Robust beam optimization method in intelligent metasurface-assisted terahertz sensing system

Abstract

The invention provides a robust beam optimization method in an intelligent metasurface-assisted terahertz sensing system. The robust beam optimization method is used for solving the problem of beam dispersion effect existing in a sensing process and a communication process in an RIS-assisted terahertz ISAC system. The communication process between the BS and the user in the terahertz sensing system is divided into two stages: a sensing stage and a communication stage. In the sensing stage, a TTD beam dispersion rapid sensing method based on RIS is provided to adjust the degree of beam offset, and a sensing Cramer-Rao lower bound and a relation between the sensing Cramer-Rao lower bound and a CSI error are deduced; in the communication stage, a robustness optimization objective function is provided based on the obtained imperfect CSI, and the transmission capacity is maximized by jointly designing an RIS reflection coefficient, time delay and sensing time. The method can effectively reduce beam dispersion and improve communication capacity.

Description

Technical Field

[0001] The present invention relates to the technical field of terahertz communication, and in particular to a robust beam optimization method in an intelligent metasurface-assisted terahertz synaesthesia system. Background Art

[0002] Integrated sensing and communication (ISAC) is a promising technology that can share spectrum and hardware between sensing and communication, thereby effectively improving resource utilization. In addition, in order to obtain higher sensing accuracy and transmission rate, terahertz (THz) technology with ultra-wide bandwidth can be applied to ISAC. However, THz signals usually suffer from severe transmission attenuation and poor scattering, which limits their transmission distance and sensing range. To solve this problem, reconfigurable smart surface (RIS) has developed into a key technology in future wireless networks. It consists of a large number of reflection units. By adjusting the RIS reflection coefficient, the direction of the beam can be adjusted. In addition, broadband multi-carrier transmission technology, such as orthogonal frequency division multiplexing (OFDM) technology, is often used in THz communication to overcome frequency selective fading. Due to the frequency-independent characteristics of RIS elements, beam dispersion exists at RIS, resulting in beams of different subcarriers pointing in different directions, thereby losing beamforming gain and reducing communication rate. In order to effectively mitigate beam dispersion, an effective solution is to increase real time delay (TTD) at the element to adjust the degree of beam dispersion by compensating for transmission delay. However, from the perspective of perception, beam dispersion may be advantageous in achieving fast perception. There have been many studies on beam dispersion, but most of the works only consider beam dispersion in the communication process or the perception process. Summary of the invention

[0003] Aiming at the beam dispersion effect problem existing in the perception process and communication process of the RIS-assisted terahertz ISAC system, the present invention proposes a robust beam optimization method in an intelligent metasurface-assisted terahertz synaesthesia system, which can effectively reduce beam dispersion and improve communication capacity.

[0004] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0005] A robust beam optimization method in a smart metasurface-assisted terahertz synaesthesia system is proposed. A RIS-assisted terahertz ISAC system is constructed, which includes a base station (BS) equipped with a single antenna, a semi-passive RIS equipped with a uniform linear array (ULA) of R passive reflective elements and Rs active reflective elements, and a single-antenna user. There are obstacles between the BS and the user, and the communication process between the BS and the user is divided into two stages: the perception stage and the communication stage.

[0006] In the perception stage, a fast beam dispersion perception method based on real-time delay (TTD) of RIS is proposed to adjust the degree of beam deviation, and the perception Cramé-Rao lower bound (CRB) and the relationship between CRB and CSI error are derived.

[0007] In the communication phase, based on the imperfect CSI obtained, a robust optimization objective function is proposed to maximize the transmission capacity by jointly designing the RIS reflection coefficient, time delay and sensing time.

[0008] In the process of solving the optimization objective function, the sensing time is first fixed, and then an alternating optimization method is proposed to solve the RIS reflection coefficient and time delay to maximize the transmission capacity.

[0009] Preferably, the communication between the BS and the user is transmitted via RIS. Referring to the uniform linear array channel model, g(t) represents the channel impulse response from the BS to the RIS, and h(t) represents the channel impulse response from the RIS to the user. The transmission bandwidth is represented by f s The center frequency is represented by f c express, represents the l1th path delay from the BS to the rth RIS element, represents the l2th path delay from the rth RIS element to the user; then and It can be expressed as:

[0010]

[0011] Where c represents the speed of light, d = λ c / 2 represents the spacing of RIS elements, λ c represents the wavelength at the center frequency; represents the l1th path delay from BS to the first RIS element, represents the l2th path delay from the first RIS element to the user; represents the normalized departure angle (angle of departure, AOD) of the BS, represents the AOD (angle of departure, AOD) of the l2th path between RIS and the user, represents the normalized AOA, represents the normalized AOD;

[0012] Therefore, the channel impulse response from the BS to the rth RIS element is expressed as:

[0013]

[0014] The channel impulse response from the rth RIS element to the user is expressed as:

[0015]

[0016] Among them, α l1 is the equivalent baseband complex gain of the l1th path, α l2 is the equivalent baseband complex gain of the l2th path; u r (t) is the signal reflected by the rth RIS element and is defined as:

[0017]

[0018] where θ=[θ1,...,θ R ] T , As the reflection coefficient of the rth RIS element, β r ∈[0,1] and Represent the amplitude and phase shift of the RIS reflection coefficient respectively; to maximize the signal power, the default amplitude is set to β r =1, Therefore, θ can be simplified to In addition, s(t) is the signal transmitted by the BS, and the signal received by the user at the rth RIS element is expressed as:

[0019] y r (t) = h r (t)*u r (t)+n r (t), (6)

[0020] Among them, n r (t) is additive white Gaussian noise; Substituting equation (5) into equation (6), y r (t) can be reformulated as:

[0021]

[0022] Therefore, the CIR of the r-th cascaded BS-RIS-user channel can be expressed as:

[0023]

[0024] Perform Fourier transform on equation (8), and the frequency domain channel response f r (f) is expressed as:

[0025]

[0026] Where α = α l1 α l2 is the equivalent complex path gain of the cascaded BS-RIS-user channel, is the normalized angle of the cascaded BS-RIS-user channel, is the normalized delay of the cascaded BS-RIS-user channel; in order to analyze the beam dispersion effect, consider a single path, set L1 = 1 and L2 = 1, then the cascaded channel response can be re-expressed as:

[0027]

[0028] in, is the equivalent angle of the cascaded BS-RIS-user channel in the case of a single path, is the equivalent delay of the cascaded BS-RIS-user channel in the case of a single path. For the convenience of description, v = sinθ BR -sinθ RU ; Therefore, the cascade channel vector J(f) = [f1(f), f2(f), ..., f R (f)] T It is expressed as:

[0029]

[0030] in,

[0031] The array gain expression at frequency f is defined as follows:

[0032]

[0033] Assume f = f c When f = f0 = v0 / 2, v0 is the equivalent beam direction at the center frequency, and is the maximum normalized array gain. Available The reflection coefficient vector θ at the center frequency c Expressed as By setting Any direction at frequency f The beam array gain obtained under this condition is expressed as:

[0034]

[0035] in, To maximize the beam gain, r should be set to 0. At this time, the relationship between the beam direction and the frequency is: From the above equation, we can see that beams of different frequencies point in different directions. This phenomenon is called beam dispersion effect.

[0036] Preferably, the process of adjusting the degree of beam deviation using the RIS-based TTD beam dispersion fast perception method is as follows:

[0037] The time domain response of the rth RIS element combined with the TTD connection is defined as t r is the delay introduced by the rth TTD, the corresponding frequency domain response can be expressed as Therefore, the frequency domain response vector is expressed as Based on the above analysis, the BS-RIS-user cascade channel response can be restated as:

[0038]

[0039] Among them, f∈[0,f s ];definition Therefore, a(Θ(f)) is expressed as For a bandwidth of f s , the subcarrier spacing of the OFDM system with M subcarriers is f s / M, then the signal received at the mth carrier is expressed as:

[0040] y(mf s / M)=J'(mf s / M) T θs(mf s / M)+n, (15)

[0041] Among them, J'(mf s / M) represents the concatenated vector at the mth carrier; by designing TTD and RIS reflection coefficients, the degree of beam dispersion is adjusted; changing TTD makes the subcarrier beam direction change with frequency f. Assuming that the frequency f increases from 0 to f s When the corresponding beam angle changes from the initial angle v0 to the final angle v M In addition, the definition is the equivalent initial angle, is the equivalent termination angle, the beam gain can be expressed as:

[0042]

[0043] Given the initial angle v0, we get θ(0)=sv0. Substituting θ(0) into equation (16), we get:

[0044]

[0045] Maximizing formula (17), the reflection coefficient is

[0046] Given an initial angle v M ,get Let Θ(f s )and Substituting formula (17) we get:

[0047]

[0048] Maximizing formula (18) yields t r :

[0049]

[0050] Therefore, the beam angle at any frequency f can be expressed as θ Rf :

[0051]

[0052] θ Rf =arcsin(sin(θ BR )-sv f ) (twenty one)

[0053] Based on the above analysis, TTD is used to adjust the degree of beam deviation to cover a specific sensing area.

[0054] Preferably, the derivation method of the perceptual Cramé-Rao lower bound is:

[0055] The echo signal received by RIS-SE at the mth carrier at time t is expressed as:

[0056]

[0057] in, represents the beam steering vector of the BS-RIS link at the mth carrier, s(t) represents the signal transmitted by the BS in time slot t, represents the RIS-RE-user-RIS-SE channel matrix, is the additive white Gaussian noise during reception; H t =α s a s (θ RU ) H (θ RU ),in

[0058] Therefore, y s,m can be re-expressed as:

[0059]

[0060] in, By collecting all received echo signals during beam dispersion, we get:

[0061]

[0062] in, N=[n(1),...,n(τ)], where x represents the angle θ f The beamforming vector at the RIS of θ is simply represented by θ for ease of representation. RU , the covariance matrix of X can be expressed as

[0063] First, consider a single user and derive the perceived CRB; by vectorizing Y, we have:

[0064]

[0065] Among them, u=α g a s (θ)q H (θ)X, Let ξ=[θ,α T ] T , represents the unknown parameter vector to be estimated, including the user's θ and the complex channel coefficient α, where α=[Re{α s},Im{α s}] T ; In order to obtain the least squares of θ, the Fisher information matrix (FIM) about θ is derived; Note The FIM used to express the estimated ξ is then expressed as:

[0066]

[0067] in,

[0068]

[0069] Where P t is the transmission power of the BS. Assuming that when beam dispersion occurs, the beam power at the subcarrier is equally divided, then the beam power at each sub-frequency is

[0070] Next, we derive the CRB for estimating θ, which corresponds to The first diagonal element of , then the estimated CRB of θ is:

[0071]

[0072] in, D1=diag(0,1,...,R s -1), D2 = diag(0,1,...,R);

[0073] Secondly, regarding α sThe estimation of can be obtained based on the maximum likelihood function (MLE) method. The maximum likelihood function is expressed as:

[0074]

[0075] Then, maximizing the likelihood function is equivalent to minimizing Therefore, the MLE can be written as For any given θ, the optimal α g for The perceptual signal-to-noise ratio is defined as

[0076] Preferably, the method for obtaining the relationship between the CRB and the CSI error is:

[0077] Use estimated value and the estimated error △θ to represent θ, To this end, it is assumed that the estimation error of θ follows a Gaussian distribution. Therefore, according to the 3s rule, the △θ angle is located at The probability of being within the range is 0.9973; then we get the following expression Among them, △g m (θ) represents the steering vector error caused by △θ, △g m The norm of (θ) can be expressed as △θ∈Θ,

[0078] To this end, we consider the case where △θ is small enough and The operation of the first-order Taylor expansion is From the second-order Taylor expansion of cosx at 0, we get Using the above trigonometric approximation, △g m The (θ)-norm bounded imperfect CSI model can be expressed as

[0079] Based on this, a close relationship between sensing CRB and imperfect CSI is established, and the achievable communication capacity of the user in T-τ is expressed as:

[0080]

[0081] in,

[0082] Preferably, the optimization objective function is:

[0083]

[0084] Where, Φ = diag (θ) represents the reflection coefficient of RIS, T m =diag(ψm,1 ,...,ψ m,R ) represents the delay matrix of RIS, and t r The time delay introduced by the r-th RIS reflection element; C1 represents the channel uncertainty constraint, C2 represents the constant modulus constraint of each RIS reflection element, C3 represents the perception time constraint, and C4 represents the constant modulus constraint of the delay of the r-th RIS reflection element at the m-th subcarrier.

[0085] Preferably, the optimization objective function is simplified by introducing auxiliary variables:

[0086] By introducing auxiliary variables, the optimization objective function is transformed into:

[0087]

[0088] Among them, |h m H ΦT m g m | 2 Translates to:

[0089] |h m H ΦT m g m | 2 =(h m H ΦT m g m )(h m H ΦT m g m ) H =h m H ΦT m g m g m H Φ H T m H h m , (32)

[0090] Will Substituting into formula (32), we get:

[0091]

[0092] Therefore, formula (33) can be transformed into:

[0093]

[0094] Among them, h m HΦT m △g m △g m H T m H Φ H h m =△g m H C m △g m , C m =T m H Φ H h m h m H ΦT m ,

[0095]

[0096] Therefore, |h m H ΦT m g m | 2 Transforms into:

[0097]

[0098] Therefore, constraint C5 is transformed into:

[0099]

[0100] in,

[0101] The following is an introduction to S-Procedure: Define variables The quadratic function of :

[0102] f i (x) = x H T i x+2Re{u i H x}+v i ,i=0,1,...,p, (37)

[0103] Among them, T i =T i H ; Consider the condition f i (x): f0(x)≥0, for all x, f i (x)≥0,i=1,...,p, if and only if τ i ≥0,i=1,...,p, we have:

[0104]

[0105] Referring to S-Procedure, C1 is equivalently transformed into:

[0106]

[0107] Among them, v m ≥0,m=1,...,M, by introducing auxiliary variables The objective function P2 is equivalent to:

[0108]

[0109] For the objective function P3, a one-dimensional search method is used to find the optimal perception time τ. Based on the given perception time τ, the objective function P3 is solved using an alternating optimization method.

[0110] Preferably, the specific method of solving the objective function P3 using the alternating optimization method is:

[0111] For a given perception time and delay, the objective function P3 is simplified to:

[0112]

[0113] Define the reflection coefficient matrix Φ = diag(u), U = uu H , rank(U)=1; transform the sub-objective function P4 into:

[0114]

[0115] Among them, C m '=T m H diag(h m )Udiag(h m H )T m ; Apply the SDR method to remove the rank(U)=1 constraint, and use the CVX tool to solve the sub-objective function P5. Then, use the Gaussian randomization method to obtain the reflection coefficient vector u of RIS. The final reflection coefficient can be expressed as Φ opt =diag(u opt );

[0116] Similar to the above analysis, after obtaining the RIS reflection coefficient matrix Φ, the objective function P3 is rewritten as:

[0117]

[0118] Since the constant modulus constraint C4 makes the sub-objective function P6 non-convex, an auxiliary variable T is introduced m=diag(t m ),F m =t m t m H , rank(F m )=1; therefore, the sub-objective function P6 is simplified to:

[0119]

[0120] Among them C m ”=h m H ΦF m Φ H h m ; The SDR method is used to remove the first-order constraints, and the CVX tool is used to solve the sub-objective function P7;

[0121] In order to solve the original optimization objective function P1, it is necessary to alternately solve the sub-objective functions P4 and P6 until convergence.

[0122] The beneficial effects of the present invention are as follows: in the perception stage, the present invention proposes a fast beam dispersion perception scheme based on real-time delay (TTD) of RIS, and derives the perception Cramé-Rao lower bound (CRB) and its relationship with CSI error; in the communication stage, the present invention proposes a robustness optimization goal based on the obtained imperfect CSI, and maximizes the transmission capacity by jointly designing the RIS reflection coefficient, time delay and perception time; effectively reduces beam dispersion and improves communication capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0124] Figure 1 This is the structural diagram of the RIS-assisted terahertz ISAC system.

[0125] Figure 2 This is a time frame structure diagram.

[0126] Figure 3 This is a structural diagram of the RIS component based on TTD.

[0127] Figure 4 is the RIS beam pattern.

[0128] Figure 5 This is the perception area coverage map based on RIS beam dispersion.

[0129] Figure 6 To perceive the relationship between CRB and the signal-to-noise ratio in different beam dispersion ranges, where θ = 0°.

[0130] Figure 7 To perceive the relationship between CRB and SNR, different user angles θ span the same 20° range.

[0131] Figure 8 This is the convergence test result of the algorithm proposed in this invention.

[0132] Fig. 9 The relationship between achievable communication capacity and perception time.

[0133] Fig.10 The relationship between achievable communication capacity and signal-to-noise ratio. DETAILED DESCRIPTION

[0134] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0135] like Figure 1 As shown in the figure, a RIS-assisted terahertz ISAC system is considered, which includes a single-antenna base station (BS), a semi-passive RIS equipped with a uniform linear array (ULA) consisting of R passive reflective elements and Rs active reflective elements, and a single-antenna user. In addition, due to unfavorable environmental propagation, it is assumed that there are obstacles between the BS and the user, and the direct link is blocked. The time frame structure includes two stages: perception and communication, as shown in Figure 2 As shown. In the sensing phase, the BS sends a sensing signal and then obtains the user's location information by collecting the echo signal reflected at the RIS. Then, in the communication phase, the BS sends a transmission signal to the user through the RIS. For convenience, R passive elements are used to reflect signals, called "-RE" units, and Rs active elements are used to receive echo signals, called "-SE" units.

[0136] Referring to the uniform linear array channel model, g(t) represents the channel impulse response (CIR) from BS to RIS, and h(t) represents the channel impulse response (CIR) from RIS to the user. Based on the far-field assumption, the RIS plane size is much smaller than the distance between the transmitter and the receiver, and the transmission bandwidth is represented by f s The center frequency is represented by f c express. represents the l1th path delay from the BS to the rth RIS element, represents the l2th path delay from the rth RIS element to the user. Then and It can be expressed as:

[0137]

[0138] Where c represents the speed of light, d = λ c / 2 represents the spacing of RIS elements, λ c Indicates the wavelength at the center frequency. represents the l1th path delay from BS to the first RIS element, It represents the l2th path delay from the first RIS element to the user. They represent the AOA (angle of arrival, AOA) of the l1th path between BS and RIS and the AOD (angle of departure, AOD) of the l2th path between RIS and user, respectively. Represent the normalized AOA and AOD respectively, and their ranges are

[0139] Therefore, the channel impulse response from the BS to the rth RIS element is expressed as:

[0140]

[0141] The channel impulse response from the rth RIS element to the user is expressed as:

[0142]

[0143] Among them, α l1 is the equivalent baseband complex gain of the l1th path, α l2 is the equivalent baseband complex gain of the l2th path. r (t) is the signal reflected by the rth RIS element and is defined as:

[0144]

[0145] where θ=[θ1,...,θ R ] T , As the reflection coefficient of the rth RIS element, β r ∈[0,1] and denote the amplitude and phase shift of the RIS reflection coefficient, respectively. To maximize the signal power, the default amplitude is set to β r =1, Therefore, θ can be simplified to In addition, s(t) is the signal transmitted by the BS, and the signal received by the user at the rth RIS element can be expressed as

[0146] y r (t) = h r (t)*u r (t)+n r (t), (6)

[0147] Among them, n r (t) is additive white Gaussian noise. Substituting equation (5) into equation (6), y r (t) can be reformulated as:

[0148]

[0149] Therefore, the CIR of the r-th cascaded BS-RIS-user channel can be expressed as:

[0150]

[0151] Perform Fourier transform on equation (8), and the frequency domain channel response f r (f) is expressed as:

[0152]

[0153] Where α = α l1 α l2 , They are defined as the equivalent complex path gain, normalized angle, and normalized delay of the cascaded BS-RIS-user channel, respectively. In order to analyze the beam dispersion effect, a single path is considered, and L1 = 1 and L2 = 1 are set. Then the cascaded channel response can be re-expressed as:

[0154]

[0155] in, They are defined as the equivalent angle and equivalent delay of the cascaded BS-RIS-user channel in the case of a single path. For convenience, v = sinθ BR -sinθ RU Therefore, the concatenated channel vector J(f) = [f1(f), f2(f), ..., f R (f)] T It is expressed as:

[0156]

[0157] in,

[0158] The array gain expression at frequency f is defined as follows:

[0159]

[0160] Assume f = f c When f = f0 = v0 / 2, v0 is the equivalent beam direction at the center frequency, and is the maximum normalized array gain. Available The reflection coefficient vector θ at the center frequency c It can be expressed as By setting Any direction at frequency f The beam array gain obtained under this condition can be expressed as:

[0161]

[0162] in, To maximize the beam gain, r should be set to 0. At this time, the relationship between the beam direction and the frequency is: From the above equation, we can see that beams of different frequencies point in different directions. This phenomenon is called beam dispersion effect.

[0163] like Figure 3 As shown in Figure 1, TTD is a frequency-dependent broadband device. By connecting TTD to each RIS element, the degree of beam dispersion can be adjusted by changing the propagation delay of the signal. The time domain response of the combination of the rth RIS element and TTD is: t r is the delay introduced by the rth TTD, the corresponding frequency domain response can be expressed as Therefore, the frequency domain response vector is expressed as Based on the above analysis, the BS-RIS-user cascade channel response can be restated as:

[0164]

[0165] Among them, f∈[0,f s ].definition Therefore, a(Θ(f)) is expressed as For a bandwidth of f s , the subcarrier spacing of the orthogonal frequency division multiplexing (OFDM) system with M subcarriers is f s / M, then the signal received at the mth carrier is expressed as:

[0166] y(mf s / M)=J'(mf s / M) T θs(mf s / M)+n, (15)

[0167] Among them, J'(mf s / M) represents the concatenated vector at the mth carrier. By designing the TTD and RIS reflection coefficients, the degree of beam dispersion can be adjusted. Changing TTD makes the subcarrier beam direction change with frequency f. Assuming that the frequency f increases from 0 to f s When the corresponding beam angle changes from the initial angle v0 to the final angle v M In addition, the definition is the equivalent initial angle, is the equivalent termination angle, the beam gain can be expressed as:

[0168]

[0169] Given the initial angle v0, we can get Θ(0)=sv0. Substituting Θ(0) into the above formula, we get:

[0170]

[0171] Maximizing formula (17), we can get the value of reflection coefficient as

[0172] Given an initial angle v M , we can get Let Θ(f s )and Substituting formula (17) we get:

[0173]

[0174] Maximizing formula (18) yields t r :

[0175]

[0176] Therefore, the beam angle at any frequency f can be expressed as θ Rf :

[0177]

[0178] θ Rf =arcsin(sin(θ BR )-sv f ) (twenty one)

[0179] Based on the above analysis, the beam dispersion pattern at RIS is as follows: Figure 4 shown.

[0180] Therefore, TTD is used to adjust the degree of beam deviation to cover a specific sensing area, such as Figure 5As shown. Next, the sensing CRB of RIS is mainly analyzed, which is used to measure the sensing performance. The echo signal received by RIS-SE at the mth carrier at time t is expressed as:

[0181]

[0182] in, represents the beam steering vector of the BS-RIS link at the mth carrier, s(t) represents the signal transmitted by the BS in time slot t, represents the RIS-RE-user-RIS-SE channel matrix, is the additive Gaussian white noise during reception. t =α s a s (θ RU ) H (θ RU ),in

[0183] Therefore, y s,m can be re-expressed as:

[0184]

[0185] in, By collecting all received echo signals during beam dispersion, we get:

[0186]

[0187] in, N=[n(1),...,n(τ)], where x represents the angle θ f The beamforming vector at the RIS of θ is simply represented by θ for ease of representation. RU , the covariance matrix of X can be expressed as

[0188] First, consider a single user and derive the perceived CRB. By vectorizing Y, we have:

[0189]

[0190] Among them, u=α g a s (θ)q H (θ)X, Let ξ=[θ,α T ] T , represents the unknown parameter vector to be estimated, including the user's θ and the complex channel coefficient α, where α=[Re{α s},Im{αs}] T In order to obtain the least squares of θ, the Fisher information matrix (FIM) about θ is derived. The FIM used to express the estimated ξ is then expressed as:

[0191]

[0192] in,

[0193]

[0194] Where P t is the transmission power of the BS. Assuming that when beam dispersion occurs, the beam power at the subcarrier is equally divided, then the beam power at each sub-frequency is Next, we derive the CRB for estimating θ, which corresponds to The first diagonal element of , then the estimated CRB of θ is:

[0195]

[0196] in, D1=diag(0,1,...,R s -1), D2=diag(0,1,...,R). s The estimation of can be obtained based on the maximum likelihood function (MLE) method. The maximum likelihood function is expressed as:

[0197]

[0198] Then, maximizing the likelihood function is equivalent to minimizing Therefore, the MLE can be written as For any given θ, the optimal α g for The perceptual signal-to-noise ratio is defined as

[0199] Although the user angle information is obtained through perception, it is difficult to obtain the exact value of θ. Next, the present invention will analyze the relationship between the user CSI error and the perceived CRB. In the present invention, the estimated value and the estimated error △θ to represent θ, To this end, it is assumed that the estimation error of θ follows a Gaussian distribution. Therefore, according to the 3s rule, the △θ angle is located at The probability of being within the range is 0.9973. Then we get the following expression Among them, △g m(θ) represents the steering vector error caused by △θ, △g m The norm of (θ) can be expressed as Among them, △θ∈Θ, To this end, we consider the case where △θ is small enough and The operation of the first-order Taylor expansion is From the second-order Taylor expansion of cosx at 0, we get Using the above trigonometric approximation, △g m The (θ)-norm bounded imperfect CSI model can be expressed as arrive A close relationship between sensing CRB and imperfect CSI has been established, and the achievable communication capacity of a user in T-τ can be expressed as:

[0200]

[0201] in,

[0202] In the communication phase, the BS will design RIS reflection beamforming based on the imperfect CSI obtained in the perception phase to maximize the communication capacity. Since the perception phase and the communication phase affect each other, a maximum communication capacity is formulated by jointly optimizing the RIS reflection coefficient and delay as well as the time of the two phases, which can be expressed as:

[0203]

[0204] Where, Φ = diag (θ) represents the reflection coefficient of RIS, T m =diag(ψ m,1 ,...,ψ m,R ) represents the delay matrix of RIS, and t r The time delay introduced by the rth RIS reflector element. In the above formula, C1 represents the channel uncertainty constraint, C2 represents the constant modulus constraint of each RIS reflector element, C3 represents the perception time constraint, and C4 represents the constant modulus constraint of the delay of the rth RIS reflector element at the mth subcarrier. Obviously, due to the coupling between the optimization variables, the optimization objective function expressed belongs to a complex non-convex problem.

[0205] In order to solve the non-convex problem, the optimization objective function is decomposed into multiple sub-objective functions, and an AO algorithm is proposed. Specifically, the S-Procedure and semidefinite relaxation (SDR) method are used to solve the sub-objective functions related to optimizing the RIS reflection coefficient and time delay. Then, a one-dimensional search is used to find the optimal perception time. Finally, these sub-objective functions are solved alternately until convergence. By introducing auxiliary variables, the optimization objective function is transformed into:

[0206]

[0207] Among them, |h m H ΦT m g m | 2 Translates to:

[0208] |h m H ΦT m g m | 2 =(h m H ΦT m g m )(h m H ΦT m g m ) H =h m H ΦT m g m g m H Φ H T m H h m , (32)

[0209] Will Substituting into formula (32), we get:

[0210]

[0211] Therefore, formula (33) can be transformed into:

[0212]

[0213] Among them, h m H ΦT m △g m △g m H T m H Φ H h m =△g m H C m △g m , C m =T m H Φ H h m h mH ΦT m ,

[0214]

[0215] Therefore, |h m H ΦT m g m | 2 Transforms into:

[0216]

[0217] Therefore, constraint C5 is transformed into:

[0218]

[0219] in,

[0220] The following is an introduction to S-Procedure: Define variables The quadratic function of :

[0221] f i (x) = x H T i x+2Re{u i H x}+v i ,i=0,1,...,p, (37)

[0222] Among them, T i =T i H Consider the condition f i (x): f0(x)≥0, for all x, f i (x)≥0,i=1,...,p, if and only if τ i ≥0,i=1,...,p, we have:

[0223]

[0224] Referring to S-Procedure, C1 is equivalently transformed into:

[0225]

[0226] Among them, v m ≥0,m=1,...,M, by introducing auxiliary variables The objective function P2 is equivalent to:

[0227]

[0228] Due to the coupling of variables τ, Φ, and T, the objective function P3 is a non-convex optimization problem, which is difficult to solve by general optimization methods. Obviously, the optimal perception time τ can be found by using a one-dimensional search method. Therefore, based on the given perception time τ, the AO method is applied to process P3.

[0229] First, the perception time τ is fixed, and then an alternating optimization scheme is proposed to solve the RIS reflection coefficient and time delay, thereby optimizing the communication capacity maximization problem. The S-Procedure algorithm and the semi-definite relaxation (SDR) method are applied. At the same time, the optimal perception time is obtained through a one-dimensional search. The specific steps are as follows:

[0230] For a given perception time and delay, the objective function P3 can be simplified as:

[0231]

[0232] Note that since the constant modulus constraint C2 is still non-convex with respect to Φ, the objective function P4 needs further transformation. Define the reflection coefficient matrix Φ = diag(u), U = uu H , rank(U) = 1. The sub-objective function P4 can be transformed into:

[0233]

[0234] Among them C m '=T m H diag(h m )Udiag(h m H )T m . Because of the rank(U)=1 constraint, the sub-objective function P5 is non-convex. Next, the SDR method is applied to remove the rank(U)=1 constraint, and the CVX tool is used to solve the optimization problem. Then, the Gaussian randomization method is used to obtain the reflection coefficient vector u of RIS. The final reflection coefficient can be expressed as Φ opt =diag(u opt ).

[0235] Similar to the above analysis, after obtaining the RIS reflection coefficient matrix Φ, the objective function P3 can be rewritten as

[0236]

[0237] Since the constant modulus constraint C4 makes the sub-objective function P6 non-convex, an auxiliary variable T is introduced m =diag(t m ),F m =t m t m H, rank(F m )=1. Therefore, the objective function P6 can be simplified as:

[0238]

[0239] Among them C m ”=h m H ΦF m Φ H h m , we still use the SDR method to remove the first-order constraints and use the CVX tool to solve P7. m At the frequency, the phase shift caused by the time delay introduced by the rth RIS element is -2πf m t r In practical applications, for all subcarriers, the delay value t of each RIS element connection is r should be the same, so only R time delays are needed. To solve this problem, the present invention uses an average method to determine each time delay. Specifically, based on the M time delays of each RIS element on the M subcarriers obtained, the average of the M time delays is calculated and recorded as the rth time delay. The above process is repeated until all R time delays are obtained.

[0240] In summary, in order to solve the original optimization objective function P1, it is necessary to alternately solve subproblems P4 and P6 until convergence. Algorithm 1 summarizes the details of the AO algorithm. In Algorithm 1, since problems P4 and P6 are convex, they are solved using the global optimal solution. Therefore, the target value of P1 is non-decreasing during the iteration process. In addition, due to the channel uncertainty constraint C1 and the limitation of BS transmit power, the maximum target value of the optimization problem has an upper limit, so Algorithm 1 is guaranteed to converge. Subsequently, the computational complexity of the proposed algorithm is analyzed. The computational complexity of the SDR-based algorithm is O(I S (R 3.5 +1)), where I S Indicates the number of loop iterations.

[0241]

[0242]

[0243] Simulation results: In the simulation part, the simulation results of the system are given to verify the performance of the proposed system. The duration of the whole process is set to T = 200ms, and the bandwidth is set to f s =6GHz, the center carrier frequency is f c =300GHz, the number of carriers is M=8. The number of RIS-RE elements and RIS-SE elements is set to R=32, R s=16, let BS transmit power P t =30dBm, noise variance s 2 = -120dBm, and the user angle is set to θ = 0°. In addition, using a typical distance-dependent path loss model, the path loss is expressed as Where C0 = -30dB represents the path loss at the reference distance d0 = 1m, d is the link distance, α is the path loss index, and the path loss index of the BS-RIS and RIS-user links is set to α = 2.2. Set the BS-RIS link distance d BR =30m, RIS-user link distance d RU =10m.

[0244] Figure 6 The relationship between perceived CRB and SNR under different beam dispersion ranges is given. It can be observed that the CRB in dB decreases monotonically with the perceived SNR because the CRB is inversely proportional to the SNR derivation. In addition, under a fixed SNR, when the beam dispersion range changes between [-80°, 80°], [-60°, 60°], [-40°, 40°], and [-20°, 20°], the CRB gradually decreases, indicating that the perception accuracy has improved. This is because, with the same number of subcarriers, a smaller beam dispersion range results in a denser distribution on the beam direction pattern, thereby improving the perception accuracy.

[0245] Figure 7 In order to utilize the relationship between CRB and SNR of the beam dispersion perception method, "beam dispersion, AoD & [0°, 20°]" represents the dispersion range, and the user AoD is randomly distributed and the perception range is [0°, 20°]. In addition, when the number of carriers M is the same, the perception performance of different dispersion ranges is different. From the simulation results, it can be seen that when the number of subcarriers is fixed, the perception performance in the range of [0°, 20°] is better than that in the range of [60°, 80°], which indicates that the perception accuracy is higher. The reason is that from formula (21), it can be seen that the expression of the subcarrier beamforming direction is a nonlinear arcsin function of the subcarrier frequency f, and from the simulation results, it can be seen that even if the OFDM subcarrier spacing is uniform, the corresponding subcarrier beamforming direction is not uniformly distributed.

[0246] The convergence performance under different comparison schemes is as follows Figure 8As shown. The method proposed in the present invention is compared with the "RIS with time delay" and "RIS without time delay" methods. The "traditional time delay" method refers to adjusting the delay value to be consistent with the delay value at the center carrier frequency; the "random time delay" method refers to randomly generating a delay value. Obviously, the "RIS with TD" method is better than the "RIS without TD" method, which further verifies the role of TTD in alleviating beam dispersion. It is worth noting that the convergence speed of the proposed method is slightly slower than that of "RIS with TD (traditional solution)" and "RIS with TD (random time delay)". This is because the proposed method involves optimizing the delay, which increases the number of iterations. At the same time, compared with other benchmark schemes, the proposed method achieved better performance, proving the superiority of the method proposed in the present invention.

[0247] The relationship between the achievable communication capacity and the perception time is as follows: Fig. 9 As shown in the figure. As the sensing time increases, the sensing accuracy increases, the CSI error decreases, and thus the channel capacity increases. When the sensing time continues to increase, the improvement of the sensing accuracy is limited. Therefore, there is a resource trade-off between sensing and communication. Obviously, under the method proposed in the present invention, in order to obtain the maximum communication capacity, setting the sensing time to 20ms is optimal. In addition, Fig. 9 It is shown that the proposed method outperforms the other two compared methods.

[0248] like Fig.10 As shown in FIG. 1 , the relationship between the achievable communication capacity and the signal-to-noise ratio is given. It can be seen that as the signal-to-noise ratio increases, the capacity of each method also increases. In addition, under the same signal-to-noise ratio, compared with the benchmark method, the method proposed in the present invention can still obtain the highest capacity, which also shows the effectiveness of the method of the present invention.

[0249] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A robust beam optimization method in a smart metasurface-assisted terahertz synaesthesia system, characterized in that: A RIS-assisted terahertz ISAC system is built, which includes a base station (BS) equipped with a single antenna, a semi-passive RIS equipped with a uniform linear array (ULA) of R passive reflective elements and Rs active reflective elements, and a single-antenna user; there are obstacles between the BS and the user, and the communication process between the BS and the user is divided into two stages: the perception stage and the communication stage; In the perception stage, a fast beam dispersion perception method based on real-time delay (TTD) of RIS is proposed to adjust the degree of beam deviation, and the perception Cramé-Rao lower bound (CRB) and the relationship between CRB and CSI error are derived. In the communication phase, based on the imperfect CSI obtained, a robust optimization objective function is proposed to maximize the transmission capacity by jointly designing the RIS reflection coefficient, time delay and sensing time. In the process of solving the optimization objective function, the sensing time is first fixed, and then an alternating optimization method is proposed to solve the RIS reflection coefficient and time delay to maximize the transmission capacity.

2. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 1 is characterized in that: The communication between BS and users is transmitted through RIS. Referring to the uniform linear array channel model, g(t) represents the channel impulse response from BS to RIS, and h(t) represents the channel impulse response from RIS to users. The transmission bandwidth is f s The center frequency is represented by f c express, represents the l1th path delay from the BS to the rth RIS element, represents the l2th path delay from the rth RIS element to the user; then and It can be expressed as: Where c represents the speed of light, d = λ c / 2 represents the spacing of RIS elements, λ c represents the wavelength at the center frequency; represents the l1th path delay from BS to the first RIS element, represents the l2th path delay from the first RIS element to the user; represents the normalized departure angle (angle of departure, AOD) of the BS, represents the AOD (angle of departure, AOD) of the l2th path between RIS and the user, represents the normalized AOA, represents the normalized AOD; Therefore, the channel impulse response from the BS to the rth RIS element is expressed as: The channel impulse response from the rth RIS element to the user is expressed as: Among them, α l1 is the equivalent baseband complex gain of the l1th path, α l2 is the equivalent baseband complex gain of the l2th path; u r (t) is the signal reflected by the rth RIS element and is defined as: where θ=[θ1,...,θ R ] T , As the reflection coefficient of the rth RIS element, β r ∈[0,1] and Represent the amplitude and phase shift of the RIS reflection coefficient respectively; to maximize the signal power, the default amplitude is set to β r =1, Therefore, θ can be simplified to In addition, s(t) is the signal transmitted by the BS, and the signal received by the user at the rth RIS element is expressed as: y r (t)=h r (t)*u r (t)+n r (t), (6) Among them, n r (t) is additive white Gaussian noise; Substituting equation (5) into equation (6), y r (t) can be reformulated as: Therefore, the CIR of the r-th cascaded BS-RIS-user channel can be expressed as: Perform Fourier transform on equation (8), and the frequency domain channel response f r (f) is expressed as: Where α = α l1 α l2 is the equivalent complex path gain of the cascaded BS-RIS-user channel, is the normalized angle of the cascaded BS-RIS-user channel, is the normalized delay of the cascaded BS-RIS-user channel; in order to analyze the beam dispersion effect, consider a single path, set L1 = 1 and L2 = 1, then the cascaded channel response can be re-expressed as: in, is the equivalent angle of the cascaded BS-RIS-user channel in the case of a single path, is the equivalent delay of the cascaded BS-RIS-user channel in the case of a single path. For the convenience of description, v = sinθ BR -sinθ RU ; Therefore, the cascade channel vector J(f) = [f1(f), f2(f), ..., f R (f)] T It is expressed as: in, The array gain expression at frequency f is defined as follows: Assume f = f c When f = f0 = v0 / 2, v0 is the equivalent beam direction at the center frequency, and is the maximum normalized array gain. Available The reflection coefficient vector θ at the center frequency c Expressed as By setting In any direction at frequency f The beam array gain obtained under this condition is expressed as: in, To maximize the beam gain, r should be set to 0. At this time, the relationship between the beam direction and the frequency is: From the above equation, we can see that beams of different frequencies point in different directions. This phenomenon is called beam dispersion effect.

3. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 2 is characterized in that: The process of adjusting the degree of beam deviation using the RIS-based TTD beam dispersion fast perception method is as follows: The time domain response of the rth RIS element combined with the TTD connection is defined as t r is the delay introduced by the rth TTD, the corresponding frequency domain response can be expressed as Therefore, the frequency domain response vector is expressed as Based on the above analysis, the BS-RIS-user cascade channel response can be restated as: Among them, f∈[0,f s ];definition Therefore, a(Θ(f)) is expressed as For a bandwidth of f s , the subcarrier spacing of the OFDM system with M subcarriers is f s / M, then the signal received at the mth carrier is expressed as: y(mf s / M)=J'(mf s / M) T θs(mf s / M)+n, (15) Among them, J'(mf s / M) represents the concatenated vector at the mth carrier; by designing TTD and RIS reflection coefficients, the degree of beam dispersion is adjusted; changing TTD makes the subcarrier beam direction change with frequency f. Assuming that the frequency f increases from 0 to f s When the corresponding beam angle changes from the initial angle v0 to the final angle v M In addition, the definition is the equivalent initial angle, is the equivalent termination angle, the beam gain can be expressed as: Given the initial angle v0, we get θ(0)=sv0. Substituting θ(0) into equation (16), we get: Maximizing formula (17), the reflection coefficient is Given an initial angle v M ,get Let Θ(f s )and Substituting formula (17) we get: Maximizing formula (18) yields t r : Therefore, the beam angle at any frequency f can be expressed as θ Rf : <h2 style=";text-align:left;direction:ltr">θ<h2 style=";text-align:left;direction:ltr"> Rf <h2 style=";text-align:left;direction:ltr"> (arcsin(sin(θ))<h2 style=";text-align:left;direction:ltr"> BR <h2 style=";text-align:left;direction:ltr"> )-sv<h2 style=";text-align:left;direction:ltr"> f <h2 style=";text-align:left;direction:ltr"> ) (21) Based on the above analysis, TTD is used to adjust the degree of beam deviation to cover a specific sensing area.

4. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 3 is characterized in that: The derivation method of the perceptual Cramé-Rao lower bound is: The echo signal received by RIS-SE at the mth carrier at time t is expressed as: in, represents the beam steering vector of the BS-RIS link at the mth carrier, s(t) represents the signal transmitted by the BS in time slot t, represents the RIS-RE-user-RIS-SE channel matrix, is the additive white Gaussian noise during reception; H t =α s a s (θ RU ) H (θ RU ),in Therefore, y s,m can be re-expressed as: in, By collecting all received echo signals during beam dispersion, we get: in, N=[n(1),...,n(τ)], where x represents the angle θ f The beamforming vector at the RIS of θ is simply represented by θ for ease of representation. RU , the covariance matrix of X can be expressed as First, consider a single user and derive the perceived CRB; by vectorizing Y, we have: Among them, u=α g a s (θ)q H (θ)X, Let ξ=[θ,α T ] T , represents the unknown parameter vector to be estimated, including the user's θ and the complex channel coefficient α, where α=[Re{α s },Im{α s }] T ; In order to obtain the least squares of θ, the Fisher information matrix (FIM) about θ is derived; Note The FIM used to express the estimated ξ is then expressed as: in, Where P t is the transmission power of the BS. Assuming that when beam dispersion occurs, the beam power at the subcarrier is equally divided, then the beam power at each sub-frequency is Next, we derive the CRB for estimating θ, which corresponds to The first diagonal element of , then the estimated CRB of θ is: in, D1=diag(0,1,...,R s -1), D2 = diag(0,1,...,R); Secondly, regarding α s The estimation of can be obtained based on the maximum likelihood function (MLE) method. The maximum likelihood function is expressed as: Then, maximizing the likelihood function is equivalent to minimizing Therefore, the MLE can be written as For any given θ, the optimal α g for The perceptual signal-to-noise ratio is defined as 5. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 4 is characterized in that: The method for obtaining the relationship between the CRB and the CSI error is: Use estimated value and the estimated error △θ to represent θ, To this end, it is assumed that the estimation error of θ follows a Gaussian distribution. Therefore, according to the 3s rule, the △θ angle is located at The probability of being within the range is 0.9973; then we get the following expression Among them, △g m (θ) represents the steering vector error caused by △θ, △g m The norm of (θ) can be expressed as △θ∈Θ, To this end, we consider the case where △θ is small enough and The operation of the first-order Taylor expansion is From the second-order Taylor expansion of cosx at 0, we get Using the above trigonometric approximation, △g m The (θ)-norm bounded imperfect CSI model can be expressed as Based on this, a close relationship between sensing CRB and imperfect CSI is established, and the achievable communication capacity of the user in T-τ is expressed as: in, 6. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 5 is characterized in that: The optimization objective function is: Where, Φ = diag (θ) represents the reflection coefficient of RIS, T m =diag(ψ m,1 ,...,ψ m,R ) represents the delay matrix of RIS, and t r The time delay introduced by the r-th RIS reflection element; C1 represents the channel uncertainty constraint, C2 represents the constant modulus constraint of each RIS reflection element, C3 represents the perception time constraint, and C4 represents the constant modulus constraint of the delay of the r-th RIS reflection element at the m-th subcarrier.

7. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 6, characterized in that: The optimization objective function is simplified by introducing auxiliary variables: By introducing auxiliary variables, the optimization objective function is transformed into: Among them, |h m H ΦT m g m | 2 Translates to: h m H ΦT m g m | 2 =(h m H ΦT m g m )(h m H ΦT m g m ) H =h m H ΦT m g m g m H Φ H T m H h m , (32) Will Substituting into formula (32), we get: Therefore, formula (33) can be transformed into: where h m H ΦT m △g m △g m H T m H Φ H h m = △g m H C m △g m ,C m = T m H Φ H h m h m H ΦT m , Therefore, |h m H ΦT m g m | 2 Transforms into: Therefore, constraint C5 is transformed into: in, The following is an introduction to S-Procedure: Define variables The quadratic function of : f i (x)=x H T i x+2Re{u i H x}+v i ,i=0,1,...,p, (37) Among them, T i =T i H ; Consider the condition f i (x): f0(x)≥0, for all x, f i (x)≥0,i=1,...,p, if and only if τ i ≥0,i=1,...,p, we have: Referring to S-Procedure, C1 is equivalently transformed into: Among them, v m ≥0,m=1,...,M, by introducing auxiliary variables The objective function P2 is equivalent to: For the objective function P3, a one-dimensional search method is used to find the optimal perception time τ. Based on the given perception time τ, the objective function P3 is solved using an alternating optimization method.

8. The robust beam optimization method in the intelligent metasurface-assisted terahertz synaesthesia system according to claim 7, characterized in that: The specific method of solving the objective function P3 using the alternating optimization method is: For a given perception time and delay, the objective function P3 is simplified to: Define the reflection coefficient matrix Φ = diag(u), U = uu H , rank(U)=1; transform the sub-objective function P4 into: Among them, C m '=T m H diag(h m )Udiag(h m H )T m ; Apply the SDR method to remove the rank(U)=1 constraint, and use the CVX tool to solve the sub-objective function P5. Then, use the Gaussian randomization method to obtain the reflection coefficient vector u of RIS. The final reflection coefficient can be expressed as Φ opt =diag(u opt ); Similar to the above analysis, after obtaining the RIS reflection coefficient matrix Φ, the objective function P3 is rewritten as: Since the constant modulus constraint C4 makes the sub-objective function P6 non-convex, the auxiliary variable T is introduced m =diag(t m ),F m =t m t m H , rank(F m )=1; therefore, the sub-objective function P6 is simplified to: Among them C m ”=h m H ΦF m Φ H h m ; The SDR method is used to remove the first-order constraints, and the CVX tool is used to solve the sub-objective function P7; In order to solve the original optimization objective function P1, it is necessary to alternately solve the sub-objective functions P4 and P6 until convergence.

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