Low and medium frequency instruction level underwater acoustic communication method under time-varying Doppler and low signal-to-noise ratio channel

Abstract

The invention discloses a low and medium frequency instruction level underwater acoustic communication method under a time-varying Doppler and low signal-to-noise ratio channel, which comprises the following steps of: generating a set containing 2a modulation symbols, mapping the set into a data frame, and adding a frame structure to form a transmitting signal; after receiving, a receiving end intercepts a pilot signal through matched filtering, Doppler estimation is carried out by adopting a grid search strategy, and an initial Doppler frequency offset factor and the position of a first symbol block are determined; estimating a signal # imgabs1 # and the position thereof according to a Doppler frequency offset factor # imgabs0 #, re-sampling the signal # imgabs1 # by using K Doppler frequency offset factors near the # imgabs2 #, performing matched filtering with each modulation symbol, determining an accurate signal # imgabs3 # of the nsym symbol block and the position thereof and a Doppler frequency offset factor # imgabs4 # according to an accumulated peak value, and correcting the width of a sliding window; and repeating the process until all symbol blocks are demodulated, and restoring the original bit according to the mapping relation. According to the method, Doppler frequency offset in each time period can be accurately estimated for compensation, and the method is suitable for instruction-level communication between underwater high-speed motion platforms.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic communication, and in particular to a medium- and low-frequency command-level underwater acoustic communication method under time-varying Doppler and low signal-to-noise ratio channels. Background Art

[0002] In the low- and medium-frequency bands, sound waves experience minimal propagation losses within underwater acoustic channels and are often used for long-distance underwater communications. However, this also makes them susceptible to environmental fluctuations. When communicating between high-speed underwater platforms, the relative speeds of the platforms fluctuate, causing the signal frequency to vary over time. This effect is particularly pronounced in the low- and medium-frequency bands. Furthermore, in long-distance communication scenarios, water attenuation and noise interference can result in poor received signal quality, making traditional modulation and demodulation methods unsuitable.

[0003] Achieving reliable communication in the presence of time-varying Doppler and strong background noise has become a computational challenge that needs to be solved urgently. Currently, spread spectrum communication is often used to increase the signal bandwidth in low signal-to-noise ratio underwater acoustic channels to enhance the system's anti-interference capabilities. However, this significantly reduces spectral efficiency, and the frame length of the spread spectrum signal is long. Due to the presence of time-varying Doppler, the Doppler frequency deviation factor within a frame of signal will inevitably change. Furthermore, the despreading process of the spread spectrum signal requires precise time synchronization with the transmitted signal, and Doppler estimation and matching decoding are also required for different spreading codes. These processes lead to excessive computational complexity, increasing system cost and maintenance difficulties. Summary of the Invention

[0004] In response to the problem of communication difficulties under time-varying Doppler and strong background noise interference in the existing technology, the present invention proposes a medium- and low-frequency command-level underwater acoustic communication method under time-varying Doppler and low signal-to-noise ratio channels, ensuring that high-speed mobile platforms can achieve stable and reliable long-distance communication under low signal-to-noise ratio.

[0005] The specific technical solutions are as follows:

[0006] A method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel comprises the following steps:

[0007] S1: Generates a linear frequency modulation signal based on the transmitter, including 2 a A set of modulation symbols According to the mapping relationship, each modulation symbol is 2 a Frequency modulation forms a data frame, adds a frame header structure containing a pilot signal to its front end, and adds a frame tail signal to the tail end to form a transmission signal;

[0008] S2: The transmitted signal is received by the receiving end through the channel. The receiving end performs frame synchronization on the received signal and determines the starting position of the frame header through matched filtering. Based on this, the starting position of the pilot signal is determined.

[0009] S3: Use grid search strategy to perform Doppler estimation on the intercepted pilot signal to determine the initial Doppler frequency deviation factor and the start position of the first symbol block

[0010] S4: Preliminary setting of the sliding window width used to intercept the first symbol block;

[0011] S5: According to the previous Doppler frequency deviation factor Estimate the nth sym The starting position of the symbol block, n sym =2,3,…,N sym , N sym is the total number of symbol blocks in the data frame, and the signal is intercepted using a sliding window by Take K Doppler frequency deviation factors at equal intervals as the center, and use the kth Doppler frequency deviation factor to Perform resampling, k = 1, 2, ..., K;

[0012] S6: The resampled signal The cross-correlation function is obtained by matching the modulation symbols in the set S, and the nth sym symbol block accurate signal Its starting position and Doppler frequency deviation factor

[0013] S7: Determine whether the estimation of all symbol blocks is completed. If so, demodulate to obtain the original bits according to the mapping relationship; if not, correct the width of the sliding window according to the current Doppler frequency offset factor, and repeat S5-S7 to estimate the next symbol block.

[0014] Furthermore, in the S1, the transmission signal includes a frame header structure, a data frame, and a frame tail signal in sequence. The frame header structure includes a pilot signal and a guard interval. The frame tail signal uses a zero guard value.

[0015] Furthermore, the S2 is implemented by the following sub-steps:

[0016] S2.1: The receiving end performs frame synchronization on the received signal. The relationship between the received signal y(t) and the transmitted signal x(t) is expressed as follows:

[0017] y(t)=h(t)*x(t)+w(t)

[0018]

[0019] Where h(t) is the impulse response of the underwater acoustic channel, w(t) is the wave with a mean of 0 and a power of σ 2 Gaussian white noise; P represents the total number of paths in the underwater acoustic channel, δ represents the impulse response, η p is the signal attenuation of the pth path, α p (t) is the Doppler frequency deviation factor of the pth path, and its value changes with time, τ p is the delay of the p-th path;

[0020] S2.2: Starting from the beginning of the received signal sequence, intercept the signal sequence with the same length as the frame header length as the initial preset frame header signal y head (t);

[0021] S2.3: Using the matched filtering method, calculate the cross-correlation function between the intercepted preset frame header signal and the frame header signal of the transmitted signal. The expression is as follows:

[0022]

[0023] Where r head (τ) represents the cross-correlation function of the frame header signal, τ represents the delay, x head (t) represents the frame header signal of the transmitted signal;

[0024] S2.4: Determine whether the correlation peak of the cross-correlation function is greater than the set threshold. If so, use the current frame header signal as the accurate frame header signal, and use the starting position of the accurate frame header signal as the starting position of the pilot signal; if not, intercept the next signal sequence on the received signal sequence with the set step size as the new preset frame header signal, and repeat S2.3-S2.4.

[0025] Furthermore, the S3 is implemented by the following sub-steps:

[0026] S3.1: Preset multiple different Doppler factors α m , m=1,2,3,…,M, M is the total number of preset Doppler factors, the pilot signal y p (t) at different Doppler factors α m Resample the signal to obtain the corresponding resampled pilot signal

[0027] S3.2: Resampled pilot signal and the original pilot signal x at the transmitter p (t) Perform matching correlation and calculate the Doppler factor α m The cross-correlation function is:

[0028]

[0029] Where, τ represents the time delay;

[0030] S3.3: Select the correlation peak of the cross-correlation function The Doppler factor corresponding to the maximum is used as the initial Doppler frequency deviation factor Its expression is as follows:

[0031]

[0032] Estimate the starting position of the first symbol block based on the initial Doppler factor

[0033]

[0034] Where, Indicates the starting position of the pilot signal, T head Indicates the duration of the frame header signal.

[0035] Furthermore, in S3.1, the resampling is performed based on the linear frequency modulation Z transform principle.

[0036] Furthermore, in S4, the sliding window width used to intercept the first symbol block is initially set to:

[0037]

[0038] Where, T sym Indicates the duration of a symbol, T over Indicates the overlap width between two adjacent sliding windows.

[0039] Furthermore, in said S5, according to the previous Doppler frequency deviation factor Estimate the nth sym The starting position of a symbol block is expressed as follows:

[0040]

[0041] Where, Indicates the nth sym The estimated starting position of the symbol block, Indicates the nth sym -1 symbol block corrected starting position, T sym Indicates the duration of a symbol.

[0042] Furthermore, the S6 is implemented by the following sub-steps:

[0043] S6.1: The nth sym Symbol block signal Perform matched filtering on each modulation symbol in the set S and calculate the cross-correlation function between them. The expression is as follows:

[0044]

[0045] Where s i represents the i-th modulation symbol, i=1,2,…,2 a ;τ represents the delay;

[0046] S6.2: Calculating Signals With each modulation symbol s i Cumulative peak after matched filtering The expression is as follows:

[0047]

[0048] The modulation symbol corresponding to the maximum cumulative peak value For nth sym symbol block accurate signal The expression is as follows:

[0049]

[0050] S6.3: Calculate modulation symbols When determined, make the peak The Doppler frequency deviation factor at the maximum is used as the estimated nth sym Doppler frequency deviation factor under symbol blocks The expression is as follows:

[0051]

[0052] S6.4: The modulation symbol corresponds to Corresponding to the Doppler frequency shift factor When determining, the nth sym The starting position of a symbol block is expressed as follows:

[0053]

[0054] Where, Indicates the nth sym The corrected starting position of the symbol block, Indicates the nth sym The starting position correction value of the symbol block, is the modulation symbol number corresponding to the maximum cumulative peak value obtained in S6.2, The Doppler frequency deviation factor number corresponding to the maximum cumulative peak value obtained in S6.3.

[0055] Furthermore, in S7, the expression for correcting the width of the sliding window according to the current Doppler frequency offset factor is as follows:

[0056]

[0057] Where, represents the corrected sliding window width, represents the sliding window width before correction, Indicates the current Doppler frequency deviation factor.

[0058] The beneficial effects of the present invention are:

[0059] (1) The present invention can accurately obtain the Doppler estimation result of the signal in each symbol block by resampling and matching filtering the signal in each symbol block, so as to ensure reliable medium and low frequency communication under the channel conditions of time-varying Doppler.

[0060] (2) The present invention ensures the efficiency of spectrum utilization through a modulation method based on linear frequency modulation signals, thereby realizing underwater medium and low frequency communications with high spectrum utilization.

[0061] (3) The present invention improves the symbol duration and the cumulative gain of the signal corresponding to a single symbol by modulating the linear frequency modulation signal while meeting the communication rate, thereby ensuring reliable medium and low frequency communication under low signal-to-noise ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of a method for medium- and low-frequency command-level underwater acoustic communication under time-varying Doppler and low signal-to-noise ratio channels in an embodiment of the present invention.

[0063] Figure 2 4 is a time-frequency diagram of 16 modulation symbols generated in an embodiment of the present invention.

[0064] Figure 3 2 is a schematic diagram of the structure of transmitting signals in an embodiment of the present invention.

[0065] Figure 4 Schematic diagram of intercepting a symbol block using a sliding window in an embodiment of the present invention.

[0066] Figure 5 1 is a schematic diagram of the theory and estimation of Doppler frequency offset factor estimation in an embodiment of the present invention.

[0067] Figure 6 This is a performance comparison chart of the method according to the embodiment of the present invention and the traditional spread spectrum communication method. DETAILED DESCRIPTION

[0068] The present invention will be described in detail below based on the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become more apparent. The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0069] A low- to medium-frequency command-level underwater acoustic communication method for time-varying Doppler and low signal-to-noise ratio channels is proposed. This method uses symbols generated based on LFM signals for modulation during the signal modulation process. At the receiving end, the signal within the symbol block intercepted by each window is resampled and matched filtered to achieve Doppler estimation and symbol estimation. Figure 1 As shown, the method includes the following steps:

[0070] S1: Based on the linear frequency modulation (LFM) signal generation at the transmitting end, it includes 2 a A set of modulation symbols According to the mapping relationship, each modulation symbol in the set S is 2 a Frequency modulation forms a data frame, and after adding the frame structure, it forms a transmission signal. S1 is specifically implemented through the following sub-steps:

[0071] S1.1: Based on LFM signal generation including 2 a A set of modulation symbols In this embodiment, a set S containing 16 modulation symbols is generated, which is S={s1,s1,…,s 16}, the expressions of each modulation symbol are shown in Table 1 below.

[0072] Table 1 Modulation symbol expression

[0073]

[0074]

[0075] Among them, f c Indicates the carrier center frequency, B represents the frequency bandwidth, T sym represents the duration of a symbol, R b represents the communication bit rate, A represents the number of modulation symbols, A = 2 a , in this embodiment, A=16.

[0076] For the communication frequency band in f down ~f up If the duration of a symbol is T sym , then the time-frequency diagram of the 16 modulation symbols is as follows Figure 2 shown.

[0077] S1.2: Perform 2 on each modulation symbol in set S according to the mapping relationship a Frequency modulation forms a data frame, that is, a bits are mapped to a symbol in turn to form a data frame x d (t).

[0078] In this embodiment, when four bits are used for 16-frequency modulation, the mapping relationship between the bits and each modulation symbol is shown in Table 2 below.

[0079] Table 2 Mapping relationship between four bits and sixteen modulation symbols

[0080]

[0081] S1.3: In the data frame x d (t) before adding the pilot signal x p (t) and the frame header structure of the guard interval x head (t), the pilot signal is the LFM signal; the frame tail signal x is added after the data frame g (t), forming the transmission signal x(t). In this embodiment, the frame tail signal is a zero protection value, and the transmission signal structure formed is as follows Figure 3 shown.

[0082] S2: The transmitter sends a transmission signal, which is received at the receiver through the channel. The receiver performs frame synchronization on the received signal y(t), performs matched filtering on the signal frame header, and determines the starting position of the frame header based on the correlation peak. And intercept the pilot signal y p (t). S2 is specifically implemented through the following sub-steps:

[0083] S2.1: The relationship between the received signal y(t) and the transmitted signal x(t) is expressed as follows:

[0084] y(t)=h(t)*x(t)+w(t)

[0085]

[0086] Where h(t) is the impulse response of the underwater acoustic channel, w(t) is the wave with a mean of 0 and a power of σ 2 Gaussian white noise; P represents the total number of paths in the underwater acoustic channel, δ represents the impulse response, η p is the signal attenuation of the pth path, α p (t) is the Doppler frequency deviation factor of the pth path, and its value changes with time, τ p is the delay of the p-th path.

[0087] S2.2: Starting from the beginning of the received signal sequence, intercept the signal sequence with the same length as the frame header length as the initial preset frame header signal y head (t).

[0088] S2.3: Use the matched filtering method to calculate the intercepted preset frame header signal y head (t) and the original frame header signal (i.e. the frame header signal of the transmitted signal) x head The cross-correlation function of (t) is expressed as follows:

[0089]

[0090] Where r head (τ) represents the cross-correlation function of the frame header signal, and τ represents the delay.

[0091] S2.4: Determine whether the correlation peak of the cross-correlation function is greater than a set threshold (in this embodiment, the threshold is set to 5 times the correlation mean). If so, the current preset frame header signal is used as the accurate frame header signal, and its corresponding frame header starting position is It is also the starting position of the pilot signal If not, the next block of signal sequence is intercepted from the received signal sequence with the set step size as a new preset frame header signal, and matched filtering and correlation peak determination are performed again (ie, S2.3-S2.4 are repeated).

[0092] S3: According to the starting position of the pilot signal Intercept pilot signal y p (t), the intercepted pilot signal is subjected to a grid search strategy for Doppler estimation, that is, the initial Doppler frequency offset factor is determined by resampling and matched filtering. and the position of the first symbol block S3 is implemented through the following sub-steps:

[0093] S3.1: Preset multiple different Doppler factors α m , m=1,2,3,…,M, M is the total number of preset Doppler factors, the pilot signal y p (t) at different Doppler factors α m Resample the signal to obtain the corresponding resampled pilot signal

[0094] In this embodiment, the resampling is performed based on the Chirp Z transform (CZT) principle, where y p (t) represents the continuous expression of the original pilot signal, y p [n] represents the discrete expression of the original pilot signal, Indicates the Doppler factor αm The continuous expression of the pilot signal after resampling, Indicates the Doppler factor α m The discrete expression of the pilot signal after resampling is shown in the figure below for the convenience of expression. p (t) and y p [n], and The detailed process of resampling is as follows:

[0095] (1) Select the appropriate number of frequency points N FFT , the expression is as follows:

[0096]

[0097] Where N p Indicates the pilot signal sequence length.

[0098] (2) For the pilot signal sequence y p [n] After carrier compensation, the generated complex sequence for:

[0099]

[0100] (3) Generate the sequences c[n], q[n], and z[l] respectively. The expressions are as follows:

[0101]

[0102] (4) Convolve the sequences c[n] and q[n], and add the first N of the convolved sequence c[n]*q[n] p -1 item and N after p The -1 term is discarded, and then the dot product is performed with the sequence z[l] to obtain Y[l]:

[0103]

[0104] (5) Exchange the first half and the second half of the Y[k] sequence, that is, perform spectrum shifting to obtain Y s [l]:

[0105] Y s [l]=fftshift(Y[l])

[0106] (6) Perform inverse fast Fourier transform on the sequence after spectrum shifting to obtain the resampled sequence

[0107]

[0108] S3.2: Resampled pilot signal and the original pilot signal x at the transmitter p (t) Perform matching correlation and calculate the Doppler factor α m The cross-correlation function is:

[0109]

[0110] S3.3: Comparison of the peak values ​​of the cross-correlation functions for different Doppler factors The size of the correlation peak is selected as the initial Doppler frequency deviation factor. Its expression is as follows:

[0111]

[0112] Estimate the starting position of the first symbol block based on the initial Doppler factor

[0113]

[0114] Where, T head Indicates the duration of the frame header signal.

[0115] S4: Initially set the sliding window width used to intercept the first symbol block The expression is as follows:

[0116]

[0117] Where, T over Indicates the overlap width between two adjacent sliding windows.

[0118] S5: According to the Doppler frequency deviation factor Estimate the nth sym The starting position of the symbol block The expression is as follows:

[0119]

[0120] Where, Indicates the nth sym The estimated starting position of the symbol block, Indicates the nth sym -1 symbol block corrected start position, N sym Indicates the total number of symbol blocks in the data frame.

[0121] like Figure 4 As shown, the width is Sliding window to the nth sym The starting position of the symbol block Intercept the nth sym The signal of a symbol block And in the previous estimated Doppler frequency deviation factor The K nearby Doppler frequency deviation factors Resampling is performed based on the CZT principle, where the Doppler frequency deviation factor numbered k is used. The resampled signal is Where k = 1, 2, ..., K. "Nearby" is defined based on a fixed frequency interval, i.e., the Doppler frequency deviation factor estimated previously With φ as the center, K / 2 frequency points are taken on the left and right, and the intervals between two adjacent frequency points are the same.

[0122] S6: The resampled signal and each modulation symbol s in the set S i Perform matched filtering to obtain the correlation function Where i = 1, 2, ..., 2 a , s i Represents the i-th modulation symbol. Then determine the n-th sym symbol block accurate signal The starting position and the estimated Doppler frequency offset factor And correct the width parameter of the sliding window. S6 is specifically implemented through the following sub-steps:

[0123] S6.1: The nth sym Symbol block signal and each modulation symbol s in the modulation symbol set S i Perform matched filtering separately and calculate the cross-correlation function between the two. The expression is as follows:

[0124]

[0125] S6.2: Calculating Signals With each modulation symbol s i Cumulative peak after matched filtering The expression is as follows:

[0126]

[0127] The modulation symbol corresponding to the maximum cumulative peak value That is the nth sym symbol block accurate signal The expression is as follows:

[0128]

[0129] S6.3: Calculate the resampled signal at K Doppler frequency offset factors With the determined modulation symbol The correlation function of The Doppler frequency deviation factor at the maximum (at this time ) as the estimated nth sym Doppler frequency deviation factor under symbol blocks The expression is as follows:

[0130]

[0131] S6.4: Modulation symbol corresponding Corresponding to the Doppler frequency shift factor When determining, the nth sym The starting position of a symbol block is expressed as follows:

[0132]

[0133] Where, Indicates the nth sym The corrected starting position of the symbol block, Indicates the nth sym The starting position correction value of the symbol block, is the modulation symbol number corresponding to the maximum cumulative peak value obtained in S6.2, The Doppler frequency deviation factor number corresponding to the maximum cumulative peak value obtained in S6.3.

[0134] S7: Determine whether the estimation of all symbol blocks is completed. If so, demodulate the original bits according to the mapping relationship specified in Table 2; if not, correct the width of the sliding window according to the current Doppler frequency offset factor, and repeat S5-S7 to estimate the next symbol block. The corrected sliding window width is expressed as follows:

[0135]

[0136] In order to verify the performance of the method of the present invention, corresponding performance simulation experiments were carried out, which are specifically described below through two embodiments.

[0137] Example 1: To verify the communication reliability of the proposed method under time-varying Doppler and low signal-to-noise ratio channel conditions, the parameters of this example are set as follows: a communication rate of 40 bits per second, a modulation symbol of 100 milliseconds, a signal transmission band of 2-3 kHz, a total transmission of 10,000 bits of information, and a sampling frequency of 12 kHz. The received signal is affected by ocean ambient noise simulated by Gaussian white noise, with a signal-to-noise ratio of -5 dB. The signal is also affected by Doppler shift and multipath interference. The maximum Doppler rate is 10 knots, and the maximum Doppler rate variation rate is 1 knot / s.

[0138] The specific parameters of the simulation signal are shown in Table 3 below.

[0139] Table 3 Specific parameters of simulation signals

[0140] parameter set up Communication rate 40bps Center frequency 2.5kHz Signal bandwidth 1kHz Number of signal bits 10000 bits Sampling frequency 12kHz Maximum Doppler rate 10kont Maximum Doppler change rate 1kont / s Maximum multipath delay 300ms Signal-to-noise ratio -5dB

[0141] Under this simulation condition, based on the modulation characteristics of the LFM signal, the Doppler frequency deviation of each symbol of the received signal is estimated using the method of the present invention. The estimation results are as follows: Figure 5 As shown in the figure, after Doppler compensation, each symbol can be accurately estimated, and the final bit error rate is 0, which shows that the method of the present invention can effectively estimate the Doppler frequency offset of each symbol.

[0142] Example 2: To verify the excellent noise immunity of the communication method proposed in this embodiment, the parameters of this embodiment are set as follows: a communication rate of 40 bps, a signal transmission frequency band of 2-3 kHz, a total transmission of 4000 bits of information, a sampling frequency of 12 kHz, a received signal noise ratio of -18 to 0 dB, and 0.5 dB intervals. Without considering multipath and Doppler effects, 100 Monte Carlo simulations were performed using the method proposed in this embodiment and a conventional direct sequence spread spectrum communication method under each signal noise ratio condition. The conventional direct sequence spread spectrum communication method uses a sequence length of 15 and BPSK modulation.

[0143] Figure 6 This is a comparison chart of simulation performance between the method of the present invention and the direct sequence spread spectrum communication method. The simulation results show that within the simulated signal-to-noise ratio range, the bit error rate of the method of the present invention is significantly lower than that of the direct sequence spread spectrum communication method, indicating that the method of the present invention has excellent noise resistance.

[0144] In summary, this paper proposes a low- to medium-frequency command-level communication method based on LFM signal modulation, a grid search strategy, and matched filtering, suitable for time-varying Doppler and low signal-to-noise ratio conditions. This method enables reliable low- to medium-frequency communication in channels with extremely low signal-to-noise ratios and time-varying Doppler, thus ensuring stable and reliable long-distance communication for underwater high-speed mobile platforms in low signal-to-noise ratio conditions.

[0145] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art will still be able to modify the technical solutions described in the foregoing examples or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the invention shall be included within the scope of protection of the invention.

Claims

1. A method for low- to medium-frequency command-level underwater acoustic communication in time-varying Doppler and low signal-to-noise ratio channels, characterized in that: The following steps are involved: S1: Generates a linear frequency modulation signal based on the transmitter, including 2 a The set of modulation symbols S = {s1,s2,…,s 2a }, each modulation symbol is 2- a Frequency modulation forms a data frame, adds a frame header structure containing a pilot signal to its front end, and adds a frame tail signal to the tail end to form a transmission signal; S2: The transmitted signal is received by the receiving end through the channel. The receiving end performs frame synchronization on the received signal and determines the starting position of the frame header through matched filtering. Based on this, the starting position of the pilot signal is determined. S3: Use grid search strategy to perform Doppler estimation on the intercepted pilot signal to determine the initial Doppler frequency deviation factor and the start position of the first symbol block S4: Preliminary setting of the sliding window width used to intercept the first symbol block; S5: According to the previous Doppler frequency deviation factor Estimate the nth sym The starting position of the symbol block, n sym =2,3,…,N sym , N sym is the total number of symbol blocks in the data frame, and the signal y is intercepted using a sliding window nsym (t); Take K Doppler frequency deviation factors at equal intervals as the center, and use the kth Doppler frequency deviation factor to Perform resampling, k = 1, 2, ..., K; S6: The resampled signal The cross-correlation function is obtained by matching the modulation symbols in the set S, and the nth sym symbol block accurate signal Its starting position and Doppler frequency deviation factor S7: Determine whether the estimation of all symbol blocks is completed. If so, demodulate to obtain the original bits according to the mapping relationship; if not, correct the width of the sliding window according to the current Doppler frequency offset factor, and repeat S5-S7 to estimate the next symbol block.

2. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: In the S1, the transmission signal includes a frame header structure, a data frame, and a frame tail signal in sequence. The frame header structure includes a pilot signal and a guard interval. The frame tail signal uses a zero guard value.

3. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: The S2 is implemented by the following sub-steps: S2.1: The receiving end performs frame synchronization on the received signal. The relationship between the received signal y(t) and the transmitted signal x(t) is expressed as follows: y(t)=h(t)*x(t)+w(t) Where h(t) is the impulse response of the underwater acoustic channel, w(t) is the wave with a mean of 0 and a power of σ 2 Gaussian white noise; P represents the total number of paths in the underwater acoustic channel, δ represents the impulse response, η p is the signal attenuation of the pth path, α p (t) is the Doppler frequency deviation factor of the pth path, and its value changes with time, τ p is the delay of the p-th path; S2.2: Starting from the beginning of the received signal sequence, intercept the signal sequence with the same length as the frame header length as the initial preset frame header signal y head (t); S2.3: Using the matched filtering method, calculate the cross-correlation function between the intercepted preset frame header signal and the frame header signal of the transmitted signal. The expression is as follows: Where r head (τ) represents the cross-correlation function of the frame header signal, τ represents the delay, x head (t) represents the frame header signal of the transmitted signal; S2.4: Determine whether the correlation peak of the cross-correlation function is greater than the set threshold. If so, use the current frame header signal as the accurate frame header signal, and use the starting position of the accurate frame header signal as the starting position of the pilot signal; if not, intercept the next signal sequence on the received signal sequence with the set step size as the new preset frame header signal, and repeat S2.3-S2.

4.

4. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: The S3 is implemented through the following sub-steps: S3.1: Preset multiple different Doppler factors α m , m=1,2,3,…,M, M is the total number of preset Doppler factors, the pilot signal y p (t) at different Doppler factors α m Resample the signal to obtain the corresponding resampled pilot signal S3.2: Resampled pilot signal and the original pilot signal x at the transmitter p (t) Perform matching correlation and calculate the Doppler factor α m The cross-correlation function is: Where, τ represents the time delay; S3.3: Select the correlation peak of the cross-correlation function The Doppler factor corresponding to the maximum is used as the initial Doppler frequency deviation factor Its expression is as follows: Estimate the starting position of the first symbol block based on the initial Doppler factor Where, Indicates the starting position of the pilot signal, T head Indicates the duration of the frame header signal.

5. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 4, characterized in that: In S3.1, the resampling is performed based on the linear frequency modulation Z transform principle.

6. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: In S4, the sliding window width used to intercept the first symbol block is initially set to: Where, T sym Indicates the duration of a symbol, T over Indicates the overlap width between two adjacent sliding windows.

7. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: In the above S5, according to the previous Doppler frequency deviation factor Estimate the nth sym The starting position of a symbol block is expressed as follows: Where, Indicates the nth sym The estimated starting position of the symbol block, Indicates the nth sym -1 symbol block corrected starting position, T sym Indicates the duration of a symbol.

8. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: The S6 is implemented by the following sub-steps: S6.1: The nth sym Symbol block signal Perform matched filtering on each modulation symbol in the set S and calculate the cross-correlation function between them. The expression is as follows: Where s i represents the i-th modulation symbol, i=1,2,…,2 a ;τ represents the delay; S6.2: Calculating Signals With each modulation symbol s i Cumulative peak after matched filtering The expression is as follows: The modulation symbol corresponding to the maximum cumulative peak value For nth sym symbol block accurate signal The expression is as follows: S6.3: Calculate modulation symbols When determined, make the peak The Doppler frequency deviation factor at the maximum is used as the estimated nth sym Doppler frequency deviation factor under symbol blocks The expression is as follows: S6.4: The modulation symbol corresponds to Corresponding to the Doppler frequency shift factor When determining, the nth sym The starting position of a symbol block is expressed as follows: Where, Indicates the nth sym The corrected starting position of the symbol block, Indicates the nth sym The starting position correction value of the symbol block, is the modulation symbol number corresponding to the maximum cumulative peak value obtained in S6.2, The Doppler frequency deviation factor number corresponding to the maximum cumulative peak value obtained in S6.

3.

9. The method for medium- and low-frequency command-level underwater acoustic communication in a time-varying Doppler and low signal-to-noise ratio channel according to claim 1, characterized in that: In S7, the expression for correcting the width of the sliding window according to the current Doppler frequency offset factor is as follows: Where, represents the corrected sliding window width, represents the sliding window width before correction, Indicates the current Doppler frequency deviation factor.

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