A dual-irs-assisted otfs multi-cell uplink joint optimization method

Abstract

The application discloses a kind of double IRS auxiliary OTFS multicell uplink joint optimization method, it is related to wireless communication technical field.The method constructs "common+special" double IRS architecture, establishes equivalent channel model covering all types of links in delay-doppler domain, combines rate, bit error rate constraint into unified SINR threshold, establishes joint optimization problem with user SINR maximization as target;Using alternate optimization framework, the problem is decomposed into three sub-problems of precoding, common and special IRS phase shift, and respectively using semi-definite programming and Charnes-Cooper transformation for convexification and iterative solution, until the optimal precoding matrix set and double IRS phase shift matrix are output after convergence.The application effectively solves the problems of weak interference coordination ability, poor high-doppler scene adaptability and non-convex optimization solution difficulty of prior art architecture, significantly improves the multicell uplink anti-interference ability and edge user transmission performance.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a dual IRS-assisted OTFS multi-cell uplink joint optimization method. Background Technology

[0002] With the rapid deployment of next-generation high-speed wireless communication services such as 6G, vehicle-to-everything (V2X), high-speed rail mobile communication, and low-altitude drone swarm communication, communication scenarios exhibit three typical characteristics: high-speed mobility, ultra-dense cellular networking, and wide-area weak coverage. In these scenarios, user equipment (UE) generally has a high mobility speed, which generates significant Doppler frequency shift in the wireless channel. If the mainstream Orthogonal Frequency Division Multiplexing (OFDM) modulation technology of 4G and 5G is used, the orthogonality between subcarriers will be destroyed by the Doppler effect, resulting in severe inter-carrier interference (ICI). This directly causes a significant decrease in the received signal-to-interference-noise ratio (SINR) and a deterioration in the bit error rate (BER), making it difficult to meet the high reliability and high-speed transmission requirements in high-speed scenarios.

[0003] To address the limitations of OFDM in adapting to highly time-varying channels, Orthogonal Time Frequency Space (OTFS) modulation technology has been proposed. This technology departs from the traditional time / frequency domain signal processing framework, performing signal modulation and channel characterization in the Delay-Doppler (DD) two-dimensional domain. It can approximate a rapidly time-varying wireless channel within a single frame as a sparse static channel within the DD domain, suppressing Doppler interference from a fundamental mechanism. This has made it a core candidate modulation scheme for 6G high-mobility communication scenarios.

[0004] Meanwhile, Intelligent Reflecting Surface (IRS), as a passive metasurface wireless enhancement technology, can artificially reshape the propagation path of radio electromagnetic waves by dynamically adjusting the phase of a massive number of reflective units. On the one hand, it constructs a constructive superposition path to enhance the useful signal power of the target user, and on the other hand, it constructs a destructive interference path to suppress various types of interference. It does not require an additional radio frequency transmission link and has low hardware costs. It is a core technical means to improve weak coverage at the edge of cellular cells and suppress interference from multiple cells.

[0005] The industry has established a mainstream research approach of "OTFS modulation + IRS-assisted transmission," aiming to balance high-speed channel adaptability and interference suppression capabilities. In practical multi-cell cellular networking, using a single cell and a single IRS makes it impossible to synchronously coordinate cross-cell interference. Furthermore, coupled non-convex problems rely solely on a single convex tool for solution, lacking an alternating optimization (AO) hierarchical solution framework and comprehensive theoretical support. Summary of the Invention

[0006] The purpose of this invention is to provide a dual IRS-assisted OTFS multi-cell uplink joint optimization method to solve multiple technical problems in the existing technology, such as weak architecture interference coordination capability, complex non-convex optimization solution and lack of theoretical support.

[0007] To achieve the above objectives, this invention provides a dual IRS-assisted OTFS multi-cell uplink joint optimization method, comprising the following steps: S1. Construct a communication system for multi-cell uplink of dual IRS-assisted OTFS and establish a signal processing link at the user transmitter. S2. Establish an equivalent channel matrix including direct links, single-reflection links, and double-reflection links to obtain the received signal and signal-to-interference-plus-noise ratio; Establishing joint optimization problems based on service quality constraints; S4. Transform the bit error rate constraint in the joint optimization problem into a SINR lower bound constraint, and merge it with the rate constraint into a SINR threshold constraint to obtain a simplified joint optimization problem. S5. Using an alternating optimization framework, the joint optimization problem is decomposed into three sub-problems: the precoding optimization sub-problem, the common IRS phase shift optimization sub-problem, and the dedicated IRS phase shift optimization sub-problem. The sub-problems are solved iteratively until convergence. S6. Output the optimal set of precoding matrices, the optimal common IRS phase shift matrix, and the optimal dedicated IRS phase shift matrix.

[0008] Therefore, this invention adopts the above-mentioned dual-IRS assisted OTFS multi-cell uplink joint optimization method, innovatively constructing a two-layer distributed collaborative architecture of global public IRS + cell-specific IRS. Relying on the DD domain, it completes accurate matrix modeling of the entire link including direct connection, single-pass, and bidirectional secondary reflection. It unifies the dual service quality constraints of rate and bit error rate through equivalent transformation, and designs a hierarchical alternating convex optimization solution framework combining AO with SDP / SDR and Charnes-Cooper transform. Compared with various comparative schemes such as existing single IRS, simplified dual IRS, OFDM matching, and single optimization algorithm, it can make full use of the multi-dimensional spatial control freedom of dual-layer IRS to efficiently suppress intra-cell and inter-cell superposition interference. It is suitable for high-Doppler high-speed communication scenarios such as high-speed rail and drones, and takes into account the transmission performance of edge users, algorithm convergence speed, large-scale array gain and multi-cell networking scalability. At the same time, it has complete mathematical theoretical support and engineering feasibility, and comprehensively solves the inherent defects of existing technical architecture, modeling, optimization, algorithm, and scenario adaptation.

[0009] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0010] Figure 1 This is an overall flowchart of the dual IRS-assisted OTFS multi-cell uplink joint optimization method of the present invention; Figure 2 This is a communication principle diagram of dual IRS-assisted OTFS multi-cell uplink according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the principle of OTFS according to an embodiment of the present invention; Figure 4 This is a convergence curve of the AO algorithm according to an embodiment of the present invention; Figure 5 This is a graph showing the change in SINR of the target user at different times according to an embodiment of the present invention; Figure 6 This is a graph showing the variation of the target user's SINR when the number of IRS reflection units is different according to an embodiment of the present invention. Figure 7 This is a graph showing the change in the target user SINR when the number of users in each cell is different according to an embodiment of the present invention. Figure 8 This is a graph showing the change in SINR of the target user when the number of cells is different according to an embodiment of the present invention; Figure 9 This is a graph showing the variation of the target user's SINR at different times with the maximum Doppler frequency shift according to an embodiment of the present invention; Figure 10 This is a graph showing the change in BER at the receiver at different times for the SNR in an embodiment of the present invention. Detailed Implementation

[0011] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0012] Please see Figures 1-3 A dual IRS-assisted OTFS multi-cell uplink joint optimization method includes the following steps: S1. Construct a communication system for multi-cell uplink of dual IRS-assisted OTFS and establish a signal processing link at the user transmitter.

[0013] S11. Construct a communication system for dual IRS-assisted OTFS multi-cell uplink, the communication system including... Each cell is equipped with one base station (BS). Each user equipment and a dedicated IRS (it is assumed that the IRS can only receive signals from this cell). K (signals emitted by individual user equipment); cell The base station in the middle, the first Each user equipment and dedicated IRS is denoted as follows: , and , , , Indicates a collection of neighborhoods. This represents a set of user equipment; a public IRS is deployed throughout the entire network area of ​​the communication system, denoted as . This forms a "public IRS plus" A two-tier distributed IRS architecture with "one dedicated IRS"; S12. The user equipment uses OTFS modulation to transmit uplink signals in the DD domain, and the communication system is built on the DD domain. Resource grid points, and These represent the time delay number and the Doppler number, respectively; let the subcarrier spacing be... The symbol interval is ,satisfy , and Each satisfies the delay resolution and Doppler resolution The bandwidth occupied by one frame of OTFS signal is All OTFS signal frame intervals are ; S13. Establish user transmitter signal processing link: User equipment The DD domain signal matrix is , Represent a M OK N The matrix of columns is processed by inverse symplectic finite Fourier transform (ISFFT) to obtain the time-frequency (TF) domain signal and converted into matrix form. Then, the time-domain transmission signal is obtained through Heisenberg transform. The parallel-to-serial conversion and precoding are performed sequentially to generate the transmitted signal. ; Matrix form of TF domain signals for: ; In the formula, and They represent M The matrix form of the discrete Fourier transform and N The matrix form of the discrete Fourier inverse transform.

[0014] S2. Establish an equivalent channel matrix including direct links, single-reflection links, and double-reflection links to obtain the received signal and signal-to-interference-plus-noise ratio.

[0015] S21, Settings and These are the delay matrix and the Doppler matrix, respectively. S22. In cell c, the IRS equipment ( , ) and base station ( ) is in a fixed position, while the user equipment ( , (is in a moving state) Indicates the community User equipment in k , The common IRS phase shift matrix is The dedicated IRS phase shift matrix is Extending both to the OTFS signal processing dimension, we obtain the extended common IRS phase shift matrix. and the extended dedicated IRS phase shift matrix ; S23. Divide the transmission link types into direct links, single-reflection links, and double-reflection links, and construct the channel matrix for each transmission link type in the DD domain; The direct link channel matrix is , Indicates the community Medium user equipment Channel matrix to base station, Indicates the user equipment sequence. ; Represents the cell sequence. ; Indicates a base station; Single-reflection links are divided into two types: those via a common IRS and those via a dedicated IRS. The channel matrices for the two types of single-reflection links are as follows: and , Represents user equipment in any cell After being reflected by the public IRS, it reaches the community. Synthetic channel matrix of the base station Indicates the community Medium user equipment The synthesized channel matrix of the base station in the same cell after reflection through the dedicated IRS; Two-reflection links are divided into two types: those that pass through a dedicated IRS and a public IRS sequentially, and those that pass through a public IRS and a dedicated IRS sequentially. The channel matrices for the two types of two-reflection links are as follows: and , Indicates the community Medium user equipment The synthesized channel matrix first passes through a dedicated IRS and then through a public RIS before reaching the base station in the same cell. Represents user equipment in any cell First reflected by the public IRS, then reflected by the dedicated IRS, before reaching the residential area. Synthetic channel matrix of the base station; S24. Superimpose the channel matrices of all transmission link types to obtain the equivalent channel matrix, expressed as: ; In the formula, Indicates user equipment in multiple cells Arrive at the community The channel matrix synthesized from all links of the base station; Indicates from Arrive at the community Channel matrix of the base station; Indicates public IRS; Indicates the community Medium user equipment arrive The channel matrix; express Channel matrix to base station; Indicates the community Dedicated IRS in China; Indicates the community Medium user equipment arrive The channel matrix; express arrive The channel matrix; Indicates the community Dedicated IRS in China; express arrive The channel matrix; Subscript abbreviations indicating public IRS; Subscript abbreviation indicating a dedicated IRS; S25. Generate cells based on the unified equivalent channel matrix. medium base station Received signal The expression for signal-to-interference-plus-noise ratio (SINR) and data rate are as follows: ; ; ; In the formula, Indicates the community Medium user equipment The channel matrix; Indicates the community Medium user equipment The signal precoding matrix; Indicates the community Medium user equipment The signal; Indicates the community Medium user equipment The channel matrix; Indicates the community Medium user equipment The signal precoding matrix; Indicates the community Medium user equipment The signal; Indicates the community Medium user equipment The signal precoding matrix; Indicates the community Medium user equipment The signal; Indicates noise; Indicates the community Medium user equipment The signal-to-noise ratio of the received signal; Indicates the community Medium user equipment The noise power in the received signal.

[0016] S3. Establish a joint optimization problem based on service quality constraints.

[0017] Select any cell Any user in As the transmitter, under the premise of satisfying the quality of service (QoS) constraints such as the minimum rate threshold and the maximum bit error rate threshold for all users (including the target user and other interfering users), the goal is to maximize the signal-to-interference-plus-noise ratio (SIR) of the target user equipment, resulting in a joint optimization problem. Service quality constraints include rate constraints. Bit error rate constraints Precoding power constraints Public IRS unit module constraints and dedicated IRS unit module constraints The expressions for the joint optimization problem and service quality constraints are: ; ; ; ; ; ; In the formula, Indicates the community Medium user equipment The set of precoding matrices for the emitted signal; Represents the minimum value of the rate; Indicates any one that is different from The neighborhood; Indicates any one that is different from User equipment; Indicates the community Medium user equipment Arrive at the community Channel matrix of the base station; Indicates the community Medium user equipment The signal precoding matrix; This represents the minimum bit error rate; This represents the maximum power of the signal precoding matrix; express Phase shift; express The reflective unit in the middle; express Phase shift; Indicates IRS c,2 The reflective unit in the middle; Indicates the community Medium user equipment The bit error rate; This represents the maximum bit error rate; for In practical OTFS systems, the following is typically used: Quadrature amplitude modulation (QAM) -quadratureamplitude modulation, -QAM). , Let be the modulation order. Under ideal conditions of additive white Gaussian noise (AWGN) channel and no inter-symbol interference (ISI), the instantaneous SINR (denoted as ) of a given received signal is... Its exact approximate expression for BER is: ; In the formula, Represents the coefficients of the rectangular QAM; Gauss Q function; Indicates the scaling factor; Indicates the instantaneous SINR of the received signal. This approximation holds true only if the received signals satisfy the Gaussian property of independent and identically distributed signals and there is no residual ISI. Although OTFS may retain slight ISI under strong delay-Doppler spread, under the conditions of typical sparse channels and ideal minimum mean-square error (MMSE) balance, the approximation error is usually lower than [value missing]. It has been verified in multiple papers that it can be used for system-level optimization modeling. Because It is strictly monotonically decreasing within its domain, therefore the constraint Equivalent to .

[0018] S4. Transform the bit error rate constraint in the joint optimization problem into a SINR lower bound constraint, and merge it with the rate constraint into a SINR threshold constraint to obtain a simplified joint optimization problem.

[0019] S41. Constrain the bit error rate Transformed into a linear SINR lower bound constraint and will and Merged into SINR threshold constraints , and The expressions are as follows: ; ; In the formula, express The minimum value; S42, SINR-based threshold constraints The simplified joint optimization problem is obtained. The expression is: ; ; but It remains a non-convex optimization problem, primarily for the following reasons: (1) The three optimization variables in the objective function and Medium-deep coupling; (2) Objective function and All of them contain non-affine terms composed of optimization variables; (3) It is a unit-modulus constraint.

[0020] S5. Using an alternating optimization framework, the joint optimization problem is decomposed into three sub-problems: the precoding optimization sub-problem, the common IRS phase shift optimization sub-problem, and the dedicated IRS phase shift optimization sub-problem. The sub-problems are solved iteratively until convergence.

[0021] S51. Variable Initialization: Initialize the common IRS phase shift matrix that satisfies the unity modulus constraint. and dedicated IRS phase shift matrix Set the iteration index Maximum number of iterations and convergence accuracy ; S52. Enter the main loop and set the iteration index. Increase by 1, and execute the three optimization stages S53-S55 sequentially until the convergence condition in S56 is met. S53, Optimization Phase 1: Perform the precoding optimization subproblem and output... ; express The Round iteration value; S531, take the results from the previous round and Substitute into the equivalent channel matrix A fixed value is obtained; and These are the common IRS phase shift matrix and the dedicated IRS phase shift matrix from the previous round, respectively; for the simplified joint optimization problem, the fixed... and Optimize the precoding matrix to obtain the precoding optimization subproblem. The expression is: ; S532, Introducing semidefinite constraints Relax the non-convex rank-one constraints Only retain ;according to Properties and Properties, and Representing the trace and vectorization of the matrix respectively, the numerator and denominator of the pre-encoded optimization subproblem are transformed into linear vector inner product form, yielding the relaxation problem. The expression is: ; ; ; ; ; ; In the formula, , and They represent , and traces; , , and They represent , , and Vectorization; express Transpose of; express Transpose of; Represents the signal precoding matrix One received MN A positive semi-definite matrix of order 1; Represents the signal precoding matrix One received MN A positive semi-definite matrix of order 1; It is the transpose symbol; , , , and They represent , , , and transpose, Indicates will A vector after vectorization Indicates to A vector after adjustment Indicates to A vector after adjustment Indicates to A vector after adjustment Indicates to A vector after adjustment; Indicate a scripture or The adjusted vector; Indicates the community Medium user equipment The noise power in the received signal; Obviously, It is a linear fractional programming problem where all denominators are positive (i.e., ...). Therefore, the Charnes-Cooper transform can be used for processing.

[0022] S533, Charnes-Cooper Transform: Introducing Auxiliary Variables ,satisfy and Through identity The linear fractional programming problem is equivalently transformed into the standard semidefinite programming (SDP) problem. ; ; ; ; ; In the formula, This represents a vector obtained by linear transformation of x; Represent a A column vector of dimension; Indicates a by The positive semi-definite matrix after linear transformation; S534, Solve using CVX tools To obtain the optimal value , and Represent y and t The optimal value; S535, from Extract ,make For each Applying the rank-one constraint yields Thus obtain ; and They represent and The optimal value, Indicates to The matrix after linear transformation; express The Round iteration value; S54. Optimization Phase Two: Execute the common IRS phase shift optimization subproblem and output... , express The Round iteration value; S541, Fixed and The common IRS phase shift optimization subproblem is obtained. The equivalent channel matrix Explicitly split into AND Irrelevant fixed parts and the phase shift vector of the common IRS The relevant linear part, then ,in express The number of reflective units in the middle, express phase shift, Indicates the corresponding number A fixed matrix obtained by multiplying the cascaded channels of a reflection unit; ; ; S542, will Both the numerator and denominator are expanded into terms related to The quadratic forms are expressed as follows: ; ; In the formula, Indicates a by L The vector formed by one reflection unit; express Transpose of; Indicates taking the real part; and Each represents a configuration or The Hermitian positive semidefinite matrix; and They represent and one of the L 1-dimensional vector; and Each represents a configuration or real numbers; S543, Introduction and The results of S542 are transformed. Indicates by One received Augmented vectors of dimension, Indicates by One received L The augmented matrix of order 1+1 is obtained as follows: ; ; In the formula, and They represent respectively by and And one L An augmented matrix of order 1+1; S544, Introducing an auxiliary variable 1 ,satisfy and , Let a positive semi-definite matrix represent the common IRS phase shift optimization subproblem. Transformed into a standard SDP problem for common IRS phase shift optimization The expression is: ; ; ; In the formula, and They represent respectively by and And one L An augmented matrix of order 1+1; S545. Solving Standard SDP Problems Using CVX Tools To obtain the optimal value , and Representing Y and t The optimal value of 1; S546, Calculation , This represents the optimal value of X, for Perform eigenvalue decomposition and extract the eigenvector corresponding to the largest eigenvalue. ,extract The former Each element constitutes a L 1-dimensional vector Through phase projection Restore the unit modulus constraint. express The Middle Phase shift of each element, update the common IRS matrix. , Indicates taking the secondary angle. This indicates that the vector is converted into a diagonal matrix. express The Round iteration value, Represent a MN An identity matrix of order 1; S55, Optimization Phase Three: Execute the dedicated IRS phase shift optimization subproblem, and output... , express The Round iteration value; S551, Fixed and This yields a dedicated IRS phase shift optimization subproblem. ; S552, Simplified Joint Optimization Problem Both the numerator and denominator are expanded into terms related to The quadratic form, Represent a L 2-dimensional vector; S553, Introduction and Transform the results of S552. Indicates by One received L 2+1 dimensional augmented vector, Indicates by One received L An augmented matrix of order 2+1; S554, Introducing Auxiliary Variable Two The dedicated IRS phase shift optimization subproblem is transformed into a standard SDP problem for dedicated IRS phase shift optimization. ; S555 Solving Standard SDP Problems Using CVX Tools To obtain the optimal value , and They represent and t The optimal value of 2; S556, Calculation , express The optimal value, for Perform eigenvalue decomposition and extract the eigenvector corresponding to the largest eigenvalue. ,extract The former Each element constitutes a L 2D vector Through phase projection Restore the unit modulus constraint. express The Middle The phase shift of each element updates the dedicated IRS matrix. , and They represent and The Round iteration value; S56, based on the first Variables after round update , , Calculate the first Total speed of wheels If the convergence condition is met or If the iteration terminates, return to S52 to begin a new iteration.

[0023] S6. After terminating the iteration, based on the first iteration... The optimal precoding matrix set is output after each round of variable updates. Optimal common IRS phase shift matrix and the optimal dedicated IRS phase shift matrix , , , .

[0024] Convergence analysis: Because SDR is used to handle rank-one constraints when solving subproblems, and eigenvalue decomposition (EVD) and unit modulus projection are introduced when restoring variables, its convergence needs to be explained from the following two aspects: Convergence on the relaxation problem: After neglecting the rank-one constraint and the unit modulus constraint, the three subproblems , and All are standard convex SDPs. Since each convex SDP can be solved exactly to the global optimum using the interior-point method, the objective function is monotonically non-decreasing at every step of the AO framework over the relaxed convex feasible region. Meanwhile, the power constraint on the relaxation problem ( ) and the relaxed unit modulus constraint ( , ,Right now This constitutes a compact feasible region, therefore the objective function value is bounded above. According to the monotone bounded theorem, the sequence of objective functions for the relaxation problem must converge; Convergence and Feasible Solution Recovery in the Original Problem: For the original non-convex problem (containing rank-one and unit modulus constraints), although the process of recovering the rank-one and unit modulus constraints through EVD and phase projection cannot theoretically guarantee the monotonicity of the objective function, the following two points are considered: 1) The aforementioned analysis has proven that the SDP relaxation of the unit modulus constraint is tight; 2) The projection operation is essentially finding the Feasible Point closest to the optimal SDP solution, and numerical experiments show that the drop in objective value caused by projection is minimal. Therefore, the algorithm exhibits good stability in actual simulations, typically converging to a high-quality local optimum (stationary point) within dozens of iterations.

[0025] Computational complexity analysis: Suppose that the dimension of the positive semidefinite matrix in the SDP problem is . The number of constraints is The time complexity of a single solution is approximately: ; In the formula, Indicate complexity; Indicates the convergence accuracy; when the number of constraints is equal to... For the same order, it can be simplified to for ease of estimation. .

[0026] Therefore: for SDP, positive semidefinite matrix (Corresponding stacked variables) The dimensions of ) are: ; In the formula, This represents the order of Y; therefore The complexity of a single iteration is .

[0027] Next to indivual Perform EVD to extract the principal feature vector (rank-1 approximation). Indicates the optimal value The optimal value matrix obtained after linear transformation has a complexity of O(n log n). It's not hard to see Compared to This is a lower-order term.

[0028] for SDP, variable matrix The dimensions are: ; In the formula, Indicates will The coefficient obtained by adding 1; therefore The complexity of a single iteration is approximately .

[0029] Next to Performing EVD to extract the principal feature vector (rank-1 approximation) has a complexity of O(n log n). ; for SDP, variable matrix The dimensions are: ; In the formula, Indicates will The coefficient obtained by adding 1; therefore The complexity of a single iteration is approximately .

[0030] When the size of the reflective unit , and While comparable, EVD complexity cannot be completely ignored, but in typical large-scale IRS configurations ( L Under this condition, the dominant item in SDP remains... Let the total number of iterations required for the algorithm to converge be . ( The total computational complexity of the entire algorithm Approximately: .

[0031] Simulation Analysis: The system simulation parameters were set according to Table 1, and the simulation results are as follows. Figures 4-10 As shown in Table 2, the simulation results are summarized in the table.

[0032] Table 1: System Simulation Parameters

[0033] Note: These represent the multipath number for User Equipment-Base Station, User Equipment-Public IRS, User Equipment-Cell Dedicated IRS, Public IRS-Base Station, and Cell Dedicated IRS-Base Station, respectively.

[0034] Table 2: Summary Table of Simulation Graphs

[0035] Figure 4 The curves showing the SINR of the proposed AO algorithm as a function of the number of iterations are presented. , , , ).from Figure 4 As can be observed, the SINR improvement of the method of this invention is most significant in the initial iteration stage. After about 5 iterations, the SINR reaches more than 90% of the steady-state value, and it converges completely within 10-15 iterations. This rapid convergence characteristic is due to the following two points: 1) In the three-step alternating optimization, each step of the SDP subproblem is solved precisely to the global optimum, ensuring that each iteration achieves effective performance improvement; 2) The fractional programming is transformed into a linear objective through the Charnes-Cooper transformation, avoiding the step size adjustment problem of gradient-based algorithms. After convergence, the SINR curve remains stable without oscillation, verifying the stability and practicality of the AO framework in the actual system, indicating that the present invention can complete joint optimization with low computational overhead.

[0036] Figure 5 Six target user SINR variation curves as a function of SNR are presented. Scheme ① is the dual IRS-OTFS of this invention, Scheme ② is single IRS-OTFS (only the common IRS is retained), Scheme ③ is dual IRS-OFDM, Scheme ④ is no IRS-OTFS (only direct links), Scheme ⑤ is dual IRS-OTFS (IRS phase shift is randomly set), and Scheme ⑥ is dual IRS-OTFS (only IRS phase shift is optimized, no precoding). Figure 5The following patterns can be observed: Scheme ① achieves the highest SINR across all SNR ranges, and the gain increases with increasing SNR, reflecting the performance gain brought about by the synergy of dual IRS architecture, OTFS modulation, and joint optimization. Scheme ② performs second best, indicating that dual IRS provides more reflection paths and spatial degrees of freedom compared to single IRS, effectively improving the received signal power. Scheme ③ is similar to Scheme ① in the low SNR region, but as SNR increases, inter-carrier interference (ICI) in high Doppler scenarios of OFDM gradually becomes a performance bottleneck, causing the curve to show an "upward" trend—that is, the SINR growth slope slows down. Scheme ④ performs the worst, indicating that without IRS assistance, relying solely on direct links cannot effectively combat multi-cell interference and channel fading. Scheme ⑤ can still obtain some gain through precoding under random phase shift, but because the reflected signals cannot be coherently superimposed, the gain is significantly lower than that of the optimized Scheme ①. Scheme ⑥ performs worse than Scheme ① but better than Scheme ⑤, indicating that joint optimization of precoding and IRS phase shift can achieve greater performance gains than optimizing either variable alone, and that the two have a synergistic effect of mutual enhancement—precoding matches the channel direction, while IRS phase shift further enhances the equivalent channel strength.

[0037] Figure 6 Four schemes are presented, showing the target user SINR as a function of the number of IRS reflective elements. The change curve ( , , Scheme ① is the dual IRS-OTFS of this invention, Scheme ② is the single IRS-OTFS (only retaining the common IRS), Scheme ③ is the dual IRS-OFDM, and Scheme ④ is the dual IRS-OTFS. Figure 6 It can be observed that the SINR of all schemes increases with... The SINR increases with the increase in [something], but the growth rates differ significantly. Scheme ① exhibits an approximately quadratic growth in SINR (the gain increases with [something]). The increase is proportional to the signal strength (i.e., the gain is proportional to the signal strength), reflecting the array gain brought about by the coherent superposition of reflected signals after IRS phase shift optimization. The growth rate of Scheme ② is significantly lower than that of Scheme ① because a single IRS can only provide one reflection link, and its ability to suppress interference and enhance signals is weaker than that of a dual IRS architecture. Scheme ③... When the value is smaller, it is close to scheme ①, but when As the number of IRS units increases, the sensitivity of OFDM to Doppler frequency offset leads to the accumulation of inter-carrier interference, causing the SINR growth rate to gradually saturate and reach a performance ceiling. Scheme ④ exhibits only linear SINR growth because random phase shifts cannot achieve coherent superposition of reflected signals, rendering the array gain essentially ineffective. These results fully verify that the dual IRS-OTFS scheme of this invention can fully utilize the advantages of large-scale array gain when the number of IRS units increases.

[0038] Figure 7 Four schemes are given, with target user SINR varying with the number of users per cell. The change curve ( , , Scheme ① is the dual IRS-OTFS of this invention, Scheme ② is a single IRS-OTFS (only retaining the common IRS), Scheme ③ is a dual IRS-OTFS (without interference cancellation, i.e., only optimizing the target user precoding, not the interfering user), and Scheme ④ is a dual IRS-OTFS (IRS phase shift randomly set). Figure 7 It can be observed that as the number of users per community increases... With the increase in the number of users, the SINR of all schemes showed a downward trend. This is because the increase in the number of users led to a simultaneous increase in intra-cell interference and inter-cell interference. However, the decrease in scheme ① was the most gradual. The SINR decrease was smallest when increasing from 2 to 8, fully demonstrating the robustness of the proposed scheme in multi-user interference environments. Scheme ② showed a significantly faster decrease rate than Scheme ①, attributed to the insufficient spatial degrees of freedom of a single IRS—it cannot simultaneously provide sufficient signal enhancement for the target user and effectively suppress interfering users. Scheme ③ exhibited the most severe performance degradation because, without precoding optimization for interfering users, the uplink signals of each user would interfere with each other, limiting the performance gain of multi-user scheduling. Scheme ④ consistently maintained the lowest SINR level with a large decrease slope, indicating that random phase shift not only fails to enhance the desired signal but may also exacerbate interference due to incoherent scattering. These results demonstrate that the method of this invention, through joint control of dual IRSs and collaborative optimization of precoding for all users, can effectively suppress multi-user interference, making it particularly suitable for densely populated communication scenarios.

[0039] Figure 8 Three schemes are given, showing the target user SINR varying with the number of cells. The change curve ( , , Scheme ① is the invented dual IRS-OTFS, Scheme ② is a single IRS-OTFS (only retaining the dedicated IRS), and Scheme ③ is a dual IRS-OTFS (without inter-cell interference coordination, i.e., the phase shift of the common IRS is only optimized for this cell, ignoring the impact on other cells). From Figure 8 It can be observed that as the number of cells increases... C With the increase of [missing information], the SINR of all schemes showed a downward trend, which is an inevitable result of the accumulation of inter-cell interference. However, the decrease in scheme ① was the slowest. During the increase from 2 to 7, the SINR only decreased by about 3.5 dB, far less than the 7 dB in Scheme ② and the 9 dB in Scheme ③. This indicates that the common IRS in the dual IRS architecture of this invention can effectively coordinate interference between multiple cells. By rationally designing the phase shift matrix of the common IRS, the reflected signals form constructive superposition at the target base station and destructive interference at adjacent base stations, thereby suppressing inter-cell interference. Scheme ② lacks a common IRS, and the dedicated IRSs of each cell cannot work together, resulting in a sharp increase in inter-cell interference as the number of cells increases. Although Scheme ③ deploys a common IRS, it only considers the channel state information (CSI) of its own cell for local optimization, ignoring the impact of the common IRS on other cells. Therefore, its interference suppression capability is significantly insufficient in high-density networking. The above results verify that the method of this invention has good scalability in ultra-dense network (UDN) scenarios.

[0040] Figure 9 The target user SINR variation curves with maximum Doppler frequency shift for three schemes are given. , , , Scheme ① is the dual IRS-OTFS of this invention, Scheme ② is the dual IRS-OFDM, and Scheme ③ is the single IRS-OTFS. From Figure 9 It can be observed that in low-speed scenarios (Doppler shift < 200 Hz), the performance difference among the three schemes is not significant, with scheme ① slightly outperforming scheme ②. As the Doppler shift increases to above 500 Hz, the SINR of scheme ② (OFDM) drops sharply. This is because OFDM severely disrupts the orthogonality between subcarriers, and the ICI power increases with the square of the Doppler shift. Schemes ① and ③, however, only show a slow decreasing trend in SINR. This is attributed to the fact that when OTFS performs channel equalization in the DD domain, the time-varying channel is approximated as a sparse impulse response in the delay-Doppler domain, and channel changes are "frozen" within one frame, making it far less sensitive to time-varying channels than OFDM. Scheme ① consistently outperforms scheme ③, demonstrating that the spatial diversity gain provided by dual IRS through two independent reflection links in high-speed scenarios helps combat the time-selective fading of the channel. These results verify the applicability of the method of this invention in high-mobility scenarios (such as high-speed rail communication and UAV communication), which is precisely the core technical advantage of OTFS compared to traditional OFDM.

[0041] Figure 10 The BER versus SNR curves for five schemes are given. , , (QPSK modulation). Scheme ① is the dual IRS-OTFS of this invention, Scheme ② is a single IRS-OTFS, Scheme ③ is dual IRS-OFDM, Scheme ④ is no IRS-OTFS, and Scheme ⑤ is dual IRS-OTFS (random phase shift). From Figure 10 It can be observed that scheme ① achieves the lowest BER in all SNR ranges, reaching 10 dB at 10 dB. -4 It drops to 10 dB at 20 dB. -5 The following solutions show improvements of approximately two and one order of magnitude compared to solution ②, respectively, directly validating the effectiveness of the dual-IRS architecture and joint optimization in improving signal quality. The BER reduction slope of solution ② is significantly smaller than that of solution ①, attributed to its weaker interference suppression and signal enhancement capabilities compared to the dual-IRS architecture. Solution ③ performs similarly to solution ① in the low SNR region, but its BER plateaus in the high SNR region (>15 dB). This is because the residual ICI of OFDM in high Doppler scenarios becomes the dominant performance factor at high SNR, making it impossible to further reduce BER by increasing transmit power. Solution ④ has the highest BER across all SNR levels, maintaining approximately 10 dB even at 30 dB. -2 This indicates that without IRS assistance, direct links cannot overcome multi-cell interference and channel fading. The BER of scheme ⑤ is slightly lower than that of scheme ④, indicating that random phase shift can still provide a slight performance improvement through incoherent scattering, but it is far less than the optimized gain of scheme ①. The above results demonstrate that the method of this invention has significant advantages in reliability, and is particularly suitable for communication scenarios with stringent transmission quality requirements.

[0042] Therefore, this invention adopts the above-mentioned dual-IRS assisted OTFS multi-cell uplink joint optimization method, innovatively constructing a two-layer distributed collaborative architecture of global public IRS + cell-specific IRS. Relying on the DD domain, it completes accurate matrix modeling of the entire link including direct connection, single-pass, and bidirectional secondary reflection. It unifies the dual service quality constraints of rate and bit error rate through equivalent transformation, and designs a hierarchical alternating convex optimization solution framework combining AO with SDP / SDR and Charnes-Cooper transform. Compared with various comparative schemes such as existing single IRS, simplified dual IRS, OFDM matching, and single optimization algorithm, it can make full use of the multi-dimensional spatial control freedom of dual-layer IRS to efficiently suppress intra-cell and inter-cell superposition interference. It is suitable for high-Doppler high-speed communication scenarios such as high-speed rail and drones, and takes into account the transmission performance of edge users, algorithm convergence speed, large-scale array gain and multi-cell networking scalability. At the same time, it has complete mathematical theoretical support and engineering feasibility, and comprehensively solves the inherent defects of existing technical architecture, modeling, optimization, algorithm, and scenario adaptation.

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A dual IRS-assisted OTFS multi-cell uplink joint optimization method, characterized in that, Includes the following steps: S1. Construct a communication system for multi-cell uplink of dual IRS-assisted OTFS and establish a signal processing link at the user transmitter. S2. Establish an equivalent channel matrix including direct links, single-reflection links, and double-reflection links to obtain the received signal and signal-to-interference-plus-noise ratio; S3. Establish a joint optimization problem based on service quality constraints; S4. Transform the bit error rate constraint in the joint optimization problem into a SINR lower bound constraint, and merge it with the rate constraint into a SINR threshold constraint to obtain a simplified joint optimization problem. S5. Using an alternating optimization framework, the joint optimization problem is decomposed into three sub-problems: the precoding optimization sub-problem, the common IRS phase shift optimization sub-problem, and the dedicated IRS phase shift optimization sub-problem. The sub-problems are solved iteratively until convergence. S6. Output the optimal set of precoding matrices, the optimal common IRS phase shift matrix, and the optimal dedicated IRS phase shift matrix.

2. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 1, characterized in that, In S1: S11. Construct a communication system for dual IRS-assisted OTFS multi-cell uplink, the communication system including... Each cell is equipped with one base station. One user equipment and one dedicated IRS; the community base station, the Each user equipment and dedicated IRS is denoted as follows: , and , , , Indicates a collection of neighborhoods. Represents a set of user equipment; A public IRS is deployed throughout the entire network area of ​​the communication system, denoted as ; S12. The user equipment uses OTFS modulation to transmit uplink signals in the DD domain, and the communication system is built on the DD domain. Resource grid points, and These represent the time delay number and the Doppler number, respectively; let the subcarrier spacing be... The symbol interval is ,satisfy , and Each satisfies the delay resolution and Doppler resolution The bandwidth occupied by one frame of OTFS signal is All OTFS signal frame intervals are ; S13. Establish user transmitter signal processing link: User equipment The DD domain signal matrix is , Represent a M OK N The column matrix is ​​processed by ISFFT to obtain the TF domain signal and converted into matrix form. The time domain transmission signal is then obtained by Heisenberg transform. The parallel-to-serial conversion and precoding are performed sequentially to generate the transmitted signal. ISFFT is the symplectic finite Fourier inverse transform, and TF is the time frequency. Matrix form of TF domain signals for: ； In the formula, and They represent M The matrix form of the discrete Fourier transform and N The matrix form of the discrete Fourier inverse transform.

3. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 2, characterized in that, In S2: S21, Settings and These are the delay matrix and the Doppler matrix, respectively. S22, Change the common IRS phase shift matrix and dedicated IRS phase shift matrix Extending to the OTFS signal processing dimension, we obtain the extended common IRS phase shift matrix. and the extended dedicated IRS phase shift matrix ; S23. Divide the transmission link types into direct links, single-reflection links, and double-reflection links, and construct the channel matrix for each transmission link type in the DD domain; The direct link channel matrix is , Indicates the community Medium user equipment Channel matrix to base station, Indicates the user equipment sequence. ; Represents the cell sequence. ; Indicates a base station; Single-reflection links are divided into two types: those via a common IRS and those via a dedicated IRS. The channel matrices for the two types of single-reflection links are as follows: and , Represents user equipment in any cell After being reflected by the public IRS, it reaches the community. Synthetic channel matrix of the base station Indicates the community Medium user equipment The synthesized channel matrix of the base station in the same cell after reflection through the dedicated IRS; Subscript abbreviations indicating public IRS; Subscript abbreviation indicating a dedicated IRS; Two-reflection links are divided into two types: those that pass through a dedicated IRS and a public IRS sequentially, and those that pass through a public IRS and a dedicated IRS sequentially. The channel matrices for the two types of two-reflection links are as follows: and , Indicates the community Medium user equipment The synthesized channel matrix first passes through a dedicated IRS and then through a public RIS before reaching the base station in the same cell. Represents user equipment in any cell First reflected by the public IRS, then reflected by the dedicated IRS, before reaching the residential area. Synthetic channel matrix of the base station; S24. Superimpose the channel matrices of all transmission link types to obtain the equivalent channel matrix, expressed as: ； In the formula, Indicates user equipment in multiple cells Arrive at the community The channel matrix synthesized from all links of the base station; Indicates from Arrive at the community Channel matrix of the base station; Indicates public IRS; Indicates the community Medium user equipment arrive The channel matrix; express Channel matrix to base station; Indicates the community Dedicated IRS in China; Indicates the community Medium user equipment arrive The channel matrix; express arrive The channel matrix; Indicates the community Dedicated IRS in China; express arrive The channel matrix; Subscript abbreviations indicating public IRS; Subscript abbreviation indicating a dedicated IRS; S25. Generate cells based on the unified equivalent channel matrix. medium base station Received signal And the signal-to-interference-plus-noise ratio, the expressions are as follows: ； ； In the formula, Indicates the community Medium user equipment The channel matrix; Indicates the community Medium user equipment The signal precoding matrix; Indicates the community Medium user equipment The signal; Indicates the community Medium user equipment The channel matrix; Indicates the community Medium user equipment The signal precoding matrix; Indicates the community Medium user equipment The signal; Indicates the community Medium user equipment The signal precoding matrix; Indicates the community Medium user equipment The signal; Indicates noise; Indicates the community Medium user equipment The signal-to-noise ratio of the received signal; Indicates the community Medium user equipment The noise power in the received signal.

4. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 3, characterized in that, In S3: By taking maximizing the signal-to-interference-plus-noise ratio (SIR) of the target user equipment as the optimization objective, and based on service quality constraints, a joint optimization problem is obtained. Service quality constraints include rate constraints. Bit error rate constraints Precoding power constraints Public IRS unit module constraints and dedicated IRS unit module constraints ; The expressions for the joint optimization problem and service quality constraints are as follows: ； ； ； ； ； ； ； In the formula, Indicates the community Medium user equipment The set of precoding matrices for the emitted signal; Represents the minimum value of the rate; Indicates any one that is different from The neighborhood; Indicates any one that is different from User equipment; Indicates the community Medium user equipment Arrive at the community Channel matrix of the base station; Indicates the community Medium user equipment The signal precoding matrix; This represents the minimum bit error rate; This represents the maximum power of the signal precoding matrix; express Phase shift; express The reflective unit in the middle; express Phase shift; express The reflective unit in the middle; Indicates the community Medium user equipment The bit error rate; This represents the maximum bit error rate; Represents the coefficients of the rectangular QAM; Represents the Gaussian Q-function; Indicates the scaling factor; The instantaneous SINR of the received signal satisfies: 。 5. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 4, characterized in that, In S4: S41. Constrain the bit error rate Transformed into a linear SINR lower bound constraint and will and Merged into SINR threshold constraints , and The expressions are as follows: ； ； In the formula, express The minimum value; S42, SINR-based threshold constraints The simplified joint optimization problem is obtained. The expression is: ； 。 6. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 5, characterized in that, In S5: S51. Variable Initialization: Initialize the common IRS phase shift matrix that satisfies the unity modulus constraint. and dedicated IRS phase shift matrix Set the iteration index Maximum number of iterations and convergence accuracy ; S52. Enter the main loop and set the iteration index. Increase by 1, and execute the three optimization stages S53-S55 sequentially until the convergence condition in S56 is met. S53, Optimization Phase 1: Perform the precoding optimization subproblem and output... ; express The Round iteration value; S54. Optimization Phase Two: Execute the common IRS phase shift optimization subproblem and output... , express The Round iteration value; S55, Optimization Phase Three: Execute the dedicated IRS phase shift optimization subproblem, and output... , express The Round iteration value; S56, based on the first Variables after round update , , Calculate the first Total speed of wheels If the convergence condition is met or If the iteration terminates, return to S52 to begin a new iteration.

7. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 6, characterized in that, In S53: S531, take the results from the previous round and Substitute into the equivalent channel matrix A fixed value is obtained; and These are the common IRS phase shift matrix and the dedicated IRS phase shift matrix from the previous round, respectively; for the simplified joint optimization problem, the fixed... and Optimize the precoding matrix to obtain the precoding optimization subproblem. The expression is: ； S532, Introducing semidefinite constraints Relax the non-convex rank-one constraints ,reserve ;according to Properties and Properties, and Representing the trace and vectorization of the matrix respectively, the numerator and denominator of the pre-encoded optimization subproblem are transformed into linear vector inner product form, yielding the relaxation problem. The expression is: ； ； ； ； ； ； In the formula, , and They represent , and traces; , , and They represent , , and Vectorization; express Transpose of; express Transpose of; Represents the signal precoding matrix One received MN A positive semi-definite matrix of order 1; Represents the signal precoding matrix One received MN A positive semi-definite matrix of order 1; It is the transpose symbol; , , , and They represent , , , and transpose, Indicates will A vector after vectorization Indicates to A vector after adjustment Indicates to A vector after adjustment Indicates to A vector after adjustment Indicates to A vector after adjustment; Indicate a scripture or The adjusted vector; Indicates the community Medium user equipment The noise power in the received signal; S533, Charnes-Cooper Transform: Introducing Auxiliary Variables ,satisfy and Through identity The linear fractional programming problem is equivalently transformed into the standard semidefinite programming (SDP) problem. ; ； In the formula, This represents a vector obtained by linear transformation of x; S534, Solve To obtain the optimal value , and Represent y and t The optimal value; S535, from Extract ,make For each Applying the rank-one constraint yields Thus obtain ; and They represent and The optimal value, Indicates to The matrix after linear transformation; express The Round iteration value.

8. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 7, characterized in that, In S54: S541, Fixed and The common IRS phase shift optimization subproblem is obtained. The equivalent channel matrix Explicitly split into AND Irrelevant fixed parts and the phase shift vector of the common IRS The relevant linear part, then ,in express The number of reflective units in the middle, express phase shift, Indicates the corresponding number A fixed matrix obtained by multiplying the cascaded channels of a reflection unit; ； ； S542, will Both the numerator and denominator are expanded into terms related to The quadratic forms are expressed as follows: ； ； In the formula, Indicates a by L The phase shift vector formed by a single reflecting unit; express Transpose of; Indicates taking the real part; and Each represents a configuration or The Hermitian positive semidefinite matrix; and They represent and one of the L 1-dimensional vector; and Each represents a configuration or real numbers; S543, Introduction and The results of S542 are transformed. Indicates by One received Augmented vectors of dimension, Indicates by One received L The augmented matrix of order 1+1 is obtained as follows: ； ； In the formula, and They represent respectively by and And one L An augmented matrix of order 1+1; S544, Introducing an auxiliary variable 1 ,satisfy and , Let a positive semi-definite matrix represent the common IRS phase shift optimization subproblem. Transformed into a standard SDP problem for common IRS phase shift optimization The expression is: ； ； ； In the formula, and They represent respectively by and And one L An augmented matrix of order 1+1; S545 Solving the Standard SDP Problem To obtain the optimal value , and Representing Y and t The optimal value of 1; S546, Calculation , This represents the optimal value of X, for Perform eigenvalue decomposition and extract the eigenvector corresponding to the largest eigenvalue. ,extract The former Each element constitutes a L 1-dimensional vector Through phase projection Restore the unit modulus constraint. express The Middle Phase shift of each element, update the common IRS matrix. , Indicates taking the secondary angle. This indicates that the vector is converted into a diagonal matrix. express The Round iteration value, Represent a MN An identity matrix of order 1.

9. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 8, characterized in that, In S55: S551, Fixed and This yields a dedicated IRS phase shift optimization subproblem. ; S552, Simplified Joint Optimization Problem Both the numerator and denominator are expanded into terms related to The quadratic form, Represent a L 2-dimensional vector; S553, Introduction and Transform the results of S552. Indicates by One received L 2+1 dimensional augmented vector, Indicates by One received L An augmented matrix of order 2+1; S554, Introducing Auxiliary Variable Two The dedicated IRS phase shift optimization subproblem is transformed into a standard SDP problem for dedicated IRS phase shift optimization. ; S555 Solving the Standard SDP Problem To obtain the optimal value , and They represent and t The optimal value of 2; S556, Calculation , express The optimal value, for Perform eigenvalue decomposition and extract the eigenvector corresponding to the largest eigenvalue. ,extract The former Each element constitutes a L 2D vector Through phase projection Restore the unit modulus constraint. express The Middle The phase shift of each element updates the dedicated IRS matrix. , and They represent and The Round iteration value.

10. The dual IRS-assisted OTFS multi-cell uplink joint optimization method according to claim 9, characterized in that, In S6: After terminating the iteration, based on the... The optimal precoding matrix set is output after each round of variable updates. Optimal common IRS phase shift matrix and the optimal dedicated IRS phase shift matrix , , , .

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