Sensing coupled emergency communication service quality assurance method
A sensing coupled emergency communication service quality assurance method includes: determining a communication latency index θ, which is taken as a communication QoS indicator, obtaining a user effective capacity C by calculating a user communication rate, calculating a detection probability P d and a false alarm rate P f according to radar echo signal energy detection results, fusing P d and P f into an effective capacity equation to obtain an expanded effective capacity, constructing an optimization problem by taking a total expanded effective capacity of the system as an objective function and taking the power, latency index and detection probability as constraints, and allocating the user power according to solution results of the optimization problem. The method can meet requirements of communication latency and detection probability of users at the same time, improve the aggregated effective capacity of the system, and can be used to guarantee multi-user communication and sensing services in post-disaster rescue scenarios.
1 . A sensing coupled emergency communication service quality assurance method, comprising:
(1) obtaining a communication latency index θ and an effective capacity C of a corresponding user:
(1a) taking the communication latency index θ as a communication quality of service (QoS) indicator, obtaining a receive signal of each user and a signal to interference plus noise ratio (SINR) γ of the corresponding user based on a general expression of multiple-in multiple-out (MIMO) signals, and obtaining a communication rate R of the corresponding user by Shannon's theorem based on γ; and
(1b) calculating, based on the communication rate R, an expression of the effective capacity C of the corresponding user by using an effective capacity theory;
(2) determining a detection probability P d and a false alarm rate P f :
(2a) separating, based on a total echo signal received by a mobile integrated sensing and communication (ISAC) base station, the total echo signal to obtain echo signals of respective users by matched filtering;
(2b) performing signal energy detection on the echo signals of the users, and modeling a user existence problem as a binary hypothesis model based on different energy amplitudes of the echo signals of the users; and
(2c) obtaining the detection probability P d and the false alarm rate P f of the corresponding user by the binary hypothesis model;
(3) building an ISAC indicator coupling framework C P d (θ):
(3a) setting empirical prediction values of probabilities of user existence and user non-existence in a detection region be H 1 and H 0 respectively;
(3b) fusing the empirical prediction values H 1 and H 0 with the effective capacity C, the detection probability P d and the false alarm rate P f to obtain an expanded effective capacity C P d (θ), that is, a fusion framework:
C
P
d
(
θ
)
=
-
1
θ
log
(
E
[
(
P
d
H
1
+
P
f
H
0
)
e
-
θ
R
]
)
(4) guaranteeing QoS of multi-user heterogeneous ISAC:
(4a) obtaining an expanded effective capacity of a m-th user as follows:
C
P
dm
(
θ
m
)
=
-
1
θ
m
log
(
E
[
(
P
dm
H
1
m
+
P
fm
H
0
m
)
e
-
θ
m
R
m
]
)
,
and obtaining a total expanded effective capacity of M users as follows:
∑
m
=
1
M
C
P
dm
(
θ
m
)
=
C
P
d
(
θ
1
,
…
,
θ
M
)
,
(4b) taking C P d (θ 1 , . . . , θ M ) as an objective function, and taking power of the M users, detection probabilities P d of the M users and communication latency indices θ of the M users as constraints, building a multi-user optimization problem P1:
P
1:
max
𝒫
c
C
P
d
(
θ
1
,
…
,
θ
M
)
s
.
t
.
𝒫
cm
≥
0
,
0
≤
m
≤
M
P
dm
≥
η
m
,
m
=
1
,
2
,
…
,
M
𝒫
≥
∑
m
=
1
M
𝒫
cm
+
∑
m
=
1
M
𝒫
sm
where represents communication power of the m-th user for communication, represents sensing power of the m-th user for sensing, η m represents a lower limit of a detection probability of the m-th user, and represents total power of the M users;
(4c) performing equivalent transformation on the multi-user optimization problem P1 from a non-convex optimization problem to a convex optimization problem; and
(4d) solving, by using a convex optimization theory, the communication power allocated to the m-th user in a multi-user system, thereby making the multi-user system maximize the total expanded effective capacity under a premise of meeting ISAC demands of the M users.
2 . The method as claimed in claim 1 , wherein in the step (1a), obtaining the receive signal of each user, the SINR γ of the corresponding user, and the communication rate R of the corresponding user, comprises:
making Δ={1, 2, . . . , M} represent a user index, baseband signals s(l) sent by the mobile ISAC base station to the M users in an l-th time slot being as follows:
s
(
l
)
=
[
s
1
(
l
)
,
s
2
(
l
)
,
s
m
(
l
)
,
…
,
s
M
(
l
)
]
T
∈
ℂ
M
where m=1, 2, . . . , M, and s m (l) represents a baseband signal sent by the mobile ISAC base station to the m-th user;
making
W
=
[
w
1
,
w
2
,
w
m
,
…
,
w
M
]
∈
ℂ
N
t
×
M
represent a precoding matrix, and performing, by the mobile ISAC base station, precoding matrix processing on the baseband signals s(l) to obtain processed transmit signals x(l):
x
(
l
)
=
W
·
s
(
l
)
receiving, by the users, the transmit signals from the mobile ISAC base station to obtain the receive signals of the users, wherein the receive signal y m (l) of the m-th user in the l-th time slot is as follows:
y
m
(
l
)
=
𝒫
cm
h
m
T
x
(
l
)
+
n
m
(
l
)
=
𝒫
cm
h
m
T
x
m
(
l
)
+
h
m
T
∑
i
≠
m
M
𝒫
ci
x
i
(
l
)
+
n
m
(
l
)
where represents the communication power of the m-th user, represents communication power of another user, n m (l) represents a white Gaussian noise with variance of σ c 2 received by the m-th user, x m (l) represents a transmit signal sent by the mobile ISAC base station to the m-th user, x i (l) represents a transmit signal sent by the mobile ISAC base station to the another user, h m ∈ represents a channel between the m-th user and the mobile ISAC base station,
h
m
T
represents a transpose of h m , an amplitude response of the channel follows Nakagami-m fading, and a probability density f |h| (x) of the channel follows the following distribution:
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
=
2
(
m
°
)
m
°
Γ
(
m
°
)
Ω
m
°
x
2
m
°
-
1
e
-
m
°
Ω
x
2
where Ω= [|h| 2 ] represents a shape parameter, represents solving an expected value, |h| represents channel amplitude gain, x=|h|, m° represents a fading parameter of Nakagami-m distribution and Γ represents a chi-square distribution function;
obtaining, based on the receive signals of the users, a SINR γ m of the m-th user:
γ
m
=
𝒫
cm
h
m
T
2
∑
i
≠
m
M
𝒫
ci
h
m
T
2
+
σ
c
2
where
h
m
T
2
represents 2 norm of the transpose of the channel between the m-th user and the mobile ISAC base; and
obtaining a communication rate R m of the m-th user according to the SINR γ m .
R
m
=
log
(
1
+
γ
m
)
.
3 . The method as claimed in claim 2 , wherein in the step (1b), the effective capacity C of the corresponding user is calculated by using the effective capacity theory, and the formula is as follows:
C
=
-
1
θ
log
(
𝔼
[
e
-
θ
R
]
)
where θ represents the communication latency index of the corresponding user, R represents the communication rate of the corresponding user, and represents solving an expected value.
4 . The method as claimed in claim 3 , wherein in the step (2a), separating the total echo signal received by the mobile ISAC base station into the echo signal of each user by the matched filtering, comprises:
the mobile ISAC base station being equipped with uniform linear arrays (ULA) with a half-wavelength interval, obtaining a receiving guide vector a r (φ) and a transmitting guide vector a t (φ) generated by the mobile ISAC base station as follows:
a
r
(
ϕ
)
=
1
N
r
[
1
,
e
j
2
π
dsin
ϕ
λ
,
…
,
e
j
2
π
(
N
r
-
1
)
dsin
ϕ
λ
]
T
a
t
(
ϕ
)
=
1
N
t
[
1
,
e
j
2
π
dsin
ϕ
λ
,
…
,
e
j
2
π
(
N
r
-
1
)
dsin
ϕ
λ
]
T
where φ represents a signal angel, N r represents a number of receive antennas on the mobile ISAC base station, N t represents a number of transmit antennas on the mobile ISAC base station, λ represents a carrier wavelength, d represents a distance between antennas on the mobile ISAC base station, and [ ] T represents a transpose;
after sensing signals transmitted by the mobile ISAC base station are reflected by the M users, obtaining the total echo signal r(l) as follows:
r
(
l
)
=
F
H
∑
m
=
1
N
𝒫
sm
ξ
m
a
r
(
ϕ
m
)
a
t
H
(
ϕ
m
)
x
(
l
)
+
z
r
(
l
)
where F=[f 1 , f 2 , f i . . . , f M ]∈ represents a receive beamforming matrix of the mobile ISAC base station, (⋅) H represents a conjugate transpose, represents an energy used by the m-th user for sensing, ξ m represents a combination of radar cross section and path loss of the m-th user, φ m represents a signal angle of the m-th user,
a
t
H
(
ϕ
m
)
represents a conjugate transpose of a t (φ m ), and z r (l) represents a receiving noise of the mobile ISAC base station;
making transmitting and receiving beamforming vectors of the mobile ISAC base station respectively be w j and f k :
w
j
=
a
t
(
)
f
k
=
a
r
(
)
where represents an estimated value of angle of departure (AoD), and represents an estimated value of angle of arrival (AoA);
performing, by the mobile ISAC base station, the matched filtering on the total echo signal r(l) to obtain the echo signal of the corresponding user y r :
y
r
=
𝒫
sm
ξ
m
❘
"\[LeftBracketingBar]"
a
r
H
(
ϕ
m
)
w
m
❘
"\[RightBracketingBar]"
❘
"\[LeftBracketingBar]"
a
t
H
(
ϕ
m
)
f
m
❘
"\[RightBracketingBar]"
+
z
m
=
𝒫
sm
ξ
m
A
r
A
t
+
z
m
where φ m represents the signal angle of the m-th user, w m represents a transmit beamforming vector applied by the base station to the m-th user, f m represents a receive beamforming vector applied by the base station to the m-th user, z m represents a sensing noise of the m-th user,
A
r
=
❘
"\[LeftBracketingBar]"
a
r
H
(
ϕ
m
)
w
m
❘
"\[RightBracketingBar]"
represents receive beamforming gain, and
A
t
=
❘
"\[LeftBracketingBar]"
a
t
H
(
ϕ
m
)
f
m
❘
"\[RightBracketingBar]"
represents transmit beamforming gain.
5 . The method as claimed in claim 1 , wherein in the step (2b), modeling the user existence problem as the binary hypothesis model, comprises:
describing an object detection problem as a binary hypothesis problem as follows:
there is no target
there is target
based on the above description, building a target detection model as follows:
x
m
=
{
z
m
,
ℋ
0
𝒫
sm
ξ
m
A
r
A
t
+
z
m
,
ℋ
1
where x m represents the echo signal of the m-th user separated by the mobile ISAC base station, represents an energy used by the m-th user for sensing, ξ m represents a combination of radar cross section and path loss of the m-th user, A r represents receiving beamforming gain, A t represents transmitting beamforming gain, and z m represents a sensing noise of the m-th user;
expressing the target detection model as the following energy detector:
❘
"\[LeftBracketingBar]"
x
❘
"\[RightBracketingBar]"
2
∼
{
N
r
σ
m
2
2
χ
2
2
,
ℋ
0
(
N
r
σ
m
2
2
+
𝒫
sm
ξ
m
2
A
r
2
A
t
2
2
)
χ
2
2
,
ℋ
1
where |x| 2 represents a signal energy received by the mobile ISAC base station, ~ represents that signal energy obeys a certain distribution, N r represents a number of receive antennas on the mobile ISAC base station,
σ
m
2
represents noise power sense by the m-th user, represents the energy used by the m-th user for sensing, and
χ
2
2
represents a chi-square distribution with 2 degrees of freedom.
6 . The method as claimed in claim 1 , wherein in the step (2c), the obtaining the detection probability P d and the false alarm rate P f of the corresponding user by the binary hypothesis model, comprises:
obtaining, based on a number of receive antennas on the mobile ISAC base station N r and noise power
σ
m
2
sensed by the m-th user, the false alarm probability P f of the corresponding user as follows:
P
f
=
Pr
(
χ
2
2
>
2
ε
N
r
σ
m
2
)
where Pr( ) represents a probability calculation,
χ
2
2
represents a chi-square distribution with 2 degrees of freedom,
ε
=
N
r
σ
m
2
2
F
χ
2
2
-
1
(
1
-
P
f
)
represents a detection threshold obtained by P f , and
F
χ
2
2
-
1
(
·
)
represents an inverse or a cumulative distribution function of the chi-square distribution with 2 degrees of freedom;
based on a signal energy |x| 2 received by the mobile ISAC base station, the number of the receive antennas on the mobile ISAC base station N r , the noise power
σ
m
2
sensed by the m-th user, power used by the m-th user for sensing , the detection threshold ε, receive beamforming gain A r and transmit beamforming gain A t , obtaining the detection probability P d of the mobile ISAC base station to the corresponding user:
P
d
=
Pr
(
❘
"\[LeftBracketingBar]"
x
❘
"\[RightBracketingBar]"
2
>
ε
❘
"\[LeftBracketingBar]"
ℋ
1
)
=
1
-
F
χ
2
2
(
2
ε
/
(
N
r
σ
m
2
)
1
+
𝒫
sm
ξ
m
2
A
r
2
A
t
2
/
N
r
σ
m
2
)
where
F
χ
2
2
(
·
)
represents the cumulative distribution function of the chi-square distribution with 2 degrees of freedom.
7 . The method as claimed in claim 6 , wherein in the step (4c), the performing equivalent transformation on the multi-user optimization problem, comprises:
obtaining the following relational expressions based on the total expanded effective capacity
C
P
d
(
θ
1
,
…
,
θ
M
)
=
∑
m
=
1
M
C
P
dm
(
θ
m
)
of the M users, the detection probability P dm of the m-th user, a prior existence probability H 1m of the m-th user, a false alarm rate P fm of the m-th user, a prior non-existence probability H 0m of the m-th user, and a boundedness of C P d (θ 1 , . . . , θ M ) determined by an effective capacity theoretical property:
0
≤
C
min
(
θ
1
,
…
,
θ
M
)
≤
C
P
d
(
θ
1
,
…
,
θ
M
)
≤
C
max
(
θ
1
,
…
,
θ
M
)
where
C
min
(
θ
1
,
…
,
θ
M
)
=
-
1
θ
max
log
(
𝔼
[
∏
m
=
1
M
A
m
e
-
∑
m
=
1
M
θ
m
log
(
1
+
γ
m
)
]
)
represents a lower limit of
C
P
d
(
θ
1
,
…
,
θ
M
)
,
C
max
(
θ
1
,
…
,
θ
M
)
=
-
1
θ
min
log
(
𝔼
[
∏
m
=
1
M
A
m
e
-
∑
m
=
1
M
θ
m
log
(
1
+
γ
m
)
]
)
represents an upper limit of C P d (θ 1 , . . . , θ M ), A m =P dm H 1m +P fm H 0m represents a total probability of base station sending information, γ m represents a SINR of the m-th user, θ max =max(θ 1 , θ 2 , θ m , . . . , θ M ) represents a maximum value of (θ 1 , θ 2 , θ m , . . . , θ M ), θ min =min(θ 1 , θ 2 , θ m , . . . , θ M ) represents a minimum value of (θ 1 , θ 2 , θ m , . . . , θ M ), θ m represents a communication latency index of the m-th user, and represents solving an expected value;
defining, based on the total probability of the base station sending information A m , the communication latency index θ m of the m-th user, and the SINR γ m of the m-th user, an equivalent expanded effective capacity function A(α) as follows:
A
(
α
)
=
△
-
1
α
log
(
𝔼
[
∏
m
=
1
M
A
m
e
-
∑
m
=
1
M
θ
m
log
(
1
+
γ
m
)
]
)
obtaining, based on continuous property of A(α) on α∈[θ min , θ max ], the following inequality:
❘
"\[LeftBracketingBar]"
A
(
θ
0
)
-
C
P
d
(
θ
1
,
…
,
θ
M
)
❘
"\[RightBracketingBar]"
≤
ϱ
where θ 0 is an only real number value obtained on [θ min , θ max ], and is a positive real number tending towards 0;
making {tilde over (C)} P d (θ 1 , . . . , θ M )=A(θ 0 ), based on continuity property of the function A(α), obtaining the following inequality:
❘
"\[LeftBracketingBar]"
C
~
P
d
(
θ
1
,
…
,
θ
M
)
-
C
P
d
(
θ
1
,
…
,
θ
M
)
❘
"\[RightBracketingBar]"
≤
ϱ
obtaining, based on the inequality |{tilde over (C)} P d (θ 1 , . . . , θ M )−C P d (θ 1 , . . . , θ M )|≤ , the following equivalent transformation for the total expanded effective capacity:
C
P
d
(
θ
1
,
…
,
θ
M
)
=
C
~
P
d
(
θ
1
,
…
,
θ
M
)
=
-
1
θ
0
log
(
𝔼
[
∏
m
=
1
M
A
m
e
-
∑
m
=
1
M
θ
m
log
(
1
+
γ
m
)
]
)
.
8 . The method as claimed in claim 7 , wherein in the step (4d), the solving, by using a convex optimization theory, the communication power allocated to the m-th user in a multi-user system, comprises:
rewriting, based on a reciprocal property of a logarithmic function, the multi-user optimization problem P1 as the following form P2:
P
2
:
min
𝒫
c
-
1
θ
0
log
(
𝔼
[
∏
m
=
1
M
A
m
e
-
∑
m
=
1
M
θ
m
log
(
1
+
γ
m
)
]
)
s
.
t
.
𝒫
cm
≥
0
,
0
≤
m
≤
M
P
dm
≥
η
m
,
m
=
1
,
TagBox[",", "NumberComma", Rule[SyntaxForm, "0"]]
2
,
…
,
M
𝒫
≥
∑
m
=
1
M
𝒫
cm
+
∑
m
=
1
M
𝒫
sm
where θ min ≤θ 0 ≤θ max , θ max represents the maximum value of (θ 1 , θ 2 , θ m . . . , θ M ), θ min represents the minimum value of (θ 1 , θ 2 , θ m , . . . , θ M ), represents solving an excepted value, θ m represents the communication latency index of the m-th user, γ m represents the SINR of the m-th user, represents the communication power of the m-th user, represents the sensing power of the m-th user, P dm represents the detection probability of the m-th user, η m represents the lower limit of the detection probability for the m-th user, and represents the total power of the M users;
transforming, based on monotonicity of a log function, the optimization problem P2 into the following form P3:
P
3
:
min
𝒫
c
E
[
∏
m
=
1
M
A
m
e
-
∑
m
=
1
M
θ
m
log
(
1
+
γ
m
)
]
=
min
𝒫
c
∏
m
=
1
M
A
m
∫
0
∞
∏
m
=
1
M
(
1
+
γ
m
)
-
β
m
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
dx
s
.
t
.
𝒫
cm
≥
0
,
0
≤
m
≤
M
P
dm
≥
η
m
,
m
=
1
,
TagBox[",", "NumberComma", Rule[SyntaxForm, "0"]]
2
,
…
,
M
𝒫
≥
∑
m
=
1
M
𝒫
cm
+
∑
m
=
1
M
𝒫
sm
where
β
m
=
-
θ
m
ln
2
,
and f |h| (x) represents a probability density distribution followed by channel amplitude response between the mobile ISAC base station and the m-th user;
based on convexity of the optimization problem P3 on a spanning space ( , . . . , ), constructing the following Lagrange equation :
ℒ
=
∏
m
=
1
M
A
m
∫
0
∞
∏
m
=
1
M
(
1
+
γ
m
)
-
β
m
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
dx
+
λ
m
(
𝒫
-
∑
m
=
1
M
𝒫
cm
-
∑
m
=
1
M
𝒫
sm
)
where λ m represents a Lagrange multiplier related to inequality constraints;
making partial derivative of the Lagrange equation to be equal to 0, and obtaining the following equation:
∂
ℒ
∂
P
cm
=
-
β
m
h
m
T
2
(
1
+
𝒫
cm
h
m
T
2
∑
i
≠
m
M
𝒫
ci
h
m
T
2
+
σ
c
2
)
-
1
×
∏
m
=
1
M
(
𝒫
cm
h
m
T
2
∑
i
≠
m
M
𝒫
ci
h
m
T
2
+
σ
c
2
)
-
β
m
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
-
λ
m
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
=
0
based on the equation of
∂
ℒ
∂
P
cm
=
-
β
m
h
m
T
2
(
1
+
𝒫
cm
h
m
T
2
∑
i
≠
m
M
𝒫
ci
h
m
T
2
+
σ
c
2
)
-
1
×
∏
m
=
1
M
(
𝒫
cm
h
m
T
2
∑
i
≠
m
M
𝒫
ci
h
m
T
2
+
σ
c
2
)
-
β
m
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
-
λ
m
f
❘
"\[LeftBracketingBar]"
h
❘
"\[RightBracketingBar]"
(
x
)
=
0
,
solving the communication power allocated by the multi-user system to the m-th user as follows:
𝒫
cm
=
∑
i
≠
m
M
𝒫
ci
h
m
T
2
+
σ
c
2
h
m
T
2
×
(
∏
m
=
1
M
λ
m
)
β
m
M
M
β
m
+
1
λ
m
β
m
h
m
T
2
∏
m
=
1
M
(
β
m
h
m
T
2
)
β
m
M
β
m
+
1
where
h
m
T
2
represents 2 norm of Nakagami-m channel gain of the m-th user, and M represents a total number of the users in the multi-user system.