Multi-user detection method and apparatus for cell-free MIMO
Embodiments of the present disclosure provide a multi-user detection method and apparatus for cell-free Multiple-Input Multiple-Output (MIMO). The method includes: receiving, by a Central Processing Unit (CPU) of a cell-free MIMO system, an MRC merged data symbol stream S MRC =H H Y of K users transmitted by an Access Point (AP), and multiplying S MRC by a conjugate transpose matrix S MRC H of S MRC to obtain a K*K matrix S MRC S MRC H ; and performing singular value decomposition on the matrix S MRC S MRC H to obtain a unitary matrix V and a diagonal matrix A, obtaining a diagonal matrix Λ according to the diagonal matrix A, and estimating sending-end data symbols of the K users by a formula {tilde over (S)}=VΛV H S MRC .
1. A multi-user detection method for cell-free Multiple-Input Multiple-Output (MIMO), comprising:
receiving, by a Central Processing Unit (CPU) of a cell-free MIMO system, a Maximal Ratio Combining (MRC) merged data symbol stream S MRC =H H Y of K users transmitted by an Access Point (AP), wherein S MRC =H H Y denotes a K*L matrix, with each row representing L data symbols of one user, and both K and L are positive integers;
multiplying S MRC by a conjugate transpose matrix S MRC H of S MRC to obtain a K*K matrix S MRC S MRC H ;
performing singular value decomposition on the matrix S MRC S MRC H or
1
L
S
MRC
S
MRC
H
or on a matrix cS MRC S MRC H formed by multiplying the matrix S MRC S MRC H by any constant c to obtain a unitary matrix V=[v 1 , v 2 , . . . v K ] and K real numbers a 1 a 2 . . . a K , such that
1
L
S
MRC
S
MRC
H
=
VAV
H
,
wherein V H is a transpose matrix of the unitary matrix V, and
A
=
[
a
1
a
2
⋱
a
K
]
is a diagonal matrix constituted by the K real numbers a 1 a 2 . . . a x as diagonal elements; or calculating K characteristic values a 1 a 2 . . . a K and corresponding K characteristic vectors v 1 , v 2 , . . . V K of the matrix S MRC S MRC H or
1
L
S
MRC
S
MRC
H
,
such that
(
1
L
S
MRC
S
MRC
H
)
v
k
=
v
k
a
k
;
obtaining a diagonal matrix
Λ
=
[
λ
1
λ
2
⋱
λ
K
]
,
wherein
λ
k
=
2
σ
4
+
4
a
k
+
σ
2
or
λ
k
=
2
σ
4
+
4
a
k
+
c
σ
2
,
c is a real number greater than 1, and σ 2 is a noise variance on received signals of the AP; and
estimating, by a formula {tilde over (S)}=VΛV H S MRC , sending-end data symbols of the K users corresponding to the data symbol stream S MRC .
2. The method according to claim 1 , wherein before obtaining the diagonal matrix Λ, the method further comprises:
receiving, by the CPU, the noise variance σ 2 transmitted by the AP, or determining, by the CPU, the noise variance σ 2 according to an attribute of the AP.
3. A non-transitory computer-readable storage medium, storing computer programs, wherein the computer programs, when being executed by a processor, causes the processor to implement the operations of the method according to claim 1 .
4. The method according to claim 1 , wherein in a case of calculating K characteristic values a 1 a 2 . . . a K and corresponding K characteristic vectors v 1 , v 2 , . . . v K of the matrix S MRC S MRC H or
1
L
S
MRC
S
MRC
H
,
such that
(
1
L
S
MRC
S
MRC
H
)
v
k
=
v
k
a
k
,
the method further comprises:
constituting a K*K unitary matrix V=[v 1 , v 2 , . . . v K ] by the K characteristic vectors v k .
5. The method according to claim 1 , wherein off-diagonal elements of the diagonal matrix
A
=
[
a
1
a
2
⋱
a
K
]
are all 0.
6. The method according to claim 1 , wherein estimating, by a formula {tilde over (S)}=VΛV H S MRC , sending-end data symbols of the K users corresponding to the data symbol stream S MRC comprises:
obtaining MMSE estimation of sending-end data symbols of the K users according to H H H+σ 2 I and S MRC .
7. A multi-user detection method for cell-free Multiple-Input Multiple-Output (MIMO), comprising:
receiving, by a Central Processing Unit (CPU) of a cell-free MIMO system, a Maximal Ratio Combining (MRC) merged data symbol stream S MRC =H H Y of K users transmitted by an Access Point (AP), wherein S MRC =H H Y denotes a K*L matrix, with each row representing L data symbols of one user, and both K and L are positive integers;
performing singular value decomposition on the matrix S MRC or 1/√{square root over (L)}S MRC to obtain a unitary matrix V=[v 1 , v 2 , . . . v K ] and K real numbers ω 1 , ω 2 , . . . ω K , such that S MRC =V(√{square root over (L)}Ω)U H or 1/√{square root over (L)}S MRC =VΩU H , wherein U H is a transpose matrix of a unitary matrix U, and Ω is a K*L matrix:
Ω
=
[
ω
1
ω
2
0
⋱
ω
K
]
;
obtaining a diagonal matrix
Λ
=
[
λ
1
λ
2
⋱
λ
K
]
,
wherein
λ
k
=
2
σ
4
+
4
a
k
+
σ
2
or
λ
k
=
2
σ
4
+
4
a
k
+
c
σ
2
,
c is a real number greater than 1, and σ 2 is a noise variance on received signals of the AP, a k =|ω k | 2 ; and
estimating, by a formula {tilde over (S)}=VΛV H S MRC , Sending-end data symbols of the K users corresponding to the data symbol stream S MRC , wherein V H is a transpose matrix of the unitary matrix V.
8. The method according to claim 7 , wherein before obtaining the diagonal matrix Λ, the method further comprises:
receiving, by the CPU, the noise variance σ 2 transmitted by the AP, or determining, by the CPU, the noise variance σ 2 according to an attribute of the AP.
9. A multi-user detection apparatus for cell-free Multiple-Input Multiple-Output (MIMO), located in a Central Processing Unit (CPU) of a cell-free MIMO system, and comprising a memory storing instructions and a processor in communication with the memory, wherein the processor is configured to execute the instructions to implement the operations of the method according to claim 8 .
10. A multi-user detection apparatus for cell-free Multiple-Input Multiple-Output (MIMO), located in a Central Processing Unit (CPU) of a cell-free MIMO system, and comprising a memory storing instructions and a processor in communication with the memory, wherein the processor is configured to execute the instructions to implement the operations of the method according to claim 7 .
11. A cell-free Multiple-Input Multiple-Output (MIMO) system, comprising the multi-user detection apparatus according to claim 10 .
12. The method according to claim 7 , wherein estimating, by a formula Š=VΛV H S MRC , sending-end data symbols of the K users corresponding to the data symbol stream S MRC comprises:
obtaining MMSE estimation of sending-end data symbols of the K users according to H H H+σ 2 I and S MRC .
13. A multi-user detection apparatus for cell-free Multiple-Input Multiple-Output (MIMO), located in a Central Processing Unit (CPU) of a cell-free MIMO system, and comprising a memory storing instructions and a processor in communication with the memory, wherein the processor is configured to execute the instructions to implement the operations of the method according to claim 12 .
14. A non-transitory computer-readable storage medium, storing computer programs, wherein the computer programs, when being executed by a processor, causes the processor to implement the operations of the method according to claim 7 .
15. A multi-user detection apparatus for cell-free Multiple-Input Multiple-Output (MIMO), located in a Central Processing Unit (CPU) of a cell-free MIMO system, and comprising a memory storing instructions and a processor in communication with the memory, wherein the processor is configured to execute the instructions to:
receive a data symbol stream S MRC =H H Y of K users transmitted by an Access Point (AP), wherein S MRC =H H Y denotes a K*L matrix, with each row representing L data symbols of one user, and both K and L are positive integers;
multiply S MRC by a conjugate transpose matrix S MRC H of S MRC to obtain a K*K matrix S MRC S MRC H ;
perform singular value decomposition on the matrix S MRC S MRC H or
1
L
S
MRC
S
MRC
H
or on a matrix cS MRC S MRC H formed by multiplying the matrix S MRC S MRC H by any constant c to obtain a unitary matrix V=[v 1 , v 2 , . . . V K ] and K real numbers a 1 a 2 . . . a K , such that
1
L
S
MRC
S
MRC
H
=
VAV
H
,
wherein V H is a transpose matrix of the unitary matrix V, and
A
=
[
a
1
a
2
⋱
a
K
]
is a diagonal matrix constituted by the K real numbers as diagonal elements; or calculate K characteristic values a 1 a 2 . . . a K and corresponding K characteristic vectors v 1 , v 2 , . . . v K of the matrix S MRC S MRC H or
1
L
S
MRC
S
MRC
H
,
such that
(
1
L
S
MRC
S
MRC
H
)
v
k
=
v
k
a
k
;
obtain a diagonal matrix
Λ
=
[
λ
1
λ
2
⋱
λ
K
]
,
wherein
λ
k
=
2
σ
4
+
4
a
k
+
σ
2
or
λ
k
=
2
σ
4
+
4
a
k
+
c
σ
2
,
c is a real number greater than 1, and σ 2 is a noise variance on received signals of the AP; and
estimate, by a formula {tilde over (S)}=VΛV H S MRC , sending-end data symbols of the K users corresponding to the data symbol stream S MRC .
16. The apparatus according to claim 15 , wherein the processor is further configured to execute the instructions to receive the noise variance σ 2 transmitted by the AP, or determine the noise variance σ 2 according to an attribute of the AP.
17. A cell-free Multiple-Input Multiple-Output (MIMO) system, comprising the multi-user detection apparatus according to claim 15 .
18. The apparatus according to claim 15 , wherein in a case of calculating K characteristic values a 1 a 2 . . . a K and corresponding K characteristic vectors v 1 , v 2 , . . . v K of the matrix S MRC S MRC H or
1
L
S
MRC
S
MRC
H
,
such that
(
1
L
S
MRC
S
MRC
H
)
v
k
=
v
k
a
k
,
the processor is further configured to execute the instructions to:
constitute a K*K unitary matrix V=[v 1 , v 2 , . . . v K ] by the K characteristic vectors v k .
19. The apparatus according to claim 15 , wherein off-diagonal elements of the diagonal matrix
A
=
[
a
1
a
2
⋱
a
K
]
are all 0.
20. The apparatus according to claim 15 , wherein the processor is configured to execute the instructions to:
obtain MMSE estimation of sending-end data symbols of the K users according to H H H+σ 2 I and S MRC .