Frequency offset estimation method and device, storage medium and program product
By acquiring and processing frequency domain signals in mobile communications, performing frequency offset precompensation and related detection, the problem of poor detection of large frequency offsets in the prior art is solved, and frequency offset estimation with higher accuracy and range is achieved, and computational complexity and resource consumption are reduced.
Patent Information
- Application Number
- CN202510152883.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-12
- Publication Date
- 2025-03-14
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The prior art cannot effectively detect and estimate large frequency deviations, resulting in the inability to achieve accurate frequency deviation compensation in certain mobile communication scenarios.
By obtaining the oversampled frequency domain local synchronization signal and the frequency domain reception signal, frequency offset precompensation is performed, and frequency domain correlation detection is performed based on the precompensation results to improve the range and accuracy of frequency offset estimation.
The frequency offset precompensation for the decimal multiple subcarrier interval particle size is realized, and the residual frequency offset is controlled within the one-half subcarrier interval range, which improves the range and accuracy of frequency offset estimation, reduces the computational complexity, and saves storage and computing resources.
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Figure CN119629002A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of mobile communications, and in particular to a frequency offset estimation method, device, storage medium and program product. Background Art
[0002] In mobile communication scenarios, the relative movement of the communicating parties may cause the receiving terminal to generate Doppler frequency offset, which is large in some application scenarios. The receiving terminal must estimate and compensate for this frequency offset during the initial synchronization phase.
[0003] The existing frequency offset estimation method generally uses the PSS (Primary Synchronization Signal) for coarse frequency offset estimation, and then combines it with the SSS (Secondary Synchronization Signal) for fine frequency synchronization. However, this method can detect a limited frequency offset range and is not applicable to scenarios where the frequency offset exceeds a certain range. Summary of the invention
[0004] The object of the present invention is to provide a frequency offset estimation method, device, storage medium and program product to address all or part of the above-mentioned problems, so as to solve the problem that the prior art cannot perform blind detection of large frequency offsets.
[0005] The technical solution adopted by the present invention is as follows: A frequency offset estimation method, comprising: Obtaining an oversampled frequency domain local synchronization signal; Obtaining a frequency domain received signal; Performing frequency offset pre-compensation based on the oversampled frequency domain local synchronization signal or the frequency domain received signal; Frequency domain correlation detection is performed based on the frequency offset pre-compensation result.
[0006] In order to solve the above problem, the present invention further provides a frequency offset estimation device, which comprises: The first module is configured to: obtain an oversampled frequency domain local synchronization signal; The second module is configured to: obtain a frequency domain received signal; The third module is configured to: perform frequency offset pre-compensation based on the oversampled frequency domain local synchronization signal or the frequency domain received signal; The fourth module is configured to perform frequency domain correlation detection based on the frequency offset pre-compensation result of the third module.
[0007] In order to solve the above problem, the present invention further provides a storage medium storing a computer program, and running the computer program can execute the above frequency offset estimation method.
[0008] To solve the above problem, the present invention further provides a device, including a processor and a storage medium, wherein the storage medium stores a computer program, and when the processor runs the computer program, the above frequency offset estimation method can be executed.
[0009] To solve the above problem, the present invention further provides a computer program product, including a computer program, and running the computer program can execute the above frequency offset estimation method.
[0010] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: The frequency offset estimation method of the present application supports frequency offset pre-compensation for fractional subcarrier spacing granularity by oversampling the local synchronization signal in the frequency domain, and can control the residual frequency offset within the range of half the subcarrier spacing (SCS), thereby improving the frequency offset estimation range and accuracy, and ensuring that the synchronization performance is basically unaffected by the frequency offset. In addition, the present application implements the frequency offset time domain pre-compensation through cyclic shift, avoiding the calculation of the pre-correction factor, eliminating the need to cache the frequency domain received signal after pre-correction, and eliminating the need for complex multiplication of the frequency domain received signal and the pre-correction factor, thereby reducing the computational complexity of the frequency offset estimation, effectively saving storage resources and computing power resources, and improving computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The present invention will now be described by way of example with reference to the accompanying drawings, in which: Figure 1 It is a flow chart of the frequency offset estimation method provided in an embodiment of the present application.
[0012] Figure 2 This is a flowchart for obtaining an oversampled frequency domain local synchronization signal provided by an embodiment of the present application.
[0013] Figure 3 This is a flowchart for obtaining a frequency domain received signal provided in an embodiment of the present application.
[0014] Figure 4 This is a flow chart of frequency domain correlation detection provided in an embodiment of the present application.
[0015] Figure 5 This is another flow chart of frequency domain correlation detection provided in an embodiment of the present application.
[0016] Figure 6 This is a flow chart of performing frequency offset estimation based on cross-correlation results provided in an embodiment of the present application. DETAILED DESCRIPTION
[0017] All features disclosed in this specification, or steps in all methods or processes disclosed, except mutually exclusive features and / or steps, can be combined in any manner.
[0018] Any feature disclosed in this specification (including any additional claims and abstract), unless otherwise stated, may be replaced by other alternative features that are equivalent or have similar purposes. That is, unless otherwise stated, each feature is only an example of a series of equivalent or similar features.
[0019] In view of the problem that the existing frequency offset estimation method is not suitable for large frequency offset detection, the embodiments of the present application provide a frequency offset estimation method, device, storage medium and program product, which are intended to improve the range and accuracy of blind frequency offset detection in mobile communications. In the embodiments of the present application, the frequency offset estimation method of the present application is described by taking the PSS signal as the local synchronization signal as an example. Without loss of generality, the local synchronization signal can use other synchronization signals in different frequency offset blind detection scenarios.
[0020] In some embodiments, Figure 1 As shown, the frequency offset estimation method includes the following three steps: S1: Obtain an oversampled frequency domain PSS signal and obtain a frequency domain received signal.
[0021] Through oversampling, the frequency domain PSS signal corresponding to the integer / non-integer multiple SCS position is obtained. In theory, the residual frequency offset can be controlled within 1 / 2 times the frequency shift step (the step can be a non-integer multiple of SCS) to improve the performance of timing synchronization and large frequency offset estimation.
[0022] As an optional implementation, the oversampled frequency domain PSS signal is obtained by performing Fourier interpolation on the time domain PSS signal. The frequency domain PSS signal of the required length can be quickly obtained by Fourier interpolation. In addition, for ease of explanation, in the implementation of this application, the Fourier transform uses the fast Fourier transform FFT (the inverse transform is IFFT).
[0023] As an optional implementation, the number of interpolation points for performing FFT interpolation on the time-domain PSS signal is an integer multiple of more than twice the length of the time-domain PSS signal.
[0024] For example, assuming that the length of the time domain PSS signal is N, the number of interpolation points of FFT interpolation is ,but It is an integer multiple of N and the multiple is not less than 2.
[0025] In some specific embodiments, the method for obtaining the oversampled frequency domain PSS signal is as follows: Figure 2 As shown, the method includes: S1.1: Perform IFFT transformation on the PSS frequency domain local signal to obtain the time domain PSS signal. Taking the frequency domain local synchronization sequence length of 127 as an example, the PSS frequency domain m sequence of length 127 is (i.e., PSS frequency domain local signal) performs N-point IFFT transformation to obtain the time domain PSS signal .
[0026] , , in, Indicates the cell ID2 number. For example, if there are 3 cells, ; N is the number of FFT points after the synchronous channel is filtered and downsampled, that is, the length of the time domain PSS signal.
[0027] S1.2: Perform FFT interpolation on the time domain PSS signal, the number of interpolation points is .
[0028] The time domain PSS signal is reversed, conjugated, and added with 0 to obtain the signal , and then proceed Point FFT transformation to obtain the oversampled frequency domain PSS signal .
[0029] , .
[0030] Signal That is the oversampled frequency domain PSS signal. The signal can be The table is stored for use in frequency deviation pre-compensation.
[0031] As an optional implementation, the frequency domain received signal is segmented and FFT is performed on the time domain received signal. That is, the frequency domain received signal includes multiple sub-segments. The segmentation of the time domain received signal is to facilitate subsequent frequency domain correlation detection.
[0032] As an optional implementation, the length of the sub-segments into which the time-domain received signal is divided is equal to the length of the oversampled frequency-domain PSS signal.
[0033] In order to better restore the time domain features in the frequency domain correlation detection step, in some optional implementations, between adjacent sub-segments into which the time domain received signal is divided, the tail of the previous sub-segment overlaps with the head of the next sub-segment.
[0034] In addition, in order to more accurately restore the time domain features, preferably, the overlapping length between adjacent sub-segments is not less than the length of the time domain local synchronization signal minus 1.
[0035] For example, the signal Rx received by the antenna is converted to digital by the RF front end and then sent to the digital front end DFE (Digital Front-End) for low-pass filtering, downsampling and other processing. Figure 3The flowchart of a method for obtaining a frequency domain received signal in some specific embodiments is shown, and the method includes: S1.3: Segment the time domain received signal. Assume that the filtered down-sampled time domain received signal output by DFE is , for the signal Each sub-segment is divided into To express, , L represents the signal The length of the segment is In adjacent sub-segments, the tail of the previous sub-segment overlaps with the head of the next sub-segment, and the overlapping length is N-1 (or exceeds N-1).
[0036] S1.4: For each sub-segment of the segment Perform FFT separately to obtain each sub-segment The corresponding frequency domain received signal .
[0037] have: , , … .
[0038] S2: Perform frequency offset pre-compensation based on the oversampled frequency domain PSS signal or the frequency domain received signal.
[0039] As an optional implementation manner, the frequency offset pre-compensation performed in step S2 includes: According to the frequency offset trial value, the oversampled frequency domain PSS signal or the frequency domain received signal is cyclically shifted. The frequency offset time domain pre-compensation is realized by cyclic shifting, and there is no need to calculate the pre-correction factor required for the coarse frequency offset compensation in the prior art, nor is there any need to cache the frequency domain received signal after pre-correction, nor is there any need to perform a complex multiplication operation of the frequency domain received signal and the pre-correction factor, which reduces the computational complexity of frequency offset estimation, effectively saves storage resources and computing power resources, and improves computing efficiency.
[0040] As an optional implementation, the frequency offset trial value in the frequency offset pre-compensation is sampled from a set frequency offset estimation range. In some feasible implementations, the frequency offset trial value is sampled (equidistantly) from the frequency offset estimation range by a predetermined frequency shift step.
[0041] The so-called frequency offset estimation range is the search interval of frequency offset blind detection, and the frequency shift step is the interval between adjacent frequency offset trial values. In some optional implementations, the frequency offset estimation range and the frequency shift step are determined based on the set maximum Doppler frequency shift value and subcarrier spacing.
[0042] The maximum Doppler shift value can be obtained based on historical data statistics of mobile communication scenarios or corresponding simulation results. For example, for LEO (Low Earth Orbit) satellites, the typical maximum Doppler shift value is 24ppm (part per million) of the carrier frequency. For other mobile communication scenarios, such as NTN (Non-Terrestrial Network) communication scenarios such as MEO (Medium Earth Orbit) satellites, HEO (High Earth Orbit) satellites and even GEO (Geosynchronous Orbit) satellites, or TN (Terrestrial Network) communication scenarios such as cellular mobile communications, there are corresponding maximum Doppler shift values. The subcarrier spacing is determined by the communication system of the specific communication scenario. For example, in a communication system scenario using multi-carrier technology, the subcarrier spacing may be OFDM (Orthogonal Frequency Division Multiplexing) subcarrier spacing.
[0043] The principle of determining the frequency offset estimation range is that in some optional implementations, the absolute value of the end value of the frequency offset estimation range is not less than the absolute value of the maximum Doppler frequency shift value. In addition, to ensure the accuracy of the frequency offset estimation, in some optional implementations, the frequency shift step size does not exceed half of the SCS.
[0044] Taking the maximum Doppler frequency shift value of 50kHz (-50kHz in the opposite direction) and SCS of 30kHz as an example, the set frequency deviation estimation range can be [-60kHz, 60kHz], and the frequency shift step is 15kHz. Usually, in order to facilitate computer execution, in the program executed by the computer, the normalized frequency deviation trial value is used for trial. In some embodiments, each frequency is normalized with SCS, then the frequency deviation estimation range is expressed as [-2,2], the frequency shift step is 1 / 2, that is, a fractional multiple of SCS, and the frequency deviation trial value is It is expressed as {-2,-1.5,-1,-0.5,0,0.5,1,1.5,2}. Each frequency offset trial value is traversed, and the oversampled frequency domain PSS signal or the frequency domain received signal is cyclically shifted to achieve frequency offset pre-compensation.
[0045] In the embodiment of the present application, there are two ways to pre-compensate the frequency offset: cyclically shift the oversampled frequency domain PSS signal, or cyclically shift the frequency domain received signal. As an optional implementation, the frequency shift directions of the cyclic shift of the oversampled frequency domain PSS signal and the frequency domain received signal are opposite.
[0046] 1) Perform cyclic shift on the oversampled frequency domain PSS signal.
[0047] The signal in the previous embodiment Take this as an example, and traverse each frequency deviation attempt value , for the signal Cyclic shift, the number of shifted subcarriers is , obviously, and The value of is an integer. The frequency domain PSS signal obtained after frequency shifting is for: , In the formula, % represents the modulo operation.
[0048] 2) Perform cyclic shift on the received signal in the frequency domain.
[0049] The frequency domain received signal { } as an example, traverse each frequency deviation attempt value , for each frequency domain received signal Cyclic shift is performed, and the number of shifted subcarriers is . Get the frequency domain received signal after frequency shift { ,in: .
[0050] S3: Perform frequency domain correlation detection based on the frequency offset pre-compensation result.
[0051] As an optional implementation manner, the frequency domain correlation detection performed in step S3 includes: S3.1: Cross-correlate the cyclically shifted one of the oversampled frequency domain local synchronization signal and the frequency domain received signal with the other. Implementing frequency domain correlation detection through cross-correlation can effectively reduce the computational complexity of frequency offset estimation and improve the efficiency of frequency offset blind detection.
[0052] Corresponding to the two methods of frequency offset pre-compensation, there are also two methods for step S3.1: 1) Cross-correlate the frequency-domain PSS signal after frequency shifting with the frequency-domain received signal, such as Figure 4 shown.
[0053] The frequency domain PSS signal after frequency shifting implemented in the previous article and the received signal in the frequency domain { } as an example, the cross-correlation result of the first method is expressed as: .
[0054] Traverse all cell ID2 and frequency deviation attempt values and subsection (corresponding to the received signal in the frequency domain ), repeat the point multiplication operation to obtain the corresponding cross-correlation result .
[0055] 2) Cross-correlate the frequency domain PSS signal with the frequency-shifted frequency domain received signal, such as Figure 5 shown.
[0056] The frequency domain PSS signal in the previous implementation and the frequency domain received signal after frequency shift { } as an example, the cross-correlation result of the second method is expressed as: .
[0057] Similarly, traverse all cell ID2, frequency offset attempt value f and sub-segments (corresponding to the received signal in the frequency domain ), repeat the point multiplication operation to obtain the corresponding cross-correlation result .
[0058] In the embodiment of the present application, the time domain sliding correlation of the synchronization signal after pre-correction is equivalent to the frequency domain point product, which greatly reduces the calculation complexity and improves the efficiency of frequency deviation blind detection.
[0059] S3.2: Perform frequency offset estimation based on the cross-correlation result.
[0060] As an optional implementation, Figure 6 As shown, step S3.2 includes the following process: S3.2.1: Convert the cross-correlation result from the frequency domain to the time domain to obtain the time domain cross-correlation result.
[0061] For each cell, for different frequency offset trial values f, there are different cross-correlation results { }, each sub-segment Corresponding Convert to the time domain respectively, and get the time domain cross-correlation result { },in: .
[0062] S3.2.2: Discard the time domain cross-correlation result { } to obtain the time domain correlation model.
[0063] When acquiring the frequency domain received signal, the time domain received signal is segmented, and there is data overlap in adjacent sub-segments. Therefore, after frequency offset pre-compensation and frequency domain correlation, there will be repeated data in the cross-correlation result.
[0064] As a feasible implementation method, the discarded duplicate data is the time domain cross-correlation result { }, the next sub-segment In the previous sub-segment Duplicate data. After removing duplicate data, the complete data constituting the time domain correlation model can be obtained.
[0065] As a feasible implementation method, the time domain correlation model is composed of the time domain cross-correlation result { } The sub-segments after discarding duplicate data are concatenated. Represents the time domain correlation model, then: .
[0066] After cascading, it is convenient to analyze the overall time domain characteristics in the same signal model.
[0067] S3.2.3: Perform frequency offset estimation based on the time domain correlation model.
[0068] As an optional implementation, step S3.2.3 includes: Traversing time domain correlation model The amplitude of each element of is used to obtain the frequency deviation trial value and / or symbol timing synchronization point corresponding to the peak point. In some specific embodiments, by searching The peak value of the frequency offset is taken as the frequency offset estimation result, or the symbol timing synchronization point and cell ID2 corresponding to the peak point are taken as the frequency offset estimation result. The frequency offset estimation result is expressed as: , In the formula, Represents cell ID 2, represents the estimated frequency offset value, Represents the symbol timing synchronization point.
[0069] After the frequency offset is estimated, frequency offset compensation can be performed according to the estimated frequency offset value.
[0070] The embodiments of the present application also verify the performance of the frequency offset estimation method proposed in the present application. The performance indicators include complexity (number of complex multiplications), memory usage and frequency offset estimation performance (maximum residual frequency offset). Among them, the memory usage indicator is based on the baseline of not performing blind frequency offset detection and performing incremental statistics.
[0071] The system parameters are set as follows: L=10000, N=256, =2048, SCS=30kHz. And it is assumed that the bit width of a time domain sampling data is 16 bits. In the prior art, the frequency offset assumption value is an integer multiple of SCS. Taking the frequency offset assumption value of 5 integer multiples of SCS as an example, its normalized frequency offset attempt value is {-2, -1, 0, 1, 2}; the frequency shift compensation of the embodiment of the present application is 1 / 2SCS, and there are a total of 9 frequency offset attempt values {-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2}.
[0072] In terms of complexity, the number of complex multiplications in the prior art (including frequency offset compensation and time domain sliding correlation) is: = 12512320, the number of complex multiplications (including FFT, frequency domain dot multiplication and IFFT) in the embodiment of the present application (two frequency offset pre-compensation methods) is: =1462272.
[0073] In terms of memory usage, the existing technology needs to cache the frequency domain received signal after pre-correction, and the memory usage is 2( + N) Bytes = 4.5kB, and the embodiment of the present application does not require any cache and the memory usage is 0.
[0074] In terms of frequency offset estimation performance, the maximum residual frequency offset in the prior art is 15kHz, i.e. 1 / 2SCS. The maximum residual frequency offset in the present application is 7.5kHz, i.e. only 1 / 4SCS.
[0075] It can be seen from the comparative experiment that the frequency offset estimation method of the present application has absolute advantages in terms of solution complexity, memory usage and maximum residual frequency offset.
[0076] The frequency offset estimation device provided in the embodiment of the present application includes a first module, a second module, a third module and a fourth module; wherein: The first module is configured to: obtain an oversampled frequency domain local synchronization signal; The second module is configured to: obtain a frequency domain received signal; The third module is configured to: perform frequency offset pre-compensation based on an oversampled frequency domain local synchronization signal or based on a frequency domain received signal; The fourth module is configured to perform frequency domain correlation detection based on the frequency offset pre-compensation result of the third module.
[0077] The specific operations performed by each module in the above-mentioned frequency offset estimation device can refer to the corresponding embodiments in the above-mentioned frequency offset estimation method, which are implemented by configuring corresponding computer instructions to execute the corresponding processes in the frequency offset estimation method, and will not be described in detail here.
[0078] The storage medium provided in the embodiment of the present application stores a computer program, and running the computer program can execute the frequency offset estimation method of the above embodiment.
[0079] The device provided in the embodiment of the present application includes a processor and a storage medium, wherein the storage medium stores a computer program. When the processor runs the computer program, the frequency offset estimation method of the above embodiment can be executed.
[0080] The computer program product provided in the embodiments of the present application includes a computer program, and running the computer program can execute the frequency offset estimation method of the above embodiments.
[0081] The present invention is not limited to the above-mentioned specific embodiments, but extends to any new features or any new combination disclosed in this specification, as well as any new method or process steps or any new combination disclosed.
Claims
1. A frequency offset estimation method, characterized in that: include: Obtaining an oversampled frequency domain local synchronization signal; Obtaining a frequency domain received signal; Performing frequency offset pre-compensation based on the oversampled frequency domain local synchronization signal or the frequency domain received signal; Frequency domain correlation detection is performed based on the frequency offset pre-compensation result.
2. The frequency offset estimation method according to claim 1, wherein: The oversampled frequency domain local synchronization signal is obtained by performing Fourier interpolation on the time domain local synchronization signal.
3. The frequency offset estimation method according to claim 2, wherein: The number of interpolation points for Fourier interpolation of the time-domain local synchronization signal is an integer multiple of more than twice the length of the time-domain local synchronization signal.
4. The frequency offset estimation method according to any one of claims 1 to 3, characterized in that: The frequency domain received signal is obtained by segmenting the time domain received signal and performing Fourier transform.
5. The frequency offset estimation method according to claim 4, wherein: The length of the sub-segments into which the time-domain received signal is divided is equal to the length of the over-sampled frequency-domain local synchronization signal.
6. The frequency offset estimation method according to claim 5, wherein: Between adjacent sub-segments divided into the time domain received signal, the tail of a previous sub-segment overlaps with the head of a subsequent sub-segment.
7. The frequency offset estimation method according to claim 6, wherein: The overlapping length between adjacent sub-segments is not less than the length of the time domain local synchronization signal minus 1.
8. The frequency offset estimation method according to claim 6 or 7, characterized in that: The frequency offset pre-compensation includes: According to the frequency offset trial value, the oversampled frequency domain local synchronization signal or the frequency domain received signal is cyclically shifted.
9. The frequency offset estimation method according to claim 8, wherein: The frequency offset trial value is obtained by sampling from a set frequency offset estimation range using a predetermined frequency shift step length.
10. The frequency offset estimation method according to claim 8, wherein: The frequency shift directions of the cyclic shift of the oversampled frequency domain local synchronization signal and the frequency domain received signal are opposite.
11. The frequency offset estimation method according to claim 8, wherein: The frequency domain correlation detection includes: Cross-correlating the cyclically shifted one of the oversampled frequency domain local synchronization signal and the frequency domain received signal with the other; The frequency offset is estimated based on the cross-correlation results.
12. The frequency offset estimation method according to claim 11, wherein: The performing frequency offset estimation according to the cross-correlation result comprises: Convert the cross-correlation result from frequency domain to time domain to obtain a time domain cross-correlation result; discarding repeated data in the time domain cross-correlation result to obtain a time domain correlation model; Frequency offset estimation is performed according to the time domain correlation model.
13. The frequency offset estimation method according to claim 12, wherein: The discarding of repeated data in the time domain cross-correlation result comprises: In each adjacent sub-segment of the time domain cross-correlation result, data in a subsequent sub-segment that is repeated with data in a previous sub-segment is discarded.
14. The frequency offset estimation method according to claim 12 or 13, characterized in that: The time domain correlation model is formed by cascading the sub-segments of the time domain cross-correlation result after discarding repeated data.
15. The frequency offset estimation method according to claim 11, wherein: Performing frequency offset estimation according to the time domain correlation model includes: The amplitude of each element of the time domain correlation model is traversed to obtain a frequency deviation trial value and / or a symbol timing synchronization point corresponding to a peak point.
16. A frequency offset estimation device, characterized in that: include: The first module is configured to: obtain an oversampled frequency domain local synchronization signal; The second module is configured to: obtain a frequency domain received signal; The third module is configured to: perform frequency offset pre-compensation based on the oversampled frequency domain local synchronization signal or the frequency domain received signal; The fourth module is configured to perform frequency domain correlation detection based on the frequency offset pre-compensation result of the third module.
17. A storage medium storing a computer program, characterized in that: Running the computer program can execute the frequency offset estimation method as described in any one of claims 1-15.
18. A device comprising a processor and a storage medium, wherein the storage medium stores a computer program, characterized in that: When the processor runs the computer program, it can execute the frequency offset estimation method as described in any one of claims 1-15.
19. A computer program product comprising a computer program, characterized in that Running the computer program can execute the frequency offset estimation method as described in any one of claims 1-15.
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