Method for intelligent reflecting surface aided terahertz secure communication system

Abstract

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.sub.BS antennas, an IRS equipped with N.sub.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.

Claims

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.sub.BS antennas, an IRS equipped with N.sub.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.sub.u∈C of the single-antenna mobile user side and the received signal y.sub.e∈C of the single-antenna eavesdropper are expressed as
y.sub.u=√{square root over (ρ)}(h.sub.ru.sup.HΘH.sub.t.sup.H+h.sub.du.sup.H)Fs+n.sub.u;
y.sub.e=√{square root over (ρ)}(h.sub.re.sup.HΘH.sub.t.sup.H+h.sub.de.sup.H)Fs+n.sub.e; where H.sub.t is a channel between the BS and the IRS; h.sub.ru is a channel between the IRS and an authorized user side; h.sub.du is a channel between the BS and the authorized user side; h.sub.re is a channel between the IRS and the single-antenna eavesdropper; h.sub.de is a channel between the BS and the single-antenna eavesdropper; ρ is an average receiving power; n.sub.u and n.sub.e are channel noises where channel noise power is δ.sup.2, F∈C.sup.N.sup.BS.sup.×1 is a hybrid precoding matrix satisfying a normalized power constraint of ∥F∥.sub.F.sup.2=1; $\Theta =\mathrm{diag}\left({\left[{\beta }_1{e}^{j{\theta }_1},{\beta }_2{e}^{j{\theta }_2},L,{\beta }_{N_{\mathrm{IRS}}}{e}^{j{\theta }_{N_{\mathrm{IRS}}}}\right]}^T\right)\in C^{N_{\mathrm{IRS}}\times N_{\mathrm{IRS}}}$ is a phase shift matrix of the IRS where {β.sub.i}.sub.i=1.sup.N.sup.IRS∈[0,1] is a reflecting coefficient and {θ.sub.i}.sub.i=1.sup.N.sup.IRS∈[0,2π] is a phase shift for each reflecting element, wherein {β.sub.i}.sub.i=1.sup.N.sup.IRS=1; the phase shift of the IRS is discrete, where the phase shift {θ.sub.i}.sub.i=1.sup.N.sup.IRS of each reflecting element belongs to a discrete phase set F, and F={0, Δθ, . . . , Δθ(2.sup.b−1)}, where b is a bit quantization number and Δθ=2π/2.sup.b is a phase spacing; a downlink secrecy rate R.sub.sec=[R.sub.U−R.sub.E].sup.+ is maximized, where R.sub.U is a data transmission rate of the authorized user side and R.sub.E is a data transmission rate of the single-antenna eavesdropper: $R_U={\log }_2\left[1+\frac{{.Math.\sqrt{\rho }\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)F.Math.}^2}{{\delta }_u^2}\right],R_E={\log }_2\left[1+\frac{{.Math.\sqrt{\rho }\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)F.Math.}^2}{{\delta }_e^2}\right],$ where F is a precoding matrix at the BS, Θ is the phase shift matrix at the IRS, the function R.sub.sec=[R.sub.U−R.sub.E].sup.+ indicates that when R.sub.sec=[R.sub.U−R.sub.E]>0, R.sub.sec=R.sub.U−R.sub.E, when R.sub.sec=[R.sub.U−R.sub.E]<0, R.sub.sec=0; F and Θ are jointly optimized to maximize the downlink secrecy rate, and an objective function established as follows $\left({\Theta }^{\mathrm{opt}},F^{\mathrm{opt}}\right)=\arg \max R_{\sec },s.t.{\theta }_n\in F,\forall n=1,\mathrm{.Math.},N_{\mathrm{IRS}},\Theta =\mathrm{diag}\left({\left[e^{j{\theta }_1},e^{j{\theta }_2},\mathrm{.Math.},e^{j{\theta }_{N_{\mathrm{IRS}}}}\right]}^T\right),{.Math.F.Math.}_F^2=1;$ 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.sup.opt and an optimal phase shift matrix Θ.sup.opt are obtained by solving the objective function; the objective function is solved by the following steps: S1, performing an initialization, wherein the discrete phase set of the IRS is $F=\left\{0,\frac{2\pi }{2^b},L,\frac{2\pi }{2^b}\left(2^b-1\right)\right\},$ where b is the bit quantization number; an initial probability phase shift matrix of the IRS is $p^{\left(0\right)}=\frac{1_{2^b\times N_{\mathrm{IRS}}}}{2^b},$ where $1_{2^b\times N_{\mathrm{IRS}}}$ is an all-ones matrix with size 2.sup.b×N.sub.IRS, a total number of the iterations of an algorithm is I.sub.1, a current iteration of the algorithm is i.sub.1=1, a total number of the iterations of a sub-algorithm I.sub.2, a current iteration of the sub-algorithm is i.sub.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.sub.elite; S2, when i.sub.1≤I.sub.1, cyclically performing S3-S11; S3, computing the optimal precoding matrix F.sup.opt=u.sub.max (A,B)/∥u.sub.max(A,B)∥.sup.2, where u.sub.max(A,B) is a generalized eigenvector based on a largest generalized eigenvalue of a matrix B.sup.−1A, and a matrix A and a matrix B are respectively written as $A=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_u^2}{\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)}^H\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right),B=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_e^2}{\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)}^H\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right);$ where I.sub.N.sub.BS is an identity matrix with size N.sub.BS×N.sub.BS; S4, when i.sub.2≤I.sub.2, cyclically performing S5-S10 S5, randomly generating S phase shift matrices {Θ.sup.s}.sub.s=1.sup.S based on a current phase probability matrix p.sup.(i) of the phase shifts of the IRS; S6, calculating an objective $\gamma =\frac{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)F.Math.}^2/{\delta }_u^2}{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)F.Math.}^2/{\delta }_e^2};$ S7, sorting {γ(Θ.sup.s)}.sub.s=1.sup.S in a descending order as γ(Θ.sup.(1))≥γ(Θ.sup.(2))≥ . . . ≥γ(Θ.sup.(S)); S8, selecting first S.sub.elite objective values γ.sup.(1), γ.sup.(2), . . . , γ.sup.(S.sup.elite.sup.), where a corresponding phase shift matrix is {Θ.sup.s}.sub.s=1.sup.S.sup.elite; S9, updating the probability matrix p.sup.(i+1) based on {Θ.sup.s}.sub.s=1.sup.S.sup.elite; S10, updating the current iteration of the sub-algorithm to be i.sub.2=i.sub.2+1; S11, updating the current iteration of the algorithm to be i.sub.1=i.sub.1+1; and S12, obtaining the optimal phase shift matrix Θ.sup.opt=Θ.sup.(1), wherein the downlink secrecy rate of the IRS aided terahertz secure communication system is R=log.sub.2γ(Θ.sup.(1)).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows the IRS aided downlink MISO terahertz communication system.

(2) FIG. 2 shows the flow chart of the disclosed cross entropy based method.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(3) The details of the present invention will be described as follows.

(4) As shown in FIG. 1, considering a downlink terahertz MISO system, a BS with N.sub.BS array antennas communicates to a single-antenna authorized user, in the presence of a single-antenna eavesdropper. Since there are obstacles between the BS and the mobile user, the line-of-sight terahertz communication link is easily blocked. In order to overcome the hindrance, the IRS equipped with N.sub.IRS reflecting elements is fixed on a surrounding wall or ceiling. All of the reflecting elements are controlled by a central controller that is connected to the BS by wires or wirelessly to share the channel state information between the BS and the IRS. In addition, a simple, low-price, low-power-consumption sensor is installed on each reflecting element, which allows mass production. The phase of the terahertz wave beams at the IRS is sensed, and then this phase information is transmitted to the central controller to intelligently controlled the phase shifts of each reflecting element on the received the wave beams, so as to improve the secrecy rate performance of the terahertz system. Since the terahertz communication suffers from high path loss, assuming the terahertz waves can be reflected on the IRS up to one time. Therefore, when the BS transmits one single data stream s∈C, the received signals y.sub.u∈C for the authorized user and y.sub.e∈C for the eavesdropper can be respectively expressed as
y.sub.u=√{square root over (ρ)}(h.sub.ru.sup.HΘH.sub.t.sup.H+h.sub.du.sup.H)Fs+n.sub.u
y.sub.e=√{square root over (ρ)}(h.sub.re.sup.HΘH.sub.t.sup.H+h.sub.de.sup.H)Fs+n.sub.e

(5) where H.sub.t is the channel between the BS and the IRS, h.sub.ru is the channel between the IRS and the authorized user, h.sub.du is the channel between the BS and the authorized user, h.sub.re is the channel between the IRS and the eavesdropper, h.sub.de is the channel between the BS and the eavesdropper, ρ is the average receiving power, n.sub.u and n.sub.e are channel noise where the noise power is δ.sup.2, F∈C.sup.N.sup.BS.sup.×1 is the hybrid precoding matrix satisfying the normalized power constraint of ∥F∥.sub.F.sup.2=1,

(6) $\Theta =\mathrm{diag}\left({\left[{\beta }_1{e}^{j{\theta }_1},{\beta }_2{e}^{j{\theta }_2},L,{\beta }_{N_{\mathrm{IRS}}}{e}^{j{\theta }_{N_{\mathrm{IRS}}}}\right]}^T\right)\in C^{N_{\mathrm{IRS}}\times N_{\mathrm{IRS}}}$
is the phase shift matrix of the IRS; for the diagonal matrix with N.sub.IRS×N.sub.IRS elements, {β.sub.i}.sub.i=1.sup.N.sup.IRS∈[0,1] is the reflecting coefficient of the reflecting elements of the IRS, and {θ.sub.i}.sub.i=1.sup.N.sup.IRS∈[0,2π] is the phase shift for each reflecting element on the wave beam. For simplicity, assuming {β.sub.i}.sub.i=1.sup.N.sup.IRS=1. In other non-ideal cases, the following formula derivation and the proposed algorithm are still feasible. And for the practical implementations, the phase shifts of the IRS are discretized, where the phase shift {θ.sub.i}.sub.i=1.sup.N.sup.IRS of each reflecting element belongs to the discrete phase shift set F. With the different construction of the IRS, the values of F are different. Conveniently, F=(0, Δθ, . . . , Δθ(2.sup.b−1)), where b is the bit quantization number and Δθ=2π/2.sup.b is the phase spacing.

(7) The present invention aims to maximize the downlink secrecy rate R.sub.sec=[R.sub.U−R.sub.E].sup.+, where R.sub.U is the data transmission rate of the authorized user and R.sub.E is the data transmission rate of the eavesdropper, and R.sub.U and R.sub.E are expressed as follows:

(8) $R_U={\log }_2\left[1+\frac{{.Math.\sqrt{\rho }\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)F.Math.}^2}{{\delta }_u^2}\right],R_E={\log }_2\left[1+\frac{{.Math.\sqrt{\rho }\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)F.Math.}^2}{{\delta }_e^2}\right],$

(9) where F is the precoding matrix at the BS, Θ is the phase shift matrix at the IRS. Besides, the function R.sub.sec=[R.sub.U−R.sub.E].sup.+ means that when R.sub.sec=[R.sub.U−R.sub.E]>0, R.sub.sec=R.sub.U−R.sub.E, otherwise R.sub.sec=0. Since the optimal value of our problem must be more than 0, the equation R.sub.sec=R.sub.U−R.sub.E is always satisfied.

(10) The matrix F and Θ are jointly optimized to maximize the secrecy rate, and an objective function is established as follows:

(11) 0$\left({\Theta }^{\mathrm{opt}},F^{\mathrm{opt}}\right)=\arg \max R_{\sec },s.t.{\theta }_n\in F,\forall n=1,\mathrm{.Math.},N_{\mathrm{IRS}},\Theta =\mathrm{diag}\left({\left[e^{j{\theta }_1},e^{j{\theta }_2},\mathrm{.Math.},e^{j{\theta }_{N_{\mathrm{IRS}}}}\right]}^T\right),{.Math.F.Math.}_F^2=1;$

(12) where the first constraint comes from the discretization of phase shifts of the reflecting elements of the IRS, the second constraint comes from the communication model of the IRS, and the third constraint comes from the normalized transmission power. The optimal precoding matrix F.sup.opt and phase shift matrix Θ.sup.opt are obtained by solving the objective function.

(13) Since this problem is related to nonconvex optimization, using current optimization techniques are hard to solve it. Fortunately, it is worth noting that there are still some implicit properties existing in this problem. Firstly, the number of the phase shift matrix Θ of the IRS is finite since each phase shift {θ.sub.n}.sub.n=1.sup.N.sup.IRS of Θ is discrete. Secondly, the precoding matrix F is an unconstrained matrix. Thirdly, the phase shift matrix Θ is independent of F. Based on these distinguishing features, such an optimization problem can be settled by iteratively optimizing Θ and F, where Θ is optimized when F is fixed, and F is optimized when Θ is fixed, respectively. Through multiple iterations, the Θ and F both converge to obtain the optimal solution.

(14) When Θ is fixed, F is optimized and the secrecy rate is maximized by

(15) $\underset{F}{\max }{\log }_2\left[\frac{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)F.Math.}^2\text{/}{\delta }_u^2}{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)F.Math.}^2\text{/}{\delta }_e^2}\right]$$s.t.{.Math.F.Math.}_F^2=1.$

(16) Note that this problem mentioned above is a typical secrecy rate optimization problem for a MISO system without the IRS, which has many solutions at present, and thus the equivalent form of this problem can be given by

(17) $\underset{F}{\max }\frac{F^H\mathrm{AF}}{F^H\mathrm{BF}}$$s.t.{.Math.F.Math.}_F^2=1,\mathrm{where}$$A=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_u^2}{\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)}^H\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right),B=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_e^2}{\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)}^H\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right);$

(18) where I.sub.N.sub.BS is an identity matrix with size N.sub.BS×N.sub.BS, according to the Rayleigh-Ritz theorem, the optimal precoding matrix can be expressed as F.sup.opt=u.sub.max(A,B)/∥u.sub.max (A,B)∥.sup.2, where u.sub.max (A,B) is the generalized eigenvector based on the largest generalized eigenvalue of matrix B.sup.−1A, and the matrix A and B are respectively expressed as

(19) $A=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_u^2}{\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)}^H\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right),B=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_e^2}{\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)}^H\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right);$

(20) When F is fixed, Θ is optimized and the secrecy rate is maximized by

(21) $\underset{\Theta }{\max }\gamma =\frac{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)F.Math.}^2\text{/}{\delta }_u^2}{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)F.Math.}^2\text{/}{\delta }_e^2}$$s.t.{\theta }_n\in F,\forall n=1,\mathrm{.Math.},N_{\mathrm{IRS}},\Theta =\mathrm{diag}\left({\left[e^{j{\theta }_1},e^{j{\theta }_2},\mathrm{.Math.},e^{j{\theta }_{N_{\mathrm{IRS}}}}\right]}^T\right).$

(22) The objective function γ is solved by optimizing the Θ. It notes that as the phase shift of the reflecting element is discrete and satisfies θ.sub.n∈F, ∀n=1, . . . , N.sub.IRS, the number of possible phase-shift matrix Θ is finite. The problem of maximizing the value of γ is solved by exhaustively comparing all the matrix Θ and finding the optimal matrix Θ.sup.opt. But the exhaustive search method has high computational complexity, which needs to compute the value γ of |F|.sup.N.sup.IRS times for different matrices Θ. In order to decrease the complexity of phase searching, a cross-entropy based phase searching algorithm is disclosed in the present invention, which is suitable for the application in practice. The cross-entropy based phase searching algorithm is an iterative algorithm. At each iterative process, the probability of the phase shift for each reflecting element is estimated by calculating the system data transmission rate of a part of matrices Θ of the IRS. With the increasing number of iterations, the phase shift matrix estimated by this algorithm is close to the phase shift matrix corresponding to the optimal system data transmission rate. The proposed algorithm can effectively reduce the searching times and computational complexity of the phase shift matrix of the IRS compared with the exhaustive search method for finding the optimal phase simultaneously from all the reflecting elements. Assuming the probability matrix of the IRS as p=[p.sub.1, p.sub.2, . . . , p.sub.N]∈C.sup.2.sup.b.sup.×N.sup.IRS where {p.sub.n}.sub.n=1.sup.N.sup.IRS=[p.sub.n,1, p.sub.n,2, . . . , p.sub.n,2.sub.b].sup.T∈C.sup.2.sup.b is the phase probability of the nth reflecting element. p.sub.n,i is the probability of the ith phase in F of n reflecting elements, and satisfies the probability constraints as 0≤p.sub.n,i≤1 and

(23) $\underset{i=1}{\overset{2^b}{.Math.}}{p}_{n,i}=1.$
Because the optimal selection for the reflecting element capable of best optimizing the system performance cannot be determined, the probability matrix is set to be equal, that is,

(24) $p^{\left(0\right)}=\frac{1}{2^b}\times 1_{2^b\times N_{\mathrm{IRS}}}$
for the first iterative process, where

(25) $1_{2^b\times N_{\mathrm{IRS}}}$
is an all-ones matrix with size 2.sup.b×N.sub.IRS. In the cross-entropy based phase searching algorithm, S phase shift matrices {Θ.sup.s}.sub.s=1.sup.S are randomly generated according to the phase probability matrix p.sup.(i) the effective channel H.sub.eff=H.sub.r.sup.HΘH.sub.t.sup.H+H.sub.d.sup.H and the corresponding value γ are computed. Then, the values {γ(Θ.sup.s)}.sub.s=1.sup.S is sorted in a descending order as γ(Θ.sup.(1))≥γ(Θ.sup.(2))≥ . . . ≥γ(Θ.sup.(S)). The first S.sub.elite values γ.sup.(1), γ.sup.(2), . . . , γ.sup.(S.sup.elite.sup.) are extracted, corresponding to matrices {Θ.sup.s}.sub.s=1.sup.S.sup.elite, and then p.sup.(i+1) is updated based on {Θ.sup.s}.sub.s=1.sup.S.sup.elite, thereby approaching the probability matrix corresponding to the optimal phase shift matrix. The step mentioned above is repeated I.sub.2 times to achieve the iterative process. The optimal phase shift matrix Θ.sup.opt can be obtained as Θ.sup.opt=Θ.sup.(1). When the optimal phase shift matrix and the optimal precoding matrix are obtained, the secrecy rate of the downlink IRS aided terahertz MISO system is calculated as R=log.sub.2γ(Θ.sup.(1)).

(26) The complexity analyses of different phase search methods, including the exhaustive search method and the cross-entropy based method, are present as follow. Specifically, the computational complexity of the exhaustive phase search method is mainly from searching all the possible phase shift matrices, which is expressed as O(|F|.sup.N.sup.IRS), while the computational complexity of the cross-entropy based phase search method is from a part of the possible phase shift matrices, which is expressed as is O(S.Math.I.sub.2).

(27) TABLE-US-00001 Methods Complexity Exhaustive search method O (|F |.sup.N.sup.IRS) Cross-entropy based method O (S .Math. I.sub.2)

(28) Based on the above system model, the present invention discloses a cross-entropy based phase search method to maximize the secrecy rate of downlink IRS aided terahertz MISO system. Compared with the exhaustive search method, the method of the present invention can effectively reduce the computational complexity with slight secrecy rate performance penalty. FIG. 2 is the flow chart of the optimization process of maximizing the secrecy rate according to the disclosed cross-entropy based phase search method.

Embodiment

(29) The present embodiment is based on the MATLAB simulation platform.

(30) The solution for solving the achievable secrecy rate optimization problem is as follows.

(31) S1, Setting the parameters of IRS aided terahertz MISO secure communication system, where the frequency is f=0.22 THz, the number of antennas at the BS is N.sub.BS=128, the number of the IRS reflecting element is N.sub.IRS=32, the discrete phase set of the IRS is F={0,π/2,π,3π/2}, and the channels H.sub.th.sub.ruh.sub.reh.sub.duh.sub.de are presented by the geometric channel model, and H.sub.t can be expressed as

(32) $H_t=\sqrt{\frac{N_{\mathrm{BS}}{N}_{\mathrm{IRS}}}{L}}\underset{l=1}{\overset{L}{.Math.}}{\alpha }_i{a}_{\mathrm{BS}}\left({\theta }_{\mathrm{BS}}\right)a_{\mathrm{IRS}}^H\left({\theta }_{\mathrm{IRS}}\right),$

(33) where the number of paths of the BS-IRS link is L=3, the path gain is α∈CN (0,1), the physical direction angles θ.sub.IRS and θ.sub.BS are uniformly generated in [0,2π]. The array response vector is

(34) $a\left({\theta }_{BS}\right)={\frac{1}{\sqrt{N_{\mathrm{BS}}}}\left[1,L,e^{j\left(N_{\mathrm{BS}}-1\right)2\pi d\sin \left({\theta }_{\mathrm{BS}}\right)/\lambda }\right]}^T,$

(35) where the antennas spacing d=λ/2=c/(2f), and the velocity of light c=3×10.sup.8 m/s. The other array response vector can be also expressed according to the expression of a(θ.sub.BS). Besides, the other channels can be also expressed according to H.sub.t.

(36) S2, Initialization: The optional phase set of the IRS

(37) 0$F=\left\{0,\frac{2\pi }{2^b},L,\frac{2\pi }{2^b}\left(2^b-1\right)\right\},$
where the bit quantization number is set as b=2. The initial probability phase shift matrix of the IRS is

(38) $p^{\left(0\right)}=\frac{1_{2^b\times N_{\mathrm{IRS}}}}{2^b},$
where

(39) $1_{2^b\times N_{\mathrm{IRS}}}$
is an all-ones matrix with size 2.sup.b×N.sub.IRS. The total number of the iterations for the algorithm is I.sub.1=10. The current iteration is i.sub.1=1. The total number of the iterations for sub-algorithm is I.sub.2=10. The current iteration is i.sub.2=1. The number of samples of the phase shift matrix is S=200. The number of optimal samples for each iteration is S.sub.elite=40.

(40) S3, When i.sub.1≤I.sub.1, cyclically performing S4-S12

(41) S4, Calculating the optimal precoding matrix F.sup.opt=u.sub.max (A,B)/∥u.sub.max (A,B)∥.sup.2, where u.sub.max(A,B) is the generalized eigenvector based on the largest generalized eigenvalue of matrix B.sup.−1A, and the matrix A and B are respectively expressed as

(42) $A=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_u^2}{\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)}^H\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right),B=I_{N_{\mathrm{BS}}}+\frac{\rho }{{\delta }_e^2}{\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)}^H\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right),$

(43) where I.sub.N.sub.BS is an identity matrix with size N.sub.BS×N.sub.BS;

(44) S5, When i.sub.2≤I.sub.2, cyclically performing S5-S10

(45) S6, Randomly generating S phase shift matrix {Θ.sup.s}.sub.s=1.sup.S based on the current probability matrix p.sup.(i) of the phase shifts of the IRS;

(46) S7, Calculating the objective

(47) $\gamma =\frac{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{ru}}^H\Theta H_t^H+h_{\mathrm{du}}^H\right)F.Math.}^2/{\delta }_u^2}{1+{.Math.\sqrt{\rho }\left(h_{\mathrm{re}}^H\Theta H_t^H+h_{\mathrm{de}}^H\right)F.Math.}^2/{\delta }_e^2};$

(48) S8, Sorting {γ(Θ.sup.s)}.sub.s=1.sup.S in a descending order as γ(Θ.sup.(1))≥γ(Θ.sup.(2))≥ . . . ≥γ(Θ.sup.(S));

(49) S9, Selecting the first S.sub.elite objective values γ.sup.(1), γ.sup.(2), . . . , γ.sup.(S.sup.elite.sup.), where the corresponding phase shift matrix is {Θ.sup.s}.sub.s=1.sup.S.sup.elite;

(50) S10, Updating the probability matrix p.sup.(i+1) based on {Θ.sup.s}.sub.s=1.sup.S.sup.elite;

(51) S11, Updating the current iteration to be i.sub.2=i.sub.2+1;

(52) S12, Updating the current iteration to be i.sub.1=i.sub.t+1;

(53) S13, Obtaining the optimal phase shift matrix Θ.sup.opt=Θ.sup.(1);

(54) S14, Calculating the secrecy rate R=log.sub.2γ(Θ.sup.(1)) of the IRS aided terahertz MISO system.

(55) The method of the present invention is tested by simulations to compare the secrecy rate performance and computational complexity of the exhaustive search method and the cross-entropy based search method. The results indicate that with the number of the reflecting elements N.sub.IRS increasing, the complexity gap between the cross-entropy based search method and the exhaustive search method becomes larger. Therefore, the cross-entropy based search method is used for the secrecy rate optimization of the IRS aided terahertz MISO system, which not only significantly reduces the computational complexity but also reduces the loss of the system date transmission rate.