (●) represents a transposed operation on a matrix, and (●) −1 represents an inversion operation on a matrix;
calculating a margin between a compressed signal Y cs and the approximate signal Ŷ, to obtain a formula r n =Y cs −Aug_tŶ; and
adding 1 to n that represents the current iteration times, so as to update a total number of iteration times, until N iterative operations are completed;
for all approximate signals Ŷ obtained in the N iterative operations, updating, based on the index k obtained in each iterative operation, the approximate signal Ŷ obtained in each iterative operation to a column that is corresponding to the index k and is in the matrix of the to-be-reconstructed signal hat_Y in the sparse domain;
recovering the original signal y based on a formula y=Ψ*hat_Y.
4. The signal sampling and recovery method applicable to an OvXDM system according to claim 3 , wherein the total number N of iteration times is selected based on a sparsity of the original signal y.
5. The signal sampling and recovery method applicable to an OvXDM system according to claim 1 , wherein the predetermined algorithm comprises basic pursuit (BP) method, a matching pursuit (MP) method, or an orthogonal matching pursuit (OMP) method.
6. The signal sampling and recovery method applicable to an OvXDM system according to claim 1 , wherein the OvXDM system is an Overlapped Time Division Multiplexing (OvTDM) system, an Overlapped Frequency Division Multiplexing (OvFDM) system, an Overlapped Code Division Multiplexing (OvCDM) system, an Overlapped Space Division Multiplexing (OvSDM) system, or an Overlapped Hybrid Division Multiplexing (OvHDM) system.
7. A signal sampling and recovery apparatus applicable to an Overlapped X Division Multiplexing (OvXDM) system, comprising a hardware processor and a memory, the hardware processor is configured to execute programming units stored in the memory, and the programming units comprise:
an observation matrix constructing unit, configured to construct, based on design parameters, an observation matrix Φ that is irrelevant to an original signal y, wherein the observation matrix Φ is a two-dimensional M*S matrix, S is a length of the original signal y, and M is smaller than S, and M/S is greater than 0.1;
a compression unit, configured to compress the original signal y based on a formula Y cs =ΦY, to obtain a M*1 compressed signal Y cs , wherein Y is a S*1 column vector that is obtained according to the original signal y; and
a reconstructing and recovery unit, configured to reconstruct the compressed signal Y cs based on a predetermined algorithm, so as to recover the original signal y.
8. The signal sampling and recovery apparatus applicable to an OvXDM system according to claim 7 , wherein the observation matrix constructing unit further comprises a first value assignment unit, configured to select a value of M based on a sparsity of the original signal y.
9. The signal sampling and recovery apparatus applicable to an OvXDM system according to claim 8 , wherein M is equal to 200.
10. The signal sampling and recovery apparatus applicable to an OvXDM system according to claim 7 , wherein the reconstructing and recovery unit comprises:
a transformation matrix constructing unit, configured to transform a S*S diagonal matrix to a sparse domain of the original signal y, to obtain an orthogonal transformation matrix Ψ;
a recovery matrix calculating unit, configured to calculate a recovery matrix T based on a formula T=ΦΨ′, where Ψ′ is a transposed matrix of Ψ;
a setting unit, configured to set a margin r n , an incremental matrix Aug_t, a 1*S to-be-reconstructed signal hat_Y in the sparse domain, and a total number N of iteration times, wherein N is a nonnegative integer, an initial value of the margin r 0 is equal to Y cs , and an initial value of the incremental matrix Aug_t is an empty matrix;
an iteration unit, configured to perform iterative calculation, and comprising:
an inner product calculating unit, configured to calculate an inner product g n of the margin and each column of the recovery matrix T, to obtain S inner products, wherein g n =T′r n−1 ;
a searching unit, configured to obtain an index k that is corresponding to an element, having a maximum absolute value, in the S inner products, wherein k meets
k
=
arg
max
i
∈
(
1
,
S
)
g
n
[
i
]
;
an extension unit, configured to store data of the k th column of the recovery matrix T in the incremental matrix Aug_t to extend the incremental matrix Aug_t, and resetting the data of the k th column of the recovery matrix T to zero; wherein when the incremental matrix Aug_t is extended each time, data corresponding to the (n−1) th iteration times is reserved, and data corresponding to the n th iteration times is added to the end of the incremental matrix, and n is the current iteration times;
an approximate signal calculating unit, configured to calculate an approximate signal Ŷ of the original signal y in the sparse domain, to obtain a formula Ŷ=(Aug_t′ Aug_t) −1 Aug_t′*Y cs ; wherein (●)′ represents a transposed operation on a matrix, and (●) −1 represents an inversion operation on a matrix;
a margin calculating unit, configured to calculate a margin between a compressed signal Y cs and the approximate signal Ŷ, to obtain a formula r n =Y cs −Aug_tŶ;
a first updating unit, configured to update r n , wherein r n =Y cs −Aug_t Ŷ; and
a second updating unit, configured to add 1 to n that represents the current iteration times, so as to update a total number of iteration times, until N iterative operations are completed;
a reconstruction unit, configured to: for all approximate signals Ŷ obtained in the N iterative operations, update, based on the index k obtained in each iterative operation, the approximate signal Ŷ obtained in each iterative operation to a column that is corresponding to the index k and is in the matrix of the to-be-reconstructed signal hat_Y in the sparse domain; and
a recovery unit, configured to recover the original signal y based on a formula y=Ψ*hat_Y.
11. The signal sampling and recovery apparatus applicable to an OvXDM system according to claim 10 , wherein the iteration unit further comprises a second value assignment unit, configured to select the total number N of iteration times based on a sparsity of the original signal y.
12. The signal sampling and recovery apparatus applicable to an OvXDM system according to claim 7 , wherein the predetermined algorithm comprises basic pursuit (BP) method, a matching pursuit (MP) method, or an orthogonal matching pursuit (OMP) method.
13. The signal sampling and recovery apparatus applicable to an OvXDM system according to claim 7 , wherein the OvXDM system is an Overlapped Time Division Multiplexing (OvTDM) system, an Overlapped Frequency Division Multiplexing (OvFDM) system, an Overlapped Code Division Multiplexing (OvCDM) system, an Overlapped Space Division Multiplexing (OvSDM system), or an Overlapped Hybrid Division Multiplexing (OvHDM) system.
14. An Overlapped X Division Multiplexing (OvXDM) system, comprising the signal sampling and recovery apparatus, wherein the signal sampling and recovery apparatus comprises a hardware processor and a memory, the hardware processor is configured to execute programming units stored in the memory, and the programming units comprise:
an observation matrix constructing unit, configured to construct, based on design parameters, an observation matrix Φ that is irrelevant to an original signal y, wherein the observation matrix Φ is a two-dimensional M*S matrix, S is a length of the original signal y, and M is smaller than S, and M/S is greater than 0.1;
a compression unit, configured to compress the original signal y based on a formula Y cs =ΦY, to obtain a M*1 compressed signal Y cs , wherein Y is a S*1 column vector that is obtained according to the original signal y; and
a reconstructing and recovery unit, configured to reconstruct the compressed signal Y cs based on a predetermined algorithm, so as to recover the original signal y.
15. The OvXDM system according to claim 14 , wherein the observation matrix constructing unit further comprises a first value assignment unit, configured to select a value of M based on a sparsity of the original signal y.
16. The OvXDM system according to claim 14 , wherein M is equal to 200.
17. The OvXDM system according to claim 14 , wherein the reconstructing and recovery unit comprises:
a transformation matrix constructing unit, configured to transform a S*S diagonal matrix to a sparse domain of the original signal y, to obtain an orthogonal transformation matrix Ψ;
a recovery matrix calculating unit, configured to calculate a recovery matrix T based on a formula T=Φψ′, where Ψ′ is a transposed matrix of Ψ;
a setting unit, configured to set a margin rn, an incremental matrix Aug_t, a 1*S to-be-reconstructed signal hat_Y in the sparse domain, and a total number N of iteration times, wherein N is a nonnegative integer, an initial value of the margin r0 is equal to Y cs , and an initial value of the incremental matrix Aug_t is an empty matrix;
an iteration unit, configured to perform iterative calculation, and comprising:
an inner product calculating unit, configured to calculate an inner product gn of the margin and each column of the recovery matrix T, to obtain S inner products, wherein g n −T′r n−1 ;
a searching unit, configured to obtain an index k that is corresponding to an element, having a maximum absolute value, in the S inner products, wherein k meets
k
=
arg
max
i
∈
(
1
,
S
)
i
∈
(
1
,
S
)
g
n
[
i
]
;
an extension unit, configured to store data of the kth column of the recovery matrix T in the incremental matrix Aug_t to extend the incremental matrix Aug_t, and resetting the data of the kth column of the recovery matrix T to zero; wherein when the incremental matrix Aug_t is extended each time, data corresponding to the (n−1)th iteration times is reserved, and data corresponding to the nth iteration times is added to the end of the incremental matrix, and n is the current iteration times;
an approximate signal calculating unit, configured to calculate an approximate signal Ŷ of the original signal y in the sparse domain, to obtain a formula Ŷ=(Aug_t′ Aug_t) −1 Aug_t′*Y cs ; wherein (●)′ represents a transposed operation on a matrix, and (●) −1 represents an inversion operation on a matrix;
a margin calculating unit, configured to calculate a margin between a compressed signal Y cs and the approximate signal Ŷ, to obtain a formula r n =Y cs −Aug_tŶ;
a first updating unit, configured to update rn, wherein r n =Y cs =Aug_tŶ; and
a second updating unit, configured to add 1 to n that represents the current iteration times, so as to update a total number of iteration times, until N iterative operations are completed;
a reconstruction unit, configured to: for all approximate signals Ŷ obtained in the N iterative operations, update, based on the index k obtained in each iterative operation, the approximate signal Ŷ obtained in each iterative operation to a column that is corresponding to the index k and is in the matrix of the to-be-reconstructed signal hat_Y in the sparse domain; and
a recovery unit, configured to recover the original signal y based on a formula y=Ψ*hat_Y.
18. The OvXDM system according to claim 17 , wherein the iteration unit further comprises a second value assignment unit, configured to select the total number N of iteration times based on a sparsity of the original signal y.
19. The OvXDM system according to claim 14 , wherein the predetermined algorithm comprises basic pursuit (BP) method, a matching pursuit (MP) method, or an orthogonal matching pursuit (OMP) method.
20. The OvXDM system according to claim 14 , wherein the OvXDM system is an Overlapped Time Division Multiplexing (OvTDM) system, an Overlapped Frequency Division Multiplexing (OvFDM) system, an Overlapped Code Division Multiplexing (OvCDM) system, an Overlapped Space Division Multiplexing (OvSDM) system, or an Overlapped Hybrid Division Multiplexing (OvHDM) system.