Joint beam design method for overcoming beam dispersion in terahertz irs communication

Abstract

This invention proposes a joint beam design method to overcome beam dispersion in terahertz IRS communication. The steps are as follows: First, an IRS-assisted terahertz multi-user communication system is constructed. Delay-aligned modulation is applied to the IRS to introduce additional delay, and the signal received by the user on the subcarrier is calculated. Second, the signal-to-dryness ratio (SDR) of the user on the subcarrier is calculated based on the SDR, and the achievable sum rate of the user is calculated based on the SDR. Finally, maximizing the achievable sum rate of the user is used as the objective function. The objective function is then decomposed into multiple sub-optimization objectives using an alternating optimization algorithm, and the SDR and MM algorithms are used to solve these sub-optimization objectives to obtain the maximum achievable sum rate of the user. This invention overcomes the beam dispersion problem caused by the frequency independence characteristics of the IRS reflector units by introducing a delay on the IRS, improving the sum rate of multiple users and thus enhancing system performance.

Description

Technical Field

[0001] This invention relates to the field of beam dispersion technology in terahertz communication technology, and in particular to a joint beam design method for overcoming beam dispersion in terahertz IRS communication. Background Technology

[0002] Terahertz (THz) communication technology, as a candidate technology for 6G, possesses extremely abundant spectrum resources and ultra-high data rates, enabling ultra-wideband resources and high-speed broadband wireless communication. The abundant terahertz spectrum resources meet the future communication needs for effective, accurate, fast, and diversified applications, and it is widely considered one of the key technologies for 5G and future 6G network communication. Intelligent Reflecting Surface (IRS) technology consists of a large number of passive reflective elements. By controlling each passive reflective unit, the reflection coefficient of the incident signal can be independently reconfigured. Due to its advantages in reconstructing the wireless channel propagation environment, reducing system power consumption, and improving channel gain, it is also considered a key technology for 6G.

[0003] The structure of IRS reflectors is relatively simple, typically equipped with frequency-independent phase-shifting circuits that can only adjust the amplitude and phase of the reflected signal. This makes the frequency of each IRS reflector independent, limiting it to frequency-independent precoding. Therefore, in IRS-assisted communication systems, each IRS reflector can only control the beam direction of a single carrier. However, in multi-carrier IRS systems, multiple carrier signals must share the same reflection phase. Consequently, for high-frequency multi-carrier systems, IRS faces severe beam dispersion, causing beams from different subcarrier frequencies to point in different directions, impacting system performance. For terahertz communication systems equipped with IRS reflectors, the performance loss caused by beam dispersion is even more severe because the IRS array size is typically larger than the base station antenna array.

[0004] Most work related to beam dispersion focuses on Uniform Linear Arrays (ULAs). In broadband systems, hybrid beamforming structures based on ULA phase shifters have attracted the attention of some scholars. The literature [Park S, Alkhateeb A, Heath R W. Dynamic subarrays for hybrid precoding in wideband mmWave MIMO systems[J].IEEE Transactions on Wireless communications,2017,16(5):2907-2920.] proposes a hybrid precoding algorithm based on orthogonal frequency division multiplexing for broadband massive MIMO systems, obtaining a near-optimal closed-loop solution. To improve the performance of hybrid precoding, the literature [Kong L, Han S, Yang C. Hybrid precoding with rate and coverage constraints for wideband massive MIMO systems[J].IEEE Transactions on Wireless communications,2018,17(7):4634-4647.] proposes an alternating optimization algorithm to iteratively optimize the analog beamformer and digital precoder, achieving near-optimal rate performance across the entire bandwidth. In addition, a codebook containing a wide beam was designed to reduce the array gain loss caused by beam squint effect. To further improve performance, a True Time Delay (TTD) was used to solve the beam dispersion problem, which can generate frequency-dependent phase by changing the time-domain delay. The literature [Zhai B, Zhu Y, Tang A, et al. THzPrism: Frequency-based beam spreading for terahertz communication systems[J]. IEEE Wireless Communications Letters, 2020, 9(6): 897-900.] designed a phased array structure called terahertz prism, which inserts a series of delayers into a traditional phased array. By setting the parameters of the delayers, the beam spread width and direction are changed, so that the beams of different subcarriers point in different directions, thereby expanding the coverage area without affecting the beam gain.Considering the time delay limitations of TTD, the literature [Nguyen DQ, Kim T. Joint delay and phase precoding under true-time delay constraints for THzmassive MIMO[C] / / ICC 2022-IEEE International Conference on Communications.IEEE,2022:3496-3501.] designed a hybrid beamforming scheme, revealing the relationship between the number of antennas and the required time extension line length for TTD, and performing joint optimization under finite time delay to form the optimal beam dispersion compensation scheme. The hybrid beamforming method using TTD can achieve near-optimal performance of all-digital precoding.

[0005] There is limited research considering beam dispersion in IRS-assisted broadband communications. Specifically, the paper [Chen Y, Chen D, Jiang T. Beam-squint mitigating in reconfigurable intelligent surface-aided wideband mmwave communications[C] / / 2021IEEE Wireless Communications and Networking Conference(WCNC).IEEE,2021:1-6.] addresses beam dispersion by maximizing the upper bound of the achievable rate using the channel covariance matrix and angle information. Furthermore, the paper [Hao W, Zhou F, Zeng M, et al. Ultra Wideband THz IRS Communications: Applications, Challenges, Key Techniques, and Research Opportunities[J].IEEE Network,2022,36(6):214-220.] investigates the relationship between IRS deployment and beam dispersion effects. While distributed IRS deployment is costly, it can mitigate beam dispersion effects; however, due to the reduced surface aperture, the received signal suffers significant energy loss. To address the inaccurate network sensing and localization caused by near-field beam dispersion in mmWave / THz communication, the paper [Li Z, Wan Z, Ying K, et al. Reconfigurable Intelligent Surface Assisted Localization Over Near-Field Beam Squint Effect[C] / / 2022 International Symposium on Wireless Communication Systems (ISWCS). IEEE, 2022: 1-6.] proposes a RIS-assisted localization paradigm, applying gradient descent and multiple signal classification (MUSIC) algorithms to achieve high-precision localization under near-field beam dispersion. Simulation results demonstrate its superiority and its ability to improve system capacity. However, existing research on IRS typically neglects the beam dispersion problem occurring in high-frequency multicarrier systems. Moreover, the aforementioned methods rely on frequency-independent precoding architectures. Furthermore, when the bandwidth is sufficiently large, such as in terahertz communication systems, the beam dispersion effect is more severe, and these methods still result in significant beam array gain losses. Summary of the Invention

[0006] To address the beam dispersion problem in high-frequency multi-carrier operations of existing IRS, this invention proposes a joint beam design method to overcome beam dispersion in terahertz IRS communication. By introducing a delay-adjustable IRS, beam dispersion can be overcome, and the system's sum rate can be improved.

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

[0008] A joint beam design method to overcome beam dispersion in terahertz IRS communication, the steps of which are as follows:

[0009] Step 1: Build an IRS-assisted terahertz multi-user communication system, including an IRS, a base station, and K users. The base station adopts a fully digital structure, the IRS adopts a uniform linear array structure, and there are obstacles between the base station and the users. Users can only receive reflected signals from the IRS.

[0010] Step 2: Apply Delay Alignment Modulation (DAM) to the IRS to introduce additional delay and calculate the signal received by the user on the subcarrier;

[0011] Step 3: Calculate the signal-to-dryness ratio (SDR) of the user on the subcarrier based on the signal received by the user on the subcarrier, and calculate the reachability and speed of the user based on the SDR;

[0012] Step 4: Use the maximization of the user's reachability and rate as the objective function;

[0013] Step 5: Decompose the objective function into multiple sub-optimization objectives using the alternating optimization algorithm, and solve the multiple sub-optimization objectives using the SDR and MM algorithms respectively to obtain the maximum reachability and rate of the user.

[0014] The signal received by the user on the subcarrier is:

[0015]

[0016] Among them, y k,m For the signal received by the k-th user on the m-th subcarrier, G t It is the transmit antenna gain, G r It is the receiving antenna gain, η m It is the path loss compensation factor. This represents the channel from the IRS to the k-th user on the m-th carrier. Represents the IRS reflection coefficient matrix. Let Θ = diag(θ1,...,θ) represent the delay matrix of the m-th carrier. R ), Tm =diag(ψ m,1 ,...,ψ m,R ), and satisfy and t r The time delay introduced for the r-th IRS reflection unit, where R represents the number of reflection units, f m Indicates the frequency of the carrier wave. It is the channel from the base station to the IRS on the m-th carrier. Let x represent the digital precoding vector of the k-th user on the m-th subcarrier. k,m This represents the transmitted signal of the k-th user on the m-th subcarrier, where n is the number of subcarriers. k,m It is the additive white Gaussian noise of the k-th user on the m-th carrier.

[0017] The signal-to-dryness ratio of the user on the subcarrier is:

[0018]

[0019] Among them, SINR k,m Let k be the signal-to-dryness ratio on the m-th carrier. Indicates the noise variance. a r (θ m ) represents the array steering vector at the transmitting end. This represents the array steering vector at the receiving end.

[0020] The a r (θ m ), The expressions are as follows:

[0021]

[0022]

[0023] in, d0 is the antenna spacing, φ t ∈[-π / 2,π / 2] represents the departure angle, φ r ∈[-π / 2,π / 2] represents the angle of arrival.

[0024] The expression for the reachability and rate of the user is:

[0025]

[0026] in, It represents the sum of the achievable rates of the k-th user across all carriers.

[0027] The objective function is:

[0028]

[0029]

[0030] |θ i |=1,i∈{1,...,R} (12c);

[0031] |ψ m,i |=1,m∈{1,…,M},i∈{1,…,R} (12d);

[0032] Among them, P max ζ represents the maximum transmit power of the base station. k It represents the weight of user k, and the superscript H indicates the conjugate transpose.

[0033] Step 5 is implemented as follows: The active and passive beams are iteratively updated using an alternating optimization algorithm. First, given the IRS reflection phase and reflection delay matrix, the base station digital precoding vector is solved using SDR. Then, the base station digital precoding vector is fixed, and the reflection phase shift and reflection delay are obtained through the MM algorithm, thereby maximizing the user's sum rate.

[0034] The method for solving the base station digital precoding vector using SDR is as follows:

[0035] Given the IRS reflection phase and reflection delay matrix, the objective function is transformed into the first sub-optimization objective:

[0036]

[0037] st(12b) (13b);

[0038] Among them, h k,m =g k,m ΘT m H m Define F k,m =h k,m h k,m H and W k,m =w k,m w k,m H At the same time, an auxiliary variable s is introduced. k,m Equation (13) can be rewritten as:

[0039]

[0040]

[0041]

[0042] rank(W k,m )=1,W k,m ≥0 (14d);

[0043] An auxiliary variable c was introduced. k,m Rewrite (14b) as follows:

[0044] s k,m c k,m ≤Tr(F k,m W k,m (15a);

[0045]

[0046] Then s k,m c k,m The upper bound satisfies:

[0047]

[0048] in, s k,m The value of the nth iteration. c k,m The nth iteration value, based on which equation (15a) is transformed into the following convex constraint:

[0049]

[0050] Finally, the optimization objective (14) can be rewritten as the SDP function shown in equation (18):

[0051]

[0052] st(14c),(15b),(17)(18b);

[0053] rank(W k,m )=1,W k,m ≥0(18c);

[0054] The optimal value of the base station digital precoding vector is obtained by solving the SDP function shown in equation (18) using the CVX toolbox.

[0055] The method for obtaining the reflection phase shift and reflection delay using the MM algorithm is as follows:

[0056] S5.1: After fixing the digital precoding vector of the base station, the objective function (12) can be transformed into:

[0057]

[0058] st|θ i|=1,i∈{1,…,R} (19b);

[0059] |ψ m,i |=1,m∈{1,…,M},i∈{1,…,R} (19c);

[0060] By introducing auxiliary variables There is α = [α 1,1 ,α 1,2 ,…α 1,K ,…α M,K ] T ,but:

[0061]

[0062] function f k,m (Θ,Τ k ) is represented as:

[0063]

[0064] Therefore, the optimization problem (19) can be transformed into:

[0065]

[0066] st(19b),(19c) (22b);

[0067] Fixed reflection phase Θ and reflection delay matrix T m By α k,m Find the partial derivative, i.e. The optimal α can be obtained, therefore the optimal solution can be written as:

[0068]

[0069] Solve for α k,m Substituting the optimal solution into equation (22) for f(Θ,Τ) k From equation (20), we can find that only the last term is related to the variables Θ and T. m Therefore, the optimization problem (22) can be divided into the following two parts: given α, solve Θ and T. m ,Right now:

[0070]

[0071] st(19b),(19c) (24b);

[0072] Let γ k,m =ζ k (1+α k,mIn the optimization problem (24), the reflection phase and reflection delay at the IRS end can be decoupled, so these two variables can be solved by alternating iterations.

[0073] With the auxiliary variable α° and the reflection delay T fixed m After °, the optimization problem (24) can be simplified to:

[0074]

[0075] st|θ i |=1,i∈{1,...,R} (25b);

[0076] Among them, h j,m =T m H m w j,m , remember g k,m ΘT m H m w j,m =g k,m Θh j,m =θ H diag(g k,m )h j,m =θ H b k,j,m Therefore, the objective function (25a) can be rewritten as:

[0077]

[0078] Introduce auxiliary variable x = [x 1,1 ,x 1,2 ,...x 1,K ,...,x M,K ] T Transforming equation (26) into its equivalent form, we have:

[0079]

[0080] Therefore, updating the reflection phase shift Θ requires the following two steps: fixing the reflection phase shift Θ and calculating x, and fixing x and calculating the reflection phase shift Θ;

[0081] First, when Θ is given, according to If the function has a local maximum, then the solution x is... m,k It can be represented as:

[0082]

[0083] Then, when x is fixed, x m,k ° and |θ H b k,j,m | 2 =θH b k,j,m b k,j,m H Substituting θ into the objective function (27), (27) can be simplified to:

[0084] f2(θ)=-θ H Uθ+2Re{θ H v}-C1 (29);

[0085] in,

[0086]

[0087]

[0088]

[0089] For ease of solving the problem, equation (29) is equivalent to:

[0090]

[0091] st|θ i |=1,i∈{1,…,R} (31b);

[0092] For any given solution θ in the t-th iteration t For any feasible solution θ, we have:

[0093]

[0094] Where X = λ max I R , λ max It is the largest eigenvalue of U, I R Represents the identity matrix of R×R;

[0095] The constructor's objective function is as follows:

[0096] g(θ|θ t )=y(θ|θ t )-2Re{θ H v} (34);

[0097] The subproblem to be solved in the t-th iteration can be represented as follows:

[0098]

[0099] st(31b) (35b);

[0100] Due to θ H θ = R, therefore we can obtain θ H Xθ=Rλ maxTo facilitate the solution, remove the other constants in equation (35a), and the optimization problem (35) can be rewritten as:

[0101]

[0102] st(31b) (36b);

[0103] Where q t =(λ max I R -U)θ t +v, then the optimal reflection phase shift of problem (36) can be expressed as:

[0104]

[0105] S5.2: The phase shift between the transmit beam at the fixed base station and the reflection at the IRS end, the target function (12) can now be expressed as:

[0106]

[0107] st(12d) (38b);

[0108] Remember c k,m =g k,m Θ, d j,m =H m w j,m ,have:

[0109]

[0110] Therefore, the objective function can be expressed as:

[0111]

[0112] By introducing the auxiliary variable y = [y 1,1 ,y 1,2 ,...y 1,K ,…,y M,K ] T We can obtain the following expression:

[0113]

[0114] Reflection delay matrix T m The update includes the following two steps: fixing the reflection phase delay matrix T m Find y and, with y fixed, find the reflection delay matrix T. m ;

[0115] First, given the reflection delay T m At that time, according to If the function has a local maximum, then the solution ym,k It can be written as:

[0116]

[0117] Then, when y is fixed, y m,k ° and Substituting into the objective function (41), we define:

[0118]

[0119]

[0120] Equation (41) can be simplified to:

[0121] f4=-ψ H Λψ+ψ H V (44);

[0122] in,

[0123] Λ=diag(Λ1,Λ2,...,Λ M (45a);

[0124]

[0125] Therefore, the optimization problem described above can be rewritten as:

[0126]

[0127] st(12d) (46b);

[0128] Using the MM algorithm to solve for the reflection delay, we can obtain:

[0129]

[0130] in,

[0131] The reflection delay T is obtained by taking the average delay value of ψ. m .

[0132] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0133] 1) For IRS-assisted terahertz communication systems that consider beam dispersion problems, this invention proposes to introduce a time-adjustable metasurface on the IRS. This scheme can overcome the beam dispersion problem caused by the frequency independence characteristics of the IRS reflection unit, improve the sum rate of multiple users, and thus improve the system performance.

[0134] 2) When solving the digital precoding problem, this invention uses SDP to transform the non-convex optimization problem into a convex problem and employs the SDR algorithm for solving it. When solving the IRS reflection beam, the non-convex problem of reflection phase shift and reflection delay coupling is decomposed into two convex problems using Lagrange multiplication and quadratic transformation. Fractional programming is performed on each problem, and the MM algorithm is used to solve the optimization problem with constant mode constraints. The proposed solution has better user and rate performance than traditional IRS designs, can overcome beam dispersion effects, and improve the quality of service for users. Attached Figure Description

[0135] 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.

[0136] Figure 1 This is a block diagram of the IRS-assisted broadband terahertz multi-user communication system of the present invention.

[0137] Figure 2 Comparison curves for the convergence performance of digital precoding in traditional IRS.

[0138] Figure 3 The convergence performance comparison curves for solving digital precoding using the method of this invention are shown.

[0139] Figure 4 For traditional IRS and the method of this invention in P max Convergence performance comparison curves at 0dB.

[0140] Figure 5 The curves show the maximum sum and rate comparison between the conventional IRS and the method of this invention at different transmit powers. Detailed Implementation

[0141] 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.

[0142] This invention provides a joint beam design method to overcome beam dispersion in terahertz IRS communication. Specifically, a fully digital structure is deployed at the base station, and a DAM (Digital Amplifier) ​​is applied to the IRS to introduce additional delay and adjust the incident signal, maximizing the sum and rate under the constraints of the transmit beam and IRS transmission coefficients. For the non-convex optimization problem, an alternating optimization algorithm is proposed to decompose it into three sub-optimization problems, which are solved using semi-definite relaxation (SDR) and majorization-minimization (MM) algorithms, respectively, for digital precoding and IRS reflection coefficients. Finally, simulations verify the effectiveness of the proposed method of introducing a delay-adjustable IRS, demonstrating its ability to overcome beam dispersion and improve the system's sum and rate.

[0143] The specific steps are as follows:

[0144] Step 1: Set up an IRS-assisted terahertz multi-user communication system, including an IRS, a base station, and K users; for example... Figure 1 As shown, the base station adopts a fully digital antenna structure, that is, it deploys N... RF There are N radio frequency chains, each connected to one antenna. T The antenna and IRS employ a uniform linear array (ULA) structure. Furthermore, to overcome the frequency-selective fading problem of broadband terahertz signals, orthogonal frequency division multiplexing (OFDM) transmission technology is used, comprising M subcarriers.

[0145] Step 2: Apply Delay-Aligned Modulation (DAM) to the IRS to introduce additional delay and calculate the signal received by the user on the subcarrier. Assume that due to wall obstructions or other obstacles, there is no direct link between the base station and the users, and the K single-antenna users can only receive reflected signals from the IRS. Therefore, the signal received by the k-th user on the m-th subcarrier is denoted as y. k,m :

[0146]

[0147] Among them, y k,m For the signal received by the k-th user on the m-th subcarrier, G t It is the transmit antenna gain, G r It is the receiving antenna gain, η m It is the path loss compensation factor. This represents the channel from the IRS to the k-th user on the m-th carrier. Represents the IRS reflection coefficient matrix. Let Θ = diag(θ1,…,θ) represent the delay matrix of the m-th carrier. R ), T m =diag(ψ m,1 ,…,ψ m,R ), and satisfy and t r The time delay introduced for the r-th IRS reflection unit, where R represents the number of reflection units, f m Indicates the frequency of the carrier wave. It is the channel from the base station to the IRS on the m-th carrier. Let x represent the digital precoding vector of the k-th user on the m-th subcarrier. k,m This represents the transmitted signal of the k-th user on the m-th subcarrier, where n is the number of subcarriers. k,m It is the additive white Gaussian noise of the k-th user on the m-th carrier. Equation (1) is the signal on the m-th carrier received by user k, which is divided into two parts: the former is the useful signal, and the latter is the interference and noise interference between users.

[0148] Although some scattering paths exist in terahertz communication channels, their power gain is much lower than that of line-of-sight channels, with an average path gain attenuation of over 20 dB. This means that other multipath effects, such as scattering, have a much smaller impact on the received signal power. Therefore, when analyzing beam dispersion effects, channel multipath effects are usually ignored, with Loss of Spectrum (LoS) being the primary factor. This invention only considers line-of-sight channels; therefore, the channel... It can be represented as:

[0149]

[0150] Where q(f) m d) represents the path complex gain, which satisfies:

[0151]

[0152] Wherein, τ(f m ) represents the medium absorption factor, and d is the distance from the base station to the IRS. H m It can be represented as:

[0153]

[0154] In the formula, a r (θ m )and The array steering vectors at the transmitting and receiving ends are represented as follows:

[0155]

[0156]

[0157] in, d0 is the antenna spacing, φ t ∈[-π / 2,π / 2] represents the departure angle, φ r ∈[-π / 2,π / 2] represents the angle of arrival. Similarly, It can be written as:

[0158]

[0159] in, and d k This represents the distance between the IRS and the k-th user. Therefore, the equivalent cascaded channel can be expressed as:

[0160] G k,m =u k,m g k,m ΘT m H m (8)

[0161] In the above formula, u k,m =G t G r η m q(f m ,d)q(f m ,d k According to the literature [Tang W, Chen MZ, Chen X, et al. Wireless communications with reconfigurable intelligent surface: Path loss modeling and experimental measurement[J]. IEEE Transactions on Wireless Communications, 2020, 20(1): 421-439.], the cascaded channel path loss of base station-IRS-user can be expressed as:

[0162]

[0163] Where χ is the gain of the IRS reflection unit.

[0164] Step 3: Calculate the signal-to-dryness ratio (SDR) of the user on the subcarrier based on the signal received by the user on the subcarrier, and calculate the reachability and speed of the user based on the SDR;

[0165] The signal-to-dryness ratio of the user on the subcarrier is:

[0166]

[0167] Among them, SINR k,m Let k be the signal-to-dryness ratio on the m-th carrier. Indicates the noise variance. a r (θ m ) represents the array steering vector at the transmitting end. This represents the array steering vector at the receiving end.

[0168] The expression for the reachability and rate of the user is:

[0169]

[0170] in, Let be the sum of the achievable rates of the k-th user across all carriers. Next, by jointly optimizing the digital precoding at the base station, the reflection coefficients at the IRS, and the delay, the weighted sum rate of the multi-user data in the IRS-assisted terahertz multi-user communication system is maximized.

[0171] Step 4: Maximize the user's reachability and rate as the objective function; the objective function is:

[0172]

[0173]

[0174] |θ i |=1,i∈{1,...,R} (12c);

[0175] |ψ m,i |=1,m∈{1,...,M},i∈{1,...,R} (12d);

[0176] Among them, P max ζ represents the maximum transmit power of the base station. k is the weight of user k, and the superscript H indicates the conjugate transpose. (12b) represents the base station transmit power limit, (12c) is the constant mode constraint of the phase shift of each IRS reflector element, and (12d) is the constant mode constraint of the phase shift caused by the delay of the i-th reflector unit of the IRS on the m-th subcarrier. Since the set of both is a unit circle, it is impossible to obtain the points inside the circle. Therefore, the set corresponding to the constant mode constraint is non-convex. Obviously, problem (12) is a non-convex optimization problem, and the mutual coupling of the digital precoding vector w, the IRS reflection phase and the delay makes them difficult to solve.

[0177] Step 5: Decompose the objective function into multiple sub-optimization objectives using the alternating optimization algorithm, and solve the multiple sub-optimization objectives using the SDR and MM algorithms respectively to obtain the maximum reachability and rate of the user.

[0178] To address the aforementioned issues, this invention employs an alternating optimization algorithm to iteratively update active and passive beams: First, given the IRS reflection phase and reflection delay, two auxiliary variables are introduced, and semidefinite relaxation is used to iteratively optimize the digital precoding; then, the base station digital precoding vector is fixed, and the reflection phase shift and reflection delay are obtained through the MM algorithm, thereby maximizing the user's sum rate.

[0179] Base station transmit beam optimization:

[0180] Given the IRS reflection phase and reflection delay matrix, the objective function (12) is transformed into the first sub-optimization objective:

[0181]

[0182] st(12b) (13b);

[0183] Among them, h k,m =g k,m ΘT m H m To facilitate further simplification, let F be defined. k,m =h k,m h k,m H and W k,m =w k,m w k,m H At the same time, an auxiliary variable s is introduced. k,m Equation (13) can be rewritten as:

[0184]

[0185]

[0186]

[0187] rank(W k,m )=1,W k,m ≥0 (14d);

[0188] Clearly, since problem (14) is still a non-convex optimization problem due to (14b) and (14d), an auxiliary variable c is introduced to solve problem (14). k,m Rewrite (14b) as follows:

[0189] s k,m c k,m ≤Tr(Fk,m W k,m (15a);

[0190]

[0191] To solve this problem, we only need to find s k,m and c k,m , then s k,m c k,m The upper bound satisfies:

[0192]

[0193] in, s k,m The value of the nth iteration. c k,m The nth iteration value, based on which equation (15a) is transformed into the following convex constraint:

[0194]

[0195] Finally, the optimization objective (14) can be rewritten as the SDP function shown in equation (18):

[0196]

[0197] st(14c),(15b),(17) (18b);

[0198] rank(W k,m )=1,W k,m ≥0 (18c);

[0199] It can be seen that problem (18) is non-convex due to the rank-one constraint, and needs to be relaxed to construct an SDR problem, which can be solved using existing convex optimization tools, such as the CVX toolbox. In summary, in order to obtain the digital precoding matrix W... k,m This requires iterative solution (18). Specifically, first, the auxiliary variables are initialized. and Solving (18) yields the optimal solution. and Next, and Substitute them separately and Update the solution and solve (18) again. Repeat the above process until the result converges or the number of iterations reaches its maximum value. Furthermore, since the SDR problem of (18) is a convex optimization problem, the solution in each iteration is optimal. Therefore, iteratively solving (18) and updating the variables can increase or at least maintain the value of the objective function. Under the condition of finite transmission power, the designed iterative algorithm guarantees that the objective function value is a monotonically non-decreasing sequence with an upper bound, and converges to at least a locally optimal stationary solution.

[0200] When rank(W) k,m When ) = 1, since W k,m =w k,m w k,m H w can be obtained through eigenvalue decomposition. k,m °. When W k,m When the rank-one constraint is not satisfied, a rank-one solution can be obtained using the Gaussian random method.

[0201] Intelligent reflector phase shift optimization:

[0202] After fixing the digital precoding vector of the base station, the objective function (12) can be transformed into:

[0203]

[0204] st|θ i |=1,i∈{1,...,R} (19b);

[0205] |ψ m,i |=1,m∈{1,...,M},i∈{1,...,R} (19c);

[0206] Although the optimal solution for the digital precoding matrix has been obtained, the optimization problem (19), while concise, is often difficult to solve due to the non-convex objective function (19a) and non-convex constraint set. This chapter, based on fractional programming techniques, applies the proposed Lagrange dual transformation to decouple the logarithmic function and introduces auxiliary variables. There is α = [α 1,1 ,α 1,2 ,...α 1,K ,...α M,K ] T Then the objective function can be written as:

[0207]

[0208] function f k,m (Θ,Τ k ) is represented as:

[0209]

[0210] Therefore, the optimization problem (19) can be transformed into:

[0211]

[0212] st(19b),(19c)(22b);

[0213] Fixed reflection phase Θ and reflection delay matrix T m To maximize this function, by adjusting α k,m Find the partial derivative, i.e. The optimal α can be obtained, therefore the optimal solution can be written as:

[0214]

[0215] Solve for α k,m Substituting the optimal solution into equation (22) for f(Θ,Τ) k From equation (20), we can find that only the last term is related to the variables Θ and T. m Therefore, the optimization problem (22) can be divided into the following two parts: given α, solve Θ and T. m ,Right now:

[0216]

[0217] st(19b),(19c)(24b);

[0218] Let γ k,m =ζ k (1+α k,m In the optimization problem (24), the reflection phase and reflection delay at the IRS end can be decoupled, so these two variables can be solved by alternating iterations.

[0219] With the auxiliary variable α° and the reflection delay T fixed m After °, the optimization problem (24) can be simplified to:

[0220]

[0221] st|θ i |=1,i∈{1,…,R} (25b);

[0222] Among them, h j,m =T m H m w j,m , remember g k,m ΘT m H m w j,m =g k,m Θh j,m=θ H diag(g k,m )h j,m =θ H b k,j,m Therefore, the objective function (equation (25a)) can be rewritten as:

[0223]

[0224] Next, a second transformation is performed, introducing an auxiliary variable x = [x 1,1 ,x 1,2 ,...x 1,K ,...,x M,K ] T Transforming the objective function (Equation (26)) into its equivalent form, we have:

[0225]

[0226] Therefore, updating the reflection phase shift Θ requires the following two steps: iteratively updating x and Θ respectively. Based on this, the solution to the above problem can be divided into the following two sub-problems: finding x while keeping the reflection phase shift Θ constant, and finding the reflection phase shift Θ while keeping x constant.

[0227] First, when Θ is given, the above equation becomes a quadratic equation in x, and it is a concave function, according to... If the function has a local maximum, then the solution x is... m,k It can be represented as:

[0228]

[0229] Then, when x is fixed, x m,k ° and |θ H b k,j,m | 2 =θ H b k,j,m b k,j,m H Substituting θ into the objective function (27), (27) can be simplified to:

[0230] f2(θ)=-θ H Uθ+2Re{θ H v}-C1 (29);

[0231] in,

[0232]

[0233]

[0234]

[0235] To facilitate solving the problem, the above problem (Equation (29)) is equivalent to:

[0236]

[0237] st|θ i |=1,i∈{1,...,R} (31b);

[0238] Due to the constant modulus constraint, this optimization problem remains difficult to solve. To solve this problem, the classic MM algorithm is employed.

[0239] The MM algorithm is widely used in resource allocation in wireless communication networks. Its main idea is to solve a difficult problem by constructing a series of more easily tractable approximate subproblems. Specifically, using θ... t The solution to the subproblem at the t-th iteration is represented by f2(θ). t Let represent the value of the objective function of the problem in the t-th iteration. Then, in the (t+1)-th iteration, an upper bound for the objective function is introduced based on the previous solutions, denoted as g(θ|θ). t In iteration (t+1), the new g(θ|θ) is used. t Solve the approximate subproblem. If the objective function g(θ|θ) t The following three conditions must be met:

[0240]

[0241] Then, the solution sequence obtained in each iteration will lead to the objective function {f2(θ)} t The values ​​of ), t=1,2,...} are monotonically decreasing until convergence. The convergent solution satisfies the KKT (Karush-Kuhn-Tucker) optimality conditions of problem (32). The first two conditions indicate that the introduced objective function g(θ|θ) is monotonically decreasing until convergence. t Its first gradient should be related to the original objective function and its gradient at point θ. t The first-order gradients at the same point are the same. The third condition implies that the constructed objective function g(θ|θ) t The objective function g(θ|θ) should represent an upper bound on the original objective. For this algorithm to be effective, the most important task is to find the objective function g(θ|θ). t It should satisfy the above three conditions and be easier to handle than f2(θ).

[0242] Next, for any given solution θ in the t-th iteration t For any feasible solution θ, we have:

[0243]

[0244] Where X = λ max IR , λ max It is the largest eigenvalue of U, I R Let R represent the identity matrix. Therefore, the objective function of the constructor is as follows:

[0245] g(θ|θ t )=y(θ|θ t )-2Re{θ H v} (34);

[0246] It can be easily verified that y(θ|θ) defined by equation (33) t ), in (34) g(θ|θ t The above three conditions must be met. Furthermore, the objective function g(θ|θ) satisfies... t This is easier to handle than the original objective function f2(θ). Specifically, the subproblem to be solved in the t-th iteration can be represented as follows:

[0247]

[0248] st(31b)(35b);

[0249] Due to θ H θ = R, therefore we can obtain θ H Xθ=Rλ max To facilitate the solution, remove the other constants in equation (35a), and the optimization problem (35) can be rewritten as:

[0250]

[0251] st(31b)(36b);

[0252] Where q t =(λ max I R -U)θ t +v, then the optimal reflection phase shift of problem (36) can be expressed as:

[0253]

[0254] Intelligent reflective surface delay optimization:

[0255] The phase shift between the transmit beam at the fixed base station and the reflection at the IRS end, the target function (12) can now be expressed as:

[0256]

[0257] st(12d)(38b);

[0258] Remember c k,m =g k,mΘ, d j,m =H m w j,m ,have:

[0259]

[0260] Therefore, the objective function can be expressed as:

[0261]

[0262] Similarly, the above equation is transformed twice by introducing an auxiliary variable y = [y 1,1 ,y 1,2 ,...y 1,K ,...,y M,K ] T We can obtain the following expression:

[0263]

[0264] It can be observed that the reflection delay matrix T m The update includes the following two steps, iteratively updating y and T respectively. m In summary, the solution to the above problem can be divided into the following two sub-problems: fixing the reflection phase delay matrix T. m Find y and, with y fixed, find the reflection delay matrix T. m ;

[0265] First, given the reflection delay T m When the above equation is transformed into a quadratic equation in y, and it is a concave function, according to... If the function has a local maximum, then the solution y m,k It can be written as:

[0266]

[0267] Then, when y is fixed, y m,k ° and Substituting into the objective function (41), we define:

[0268]

[0269]

[0270] Equation (41) can be simplified to:

[0271] f4=-ψ H Λψ+ψ H V (44);

[0272] in,

[0273] Λ=diag(Λ1,Λ2,...,Λ M (45a);

[0274]

[0275] Therefore, the optimization problem described above can be rewritten as:

[0276]

[0277] st(12d)(46b);

[0278] Using the MM algorithm to solve for the reflection delay, we can obtain:

[0279]

[0280] in,

[0281] It is worth noting that, unlike traditional IRS-assisted terahertz communication systems which design a phase shift in each reflecting unit to adapt to all carriers, Equation (12) introduces H m A time delay can be introduced to adjust the phase of the signal, exerting different effects on different frequencies. Therefore, solving for the delay matrix is ​​a challenging task.

[0282] The above method yields MR solutions, as shown in equation (47). In fact, a delay is introduced for each of the R reflection units of the IRS, i.e., t = [t1, t2, ..., t3]. R ] T At subcarrier frequency f m At point r, for the r-th IRS reflecting unit, the resulting phase shift is -2πf m t r .according to p t Should meet However, the MR phase shifts obtained through the above transformation may not necessarily satisfy the delay introduced by a single IRS reflection unit. For example, when t r When determined, the solution is obtained using the MM algorithm. and It may not be able to meet the requirements. and In other words, the delay t of each reflection unit may be different. To solve this problem, the average value method is used to determine each delay, that is, based on the solved MR phase shifts υ = [υ 1,1 ,...υ 1,R ,υ 2,1 ,...,υ 2,R ,...υ M,1 ,...,υM,R To ensure that all the obtained delay values ​​t are positive, subtract 2π from all the obtained phase shift values ​​to obtain υ. m,r -2π∈[-3π,-π], then divide each by -2πf. m We obtain M delays under the r-th reflecting element, and average these M delay values ​​to get the delay value introduced by the r-th reflecting unit. At this time, we can obtain t = [t1, t2, ..., t3]. R ] T Then use The reflection delay matrix of the IRS can be obtained.

[0283] Based on the above analysis, Table 1 summarizes the details of the alternating optimization algorithm. When the algorithm converges, the optimal phase shift φ can be obtained. * =arg(q t ).

[0284] Table 1. Alternating optimization algorithm steps for objective function (12)

[0285]

[0286] Experimental simulation analysis

[0287] Table 2 Simulation Parameters

[0288]

[0289] This experiment will evaluate the performance of the proposed scheme in an IRS-assisted broadband terahertz communication system through simulation analysis. The scheme proposed in this chapter introduces a delay in each reflection unit of the IRS. Therefore, the difference from the traditional IRS, which only needs to solve the reflection phase shift, is that an additional phase shift matrix caused by the delay should also be solved. The specific simulation parameters are shown in Table 2.

[0290] Figure 2 and Figure 3 The convergence performance of the traditional IRS and the proposed DAM algorithm in solving digital precoding problems is plotted separately. The "nth iteration" labeled in the figure represents the outer iteration. Observation reveals that in each outer iteration, the inner iteration algorithm typically converges after approximately 5 iterations. Furthermore, the difference between the second and third iterations is much smaller than the difference between the first and second iterations, indicating that the outer iteration loop also converges relatively quickly. In addition, the maximum sum rate of the traditional IRS in the fourth iteration is about 15% smaller than that of the proposed DAM algorithm. Therefore, the proposed DAM algorithm can improve the user's sum rate, providing a solution for improving system performance and overcoming beam dispersion effects.

[0291] Figure 4The convergence performance of the traditional IRS and the proposed delay-introducing scheme was compared under the entire algorithm optimization, demonstrating that when the base station's maximum transmit power P... max The maximum sum rate for users at 0dB is shown in the figure below. It is clear that the maximum sum rate of each carrier converges quickly, reaching a stable state. Furthermore, the maximum sum rate of the proposed DAM scheme is significantly higher than that of the traditional IRS scheme because the introduction of IRS overcomes beam dispersion effects, increases the beam array gain in a certain direction, and improves system performance. Simulation results also demonstrate the superiority of the proposed scheme.

[0292] Figure 5 The graph compares the maximum sum rate of the two methods under different transmit powers. It shows that as the maximum transmit power of the base station increases, the maximum sum rate of users per subcarrier also increases. Similarly, the proposed method of introducing delay can significantly improve the system's sum rate.

[0293] This invention addresses the beam dispersion problem in IRS-assisted terahertz communication systems. It proposes introducing a time-adjustable metasurface onto the IRS, which overcomes the beam dispersion issue caused by the frequency-independent characteristics of the IRS reflection units, improving the sum rate for multiple users and thus enhancing system performance. In solving the digital precoding problem, the SDP is used to transform the non-convex optimization problem into a convex one, which is then solved using the SDR algorithm. When solving for the IRS reflection beam, the Lagrange multiplication and quadratic transformation is used to decompose the non-convex problem of reflection phase shift and reflection delay coupling into two convex problems, which are then subjected to fractional programming. The MM algorithm is used to solve the optimization problem with constant mode constraints. Simulation results demonstrate that the proposed scheme outperforms traditional IRS designs in terms of user sum rate, overcomes beam dispersion effects, and improves the quality of service for users.

[0294] 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 joint beam design method to overcome beam dispersion in terahertz IRS communication, characterized in that, The steps are as follows: Step 1: Build an IRS-assisted terahertz multi-user communication system, including an IRS, a base station, and K users. The base station adopts a fully digital structure, the IRS adopts a uniform linear array structure, and there are obstacles between the base station and the users. Users can only receive reflected signals from the IRS. Step 2: Apply Delay Alignment Modulation (DAM) to the IRS to introduce additional delay and calculate the signal received by the user on the subcarrier; The signal received by the user on the subcarrier is: （1）； in, For the signal received by the k-th user on the m-th subcarrier, , It is the transmit antenna gain. It is the receiving antenna gain. It is the path loss compensation factor. This represents the channel from the IRS to the k-th user on the m-th carrier. Represents the IRS reflection coefficient matrix. This represents the delay matrix of the m-th carrier. , and satisfy and , The time delay introduced for the r-th IRS reflection unit, where R represents the number of reflection units. Indicates the frequency of the carrier wave. It is the channel from the base station to the IRS on the m-th carrier. This represents the digital precoding vector of the k-th user on the m-th subcarrier. This represents the transmitted signal of the k-th user on the m-th subcarrier. It is the additive white Gaussian noise of the k-th user on the m-th carrier; Step 3: Calculate the signal-to-dryness ratio (SDR) of the user on the subcarrier based on the signal received by the user on the subcarrier, and calculate the reachability and speed of the user based on the SDR; Step 4: Use the maximization of the user's reachability and rate as the objective function; Step 5: Decompose the objective function into multiple sub-optimization objectives using the alternating optimization algorithm, and solve the multiple sub-optimization objectives using the SDR and MM algorithms respectively to obtain the maximum reachability and rate of the user; An alternating optimization algorithm is used to iteratively update the active and passive beams: First, given the IRS reflection phase and reflection delay matrix, the base station digital precoding vector is solved using SDR; then, the base station digital precoding vector is fixed, and the reflection phase shift and reflection delay are obtained through the MM algorithm, thereby maximizing the user's sum rate.

2. The joint beam design method to overcome beam dispersion in terahertz IRS communication according to claim 1, characterized in that, The signal-to-dryness ratio of the user on the subcarrier is: （10）； in, Let k be the signal-to-dryness ratio on the m-th carrier. , Indicates the noise variance. , This represents the array steering vector at the transmitting end. This represents the array steering vector at the receiving end. 3.The joint beam design method for overcoming beam dispersion in THz IRS communication of claim 2, wherein, The , The expressions of the above are respectively: （5）； （6）； in, , , Antenna spacing, Indicates the angle of departure. Indicates the angle of arrival.

4. The joint beam design method to overcome beam dispersion in terahertz IRS communication of claim 2, wherein, The expression for the reachability and rate of the user is: （11）； wherein, is the sum of the achievable rates for the kth user over all carriers.

5. The joint beam design method to overcome beam dispersion in terahertz IRS communication according to claim 4, characterized in that, The objective function is: （12a）； （12b）； （12c）； （12d）； wherein denotes the maximum transmit power of the base station, is the weight of user k, the superscript H denotes the conjugate transpose.

6. The joint beam design method to overcome beam dispersion in terahertz IRS communication according to claim 5, characterized in that, The method for solving the base station digital precoding vector using SDR is as follows: Given the IRS reflection phase and reflection delay matrix, the objective function is transformed into the first sub-optimization objective: （13a）； （13b）； in, ,definition and At the same time, auxiliary variables are introduced. Equation (13) can be rewritten as: （14a）； （14b）； （14c）； （14d）； An auxiliary variable is introduced Rewriting (14b) as （15a）； （15b）； but The upper bound satisfies: （16）； in, express The value of the nth iteration. express The value of the nth iteration is given. Based on this, equation (15a) is transformed into the following convex constraint: （17）； Finally, the optimization objective (14) can be rewritten as the SDP function shown in equation (18): （18a）； （18b）； （18c）； The optimal value of the base station digital precoding vector is obtained by solving the SDP function shown in equation (18) using the CVX toolbox.

7. The joint beam design method to overcome beam dispersion in terahertz IRS communication according to claim 6, characterized in that, The method for obtaining the reflection phase shift and reflection delay using the MM algorithm is as follows: S5.1: After fixing the digital precoding vector of the base station, the objective function (12) can be transformed into: （19a）； （19b）； （19c）； By introducing auxiliary variables There are Then: （20）； Function is represented as: （21）； Therefore, the optimization problem (19) can be transformed into: （22a）； （22b）； Fixed reflection phase and reflection delay matrix Through the Find the partial derivative, i.e. This can yield the optimal result. Therefore, the optimal solution can be written as: （23）； Solve Substituting the optimal solution into equation (22) It can be observed that only the last term of equation (20) is related to the variable. and Therefore, the optimization problem (22) can be divided into the following two parts, given Solve and ,Right now: （24a）； （24b）； Recall ; in the optimization problem (24), the reflection phase and the reflection delay at the IRS end can be decoupled, so these two variables are solved by an alternating iterative manner; With fixed auxiliary variables and reflection delay Then, the optimization problem (24) can be simplified to: （25a）； （25b）； wherein , record Thus, the objective function (25a) can be rewritten as: （26）； Introducing auxiliary variables Equivalently transforming equation (26), we have: （27）； Therefore, the reflection phase shift The update requires the following two steps: fixing the reflection phase shift beg and fixed Find the phase shift of the reflection. ; First, when Given that The function has a maximum value, then the solution Can be expressed as: （28）； Then fix When, the And Into the objective function (27), (27) can be simplified as: （29）； in, （30a）； （30b）； （30c）； For ease of solving the problem, equation (29) is equivalent to: （31a）； （31b）； For any given solution in the tth iteration and any feasible solution there is: （33）； in, , yes The largest eigenvalue, express The identity matrix; The constructor's objective function is as follows: （34）； The subproblem to be solved in the t-th iteration can be represented as follows: （35a）； （35b）； because Therefore, we can obtain To facilitate the solution, remove the other constants in equation (35a), and the optimization problem (35) can be rewritten as: （36a）； （36b）； where The optimal reflection phase shift for problem (36) can then be expressed as: （37）； S5.2: The phase shift between the transmit beam at the fixed base station and the reflection at the IRS end, the target function (12) can be expressed as: （38a）； （38b）； Recall , , （39）； Therefore, the objective function can be expressed as: （40）； By introducing auxiliary variables The following expression can be obtained: （41）； Reflection delay matrix The update includes the following two steps: fixing the reflection phase delay matrix beg and fixed Find the reflection delay matrix ; First, given the reflection delay At that time, according to If the time function has a maximum value, then the solution is... It can be written as: （42）； Then the At the time of fixation, put and into the objective function (41), defined: （43a）； （43b）； Equation (41) can be simplified to: （44）； in, （45a）； （45b）； Therefore, the optimization problem described above can be rewritten as: （46a）； （46b）； Using the MM algorithm to solve for the reflection delay, we can obtain: （47）； wherein ; By taking the average of the delay time, the reflection delay time is obtained .​

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