Transmit method based on satellite massive MIMO integrated sensing and communication
Disclosed is a transmit method based on satellite massive Multiple-Input Multiple-Output (MIMO) integrated sensing and communication, where a satellite end is equipped with a massive MIMO array to implement an integrated sensing and communication system. The satellite end sends a communication signal to multiple user terminals based on statistical properties of electromagnetic wave propagation, and detects multiple targets simultaneously, thus realizing simultaneous communication of the satellite end with the user terminals and sensing for the targets. The present disclosure fully utilizes the spectrum resources, implements a flexible switch between wireless communication and target sensing functions based on a satellite, and mitigates the effects of the beam squint on system performance, thus greatly improving communication performance and radar resolution and being applicable for construction of an integrated network of space, air, ground and sea to achieve global coverage.
1. A transmit method based on satellite massive Multiple-Input Multiple-Output (MIMO) integrated sensing and communication, comprising:
providing a satellite end with a massive MIMO antenna array which simultaneously serves multiple users and detects multiple targets, wherein communication and sensing use the same spectrum resources and the same hardware platform, and integrated sensing and communication is implemented by transmitting a signal to focus on communication or sensing;
estimating, by the satellite end, statistical status information of electromagnetic wave propagation according to received uplink and downlink pilot signals, wherein for a communication process, the statistical status information of electromagnetic wave propagation is a channel gain and a channel direction vector between the satellite end and user terminals;
for a sensing process, configuring the statistical status information of electromagnetic wave propagation with angles of departure of the targets;
according to the statistical status information of electromagnetic wave propagation, transmitting, by the satellite end, a directional beam to a detection target and a downlink signal to each user terminal by means of integrated sensing and communication precoding; and
during dynamic movement of the satellite and the user terminals as well as the targets, updating the integrated sensing and communication precoding with a change in the statistical status information of electromagnetic wave propagation between the satellite and the user terminals as well as the targets.
2. The transmit method based on satellite massive MIMO integrated sensing and communication according to claim 1 , wherein in the simultaneously implementing communication and sensing, performance of communication and sensing is weighed by introduction of a weighting coefficient.
3. The transmit method based on satellite massive MIMO integrated sensing and communication according to claim 2 , wherein the integrated sensing and communication precoding comprises the following steps:
to ensure the-radar sensing performance while seeking maximum energy efficiency of communication, establishing an optimization problem based on equation (1):
P
1
:
maximize
{
V
[
m
]
,
W
[
m
]
,
U
[
m
]
}
m
=
1
M
∑
k
=
1
K
R
k
P
total
(
1
)
s
.
t
.
∑
k
=
1
K
∑
m
=
1
M
V
[
m
]
w
k
[
m
]
2
2
≤
P
,
V
[
m
]
∈
S
,
∀
m
,
V
[
m
]
W
[
m
]
-
B
rad
[
m
]
U
[
m
]
F
2
≤
ε
,
∀
m
,
U
[
m
]
U
H
[
m
]
=
I
P
r
,
∀
m
,
wherein K denotes the number of users; R k denotes a communication rate between the satellite and a kth user; P total denotes a total transmission power; M denotes the number of sub-carriers; V[m] denotes a constant-modulus RF precoder; W[m] denotes a baseband precoder; w k [m] denotes a baseband precoding vector for the kth user; P denotes the power budget; S denotes constraints analog precoders need to satisfy; B rad [m] denotes an optimal sub-array radar precoder; U[m] denotes an auxiliary unitary matrix introduced at an mth sub-carrier; ε is an Euclidean distance tolerance term between a hybrid precoder and the radar precoder; I P r is a unit matrix of an order P r ×P r ; P r denotes the number of targets; and ∥*∥, denotes the Frobenius-norm of a matrix F;
for the optimization problem P 1 , regarding the product of the analog and digital precoders as a whole and disregarding irrelevant constraints for the moment, obtaining a fully digital precoding problem P 2 by equation (2):
P
2
:
maximize
{
B
[
m
]
}
m
=
1
M
∑
k
=
1
K
R
k
P
total
(
2
)
s
.
t
.
∑
k
=
1
K
∑
m
=
1
M
b
k
[
m
]
2
2
≤
P
.
wherein B[m] denotes a hybrid precoding matrix, and b k [m]=V[m]w k [m] denotes a precoding matrix for the kth user;
considering statistical properties of wave propagation, using a tight bound R k [m] of R k [m] as a replacement based on equation (3):
R
k
[
m
]
≤
R
_
k
[
m
]
▯
log
(
1
+
γ
k
❘
"\[LeftBracketingBar]"
v
k
H
[
m
]
b
k
[
m
]
❘
"\[RightBracketingBar]"
2
∑
ℓ
≠
k
γ
k
❘
"\[LeftBracketingBar]"
v
k
H
[
m
]
b
ℓ
[
m
]
❘
"\[RightBracketingBar]"
2
+
N
0
)
.
(
3
)
wherein R k [m] denotes the rate of the kth user on the mth sub-carrier, γ k is channel energy between the satellite and the kth user, v k [m] denotes an array response vector at the mth sub-carrier with a frequency of f m , and N 0 denotes the noise power;
letting B (i) ={B (i) [m]} m=1 M be a precoding matrix set of all the sub-carriers, and transforming the problem P 2 into a series of sub-problems P 3 (i) by means of the Dinkelbach algorithm, wherein i=1, 2, . . . , based equation (4):
P
3
(
i
)
:
maximize
B
(
i
)
F
(
B
(
i
)
,
η
(
i
)
)
=
∑
k
=
1
K
R
_
k
(
B
(
i
)
)
-
η
(
i
)
P
total
(
B
(
i
)
)
(
4
)
s
.
t
.
∑
k
=
1
K
∑
m
=
1
M
b
k
(
i
)
[
m
]
2
2
≤
P
.
wherein R k (B (i) ) denotes the tight bound of a rate associated with the precoding matrix set of all the sub-carriers, P total (B (i) ) denotes the total power associated with the precoding matrix set of all the sub-carriers, and the auxiliary variable η (i) meets the following equation (5):
η
(
i
)
=
∑
k
=
1
K
R
_
k
(
B
(
i
-
1
)
)
P
total
(
B
(
i
-
1
)
)
;
(
5
)
taking an ith sub-problem into consideration, and omitting the serial number i for convenience; letting b k [m]=b k,m and v k [m] k,m , and then expressing the problem P 3 (i) based equation (6):
P
3
:
maximize
B
F
(
B
)
=
∑
k
=
1
K
∑
m
=
1
M
log
(
1
+
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
∑
ℓ
≠
k
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
+
N
0
)
-
η
(
ξ
b
k
,
m
2
2
+
P
t
)
(
6
)
s
.
t
.
∑
k
=
1
K
∑
m
=
1
M
b
k
,
m
2
2
≤
P
.
wherein 1/ζ is effectiveness of an amplifier, and P t is static power consumption;
by introducing an auxiliary variable λ={λ k,m } k=1,m=1 K,M and by means of Lagrangian dual transformation, transforming the problem P 3 into P 4 based on equation (7):
P
4
:
maximize
B
,
λ
F
(
B
,
λ
)
=
∑
k
=
1
K
∑
m
=
1
M
log
(
1
+
λ
k
,
m
)
+
(
1
+
λ
k
,
m
)
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
∑
ℓ
≠
k
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
+
N
0
-
λ
k
,
m
-
η
(
ξ
b
k
,
m
2
2
+
P
t
)
(
7
)
s
.
t
.
∑
k
=
1
K
∑
m
=
1
M
b
k
,
m
2
2
≤
P
.
wherein λ k,m denotes an auxiliary variable; and
when B is fixed, F(B, λ) is a concave function for the variable λ k,m , and let ϑF/ϑλ k,m =0, to obtain:
λ
k
,
m
opt
=
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
k
,
m
❘
"\[RightBracketingBar]"
2
∑
ℓ
≠
k
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
+
N
0
.
(
8
)
wherein λ k,m opt denotes an optimal value of the auxiliary variable;
by introducing the auxiliary variable ρ={ρ k,m } k=1,m=1 K,M and by means of quadratic transformation, transforming the problem P 4 into equations (9) and (10):
P
5
:
maximize
B
,
λ
,
ρ
F
(
B
,
λ
,
ρ
)
(
9
)
s
.
t
.
∑
k
=
1
K
∑
m
=
1
M
b
k
,
m
2
2
≤
P
.
wherein ρ k,m denotes the auxiliary variable; and
F
(
B
,
λ
,
ρ
)
=
∑
k
=
1
K
∑
m
=
1
M
log
(
1
+
λ
k
,
m
)
-
λ
k
,
m
+
2
(
1
+
λ
k
,
m
)
γ
k
ℜ
{
b
k
,
m
H
v
k
,
m
ρ
k
,
m
}
-
❘
"\[LeftBracketingBar]"
ρ
k
,
m
❘
"\[RightBracketingBar]"
2
(
∑
K
ℓ
≠
k
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
+
N
0
)
-
η
(
ξ
b
k
,
m
2
2
+
P
t
)
.
(
10
)
wherein {*} denotes an operator for evaluation of a real part; and
letting ∂F/∂ρ k,m =0, to obtain:
ρ
=
(
1
+
λ
k
,
m
)
γ
k
v
k
,
m
H
b
k
,
m
∑
K
ℓ
=
1
γ
k
❘
"\[LeftBracketingBar]"
v
k
,
m
H
b
ℓ
,
m
❘
"\[RightBracketingBar]"
2
+
N
0
.
(
11
)
wherein ρ k,m opt denotes an optimal value of the auxiliary variable;
when (η,λ,ρ) is fixed, a target function of the problem P 5 being convex for the variable b k,m , and then using the Lagrangian operator method for evaluation; and specifically, introducing the Lagrange multiplier t, and then expressing the Lagrange function of the problem P 5 based on equation (12):
L
(
ℬ
,
λ
,
ρ
,
t
)
=
F
(
ℬ
,
λ
,
ρ
)
+
t
(
∑
K
k
=
1
∑
M
m
=
1
b
k
,
m
2
2
-
P
)
.
(
12
)
wherein from KKT conditions, the following equations (13) and (14) are obtained:
b
k
,
m
opt
=
(
∑
K
ℓ
=
1
❘
"\[LeftBracketingBar]"
ρ
ℓ
,
m
❘
"\[RightBracketingBar]"
2
γ
ℓ
v
ℓ
,
m
v
ℓ
,
m
H
+
(
ηξ
+
t
)
I
)
-
1
(
1
+
λ
k
,
m
)
γ
k
ρ
k
,
m
v
k
,
m
,
(
13
)
t
=
arg
min
t
≥
0
b
k
,
m
opt
2
2
≤
P
.
(
14
)
wherein b k,m opt denotes an optimal value of a precoding vector and I denotes a unit matrix;
for the mth sub-carrier, after an equivalent fully digital pre-coding matrix B com [m] is obtained, introducing a weighting coefficient ζ to weigh the performance of communication and sensing modules, wherein a corresponding minimization problem for a weighted sum is:
Q
1
:
minimize
V
[
m
]
,
W
[
m
]
,
U
[
m
]
f
(
V
[
m
]
,
W
[
m
]
,
U
[
m
]
)
=
ζ
V
[
m
]
W
[
m
]
-
B
com
[
m
]
F
2
+
(
1
-
ζ
)
V
[
m
]
W
[
m
]
-
U
[
m
]
F
2
(
15
)
s
.
t
.
V
[
m
]
∈
S
,
∀
m
,
B
com
[
m
]
F
2
=
V
[
m
]
W
[
m
]
F
2
,
U
[
m
]
U
H
[
m
]
=
I
P
,
∀
m
;
;
and for any sub-carrier m, analog and digital precoding vectors are obtained by means of iterative solution, and the mark number m is omitted in the following description;
for the analog precoders using the fully connected structure:
(1) for the fixed V and W, transforming the problem Q 1 into:
Q
2
:
minimize
U
VW
-
B
rad
U
F
2
(
16
)
s
.
t
.
UU
H
=
I
P
r
,
obtaining a solution to the problem Q 2 by means of singular value decomposition, namely:
U=QI P r ×K R, (17)
wherein Q and R are results after singular value decomposition is performed for B rad H VW, that is, QΣR=B rad H VW, Q and R being unitary matrixes and Σ being a diagonal matrix; and I P r ×K =[I P r , 0] is a sparse matrix;
(2) for the fixed V and U, transforming the problem Q 1 into:
Q
3
:
minimize
W
ζ
VW
-
B
com
F
2
+
(
1
-
ζ
)
VW
-
B
rad
U
F
2
(
18
)
s
.
t
.
B
com
F
2
=
AW
F
2
,
wherein for the problem Q 3 , its target function is expressed as a weighted sum of two F norms; and let the auxiliary matrixes A=[√{square root over (ζ)}V T , √{square root over (1−ζ)}V T ] T ∈C 2N t ×M t and C=[√{square root over (ζ)}B com T , √{square root over (1−ζ)}U T B rad T ] T ∈C 2N t ×K , to obtain A H A=V H V; and thus, the problem Q 3 is transformed into:
Q
4
:
minimize
W
AW
-
C
F
2
s
.
t
.
B
com
=
AW
F
2
,
;
(
19
)
then, updating the digital precoder W based on equations (20) and (21):
W
=
(
A
H
A
)
-
1
A
H
C
=
(
V
H
V
)
-
1
A
H
C
,
(
20
)
W
=
B
com
F
VW
F
W
.
(
21
)
(3) letting G=[√{square root over (ζ)}W, √{square root over (1−ζ)}W]∈ M 1 2K and T=[√{square root over (ζ)}B com , √{square root over (1−ζ)}B rad U]∈ N t ×2K be auxiliary matrixes, and for the fixed W and U, transforming the problem Q 1 into:
Q
5
:
minimize
W
VG
-
T
F
2
s
.
t
.
V
∈
S
FC
,
;
(
22
)
letting the auxiliary matrix Y=GG H , wherein its maximum characteristic value is λ max (Y); and then transforming the problem Q 5 into:
V =exp{−ø∠ Z T }, (23)
wherein ø=√{square root over (−1)}, Z=GT H −(Y−λ max (Y)I M t )V H is an auxiliary matrix, and ∠ denotes an operator for evaluation of an angle; and
repeating steps (1) to (3) till the target function/converges;
for the analog precoder having the partially connected structure, the (i,j)th element thereof being [V] i,j =exp{øϕ i,j }, and ∀i, j=┌i/N g ┐, wherein ┌*┐ denotes an operator for evaluation of an upper bound; ϕ i,j being an angle of the (i,j)th element in the matrix, and N g =N t /M t ; and a corresponding analog precoding matrix meeting
VW
F
2
=
N
g
W
F
2
=
B
com
F
2
;
(a) for the fixed V and W, transforming the problem Q 1 into:
Q
6
:
minimize
U
VW
-
B
r
ad
U
F
2
(
24
)
s
.
t
.
UU
H
=
I
P
r
,
obtaining a solution to the problem Q 6 by means of singular value decomposition, namely:
U=QI P r ×K R, (25)
wherein Q and R are results after singular value decomposition is performed for B mod H VW, that is, QΣR=B mod H VW, Q and R being unitary matrixes and Σ being a diagonal matrix; and I P r ×K =[I P r , 0] is a sparse matrix;
(b) letting Let A=[√{square root over (ζ)}V T , √{square root over (1−ζ)}V T ] T ∈ 2N t ×M t and C=[√{square root over (ζ)}B com T , √{square root over (1−ζ)}U T B rad T ] T ∈ 2N t ×K be auxiliary matrixes, and for the fixed V and U, transforming the problem Q 1 into:
Q
7
:
minimize
W
A
H
C
-
W
F
2
s
.
t
.
W
F
=
B
com
F
N
g
,
;
(
26
)
and then, updating the digital precoder W as follows:
W
=
B
com
F
N
g
A
H
C
A
H
C
F
.
(
27
)
(c) letting the auxiliary matrixes a=[√{square root over (ζ)}[B com ] i,: , √{square root over (1−ζ)}[B rad U] i,: ] and p=[√{square root over (ζ)}[W] j,: , √{square root over (1−ζ)}[W] j,: ], wherein [*] i,: denotes the ith row of the matrix and [*] j,: denotes the jth row of the matrix; and for the fixed W and U, transforming the problem Q 1 into:
Q
8
:
minimize
V
a
-
exp
{
⌀ϕ
i
,
j
}
p
2
2
(
28
)
s
.
t
.
V
∈
S
PC
,
then, expressing a solution to the problem Q 8 as follows:
[
V
]
i
,
j
=
exp
{
⌀∠
(
ap
H
)
}
,
∀
i
,
∀
j
=
⌈
i
N
g
⌉
;
(
29
)
repeating steps (a) to (c) till the target function f converges.