A SOR-PCG-based LMMSE detection method and a signal detection module

Abstract

This invention relates to wireless communication signal detection technology, and discloses an LMMSE detection method and signal detection module based on SOR-PCG. The method divides the OTSM frame signal into multiple time-domain blocks, constructs a coefficient matrix and constant term vector for each time-domain block, and transforms LMMSE detection into solving a system of linear equations. The range of operations for non-zero elements is limited based on the striped sparse structure of the coefficient matrix. A SOR-based preprocessing matrix is ​​constructed, and preprocessing is completed through forward and backward recursion. The PCG algorithm is used to solve the linear equations, updating the solution and residuals according to the step size factor, and updating the search direction according to the search direction factor. When the maximum number of iterations is reached or the residuals are within the tolerance range, iteration stops, and the final solution is output, thus obtaining the transmitted symbol vector estimate for each time-domain block. This method reduces the computational complexity of direct matrix inversion and reduces storage space, making it suitable for signal detection in OTSM receivers.

Description

Technical Field

[0001] This invention belongs to the field of signal detection, specifically relating to an LMMSE detection method and signal detection module based on SOR-PCG. Background Technology

[0002] Future wireless communications need to deliver reliable transmission in high-speed mobile scenarios such as low-Earth orbit satellites, high-speed trains, and drones. Traditional Orthogonal Frequency Division Multiplexing (OFDM) is susceptible to severe inter-carrier interference in high-speed mobile scenarios, making it difficult to meet the requirements. While Orthogonal Time Frequency Space (OTFS) can effectively combat dual-selection channels, its transceiver modulation complexity is high. Orthogonal Time-Sequence Multiplexing (OTSM), on the other hand, maps information symbols to the delay-sequence domain, enabling the system to maintain near-OTFS performance while significantly reducing modulation complexity, providing a low-complexity solution for high-mobility wireless communications.

[0003] Currently, the Linear Minimum Mean Square Error (LMMSE) detection method is widely used in high-mobility wireless communication signal detection due to its strong anti-interference capability. However, traditional LMMSE detection methods require direct inversion of the coefficient matrix, resulting in high computational complexity. Existing research often uses LU decomposition to replace direct inversion, but its computational complexity still increases cubically with the matrix dimension, making it difficult to meet the requirements of future large-scale wireless communication systems for low complexity and low latency. Existing research has found that since the coefficient matrix of LMMSE detection has symmetric positive definite properties, the transmitted signal can be solved iteratively using the conjugate gradient (CG); however, when the condition number of the coefficient matrix is ​​large, the convergence speed of CG is slow, requiring multiple iterations to achieve successful demodulation.

[0004] In view of this, the present invention is hereby proposed. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and propose an LMMSE detection method and signal detection module based on SOR-PCG. By performing SOR preprocessing on the coefficient matrix, the condition number of the processed matrix is ​​reduced, thereby accelerating the convergence speed of the CG algorithm while ensuring detection performance.

[0006] On the one hand, see Figure 8 This invention provides a method for detecting LMMSE based on SOR-PCG, comprising: Step 1: Divide the OTSM frame signal into multiple time-domain blocks and construct a coefficient matrix for each time-domain block. and constant term vector The LMMSE detection is transformed into solving a system of linear equations; Step 2: Based on the coefficient matrix The banded sparse structure limits the range of operations for non-zero elements; Step 3: Construct a SOR-based preprocessing matrix ; Step 4: Solve the linear equation system using the PCG algorithm, adjusting the step size factor during the iteration process. Update the solution, residuals, and based on the search direction factor. Update the search direction, and stop iterating when the maximum number of iterations is reached or the residual is within the tolerance range. Output the final solution, which is the estimated value of the transmitted symbol vector for each time domain block.

[0007] Furthermore, step 1 specifically includes: Step 1.1: Divide the OTSM frame signal into... N There are 1 time-domain block, each time-domain block having a length of 1 M The total frame length is For the first n There are 10 time-domain blocks, of which Within the current time block, the channel is treated as a quasi-static channel, and a time-domain input-output relationship is established: Formula (1) In formula (1), the meanings of each parameter are as follows: This represents the channel matrix of the nth time-domain block; This represents the received signal vector of the nth time-domain block; This represents the transmit symbol vector of the nth time-domain block; This represents the Gaussian white noise vector of the nth time-domain block; Step 1.2: Based on the sparse banded characteristics of the time-domain channel matrix, construct a constant term vector. sum coefficient matrix : Formula (2) Formula (3) In formula (3), the meanings of each parameter are as follows: Indicates the noise variance; Represents the identity matrix; Step 1.3: Transform the LMMSE detection into solving a system of linear equations: Formula (4) In formula (4), This represents the estimated value of the transmitted symbol vector.

[0008] Furthermore, based on the coefficient matrix The striped sparse structure determines the set of column indices for non-zero elements in each row, and during matrix generation, matrix multiplication, and vector update, operations are performed only on the non-zero elements in the set of column indices.

[0009] Furthermore, the coefficient matrix Let be a banded matrix; The half bandwidth is Then its bandwidth is And for any matrix element Satisfy: When hour, .

[0010] Furthermore, for the coefficient matrix The Rows, the set of column indices of their non-zero elements for: Formula (5).

[0011] Furthermore, step 3 specifically includes: Step 3.1: First, construct a diagonal matrix. : Formula (6) In formula (6), the meanings of each parameter are as follows: Denotes the relaxation factor, and satisfies ; Represents any matrix element; Represents a diagonal matrix child elements; Step 3.2, let Coefficient matrix The strictly upper triangular matrix is ​​constructed as follows: Formula (7) In formula (7), It is an upper triangular matrix. Its child elements; Step 3.3: Obtain the preprocessing matrix : Formula (8) Combined with preprocessing equations Substituting formula (8) into the equation, we get: Formula (9) In formula (9), the meanings of each parameter are as follows: This represents the residual after preprocessing; r represents the residual; The solution process of the above formula (9) is decomposed into two steps of solving trigonometric equations: forward recursion and backward recursion. First, solve the trigonometric equations to get : Formula (10) Solve the upper trigonometric equation to get : Formula (11) In formulas (10) and (11), Indicates the intermediate vector; Forward recursion solution and backward recursion solution They are represented as follows: Formula (12) Formula (13) In formula (12), Indicates from 1 to ; In formula (13), Indicates from Up to 1.

[0012] Furthermore, step 4 specifically includes: make Calculate the initial residual Select the preprocessing matrix ,calculate Set the initial search direction And calculate the inner product of the initial residuals. At the same time, set the maximum number of iterations. With tolerance ; For the The next iteration ( First calculate And by utilizing a banded sparse structure, multiplication and addition operations are performed only on the elements within the set, i.e. Then calculate the step size factor. and update the solution vector. and residual vector ;when When the time is up, stop the iteration and output the current solution. If the convergence condition is not met, continue the calculation. Calculate the new residual inner product Calculate the search direction factor , and according to Update the search direction; repeat the above detection for all time-domain blocks to obtain the detection output of the OTSM frame signal.

[0013] Furthermore, during the PCG iteration process, the calculation Only for sets Perform multiplication and addition operations on the elements within.

[0014] Furthermore, the termination condition of the PCG algorithm includes the residual satisfying Or when the maximum number of iterations is reached. When the time comes, output the solution.

[0015] Furthermore, the relaxation factor The value range is from 1.0 to 1.4.

[0016] On the other hand, the present invention also provides a signal detection module in an OTSM receiver, which applies the LMMSE detection method described above in part or in whole. The signal detection module includes a block buffer unit, a channel matrix generation unit, a sparse coefficient matrix construction unit, a SOR preprocessing unit, a PCG iteration unit, a convergence decision unit, and a result output unit; wherein: The block buffer unit is used to buffer the time-domain block received signal vector. ; The channel matrix generation unit is used to generate a striped sparse time-domain channel matrix based on the channel estimation results corresponding to the current time-domain block. ; The sparse coefficient matrix construction unit is used to construct the unit based on Generate a striped sparse coefficient matrix vector of constant terms ; The SOR preprocessing unit is used to process the coefficient matrix. Construct a diagonal matrix Upper triangular matrix and preprocessing matrix And complete it using forward and backward recursion. Solving for; The PCG iteration unit is used to determine the step size factor. Update the solution, residuals, and based on the search direction factor. Update search direction; The convergence decision unit is used to determine whether to terminate the iteration based on the termination condition; The result output unit is used to output the detection results. .

[0017] Furthermore, matrix multiplication and trigonometric equation solving are performed only on the non-zero region of the strip to reduce the number of multiplications and additions and storage space; the PCG iterative method only requires a small number of iterations to complete signal detection, and its iterative process can be implemented in a single-loop pipeline mode; the overall computational load is small, the storage space is small, and the pipeline does not require complex control, thus facilitating simple implementation on FPGA.

[0018] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects: 1. The LMMSE detection based on each time-domain block is transformed into solving a system of linear equations and using the PCG algorithm with SOR preprocessing instead of direct matrix inversion. Utilizing the banded sparsity of the time-domain channel matrix and the coefficient matrix constructed from it, operations are performed only on the non-zero regions of the banded matrix during matrix generation, matrix multiplication, preprocessing, and vector updating, which helps reduce the number of multiplications and additions and storage space. Under typical system parameters, the SOR-PCG-based LMMSE detection method can typically approximate the detection performance of direct inverted LMMSE within approximately two iterations, reducing computational complexity. Furthermore, the computational complexity of the SOR-PCG-based LMMSE detection method is reduced by 50% compared to the CG-based LMMSE detection method (requiring 7 iterations), and compared to the LU decomposition-based LMMSE detection method, the computational complexity is reduced from cubic to quadratic. 2. Extensive simulations have verified that, under common modulation schemes and typical channel conditions, this invention can maintain a bit error rate performance close to that of direct inverse LMMSE detection while reducing complexity, without performance loss, thus ensuring the communication quality of the OTSM system. 3. The structure design is optimized to address the characteristic of the OTSM channel matrix having a strip-shaped sparse structure, which significantly reduces the computational load of the algorithm. The PCG structure is simple and can be implemented using a single-loop pipeline and mapped to an FPGA. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the time-domain channel model of an OTSM system. Figure 2 A comparison of condition numbers for different relaxation factors in the SOR-PCG algorithm; Figure 3 A comparison of BER (Benefit Result) for different relaxation factors in the SOR-PCG algorithm; Figure 4 This is a performance comparison chart of different detection algorithms; Figure 5The BER performance of the SOR-PCG algorithm and the direct inversion algorithm under BPSK and 4QAM modulation schemes; Figure 6 In order to be in , BER performance of SOR-PCG algorithm and direct inversion algorithm under different conditions; Figure 7 The BER performance of the SOR-PCG algorithm and the direct inversion algorithm under different Doppler frequency shifts; Figure 8 This is a flowchart of an LMMSE detection method based on SOR-PCG. Detailed Implementation

[0020] Exemplary embodiments will now be described in detail. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples consistent with some aspects of the invention as detailed in the appended claims.

[0021] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0022] Example 1: Example of LMMSE detection method For a SOR-PCG-based LMMSE detection method, this embodiment takes the signal detection module in an OTSM receiver as an example, combined with... Figure 1 Step-by-step instructions: Step 1: Divide the OTSM frame signal into multiple time-domain blocks and construct a coefficient matrix for each time-domain block. and constant term vector The LMMSE detection is transformed into solving a system of linear equations; Specifically, step 1 includes: Step 1.1: Divide the OTSM frame signal into... N There are 1 time-domain block, each time-domain block having a length of 1 M The total frame length is For the first n There are 10 time-domain blocks, of which Within the current time block, the channel is treated as a quasi-static channel, and a time-domain input-output relationship is established: Formula (1) In formula (1), the meanings of each parameter are as follows: This represents the channel matrix of the nth time-domain block; This represents the received signal vector of the nth time-domain block; This represents the transmit symbol vector of the nth time-domain block; This represents the Gaussian white noise vector of the nth time-domain block; Step 1.2: Based on the sparse banded characteristics of the time-domain channel matrix, construct a constant term vector. sum coefficient matrix : Formula (2) Formula (3) In formula (3), the meanings of each parameter are as follows: Indicates the noise variance; Represents the identity matrix; Step 1.3: Transform the LMMSE detection into solving a system of linear equations: Formula (4) In formula (4), This represents the estimated value of the transmitted symbol vector.

[0023] Step 2: Based on the coefficient matrix The banded sparse structure limits the range of operations for non-zero elements; Due to the time-domain channel matrix It has sparse banded properties, and the coefficient matrix constructed from it Also a striped matrix; let... The half bandwidth is ,but The bandwidth is And for any matrix element ,when hour, For the coefficient matrix The A row, whose set of non-zero element column indices can be represented as: Formula (5).

[0024] Therefore, in the processes of matrix generation, matrix multiplication, and vector update, only non-zero elements within the set are operated on, thereby reducing the computational complexity of LMMSE detection.

[0025] Step 3: To avoid modifying the coefficient matrix Direct inversion: This embodiment uses the PCG algorithm based on SOR preprocessing to solve the linear equation system. The preprocessing matrix... The construction method is as follows: Step 3.1: First, construct a diagonal matrix. : Formula (6) In formula (6), the meanings of each parameter are as follows: Denotes the relaxation factor, and satisfies ; Represents any matrix element; Represents a diagonal matrix child elements; Step 3.2, let Coefficient matrix The strictly upper triangular matrix is ​​constructed as follows: Formula (7) In formula (7), It is an upper triangular matrix. Its child elements; Step 3.3: Obtain the preprocessing matrix : Preprocessing matrix : Formula (8) Combined with preprocessing equations Substituting formula (7) into the equation, we get: Formula (9) In formula (9), the meanings of each parameter are as follows: This represents the residual after preprocessing; r represents the residual; The solution process of the above formula (9) is decomposed into two steps of solving trigonometric equations: forward recursion and backward recursion. First, solve the trigonometric equations to get : Formula (10) Solve the upper trigonometric equation to get : Formula (11) In formulas (10) and (11), Indicates the intermediate vector; Forward recursion solution and backward recursion solution They are represented as follows: Formula (12) Formula (13) In formula (12), Indicates from 1 to ; In formula (13), Indicates from Up to 1.

[0026] Step 4: When solving the linear equation system using the PCG algorithm, the following steps can be performed: Step 4.1, Initialization: Let Calculate the initial residual Select the above preprocessing matrix ,calculate Set the initial search direction Calculate the inner product of the initial residuals At the same time, set the maximum number of iterations. With tolerance ; Step 4.2, Perform iteration: For the first... The next iteration ( First calculate And by utilizing a banded sparse structure, multiplication and addition operations are performed only on the elements within the set, i.e. Then calculate the step size factor. and update the solution vector. and residual vector ; Step 4.3: Perform convergence judgment: when the following conditions are met... When the time is up, stop the iteration and output the current solution. As the first n The estimated transmitted symbols for each time-domain block are calculated; if the convergence condition is not met, the calculation continues. Calculate the new residual inner product ,calculate , and according to Update search direction; Step 4.4: Terminate the iteration and output the results: When the convergence condition is met during the iteration process, output the corresponding result. And terminate the iteration; when the maximum number of iterations is reached. If convergence is still not achieved, the final solution of the current iteration is output as the detection result. Steps 4.1 to 4.4 are repeated for all time-domain blocks to obtain the detection output of the OTSM frame signal.

[0027] In practical systems, the matrix half-bandwidth Typically much smaller , Therefore, the complexity expression can be approximated by the dominant term (ignoring the dominant term). (Approximate or minor terms), thus focusing on the impact of core parameters on complexity, and the complexity of different algorithms. , , Related, but since the complexity of each algorithm is similar to... They show a linear positive correlation. It can be considered a uniform "scale factor", therefore no analysis is required. The impact on complexity is also due to the matrix half-bandwidth. (make (where is a constant) and Strongly correlated, therefore the core parameters for complexity analysis can focus on .

[0028] The table below compares the computational complexity of the direct inversion algorithm, LU decomposition algorithm, CG algorithm, and SOR-PCG algorithm. The number of iterations in an iterative algorithm, and the complexity of LU decomposition. In cubic order, both the CG algorithm and the SOR-PCG algorithm are similar to... The complexity of LU decomposition is quadratic, and in large-scale systems, it grows the fastest. The larger the number of iterations, the more pronounced the difference in complexity becomes. The complexity of the CG algorithm and the SOR-PCG algorithm increases with the number of iterations. The increase shows a linear upward trend. Under the same number of iterations, the complexity of the SOR-PCG algorithm is higher than that of the CG algorithm due to the additional computation introduced by the SOR preprocessing. After a large number of simulations, the CG algorithm and the SOR-PCG algorithm require at least 7 and 2 iterations respectively, under the requirement of basically no loss in detection performance.

[0029] The SOR-PCG algorithm uses preprocessing techniques to improve the quality of the processed matrix. The condition number decreases. The condition number is defined as norm and The product of the norms of the inverses, i.e. . The larger the condition number, the more ill-conditioned the expression, and the worse its numerical stability; conversely, the larger the condition number, the worse the expression. The smaller the condition number, the better the numerical stability. However, the preprocessing matrix... In its construction, the relaxation factor Choosing the appropriate value is very difficult. Given a signal-to-noise ratio of 16dB and a iteration count of 2, It is 64. With a value of 32, different relaxation factors were obtained. A comparison of matrix condition number and bit error rate. Based on... Figure 2 and Figure 3 From different relaxation factors The comparison of the condition number and BER of the coefficient matrix shows that the CG algorithm does not undergo preprocessing, so the condition number and BER of the coefficient matrix remain at a high value. The condition number of the SOR-PCG algorithm increases with... The changes exhibit a U-shaped distribution, when When the condition number is in the range of 1.0 to 1.4, it drops to the lowest level, reflecting that the preprocessing matrix has the best effect on improving the ill-conditioning of the original matrix within this range. The bit error rate of SOR-PCG is also the lowest in this range. When it is less than 1.2, BER follows Increase rapidly and decrease when After exceeding 1.4, BER follows Increases sharply. Relaxant factor The value of the relaxation factor directly affects the numerical stability and bit error rate performance of SOR-PCG, so the relaxation factor should be selected in the range of 1.0 to 1.4.

[0030] Example 2: Signal Detection Module Example The above method can be used in the signal detection module of an OTSM receiver. This signal detection module includes a block buffer unit, a channel matrix generation unit, a sparse coefficient matrix construction unit, a SOR preprocessing unit, a PCG iteration unit, a convergence decision unit, and a result output unit; wherein: The block buffer unit is used to buffer the time-domain block received signal vector. ; The channel matrix generation unit is used to generate a striped sparse time-domain channel matrix based on the channel estimation results corresponding to the current time-domain block. ; The sparse coefficient matrix construction unit is used to construct the unit based on Generate a striped sparse coefficient matrix vector of constant terms ; The SOR preprocessing unit is used to process the coefficient matrix. Construct a diagonal matrix Upper triangular matrix and preprocessing matrix And complete it using forward and backward recursion. Solving for; The PCG iteration unit is used to determine the step size factor. Update the solution, residuals, and based on the search direction factor. Update search direction; The convergence decision unit is used to determine whether to terminate the iteration based on the termination condition; The result output unit is used to output the detection results. .

[0031] In hardware implementation, matrix multiplication and trigonometric equation solving are performed only on the strip of non-zero regions, thereby reducing the number of multiplications and additions and storage space. Since the data dependencies are clear in the PCG iteration process, a single-loop pipeline can be used for implementation and can be mapped to an FPGA for processing.

[0032] In Example 2, the system parameters can be set as follows: =32、 =64, modulation method is BPSK, carrier frequency is 4GHz, subcarrier spacing is 15kHz, channel model is EVA, user moving speed is 500km / h, relaxation factor Take 1.2, Figure 4 To compare the performance of different detection algorithms, for both CG and SOR-PCG algorithms, the more iterations, the better the BER performance, indicating that multiple iterations bring the algorithm closer to the optimal solution. At the same number of iterations, SOR-PCG performs better but has higher complexity; while preprocessing increases computation, it also accelerates convergence. In the BPSK modulation scenario, CG requires 7 iterations, achieving a BER performance (as the lower bound of LMMSE detection performance) that is essentially the same as the direct inversion LMMSE detection algorithm, with a computational complexity of 1.29e5. SOR-PCG, on the other hand, requires only 2 iterations, with a computational complexity of 0.57e5, half that of CG. The BER performance of both the LU decomposition algorithm and the SOR-PCG algorithm is essentially the same as that of the direct inversion algorithm. This shows that SOR-PCG achieves the same LMMSE performance with lower computational overhead. In summary, without compromising LMMSE detection performance, the SOR-PCG algorithm has lower complexity in large-scale scenarios, significantly reducing computational load.

[0033] Based on Table 2 above, such as Figure 5 As shown, the BER performance of the SOR-PCG algorithm and the direct inversion algorithm are compared under BPSK and 4QAM modulation schemes; Figure 6 As shown, in , The BER performance of the SOR-PCG algorithm and the direct inversion algorithm under different conditions; such as Figure 7 As shown, the BER performance of the SOR-PCG algorithm and the direct inversion algorithm are compared under different Doppler frequency shifts. It can be seen that the SOR-PCG algorithm only needs to iterate twice to achieve a bit error rate performance that is basically the same as that of the direct inversion algorithm in various typical communication scenarios such as different modulation methods, different system sizes and different time-varying channels.

[0034] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A SOR-PCG based LMMSE detection method, characterized in that, include: Step 1: Divide the OTSM frame signal into multiple time-domain blocks and construct a coefficient matrix for each time-domain block. and constant term vector The LMMSE detection is transformed into solving a system of linear equations; Step 2: Based on the coefficient matrix The banded sparse structure limits the range of operations for non-zero elements; Step 3: Construct a SOR-based preprocessing matrix ; Step 4: Solve the linear equation system using the PCG algorithm, during the iteration process. Based on step size factor Update the solution, residuals, and based on the search direction factor. Update the search direction, and stop iterating when the maximum number of iterations is reached or the residual is within the tolerance range. Output the final solution, which is the estimated value of the transmitted symbol vector for each time domain block.

2. The LMMSE detection method according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Divide the OTSM frame signal into... N There are 1 time-domain block, each time-domain block having a length of 1 M The total frame length is For the first n There are 10 time-domain blocks, of which Within the current time block, the channel is treated as a quasi-static channel, and a time-domain input-output relationship is established: Official (1) In formula (1), the meanings of each parameter are as follows: This represents the channel matrix of the nth time-domain block; This represents the received signal vector of the nth time-domain block; This represents the transmit symbol vector of the nth time-domain block; This represents the Gaussian white noise vector of the nth time-domain block; Step 1.2: Based on the sparse banded characteristics of the time-domain channel matrix, construct a constant term vector. sum coefficient matrix : Official (2) Official (3) In formula (3), the meanings of each parameter are as follows: Indicates the noise variance; Represents the identity matrix; Step 1.3: Transform the LMMSE detection into solving a system of linear equations: Official (4) In formula (4), This represents the estimated value of the transmitted symbol vector.

3. The LMMSE detection method according to claim 1, characterized in that, Based on the coefficient matrix The striped sparse structure determines the set of column indices for each row of non-zero elements, and during matrix generation, matrix multiplication, and vector update, operations are performed only on the non-zero elements within the set of column indices.

4. The LMMSE detection method according to claim 3, characterized in that, The coefficient matrix Let be a banded matrix; The half bandwidth is Then its bandwidth is And for any matrix element Satisfy: When hour, .

5. The LMMSE detection method according to claim 4, characterized in that, For the coefficient matrix The Rows, the set of column indices of their non-zero elements for: Official (5).

6. The LMMSE detection method according to claim 1, characterized in that, Step 3 specifically includes: Step 3.1: First, construct a diagonal matrix. : Official (6) In formula (6), the meanings of each parameter are as follows: Denotes the relaxation factor, and satisfies ; Represents any matrix element; Represents a diagonal matrix child elements; Step 3.2, let Coefficient matrix The strictly upper triangular matrix is ​​constructed as follows: Official (7) In formula (7), It is an upper triangular matrix. Its child elements; Step 3.3: Obtain the preprocessing matrix : Official (8) Combined with preprocessing equations Substituting formula (8) into the equation, we get: Official (9) In formula (9), the meanings of each parameter are as follows: This represents the residual after preprocessing; r represents the residual; The solution process of the above formula (9) is decomposed into two steps of solving trigonometric equations: forward recursion and backward recursion. First, solve the trigonometric equations to get : Official (10) Solve the upper trigonometric equation to get : Official (11) In formulas (10) and (11), Indicates the intermediate vector; Forward recursion solution and backward recursion solution They are represented as follows: Official (12) Official (13) In formula (12), Indicates from 1 to ; In formula (13), Indicates from Up to 1.

7. The LMMSE detection method according to claim 1, characterized in that, Step 4 specifically includes: make Calculate the initial residual Select the preprocessing matrix ,calculate Set the initial search direction And calculate the inner product of the initial residuals. At the same time, set the maximum number of iterations. With tolerance ; For the The next iteration ( First calculate And by utilizing a banded sparse structure, multiplication and addition operations are performed only on the elements within the set, i.e. Then calculate the step size factor. and update the solution vector. and residual vector ;when When the time is up, stop the iteration and output the current solution. If the convergence condition is not met, continue the calculation. Calculate the new residual inner product Calculate the search direction factor , and according to Update the search direction; repeat the above detection for all time-domain blocks to obtain the detection output of the OTSM frame signal.

8. A signal detection module in an OTSM receiver, characterized in that, The LMMSE detection method of any one of claims 1 to 7 is applied to the signal detection module, wherein the signal detection module includes a block buffer unit, a channel matrix generation unit, a sparse coefficient matrix construction unit, a SOR preprocessing unit, a PCG iteration unit, a convergence decision unit, and a result output unit; wherein: The block buffer unit is used to buffer the time-domain block received signal vector. ; The channel matrix generation unit is used to generate a striped sparse time-domain channel matrix based on the channel estimation results corresponding to the current time-domain block. ; The sparse coefficient matrix construction unit is used to construct the unit based on Generate a striped sparse coefficient matrix vector of constant terms ; The SOR preprocessing unit is used to process the coefficient matrix. Construct a diagonal matrix Upper triangular matrix and preprocessing matrix And complete it using forward and backward recursion. Solve for; The PCG iteration unit is used to determine the step size factor. Update the solution, residuals, and based on the search direction factor. Update search direction; The convergence decision unit is used to determine whether to terminate the iteration based on the termination condition; The result output unit is used to output the detection results. .

9. The signal detection module according to claim 8, characterized in that, Matrix multiplication and trigonometric equation solving are performed only on the non-zero region of the strip to reduce the number of multiplications and additions and storage space; the PCG iterative method requires only a few iterations to complete signal detection, and its iterative process can be implemented in a single-loop pipeline mode; the overall computational load is small, the storage space is small, and the pipeline does not require complex control, thus facilitating simple implementation on FPGA.

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