High-speed mobile underwater acoustic communication Doppler estimation compensation method

Abstract

The invention discloses a high-speed mobile underwater acoustic communication Doppler estimation compensation method, which comprises the following steps: receiving an underwater acoustic communication signal with a Doppler effect in a specific frame format, carrying out local refining amplification on the frequency of a CW signal through a Zoom-FFT algorithm, and determining Doppler within a preset range; estimating the frequency offset of the LFM signal through an AF algorithm, and compensating Doppler frequency shift through resampling; the residual Doppler effect after compensation is eliminated through code element residual phase offset, sent bipolar code elements are changed into complex field code elements, complex field code element information is converted, and when the information is used for demodulation, the complex field code elements offset phases between the code elements through inverse transformation. According to the method, estimation compensation of large Doppler and residual Doppler is completed, the problems of low Doppler estimation precision under a low signal-to-noise ratio, more matched correlators, long time consumption, large Doppler compensation difficulty and residual Doppler signal phase compensation under low complexity are solved, and a key technical support is provided for stable operation of a high-speed mobile underwater acoustic communication system.

Description

Technical Field

[0001] The invention relates to the field of underwater acoustics, and in particular to a Doppler estimation and compensation method for high-speed mobile underwater acoustic communication. Background Art

[0002] The application of marine underwater unmanned system platforms is increasing. Among them, unmanned boats, AUVs, unmanned ships, and UUVs can perform tasks such as ocean observation and shipwreck search in relatively complex marine environments. The information exchange of these marine unmanned platforms is inseparable from underwater acoustic communication. The underwater acoustic channel has the characteristics of severe Doppler spread, limited spectrum resources, and low signal-to-noise ratio. The acoustic wave information transmission environment is relatively harsh, and the stability of underwater acoustic communication is difficult to guarantee. Therefore, higher requirements are placed on stable marine communication technology.

[0003] Since the propagation speed of underwater sound is much lower than that of electromagnetic waves, underwater acoustic communication between mobile underwater platforms is seriously affected by Doppler. In the communication system, the Doppler effect will cause the phase of the demodulated signal to rotate, seriously affecting the stability of underwater acoustic communication. Therefore, how to suppress the Doppler effect in the underwater acoustic communication system of a fast-moving underwater platform is the core research direction for the stable operation of the underwater communication system. Extensive research has been carried out at home and abroad on Doppler estimation and compensation technology in underwater acoustic communication of mobile platforms.

[0004] The patent with publication number CN108833312A discloses a time-varying sparse water acoustic channel estimation method based on the delay-Doppler domain, including delay-Doppler domain modeling for the time-varying water acoustic channel, in order to obtain a sparse two-dimensional domain expression, based on the delay-Doppler domain expression. The block-by-block training mode is adopted, and the Schmidt orthogonal matching pursuit algorithm is combined to iteratively optimize the sparse water acoustic channel impulse response function in the delay-Doppler domain, and the estimated delay-Doppler domain water acoustic channel information is used at the receiving end to construct a minimum mean square error equalizer based on the channel information to recover the transmitted signal.

[0005] The patent with publication number CN110247867A discloses an underwater acoustic Doppler estimation method and device, an underwater acoustic communication method and system, including sending two hyperbolic frequency modulation signals at the transmitting end, and using the matched filter output of the first hyperbolic frequency modulation signal and the matched filter output of the second hyperbolic frequency modulation signal to re-correlate at the receiving end, so as to obtain the matched filter output of the first hyperbolic frequency modulation signal and the overall relative time shift of the second hyperbolic frequency modulation signal, and then estimate the Doppler factor.

[0006] The patent with publication number CN112822135A discloses a single-carrier high-speed underwater acoustic communication method, which includes the following steps: (1) single-carrier signal coding modulation, the transmitter converts the original information sequence into serial-to-parallel and maps it to the QPSK phase set, and then adds a training sequence before the mapped phase sequence and modulates it before sending it out; (2) channel estimation, after the receiving end completes signal detection and synchronization, it estimates the channel using the locally known training sequence; (3) frequency domain zero-forcing equalization processing, using the estimated channel to construct a weight matrix in the frequency domain, and multiply it with the received signal to achieve channel equalization processing; (4) decision feedback equalization processing, the signal after frequency domain zero-forcing equalization processing is inverse Fourier transformed back to the time domain and finally decoded using a decision feedback equalizer with an embedded phase-locked loop.

[0007] The paper [Hu Yaohui, et al., A combined differential spread spectrum underwater acoustic communication method for underwater mobile communication [J], Journal of Electronics and Information Technology, 2022] discloses that combined differentials realize polar differential decoding between two-dimensional combinations to solve the Doppler problem, and polar modulation is added after energy mapping decoding to improve spectrum utilization. The paper [Wei Zhuoqun, Research on Mobile Robust Spread Spectrum Underwater Acoustic Communication Technology [D], 2018] discloses a delay-Doppler estimation method based on narrowband mutual ambiguity function, which can accurately estimate the Doppler of mobile node underwater communication. The direct spread signal is used between every two symbols for real-time Doppler estimation and compensation, and resampling is used for Doppler compensation, but it is not suitable for eliminating residual Doppler effect in special cases. The paper [Qin Hao, Research on Reliability of Underwater Mobile Node Communication [D], 2016] discloses an improved Pisarenko harmonic decomposition method based on polynomials to estimate Doppler, but it has high complexity and is not suitable for variable Doppler communication.

[0008] The Doppler effect of underwater acoustic communication on high-speed mobile platforms cannot completely compensate for the Doppler, or exceeds the Doppler tolerance of the existing Doppler estimation and compensation algorithm itself, and cannot solve the Doppler effect well. At a low signal-to-noise ratio, the estimation is inaccurate, the estimation time is long, the residual Doppler compensation is incomplete, and the algorithm is complex. The existing Doppler estimation technology has block Doppler estimation, with LFM signals before and after the signal, and the Doppler estimation value is obtained by matching filtering. This method has low estimation accuracy, and the obtained Doppler is the average Doppler, which cannot completely compensate for the Doppler of the signal. The fuzzy function Doppler estimation algorithm has a long estimation time and poor real-time performance. The fuzzy function is used to estimate the Doppler, and the residual Doppler is eliminated by the decision feedback equalizer embedded in the phase-locked loop. The algorithm complexity is high, the estimation is slow, and it is not suitable for the downshift implementation of the algorithm. Summary of the invention

[0009] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a Doppler estimation and compensation method for high-speed mobile underwater acoustic communication.

[0010] The objective of the present invention is achieved through the following technical solutions: The present invention provides a Doppler estimation and compensation method for high-speed mobile underwater acoustic communication, comprising the following steps: S1, receiving an underwater acoustic communication signal of a specific frame format with a Doppler effect, locally refining and amplifying the frequency of the CW signal through a Zoom-FFT algorithm, for fast and accurate Doppler estimation, and determining the Doppler of the communication signal within a preset range; S2, estimate the frequency deviation of the LFM signal through the AF algorithm, which is used to reduce the Doppler search step size, further refine the Doppler estimation, and compensate for the Doppler frequency shift through resampling; S3. The Doppler effect remaining after compensation is completely eliminated by cancelling the residual phase of the code elements, and the transmitted bipolar code elements are converted into complex domain code elements. The complex domain code element information is transformed. When used for demodulation, the complex domain code elements cancel the phase between the code elements by inverse transformation.

[0011] Furthermore, the step S1 specifically includes: For CW signal Spectrum migration: , move to the center frequency Get the signal ,in is the unit rotation factor; Calculate the sampling ratio ,in is the sampling frequency; Calculation of CW Signal The total number of sampling points ,in For analysis points; Through the digital low-pass filter, retain Signal in frequency band The frequency band that needs to be refined within the range is used to obtain the signal , ,in is the impulse response, and the cutoff frequency of the digital low-pass filter is ; If the sampling frequency is , for the signal Take a data point every D-1 to get a coarse-grained signal ; For coarse-grained signal Perform N-point complex FFT, intercept the refined spectrum fft result, move it in the opposite direction, connect it front and back, convert it into actual frequency, and get the refined FFT transformation result , the obtained frequency is subtracted from the original frequency to obtain the approximate Doppler frequency deviation.

[0012] Preferably, the step S2 specifically includes: local Based on the Doppler range determined by the Zoom-FFT algorithm, a small step size Doppler factor is used Change, the local LFM signal after Doppler change and the received signal Perform correlation, select the maximum value of the ambiguity function AF of the signal, and resample the received signal to compensate for the Doppler frequency deviation based on the Doppler estimated by the Zoom-FFT-AF combined with the Doppler algorithm; where AF is defined as ; is the signal delay; is the Doppler shift; the time function of the linear frequency modulated pulse signal Expressed as ; Where A is the signal amplitude, T is the transmission period of each code element; like When , the AF of the LFM signal is: ; Received signal With local Doppler factor The changed signal is correlated, and its fuzzy function expression can be expressed as: , where r is the received signal.

[0013] Preferably, the code element residual phase cancellation in step S3 eliminates the residual Doppler effect after compensation, specifically comprising: at the transmitting end, performing complex domain code element transformation on the PSK code element: ; in is the bipolar complex domain code element, is the information before transformation, is the intermediate transformation symbol, is the transformed codeword, for The phase information corresponding to the code element, for The phase information corresponding to the code element, for The phase information corresponding to the code element is then Perform spectrum spreading, raised cosine filtering, up-sampling and up-conversion modulation to obtain a transmission signal; The received underwater acoustic Doppler signal is demodulated, raised cosine filtered and despread accordingly based on the receiving end, and the complex domain codewords before the decision are inversely transformed accordingly based on the transmitting end: ; in To offset the I / Q path pre-decision data once, is the complex domain amplitude information of the transformed code element, is the corresponding phase information, It is the data before I / Q path decision after symbol phase offset transformation. for Its own phase information, and then Take out the real part and the imaginary part to make a decision and get the code element information.

[0014] The beneficial effects of the present invention are: 1) The present invention uses the Zoom-FFT algorithm to quickly and accurately estimate the frequency of the CW signal, locks the signal Doppler in a small range, and further searches and estimates the Doppler in a small step size through the LFM signal AF algorithm, thereby solving the problem of estimating a large Doppler with high computational complexity and low precision under low signal-to-noise ratio.

[0015] 2) The present invention utilizes the characteristics of the phase information between code elements to perform specific transformations on the complex domain code element information of the transmitted data. During demodulation, the phases between the complex domain code elements are offset by specific inverse transformations. The algorithm has low complexity and is easy to implement. It solves the problem of residual Doppler compensation after Doppler compensation and provides key technical support for stable underwater mobile communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A schematic flow chart of a Doppler estimation and compensation method for high-speed mobile underwater acoustic communication according to an embodiment of the present invention; Figure 2 A schematic diagram of a transmission signal structure of a Doppler estimation and compensation method for high-speed mobile underwater acoustic communication according to an embodiment of the present invention; Figure 3 A schematic diagram of the Doppler estimation process of the Zoom-FFT algorithm according to an embodiment of the present invention; Figure 4 A schematic diagram of the Doppler estimation structure of the AF algorithm according to an embodiment of the present invention; Figure 5 A schematic diagram of the flow chart of the Zoom-FFT-AF Doppler joint estimation algorithm according to an embodiment of the present invention; Figure 6 A schematic diagram of Doppler factor estimation NMSE of Zoom-FFT-AF and AF algorithms according to an embodiment of the present invention; Figure 7 A signal demodulation constellation simulation diagram with and without Doppler compensation using a code element residual phase cancellation algorithm according to an embodiment of the present invention, wherein (a) is without Doppler compensation and (b) is with Doppler compensation; Figure 8Schematic diagram of bit error rate compensation estimated by different Doppler factors under the corresponding algorithm of an embodiment of the present invention, where (a) is a Doppler factor of 0.002 and (b) is a Doppler factor of 0.02. DETAILED DESCRIPTION

[0017] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0018] The present invention provides a Doppler estimation and compensation method for high-speed mobile underwater acoustic communication, and its overall flow chart is as follows: Figure 1 As shown in the figure, the signal with Doppler effect first uses the Zoom-FFT algorithm to locally refine and amplify the frequency of the CW signal, and then quickly and accurately estimates the Doppler, and determines the Doppler of the communication information within a smaller range. The LFM signal AF algorithm is used to reduce the algorithm search step size and further estimate the Doppler. At this time, the Doppler estimation of the signal is relatively accurate. Then, the Doppler frequency shift is compensated by resampling. The compensated signal still has residual Doppler influence, which seriously affects the demodulation quality of the signal. Finally, the Doppler effect is completely eliminated by the code element residual phase cancellation technology. The characteristics of the phase information between code elements are used as a whole to convert the transmitted bipolar code elements into complex domain code elements. The complex domain code element information is specifically converted to achieve the phase cancellation between the complex domain code elements during demodulation through this specific inverse transformation, so as to ensure the stable transmission of underwater acoustic communication information.

[0019] For example, CW signals are easily submerged by complex ocean noise at low signal-to-noise ratios. The CW signal frequency is roughly estimated by the Zoom-FFT algorithm. LFM signals still have good delay and frequency shift resolution at low signal-to-noise ratios. The schematic diagram of the transmission signal structure is shown in Figure 2 As shown, a rough Doppler estimation is performed on the CW signal and a fine Doppler estimation is performed on the LFM signal, thereby substantially eliminating the Doppler effect of the signal.

[0020] For example, the Zoom-FFT algorithm can locally refine and amplify the frequency of the signal to obtain a higher resolution. Compared with direct FFT, it has less data and shorter computing time. The Zoom-FFT algorithm realizes frequency estimation through the frequency shift method. The schematic diagram of the Doppler estimation process of the Zoom-FFT algorithm is shown in Figure 3 shown.

[0021] Specifically, the spectrum of a single-frequency signal is shifted: ; Then calculate the sampling ratio , also called the refinement factor, is the sampling frequency, is the center frequency. Total number of signal sampling points , The low-pass filtering before sampling can prevent the frequency after sampling from aliasing. Design a low-pass digital filter and calculate the impulse response. , get the signal ; Filter out the frequency band signal that needs to be analyzed through a low-pass digital filter. The cutoff frequency of the low-pass digital filter is . Assume the original sampling frequency is , the number of sampling points is N, then the frequency resolution is , when the resampling frequency is When the number of sampling points N remains unchanged, the frequency resolution is , in the original The frequency resolution after processing is increased by D times at the sampling rate, and the resampled output Finally, Perform N-point FFT. The spectrum line at this time is not the spectrum line of the actual signal. It needs to be moved in the opposite direction, intercepted and connected front and back to become the actual spectrum, and reorganized to obtain the refined frequency .

[0022] Specifically, the frequency shift and delay of the signal can be obtained by analyzing the ambiguity function (AF) of the signal. AF describes the joint characteristics of the signal in the time and frequency domains. When the delay and Doppler characteristic parameters of the constructed original signal are completely consistent with those of the signal passing through the underwater acoustic channel, the AF value at this time delay and Doppler is the largest, at its origin. Therefore, the maximum value of AF can be used to estimate the Doppler frequency shift of the signal passing through the channel. AF is defined as ,in, is the signal delay; is the Doppler frequency shift, and the time function of the linear frequency modulation (LFM) pulse signal can be expressed as ; Where A is the signal amplitude, T is the transmission period of each code element; if When , the AF of the LFM signal is: ; AF ​​algorithm Doppler estimation structure diagram as shown Figure 4 As shown, it is composed of several groups of correlators, and the local LFM of correlator 0 is , the local LFM of correlator 1 is , the local LFM of correlator M is , the received signal With local Doppler factor The changed signal is correlated, and its fuzzy function expression can be expressed as: ; where r is the received signal, and then the maximum AF value is determined to be the Doppler frequency shift generated by the signal passing through the channel. To estimate the Doppler frequency shift, since the Doppler estimation range is unknown, the original LFM signal needs to be searched for Doppler in a larger range. This algorithm needs to reduce the Doppler search step size to accurately estimate the Doppler factor, so a large number of correlators are required, resulting in a long estimation time, which is not suitable for the real-time nature of the communication system.

[0023] For example, after the Zoom-FFT algorithm estimates the approximate Doppler range, the AF algorithm searches and estimates in a smaller Doppler range with a small step length, which can reduce the estimation time and increase the estimation accuracy. The schematic diagram of the Zoom-FFT-AF Doppler joint estimation process is shown in the figure. Figure 5 As shown, the solid line indicates that the range of the AF algorithm is , the step size is 1, and the dotted line indicates that the range of the Zoom-FFT-AF algorithm is , the step size is 0.1. The CW signal and LFM signal take T=0.05s, under the premise of signal-to-noise ratio of -10db, moving speed of 2-30m / s, and the same correlator, the Zoom-FFT-AF (joint estimation) algorithm searches for a speed step of 0.1m / s and a search range of ±0.5m / s; the AF algorithm searches for a speed step of 1m / s and a search range of ±5m / s. The simulation results of the normalized mean square error of Doppler estimation by the simulation AF algorithm and the Zoom-FFT-AF algorithm are shown in the figure below. Figure 6 As shown, it can be obtained that if the Doppler range is determined in advance, the Doppler estimation accuracy of the Zoom-FFT-AF algorithm will be better under the premise of the same amount of calculation.

[0024] Specifically, the transmitted codeword is recorded as , which is obtained by converting the binary transmission signal into bipolar information, and then converting it into BPSK (a+ib, a is ±1, b is 0) or QPSK (a+ib, a, b is ±) format to obtain code elements , this code element is a complex number, which is the information before a specific transformation. In the form of a+ib, it is transformed into : ; is the symbol information to be modulated next, which is a complex signal, is 0, 1, …, , The code element is in the form of a+b. They are The code element corresponds to its own phase information, and then the signal is spread spectrum, upsampled by raised cosine filtering, multiplied by the carrier for up-conversion, the signal frame format is constructed, and the signal is transmitted. The received signal is , the carrier is , the demodulated signal is expressed as: ; The baseband signal after low-pass filtering and despreading is: .

[0025] Specifically, after despreading is the baseband codeword information before the decision through the channel, It is the Doppler frequency shift. At this time, the Doppler information can be regarded as a cosine signal, which modulates the baseband information. The information is periodically reversed in phase in the envelope formed by the modulation. The corresponding discrete signal is , is the complex domain codeword information, for Symbol phase information, T is each symbol transmission period, its phase information It is the original phase information of the baseband information and does not affect the stability of the system. The form is , and is the bipolar symbol information of the signal before the decision after channel demodulation. According to the symbol transformation process at the transmitting end, the primary phase cancellation transformation can be expressed as: ; To offset the I / Q path pre-decision data once, is the complex domain amplitude information of the transformed code element, for Contains Doppler phase information, baseband signal There are still some left This will cause the information phase to shift and make it difficult to demodulate. From the symbol transformation process at the transmitter, it is known that the phase offset transformation between symbols needs to be performed again. The offset result is expressed as: ; It is the data before I / Q path decision after symbol phase offset transformation. for The baseband signal completely eliminates the Doppler effect. The real part and the imaginary part are taken out for judgment to obtain the code element information. The code element phase discussed above does not affect the information demodulation, so no special processing is required.

[0026] For example, under the conditions of sampling frequency 48000, bandwidth 4000hz, spread spectrum period 31, Doppler size 0.002, and signal-to-noise ratio 0db, the signal demodulation constellation simulation diagram with and without code element residual phase cancellation algorithm for Doppler compensation is as follows: Figure 7 As shown, (a) is without Doppler compensation, and (b) is with Doppler compensation. From the simulated constellation, it can be obtained that under the influence of a small Doppler, the phase of the signal constellation diagram without Doppler estimation and compensation technology rotates, while the signal demodulation constellation diagram with code element residual phase cancellation technology is better and the signal phase information can be clearly distinguished.

[0027] For example, since the code source residual phase cancellation algorithm requires that the code element time length must be much smaller than the envelope time length of the Doppler modulated baseband signal in order to achieve Doppler compensation between code elements, it is impossible to compensate for larger Doppler signals. Under the Doppler preliminary compensation of the Zoom-FFT-AF Doppler joint estimation algorithm, the remaining Doppler of the signal is already very small, which can fully meet the Doppler tolerance of the code element residual phase cancellation algorithm. Under the conditions of sampling frequency 48000, bandwidth 4000hz, spread spectrum period 31, and Doppler factor size of 0.002 and 0.02, the compensation bit error rate of different Doppler factors estimated under the corresponding algorithm is as follows Figure 8 As shown, (a) is the Doppler factor of 0.002, the asterisk line in Figure (a) is the position without Doppler estimation compensation, and the circle line is the code element residual phase cancellation; (b) is the Doppler factor of 0.02, the circle line in Figure (b) is the code element residual phase cancellation, and the asterisk line is the Zoom-FFT-AF code element residual phase cancellation; From the simulation results, it can be seen that when the Doppler factor is small, the code element residual phase cancellation algorithm can compensate for the Doppler frequency deviation well, and when the Doppler factor is large, the code element residual phase cancellation algorithm can no longer compensate for the Doppler frequency deviation, which exceeds the Doppler tolerance of this algorithm. The Zoom-FFT-AF code element residual phase cancellation algorithm can well compensate for the frequency deviation caused by large Doppler.

[0028] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. A Doppler estimation and compensation method for high-speed mobile underwater acoustic communication, characterized in that: The following steps are involved: S1, receiving an underwater acoustic communication signal of a specific frame format with a Doppler effect, locally refining and amplifying the frequency of the CW signal through a Zoom-FFT algorithm, for fast and accurate Doppler estimation, and determining the Doppler of the communication signal within a preset range; S2, estimate the frequency deviation of the LFM signal through the AF algorithm, which is used to reduce the Doppler search step size, further refine the Doppler estimation, and compensate for the Doppler frequency shift through resampling; S3. The Doppler effect remaining after compensation is completely eliminated by cancelling the residual phase of the code elements, and the transmitted bipolar code elements are converted into complex domain code elements. The complex domain code element information is transformed. When used for demodulation, the complex domain code elements cancel the phase between the code elements by inverse transformation.

2. A Doppler estimation and compensation method for high-speed mobile underwater acoustic communication according to claim 1, characterized in that: The step S1 specifically includes: For CW signal Spectrum migration: , move to the center frequency Get the signal ,in is the unit rotation factor; Calculate the sampling ratio ,in is the sampling frequency; Calculation of CW Signal The total number of sampling points ,in To analyze the points; Through the digital low-pass filter, retain Signal in frequency band The frequency band that needs to be refined within the range is used to obtain the signal , ,in is the impulse response, and the cutoff frequency of the digital low-pass filter is ; If the sampling frequency is , for the signal Take a data point every D-1 to get a coarse-grained signal ; For coarse-grained signal Perform N-point complex FFT, intercept the refined spectrum fft result, move it in the opposite direction, connect it front and back, convert it into actual frequency, and get the refined FFT transformation result , the obtained frequency is subtracted from the original frequency to obtain the approximate Doppler frequency deviation.

3. A Doppler estimation and compensation method for high-speed mobile underwater acoustic communication according to claim 2, characterized in that: The step S2 specifically includes: local Based on the Doppler range determined by the Zoom-FFT algorithm, a small step size Doppler factor is used Change, the local LFM signal after Doppler change and the received signal Correlation is performed, the maximum value of the ambiguity function AF of the signal is selected, and based on the Doppler estimated by the Zoom-FFT-AF combined with the Doppler algorithm, the received signal is resampled to compensate for the Doppler frequency deviation; where AF is defined as ; is the signal delay; is the Doppler shift; the time function of the linear frequency modulated pulse signal Expressed as ; Where A is the signal amplitude, T is the transmission period of each code element; like When , the AF of the LFM signal is: ； Received signal With local Doppler factor The changed signal is correlated, and its fuzzy function expression can be expressed as: , where r is the received signal.

4. A Doppler estimation and compensation method for high-speed mobile underwater acoustic communication according to claim 3, characterized in that: The code element residual phase cancellation in step S3 eliminates the residual Doppler effect after compensation, specifically comprising: at the transmitting end, performing complex domain code element transformation on the PSK code element: ； in is the bipolar complex domain code element, is the information before transformation, is the intermediate transformation codeword, is the transformed codeword, for The phase information corresponding to the code element, for The phase information corresponding to the code element, for The phase information corresponding to the code element is then Perform spectrum spreading, raised cosine filtering, up-sampling and up-conversion modulation to obtain a transmission signal; The received underwater acoustic Doppler signal is demodulated, raised cosine filtered and despread accordingly based on the receiving end, and the complex domain codewords before the decision are inversely transformed accordingly based on the transmitting end: ； in To offset the I / Q path pre-decision data once, is the complex domain amplitude information of the transformed code element, is the corresponding phase information, It is the data before I / Q path decision after symbol phase offset transformation. for Its own phase information, and then Take out the real part and the imaginary part to make a decision and get the code element information.

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