# US 12,119,911 B1 · Superdirective antenna array multi-user precoding method, device and medium

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- Number: US 12,119,911 B1
- Document ID: US12119911B1
- Status: Granted
- Kind: B1
- Application number: 18/419,473
- Filed: 2024-01-22
- Granted: 2024-10-15
- Earliest claimed: 2023-06-12
- Assignees: Huazhong University of Science and Technology
- Applicants: Huazhong University of Science and Technology
- Inventors: Haifan Yin; Liangcheng Han; Desheng Wang
- Web page: https://patentgrep.com/patent/US12119911B1

## CPC

- H04B 7/0634: {Antenna weights or vector/matrix coefficients}
- H04B 7/0452: Multi-user MIMO systems
- H04B 7/0456: Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
- H04B 7/0479: {for multi-dimensional arrays, e.g. horizontal or vertical pre-distortion matrix index [PMI]}
- H04B 7/0626: {Channel coefficients, e.g. channel state information [CSI]}
- Y02D 30/70: in wireless communication networks
- H04B: TRANSMISSION
- Y02D: CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE

## Abstract

A superdirective antenna array multi-user precoding method, a device, and a medium belonging to the field of wireless communication are provided. The method includes: constructing a unitary matrix U ∈ CM×M for terminal users U, last N(N≤K−1) columns of the unitary matrix U being an orthonormal basis of the interfering user channel space span {hi,i=1, . . . ,K,i≠u} respectively, where N is a dimension of the interfering user channel space, M is the total number of antennas on a network device side, K is the total number of terminal users communicating, and M≥K is satisfied; intercepting the first M−N rows of a matrix UHhu to obtain a matrix ηu, where ηu ∈ C(M−N)×1, hu represents channel state information of the uth terminal user, and the superscript H represents a conjugate transpose; intercepting first M−N rows and first M−N columns of a matrix UHZU to obtain a matrix , where ∈ C(M−N)×(M−N) a matrix Z ∈CM×M, elements in Z represent coupling coefficients of any two antennas; calculating a precoding matrix au=U a u = U ⁡ ( α u 0 ) of the uth terminal user, where αu=−1ηu*.

## Claims

### Claim 1

A superdirective antenna array multi-user precoding method, the method comprising:
constructing a unitary matrix U ∈ CM×M for terminal users u, last N(N≤K−1) columns of the unitary matrix U being an orthonormal basis of an interfering user channel space span {hi,i=1, . . . ,K,i≠u} respectively, wherein N is a dimension of an interfering user channel space, hi ∈ CM×1 represents a channel state information of an ith terminal user, M is a total number of antennas on a network device side, K is a total number of terminal users communicating, and M≥K is satisfied;
intercepting first M−N rows of a matrix UHhu to obtain a matrix ηu, wherein ηu ∈ C(M−N)×1, hu represents a channel state information of a uth terminal user, and a superscript H represents a conjugate transpose;
intercepting first M−N rows and first M−N columns of a matrix UHZU to obtain a matrix , wherein ∈C(M−N)×(M−N), a matrix Z ∈ CM×M, and elements in z represent coupling coefficients of any two antennas; and
calculating a precoding matrix au=U
a
u
=
U
⁡
(
α
u
0
)
of the uth terminal user, where
αu=−1ηu*, and a superscript * represents a conjugation.

### Claim 2 (depends on 1)

The superdirective antenna array multi-user precoding method according to claim 1, wherein before intercepting first M−N rows and first M−N columns of the matrix UHZU to obtain the matrix , the method further comprises: updating matrix z to Z+Λ, wherein Λ ∈CM×M is a regularization matrix of the matrix Z.

### Claim 3 (depends on 2)

The superdirective antenna array multi-user precoding method according to claim 2, wherein the regularization matrix Λ is:
A
=
r
loss
R
r
⁢
a
⁢
d
⁢
I
m
,
r
loss
=
L
6
⁢
π
⁢
a
⁢
π
⁢
f
⁢
μ
σ
,
and
R
r
⁢
a
⁢
d
≈
2
⁢
4
.
7
⁢
(
kL
/
2
)
2
.
5
,
wherein rloss and Rrad are a loss and a radiation impedance of an antenna respectively, IM is a unit matrix of M×M, and L, α, ƒ, ƒ, μ, σ, and κ are a length, a radius, an operating frequency, a magnetic permeability, a conductivity and a wave number of an antenna respectively.

### Claim 4 (depends on 2)

The superdirective antenna array multi-user precoding method according to claim 2, wherein the regularization matrix Λ is:
Λ
=
ϵ
2
4
⁢
π
⁢
∫
0
2
⁢
π
∫
0
π
❘
"\[LeftBracketingBar]"
k
⁡
(
θ
,
ϕ
)
❘
"\[RightBracketingBar]"
2
⁢
d
⁢
θ
⁢
d
⁢
ϕ
⁢
I
M
,
wherein ϵ2 is a Gaussian noise power, κ(θ, Φ) is a pattern function of an antenna, θ and Φ are far-field coordinate components in a spherical coordinate system, and IM is a unit matrix of M×M.

### Claim 5 (depends on 2)

The superdirective antenna array multi-user precoding method according to claim 2, wherein the regularization matrix Λ is:
A
=
r
loss
R
r
⁢
a
⁢
d
⁢
I
M
+
ϵ
2
4
⁢
π
⁢
∫
0
2
⁢
π
∫
0
π
❘
"\[LeftBracketingBar]"
k
⁡
(
θ
,
ϕ
)
❘
"\[RightBracketingBar]"
2
⁢
d
⁢
θ
⁢
d
⁢
ϕ
⁢
I
M
,
r
loss
=
L
6
⁢
π
⁢
a
⁢
π
⁢
f
⁢
μ
σ
,
and
R
r
⁢
a
⁢
d
≈
24.7
(
kL
/
2
)
2
.
5
wherein rloss and Rrad are a loss and a radiation impedance of an antenna respectively, IM is a unit matrix of M×M, L, α, ƒ, μ, σ, and κ are a length, a radius, an operating frequency, a magnetic permeability, a conductivity and a wave number of an antenna respectively, ϵ2 is a Gaussian noise power, κ(θ, Φ) is a pattern function of the antenna, and θ and Φ are far-field coordinate components in a spherical coordinate system.

### Claim 6 (depends on 1)

The superdirective antenna array multi-user precoding method according to claim 1, wherein the constructing the unitary matrix U ∈ CM×M specifically is:
constructing a total interference covariance matrix:
R
int
=
∑
i
≠
u
(
h
i
⁢
h
i
H
)
,
performing a singular value decomposition (SVD) decomposition on Rint to obtain:
Rint=WHΛW,
wherein W is a unitary matrix, unitary matrix U is:
[last (M−N) columns of W, first N columns of W].

### Claim 7 (depends on 1)

The superdirective antenna array multi-user precoding method according to claim 1, wherein the matrix
Z
=
[
z
11
⋯
z
1
⁢
M
⋮
⋱
⋮
z
M
⁢
1
⋯
z
MM
]
,
z
m
⁢
n
=
1
4
⁢
π
⁢
∫
0
2
⁢
π
∫
0
π
❘
"\[LeftBracketingBar]"
k
⁡
(
θ
,
ϕ
)
❘
"\[RightBracketingBar]"
2
⁢
e
jk
⁢
r
^
·
r
m
⁢
e
-
jk
⁢
r
^
·
r
n
⁢
sin
⁢
θ
⁢
d
⁢
θ
⁢
d
⁢
ϕ
,
wherein zmn represents a coupling coefficient of a mth antenna and a nth antenna, κ(θ, Φ) is a pattern function of an antenna, θ and Φ are far-field coordinate components in a spherical coordinate system, k is a wave number of an antenna, {circumflex over (r)} is a unit vector in a spherical coordinate system, rm and rn are the coordinates of the mth antenna and the nth antenna respectively, m=1, . . . ,M, and n=1, . . . ,M.

### Claim 8 (depends on 1)

The superdirective antenna array multi-user precoding method according to claim 1, wherein each of the last N(N≤K−1) columns of the unitary matrix U being an orthonormal basis of an interfering user channel space span {hi,i=1, . . . ,K,i≠u}, comprises:
letting [ν1, . . . ,νK−1] ∈ CM×(K−1) be a matrix formed by an interfering user channel vector, if N=K−1, the last K−1 columns of the unitary matrix U are
v
_
i

v
_
i

,
i=1, . . . , K−1, wherein:
{
v
_
1
=
v
1

v
1

v
_
2
=
v
2
-
v
_
1
H
⁢
v
2

v
_
1

⁢
v
_
1
,
v
_
3
=
v
3
-
v
_
1
H
⁢
v
3

v
_
1

⁢
v
_
1
-
v
_
2
H
⁢
v
3

v
_
2

⁢
v
_
2
⋮
v
_
K
-
1
=
v
K
-
1
=
v
_
1
H
⁢
v
K
-
1

v
_
1

⁢
v
_
1
-
…
-
v
_
K
-
2
H
⁢
v
K
-
1

v
_
K
-
2

⁢
v
_
K
-
2
;
if N≤K−1, obtaining N non-zero vectors after calculating
v
_
i

v
_
i

,
i=1, . . . , K−1, selecting the N non-zero vectors as the last N columns of U.

### Claim 9

A superdirective antenna array multi-user precoding method, the method comprising:
constructing a unitary matrix w ∈ CM×M for terminal users U, first N(N≤K−1) columns of the unitary matrix w being an orthonormal basis of an interfering user channel space span {hi,i=1, . . . ,K,i≠u} respectively, wherein N is a dimension of an interfering user channel space, hi ∈CM×1 represents a channel state information of an ith terminal user, M is a total number of antennas on a network device side, K is a total number of terminal users communicating, and M≥K is satisfied;
intercepting last M−N columns of unitary matrix w and obtaining a matrix R, A wherein R ∈CM×(M−N); and
calculating a precoding matrix au=RRHauopt of the uth terminal user, wherein auopt=Z−1hu*, hu represent a channel state information of the uth terminal user, a matrix z ∈ CM×M, elements in Z represent coupling coefficients of any two antennas, a superscript H represents a conjugate transpose, and a superscript * represents a conjugation.

### Claim 10

A network device, comprising:
a structural circuit configured to construct a unitary matrix U ∈ CM×M for terminal users u, last N(N≤K−1) columns of the unitary matrix U is an orthonormal basis of an interfering user channel space span {hi,i=1, . . . ,K,i≠u} respectively, N is a dimension of an interfering user channel space, hi ∈ CM×1 represents a channel state information of the ith terminal user, M is a total number of antennas on a network device side, K is a total number of terminal users communicating, and M≥K is satisfied;
a first interception circuit configured to intercept first M−N rows of a matrix UHhu to obtain a matrix ηu, wherein ηu ∈C(M−N)×1 represents a channel state information of an uth terminal user, a superscript H represents a conjugate transpose;
a second interception circuit configured to intercept first M−N rows, first M−N columns of a matrix UHZU to obtain a matrix , wherein ∈C(M−N)×(M−N) a matrix z ∈ CM×M, elements in z represent coupling coefficients of any two antennas; and
a calculation circuit configured to calculate a precoding matrix au=U
a
u
=
U
⁡
(
α
u
0
)
of an uth terminal user, wherein au=−1ηu*, a superscript * represents a conjugation.

### Claim 11

A network device, comprising:
a structural circuit configured to construct a unitary matrix w ∈ CM×M for terminal users u, first N(N≤K−1) columns of the unitary matrix w is an orthonormal basis of an interfering user channel space span {hi,i=1, . . . ,K,i≠u}respectively, N is a dimension of an interfering user channel space, hi ∈ CM×1 represents a channel state information of an ith terminal user, M is a total number of antennas on a network device side, K is a total number of terminal users communicating, and M≥K is satisfied;
an interception circuit configured to intercept last M−N columns of an A unitary matrix w to obtain a matrix R, wherein R ∈ CM×(M−N); and
a calculation circuit configured to calculate a precoding matrix au=RRHauopt of an uth terminal user, wherein auopt=Z−1hu*, a superscript * represents a conjugation, hu represent a channel state information of an uth terminal user, a matrix z ∈ CM×M, elements in z represent coupling coefficients of any two antennas, and a superscript H represents a conjugate transpose.

### Claim 12 (depends on 1)

An electronic device, comprising:
a processor; and
a memory, configured to store an executable command of the processor,
wherein the processor is configured to execute the superdirective antenna array multi-user precoding method according to claim 1 by executing the executable command.

### Claim 13 (depends on 1)

A non-transitory computer readable storage medium, the non-transitory computer readable storage medium stores a computer-executable command, when a processor executes the computer-executable command, the superdirective antenna array multi-user precoding method according to claim 1 is implemented.