Adaptive step-size symbol iteration inverse fast computation method for non-terrestrial networks

Abstract

The application relates to an adaptive step size symbol iteration reciprocal fast calculation method for a non-ground network. The method comprises the following steps: acquiring a positive integer including a channel quality indicator value, a power control factor or a resource allocation weight value in non-ground network communication processing; calculating a logarithmic characteristic and normalizing the logarithmic characteristic, selecting a scaling factor according to the interval where the normalized value is located to obtain a scaled value and a compensation factor; determining a starting iteration index; determining a symbol direction according to a current error, and generating an adaptive step size based on the absolute value of the error; updating a reciprocal approximation value by using the symbol direction, the adaptive step size and a second-order correction term, simultaneously updating an auxiliary variable by using an exponential moving average, and then updating a normalized error; stopping when a precision or a maximum iteration number is met, restoring the reciprocal by using the compensation factor and outputting the reciprocal to a power control, beamforming or resource scheduling module. The application has the advantages of low resource and strong adaptability, and is suitable for a resource-limited platform such as a satellite-borne FPGA.

Description

Technical Field

[0001] This application relates to the field of non-terrestrial network communication signal processing technology, and in particular to an adaptive step-size symbolic iterative reciprocal fast calculation method for non-terrestrial networks. Background Technology

[0002] Non-terrestrial networks (NTNs) typically consist of low-Earth orbit (LEO), medium-Earth orbit (MEO), and high-Earth orbit (HEO) satellites, relay platforms, and ground terminals, and are a key technology for achieving seamless global coverage and emergency communication. In NTN systems, operations such as channel estimation, transmit power control, beamforming coefficient normalization, and multi-user scheduling weight calculation are frequently required between onboard equipment and terminals. These processes extensively involve the rapid calculation of the reciprocals of positive integers. Because satellite platforms and terminal equipment are highly sensitive to power consumption, size, and hardware resources, and because onboard FPGAs require extremely high reliability and real-time performance, traditional approaches—directly using dividers or offline generation of large-capacity lookup tables (LUTs)—face severe challenges. On the one hand, hardware dividers consume a large number of logic gates and multipliers, significantly reducing the maximum operating frequency of the onboard FPGA and increasing power consumption and cost. On the other hand, if LUTs are used to store the reciprocals of different input ranges, the table size expands rapidly as the dynamic range of signals in NTNs increases (e.g., the link loss difference from low-Earth orbit satellites to ground terminals can reach tens of decibels). Once system parameters—quantization bit width or accuracy requirements—change, the entire lookup table needs to be regenerated and reprogrammed, lacking flexibility and scalability. Furthermore, the rapid channel changes in NTN environments require algorithms with adaptive convergence capabilities. While the traditional Cordic method avoids large resource consumption, its fixed step-size mechanism has a slow convergence speed, making it difficult to meet real-time processing requirements. Summary of the Invention

[0003] Therefore, it is necessary to provide a fast calculation method for adaptive step-size symbolic iterative reciprocals for non-terrestrial networks, which can achieve fast data processing in non-terrestrial networks with low hardware resource overhead, high adaptive convergence speed, and flexible configuration.

[0004] An adaptive step-size symbolic iterative reciprocal fast calculation method for non-terrestrial networks, the method comprising: Step 1: Obtain the parameters to be normalized in the non-terrestrial network communication processing. The parameters to be normalized are positive integers, including at least one of the channel quality indication value, power control factor, or resource allocation weight value. Calculate the logarithmic characteristic of the positive integers and use the logarithmic characteristic to normalize the positive integers to obtain normalized values. Select a scaling factor according to the numerical range of the normalized value and use the scaling factor to scale the normalized value to obtain scaled values. At the same time, record the compensation factor, which is used for subsequent numerical restoration. Step 2: Initialize the auxiliary variables, reciprocal approximation values, and normalization errors used for iterative calculations; and determine the starting iteration index based on the preset maximum number of iterations and scaling factor; Step 3: For the current iteration index, determine the sign direction based on the current normalization error value, and generate an adaptive step size based on the current iteration index and the absolute value of the current normalization error. Step 4: Update the reciprocal approximation value using the sign direction, adaptive step size, and current normalization error to obtain the updated reciprocal approximation value; update the auxiliary variable using the sign direction and the auxiliary variable from the previous time step to obtain the updated auxiliary variable; then update the normalization error using the scaled value and the updated reciprocal approximation value to obtain the updated normalization error. Step 5: Determine if the iteration termination condition is met. If it is met, terminate the iteration and output the current approximate reciprocal value. Otherwise, increment the iteration index and return to step 3. Step 6: After the iteration stops, the approximate reciprocal value of the output is restored according to the compensation factor to obtain the reciprocal of the positive integer, and the reciprocal is output to the power control module, beamforming module or resource scheduling module in the non-terrestrial network communication processing.

[0005] The aforementioned adaptive step-size symbol iteration reciprocal fast calculation method for non-terrestrial networks first performs logarithmic eigenvalue decomposition and quadratic scaling on the channel quality indicator, power control factor, or resource allocation weight values ​​in the NTN system. This maps the large dynamic range input to a fixed small interval, thereby compressing the dynamic range required for subsequent iterations and making the number of iterations independent of the input value. By introducing a step-size mechanism that adaptively adjusts based on the absolute value of the current normalized error, the step-size automatically increases when the error is large to accelerate convergence and tends to stabilize when the error is small, achieving a dynamic balance between convergence speed and accuracy. Furthermore, a second-order correction term is used to add an extra adjustment step-size when the error is large, giving the iteration superlinear convergence characteristics. At the same time, the exponential moving average of historical symbols is used to smooth the symbol direction, effectively suppressing symbol oscillations when the error crosses zero and ensuring the stability of the iteration under a wide range of inputs. Compared to existing technologies that directly use dividers or offline lookup tables, this application only requires shifting, addition, comparison, and sign determination operations, eliminating the need for multipliers and dividers, as well as large-capacity storage tables. This significantly reduces the hardware overhead and power consumption of resource-constrained platforms such as onboard FPGAs. Compared to traditional Cordic fixed-step iterations, this application offers faster convergence speed and stronger adaptability, meeting the real-time processing requirements of rapidly changing NTN channels. Furthermore, it exhibits good flexibility and scalability. By adjusting the golden ratio constant, second-order correction coefficients, and maximum number of iterations, a flexible balance can be struck between convergence speed and computational accuracy. Moreover, when the system bit width or accuracy is upgraded, there is no need to regenerate the lookup table, significantly improving the resource efficiency and adaptability of the signal processing unit in the NTN communication system. Attached Figure Description

[0006] Figure 1 This is a flowchart illustrating a fast calculation method for adaptive step-size symbolic iterative reciprocal for non-terrestrial networks in one embodiment. Figure 2 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0007] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0008] In one embodiment, such as Figure 1 As shown, an adaptive step-size symbolic iterative reciprocal fast calculation method for non-ground networks is provided, including the following steps: Step 1: Obtain the parameters to be normalized in the non-terrestrial network communication processing. The parameters to be normalized are positive integers including at least one of the channel quality indication value, power control factor, or resource allocation weight value. Calculate the logarithmic characteristic of the positive integers and use the logarithmic characteristic to normalize the positive integers to obtain normalized values. Select a scaling factor according to the numerical range of the normalized value and use the scaling factor to scale the normalized value to obtain scaled values. At the same time, record the compensation factor, which is used for subsequent numerical restoration.

[0009] Taking positive integers with actual physical meaning in the NTN system, including channel quality indicators reflecting link quality, factors used for power control, and resource allocation weights in multi-user scheduling, as input, the logarithmic characteristic with base 2 is calculated. Normalize N to ; the interval is obtained Subsequently, according to Further select the scaling factor for the sub-interval. :like but ,like but Thus, the scaled values ​​are obtained. Guaranteed value Restricted to [ , Within this narrower range, the secondary scaling process effectively compresses the dynamic range of the input value, making the convergence behavior of subsequent iterations essentially independent of the specific size of N. This avoids the problem of a surge in iterations or non-convergence caused by an excessively large input dynamic range.

[0010] Step 2: Initialize the auxiliary variables, reciprocal approximation, and normalization error used for iterative calculations; and determine the starting iteration index based on the preset maximum number of iterations and scaling factor.

[0011] Set the initial state required for iteration: auxiliary variables Exponential smoothing for subsequent sign direction; reciprocal approximation The initial value can be 0 or obtained from a small lookup table to further accelerate convergence; normalization error This represents the deviation between the current approximation and the true reciprocal. (Initial iteration index) The design of this starting index ensures that the initial value of the iteration step size matches the input range and the maximum number of iterations, avoiding wasting invalid iterations starting from index 0, thereby improving overall computational efficiency.

[0012] Step 3: For the current iteration index, determine the sign direction based on the current normalization error value, and generate an adaptive step size based on the current iteration index and the absolute value of the current normalization error.

[0013] First, based on the current normalization error The polarity determines the approximation direction: if ,but This indicates that the current approximation is too large and needs to be reduced. ,but This indicates that the current approximate value is too small and needs to be increased. ,but ,in This is the current auxiliary variable, which only occurs when the error is exactly zero, used to maintain directional stability. Then, an adaptive step size is generated. This step size is characterized by: when the error... When the value is large, the step size is at the base value. The amplitude is significantly amplified, thereby accelerating the convergence speed; when the error As it approaches 0, the step size approaches This ensures fine-tuning in the later stages of convergence. This nonlinear adaptive mechanism allows the algorithm to dynamically adjust the step size based on the current approximation error, resulting in better convergence efficiency compared to the fixed step size of traditional Cordic algorithms.

[0014] Step 4: Update the reciprocal approximation value using the sign direction, adaptive step size, and current normalization error to obtain the updated reciprocal approximation value; update the auxiliary variable using the sign direction and the auxiliary variable from the previous time step to obtain the updated auxiliary variable; and then update the normalization error using the scaled value and the updated reciprocal approximation value to obtain the updated normalization error.

[0015] Perform the core iterative update: First, update the reciprocal approximation value to... When the error is large, This term further increases the adjustment amount, giving the iteration superlinear convergence property. Next, the auxiliary variable is updated; this is an exponential moving average of the historical sign direction, its function being to ensure the error crosses zero (i.e., ...). To suppress oscillations (when the sign changes frequently), iterative stability is improved. Finally, the normalized error is updated to prepare feedback for the next iteration. The above three update steps are tightly coupled, realizing nonlinear adaptive approximation based on error feedback.

[0016] Step 5: Determine if the iteration termination condition is met. If it is met, terminate the iteration and output the current approximate reciprocal value. Otherwise, increment the iteration index and return to step 3.

[0017] Two iteration termination conditions are provided: one is the absolute value of the current normalization error. If the approximation value is less than a preset accuracy threshold, it is already sufficiently accurate, and early termination of the iteration can save computational resources; secondly, if the number of iterations reaches the preset maximum number of iterations M, it is forcibly terminated to ensure real-time performance. This dual termination mechanism provides a flexible choice between accuracy and computational latency.

[0018] Step 6: After the iteration stops, the approximate reciprocal value of the output is restored according to the compensation factor to obtain the reciprocal of the positive integer, and the reciprocal is output to the power control module, beamforming module or resource scheduling module in the non-terrestrial network communication processing.

[0019] This step will use the approximate value after iterative convergence. Multiply by the reciprocal of the compensation factor to restore: Because C contains the values ​​from the previous scaling steps. and This restoration operation can accurately recover the reciprocal of the original positive integer N. The final result is directly output to the specific functional modules of NTN communication processing, including coefficient multiplication in power control, weight normalization in beamforming, and proportional fairness calculation in resource scheduling, thereby completing the practical application of reciprocal calculation in the entire communication link.

[0020] The aforementioned fast method for adaptive step-size sign-based iterative reciprocal calculation for non-terrestrial networks compresses the iterative dynamic range by performing logarithmic decomposition and quadratic scaling on the normalized positive integer to map the large dynamic range input to a fixed small interval. Superlinear convergence is achieved through an adaptive step size based on the absolute value of the error and a second-order correction term. Oscillations are suppressed by using an exponential moving average of historical signs. The entire method requires only shift, addition, comparison, and sign determination operations, eliminating the need for dividers, multipliers, and large-capacity lookup tables. It can rapidly and stably obtain high-precision reciprocal results with extremely low hardware overhead on resource-constrained platforms such as low-Earth orbit / medium-Earth orbit / high-Earth orbit satellites, significantly improving the resource efficiency and adaptability of signal processing units in NTN communication systems.

[0021] In a later embodiment, the process of calculating the logarithmic characteristics of positive integers is as follows: , Positive integer; normalized value , making .

[0022] Specifically, the problem of large dynamic range input is transformed into a problem of fixed interval. The numerical processing within the system makes the design of the iteration step size no longer dependent on... The absolute size of the value ensures the algorithm's broad adaptability to link losses ranging from minimal to maximum in NTN.

[0023] In a subsequent embodiment, a scaling factor is selected based on the numerical range of the normalized value, and the normalized value is scaled using the scaling factor to obtain a scaled value; simultaneously, a compensation factor is recorded, including: according to Choose the scaling factor within the numerical range. For: If ,but ;like ,but The normalized values ​​are scaled using a scaling factor to obtain the scaled values. , making The compensation factor is recorded as follows: ,in, This indicates logarithmic characteristics.

[0024] Specifically, this secondary scaling will reduce the original The range was further compressed to [ , The interval is symmetrical about 1. On one hand, a narrower interval results in a smaller upper limit for the initial iteration error, thus reducing the number of iterations required; on the other hand, the symmetrical interval is beneficial for the balance of sign determination, avoiding convergence behavior biased to one side. Compensation factor The introduction of this ensures that the final result can be accurately reproduced without losing any information.

[0025] In a subsequent embodiment, determining the starting iteration index based on a preset maximum number of iterations and a scaling factor includes: The starting iteration index is determined based on the preset maximum number of iterations and the scaling factor. Where M is the preset maximum number of iterations. This is the scaling factor.

[0026] Specifically, because the step size formula includes Item, if from i The iteration starts at 0, and the step size in the first few steps is too small. For steps that have already been scaled to [...] , For the interval N', it is unnecessary. This embodiment calculates... The algorithm then rounds down to obtain a suitable starting index, ensuring that the iteration begins at an index whose step size matches the problem size. This avoids invalid iterations, shortens computation time, and improves real-time processing capabilities.

[0027] In a subsequent embodiment, determining the sign direction based on the current normalization error value includes: If the current normalization error ,but ;like ,but ;like ,but ,in This is the current auxiliary variable.

[0028] Specifically, the sign direction determines the approximation's trajectory: a negative error indicates the current approximation is too large and needs adjustment towards decreasing; a positive error indicates it is too small and needs adjustment towards increasing. When the error is exactly zero, the sign of the historical smoothed value is used as the direction to avoid abrupt changes. The sign direction provides clear directional guidance and maintains directional continuity when the error is zero, preventing oscillations.

[0029] In a subsequent embodiment, generating an adaptive step size based on the current iteration index and the absolute value of the current normalization error includes: An adaptive step size is generated based on the current iteration index and the absolute value of the current normalization error.

[0030] in, The golden ratio constant is the preset ratio. This represents the absolute value of the current normalization error. This is the index for the current iteration.

[0031] Specifically, the larger the error, the more significant the amplification effect, thus greatly accelerating the convergence speed; when the error is small, the amplification factor approaches 1, and the step size returns to the baseline value. This ensures fine-tuning in the later stages of convergence. This mechanism gives the algorithm nonlinear adaptive characteristics, which is superior to the fixed step size of traditional Cordic algorithms.

[0032] In a subsequent embodiment, the updated reciprocal approximation is obtained by updating the reciprocal approximation using the sign direction, adaptive step size, and current normalization error, including: The updated reciprocal approximation is obtained by updating the sign direction, adaptive step size, and current normalization error.

[0033] in, These are the preset second-order correction coefficients. The square of the current normalization error. It is the reciprocal approximation. For the direction of the symbol, For adaptive step size.

[0034] Specifically, by introducing a second-order correction term, the iteration convergence speed is improved from linear to superlinear, meaning that higher accuracy can be obtained with the same number of iterations, or fewer iterations are required to achieve the same accuracy. This is particularly important for scenarios with high real-time requirements in NTN.

[0035] In a subsequent embodiment, the updated auxiliary variable is obtained by updating the auxiliary variable using the sign direction and the auxiliary variable from the previous time step, including: The updated auxiliary variable is obtained by updating the auxiliary variable using the sign direction and the auxiliary variable from the previous time step.

[0036] in, This is an auxiliary variable from the previous moment. The direction of the symbol.

[0037] Specifically, this formula is an exponential moving average, with coefficients 0.9 and 0.1 smoothing the historical trajectory of the sign direction. When the error repeatedly crosses zero... When the number changes frequently, Instead of drastic jumps, the changes are gradual, thus stabilizing the iterative process. This effectively suppresses sign oscillations, avoids convergence difficulties caused by frequent direction switching, and ensures that the algorithm can still converge stably under a wide range of inputs.

[0038] In a subsequent embodiment, the normalization error is updated using the scaled value and the updated reciprocal approximation to obtain the updated normalization error, including: The updated normalization error is obtained by updating the normalization error using the scaled value and the updated reciprocal approximation.

[0039] in, These are scaled values. This is the updated reciprocal approximation.

[0040] Specifically, the error calculation involves only one multiplication and subtraction operation, making hardware implementation simple, and the range of the error value is consistent with... The intervals directly correspond, facilitating unified processing.

[0041] In a subsequent embodiment, the iteration termination condition is the absolute value of the current normalization error. The accuracy is less than the preset precision threshold, or the current iteration count has reached the maximum iteration count; The method of restoration based on the compensation factor is as follows: ,in, It is the reciprocal approximation. It is a positive integer. As a compensation factor, Scaling factor It has logarithmic characteristics.

[0042] Specifically, the preset accuracy threshold and the maximum number of iterations M can be preset based on the system's allowed latency and resources. The division in the reduction formula is converted to multiplication. Move right again LBitwise operations can be implemented in binary hardware via shifting, eliminating the need for a divider. This provides double abort protection, balancing precision and real-time performance; the restoration process requires no complex calculations, further reducing hardware overhead.

[0043] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0044] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 2 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements an adaptive step-size symbolic iterative reciprocal fast calculation method for non-terrestrial networks. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device casing, or an external keyboard, touchpad, or mouse.

[0045] Those skilled in the art will understand that Figure 2 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0046] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0047] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0048] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A fast method for adaptive step-size symbolic iterative reciprocal calculation for non-ground networks, characterized in that, The method includes: Step 1: Obtain the parameter to be normalized in the non-terrestrial network communication processing. The parameter to be normalized is a positive integer including at least one of channel quality indication value, power control factor, or resource allocation weight value. Calculate the logarithmic feature of the positive integer and use the logarithmic feature to normalize the positive integer to obtain a normalized value. Select a scaling factor according to the numerical range of the normalized value and use the scaling factor to scale the normalized value to obtain a scaled value. Simultaneously, record the compensation factor, which is used for subsequent numerical restoration. Step 2: Initialize the auxiliary variables, reciprocal approximation values, and normalization errors used for iterative calculations; and determine the starting iteration index based on the preset maximum number of iterations and the scaling factor. Step 3: For the current iteration index, determine the sign direction based on the current normalization error value, and generate an adaptive step size based on the current iteration index and the absolute value of the current normalization error. Step 4: Update the reciprocal approximation value using the sign direction, the adaptive step size, and the current normalization error to obtain the updated reciprocal approximation value; update the auxiliary variable using the sign direction and the auxiliary variable from the previous time step to obtain the updated auxiliary variable; then update the normalization error using the scaled value and the updated reciprocal approximation value to obtain the updated normalization error. Step 5: Determine if the iteration termination condition is met. If it is met, terminate the iteration and output the current approximate reciprocal value. Otherwise, increment the iteration index and return to step 3. Step 6: After the iteration stops, the approximate reciprocal value of the output is restored according to the compensation factor to obtain the reciprocal of the positive integer, and the reciprocal is output to the power control module, beamforming module or resource scheduling module in the non-terrestrial network communication processing.

2. The method according to claim 1, characterized in that, The process of calculating the logarithmic characteristics of the positive integer is as follows: , The normalized value is a positive integer. , making .

3. The method according to claim 1, characterized in that, A scaling factor is selected based on the numerical range of the normalized value, and the normalized value is scaled using the scaling factor to obtain a scaled value; simultaneously, compensation factors are recorded, including: according to Choose the scaling factor within the numerical range. For: If ,but ;like ,but The normalized value is scaled using the scaling factor to obtain the scaled value. , making The compensation factor is recorded as follows: ,in, This indicates logarithmic characteristics.

4. The method according to claim 1, characterized in that, Determining the starting iteration index based on the preset maximum number of iterations and the scaling factor includes: The starting iteration index is determined based on the preset maximum number of iterations and the scaling factor. Where M is the preset maximum number of iterations. This is the scaling factor.

5. The method according to claim 1, characterized in that, The sign direction is determined based on the current normalization error value, including: If the current normalization error ,but ;like ,but ;like ,but ,in This is the current auxiliary variable.

6. The method according to claim 1, characterized in that, An adaptive step size is generated based on the current iteration index and the absolute value of the current normalization error, including: An adaptive step size is generated based on the current iteration index and the absolute value of the current normalization error. in, The golden ratio constant is the preset ratio. This represents the absolute value of the current normalization error. This is the index for the current iteration.

7. The method according to claim 1, characterized in that, The updated reciprocal approximation is obtained by updating the reciprocal approximation using the sign direction, the adaptive step size, and the current normalization error, including: The updated reciprocal approximation is obtained by using the sign direction, the adaptive step size, and the current normalization error to update the reciprocal approximation. in, These are the preset second-order correction coefficients. The square of the current normalization error. It is the reciprocal approximation. For the direction of the symbol, For adaptive step size.

8. The method according to claim 1, characterized in that, The updated auxiliary variable is obtained by updating the auxiliary variable using the sign direction and the auxiliary variable from the previous time step, including: The updated auxiliary variable is obtained by updating the auxiliary variable using the sign direction and the auxiliary variable from the previous time step. in, This is an auxiliary variable from the previous moment. The direction of the symbol.

9. The method according to claim 1, characterized in that, The normalization error is updated using the scaled value and the updated reciprocal approximation, including: The updated normalization error is obtained by updating the normalization error using the scaled value and the updated reciprocal approximation. in, These are scaled values. This is the updated reciprocal approximation.

10. The method according to claim 1, characterized in that, The iteration termination condition is the absolute value of the current normalization error. The accuracy is less than the preset precision threshold, or the current iteration count has reached the maximum iteration count; The method of restoration based on the compensation factor is as follows: ,in, It is the reciprocal approximation. It is a positive integer. As a compensation factor, Scaling factor It has logarithmic characteristics.

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