A burst communication system carrier frequency offset estimation method based on phase flip compensation

Abstract

The application discloses a burst communication system carrier frequency offset estimation method based on phase flip compensation and belongs to the technical field of carrier synchronization and frequency offset estimation in a burst communication system. The application solves the problem that the existing Fitz algorithm cannot consider estimation range and estimation accuracy. The application is specifically as follows: step one, a sending end of the burst communication system adds a frame synchronization head to data to be sent before the data, that is, the frame synchronization head and the data to be sent are framed, and then the framed data is modulated and sent; step two, after a receiving end of the burst communication system demodulates the received signal, the cross-correlation function of the demodulated signal is calculated, and then an initial frequency offset estimation value is obtained based on the cross-correlation function; and step three, phase flip compensation is performed on the initial frequency offset estimation value to obtain a final frequency offset estimation result. The method can be applied to the estimation of the carrier frequency offset in the burst communication system.

Description

Technical Field

[0001] This invention belongs to the field of carrier synchronization and frequency offset estimation technology in burst communication systems, specifically relating to a carrier frequency offset estimation method for burst communication systems based on phase flip compensation. Background Technology

[0002] Carrier synchronization and frequency offset estimation have always been key areas of research in digital receivers. Carrier synchronization algorithms mainly fall into two categories: closed-loop synchronization, which uses feedback control to achieve carrier recovery; and open-loop synchronization, which directly estimates the carrier frequency and phase error and compensates for them during demodulation. Burst communication systems have high requirements for processing delay, but closed-loop carrier synchronization algorithms have too long synchronization times and are unsuitable for burst communication systems. Conversely, open-loop carrier synchronization algorithms directly estimate and compensate for frequency offset, offering faster synchronization speeds and making them more suitable for burst communication systems.

[0003] Open-loop carrier synchronization algorithms are divided into time-domain algorithms and frequency-domain algorithms. Compared with frequency-domain carrier synchronization algorithms, time-domain carrier synchronization algorithms have higher estimation accuracy and lower computational complexity, making them more suitable for bursty communication systems. Classic open-loop time-domain carrier synchronization algorithms include the Kay algorithm, the Fitz algorithm, and the L&R algorithm, among which the Fitz algorithm has relatively superior performance.

[0004] The Fitz algorithm was proposed by Michael P. Fitz in 1991, and its theory is as follows:

[0005] Assume the received signal, after down-conversion, matched filtering, and sampling, results in the following signal:

[0006] r k =d k e j(2πfkT+θ) +n k (1)

[0007] Where, d k It is a modulated symbol, f is the frequency offset between the received signal and the local carrier, θ is the phase difference, and n k It is a Gaussian random variable, and n k The mean is 0, the two-sided power spectral density is N0 / 2, and T is the symbol period.

[0008] Assume |d k | 2 =1, demodulate the received signal, that is, demodulate the received signal r k Multiplying by the conjugate of the modulation symbol, we get:

[0009] z k =e j(2πfkT+θ) +υ k (2)

[0010] in, And var(υ) k ) = N0.

[0011] Remember z k The autocorrelation function is:

[0012]

[0013] Where L0 is the length of the autocorrelation function, L0 is an integer and satisfies 1≤L0≤N, and N is the length of the pilot sequence.

[0014] z k Substituting the expression into the above formula, we get:

[0015] R m =e j(2πfmT) +w k (4)

[0016] Among them, w k Let the noise variable have zero mean, and the error be denoted as:

[0017] e m =arg(R) m )-2πfmT(5)

[0018] Since the range of m is 1≤m≤L0-1 and 1≤L0≤N, and R only has a certain value when |2πfmT|≤π. m Only by ensuring that the estimated phase does not flip and that the obtained frequency offset is correct can the normalized frequency offset estimation range of the Fitz algorithm be derived as follows:

[0019]

[0020] in, This represents the estimated frequency offset value.

[0021] It is easy to see from equation (6) that the estimation range of the Fitz algorithm is related to the length N of the autocorrelation sequence, and a trade-off needs to be made between computational complexity and estimation accuracy. N can be appropriately selected according to the situation. When the channel environment of the communication system is highly dynamic, that is, when the frequency offset range is large, a smaller N should be selected to make a rough estimate of the frequency offset. When the actual frequency offset range is small, a larger N can be selected to make a more precise estimate of the frequency offset.

[0022] When the signal-to-noise ratio is large, the error e in equation (5) m It is very small, so averaging it gives:

[0023]

[0024] The expression for frequency offset estimation using the Fitz algorithm can be obtained by rearranging:

[0025]

[0026] In burst communication systems, the carrier frequency offset is large. If the Fitz algorithm is used for estimation, the autocorrelation length needs to be set very small. At this time, the estimation range increases, but the estimation accuracy decreases. Therefore, the existing Fitz algorithm still cannot achieve both increasing the estimation range and improving the estimation accuracy. Proposing a method that balances the estimation range and the estimation accuracy is an urgent problem to be solved. Summary of the Invention

[0027] The purpose of this invention is to solve the problem that the existing Fitz algorithm cannot balance the estimation range and estimation accuracy, and to propose a carrier frequency offset estimation method for burst communication systems based on phase reversal compensation.

[0028] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a carrier frequency offset estimation method for burst communication systems based on phase reversal compensation, the method specifically including the following steps:

[0029] Step 1: The transmitting end of the burst communication system adds a frame synchronization header before the data to be transmitted, that is, it frames the frame synchronization header and the data to be transmitted, and then modulates and transmits the framed data.

[0030] Step 2: After the receiver of the burst communication system demodulates the received signal, it calculates the cross-correlation function of the demodulated signal and then obtains the initial frequency offset estimate based on the cross-correlation function.

[0031] Step 3: Perform phase reversal compensation on the initial frequency offset estimate to obtain the final frequency offset estimate.

[0032] The beneficial effects of this invention are:

[0033] This invention first designs a pilot structure with a certain interval. Based on the designed pilot structure and the traditional autocorrelation Fitz algorithm, a coarse estimate of the frequency offset is obtained. Then, a designed phase reversal compensation method is used to reasonably compensate the calculated coarse estimate of the frequency offset, thereby effectively improving the estimation accuracy and range of the frequency offset. Theoretical derivation and experiments of the Cramer-Rao bound both demonstrate that the cross-correlation-based Fitz algorithm of this invention can effectively improve the estimation accuracy and range of the frequency offset. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the frame synchronization header structure;

[0035] Figure 2 This is a schematic diagram of the frame structure;

[0036] Figure 3 This is a comparison chart of autocorrelation Fitz algorithm estimations;

[0037] Figure 4 This is a comparison chart of autocorrelation and cross-correlation estimations using the Fitz algorithm;

[0038] Figure 5 This is a comparison chart of bit error rates after frequency offset compensation;

[0039] Figure 6 It is a data-assisted mode receiver model. Detailed Implementation

[0040] Theoretical basis

[0041] 1. Pilot structure design

[0042] With the pilot block size set to 2, the test data set consisting of 1 sequence of all 1s, we can obtain... Figure 1 The frame synchronization header structure is shown. The pilot section uses an m-sequence of length 31, which can utilize the good correlation characteristics of the m-sequence for synchronization establishment; the test data section has a length of 224, which is much longer than the pilot section.

[0043] 2. Derivation of the Craméro boundary

[0044] The Cramer-Rao Bound (CRB) for carrier frequency offset estimation refers to the lower bound of the mean square error (MSE) of any unbiased estimation method when estimating carrier frequency offset. The CRB provides a theoretically optimal estimation performance, measuring the impact of noise and signal structure on the estimation accuracy. Figure 2 The frame format shown provides a simple derivation of the Cramer-Rao boundary in carrier frequency offset:

[0045] First, define the parameter matrix to be estimated, which includes frequency offset and phase offset, as α = [f θ]. T and a parameter estimation matrix Therefore when At that time, the pilot sequence at the receiving end The probability density function is:

[0046]

[0047] The time set Z traverses all pilot symbols, i.e., Z = {0, 1, ..., P-1, P+M, ..., 2P+M-1, ..., mP+(m-1)M-1}, P i ,i=1,2,...,m is the length of each pilot segment, M i,i=1,2,...,m is the length of each data segment, and m is the number of pilot blocks.

[0048] Generally, the Cramer-Rao bound for frequency offset estimation can be calculated using the Fisher Information Matrix (FIM). The Fisher Information Matrix is ​​given below:

[0049]

[0050] Assuming the channel conditions are Gaussian white noise, and the prior probabilities of the transmitted signals are equal and independent, then we can obtain:

[0051]

[0052] In the formula, It is the modulated signal after estimating the frequency offset and phase offset rotation, σ 2 =N0 / 2 is the variance of the noise. Since the first exponential term in equation (11) is independent of the sampling time k, it can be ignored. Further simplification yields:

[0053]

[0054] And because r k s k =z k , z k Since it is the demodulated sequence, we have

[0055]

[0056] in, By defining the left end as equal to the right end, substituting equation (13) into the Fisher information matrix, we can obtain:

[0057]

[0058] Further calculations yield the following:

[0059]

[0060] From the above derivation, it can be seen that the first row and first column of the Fisher information matrix is ​​the objective function, let it be... Performing the inverse operation yields the Cramer-Rao bound for the corresponding frequency offset estimate, denoted as CRB(f). Solving for T(f) is equivalent to deriving the summation term. therefore

[0061]

[0062] And because of the pilot symbol spacing D i =P i+M i Simplifying the above equation yields

[0063]

[0064] As can be seen from equation (17), the magnitude of T(f) is related to the pilot length P. i The interval D between the pilot symbols i It is related to, and related to P i 3 and D i 2 If it is directly proportional to P, then the magnitude of CRB(f) is related to P. i 3 and It is inversely proportional, therefore it can be adjusted by changing the pilot symbol spacing D. i and pilot length P i Improve the performance of estimation.

[0065] Because T(f) and CRB(f) are inverses, that is, CRB(f) = [T(f)] -1 Therefore there is

[0066]

[0067] According to the pilot structure, let the length of the pilot be P, the length of the data be M, the interval between pilots be D = P + M, and the number of pilots be m.

[0068]

[0069] When using an autocorrelation-based carrier frequency offset estimation algorithm, no correlation calculations between multiple pilot blocks are involved; only a single pilot block is needed, i.e., D=0, m=1. Therefore, the Cramer-Rao bound of the autocorrelation-based carrier frequency offset estimation method is...

[0070]

[0071] Comparing equations (19) and (20), since the pilot interval D >> 1, CRB2(f) >> CRB1(f). That is, with the same frame structure, when using pilot sequences of the same length for carrier frequency offset estimation, the theoretical lower bound of the cross-correlation-based algorithm is much smaller than that of the autocorrelation-based algorithm. We can adjust the pilot symbol interval to make the cross-correlation-based algorithm's estimation accuracy much higher than that of the autocorrelation-based algorithm. Therefore, this invention proposes the following carrier frequency offset estimation method based on the cross-correlation function.

[0072] Specific Implementation Method 1: The carrier frequency offset estimation method for a burst communication system based on phase reversal compensation described in this implementation method specifically includes the following steps:

[0073] Step 1: The transmitting end of the burst communication system adds a frame synchronization header before the data to be transmitted, that is, it frames the frame synchronization header and the data to be transmitted, and then modulates and transmits the framed data.

[0074] Step 2: After the receiver of the burst communication system demodulates the received signal, it calculates the cross-correlation function of the demodulated signal and then obtains the initial frequency offset estimate based on the cross-correlation function.

[0075] Step 3: Perform phase reversal compensation on the initial frequency offset estimate to obtain the final frequency offset estimate.

[0076] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the frame synchronization header sequentially includes a pilot block, a test data sequence, and a pilot block, and the pilot blocks at both ends of the test data sequence are the same pilot block.

[0077] The other steps and parameters are the same as in Specific Implementation Method 1.

[0078] When calculating the cross-correlation function, this invention only needs to use the pilot part of the data. A pilot block consists of 1 bit and an m sequence of length 31.

[0079] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the cross-correlation function of the demodulation signal is:

[0080]

[0081] Where z(k) represents the k-th pilot symbol after demodulation, z * (k) denotes the conjugate of z(k);

[0082] D represents the spacing of the pilot blocks (equal to the length of one pilot block plus the length of the test data);

[0083] N represents the length of the cross-correlation sequence;

[0084] R D (m) represents the m-th element in the cross-correlation sequence;

[0085] m+D represents the cross-correlation delay length;

[0086] z(k+m+D) represents the k+m+Dth symbol after demodulation.

[0087] Other steps and parameters are the same as in specific implementation method one or two.

[0088] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the length of the cross-correlation sequence is N = λL, 0 < λ ≤ 1, where L is the length of the pilot block.

[0089] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0090] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the initial frequency offset estimate obtained based on the cross-correlation function is specifically as follows:

[0091] R D (m)=e j(2π(m+D)fT+θ) +w(22)

[0092] Where w is a zero-mean noise variable;

[0093] f represents frequency offset;

[0094] e represents the base of the natural logarithm;

[0095] j represents the imaginary unit;

[0096] T represents the symbol interval;

[0097] θ represents phase bias;

[0098] Let the error e(m) be:

[0099] e(m) = arg(R) D (m))-2π(m+D)fT(23)

[0100] Where, arg(R) D (m) represents the calculation of R. D (m) phase angle;

[0101] To ensure the accuracy of the estimation, |2π(α+D)fT|≤π must be satisfied. Therefore, the normalized frequency offset estimation range of the Fitz algorithm based on cross-correlation is:

[0102]

[0103] When the signal-to-noise ratio is large, the error e(m)≈0, therefore let e(m)=0, and take the average of equation (23) to get:

[0104]

[0105] Further simplification of equation (25) yields:

[0106]

[0107] The initial frequency offset estimation result f based on the cross-correlation Fitz algorithm is then... efor:

[0108]

[0109] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0110] Regarding the cross-correlation value R D (m) When calculating the phase angle, due to the existence of the pilot interval D, |2π(m+D)fT|>π, which exceeds the range of [-π,π). The phase angle obtained at this time is modulo 2π, not the true phase angle. Therefore, the phase difference is incorrectly estimated, resulting in an incorrect frequency offset estimate. This phenomenon is called phase flip. Therefore, this invention performs phase flip compensation.

[0111] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the specific process of step three is as follows:

[0112] Due to the presence of the pilot spacing D, when the frequency offset is large, the phase of R(1) has a high probability of phase flipping when m=1. Therefore, the input terminal receives the frequency offset value estimated by the Fitz algorithm with a small autocorrelation length. Used to estimate the true phase Q(1) of R(1), avoiding impact on subsequent phase flip compensation. Therefore:

[0113] Step 3: 1. Obtain the coarse frequency offset estimate based on the Fitz algorithm (i.e., the traditional Fitz algorithm) which is based on autocorrelation. Calculate the first element R in the cross-correlation sequence D (1) Phase Q(1) after flip compensation:

[0114]

[0115] Step 3.2: Initialize m = 2;

[0116] Step 3: Calculate the m-th element R in the cross-correlation sequence. D The phase Q(m) after flip compensation:

[0117] Steps three and four: Determine whether m = N is satisfied;

[0118] If m < N, then let m = m + 1 and return to step 3.3.

[0119] If m = N, then proceed to step three five;

[0120] Step 35: Perform phase reversal compensation on the initial frequency offset estimate based on Q(m), m=1,2,…,N, and calculate the final frequency offset estimate.

[0121] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0122] The specific execution flow of step three is shown in Table 1:

[0123] Table 1. Cross-correlation Fitz algorithm based on phase reversal compensation

[0124]

[0125] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the specific process of step three is as follows:

[0126] Ignoring the effects of noise, R D The true phase φ(m) of (m) is:

[0127] φ(m)=2πfT(m+D)(29)

[0128] The true value of the current phase is predicted using the phase after flip compensation of the first m-1 elements, i.e., by averaging the phase values ​​after flip compensation of the first m-1 elements in the cross-correlation sequence:

[0129]

[0130] Rearranging equation (30) yields:

[0131]

[0132] but

[0133]

[0134] Comparing equations (29) and (32), we find that:

[0135]

[0136] For R D The phase φ(m) of (m) is flipped and compensated, and then...

[0137] Q(m)=arg(R D (m))+2πM0(34)

[0138] Where Q(m) represents R D (m) represents the phase after flip compensation, and M0 represents the number of phase flips.

[0139] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0140] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the method for calculating the number of phase flips M0 is as follows:

[0141] Subtract Q(m) from φ(m), and then... Calculate M0 by substituting f into the difference result:

[0142]

[0143] Where 0 ≤ M ≤ N, and M is an integer. This means calculating the value of M that minimizes the range of values.

[0144] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0145] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the specific process of step three and five is as follows:

[0146]

[0147] in, This represents the final frequency offset estimation result.

[0148] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0149] Experimental Section

[0150] When conducting the experiment, according to Figure 6 The data-assisted synchronization mode shown first involves framing the frame synchronization header and data bits at the transmitting end according to the designed frame structure, then modulating the framing result and adding a frequency offset to the modulation result. At the receiving end, the frame is deframed based on the frame synchronization, the frequency offset is estimated using the frame synchronization header, the frequency offset is compensated based on the frequency offset estimation result, and finally the frequency offset compensated data is demodulated to obtain the recovered data bits.

[0151] For carrier frequency offset estimation algorithms, estimation performance is typically measured by two metrics: estimation accuracy and estimation range. This invention uses the comparison between the normalized frequency offset estimate and the actual normalized frequency offset value to measure the estimation range, and uses the normalized mean square error (NMSE) to measure the estimation accuracy. Its expression is:

[0152]

[0153] Where T is the symbol rate. To estimate the frequency offset, f d This represents the actual frequency offset.

[0154] In addition, normalized estimation bias is also frequently used to measure the estimation performance of an algorithm, and its expression is:

[0155]

[0156] if If it is zero, then the estimated value It is an unbiased estimate; otherwise, the estimate is a biased estimate.

[0157] (1) Improve the estimation range of the algorithm

[0158] With autocorrelation lengths set to 32 and 16, phase-flip compensation was performed on the Fitz algorithm with an autocorrelation length of 64. The normalized true frequency offset range was -0.1 to 0.1, the step size was 0.01, and the Monte Carlo iterations were 10000. Under Gaussian white noise channel, the estimation range of the phase-flip compensated Fitz algorithm is as follows: Figure 3 As shown, the black curve corresponds to the square marker. Theoretically, the estimation range when the autocorrelation length is 64 is smaller than the estimation range when the autocorrelation length is 16 and 32. However, due to phase flip compensation, it can be seen that the estimation range of the black curve is much larger than that of the blue and red curves, and the frequency offset can still be correctly estimated when the normalized frequency offset reaches 0.1.

[0159] (2) Improve the estimation accuracy of the algorithm

[0160] The improved algorithm proposed in this invention was simulated to verify its estimation performance. The normalized true frequency offset was set to 0.01, which exceeds the estimation range of the cross-correlation Fitz algorithm. E s With / N0 set to 10dB and Monte Carlo iterations set to 10000, the estimation accuracy of the improved algorithm is as follows under Gaussian white noise channel: Figure 4 As shown in the figure, corresponding to the blue curve, it can be seen that the mean squared error curve of the algorithm of this invention is close to the Cramer-Rao bound of the cross-correlation algorithm, but lower than the Cramer-Rao bound of the autocorrelation algorithm; meanwhile, the estimation accuracy of the cross-correlation Fitz algorithm shown by the black curve does not increase with E s The improvement is due to the increase of / N0, and it is still some distance from the Cramer-Rao bound of the cross-correlation algorithm. Therefore, it can be concluded that the cross-correlation Fitz algorithm based on phase reversal compensation proposed in this invention effectively increases the estimation range of the cross-correlation Fitz algorithm, while the estimation accuracy is about two orders of magnitude higher than that of the autocorrelation Fitz algorithm based on phase reversal compensation.

[0161] (3) Frequency offset compensation effect

[0162] The normalized true frequency offset is set to 0.01, E s The range of / N0 is 0dB-10dB, the Monte Carlo simulation is set to 10000, and the burst frame count is 100. After compensating the data with the frequency offset estimated by the method of this invention, the resulting bit error rate curve is as follows: Figure 5As shown, the improved algorithm closely approximates the theoretical bit error rate (BER) curve. Compared to the BER curves compensated by the Fitz algorithm with autocorrelation lengths of 32 and 16, the improved algorithm exhibits a signal-to-noise ratio (SNR) advantage of 1 dB and 2.5 dB, respectively. It is also evident that without frequency offset estimation and compensation, the BER approaches 1, making it difficult for the system to function properly.

[0163] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for carrier frequency offset estimation in a phase-reversal-compensation-based burst communication system, characterized by, The method specifically comprises the following steps: Step one, the sending end of the burst communication system adds a frame synchronization header to the data to be sent, that is, frames the frame synchronization header and the data to be sent, and then modulates and sends the framed data; Step two, the receiving end of the burst communication system calculates the cross-correlation function of the demodulated signal after demodulating the received signal, and then obtains an initial frequency offset estimation value based on the cross-correlation function; The initial frequency offset estimation value is obtained based on the cross-correlation function, and specifically is: R D (m) = e j(2π(m+D)fT+θ) + w (22) Wherein, w is a zero-mean noise variable; f represents the frequency offset; e represents the base number of natural logarithm; j represents the imaginary unit; T represents the symbol interval; θ represents the phase offset; R D (m) denotes the mth element in the cross-correlation sequence; D represents the interval of the pilot block; m+D represents the cross-correlation delay length; Let the error e(m) be: e(m) = arg(R D (m))-2π(m+D)fT (23) where arg(R D (m)) denotes the phase angle of R D (m). Let e(m)=0, and average formula (23) to obtain: Wherein, N represents the length of the cross-correlation sequence; Further, formula (25) is arranged to obtain: The initial frequency offset estimation result f e is: Step three, phase flip compensation is performed on the initial frequency offset estimation value to obtain a final frequency offset estimation result.

2. The method of claim 1, wherein, The frame synchronization header sequentially comprises a pilot block, a test data sequence and a pilot block, and the pilot blocks at both ends of the test data sequence are the same pilot block.

3. The method of claim 2, wherein, The cross-correlation function of the demodulated signal is: where z(k) denotes the kth pilot symbol after demodulation, z * (k) denotes the conjugate of z(k); z(k+m+D) represents the k+m+D th symbol after demodulation.

4. The method of claim 3, wherein, The length N of the cross-correlation sequence is λL, 0<λ≤1, and L is the length of the pilot block.

5. The method of claim 4, wherein, The specific process of step three is: Step three one, the coarse frequency offset estimation value obtained according to the Fitz algorithm based on self-correlation Calculate the first element R in the cross-correlation sequence D The flip compensation phase Q(1) of (1): Step three two, initialize m=2; Step three, compute the mth element R of the cross-correlation sequence D (m) the phase Q(m) after flip compensation Step three four, judge whether m=N is satisfied; If m If m=N, execute step three five; Step three five, phase flip compensation is performed on the initial frequency offset estimation value according to Q(m), m=1, 2,…, N, and the final frequency offset estimation result is calculated.

6. The method of claim 5, wherein, The specific process of step three three is: R D The true phase φ(m) of (m) is: φ(m)=2πfT(m+D) (29) The average of the flip-compensated phase values of the first m-1 elements in the cross-correlation sequence is calculated: Formula (30) is arranged to obtain: Then By comparing formula (29) and formula (32), it is obtained that: R D (m) are phase flipped, and have Q(m) = arg(R D (m)) + 2πM0 (34) where Q(m) represents R D (m) the corresponding phase after roll compensation, M0 represents the number of phase roll.

7. The method of claim 6, wherein, The calculation method of the phase flip times M0 is: Wherein, 0≤M≤N, and M is an integer.

8. The method of claim 7, wherein, The specific process of step three five is: wherein denotes the final frequency offset estimation result.

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