Intelligent Metasurface Array Beamforming Design Method Based on Orthogonal Time-Frequency-Space Technology

Abstract

A beamforming design method for intelligent metasurface arrays based on orthogonal time-frequency-space technology includes: aggregating multipath channels under direct illumination into cascaded channels with near-field direction vectors; randomly initializing the phase shift of intelligent metasurface units; establishing an effective channel matrix based on the cascaded channels; then establishing a multi-user and rate objective function; maximizing the objective function through phase shift optimization using a hierarchical search strategy; repeatedly executing the hierarchical search strategy to search and optimize subsequent blocks until the number of intelligent metasurface units in each block reaches a preset value; then performing an exhaustive search in the final block, thus completing one iteration; repeating the iteration until the maximum number of iterations is reached; outputting the final optimal phase shift; and implementing beamforming design based on the final optimal phase shift. This invention can reduce the complexity of beamforming design and ensure reliable transmission of high capacity during high-speed movement.

Description

Technical Field

[0001] This invention relates to the field of wireless communication network technology, and more specifically to a smart metasurface array beamforming design method based on orthogonal time-frequency-space technology. Background Technology

[0002] In the context of 6G millimeter-wave and terahertz communication, the high-speed mobility of scenarios such as drones presents both core challenges and opportunities. The millimeter-wave band enables ultra-high-capacity transmission and is fundamental for massive sensor data exchange and real-time ultra-high-definition image transmission. However, the drastic Doppler shift and rapid channel changes caused by high-speed movement severely impact the reliability of millimeter-wave narrow-beam links.

[0003] Current communication systems based on Long Term Evolution (LTE) technology rely on Orthogonal Frequency Division Multiplexing (OFDM). In high-speed mobile scenarios, Doppler frequency shift interference and obstacle blockage make beam alignment difficult, significantly degrading the quality of received signals, especially in millimeter-wave environments. As communication frequency bands continue to increase, these problems will become increasingly prominent. The emergence of Orthogonal Time-Frequency Spacetime (OTFS) and Ultra-Large-Scale Intelligent Metasurfaces (XL-RIS) technologies offers new possibilities for solving these problems. OTFS technology, by transmitting symbols in the time-delay Doppler domain and fully utilizing the full diversity gain, effectively suppresses Doppler frequency shift interference, achieving reliable and stable communication. The introduction of XL-RIS enables a larger near-field range at a lower cost. Simultaneously, by flexibly adjusting cell phase shifts, it increases the system's optimization freedom and raises the upper limit of system performance, allowing for precise beam control and enabling subsequent system designs to achieve greater performance improvements in the near field.

[0004] However, most existing technologies combine orthogonal time-frequency space with intelligent metasurfaces (RIS). This combination only considers the difference in far-field direction vectors. But XL-RIS combined with millimeter waves can generate a sufficiently large near-field range. If existing combination technologies are used, it will lead to performance loss. In addition, although the introduction of XL-RIS can effectively utilize the characteristics of high-frequency signal and large aperture array to enable a larger near-field range, thereby obtaining greater near-field gain and ensuring the reliability of high-frequency communication transmission in high-speed mobile scenarios, it also brings complex high-dimensional phase shift optimization problems, increases the complexity of beamforming design, and makes it difficult to guarantee reliable transmission of large capacity in high-speed mobile scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a smart metasurface array beamforming design method based on orthogonal time-frequency-space technology, so as to reduce the complexity of beamforming design and ensure reliable transmission of large capacity during high-speed movement.

[0006] A smart metasurface array beamforming design method based on orthogonal time-frequency-space technology includes:

[0007] Step S1: Under the premise that the base station and the user conduct downlink communication through the deployed smart metasurface array, the information symbols are modulated using orthogonal time-frequency space technology, the transmitted information is mapped to the time-delay Doppler domain, and then the transmitted information is modulated to the time domain using inverse sine Fourier transform and Heisenberg transform. The multipath channels under direct illumination are aggregated into cascaded channels with near-field direction vectors so that the time-domain transmitted information can be transmitted through the cascaded channels. The phase shift of each smart metasurface unit in the smart metasurface array is randomly initialized.

[0008] Step S2: The randomly initialized phase shift from Step S1 is used as the initial phase shift. An effective channel matrix is ​​established based on the cascaded channels. Then, a multi-user and rate objective function is established based on the effective channel matrix. The objective function is maximized through phase shift optimization. A layered search strategy to improve search accuracy is used for phase shift optimization. First, several adjacent smart metasurface units in the smart metasurface array are divided into a first-level block. The same phase shift is used within each first-level block. The lowest quantization bit phase shift is used to sequentially traverse each first-level block, locking the phase shift optimization direction and recording the current optimal phase shift for each first-level block. Next, the smart metasurface units in each first-level block are divided into multiple second-level blocks. The same search strategy as in the first-level blocks is used, and the same phase shift is maintained within the second-level blocks. The smart metasurface units in the second-level blocks undergo further searching based on the current optimal phase shift of the first-level blocks, and the current optimal phase shift of the second-level blocks is recorded.

[0009] Step S3: Based on the current optimal phase shift of the secondary block, the hierarchical search strategy is repeatedly executed to search and optimize the subsequent blocks at each level until the number of intelligent metasurface units in each block after hierarchical division reaches a preset value. Then, an exhaustive search is performed in the last block to complete one iteration. The iteration is repeated until the maximum number of iterations is reached, and the final optimal phase shift is output. The beamforming design is then implemented based on the final optimal phase shift.

[0010] The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology provided by the present invention has the following beneficial effects:

[0011] 1. This invention employs orthogonal time-frequency-space technology for transmission symbol modulation and low-cost XL-RIS devices for phase shift control. This aggregates multipath channels in direct-light conditions into cascaded channels with near-field direction vectors, enabling communication to transition from the original far-field scenario to the current near-field scenario. This effectively transforms the adverse factors in high-frequency communications such as millimeter waves, such as the susceptibility of signal propagation to obstruction and the challenge of communication link reliability, into greater performance gains in the near-field scenario, reducing performance losses. Furthermore, the time-domain received signal is obtained based on the cascaded channels with near-field direction vectors, providing a foundation for the subsequent derivation of a reliable effective channel matrix.

[0012] 2. In existing technologies, beamforming design for near-field ultra-large-scale arrays presents certain challenges. Exhaustive search and traditional convex optimization methods face extremely high computational complexity during optimization. This invention employs a hierarchical search strategy for phase shift optimization. By combining coarse and fine search, it first quickly determines the main direction of phase shift optimization with relatively low phase shift quantization precision. Then, it continuously improves the precision of phase quantization, ultimately obtaining the optimal phase shift vector for beamforming design. This approach improves performance while reducing computational complexity, significantly lowering computational overhead and enabling better real-time response. The beamforming method provided by this invention can significantly improve the reliability of high-frequency communication in high-speed mobile scenarios, ensuring reliable transmission of large-capacity information. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology provided by the present invention. Detailed Implementation

[0014] To facilitate understanding of the present invention, a more complete description will be given below with reference to various embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0015] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0016] Please see Figure 1 The embodiments of the present invention provide a smart metasurface array beamforming design method based on orthogonal time-frequency-space technology, including steps S1-S3:

[0017] Step S1: Under the premise that the base station and the user conduct downlink communication through the deployed smart metasurface array, the information symbols are modulated using orthogonal time-frequency space technology, the transmitted information is mapped to the time-delay Doppler domain, and then the transmitted information is modulated to the time domain using inverse sine Fourier transform and Heisenberg transform. The multipath channels in the direct-light state are aggregated into cascaded channels with near-field direction vectors so that the time-domain transmitted information can be transmitted through the cascaded channels, and the phase shift of each smart metasurface unit in the smart metasurface array is randomly initialized.

[0018] In the downlink communication process between the base station and the user through the deployed smart metasurface array, the downlink communication is divided into two parts: the channel from the base station to the smart metasurface unit. And the channel from the smart metasurface unit to the user They respectively satisfy the following formulas:

[0019]

[0020]

[0021] in, This represents the channel from the base station to the smart metasurface unit. This represents the channel from the smart metasurface unit to the user. This represents the first term in the channel from the base station to the smart metasurface unit. Strip diameter gain, Indicates the first The time delay exponent corresponding to the stripe diameter after discretization by the time delay Doppler domain grid. Indicates the first The Doppler frequency shift index corresponding to the stripe diameter after time-delay Doppler domain grid discretization. This represents the number of channel diameters from the base station to the smart metasurface unit. Represents the impulse function. Represents the time delay variable. Represents the Doppler frequency shift variable. This represents the first [unit / level] in the channel from the smart metasurface unit to the user. Strip diameter gain, Indicates the first The time delay exponent corresponding to the stripe diameter after discretization by the time delay Doppler domain grid. Indicates the first The Doppler frequency shift index corresponding to the stripe diameter after time-delay Doppler domain grid discretization. This represents the number of channel diameters from the smart metasurface unit to the user. It is the near-field direction vector from the base station to the smart metasurface unit. It is the near-field direction vector from the intelligent metasurface unit to the user. and These represent the Cartesian coordinates at the base station and the user, respectively.

[0022] Specifically, concatenating the two channels above yields a concatenated channel, which satisfies the following equation:

[0023]

[0024]

[0025]

[0026]

[0027] in, Indicates a cascaded channel. It is the first channel from the base station to the intelligent metasurface unit. The first step from the stripe diameter and smart metasurface unit to the user channel Path gain of a path formed by cascading stripes. It is the first channel from the base station to the intelligent metasurface unit. The first step from the stripe diameter and smart metasurface unit to the user channel The time delay parameters of a path formed by cascading stripes. It is the first channel from the base station to the intelligent metasurface unit. The first step from the stripe diameter and smart metasurface unit to the user channel Doppler parameters of a path formed by cascading stripes. It is the near-field direction vector cascaded through intelligent metasurface arrays.

[0028] The time-domain received signal, considering the near-field direction vector, is reflected by the smart metasurface array. , This provides a foundation for the subsequent derivation of a reliable and effective channel matrix.

[0029] The time-domain transmitted signal obtained by OTFS modulation is transmitted through a cascaded channel, while the phase shift of each unit on the smart metasurface is initialized.

[0030] Step S2: The randomly initialized phase shift from Step S1 is used as the initial phase shift. An effective channel matrix is ​​established based on the cascaded channels, and a multi-user and rate objective function is established based on the effective channel matrix. The objective function is maximized through phase shift optimization. A layered search strategy to improve search accuracy is adopted for phase shift optimization. First, several adjacent smart metasurface units in the smart metasurface array are divided into a first-level block. The same phase shift is used within each first-level block. The lowest quantization bit phase shift is used to sequentially traverse each first-level block, locking the phase shift optimization direction and recording the current optimal phase shift for each first-level block. Then, the smart metasurface units in each first-level block are divided into multiple second-level blocks. The same search strategy as in the first-level blocks is adopted, and the same phase shift is maintained within the second-level blocks. The smart metasurface units in the second-level blocks further search based on the current optimal phase shift of the first-level blocks, and the current optimal phase shift of the second-level blocks is recorded.

[0031] Among them, the Effective channel matrix for each user The expression is:

[0032]

[0033] in, express A cyclic shift matrix of dimension, express A cyclic shift matrix of dimension, This represents the number of grid cells corresponding to the time delay axis direction in the time delay Doppler grid. This represents the number of grid cells corresponding to the Doppler axis direction in the time-delay Doppler grid. and These are the exponents of the Doppler cyclic shift matrix and the time delay shift matrix, respectively. It is the phase shift vector of the intelligent metasurface array. Indicates transpose. The first term represents the channel from the base station to the intelligent metasurface unit. Strip diameter and intelligent metasurface unit up to the first The first user channel The near-field channel direction vector of the path formed by cascading stripes. It is a natural constant. It is the imaginary unit. It represents the Kronecker product.

[0034] in, Satisfy the following formula:

[0035]

[0036] in, This indicates the connection between the base station and the intelligent metasurface unit, and between the intelligent metasurface unit and the first... The near-field effective distance of two direct-view channels for a user after passing through the cascaded intelligent metasurface units in the first row and first column. This indicates the connection between the base station and the intelligent metasurface unit, and between the intelligent metasurface unit and the first... The two direct channels of the user pass through the first... line, number The near-field effective range of a series of cascaded intelligent metasurface units. This indicates the connection between the base station and the intelligent metasurface unit, and between the intelligent metasurface unit and the first... The two direct channels of the user pass through the first... line, number The near-field effective distance after cascading intelligent metasurface units; in this embodiment, the intelligent metasurface array specifically refers to the XL-RIS array, which is a rectangular planar array with a total of One intelligent metasurface unit This represents the number of cells in each row of the smart metasurface array. This indicates the number of cells in each column of the smart metasurface array.

[0037] In step S2, the objective function for multiple users and rate is expressed as follows:

[0038]

[0039] in, Describe the objective function. Indicates the total number of users. This indicates that determinant operations are being performed. Is with identity matrices of the same dimension It's the signal-to-noise ratio. This indicates the conjugate transpose operation.

[0040] To reduce the complexity of phase shift optimization, this embodiment employs a hierarchical search strategy for phase shift optimization, specifically including:

[0041] First of all Each intelligent metasurface unit is divided into A first-level block with a coarse phase shift, Each first-level block contains Each intelligent metasurface unit maintains consistent phase shift within its primary block, employing a 1-quantization bit (i.e., ... The phase shift algorithm sequentially iterates through each first-level block. If the objective function value increases after phase shift optimization, optimization is performed; otherwise, optimization is not performed. The current optimal phase shift for each first-level block is recorded. After optimizing all first-level blocks, starting from the first first-level block, the first first-level block is divided into... Each of the two secondary blocks contains [number] blocks. Each intelligent metasurface unit performs a further search based on the current optimal phase shift in the first-level block. Specifically, it searches for a finer phase shift near the optimal phase shift determined in the first-level block. For example, the optimal phase shift during the first 1-quantization bit is... At this time, it can be adopted Nearby 2 quantized bits, i.e. Similarly, optimization is performed only when the value of the objective function increases after phase shift optimization, which can achieve a more refined search. After updating all the second-level blocks in the first-level block, the current optimal phase shift of each second-level block in the first-level block is recorded for the next round of higher-precision search. This process is repeated until all second-level blocks have been searched, and then the optimal phase shift of all second-level blocks is recorded.

[0042] Step S3: Based on the current optimal phase shift of the secondary block, the hierarchical search strategy is repeatedly executed to search and optimize the subsequent blocks at each level until the number of intelligent metasurface units in each block after hierarchical division reaches a preset value. Then, an exhaustive search is performed in the last block to complete one iteration. The iteration is repeated until the maximum number of iterations is reached, and the final optimal phase shift is output. The beamforming design is then implemented based on the final optimal phase shift.

[0043] Specifically, based on the current optimal phase shift of each secondary block obtained in step S2, each tertiary block is searched. Similar to the search in the secondary blocks, it starts from the first secondary block in the first primary block and divides it into... There are 3-level blocks, and each 3-level block has Each intelligent metasurface unit, the third-level block uses a better 3-quantization bit near the optimal phase shift of the second-level block, such as the optimal phase shift being... In this case, the 3 quantized bits near it are used, i.e. The phase-shift quantization bits can be synchronized with the block partitioning level. The phase-shift optimization method for subsequent blocks at each level follows this hierarchical search method until the number of smart metasurface units in each block after partitioning reaches a preset value. Then, an exhaustive search is performed in the final block. Since the number of units has been reduced to a relatively low level at this point, applying an exhaustive search at this level will not increase the computational complexity much. This completes one iteration. The iteration is repeated until the set maximum number of iterations is reached. At that time, the final optimal phase shift is output, and based on this final optimal phase shift, low-complexity beamforming design can be realized in the near field.

[0044] In summary, the intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology described above has the following beneficial effects:

[0045] 1. This invention employs orthogonal time-frequency-space technology for transmission symbol modulation and low-cost XL-RIS devices for phase shift control. This aggregates multipath channels in direct-light conditions into cascaded channels with near-field direction vectors, enabling communication to transition from the original far-field scenario to the current near-field scenario. This effectively transforms the adverse factors in high-frequency communications such as millimeter waves, such as the susceptibility of signal propagation to obstruction and the challenge of communication link reliability, into greater performance gains in the near-field scenario, reducing performance losses. Furthermore, the time-domain received signal is obtained based on the cascaded channels with near-field direction vectors, providing a foundation for the subsequent derivation of a reliable effective channel matrix.

[0046] 2. In existing technologies, beamforming design for near-field ultra-large-scale arrays presents certain challenges. Exhaustive search and traditional convex optimization methods face extremely high computational complexity during optimization. This invention employs a hierarchical search strategy for phase shift optimization. By combining coarse and fine search, it first quickly determines the main direction of phase shift optimization with relatively low phase shift quantization precision. Then, it continuously improves the precision of phase quantization, ultimately obtaining the optimal phase shift vector for beamforming design. This approach improves performance while reducing computational complexity, significantly lowering computational overhead and enabling better real-time response. The beamforming method provided by this invention can significantly improve the reliability of high-frequency communication in high-speed mobile scenarios, ensuring reliable transmission of large-capacity information.

Claims

1. A method for intelligent metasurface array beamforming design based on orthogonal time-frequency-space technology, characterized in that, include: Step S1: Under the premise that the base station and the user conduct downlink communication through the deployed smart metasurface array, the information symbols are modulated using orthogonal time-frequency space technology, the transmitted information is mapped to the time-delay Doppler domain, and then the transmitted information is modulated to the time domain using inverse sine Fourier transform and Heisenberg transform. The multipath channels under direct illumination are aggregated into cascaded channels with near-field direction vectors so that the time-domain transmitted information can be transmitted through the cascaded channels. The phase shift of each smart metasurface unit in the smart metasurface array is randomly initialized. Step S2: The randomly initialized phase shift from Step S1 is used as the initial phase shift. An effective channel matrix is ​​established based on the cascaded channels. Then, a multi-user and rate objective function is established based on the effective channel matrix. The objective function is maximized through phase shift optimization. A layered search strategy to improve search accuracy is used for phase shift optimization. First, several adjacent smart metasurface units in the smart metasurface array are divided into a first-level block. The same phase shift is used within each first-level block. The lowest quantization bit phase shift is used to sequentially traverse each first-level block, locking the phase shift optimization direction and recording the current optimal phase shift for each first-level block. Next, the smart metasurface units in each first-level block are divided into multiple second-level blocks. The same search strategy as in the first-level blocks is used, and the same phase shift is maintained within the second-level blocks. The smart metasurface units in the second-level blocks undergo further searching based on the current optimal phase shift of the first-level blocks, and the current optimal phase shift of the second-level blocks is recorded. Step S3: Based on the current optimal phase shift of the secondary block, the hierarchical search strategy is repeatedly executed to search and optimize the subsequent blocks at each level until the number of intelligent metasurface units in each block after hierarchical division reaches a preset value. Then, an exhaustive search is performed in the last block to complete one iteration. The iteration is repeated until the maximum number of iterations is reached, and the final optimal phase shift is output. The beamforming design is then implemented based on the final optimal phase shift.

2. The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology according to claim 1, characterized in that, In step S1, during downlink communication between the base station and the user via the deployed intelligent metasurface array, the following equation is satisfied: in, This represents the channel from the base station to the smart metasurface unit. This represents the channel from the smart metasurface unit to the user. This represents the first term in the channel from the base station to the smart metasurface unit. Strip diameter gain, Indicates the first The time delay exponent corresponding to the stripe diameter after discretization by the time delay Doppler domain grid. Indicates the first The Doppler frequency shift index corresponding to the stripe diameter after time-delay Doppler domain grid discretization. This represents the number of channel diameters from the base station to the smart metasurface unit. Represents the impulse function. Represents the time delay variable. Represents the Doppler frequency shift variable. This represents the first [unit / level] in the channel from the smart metasurface unit to the user. Strip diameter gain, Indicates the first The time delay exponent corresponding to the stripe diameter after discretization by the time delay Doppler domain grid. Indicates the first The Doppler frequency shift index corresponding to the stripe diameter after time-delay Doppler domain grid discretization. This represents the number of channel diameters from the smart metasurface unit to the user. It is the near-field direction vector from the base station to the smart metasurface unit. It is the near-field direction vector from the intelligent metasurface unit to the user. and These represent the Cartesian coordinates at the base station and the user, respectively.

3. The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology according to claim 2, characterized in that, In step S1, the cascaded channels satisfy the following equation: in, Indicates a cascaded channel. It is the first channel from the base station to the intelligent metasurface unit. The first step from the stripe diameter and smart metasurface unit to the user channel Path gain of a path formed by cascading stripes. It is the first channel from the base station to the intelligent metasurface unit. The first step from the stripe diameter and smart metasurface unit to the user channel The time delay parameters of a path formed by cascading stripes. It is the first channel from the base station to the intelligent metasurface unit. The first step from the stripe diameter and smart metasurface unit to the user channel Doppler parameters of a path formed by cascading stripes. It is the near-field direction vector cascaded through intelligent metasurface arrays.

4. The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology according to claim 3, characterized in that, In step S2, the first Effective channel matrix for each user The expression is: in, express A cyclic shift matrix of dimension, express A cyclic shift matrix of dimension, This represents the number of grid cells corresponding to the time delay axis direction in the time delay Doppler grid. This represents the number of grid cells corresponding to the Doppler axis direction in the time-delay Doppler grid. and These are the exponents of the Doppler cyclic shift matrix and the time delay shift matrix, respectively. It is the phase shift vector of the intelligent metasurface array. Indicates transpose. The first term represents the channel from the base station to the intelligent metasurface unit. Strip diameter and intelligent metasurface unit up to the first The first user channel The near-field channel direction vector of the path formed by cascading stripes. It is a natural constant. It is the imaginary unit. It represents the Kronecker product.

5. The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology according to claim 4, characterized in that, In step S2, Satisfy the following formula: in, This indicates the connection between the base station and the intelligent metasurface unit, and between the intelligent metasurface unit and the first... The near-field effective distance of two direct-view channels for a user after passing through the cascaded intelligent metasurface units in the first row and first column. This indicates the connection between the base station and the intelligent metasurface unit, and between the intelligent metasurface unit and the first... The two direct channels of the user pass through the first line, number The near-field effective range of a series of cascaded intelligent metasurface units. This indicates the connection between the base station and the intelligent metasurface unit, and between the intelligent metasurface unit and the first... The two direct channels of the user pass through the first line, number The near-field effective range of a cascaded intelligent metasurface unit cell. This represents the number of cells in each row of the smart metasurface array. This indicates the number of cells in each column of the smart metasurface array.

6. The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology according to claim 5, characterized in that, In step S2, the objective function for multiple users and rate is expressed as follows: in, Describe the objective function. Indicates the total number of users. This indicates that determinant operations are being performed. Is with identity matrices of the same dimension It's the signal-to-noise ratio. This indicates the conjugate transpose operation.

7. The intelligent metasurface array beamforming design method based on orthogonal time-frequency-space technology according to claim 6, characterized in that, In step S2, a hierarchical search strategy is used for phase shift optimization, specifically including: First of all Each intelligent metasurface unit is divided into A first-level block with a coarse phase shift, Each first-level block contains Each intelligent metasurface unit maintains a consistent phase shift within its first-level blocks. A 1-quantization bit phase shift is used to sequentially traverse each first-level block. If the objective function value increases after phase shift optimization, optimization is performed; otherwise, it is not. The current optimal phase shift for each first-level block is recorded. After optimizing all first-level blocks, starting from the first first-level block, it is divided into... Each of the two secondary blocks contains [number] blocks. Each intelligent metasurface unit performs further searches based on the current optimal phase shift of the first-level block. Similarly, optimization is only performed if the value of the objective function increases after phase shift optimization. After updating all second-level blocks in the first-level block, the current optimal phase shift of each second-level block in the first-level block is recorded. This process is repeated until all second-level blocks have been searched, and then the optimal phase shift of all second-level blocks is recorded.

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