A multi-carrier phase ranging method for interference channel scenarios
By screening and processing channels in interference channel scenarios, combining signal-to-noise ratio estimation and frequency domain analysis, efficient ranging of multi-carrier phase ranging method is achieved, solving the problem of low accuracy of traditional methods in interference environments, and enhancing measurement 距的可靠性和精度。
Patent Information
- Application Number
- CN202410972070.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-19
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2044-07-19
AI Technical Summary
In the interference channel scenario, the accuracy of the traditional single-carrier phase ranging method is seriously affected and cannot effectively deal with the ranging requirements in complex interference environments.
A multi-carrier phase ranging method is designed. By obtaining the interference indication value of each channel at the initiator and the receiver, combining the judgment and screening of available channels, dividing them into continuous frequency segments for ranging calculation, and using weighted average to obtain The final ranging result uses signal-to-noise ratio estimation and frequency domain processing to reduce the impact of interference on ranging accuracy.
It realizes efficient ranging in interfering channel scenarios, and through intelligent screening of channel resources and frequency segmentation processing, the reliability and accuracy of ranging results are enhanced.
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Figure CN118688777B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of ranging technology, and in particular to a multi-carrier phase ranging method applied to an interference channel scenario. Background Art
[0002] In wireless communication and positioning systems, accurately measuring the distance between devices is a key requirement for many applications, especially in interference channel scenarios. The frequency band (2.402~2.480GHz) where the communication is located is interfered by other devices, and some channels (each 1MHz interval is defined as a channel) may be interfered. The presence and intensity level of interference can be identified. By identifying the interference intensity, channels with less interference can still be used for distance estimation, which is beneficial to improving ranging accuracy. In the case of really large interference, the data of the channel is unavailable. If the channel response needs to be used for ranging, the channel response of the channel needs to be estimated. Although the traditional single-carrier phase ranging method can provide higher accuracy under ideal conditions, its performance will be seriously affected in complex interference channels. Therefore, it is particularly important to develop a multi-carrier phase ranging method that can effectively deal with interference channels. Summary of the invention
[0003] The purpose of the present invention is to solve the above problem and designs a multi-carrier phase ranging method applied to interference channel scenarios.
[0004] The present invention provides a multi-carrier phase ranging method applied to an interference channel scenario, and the multi-carrier phase ranging method applied to an interference channel scenario comprises the following steps:
[0005] Step 1: obtaining an interference indication value of each channel of an initiating end and a receiving end, combining the interference indication value of the initiating end with the interference indication value of the receiving end to obtain interference indication values of all channels;
[0006] Step 2: determine whether the interference indication value of all channels is less than the interference indication threshold. If so, all channels can be used for ranging calculation. If not, obtain a channel that is not less than the interference indication threshold and mark the channel as unavailable.
[0007] Step 3: Obtain all available channels determined in step 2, divide all available channels into continuous frequency segments, determine the length of the frequency segments and filter out frequency segments that can be used for ranging calculations, perform ranging calculations on the filtered frequency segments respectively, and perform weighted averaging on the ranging results obtained for each frequency segment to obtain the final ranging result.
[0008] Optionally, in a first implementation manner of the present invention, the calculation process of the interference indication value of each channel in step 1 includes the following steps:
[0009] A single tone of preset duration is sent from the initiator to the receiver, and after down-conversion, the frequency of the single tone observed at the receiver is less than 10kHz, thereby obtaining a single tone signal, and an AD converter at the receiver samples the single tone signal;
[0010] After removing the non-single-cause transition signal at the boundary of the single tone, sample N-point single tone data, perform fast Fourier transform on the N-point single tone data, and find the peak position;
[0011] The power of the single tone signal is obtained by adding up the values of the peak position and the n positions before and after it in the fast Fourier transform result, where n=1,2,...,n;
[0012] Add up the values of the remaining positions in the fast Fourier transform result to get the power of the noise;
[0013] The power of the single tone signal is divided by the power of the noise and the result is expressed in logarithm to obtain a signal-to-noise ratio estimation value, and the signal-to-noise ratio estimation value is used as the interference indication value.
[0014] Optionally, in a second implementation of the present invention, the sampling rate of the AD converter is oversampled by 8 times, 12 times or 16 times, and the frequency corresponding to the peak position is the frequency of the single tone.
[0015] Optionally, in a third implementation of the present invention, the length of the frequency segment is the number of continuous usable channels.
[0016] Optionally, in a fourth implementation of the present invention, the process of screening frequency segments that can be used for ranging calculation in step 3 includes the following steps:
[0017] Obtain all frequency segments, determine whether there is a frequency segment in all frequency segments whose length is greater than a first preset frequency segment threshold, and if so, obtain the longest frequency segment that satisfies the condition of being greater than the first preset frequency segment threshold for ranging calculation;
[0018] If otherwise, it is determined whether there is a frequency segment of all frequency segments whose length is greater than the second preset frequency segment threshold, then the longest frequency segment satisfying the condition of being greater than the second preset frequency segment threshold is obtained for ranging calculation;
[0019] If the length of the frequency segment in all frequency segments is not greater than the second preset frequency segment threshold, then two frequency segments are selected from all frequency segments, and the unavailable channels between the two frequency segments are interpolated. After interpolation, the two previous and next frequency segments are combined to form a long frequency segment for ranging calculation.
[0020] Optionally, in a fifth implementation of the present invention, when selecting frequency segments, the number of unavailable channels between frequency segments is the smallest among all selections and is less than a threshold for the number of interpolable channels, and the interpolation order of the channels to be interpolated is determined according to the number of channels in adjacent frequency segments.
[0021] Optionally, in a sixth implementation of the present invention, the interpolation process in step 3 includes the following steps:
[0022] Obtain the channel that needs to be interpolated, and obtain the phase response from the square root of the channel response;
[0023] Traverse the phase differences of all channels and their adjacent channels, compare the phase difference of each channel with its adjacent channels, and if the difference is close to the phase π error, adjust the phase of the current channel by ±π;
[0024] After completing a round of calibration, the phase continuity of all channels is rechecked. After the calibration is completed, the phase interpolation adopts the linear interpolation method and the amplitude interpolation adopts the quadratic interpolation method to obtain the complex channel response corresponding to each interpolation point.
[0025] Optionally, in a seventh implementation of the present invention, after completing one round of correction, the phase continuity of all channels is rechecked. After the correction is completed, the phase interpolation adopts a linear interpolation method and the amplitude interpolation adopts a quadratic interpolation method to obtain a complex channel response corresponding to each interpolation point, including:
[0026] Linear interpolation is performed using the corrected adjacent channel phase values and proportionally distributed to the points to be interpolated to obtain a continuous and smooth phase distribution;
[0027] For each amplitude point to be interpolated, three adjacent known amplitude values are used to perform quadratic polynomial fitting to determine the amplitude value of the amplitude point to be interpolated;
[0028] After the phase and amplitude interpolation is completed, a corresponding complex channel response is generated for each interpolation point.
[0029] In the technical solution provided by the present invention, the interference indication value of each channel of the initiator and the receiver is obtained, and the interference indication value of the initiator and the interference indication value of the receiver are combined to obtain the interference indication values of all channels; it is judged whether the interference indication values of all channels are less than the interference indication threshold, if so, all channels can be used for ranging calculation, otherwise, a channel not less than the interference indication threshold is obtained, and the channel is marked as unavailable; all available channels obtained by the judgment in step 2 are obtained, all available channels are divided into continuous frequency segments, the length of the frequency segment is judged and the frequency segment that can be used for ranging calculation is screened out, ranging calculation is performed on the screened frequency segments respectively, and the ranging results obtained by each frequency segment are weighted averaged to obtain the final ranging result; the present invention realizes intelligent screening and efficient utilization of channel resources by evaluating the interference indication value of the channel, effectively reduces the influence of interference on ranging accuracy, reduces the influence of a single channel or frequency segment error on the overall ranging result through frequency segmentation and weighted average processing, and enhances the reliability of the ranging result. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the following detailed description of the preferred embodiment.The drawings are only for the purpose of illustrating the preferred embodiments and are not to be construed as limiting the invention.
[0031] Figure 1 A schematic diagram of the process flow of a multi-carrier phase ranging method applied to an interference channel scenario provided by the present invention;
[0032] Figure 2 A schematic diagram of continuously available frequency bands within the BLE frequency band provided by the present invention;
[0033] Figure 3 A schematic diagram of the relationship between the signal-to-noise ratio estimation result of the channel provided by the present invention and the actual added signal-to-noise ratio;
[0034] Figure 4 A schematic diagram of a first embodiment of a ranging solution using an interference adaptive frequency band provided by the present invention;
[0035] Figure 5 A schematic diagram of a second embodiment of a ranging solution using an interference adaptive frequency band provided by the present invention;
[0036] Figure 6 A schematic diagram of the FFT result of a single tone signal provided by the present invention. DETAILED DESCRIPTION
[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0038] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 A flow chart of a multi-carrier phase ranging method applied to an interference channel scenario provided by an embodiment of the present invention is provided. Based on the flow chart, the method specifically includes the following steps:
[0039] Step 1: Obtain interference indication values of each channel of the initiating end and the receiving end, combine the interference indication value of the initiating end with the interference indication value of the receiving end, and obtain interference indication values of all channels;
[0040] Step 2: determine whether the interference indication value of all channels is less than the interference indication threshold. If so, all channels can be used for ranging calculation. If not, obtain a channel that is not less than the interference indication threshold and mark the channel as unavailable.
[0041] Step 3: Obtain all available channels determined in step 2, divide all available channels into continuous frequency segments, determine the length of the frequency segments and filter out the frequency segments that can be used for ranging calculations, perform ranging calculations on the filtered frequency segments respectively, and perform weighted averaging on the ranging results obtained for each frequency segment to obtain the final ranging result.
[0042] In an embodiment of the present invention, a set of phase ranging devices (initiator and reflector) and systems are specified based on the channel sounding chapter of the Bluetooth Low Energy (BLE) standard to perform ranging, mainly to solve how to obtain better ranging accuracy in interference scenarios, wherein the initiator is the initiating end in the above steps, and the reflector is the receiving end in the above steps.
[0043] 1. The interference indication of each channel comes from the signal-to-noise ratio estimation of the signal on each channel at the receiving end. The signal-to-noise ratio estimation value is used as the interference indication value of the end and is sent to the ranging calculation unit (usually at the initiator end or a third-party processor) together with the measured IQ phase data.
[0044] 1) Single tone signal used to calculate interference indication
[0045] In the single-tone ranging process of each channel, the initiator sends a single tone of a certain length to the reflector. After down-conversion, the frequency of the single tone observed at the receiving end is less than 10kHz, and a single-tone signal is obtained. The AD converter at the receiving end samples the single-tone signal at a certain sampling rate. Since the bandwidth of the BLE signal is 1M or 2M, the sampling rate of the AD converter is generally 8 times, 12 times or 16 times oversampling. Since the sampling rate of AD is high enough relative to the single-tone frequency, it provides a basis for time domain or frequency domain signal-to-noise ratio estimation.
[0046] In this embodiment, the AD converter is used to convert analog signals into digital signals. All signals are represented in the form of binary codes. Therefore, it is necessary to convert analog signals of physical quantities such as voltage, current, etc. into digital signals for processing. The basic working principle of the AD converter is to sample the analog input signal through a sampling and holding circuit, and then convert it into a digital signal through quantization and encoding. This process can be subdivided into four steps: sampling, holding, quantization and encoding. Among them, sampling is to convert the instantaneous value of the analog signal into a series of time-discrete pulse values at a certain time interval; holding is to save the discontinuous instantaneous sampling value output by the sampling circuit to make it a time-continuous signal; quantization is to quantize each value of the continuous value (analog quantity) (that is, convert it into the closest integer value) and output it as a digital quantity; encoding is to convert the quantized value into a binary code and then output it.
[0047] 2) Single-tone based interference indication estimation
[0048] The interference indication is an estimation of the signal-to-noise ratio. A higher signal-to-noise ratio indicates less interference, while a lower signal-to-noise ratio indicates greater interference.
[0049] The signal-to-noise ratio estimation uses the frequency domain estimation method to sample N-point single-tone data. It is necessary to remove the non-single-cause transition signal at the boundary of the single tone. Then, the N-point single-tone data is subjected to Fast Fourier Transformation (FFT) to find the peak position. The frequency corresponding to the peak position is the frequency of the single tone. Then, the values of the corresponding single tone position and the ext_num positions before and after it in the FFT result are added together to obtain the power of the single tone signal; the values of the remaining positions of the FFT are added together to obtain the power of the noise. The signal-to-noise ratio estimate is obtained by dividing the power of the signal by the power of the noise and expressing it logarithmically. This signal-to-noise ratio estimate can be used as an interference indicator.
[0050] In this embodiment, FFT is a fast algorithm of Discrete Fourier Transform (DFT for short), which can convert a signal from the time domain to the frequency domain, so as to analyze the frequency components of the signal. In a multi-carrier phase ranging method applied to an interference channel scenario, a multi-carrier signal is composed of a plurality of sub-carriers of different frequencies, each of which can carry different information. FFT can convert the multi-carrier signal from the time domain to the frequency domain, so as to separate the frequency components of each sub-carrier, which is crucial for the multi-carrier phase ranging method, because the phase information of each sub-carrier can be used for ranging calculation; in an interference channel, a signal may be affected by noise, multipath effects and other interferences; FFT can help identify the spectral characteristics of noise and interference, and use appropriate signal Processing technology can filter it out, thereby improving the anti-interference ability of ranging; by analyzing the frequency domain characteristics of multi-carrier signals through FFT, more accurate phase information can be obtained. Phase information is one of the key parameters of ranging, and its accuracy directly affects the accuracy of ranging. FFT can provide high-resolution frequency domain analysis, thereby obtaining more accurate phase information and improving ranging accuracy; the FFT algorithm itself is efficient and real-time, suitable for processing large amounts of data and real-time applications. In the multi-carrier phase ranging method, FFT can be used to process the received multi-carrier signals in real time, extract the phase information of each sub-carrier, and perform ranging calculations through optimization algorithms; the FFT algorithm is implemented on various hardware platforms, such as DSP (Digital Signal Processor), FPGA (Field-Programmable Gate Array) and ASIC (Application-Specific Integrated Circuit), etc. These hardware platforms can provide high-performance FFT computing capabilities and support the real-time application of multi-carrier phase ranging methods. By analyzing the frequency domain characteristics of multi-carrier signals through FFT, more accurate phase information can be extracted to improve the anti-interference ability and accuracy of ranging. At the same time, the high efficiency and real-time performance of the FFT algorithm also provide strong support for the practical application of the multi-carrier phase ranging method.
[0051] 2. Combine the interference indications from the reflector and initiator to adaptively select the channel for ranging calculation:
[0052] 1) If the interference indication values of all channels are smaller than the interference indication threshold, all channels can be used for ranging calculation;
[0053] 2) If the interference indication value of a channel is not less than the interference indication threshold, the channel is marked as unavailable; if a channel is agreed to be unavailable, the channel is marked as unavailable. All available channels are divided into continuous frequency segments. The length of the frequency segment is the number of continuous available channels in the segment. Please refer to Figure 2 As shown in the schematic diagram of continuously available frequency bands in the BLE frequency band, the length of the i-th frequency band is Li.
[0054] 3) In all frequency segments, determine whether the length of any frequency segment in all frequency segments is greater than the first preset frequency segment threshold, if so, obtain the longest frequency segment that satisfies the condition of being greater than the first preset frequency segment threshold for ranging calculation; if not, determine whether the length of any frequency segment in all frequency segments is greater than the second preset frequency segment threshold, obtain the longest frequency segment that satisfies the condition of being greater than the second preset frequency segment threshold for ranging calculation, and perform weighted averaging of ranging results obtained for each frequency segment to obtain the final ranging result; if the length of any frequency segment in all frequency segments is not greater than the second preset frequency segment threshold, Among the available frequency segments, two frequency segments are selected, and the unavailable channels between the two frequency segments are interpolated. After interpolation, the two frequency segments before and after are combined to form a long frequency segment, and the ranging calculation is performed. When selecting the frequency segments, the number of unavailable channels between the frequency segments is the smallest among all the selections and is less than the threshold of the number of interpolable channels. The interpolation order of the channels to be interpolated is determined according to the number of channels in the adjacent frequency segments, and then the unavailable channels between the two frequency segments are interpolated. If the above conditions are not met, the channel scanning result is unavailable, and the ranging operation is skipped to avoid very unreliable ranging results.
[0055] In the embodiment of the present invention, for channels that need to be interpolated, the number of channels to be interpolated should be less than the threshold of interpolable channels. The interpolation order of the channels to be interpolated needs to be determined according to the number of channels in adjacent frequency segments. Channel interpolation needs to perform amplitude interpolation of channel response and phase interpolation of channel response respectively, and the amplitude interpolation adopts quadratic interpolation and the phase interpolation adopts linear interpolation.
[0056] In an embodiment of the present invention, the phase response of all channels used for interpolation is obtained. The phase response is obtained from the square root of the channel response. The ambiguity of phase π is introduced in the square root process. A method for removing the ambiguity is provided herein. Due to the influence of interference, before the interpolation channel to be interpolated is interpolated, a phase interference removal process is performed on the existing channel. The phase response jump of the adjacent channel will not exceed a certain threshold. If it exceeds, it indicates that there is an erroneous phase π error caused by interference, which is corrected. The phase interpolation adopts a linear interpolation method, and the amplitude interpolation adopts a quadratic interpolation method.
[0057] In an embodiment of the present invention, a channel that needs to be interpolated is obtained, and a phase response is obtained from the square root of the channel response; the phase differences of all channels and their adjacent channels are traversed, and the phase difference of each channel with its adjacent channels is compared. If the difference is close to the phase π error, the phase ±π of the current channel is adjusted; after completing a round of correction, the phase continuity of all channels is rechecked. After the correction is completed, the phase interpolation adopts a linear interpolation method and the amplitude interpolation adopts a quadratic interpolation method to obtain the complex channel response corresponding to each interpolation point.
[0058] In an embodiment of the present invention, linear interpolation is performed using corrected adjacent channel phase values and proportionally distributed to points to be interpolated to obtain a continuous and smooth phase distribution; for each amplitude point to be interpolated, a quadratic polynomial fitting is performed using three adjacent known amplitude values to determine the amplitude value of the amplitude point to be interpolated; after completing the interpolation of phase and amplitude, a corresponding complex channel response is generated for each interpolation point.
[0059] See also Figure 3 As shown, by estimating the signal-to-noise ratio of the single-tone signal received by the devices at both ends, an estimation result with an error within 3 dB can be given, and the accuracy of the estimation result is sufficient to assist in the judgment of the interference level.
[0060] See also Figure 4 As shown, a schematic diagram of a first embodiment of a ranging solution using an interference adaptive frequency band provided by an embodiment of the present invention uses all scanning frequency channels to measure the distance of 0~11m in an office environment. The average result of 10 tests deviates greatly from the actual distance, has large fluctuations, and the distance is non-linear.
[0061] See also Figure 5 As shown, a second embodiment of the present invention provides a schematic diagram of a ranging solution based on an interference adaptive frequency band, wherein a ranging solution based on an interference adaptive frequency band is used to Figure 4 The test was conducted in the same environment. The results showed that the distance measurement accuracy was higher, and the fluctuation of each test result relative to the actual distance was smaller, and the distance measurement result was linear.
[0062] See also Figure 6 As shown, the interference indication (SNR) estimation uses FFT in the frequency domain, and the FFT result of the single-tone signal.
[0063] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.
Claims
1. A multi-carrier phase ranging method applied to an interference channel scenario, characterized in that: The multi-carrier phase ranging method applied to the interference channel scenario comprises the following steps: Step 1: obtaining an interference indication value of each channel of an initiating end and a receiving end, combining the interference indication value of the initiating end with the interference indication value of the receiving end to obtain interference indication values of all channels; Step 2: determine whether the interference indication value of all channels is less than the interference indication threshold. If so, all channels can be used for ranging calculation. If not, obtain a channel that is not less than the interference indication threshold and mark the channel as unavailable. Step 3: Obtain all available channels determined in step 2, divide all available channels into continuous frequency segments, determine the length of the frequency segments and filter out frequency segments that can be used for ranging calculation, perform ranging calculation on the filtered frequency segments respectively, and perform weighted averaging on the ranging results obtained in each frequency segment to obtain the final ranging result; The calculation process of the interference indication value of each channel in step 1 includes the following steps: A single tone of preset duration is sent from the initiator to the receiver, and after down-conversion, the frequency of the single tone observed at the receiver is less than 10kHz, thereby obtaining a single tone signal, and an AD converter at the receiver samples the single tone signal; After removing the non-single-cause transition signal at the boundary of the single tone, sample N-point single tone data, perform fast Fourier transform on the N-point single tone data, and find the peak position; The power of the single tone signal is obtained by adding up the values of the peak position and the n positions before and after it in the fast Fourier transform result, where n=1,2,...,n; Add up the values of the remaining positions in the fast Fourier transform result to get the power of the noise; Divide the power of the single tone signal by the power of the noise and express it in logarithm to obtain a signal-to-noise ratio estimate, and use the signal-to-noise ratio estimate as an interference indication value; The length of the frequency segment is the number of continuous usable channels; The process of selecting the frequency segments that can be used for ranging calculation in step 3 includes the following steps: Obtain all frequency segments, determine whether there is a frequency segment in all frequency segments whose length is greater than a first preset frequency segment threshold, and if so, obtain the longest frequency segment that satisfies the condition of being greater than the first preset frequency segment threshold for ranging calculation; If otherwise, it is determined whether there is a frequency segment of all frequency segments whose length is greater than the second preset frequency segment threshold, then the longest frequency segment satisfying the condition of being greater than the second preset frequency segment threshold is obtained for ranging calculation; If the length of the frequency segment in all the frequency segments is not greater than the second preset frequency segment threshold, two frequency segments are selected from all the frequency segments, and the unavailable channels between the two frequency segments are interpolated. After the interpolation, the two previous and next frequency segments are combined to form a long frequency segment, and the ranging calculation is performed; When selecting frequency segments, the number of unavailable channels between frequency segments is the smallest among all selections and is less than the threshold of the number of interpolable channels, and the interpolation order of the channels to be interpolated is determined according to the number of channels in adjacent frequency segments; The interpolation process in step 3 includes the following steps: Obtain a channel that needs to be interpolated, and obtain a phase response from the square of the channel response of the channel; Traverse the phase differences of all channels and their adjacent channels, compare the phase difference of each channel with its adjacent channels, and if the difference is close to the phase π error, adjust the phase of the current channel by ±π; After completing a round of calibration, the phase continuity of all channels is rechecked. After the calibration is completed, the phase interpolation adopts the linear interpolation method and the amplitude interpolation adopts the quadratic interpolation method to obtain the complex channel response corresponding to each interpolation point.
2. A multi-carrier phase ranging method applied to an interference channel scenario as claimed in claim 1, characterized in that: The sampling rate of the AD converter is oversampled by 8 times, 12 times or 16 times, and the frequency corresponding to the peak position is the frequency of the single tone.
3. A multi-carrier phase ranging method applied to an interference channel scenario as claimed in claim 1, characterized in that: After completing one round of calibration, the phase continuity of all channels is rechecked. After the calibration is completed, the phase interpolation adopts a linear interpolation method and the amplitude interpolation adopts a quadratic interpolation method to obtain the complex channel response corresponding to each interpolation point, including: Linear interpolation is performed using the corrected adjacent channel phase values and proportionally distributed to the points to be interpolated to obtain a continuous and smooth phase distribution; For each amplitude point to be interpolated, three adjacent known amplitude values are used to perform quadratic polynomial fitting to determine the amplitude value of the amplitude point to be interpolated; After the phase and amplitude interpolation is completed, a corresponding complex channel response is generated for each interpolation point.
