4FSK Demodulation Method Based on Multi-Symbol Joint Estimation

Abstract

This invention discloses a 4FSK demodulation method based on multi-symbol joint estimation, belonging to the field of signal demodulation technology. The method includes: acquiring IQ signals and performing instantaneous frequency measurement on the IQ signals to obtain a first instantaneous frequency waveform; performing symbol rate estimation based on the first instantaneous frequency waveform to obtain a symbol rate estimate; generating a frequency signal to be measured based on the IQ signals and the current sampling rate; performing instantaneous frequency measurement on the frequency signal to be measured to obtain a second instantaneous frequency waveform; estimating the starting position of a symbol based on the second instantaneous frequency waveform using multi-symbol variance joint estimation; calculating the frequency estimate of the symbol based on the starting position of the symbol; and performing symbol discrimination based on the frequency estimate of the symbol using the minimum distance criterion to recover symbol information. This invention has strong noise resistance.

Description

Technical Field

[0001] This invention belongs to the field of signal demodulation technology, and in particular relates to a 4FSK demodulation method based on multi-symbol joint estimation. Background Technology

[0002] Frequency Shift Keying (FSK) is a commonly used waveform modulation method with advantages such as good noise immunity, long transmission distance, and low bit error rate. In systems such as low-speed data communication, shortwave communication, and low-power local area networks, the demodulation of FSK signals is generally divided into coherent demodulation and non-coherent demodulation.

[0003] Coherent demodulation uses a local carrier wave of the same frequency and phase to multiply the received signal, thus achieving coherent demodulation. However, when the frequency and phase are not synchronized, the demodulated output will be severely distorted. To avoid this problem, a digital phase-locked loop (PLL) is introduced for carrier synchronization. However, when the signal duration is short, the PLL has a high probability of losing lock.

[0004] Noncoherent demodulation does not require strict carrier synchronization, is simple in principle, and is easy to implement. Currently, noncoherent demodulation algorithms for 4FSK include delay-based frequency discrimination, envelope detection, and differential demodulation.

[0005] The time-delay frequency discrimination method multiplies the down-converted baseband signal with the delayed conjugate baseband signal to obtain a differential signal. The arctangent of the differential signal is then used for frequency discrimination, followed by matched filtering to obtain the demodulated signal. This method strictly requires the delay time to be an integer multiple of the symbol period, making it suitable for ideal conditions.

[0006] Envelope detection involves passing the 4FSK signal through four bandpass filters, extracting the envelopes of the four branch output signals, and inputting them into a decision circuit for comparison and judgment. This method is highly susceptible to noise, and the envelopes of the four branch output signals all have transition regions, making it prone to misjudgment.

[0007] Differential demodulation involves orthogonally decomposing the signal to obtain in-phase and quadrature components. The instantaneous frequency is obtained by multiplying and subtracting the quadrature and in-phase components with offsets. After calculating the instantaneous frequency, bit synchronization signals need to be extracted. The instantaneous frequency is then subjected to sampling threshold decision to obtain symbol information, and the transmitted bit information is recovered according to the modulation mapping relationship. When the symbol rate estimation is inaccurate, fixed symbol synchronization will lead to a decrease in demodulation error rate performance. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a 4FSK demodulation method based on multi-symbol joint estimation.

[0009] The objective of this invention is achieved through the following technical solution: a 4FSK demodulation method based on multi-symbol joint estimation, comprising:

[0010] Acquire the IQ signal and perform instantaneous frequency measurement on the IQ signal to obtain the first instantaneous frequency waveform;

[0011] Symbol rate estimation is performed based on the first instantaneous frequency waveform to obtain the symbol rate estimate;

[0012] Determine whether the current sampling rate meets the preset conditions: if yes, then determine the IQ signal as the frequency signal to be measured; if no, then resample the IQ signal to a resampled signal whose sampling rate meets the preset conditions, and determine the resampled signal as the frequency signal to be measured; perform instantaneous frequency measurement on the frequency signal to be measured to obtain the second instantaneous frequency waveform;

[0013] Based on the second instantaneous frequency waveform, the starting position of the symbol is estimated by jointly estimating the variance of multiple symbols;

[0014] Calculate the frequency estimate of the symbol based on its starting position;

[0015] Based on the frequency estimate of the symbol, the symbol is identified using the minimum distance criterion, and the symbol information is recovered.

[0016] Furthermore, the formula for calculating instantaneous frequency is:

[0017]

[0018]

[0019]

[0020] In the formula, f(n) represents the instantaneous frequency, and fs represents the sampling rate. Indicates the unfolded instantaneous phase. For the instantaneous phase of the signal, The range of values ​​is n is an integer greater than 0.

[0021] Further, symbol rate estimation is performed based on the first instantaneous frequency waveform to obtain a symbol rate estimate, including:

[0022] Perform a difference operation on the first instantaneous frequency waveform f(n) to obtain the first difference sequence d1(n);

[0023] Perform a difference operation on the first difference sequence d1(n) to obtain the second difference sequence d2(n);

[0024] Taking the absolute value of the second difference sequence d2(n) yields the sequence D_abs(n);

[0025] Perform a fast Fourier transform on the D_abs(n) sequence to obtain the F_fft(n) sequence;

[0026] Find the position Max_i of the maximum value in the right half of the F_fft(n) sequence;

[0027] The symbol rate estimate is calculated using the following formula:

[0028]

[0029] In the formula, R_esi represents the symbol rate estimate, fs represents the sampling rate, and N is the number of signal sampling points used to estimate the symbol rate.

[0030] Further, determine whether the current sampling rate meets the preset conditions, including:

[0031] Based on the symbol rate estimate, determine whether the current sampling rate satisfies the condition that the number of sampling points in each symbol is an integer. If yes, the current sampling rate satisfies the preset condition; otherwise, the current sampling rate does not satisfy the preset condition.

[0032] Further, the IQ signal is resampled into a resampled signal with a sampling rate that meets a preset condition, including:

[0033] Based on the symbol rate estimate, the IQ signal is resampled into a resampled signal with a sampling rate that meets a preset condition.

[0034] Furthermore, based on the second instantaneous frequency waveform, the starting position of the symbol is estimated using the joint variance of multiple symbols, including:

[0035] S510. Determine a sampling point in the second instantaneous frequency waveform as the starting point, and then execute S520;

[0036] S520. Based on the starting point, simultaneously calculate the variance of the instantaneous frequency of N signal segments with an interval of m sampling points and a length of m sampling points, and then execute S530;

[0037] S530. Sum the variances of the instantaneous frequencies of the N signal segments to obtain a variance sum, and then execute S540;

[0038] S540. Determine whether the number of variances obtained has reached the first preset value N′. If not, execute S550; if yes, execute S560. Wherein, the first preset value N′ is the number of sampling points within a single symbol.

[0039] S550. Update the position of the starting point to the next sampling point corresponding to the current sampling point of the starting point, and then execute S520;

[0040] S560. Determine the starting position of the symbol by the variance with the smallest median among the N′ variances and the corresponding starting point.

[0041] Furthermore, in S510, if the starting position of the first symbol is to be estimated, the first sampling point is determined as the starting point; otherwise, the sampling point at the starting position of the previous symbol plus m / 2 sampling points is determined as the starting point.

[0042] Further, calculating the frequency estimate of the symbol based on its starting position includes:

[0043] The symbols are divided based on their starting positions;

[0044] Calculate the average instantaneous frequency between the start and end positions of each symbol, and determine this average value as the frequency estimate of the symbol;

[0045] The ending position of a symbol is the starting position of the next symbol.

[0046] Furthermore, the 4FSK demodulation method also includes:

[0047] The first instantaneous frequency waveform and / or the second instantaneous frequency waveform are subjected to low-pass filtering, wherein the cutoff frequency of the low-pass filter is the symbol rate value.

[0048] The beneficial effects of this invention are as follows: This invention provides a 4FSK demodulation method based on multi-symbol joint estimation. This method calculates the instantaneous phase of the in-phase and quadrature components of the baseband IQ signal, and obtains the instantaneous frequency signal after differential calculation of the instantaneous phase. A segment of the instantaneous frequency signal is used to estimate the symbol rate. The estimated symbol rate is used to resample the signal, making the resampled output signal approximately an integer multiple of the symbol rate. The symbol start point is estimated using the variance of the instantaneous frequencies of multiple symbols. The optimal decision point for the symbol is obtained based on the start point. The mapping position is determined using the minimum distance between the average value within the symbol and the ideal frequency point, thereby demodulating the signal. Compared to envelope detection, this invention is based on instantaneous frequency demodulation, therefore, it has stronger noise immunity and eliminates the problem of a transition region. Compared to delay frequency discrimination and differential demodulation algorithms, which require strict symbol synchronization, this invention can locate the start and end positions of symbols based on the instantaneous frequency variation patterns of multiple symbols, without requiring strict symbol synchronization. This invention uses the average instantaneous frequency between the start and end positions as the decision statistic for symbol decision, eliminating the need for a separate sampling clock and simplifying the algorithm implementation. Furthermore, this invention estimates the optimal position of the symbol decision point by jointly estimating the instantaneous frequency variance of multiple symbols, effectively avoiding the problem of consecutive symbol synchronization failures caused by errors in individual symbols. When there is a certain deviation between the symbol rate and the actual symbol rate, this invention can also track and adjust the optimal decision position of the symbol through joint estimation of multiple symbols, correcting the impact of the symbol rate deviation and avoiding symbol synchronization failures. In summary, this invention has strong noise resistance, a certain fault tolerance capability for symbol rate estimation, and good practicality. This invention has also been effectively verified on simulated signals and various real signals. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of a 4FSK demodulation method based on multi-symbol joint estimation in this invention;

[0050] Figure 2 This is a spectrum diagram of a 4FSK modulated signal in one embodiment;

[0051] Figure 3 for Figure 2 A schematic diagram of the corresponding instantaneous frequency measurement results without low-pass filtering;

[0052] Figure 4 for Figure 2 A schematic diagram of the corresponding instantaneous frequency measurement results after low-pass filtering;

[0053] Figure 5 for Figure 2 A schematic diagram of the corresponding extracted symbol rate spectrum;

[0054] Figure 6 for Figure 2Schematic diagram of corresponding symbolic joint estimation sample points;

[0055] Figure 7 for Figure 2 The corresponding multi-symbol joint variance and SumVar sequence curves;

[0056] Figure 8 for Figure 2 The corresponding instantaneous frequency curve division diagram;

[0057] Figure 9 for Figure 2 The corresponding 4FSK demodulation result bitmap. Detailed Implementation

[0058] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] See Figures 1 to 9 This invention provides a 4FSK demodulation method based on multi-symbol joint estimation:

[0060] like Figure 1 As shown, the 4FSK demodulation method based on multi-symbol joint estimation includes S100 to S700.

[0061] S100. Acquire the IQ signal and perform instantaneous frequency measurement on the IQ signal to obtain the first instantaneous frequency waveform.

[0062] In some embodiments, when acquiring the IQ signal, the number of IQ points can be 1024, and the calculated symbol rate error is on the order of one-thousandth.

[0063] In some embodiments, instantaneous frequency measurement is obtained by differentially analyzing the instantaneous phase after unwinding it.

[0064] The formula for calculating instantaneous frequency is:

[0065] Calculate the instantaneous phase of a complex signal (i.e., an IQ signal, where I is the real part of the complex signal and Q is the imaginary part of the complex signal) r(n), n = 1, 2, ..., N. in, imag(r(n)) is the imaginary part of the complex signal r(n), and real(r(n)) is the real part of the complex signal r(n).

[0066] In this embodiment, unwinding is used to obtain continuously changing, foldless instantaneous phase values. The specific process is as follows:

[0067]

[0068] Where C(n) is initially 0, The instantaneous phase of the signal, with values ​​ranging from 0 to 2π.

[0069] The instantaneous frequency f(n) is calculated from the derivative of the unfolded instantaneous phase value. The formula is as follows:

[0070]

[0071] In the formula, fs represents the sampling rate.

[0072] In some embodiments, after obtaining the first instantaneous frequency waveform, the first instantaneous frequency waveform is subjected to low-pass filtering, wherein the cutoff frequency of the low-pass filter is the initial symbol rate value, which is set when demodulating the 4FSK signal, and its value may deviate from the true symbol rate by a certain amount (within ±20%).

[0073] Figure 2 The spectrum of the complex baseband signal modulated by 4FSK is shown. The simulation conditions are: symbol period of 132, symbol rate of 1.2Msps, modulation mode of 4FSK, Eb / N0 = 14.8dB, and data frame count of 500 frames, where Eb is the energy of a single bit of the signal and N0 is the noise power spectral density.

[0074] Figure 3 for Figure 2 The signal spectrum diagram shown is the instantaneous frequency measurement result without low-pass filtering. It can be seen that there are obvious jump characteristics near the frequencies of -1800kHz, -600kHz, 600kHz, and 1800kHz, which are the positions of the signal symbol mapping.

[0075] Figure 4 for Figure 2 The signal spectrum shown is the instantaneous frequency measurement result after low-pass filtering. The low-pass filter cutoff frequency is set to the symbol rate value. It can be seen that the filtered signal removes some noise and is smoother. The frequency jump characteristics are more obvious near -1800kHz, -600kHz, 600kHz, and 1800kHz.

[0076] S200. Based on the first instantaneous frequency waveform, perform symbol rate estimation to obtain the symbol rate estimate.

[0077] In some embodiments, symbol rate estimation is performed based on the first instantaneous frequency waveform to obtain a symbol rate estimate, including:

[0078] Perform a difference operation on the first instantaneous frequency waveform f(n) to obtain the first difference sequence d1(n);

[0079] Perform a difference operation on the first difference sequence d1(n) to obtain the second difference sequence d2(n);

[0080] Taking the absolute value of the second difference sequence d2(n) yields the sequence D_abs(n);

[0081] Perform a fast Fourier transform on the D_abs(n) sequence to obtain the F_fft(n) sequence;

[0082] Find the position Max_i of the maximum value in the right half of the F_fft(n) sequence;

[0083] The symbol rate estimate is calculated using the following formula:

[0084]

[0085] In the formula, R_esi represents the symbol rate estimate, fs represents the sampling rate; f(0) = 0; d1(0) = 0; d2(0) = 0; D abs(0) =0;F fft(0) =0; n=1,…,N, where N is the number of signal sampling points used to estimate the symbol rate; d1(n)=f(n)-f(n-1); d2(n)=d1(n)-d1(n-1); D_abs(n)=|d2(n)|.

[0086] Figure 5 To Figure 4 The schematic diagram of the symbol rate spectrum obtained by estimating the symbol rate from the frequency measurement results shows that the estimated symbol rate value is 1.2 Msps, which is in complete agreement with the initial simulation settings.

[0087] S300. Determine whether the current sampling rate meets the preset conditions: if yes, then determine the IQ signal as the frequency signal to be measured; if no, then resample the IQ signal to a resampled signal whose sampling rate meets the preset conditions, and determine the resampled signal as the frequency signal to be measured.

[0088] In some embodiments, determining whether the current sampling rate meets a preset condition includes: determining whether the current sampling rate satisfies the condition that the number of sampling points in each symbol is an integer based on the symbol rate estimate; if yes, the current sampling rate meets the preset condition; otherwise, the current sampling rate does not meet the preset condition.

[0089] In some embodiments, resampling the IQ signal into a resampled signal with a sampling rate that meets a preset condition includes: resampling the IQ signal into a resampled signal with a sampling rate that meets a preset condition based on the symbol rate estimate.

[0090] Since the 4FSK multi-symbol joint estimation algorithm expects the number of sampling points within each symbol to be an integer, this embodiment determines whether the initial sampling rate meets this condition based on the estimated symbol rate. If not, the signal is resampled to ensure the new sampling rate satisfies the requirement that the number of sampling points per symbol is an integer. In 4FSK signal demodulation, the number of sampling points per symbol is generally set to 8 or more. That is, if the initial sampling rate satisfies the expectation that the number of sampling points per symbol is an integer, the resampling process is skipped; otherwise, resampling is performed.

[0091] When resampling the input IQ signal based on the estimated symbol rate, if the original input sampling rate is fsi and the estimated symbol rate is Resti, and the number of samples per symbol is m, then the sampling rate of the resampled signal is greater than the signal bandwidth Bw × 2 and equal to Resti × m, where m is an integer greater than or equal to 8. The resampled IQ signal is then calculated and output.

[0092] S400. Perform instantaneous frequency measurement on the frequency signal to be measured to obtain a second instantaneous frequency waveform.

[0093] The first instantaneous frequency measurement is for estimating the symbol rate, and only a segment of data is selected for the measurement. The second instantaneous frequency measurement is for the demodulated signal, so the frequency of all signals is measured.

[0094] In some embodiments, after obtaining the second instantaneous frequency waveform, the second instantaneous frequency waveform is subjected to low-pass filtering, and the cutoff frequency of the low-pass filter is the symbol rate value.

[0095] S500. Based on the second instantaneous frequency waveform, estimate the starting position of the symbol using the joint variance of multiple symbols.

[0096] In some embodiments, the starting position of a symbol is estimated using the multi-symbol variance joint estimation based on the second instantaneous frequency waveform, including S510 to S560.

[0097] S510. Determine a sampling point in the second instantaneous frequency waveform as the starting point, and then execute S520.

[0098] In some embodiments, during step S510, if the starting position of the first symbol is to be estimated, the first sampling point is determined as the starting point; otherwise, the sampling point m / 2 points after the starting position of the previous symbol is determined as the starting point. That is, if the starting position of the first symbol is to be estimated, the first sampling point is used as the starting point; if the starting position of the second or subsequent symbols is to be estimated, the m / 2th sampling point after the sampling point corresponding to the starting position of the previous symbol is determined as the starting point.

[0099] S520. Based on the starting point, simultaneously calculate the variance of the instantaneous frequency of N signal segments with an interval of m sampling points and a length of m sampling points, and then execute S530.

[0100] S530. Sum the variances of the instantaneous frequencies of the N signal segments to obtain a variance sum, and then execute S540.

[0101] S540. Determine whether the number of variances obtained has reached the first preset value N′. If not, proceed to S550; if yes, proceed to S560. The first preset value N′ is the number of sampling points within a single symbol.

[0102] S550. Update the position of the starting point to the next sampling point corresponding to the current sampling point of the starting point, and then execute S520.

[0103] S560. Determine the starting position of the symbol by the variance with the smallest median among the N′ variances and the corresponding starting point.

[0104] In some embodiments, when estimating the starting position of a symbol, it is necessary to first determine whether the remaining number of sampling points meets the computational requirements for joint estimation of the variance of multiple symbols. If so, subsequent processing is performed. After each symbol is demodulated, the starting position of the next symbol needs to be re-determined.

[0105] Since the instantaneous frequency of each sample point equals the actual carrier frequency plus noise, the difference in instantaneous frequency between different sample points within the same symbol comes only from noise. When adjacent symbol information is different, the frequency interval between adjacent symbols in 4SFK equals the symbol rate. Therefore, for sample points corresponding to different symbols, the difference in their instantaneous frequency equals noise plus frequency interval, which is much greater than the difference in instantaneous frequency between sample points within the same symbol.

[0106] Let m be the number of sampling points within a symbol. The instantaneous frequency value of each sampling point within the same symbol roughly fluctuates around the mean of the symbol's instantaneous frequency. This fluctuation is represented by the variance of the symbol's instantaneous frequency. If the number of sampling points for calculating the variance is set to N, the variance value is relatively small when the starting point of the calculation is exactly at the symbol's starting point. When the starting point of the calculation deviates from the symbol's starting point, the sampling points included in the calculation include those of the next symbol. When two symbols do not have the same information, there will be a symbol jump, and the calculated variance value will be larger than when there is no deviation. The variance is calculated and summed simultaneously for multiple symbols (let's say N symbols) after instantaneous frequency measurement filtering. That is, starting from a certain starting point, the variance of N signal segments with an interval of m and a length of m is calculated simultaneously, and the N variances are summed. By traversing all sampling points within a symbol, the position with the smallest sum of variances is the symbol's starting point.

[0107] like Figure 6As shown, let N be the number of symbols in the joint estimation, and m be the number of samples within a symbol. Using sample point 1 as the baseline, calculate the multi-symbol variance sum SumVar(1). Sample points 1 to m constitute the first symbol, and the variance of the first symbol is defined as Var(1); sample points m+1 to m+m constitute the second symbol, and the variance of the second symbol is defined as Var(2); and so on, summing the N variances to obtain a single variance sum: Add 1 to the sampling point position used as the reference, that is, calculate the multi-symbol variance and SumVar(2) with sampling point 2 as the reference. By analogy, we can calculate: SumVar(2),...,SumVar(m).

[0108] The multi-symbol variance sum is calculated sequentially for the frequency-measuring filtered sequence, and the resulting variance sum sequence curve is shown below. Figure 7 As shown. The simulation uses 8 samples per symbol. From the multi-symbol joint variance and sequence, it can be seen that each symbol has a minimum point, and the interval between the minimum points is approximately 8, which is consistent with the simulation conditions. The minimum point is the starting position of a symbol.

[0109] S600. Calculate the frequency estimate of the symbol based on the starting position of the symbol.

[0110] In some embodiments, calculating the frequency estimate of a symbol based on its starting position includes: dividing each symbol into segments based on its starting position; calculating the average instantaneous frequency between the starting position and the ending position of each symbol, and determining the average value as the frequency estimate of the symbol; wherein the ending position of a symbol is the starting position of the next symbol, and for the last symbol, if the number of sampling points within the symbol is less than the expected number of sampling points, the last position of the signal sequence is used as the ending position, and any insufficient points are padded with zeros.

[0111] In this embodiment, once the starting position of a symbol is determined, the symbols can be divided. A schematic diagram of the symbol division is shown below. Figure 8 As shown. By Figure 8 It can be seen that the instantaneous frequency variance estimation based on multi-symbol joint estimation can accurately classify each symbol. The average instantaneous frequency between the start and end positions of each symbol is the frequency estimate of that symbol.

[0112] S700. Based on the frequency estimate of the symbol, the symbol is identified using the minimum distance criterion, and the symbol information is recovered.

[0113] Based on the principle of minimum distance, symbol discrimination is performed using the symbol frequency estimate, and the symbol information can be recovered. If the symbol frequency estimate is close to the lowest frequency point of 4FSK, the symbol information output is '00'; if it is close to the second frequency point, the symbol output is '01', and so on, '10' and '11' respectively, thus completing demodulation.

[0114] 4FSK demodulation result bitmap illustration Figure 9 As shown, the simulation conditions are: signal frame length 262.

[0115] Based on the starting position of the symbol, the instantaneous frequency values ​​of m sampling points within the symbol are weighted and averaged, with the middle positions having a higher weight. The distance between the averaged instantaneous frequency value and four ideal frequency values ​​is compared, and the one with the smallest distance is the symbol frequency, which is mapped to the corresponding demodulated bit output. Let the averaged instantaneous frequency within the symbol be favg, and the four ideal frequency points from low to high be f1, f2, f3, and f4; the position of the minimum value can be calculated using the formula: [loc,~]=min[abs(f1-favg,f2-favg,f3-favg,f4-favg)]; the bit information can be mapped through the corresponding position.

[0116] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A 4FSK demodulation method based on multi-symbol joint estimation, characterized in that, include: Acquire the IQ signal and perform instantaneous frequency measurement on the IQ signal to obtain the first instantaneous frequency waveform; Symbol rate estimation is performed based on the first instantaneous frequency waveform to obtain the symbol rate estimate; Determine whether the current sampling rate meets the preset conditions: if yes, then determine the IQ signal as the frequency signal to be measured; if no, then resample the IQ signal to a resampled signal whose sampling rate meets the preset conditions, and determine the resampled signal as the frequency signal to be measured. The frequency signal to be measured is instantaneously measured to obtain a second instantaneous frequency waveform; Based on the second instantaneous frequency waveform, the starting position of the symbol is estimated by jointly estimating the variance of multiple symbols; Calculate the frequency estimate of the symbol based on its starting position; Based on the frequency estimate of the symbol, the symbol is identified using the minimum distance criterion, and the symbol information is recovered. Based on the second instantaneous frequency waveform, the starting position of the symbol is estimated using the joint variance of multiple symbols, including: S510. Determine a sampling point in the second instantaneous frequency waveform as the starting point, and then execute S520; S520. Based on the starting point, simultaneously calculate the variance of the instantaneous frequency of N signal segments with an interval of m sampling points and a length of m sampling points, and then execute S530; S530. Sum the variances of the instantaneous frequencies of the N signal segments to obtain a variance sum, and then execute S540; S540. Determine whether the number of variances obtained has reached the first preset value N´. If not, execute S550. If yes, execute S560. Wherein, the first preset value N´ is the number of sampling points within a single symbol. S550. Update the position of the starting point to the next sampling point corresponding to the current sampling point of the starting point, and then execute S520; S560. Determine the starting position of the symbol by the variance with the smallest median among the N' variances and the corresponding starting point.

2. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, The formula for calculating instantaneous frequency is: = In the formula, fs represents the instantaneous frequency, and fs represents the sampling rate. Indicates the unfolded instantaneous phase. For the instantaneous phase of the signal, The range of values ​​is , =0, where n is an integer greater than 0.

3. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, Symbol rate estimation is performed based on the first instantaneous frequency waveform to obtain the symbol rate estimate, including: For the first instantaneous frequency waveform Perform difference operations to obtain the first difference sequence d1(n); Perform a difference operation on the first difference sequence d1(n) to obtain the second difference sequence d2(n); Taking the absolute value of the second difference sequence d2(n) yields the sequence D_abs(n); Perform a fast Fourier transform on the D_abs(n) sequence to obtain the F_fft(n) sequence; Find the position Max_i of the maximum value in the right half of the F_fft(n) sequence; The symbol rate estimate is calculated using the following formula: In the formula, R_esi represents the symbol rate estimate, and fs represents the sampling rate; .

4. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, Determine whether the current sampling rate meets the preset conditions, including: Based on the symbol rate estimate, determine whether the current sampling rate satisfies the condition that the number of sampling points in each symbol is an integer. If yes, the current sampling rate satisfies the preset condition; otherwise, the current sampling rate does not satisfy the preset condition.

5. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, Resampling the IQ signal into a resampled signal with a sampling rate that meets a preset condition includes: Based on the symbol rate estimate, the IQ signal is resampled into a resampled signal with a sampling rate that meets a preset condition.

6. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, In step S510, if the starting position of the first symbol is to be estimated, the first sampling point is determined as the starting point; otherwise, the sampling point at the starting position of the previous symbol plus m / 2 sampling points is determined as the starting point.

7. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, Calculating the frequency estimate of the symbol based on its starting position includes: The symbols are divided based on their starting positions; Calculate the average instantaneous frequency between the start and end positions of each symbol, and determine this average value as the frequency estimate of the symbol; The ending position of a symbol is the starting position of the next symbol.

8. The 4FSK demodulation method based on multi-symbol joint estimation according to claim 1, characterized in that, The 4FSK demodulation method also includes: The first instantaneous frequency waveform and / or the second instantaneous frequency waveform are subjected to low-pass filtering, wherein the cutoff frequency of the low-pass filter is the symbol rate value.

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