Terahertz isac system design method based on delay alignment modulation and active ris

Abstract

The application provides a terahertz ISAC system design method based on delay alignment modulation and active RIS, and the steps are as follows: firstly, an active RIS assisted terahertz communication and sensing integrated (ISAC) system is built, and the signal received by the user and the signal signal-to-noise ratio of the terahertz ISAC system are calculated; secondly, the non-coherent accumulation is used to calculate the illumination power at the static target, and the received thermal noise at the static target and the power consumed by the active RIS are calculated based on the active RIS; finally, the reflection coefficient of the active RIS and the transmission beam forming vector at the DFBS are jointly designed to maximize the illumination power of the target, and the semi-definite program relaxation technology is used for solving. The application optimizes the transmission beam forming vector of the DFBS and the reflection coefficient of the active RIS, improves the sensing performance and guarantees the communication quality; the terahertz ISAC system utilizes the unique advantages of RIS and DAM, and provides incomparable benefits in the aspects of sensing and communication performance.

Description

Technical Field

[0001] This invention relates to the field of terahertz communication technology, and in particular to a design method for a terahertz ISAC system based on time-delay aligned modulation and active RIS. Background Technology

[0002] The explosive growth in the number of electronic devices may lead to problems such as spectrum congestion in the future. Integrated Sensing and Communication (ISAC) is a promising technology that has attracted much attention in 6G systems. ISAC can achieve efficient spectrum sharing between communication and sensing signals, and simultaneously realize both communication and sensing functions through dual-function base stations (DFBS).

[0003] Reconfigurable Intelligent Surfaces (RIS) also play a crucial role in 6G systems. RIS consists of numerous elements that can intelligently and instantaneously change their surface physical properties. By altering these physical properties, the environment in which wireless signals propagate can be modified, improving signal quality and extending coverage by introducing additional paths. However, due to the effects of multiplicative fading, using RIS in many wireless environments does not yield significant capacity gains, especially when direct link signals are strong. To address this issue, the literature [Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. Vincent Poor, “Active RIS vs. Passive RIS: Which Will Prevail in 6G?”, IEEE Trans. Commun., pp. 1–1, Dec. 2022.] and [K. Zhi, C. Pan, H. Ren, KK Chai, and M. Elkashlan, “Active RIS Versus Passive RIS: Which is Superior With the Same Power Budget?”, IEEE Commun. Lett., vol. 26, no. 5, pp. 1150–1154, May. 2022.] proposed active RIS, which can simultaneously reflect and amplify signals. Each reflecting element is equipped with a power amplifier, which can be used to compensate for the large path loss of the reflecting link and overcome “multiplicative fading”.

[0004] Naturally, RIS-assisted ISAC systems have attracted the attention of researchers. In the paper [AASalem, MHIsmail, and ASIbrahim, “Active Reconfigurable Intelligent Surface-Assisted MISO Integrated Sensing and Communication Systems for Secure Operation,” IEEE Trans. Veh. Technol., pp. 1–13, Dec. 2022.], the authors investigated the physical layer security problem of an active RIS-assisted multi-user system being eavesdropped on by unmanned aerial vehicles (UAVs), using DFBS to sense the location of UAVs, and maximizing the system's confidentiality through appropriate design. The literature [RPSankar and SPChepuri, “Beamforming in Hybrid RIS assisted Integrated Sensing and Communication Systems,” in Proc. of the European Signal Process. Conf. (EUSIPCO), Belgrade, Serbia, Aug. 2022.] studies a hybrid RIS-assisted ISAC system serving multiple users and targets. It maximizes the minimum target illumination power by optimizing the reflection coefficient of the hybrid RIS and the transmit beamforming vector of the DFBS, while ensuring the quality of user communication. The literature also discusses the power upper limit constraint problem of the hybrid RIS.

[0005] However, there is a very important but often overlooked problem. Existing research ignores the impact of delay differences, optimistically assuming that multiple RIS links and direct links can achieve perfect time synchronization, and optimizes parameters based on this to improve system performance. However, in practical applications, due to differences in path distance, multiple signals cannot arrive at the user end simultaneously. If traditional complex equalization or multicarrier processing is used, system optimization becomes particularly complex. Fortunately, an emerging technique called Delay Alignment Modulation (DAM) can easily solve this problem. By intentionally introducing a delay at the base station and properly designing the transmit beamforming vector, multipath signals can arrive at the receiver simultaneously and can be effectively superimposed, eliminating inter-symbol interference (ISI) and thus forming an ISI-free additive white Gaussian noise (AWGN) system. DAM can avoid some of the disadvantages of OFDM, such as lower implementation complexity and peak-to-average power ratio (PAPR), while achieving higher spectral efficiency. However, it only has superior performance for multipath sparse channels, which can be achieved with high-frequency carriers (such as millimeter waves and terahertz). Summary of the Invention

[0006] Due to the multiplicative fading effect of RIS, its use in many wireless environments cannot produce significant capacity gain. Furthermore, ignoring the impact of delay differences makes system optimization a particularly complex technical problem. This invention proposes a terahertz ISAC system design method based on delay-aligned modulation and active RIS. Based on a basic terahertz ISAC architecture using active RIS and DAM to serve a single-antenna user and a static target, the invention first introduces the system model and demonstrates the simplified principle of DAM to achieve simultaneous and constructive reception of user multipath signals. Then, it optimizes the DFBS transmit beamforming vector and the reflection coefficient of the active RIS to improve sensing performance and ensure communication quality.

[0007] The technical solution of this invention is implemented as follows:

[0008] A design method for a terahertz ISAC system based on time-delay aligned modulation and active RIS, the steps of which are as follows:

[0009] Step 1: Build an active RIS-assisted terahertz communication sensing integrated (ISAC) system, including a single-antenna user, a static target, and a dual-function base station (DFBS); wherein, the DFBS is assisted by delay-aligned modulation (DAM);

[0010] Step 2: Calculate the received signal and signal-to-noise ratio based on the terahertz ISAC system;

[0011] Step 3: Calculate the illumination power at the static target using incoherent accumulation, and simultaneously calculate the thermal noise received at the static target and the power consumed by the active RIS based on the active RIS.

[0012] Step 4: Construct the objective function based on the signal and signal-to-noise ratio received by the user in Step 2, the thermal noise received at the static target in Step 3, and the power consumed by the active RIS.

[0013] Step 5: The objective function is transformed into two sub-objective functions using the alternating optimization method. Then, the semi-definite relaxation technique is used to solve the two sub-objective functions respectively to obtain the optimal transmit beamforming vector and reflection coefficient.

[0014] The expression for the signal received by the user is:

[0015]

[0016] Where y[n] is the signal received by the user, and the superscript H indicates the conjugate transpose. Let s[n-n2] be the channel vector from DFBS to user c, and s[n-n2] represent the signal transmitted by the base station to user c. This represents the channel vector from RIS to user c, where Θ is the reflection coefficient. The channel matrix from DFBS to RIS is represented by M, where M represents the number of antennas in the DFBS and N represents the number of reflective elements in the active RIS. This represents the transmit beamforming vector associated with the direct-fire link. This represents the transmit beamforming vector associated with the RIS link; It is Gaussian white noise with variance σ. 2 ; It is the introduced thermal noise, with a variance of I N An identity matrix of dimension N; n2 represents the channel discrete delay of the DFBS-RIS-User symbol duration.

[0017] The expression for signal-to-noise ratio is:

[0018]

[0019] Where γ(w1,w2,Θ) is the signal-to-noise ratio.

[0020] The expression for the lighting power is:

[0021]

[0022] Where p(w,Θ) is the illumination power at the target, and w is the transmitted beamforming vector. Let be the channel vector from DFBS to target s. Let be the channel vector from RIS to target s.

[0023] The expression for the thermal noise received at the static target is:

[0024]

[0025] Where r(Θ) is the thermal noise received at the static target;

[0026] The power consumed by the active RIS is:

[0027]

[0028] Among them, P ris (w,Θ) represents the power consumed by the active RIS.

[0029] The objective function is:

[0030]

[0031] stγ(w,Θ)≥γ min (12b)

[0032] w1 2 +‖w2‖ 2 ≤P BS (12c)

[0033] P RIS (w,Θ)≤P RIS (12d)

[0034]

[0035] r(Θ)≤r max , (12f)

[0036] |θ i |≤η,i∈[1:N], (12g)

[0037] Among them, P BS This is the maximum transmit power of the DFBS, P RIS The maximum reflected power of an active RIS, r max For the target's maximum thermal noise power, γ min The minimum signal-to-noise ratio for the user is represented by η, the upper limit of the amplification factor is represented by θ. i This represents the i-th RIS element.

[0038] In step five, the specific implementation method is as follows:

[0039] S5.1: Fixed w, optimized Θ

[0040] Given a fixed transmit beamforming vector w, the objective function Transform into the first sub-objective function

[0041]

[0042] st(12b),(12d),(12f),(12g) (13b)

[0043] Define the following symbols:

[0044]

[0045] D2 = diag(Gw1) H +diag(Gw2)diag(Gw2) H .

[0046] Let v H =(Θ H ,1), will Transform into form:

[0047]

[0048] st:v H Rv≤r max ,v H Dv≤P RIS (15b)

[0049] v H Av≥v H Fv, (15c)

[0050] |v k |≤η,k∈[1:N], (15d)

[0051] v N+1 =1, (15e)

[0052] Among them, A=a*a H ,

[0053] Introduce a new matrix variable V = vv H And according to Tr(v H Cv)=Tr(Cvv H The principle of ) = Tr(CV) is used to apply SDR to non-convex constraints. Convert to convex constraint

[0054]

[0055] Tr(AV)≥Tr(FV),Tr(RV)≤r max (16b)

[0056] Tr(DV)≤P RIS (16c)

[0057] V(k,k)≤η 2 ,k∈[1:N], (16d)

[0058] V(N+1,N+1)=1, (16e)

[0059] rank(V)=1,V≥0, (16f)

[0060] Relax the 16f constraint, i.e., rank(V) = 1, and solve using the convex optimization toolbox. Get V opt V was randomized using the Gaussian randomization method. opt By derivation, the optimal v that satisfies equations (12b), (12d), (12g), (12f), and (13a) is obtained, and the optimal Θ is obtained based on the optimal v;

[0061] S5.2: Fixed Θ, optimized w

[0062] The objective function Transform into the second sub-objective function

[0063]

[0064] st(12b),(12c),(12e),(12d). (17b)

[0065] Define intermediate variables:

[0066]

[0067] Where Q1 and Q2 are both intermediate variables, I M Represents an identity matrix of dimension M;

[0068] By using w1 = Q1b1 and w2 = Q2b2, we obtain b1 and b2, thus ensuring that the obtained w satisfies (12e) while maximizing (17a); Define And B = bb H Furthermore, by using the SDR method to relax rank(B) = 1, equation (17) can be restated as follows:

[0069]

[0070] stTr(TB)≥val,Tr(QB)≤P BS (19b)

[0071] Tr(UB)≤val2,B≥0. (19c)

[0072] Define the following symbols:

[0073]

[0074] B is obtained using convex optimization tools. opt Gaussian randomization was used for B opt By derivation, we obtain the variable w that satisfies equations (12b), (12c), (12d), (12e), and (17a).

[0075] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0076] 1) The active RIS used in this invention can increase the signal strength by amplifying the incident signal and increase the gain of the cascaded channel by changing the phase of the RIS.

[0077] 2) DAM is a technique that intentionally introduces a time delay at the base station so that signals can reach users simultaneously and constructively, avoiding inter-symbol interference (ISI) and greatly improving communication quality.

[0078] 3) An alternating optimization algorithm is proposed to jointly optimize the transmit beamforming vector and the reflection coefficient, so as to maximize the target illumination power while ensuring the user communication quality. Attached Figure Description

[0079] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0080] Figure 1 This is a system model diagram of the present invention.

[0081] Figure 2 This is a transmission architecture diagram of the DAM of the present invention.

[0082] Figure 3 This is the curve showing the relationship between the objective function of this invention and the number of iterations.

[0083] Figure 4 This is a curve showing the relationship between the lighting power and the number of RIS in this invention.

[0084] Figure 5 This is a curve showing the relationship between the spectral efficiency and the number of RIS in this invention. Detailed Implementation

[0085] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0086] This invention proposes a terahertz ISAC system design method based on time-delay aligned modulation and active RIS, based on a fundamental terahertz ISAC architecture using active RIS and DAM to serve a single-antenna user and a static target. First, the system model is introduced and the simplified principle of DAM is demonstrated to achieve simultaneous and constructive reception of user multipath signals. Then, the transmit beamforming vector of DFBS and the reflection coefficient of active RIS are optimized to improve sensing performance and ensure communication quality. This optimization problem considers the thermal noise introduced by active RIS and the power limitations of DFBS and active RIS. Alternating optimization (AO) and semidefinite programming (SDP) relaxation techniques are employed to transform the non-convex problem into two convex subproblems. Finally, simulation results demonstrate the convergence of the proposed algorithm and showcase its superior performance with the addition of active RIS and DAM. The specific steps are as follows:

[0087] Step 1: Construct an active RIS-assisted terahertz communication sensing integrated (ISAC) system, including a single-antenna user, a static target, and a dual-function base station (DFBS); wherein the DFBS is assisted by delay-aligned modulation (DAM); as shown Figure 1 As shown. A DFBS consists of a uniform linear array of M antennas, supplemented by a DAM. An active RIS consists of a uniform planar array of N reflecting elements. Define Θ = diag(θ) as the diagonal matrix of reflection coefficients, where θ = [θ1,…,θ2]. N ] H and Where β i and Let represent the amplitude and phase shift of the i-th RIS element, respectively. For active RIS, since each active element is equipped with a power amplifier, β is typically set... i ≤η and η≥1, where η represents the upper limit of the magnification factor.

[0088] definition Let DFBS be the channel vector from user c / target s. The channel matrix representing DFBS to RIS, This represents the channel vector from RIS to user c / target s. Since the power gain of the line-of-sight (LoS) path in millimeter-wave / terahertz communication is much higher than that of the non-line-of-sight path, only the LoS path is considered in practical scenarios. Therefore, the channel matrix or channel vector can be expressed as: exist In, α R , and ψ r Let and represent the complex gain coefficient, departure angle (AoD), and arrival angle (AoA) of the DFBS-RIS channel, respectively. Assuming the spacing between RIS elements and the spacing between DFBS elements are both half a wavelength, then... The parameter settings for other channel models are the same as for G.

[0089] Step 2: Calculate the received signal and signal-to-noise ratio based on the terahertz ISAC system;

[0090] The equivalent channel impulse response received by the user can be expressed as:

[0091]

[0092] Where n1 and n2 represent the channel discrete delay of the DFBS-User channel and the DFBS-RIS-User symbol duration, respectively.

[0093] The traditional single-carrier single-user transmission signal is as follows:

[0094] x[n]=ws[n], (2)

[0095] If we simply add an active RIS and take into account the introduced thermal noise, the signal received by the user is:

[0096]

[0097] in It is Gaussian white noise. It is the introduced thermal noise.

[0098] If DAM is used, the signal transmitted from DFBS can be represented as:

[0099] x[n]=w1s[n-κ]+w2s[n] (4)

[0100] Where κ is the delay intentionally introduced at the base station. and These represent the transmit beamforming vectors related to the direct-fire link and the RIS link, respectively. At this point, the signal received by the user is:

[0101]

[0102] Clearly, the signal received by the user is very chaotic. However, if we let κ = n2 - n1, the signal received by the user becomes:

[0103]

[0104] It can be observed that the time delays of the first and second terms are the same; if n² is known, there will be no interference between them. The third and fourth terms can be eliminated through zero-forcing beamforming (ZF), i.e. and In this configuration, signals from both the direct-line and RIS links can arrive at the user simultaneously and constructively, enabling unbalanced single-carrier communication unaffected by ISI and only affected by thermal noise and AWGN. The signal received by the user is:

[0105]

[0106] Where y[n] is the signal received by the user, and the superscript H indicates the conjugate transpose. Let s[n-n2] be the channel vector from DFBS to user c, and s[n-n2] be the signal transmitted from base station to user. This represents the channel vector from RIS to user c, where Θ is the reflection coefficient. The channel matrix from DFBS to RIS is represented by M, where M represents the number of antennas in the DFBS and N represents the number of reflective elements in the active RIS. This represents the transmit beamforming vector associated with the direct-fire link. This represents the transmit beamforming vector associated with the RIS link; It is Gaussian white noise with variance σ. 2 ; It is the introduced thermal noise, with a variance of I N n represents the identity matrix of dimension N; n2 represents the channel discrete delay of the duration of the DFBS-RIS-User symbol.

[0107] The expression for signal-to-noise ratio (SNR) is:

[0108]

[0109] Where γ(w1,w2,Θ) is the signal-to-noise ratio.

[0110] Figure 2 This is a simplified diagram of the DAM. It should be noted that the DAM model proposed in this invention only considers two paths, and n2 is significantly larger than n1. max=n2. This invention requires the introduction of two time delays κ1 = n max -n1 and κ2 = n max -n2. It's also easy to see that κ2 = 0. Therefore, the delay that needs to be added for κ2 is omitted, but the subsequent processing is retained.

[0111] Step 3: Calculate the illumination power at the static target using incoherent accumulation, and simultaneously calculate the thermal noise received at the static target and the power consumed by the active RIS based on the active RIS.

[0112] For the sensing target, it is assumed that signals cannot arrive at the target simultaneously. Illumination power plays a crucial role in the sensing process. Specifically, the primary sensing performance metric for the target user is the signal-to-noise ratio (SNR), but this depends on the illumination power. Therefore, the sensing performance criterion, i.e., illumination power, is adopted. Since the signals arrive at the target at different times, they are incoherent. Using incoherent accumulation, the illumination power at the target can be considered as the superposition of signal powers, which can be expressed as:

[0113]

[0114] Where p(w,Θ) is the illumination power at the target, and w is the transmitted beamforming vector. The channel vector from DFBS to target s. Let be the channel vector from RIS to target s.

[0115] When designing an active RIS-assisted communication system, the additional thermal noise introduced by the active RIS must be considered. This is because the power amplifier introduced by the active RIS can significantly affect the overall noise level. Therefore, taking this noise into account is crucial when evaluating system performance. Specifically, the thermal noise received at the target location can be expressed as:

[0116]

[0117] Where r(Θ) is the thermal noise received at the static target.

[0118] The power constraints of active RIS must also be considered. The power consumption of an active RIS is as follows:

[0119]

[0120] Among them, P ris (w,Θ) represents the power consumed by the active RIS.

[0121] Step 4: Construct the objective function based on the signal and signal-to-noise ratio received by the user in Step 2, the thermal noise received at the static target in Step 3, and the power consumed by the active RIS. The purpose of this invention is to improve target sensing performance while taking into account the user's communication performance. Fortunately, using DAM can significantly improve the user's communication efficiency. BS and P RIS These are the maximum transmit power of the DFBS and the maximum reflect power of the active RIS. Due to the presence of the power amplifier, the signal in the RIS link is contaminated by thermal noise, so it needs to be limited to a relatively small range to obtain optimal performance, let r max The maximum thermal noise power constraint is set for the target. To ensure the quality of user communication, γ is specified. min The minimum signal-to-noise ratio represents the user's input. Based on the above description, the objective function is expressed as:

[0122]

[0123] stγ(w,Θ)≥γ min (12b)

[0124] w1 2 +‖w2‖ 2 ≤P BS (12c)

[0125] P RIS (w,Θ)≤P RIS (12d)

[0126]

[0127] r(Θ)≤r max , (12f)

[0128] |θ i |≤η,i∈[1:N], (12g)

[0129] Among them, P BS This is the maximum transmit power of the DFBS, P RIS The maximum reflected power of an active RIS, r max For the target's maximum thermal noise power, γ min The minimum signal-to-noise ratio for the user is represented by η, the upper limit of the amplification factor is represented by θ. i This represents the i-th RIS element.

[0130] Where (12a) is the objective function to be optimized. (12b) is the signal-to-noise ratio constraint added to ensure communication quality. (12c) and (12d) are the total power constraints of the DFBS and active RIS. (12e) is the ZF constraint for achieving ISI-free communication. (12f) limits the thermal noise received by the target signal to a certain range, so that it slightly interferes with the target signal. (12g) is the amplitude constraint, which controls the maximum amplification factor of the signal that each active element can amplify.

[0131] Step 5: The objective function is transformed into two sub-objective functions using the alternating optimization method. Then, the semi-definite relaxation technique is used to solve the two sub-objective functions respectively to obtain the optimal transmit beamforming vector and reflection coefficient.

[0132] Due to the coupling of w and Θ in (12a), (12b), and (12d) and the ZF constraint in (12e), optimization problem (12) is a nonlinear and nonconvex problem, making it difficult to obtain the optimal solution directly. Therefore, an alternating optimization method is used to solve this complex problem. Given a fixed transmit beamforming vector w, the reflection coefficient Θ is optimized, and vice versa, thus transforming the objective function into two easily optimized sub-objective functions. Then, through equation transformation, these two sub-objective functions are transformed into more easily solvable forms, and solved using semidefinite program relaxation techniques (SDR).

[0133] S5.1: Fixed w, optimized Θ

[0134] Given a fixed transmit beamforming vector w, the objective function Transform into the first sub-objective function

[0135]

[0136] st(12b),(12d),(12f),(12g) (13b)

[0137] First, (13) can be transformed into an expression in terms of Θ by a simple substitution, i.e., f H Θ H =θ H diag(f H ) and Θ H Gw=θ H diag(Gw). Then let v H =(θ H ,1) can produce a simpler solution.

[0138] At this point, the problem remains complex, and there is no clear direction on how to solve it. However, by using specific formula transformations, the optimization problem can be transformed into a more easily solvable form, and more insights can be gained. For simplicity, the following notation is introduced:

[0139]

[0140] D2 = diag(Gw1) H +diag(Gw2)diag(Gw2) H .

[0141] After applying the above transformation, The following simplified form can be obtained by replacing (14) with (13):

[0142]

[0143] st:v H Rv≤r max ,v H Dv≤P RIS (15b)

[0144] v H Av≥v H Fv, (15c)

[0145] |v k |≤η,k∈[1:N], (15d)

[0146] |v N+1 |=1, (15e)

[0147] Among them, A=a*a H ,

[0148] It can be observed that, due to the nonconvexity of (15a), (15c), and (15e), the problem has been reformulated as a quadratic constrained quadratic programming (QCQP) problem with nonconvex constraints. Semidefinite relaxation (SDR) can be used to transform this problem into a convex one. A new matrix variable V = vv is introduced. H And use this fact Tr(v H Cv)=Tr(Cvv H =Tr(CV), converts a non-convex constraint to a convex constraint. After using SDR, It can be represented in convex form:

[0149]

[0150] Tr(AV)≥Tr(FV),Tr(RV)≤r max (16b)

[0151] Tr(DV)≤P RIS (16c)

[0152] V(k,k)≤η 2 ,k∈[1:N], (16d)

[0153] V(N+1,N+1)=1, (16e)

[0154] rank(V)=1,V≥0, (16f)

[0155] (16) remains a non-convex problem, but if the constraint of equation (16f) is relaxed, i.e., rank(V) = 1, (16) is transformed into a convex problem, which can be solved using the convex optimization toolbox. Get V opt V was randomized using the Gaussian randomization method. opt By derivation, the optimal v that satisfies equations (12b), (12d), (12g), (12f), and (13a) is obtained, and the optimal Θ is obtained based on the optimal v.

[0156] S5.2: Fixed Θ, optimized w

[0157] The objective function Transform into the second sub-objective function

[0158]

[0159] st(12b),(12c),(12e),(12d). (17b)

[0160] For equation (12e), define the intermediate variable:

[0161]

[0162] Where Q1 and Q2 are both intermediate variables, I M This represents an identity matrix of dimension N.

[0163] By using w1 = Q1b1 and w2 = Q2b2, we obtain b1 and b2, thus ensuring that the obtained w satisfies (12e) while maximizing (17a); define b H =(b1) H b2 H ) and B = bb H Furthermore, by using the SDR method to relax rank(B) = 1, equation (17) can be restated as follows:

[0164]

[0165] stTr(TB)≥val,Tr(QB)≤P BS (19b)

[0166] Tr(UB)≤val2,B≥0. (19c)

[0167] Define the following symbols:

[0168]

[0169] B is obtained using convex optimization tools. opt Gaussian randomization was used for B opt By derivation, we obtain the variable w that satisfies equations (12b), (12c), (12d), (12e), and (17a).

[0170] In summary, the optimization method of this invention can be simply divided into two stages: (a) optimizing Θ with a fixed w, and (b) optimizing w with a fixed Θ. (a) and (b) are repeated until the results converge. It should be noted that stage (b) must be performed in the final stage to ensure ZF constraints.

[0171] Experimental simulation

[0172] Default settings: M=8, N=64, γ min =10, r max = -90dBm, η = 20. The total power is 16dBm, 80% is allocated to the DFBS, and the remainder is allocated to the active RIS. The DFBS and RIS are located at (0, 0, 0)m and (10, 8, 5)m respectively. The user and target positions are randomly placed within a circle with a radius of 5m centered at (0, 10, 0)m. Path loss is set as follows:

[0173]

[0174] Where d is the distance between the two devices. PL d and PL r These represent the path loss for the direct link and the RIS link, respectively.

[0175] Figure 3 The convergence performance of the optimization algorithm under different parameter settings is shown. It is evident that the optimization algorithm can converge quickly using AO and SDR, proving its effectiveness.

[0176] Figure 4The relationship between the number of RIS elements and illumination power is shown. To ensure fairness, the DFBS power of the "PassiveRIS", "Random RIS", and "Without RIS" scenarios was set to the same total power as "Active RIS". The results show that when the number of RIS elements is the same, although the total power is the same, the illumination power of the "Active RIS" scheme is significantly higher than the other schemes. As the number of RIS elements increases, the illumination power of "Active RIS" increases at a much higher rate than the other schemes. It is important to emphasize that due to the limited gain provided by passive RIS, the curve growth for "Passive RIS" and "Random RIS" is very slow. A significant gain only occurs when the number of RIS elements is sufficiently large. It is noteworthy that the perception performance of "Random RIS" is even lower than that of "Without RIS", which is reasonable. Because of the presence of DAM, to ensure ZF constraints improve user communication quality, the degrees of freedom of the precoding vector are reduced, resulting in the performance of "Random RIS" being slightly lower than that of "Without RIS". This highlights the importance of optimizing the RIS reflection coefficients.

[0177] Figure 5 This shows the relationship between the spectral efficiency of different schemes and the number of RIS elements when lighting power is constrained and the user's signal-to-noise ratio is the optimization objective function. Note that we also used Dinkelbach's Transform to address this non-convex problem. Without considering DAM, the signal from the direct link will arrive at the user earlier than the signal from the RIS link. Therefore, we treat the signal from the direct link as the user's desired signal and the signal from the RIS link as interference. Clearly, when the number of RIS elements is the same, the spectral efficiency of "Active RIS with DAM" is significantly higher than the other two schemes. When the number of RIS elements is 25, the spectral efficiency of "Active RIS with DAM" is 35.6% higher than "Active RIS without DAM," while the spectral efficiency of "Passive RIS with DAM" is about 3.1% higher. In the scheme using DAM, the signal from the RIS link is the signal the user needs. Therefore, as the number of RIS elements increases, the signal from the RIS link becomes stronger, and the user's communication quality improves. However, without DAM, the signal from the RIS link is equivalent to ISI, which is signal interference and degrades the user's communication quality. As the number of RIS increases, the spectral efficiency will decrease.

[0178] In summary, applying active RIS and DAM in terahertz ISAC systems can significantly improve system performance with only a slight increase in hardware cost while maintaining the same power consumption.

[0179] This invention investigates an active RIS-assisted terahertz ISAC system based on DAM. Specifically, an alternating optimization algorithm is proposed to jointly optimize the transmit beamforming vector and reflection coefficient, maximizing target illumination power while ensuring user communication quality. To address this issue, the SDR method is employed and implemented using CVX. Simulation results demonstrate that the active RIS using DAM outperforms other schemes in both communication and sensing performance, proving that the terahertz ISAC system leverages the unique advantages of RIS and DAM to provide unparalleled benefits in sensing and communication performance.

[0180] 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 principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a terahertz ISAC system based on time-delay aligned modulation and active RIS, characterized in that, The steps are as follows: Step 1: Build an active RIS-assisted terahertz communication sensing integrated (ISAC) system, including a single-antenna user, a static target, and a dual-function base station (DFBS); wherein, the DFBS is assisted by delay-aligned modulation (DAM); Step 2: Calculate the received signal and signal-to-noise ratio based on the terahertz ISAC system; The expression for the signal received by the user is: （7） in, The signal received by the user, with the superscript H indicating conjugate transpose. For DFBS to users The channel vector, This indicates that the base station transmits a signal that reaches user c. Indicates RIS to users The channel vector, The reflection coefficient, The channel matrix from DFBS to RIS is represented by M, where M represents the number of antennas in the DFBS and N represents the number of reflective elements in the active RIS. This represents the transmit beamforming vector associated with the direct-fire link. This represents the transmit beamforming vector associated with the RIS link; It is Gaussian white noise with variance of ; It is the introduced thermal noise, with a variance of ; An identity matrix of dimension N; The channel discrete delay represents the duration of the DFBS-RIS-User symbol; The expression for signal-to-noise ratio is: （8） in, Signal-to-noise ratio; Step 3: Calculate the illumination power at the static target using incoherent accumulation, and simultaneously calculate the thermal noise received at the static target and the power consumed by the active RIS based on the active RIS. The expression for the lighting power is: （9） in, The illumination power at the target location, For the transmit beamforming vector, For DFBS to target The channel vector, For RIS to the target The channel vector; The expression for the thermal noise received at the static target is: （10） in, Thermal noise received at a static target location; The power consumed by the active RIS is: （11） in, Power consumed by the active RIS; Step 4: Construct the objective function based on the signal and signal-to-noise ratio received by the user in Step 2, the thermal noise received at the static target in Step 3, and the power consumed by the active RIS. The objective function is: （12a） （12b） （12c） （12d） （12e） （12f） （12g） in, This is the maximum transmit power of DFBS. This is the maximum reflected power of an active RISC. The maximum thermal noise power of the target The minimum signal-to-noise ratio representing the user, This represents the upper limit of the magnification. Indicates the first One RIS element; Step 5: The objective function is transformed into two sub-objective functions using the alternating optimization method. Then, the semi-definite relaxation technique is used to solve the two sub-objective functions respectively to obtain the optimal transmit beamforming vector and reflection coefficient. In step five, the specific implementation method is as follows: S5.1: Fixed ,optimization Given a fixed transmit beamforming vector objective function Transform into the first sub-objective function : （13a） （13b） Define the following symbols: （14） make ,Will Transform into form: （15a） （15b） （15c） （15d） （15e） in, ; Introducing a new matrix variable and according to The principle is to use SDR to transform non-convex constraints. Convert to convex constraint : （16a） （16b） （16c） （16d） （16e） （16f） Relax the dropout (16f) constraint, i.e. Solve using the convex optimization toolbox ,get ; Using Gaussian randomization method Through derivation, we obtain the optimal equations satisfying (12b), (12d), (12g), (12f), and (13a). According to the optimal Find the optimal ; S5.2: Fixed ,optimization The objective function Transform into the second sub-objective function : （17a） （17b） Define intermediate variables: （18） in, , All are intermediate variables. Represents an identity matrix of dimension M; By using and ,get and Thus ensuring the acquisition Satisfy (12e) while maximizing (17a); Define and And relaxation is achieved using the SDR method. Equation (17) can be restated as: （19a） （19b） （19c） Define the following symbols: （20） Obtained using convex optimization tools Using Gaussian randomization method for Through derivation, we obtain the variables that satisfy equations (12b), (12c), (12d), (12e), and (17a). .

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