Method for intelligent reflecting surface aided terahertz secure communication system
View Patent ↗A design method for an intelligent reflecting surface (IRS) aided terahertz secure communication system is provided. The IRS aided terahertz multi-input single-output (MISO) system includes a base station (BS) equipped with N BS antennas, an IRS equipped with N IRS reflecting elements, a single-antenna user and a single-antenna eavesdropper. The BS transmits signals by the active hybrid beamforming to the relay of the IRS, and the IRS adjusts the signals and reflects the signals to the mobile user, which suppresses the received signal of the eavesdropper. The present invention maximizes the downlink secrecy rate by establishing a joint optimization function and maximizes the system data transmission rate by a cross-entropy based search method.
1. A design method for an intelligent reflecting surface (IRS) aided terahertz secure communication system, wherein,
the IRS aided terahertz secure communication system comprises a base station (BS) equipped with N BS antennas, an IRS equipped with N IRS reflecting elements, and a single-antenna mobile user side and a single-antenna eavesdropper;
the BS transmits wave beam signals to a relay consisting of the IRS through active hybrid beamforming, and the IRS adjusts phase shifts of all the reflecting elements to transmit the wave beam signals to the single-antenna mobile user side and simultaneously suppress a received signal of the single-antenna eavesdropper;
terahertz waves are reflected by the IRS once;
when the BS transmits one single data stream s∈C, a received signal y u ∈C of the single-antenna mobile user side and the received signal y e ∈C of the single-antenna eavesdropper are expressed as
y u =√{square root over (ρ)}( h ru H ΘH t H +h du H ) Fs+n u ;
y e =√{square root over (ρ)}( h re H ΘH t H +h de H ) Fs+n e ;
where H t is a channel between the BS and the IRS; h ru is a channel between the IRS and an authorized user side; h du is a channel between the BS and the authorized user side; h re is a channel between the IRS and the single-antenna eavesdropper; h de is a channel between the BS and the single-antenna eavesdropper; ρ is an average receiving power; n u and n e are channel noises where channel noise power is δ 2 , F∈C N BS ×1 is a hybrid precoding matrix satisfying a normalized power constraint of ∥F∥ F 2 =1;
Θ
=
diag
(
[
β
1
e
j
θ
1
,
β
2
e
j
θ
2
,
L
,
β
N
IRS
e
j
θ
N
IRS
]
T
)
∈
C
N
IRS
×
N
IRS
is a phase shift matrix of the IRS where {β i } i=1 N IRS ∈[0,1] is a reflecting coefficient and {θ i } i=1 N IRS ∈[0,2π] is a phase shift for each reflecting element, wherein {β i } i=1 N IRS =1; the phase shift of the IRS is discrete, where the phase shift {θ i } i=1 N IRS of each reflecting element belongs to a discrete phase set F, and F={0, Δθ, . . . , Δθ(2 b −1)}, where b is a bit quantization number and Δθ=2π/2 b is a phase spacing;
a downlink secrecy rate R sec =[R U −R E ] + is maximized, where R U is a data transmission rate of the authorized user side and R E is a data transmission rate of the single-antenna eavesdropper:
R
U
=
log
2
[
1
+
ρ
(
h
ru
H
Θ
H
t
H
+
h
du
H
)
F
2
δ
u
2
]
,
R
E
=
log
2
[
1
+
ρ
(
h
re
H
Θ
H
t
H
+
h
de
H
)
F
2
δ
e
2
]
,
where F is a precoding matrix at the BS, Θ is the phase shift matrix at the IRS, the function R sec =[R U −R E ] + indicates that when R sec =[R U −R E ]>0, R sec =R U −R E , when R sec =[R U −R E ]<0, R sec =0;
F and Θ are jointly optimized to maximize the downlink secrecy rate, and an objective function established as follows
(
Θ
opt
,
F
opt
)
=
arg
max
R
sec
,
s
.
t
.
θ
n
∈
F
,
∀
n
=
1
,
…
,
N
IRS
,
Θ
=
diag
(
[
e
j
θ
1
,
e
j
θ
2
,
…
,
e
j
θ
N
IRS
]
T
)
,
F
F
2
=
1
;
where the first constraint comes from discretization of the phase shifts of the IRS, the second constraint comes from a communication model of the IRS, and the third constraint comes from a normalized transmission power; an optimal precoding matrix F opt and an optimal phase shift matrix Θ opt are obtained by solving the objective function; the objective function is solved by the following steps:
S 1 , performing an initialization, wherein the discrete phase set of the IRS is
F
=
{
0
,
2
π
2
b
,
L
,
2
π
2
b
(
2
b
-
1
)
}
,
where b is the bit quantization number; an initial probability phase shift matrix of the IRS is
p
(
0
)
=
1
2
b
×
N
IRS
2
b
,
where
1
2
b
×
N
IRS
is an all-ones matrix with size 2 b ×N IRS , a total number of the iterations of an algorithm is I 1 , a current iteration of the algorithm is i 1 =1, a total number of the iterations of a sub-algorithm I 2 , a current iteration of the sub-algorithm is i 2 =1, a number of samples of the phase shift matrix for each iteration is S, a number of optimal samples of the phase shift matrix for each iteration is S elite ;
S 2 , when i 1 ≤I 1 , cyclically performing S 3 -S 11 ;
S 3 , computing the optimal precoding matrix F opt =u max (A,B)/∥u max (A,B)∥ 2 , where u max (A,B) is a generalized eigenvector based on a largest generalized eigenvalue of a matrix B −1 A, and a matrix A and a matrix B are respectively written as
A
=
I
N
BS
+
ρ
δ
u
2
(
h
ru
H
Θ
H
t
H
+
h
du
H
)
H
(
h
ru
H
Θ
H
t
H
+
h
du
H
)
,
B
=
I
N
BS
+
ρ
δ
e
2
(
h
re
H
Θ
H
t
H
+
h
de
H
)
H
(
h
re
H
Θ
H
t
H
+
h
de
H
)
;
where I N BS is an identity matrix with size N BS ×N BS ;
S 4 , when i 2 ≤I 2 , cyclically performing S 5 -S 10
S 5 , randomly generating S phase shift matrices {Θ s } s=1 S based on a current phase probability matrix p (i) of the phase shifts of the IRS;
S 6 , calculating an objective
γ
=
1
+
ρ
(
h
ru
H
Θ
H
t
H
+
h
du
H
)
F
2
/
δ
u
2
1
+
ρ
(
h
re
H
Θ
H
t
H
+
h
de
H
)
F
2
/
δ
e
2
;
S 7 , sorting {γ(Θ s )} s=1 S in a descending order as γ(Θ (1) )≥γ(Θ (2) )≥ . . . ≥γ(Θ (S) );
S 8 , selecting first S elite objective values γ (1) , γ (2) , . . . , γ (S elite ) , where a corresponding phase shift matrix is {Θ s } s=1 S elite ;
S 9 , updating the probability matrix p (i+1) based on {Θ s } s=1 S elite ;
S 10 , updating the current iteration of the sub-algorithm to be i 2 =i 2 +1;
S 11 , updating the current iteration of the algorithm to be i 1 =i 1 +1; and
S 12 , obtaining the optimal phase shift matrix Θ opt =Θ (1) , wherein the downlink secrecy rate of the IRS aided terahertz secure communication system is R=log 2 γ(Θ (1) ).