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

Abstract

The invention 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. According to the invention, the problem that the existing Fitz algorithm cannot give consideration to both the estimation range and the estimation precision is solved. The method specifically comprises the following steps: step 1, a sending end of a burst communication system adds a frame synchronization head before to-be-sent data, namely framing the frame synchronization head and the to-be-sent data, and then modulating and sending the framed data; step 2, a receiving end of the burst communication system demodulates the received signal, calculates a cross-correlation function of the demodulated signal, and obtains an initial frequency offset estimation value based on the cross-correlation function; and step 3, performing phase flip compensation on the initial frequency offset estimation value to obtain a final frequency offset estimation result. The method can be applied to estimation of carrier frequency offset in a burst communication system.

Description

Technical Field

[0001] The present invention belongs to the technical field of carrier synchronization and frequency offset estimation in burst communication systems, and particularly relates to a method for estimating carrier frequency offset in a burst communication system based on phase flip compensation. Background Art

[0002] Carrier synchronization and frequency offset estimation have always been the focus of research on digital receivers. There are mainly two categories of carrier synchronization algorithms. One is closed-loop synchronization, that is, using a feedback control method to achieve carrier recovery; the other is open-loop synchronization, that is, directly estimating the carrier frequency and phase error and directly compensating during demodulation. Burst communication systems have relatively high requirements for processing delay, while the synchronization time of closed-loop carrier synchronization algorithms is too long and not suitable for burst communication systems. On the contrary, open-loop carrier synchronization algorithms directly estimate and compensate for frequency offset, with fast synchronization speed and are 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, and are more suitable for burst communication systems. Classic open-loop time-domain carrier synchronization algorithms include the Kay algorithm, the Fitz algorithm, and the L&R algorithm. Among them, the performance of the Fitz algorithm is relatively better.

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

[0005] Assume that the signal obtained after down-conversion, matched filtering, and sampling of the received signal is:

[0006] r k =d k e j(2πfkT+θ) +n k (1)

[0007] Where d k is the modulated symbol, f is the frequency offset between the received signal and the local carrier, θ is the phase difference, n k is a Gaussian random variable, and the mean of n k 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, multiply the received signal r k by the conjugate of the modulation symbol, and we can get:

[0009] z k =e j(2πfkT+θ) +υ k (2)

[0010] Among them, and var(υ k ) = N0.

[0011] Denote the autocorrelation function of z k as:

[0012]

[0013] Among them, 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] Substitute the expression of z k into the above formula, and we can get:

[0015] R m = e j(2πfmT) + w k (4)

[0016] Among them, w k is a zero-mean noise variable. Denote the error as:

[0017] e m = arg(R m ) - 2πfmT (5)

[0018] Since the value range of m is 1 ≤ m ≤ L0 - 1, and 1 ≤ L0 ≤ N, and only when |2πfmT| ≤ π, the estimated phase of R m will not flip, and the estimated frequency offset is correct. Thus, the normalized frequency offset estimation range of the Fitz algorithm can be obtained as:

[0019]

[0020] Among them, represents the estimated frequency offset value.

[0021] It is not difficult 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 considered 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 dynamically changing, that is, when the frequency offset range is large, a smaller N should be selected to roughly estimate the frequency offset. When the actual frequency offset range is small, a larger N can be considered to estimate the frequency offset more precisely.

[0022] When the signal-to-noise ratio is large, the error e m in Equation (5) is very small. Taking the average of it, we get:

[0023]

[0024] It can be sorted out that the frequency offset estimation expression of the Fitz algorithm is as follows:

[0025]

[0026] In a burst communication system, the carrier frequency offset is very large. If the Fitz algorithm is used for estimation, the length of the autocorrelation 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 an increased estimation range and improved estimation accuracy. Proposing a method that takes both the estimation range and estimation accuracy into account is an urgent problem to be solved at present. Summary of the Invention

[0027] The purpose of the present invention is to solve the problem that the existing Fitz algorithm cannot take both the estimation range and estimation accuracy into account, and a carrier frequency offset estimation method for a burst communication system based on phase flip compensation is proposed.

[0028] The technical solution adopted by the present invention to solve the above technical problems is: a carrier frequency offset estimation method for a burst communication system based on phase flip compensation, and the method specifically includes the following steps:

[0029] Step 1: The sending end of the burst communication system adds a frame synchronization header before 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;

[0030] Step 2: After the receiving end of the burst communication system demodulates the received signal, calculates the cross-correlation function of the demodulated signal, and then obtains an initial frequency offset estimation value based on the cross-correlation function;

[0031] Step 3: Perform phase flip compensation on the initial frequency offset estimation value to obtain the final frequency offset estimation result.

[0032] The beneficial effects of the present invention are as follows:

[0033] The present invention first designs a pilot structure with a certain interval, obtains a rough estimation value of the frequency offset based on the designed pilot structure and the Fitz algorithm of traditional autocorrelation, and then uses the designed phase flip compensation method to reasonably perform phase flip compensation on the calculated rough estimation value of the frequency offset, thereby effectively improving the estimation accuracy and estimation range of the frequency offset. Both the theoretical derivation and experiments of the Cramer-Rao bound illustrate that the Fitz algorithm based on cross-correlation of the present invention can effectively improve the estimation accuracy and estimation range of the frequency offset. Brief Description of the Drawings

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

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

[0036] Figure 3 is the comparison graph estimated by the autocorrelation Fitz algorithm;

[0037] Figure 4 is the comparison graph estimated by the autocorrelation and cross-correlation Fitz algorithms;

[0038] Figure 5 is the comparison graph of the bit error rate after frequency offset compensation;

[0039] Figure 6 is the data-aided mode receiver model. Specific implementation manners

[0040] Theoretical basis

[0041] 1. Pilot structure design

[0042] Set the number of pilot blocks to 2, the number of test data to 1, and the test data to a sequence of all 1s. Therefore, the Figure 1 shown frame synchronization header structure can be obtained. The pilot part uses an m-sequence with a length of 31, and the good correlation characteristics of the m-sequence can be used to establish synchronization; the length of the test data part is 224, which is much larger than the length of the pilot part.

[0043] 2. Derivation of the Cramer-Rao bound

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

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

[0046]

[0047] where 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 segment of the pilot, and M i, where \(i = 1, 2, \cdots, m\) is the length of each segment of data, and \(m\) is the number of pilot blocks.

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

[0049]

[0050] Assume that the channel condition is an additive white Gaussian noise (AWGN) channel, and the prior probabilities of the transmitted signals are equal and independent. Then, we can obtain:

[0051]

[0052] In the formula, is the modulated signal after rotation by the estimated frequency offset and phase offset, and \(\sigma\) 2 = \(N_0 / 2\) is the variance of the noise. Since the first exponential term in Equation (11) is independent of the sampling time \(k\), this term can be ignored. After further simplification, we can get:

[0053]

[0054] Also, because \(r\) k \(s\) k = \(z\) k , where \(z\) k is the demodulated sequence, so we have

[0055]

[0056] Among them, means that the left side of the definition is equal to the right side. Substituting Equation (13) into the Fisher Information Matrix, we can get:

[0057]

[0058] After further calculation, we can get:

[0059]

[0060] From the above derivation, it can be seen that the element in the first row and first column of the Fisher Information Matrix is the objective function. Let it be Performing the inverse operation on it, we can obtain the corresponding Cramer-Rao bound of frequency offset estimation, denoted as CRB(f). Solving T(f) is equivalent to deriving the summation term Therefore

[0061]

[0062] Also, because the pilot symbol interval \(D\) i = \(P\) i+M i , arranging the above formula gives

[0063]

[0064] It can be seen from Equation (17) that the magnitude of T(f) is related to the pilot length P i and the interval D between pilot symbols i is related, and is proportional to P i 3 and D i 2 is proportional. Then the magnitude of CRB(f) is inversely proportional to P i 3 and is inversely proportional. Therefore, the performance of the estimation can be improved by adjusting the pilot symbol interval D i and the pilot length P i .

[0065] Because T(f) and CRB(f) are reciprocal relationships, that is, CRB(f)=[T(f)] -1 , so there is

[0066]

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

[0068]

[0069] When using the carrier frequency offset estimation algorithm based on autocorrelation, there is no correlation operation between multiple pilot blocks, and only a single pilot block is needed, that is, D = 0, m = 1. Therefore, the Cramer-Rao bound of the carrier frequency offset estimation method based on autocorrelation is

[0070]

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

[0072] Specific Embodiment 1: A carrier frequency offset estimation method for a burst communication system based on phase flip compensation described in this embodiment, the 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, frames the frame synchronization header and the data to be transmitted, and then modulates and transmits the framed data.

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

[0075] Step 3: Perform phase flip compensation on the initial frequency offset estimation value to obtain the final frequency offset estimation result.

[0076] Specific Embodiment 2: The difference between this embodiment and Specific Embodiment 1 is 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 blocks.

[0077] Other steps and parameters are the same as those in Specific Embodiment 1.

[0078] When calculating the cross-correlation function in the present invention, only the data of the pilot part needs to be used. A pilot block consists of 1 bit 1 plus an m-sequence with a length of 31.

[0079] Specific Embodiment 3: The difference between this embodiment and Specific Embodiment 1 or 2 is that the cross-correlation function of the demodulated signal is:

[0080]

[0081] where z(k) represents the k-th pilot symbol after demodulating the information, and z * (k) represents the conjugate of z(k);

[0082] D represents the interval of the pilot block (equal to the length of a 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 + D)-th symbol after demodulating the information.

[0087] Other steps and parameters are the same as those in Specific Embodiment 1 or 2.

[0088] Embodiment 4: The difference between this embodiment and any one of Embodiments 1 to 3 is that the length N of the cross-correlation sequence is N = λL, where 0 < λ ≤ 1 and L is the length of the pilot block.

[0089] Other steps and parameters are the same as those in any one of Embodiments 1 to 3.

[0090] Embodiment 5: The difference between this embodiment and any one of Embodiments 1 to 4 is that the initial frequency offset estimate value obtained based on the cross-correlation function is specifically:

[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 the 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 the phase offset;

[0098] The error e(m) is denoted as:

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

[0100] where arg(R D (m)) represents calculating the phase angle of R D (m);

[0101] To ensure the correctness of the estimation, it is necessary to satisfy |2π(α + D)fT| ≤ π. 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 relatively large, the error e(m) ≈ 0. Therefore, let e(m) = 0, and taking the average of Equation (23) gives:

[0104]

[0105] Further arranging Equation (25) gives:

[0106]

[0107] Then the initial frequency offset estimation result f of the Fitz algorithm based on cross-correlation eis as follows:

[0108]

[0109] Other steps and parameters are the same as those in any one of the first to fourth specific embodiments.

[0110] When calculating the phase angle of the cross-correlation value R D (m), due to the existence of the pilot interval D, |2π(m + D)fT| > π, exceeding the range of [-π, π). At this time, the obtained phase angle is the result of taking the modulus 2π, rather than the true phase angle. Therefore, the phase difference is misestimated, and the obtained frequency offset estimation value is incorrect. This phenomenon is called phase flipping. Therefore, the present invention performs phase flipping compensation.

[0111] Specific embodiment six: The difference between this embodiment and any one of the first to fifth specific embodiments is that the specific process of step three is as follows:

[0112] Due to the existence of the pilot interval D, when the frequency offset is large, at m = 1, the phase of R(1) has a high probability of undergoing phase flipping. Therefore, the frequency offset value estimated by the Fitz algorithm with a smaller autocorrelation length is input at the input end to estimate the true phase Q(1) of R(1) and avoid affecting subsequent phase flipping compensation. Therefore:

[0113] Step three one: Calculate the phase Q(1) after flipping compensation of the first element R in the cross-correlation sequence according to the coarse frequency offset estimation value obtained by the autocorrelation-based Fitz algorithm (i.e., the traditional Fitz algorithm) D (1):

[0114]

[0115] Step three two: Initialize m = 2;

[0116] Step three three: Calculate the phase Q(m) after flipping compensation of the m-th element R D (m) in the cross-correlation sequence:

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

[0118] If m < N, then let m = m + 1 and return to execute step three three;

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

[0120] Step three five: Perform phase flipping compensation on the initial frequency offset estimation value according to Q(m), m = 1, 2,..., N, and calculate the final frequency offset estimation result.

[0121] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0122] The specific execution process of Step 3 is shown in Table 1:

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

[0124]

[0125] Specific Embodiment Seven: The difference between this embodiment and any one of the first to sixth specific embodiments is that the specific process of Step 33 is as follows:

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

[0127] φ(m) = 2πfT(m + D) (29)

[0128] Using the phase after flip compensation of the first m - 1 elements to predict the current true phase value, that is, averaging the phase values after flip compensation of the first m - 1 elements in the cross-correlation sequence:

[0129]

[0130] After organizing Equation (30), we get:

[0131]

[0132] Then

[0133]

[0134] By comparing Equation (29) and Equation (32), we obtain:

[0135]

[0136] Performing flip compensation on the phase φ(m) of R D (m), we have

[0137] Q(m) = arg(R D (m)) + 2πM0 (34)

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

[0139] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0140] Specific Embodiment Eight: The difference between this embodiment and any one of the first to seventh specific embodiments is that the calculation method of the number of phase flips M0 is:

[0141] Subtract Q(m) from φ(m), and substitute it into f in the subtraction result to calculate M0:

[0142]

[0143] where 0 ≤ M ≤ N, and M is an integer, indicating to calculate M that makes the value reach the minimum.

[0144] Other steps and parameters are the same as those in any one of the first to seventh specific embodiments.

[0145] Specific Embodiment Nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that the specific process of step three to five is as follows:

[0146]

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

[0148] Other steps and parameters are the same as those in any one of the first to eighth specific embodiments.

[0149] Experimental Part

[0150] When conducting the experiment, it is carried out according to the Figure 6 data-aided synchronization mode shown. First, at the transmitter, according to the designed frame structure, frame synchronization headers and data bits are framed, then the framed result is modulated, and a frequency offset is added to the modulation result; at the receiver, the frame is decoded based on frame synchronization, the frequency offset is estimated using the frame synchronization header, the frequency offset of the data is compensated according to the frequency offset estimation result, and finally the data after frequency offset compensation is demodulated to obtain the recovered data bits.

[0151] For the carrier frequency offset estimation algorithm, the estimation performance of the algorithm is usually measured by two indicators: estimation accuracy and estimation range. The present invention uses the comparison between the normalized frequency offset estimation value 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, and its expression is:

[0152]

[0153] where T is the symbol rate, is the estimated frequency offset, f d is the actual frequency offset.

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

[0155]

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

[0157] (1) Estimation range of the improved algorithm

[0158] Set the lengths of autocorrelation to 32 and 16 respectively, perform phase flip compensation on the Fitz algorithm with an autocorrelation length of 64. The normalized true frequency offset range is from -0.1 to 0.1, the step size is 0.01, and the number of Monte Carlo runs is 10000. Under the Gaussian white noise channel, the estimation range of the Fitz algorithm with phase flip compensation is as Figure 3 shown, corresponding to the black curve with square markers. Theoretically, the estimation range with an autocorrelation length of 64 is less than that with autocorrelation lengths of 16 and 32. However, due to the phase flip compensation, it can be seen that the estimation range of the black curve is much larger than those 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) Estimation accuracy of the improved algorithm

[0160] For the improved algorithm proposed in the present invention, simulations are carried out to verify its estimation performance. The normalized true frequency offset is set to 0.01, which exceeds the estimation range of the cross-correlation Fitz algorithm. E s / N0 is set to 10 dB, and the number of Monte Carlo runs is set to 10000. Under the Gaussian white noise channel, the estimation accuracy of the improved algorithm is as Figure 4 shown, corresponding to the blue curve. It can be seen that the mean square error curve of the algorithm of the present invention is close to the Cramer-Rao bound of the cross-correlation algorithm and lower than that of the autocorrelation algorithm; at the same time, the estimation accuracy of the cross-correlation Fitz algorithm shown by the black curve does not increase with the increase of E s / N0, and there is a certain 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 flip compensation proposed in the present invention effectively increases the estimation range of the cross-correlation Fitz algorithm, and the estimation accuracy is about two orders of magnitude higher than that of the autocorrelation Fitz algorithm with phase flip compensation.

[0161] (3) Frequency offset compensation effect

[0162] The normalized true frequency offset is set to 0.01, the range of E s / N0 is from 0 dB to 10 dB, the number of Monte Carlo runs is set to 10000, and the number of burst frames is 100. After compensating the data with the frequency offset estimated according to the method of the present invention, the obtained bit error rate curve is as Figure 5As shown, it is very close to the theoretical bit error rate curve. Compared with the bit error rate curves compensated by the Fitz algorithm with autocorrelation lengths of 32 and 16, the improved algorithm has signal-to-noise ratio advantages of 1 dB and 2.5 dB respectively. At the same time, it is not difficult to see that if frequency offset estimation and compensation are not performed, the bit error rate approaches 1 and the system is difficult to work properly.

[0163] The above examples of the present invention are only for illustrating in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manner of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is impossible to list all the implementation manners here. Any obvious changes or variations derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A method for estimating carrier frequency offset in a burst communication system based on phase flip compensation, characterized in that: The method specifically comprises the following steps: Step 1: The transmitting 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 2: After demodulating the received signal, the receiving end of the burst communication system calculates the cross-correlation function of the demodulated signal, and then obtains an initial frequency offset estimation value based on the cross-correlation function; Step 3: Perform phase flip compensation on the initial frequency offset estimation value to obtain the final frequency offset estimation result.

2. The method for estimating carrier frequency offset of a burst communication system based on phase flip compensation according to claim 1, characterized in that: The frame synchronization header includes a pilot block, a test data sequence and a pilot block in sequence, and the pilot blocks at both ends of the test data sequence are the same pilot blocks.

3. The method for estimating carrier frequency offset of a burst communication system based on phase flip compensation according to claim 2, characterized in that: The cross-correlation function of the demodulated signal is: Where z(k) represents the kth pilot symbol after the modulation information is removed, z * (k) represents the conjugate of z(k); D represents the interval of the pilot block; N represents the length of the cross-correlation sequence; R D (m) represents the mth element in the cross-correlation sequence; m+D represents the cross-correlation delay length; z(k+m+D) represents the k+m+Dth symbol after the modulation information is removed.

4. The method for estimating carrier frequency offset of a burst communication system based on phase flip compensation according to claim 3, characterized in that: The length of the mutual correlation sequence is N=λL, 0<λ≤1, and L is the length of the pilot block.

5. The method for estimating carrier frequency offset of a burst communication system based on phase flip compensation according to claim 4, characterized in that: The obtaining of the initial frequency offset estimation value based on the cross-correlation function is specifically as follows: R D (m)=e j(2π(m+D)fT+θ) +w (22) Where w is a zero-mean noise variable; f represents frequency deviation; e represents the base of natural logarithm; j represents the imaginary unit; T represents the symbol interval; θ represents the phase deviation; The error e(m) is recorded as: e(m)=arg(R D (m))-2π(m+D)fT (23) Among them, arg(R D (m)) represents the calculation of R D The phase angle of (m); Let e(m) = 0, and find the average of equation (23): Further rearrangement of formula (25) yields: Then the initial frequency offset estimation result f e for:

6. The method for estimating carrier frequency offset in a burst communication system based on phase flip compensation according to claim 5, characterized in that: The specific process of step three is: Step 31: Get the rough frequency offset estimate based on the autocorrelation-based Fitz algorithm Calculate the first element R in the cross-correlation sequence D The phase Q(1) after flip compensation of (1): Step 32: Initialize m=2; Step 3. Calculate the mth element R in the cross-correlation sequence D The phase Q(m) after flip compensation of (m): Step 34: Determine whether m=N is satisfied; If m<N, set m=m+1 and return to execute step 33; If m=N, then execute step 35; Step 35: Perform phase flip compensation on the initial frequency offset estimation value according to Q(m), m=1,2,…,N, and calculate the final frequency offset estimation result.

7. The method for estimating carrier frequency offset in a burst communication system based on phase flip compensation according to claim 6, characterized in that: The specific process of step 33 is as follows: R D The true phase φ(m) of (m) is: φ(m)=2πfT(m+D) (29) Average the flip-compensated phase values ​​of the first m-1 elements in the cross-correlation sequence: After rearranging formula (30), we can get: but Comparing equation (29) and equation (32), we can get: R D The phase φ(m) of (m) is flipped and compensated, Q(m)=arg(R D (m))+2πM0 (34) Where Q(m) represents R D (m) corresponds to the phase after flip compensation, and M0 represents the number of phase flips.

8. The method for estimating carrier frequency offset in a burst communication system based on phase flip compensation according to claim 7, characterized in that: The calculation method of the phase reversal number M0 is: Wherein, 0≤M≤N, and M is an integer.

9. The method for estimating carrier frequency offset in a burst communication system based on phase flip compensation according to claim 8, characterized in that: The specific process of step three and five is as follows: in, Represents the final frequency offset estimation result.

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