High-speed modulation and demodulation method for dynamic underwater acoustic network

Abstract

The invention discloses a high-speed modulation and demodulation method for a dynamic underwater acoustic network, and the method also employs an orthogonal sequence multiplexing modulation and demodulation technology based on a Zadoff-Chu (ZC) sequence, and combines the setting of a cyclic displacement interval to construct a plurality of sub-channels, thereby achieving the multi-path separation, and reducing the average transmitting power of a system at the same time. In the aspect of multi-user access, interference among multiple users is regarded as additive white noise by using quasi-orthogonal characteristics among different ZC root sequences, so that uncoordinated random concurrent access is supported; differential modulation between sub-channels in a symbol is adopted, and the requirement for phase tracking is lowered; and a receiving end converts multipath amplitude information into soft decision information through cyclic correlation spectrum calculation and multipath diversity technologies, so that the calculation complexity is reduced, and the throughput of the time-varying underwater acoustic system is improved while the multi-user access efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of underwater acoustic communication network, and relates to modulation and demodulation technology (waveform design) for multi-user access under dynamic underwater acoustic channel, in particular to a high-rate modulation and demodulation method for dynamic underwater acoustic network. BACKGROUND

[0002] With the popularization of underwater activities, the demand for underwater communication and networking is growing. Due to the rapid attenuation of radio frequency signals and electromagnetic wave signals under water, acoustic signals are widely used for underwater communication. In addition to the influence of multipath transmission, underwater communication and networking also face the influence of dynamic channel changes. The movement of underwater acoustic devices and the time-varying nature of water bodies and the Doppler effect cause the parameters of the underwater acoustic channel to change rapidly over time. This dynamic channel characteristic brings two major technical difficulties: first, the implementation of traditional channel estimation and equalization methods in a rapidly time-varying environment is more difficult, as it requires frequent parameter updates, high computational complexity, and difficulty in ensuring real-time performance; second, multi-user coordination in a dynamic environment is difficult, and traditional multiple access schemes have high coordination costs and limited system throughput. Therefore, there is an urgent need for efficient communication methods that adapt to dynamic underwater acoustic channels.

[0003] Many existing underwater acoustic communication and networking technologies have been proposed, such as FSK, CSS, DSSS, etc. These belong to the previous generation of communication technologies, with relatively low rates, allowing only a single bit or a small number of bits to be transmitted per symbol. OFDM (Orthogonal Frequency Division Multiplexing) is a multicarrier modulation technology that can achieve high transmission rates, but is particularly sensitive to dynamic channels, especially the Doppler effect, and has performance bottlenecks under dynamic channels. OCDM (Orthogonal Chirp Division Multiplexing) and OTFS, while to some extent, can overcome the influence of dynamic channels, but only support point-to-point communication, lacking support for networking.

[0004] There are some underwater acoustic networking technologies based on media access control (Media Access Control, MAC) protocols, such as TDMA, FDMA, which can be combined with the above-mentioned OCDM, OTFS modulation technology for underwater networking. However, the TDMA scheme needs to be transmitted in coordination with all users, and the underwater acoustic wave propagation speed (≈1500m / s) is slow, not only the guard interval needs to be increased, but also in the underwater unreliable communication scene (in dynamic and mobile environment) will bring a lot of protocol overhead, and the time slot synchronization becomes extremely difficult to realize; The FDMA scheme needs to pre-allocate bandwidth guard interval, and alleviate the Doppler spread by reserving a wide guard band, which wastes a certain bandwidth, and the pre-allocation mechanism wastes resources in the dynamic access scene, which makes a sacrifice in efficiency and flexibility; CDMA (Code Division Multiple Access, Code Division Multiple Access) technology supports multi-user random access networking, eliminating the overhead of coordination protocols, but only allows a single bit to be transmitted in a symbol, the rate is low, and in the random access scene, complex channel estimation and equalization technology is needed.

[0005] In related patents, Chinese patent CN101567727A (a differential cyclic shift spread spectrum underwater acoustic communication method) is based on the modulation technology of spread spectrum sequence, and Chinese patent CN119363285B (a method for high-speed non-coordinated concurrent access of underwater acoustic Internet of Things) is based on the modulation technology of Zadoff-Chu sequence. Although the spectral efficiency is improved by index modulation, the single-carrier transmission strategy is still adopted, and the overall data rate is still low, which is difficult to meet the demand of medium-high rate underwater communication. SUMMARY

[0006] The main purpose of the present application is to provide a high-speed modulation and demodulation method for dynamic underwater acoustic networks, to solve the problems in the prior art, to realize multi-path separation while reducing the average transmit power of the system, to support non-coordinated random concurrent access, to reduce the demand and computational complexity of phase tracking, and to improve the throughput of time-varying underwater acoustic systems while solving the multi-user access efficiency.

[0007] In order to achieve the above purpose, the solution of the present application is: A high-speed modulation and demodulation method for dynamic underwater acoustic networks, comprising the following steps: S11. The transmitter allocates a unique root sequence to each user, and constructs a multiplexing sub-channel based on the ZC sequence through cyclic shift, each sub-channel being used to carry information; S12. According to the equal cyclic shift interval , the transmitter performs zero-padding on the data to be modulated to form a data vector, and cuts the data vector into multiple multiplexed symbols according to the data length corresponding to each symbol, and then performs differential modulation on the data vector corresponding to each multiplexed symbol; S13. For each multiplexed symbol, the transmitter performs matrix multiplication on the data vector and the cyclic matrix by using fast FFT transformation, modulates the data onto each sub-channel of the multiplexed waveform, and superimposes them; S14. For each multiplexed symbol, the transmitter adds a CP with a length of to the front of the signal; S15. The transmitter combines the signals of all multiplexed symbols, adds a preamble, performs pulse shaping, up-converts to the acoustic frequency band, and transmits the signal; S21. The receiver uses a sliding correlator to implement two-stage frame synchronization, which includes signal detection and user matching; S22. Using fast Fourier transform to calculate the cyclic correlation spectrum and extract the multipath weight: after identifying the starting position of each multiplexed symbol by performing frame synchronization, the receiver uses fast Fourier transform to calculate the cyclic correlation spectrum, uses a soft decision decoding algorithm based on multipath diversity, extracts the amplitude and phase information of each path by traversing multiple peak positions in the cyclic correlation spectrum, and combines the differential demodulation between sub-channels to output soft decision information and hard decision results; S23. Calculate the symbol likelihood probability according to the multipath weight: in order to use the extracted multipath weight, a soft decision decoding method based on the cyclic correlation spectrum of multiple equally spaced cyclic shift sequences is proposed, and the specific steps are as follows: according to the multipath peak weight, traverse multiple potential peaks, retain the amplitude and phase results of these peaks, and give the unnormalized likelihood probability of the data modulated on the sub-channel.

[0008] S11 is specifically: For a user assigned with a root index , the root sequence is defined as: ; wherein, ZC sequence index is represented by ; the base of the natural logarithm function is represented by ; the imaginary unit is represented by ; the length of the ZC sequence is represented by Based on the zero autocorrelation characteristic of the ZC sequence, the transmitter constructs a cyclic matrix by a series of root sequences with different cyclic shifts to provide orthogonal multiplexing sub-channels, denoted as: ; wherein, the cyclic matrix is represented by ; the complex domain is represented by Each column of the cyclic matrix corresponds to a ZC root sequence with an incremental cyclic shift.

[0009] S12 is specifically: The data to be modulated is denoted as , wherein represents the total length of the original data; the data to be modulated is zero-padded: ; wherein, represents the index of the modulated data after zero-padding; The original data is allocated to each multiplexed symbol, and the number of enabled sub-channels is predetermined to be , wherein the first sub-channel is the differential reference of the next sub-channel, and the number of multiplexed symbols required is . .

[0010] S13 is specifically: The transmitter calculates the actual transmission sequence, and performs matrix multiplication with the circulant matrix ; first, eigenvalue decomposition is performed on the circulant matrix, and then matrix multiplication is quickly performed through Fourier transform, to modulate the sequence to be transmitted onto each sub-channel, and the formula is: ; wherein, represents the modulated sequence to be transmitted; and respectively represent an N-point discrete Fourier transform (DFT) matrix and an inverse discrete Fourier transform (IDFT) matrix; and respectively represent a fast Fourier transform (FFT) operation and an inverse fast Fourier transform (IFFT) operation; represents the eigenvalue vector corresponding to the circulant matrix generated by the root sequence of the transmitter; represents taking a diagonal matrix.

[0011] In S14, the transmission sequence with CP is defined as: ; wherein the superscript represents taking the transpose.

[0012] In S15, the preamble is composed of two chirp signals for wake-up and two repeated ZC root sequences.

[0013] S21 is specifically: The receiver first performs frame detection, detects the chirp signal of the passband using a sliding correlator, performs down-conversion and matched filtering on the subsequent signal after detecting the chirp signal, performs cross-correlation operation on the passband baseband signal using a plurality of user corresponding ZC root sequence sliding correlators until the corresponding user is traversed, retains the potential correlation peak position and the corresponding root index, and determines the starting position of the data symbol.

[0014] S22 is specifically: For a single multiplexed symbol received by the receiver , when the starting position of the multiplexed symbol is found, the ZC root sequence is used to calculate the cyclic correlation spectrum; the calculation process is the inverse process of the fast matrix multiplication using Fourier transform in S12; finally, the receiver obtains the cyclic correlation spectrum The absolute value of the cyclic correlation spectrum is: ; wherein, represents the complex conjugate of the eigenvector of the cyclic matrix constructed by the ZC root sequence; To calculate the weight of each path, a multipath weight vector is defined, and the cumulative correlation energy of the sliding window along the cyclic shift interval starting from different offsets is calculated, and the formula is as follows: ; wherein, represents the index when traversing along the cyclic shift interval .

[0015] S23 is specifically: For the receiver that has calculated the multipath peak weight, the data modulated on the th subchannel is The unnormalized likelihood probability is calculated according to the following formula: ; wherein, represents the multipath weight traversal index; is an indicator function, that is, when the equation in the square brackets is true, its value is 1, otherwise it is 0; represents a base number; , respectively represent the estimation results of the phases on the th subchannel and the th subchannel; represents the traversal index for the multi-ary symbol.

[0016] After adopting the above technical solution, the application has the following technical effects: The proposed ZC sequence-based orthogonal sequence multiplexing modulation and demodulation method can solve the following problems with low overhead: (I) signal interference between different users during random concurrent access in underwater acoustic networks; (II) high communication rate in dynamic multipath underwater acoustic channels; and (III) high communication reliability in dynamic multipath underwater acoustic channels. Specifically, (I) the proposed method utilizes the low cross-correlation characteristic of the ZC sequence to whiten multi-user interference using the corresponding waveform; (II) it utilizes the zero cross-correlation characteristic of the ZC sequence to construct multiple orthogonal sub-channels for data transmission; and (III) it is implemented using zero-padding and intra-symbol differential modulation characteristics. The differential modulation ensures low implementation complexity. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the orthogonal sequence multiplexing modulation and demodulation method based on ZC sequences of the present invention.

[0018] Figure 2 This is a schematic diagram of the transmitter modulation data of the present invention.

[0019] Figure 3 The transmitter of this invention adopts An example of transmitting a signal and the receiver calculating the cyclic correlation spectrum.

[0020] Figure 4 The transmitter of this invention adopts An example of transmitting a signal and the receiver extracting the multipath weight.

[0021] Figure 5 This is a performance comparison chart of the present invention with other modulation methods in an underwater acoustic channel. Detailed Implementation

[0022] To further explain the technical solution of the present invention, the present invention will be described in detail below through specific embodiments.

[0023] refer to Figure 1 , Figure 2 As shown, this invention discloses a high-speed modulation and demodulation method for dynamic underwater acoustic networks. This method also employs orthogonal sequence multiplexing modulation and demodulation technology based on Zadoff-Chu (ZC) sequences, but incorporates a cyclic shift interval setting. The multiple sub-channels are constructed to realize multipath separation while reducing the average transmission power of the system; in terms of multi-user access, the quasi-orthogonal characteristics between different ZC root sequences are used to regard the multi-user interference as additive white noise, thereby supporting random concurrent access without coordination; the differential modulation between sub-channels within a symbol is adopted to reduce the demand for phase tracking; the multipath amplitude information is converted into soft decision information by the receiving end through cyclic correlation spectrum calculation and multipath diversity technology, thereby reducing the calculation complexity and improving the throughput of the time-varying underwater acoustic system while solving the multi-user access efficiency. The above method specifically includes the following steps: S11. The transmitter allocates a unique root sequence to each user, and constructs multiplexing sub-channels based on ZC sequences through cyclic shift, and each sub-channel is used to carry information.

[0024] Specifically, for a user allocated with a root index , the root sequence is defined as: ; wherein, represents the index of the ZC sequence; represents the base of the natural logarithm function; represents the imaginary unit; represents the length of the ZC sequence; Based on the zero autocorrelation characteristics of the ZC sequence, the transmitter constructs a cyclic matrix through a series of root sequences with different cyclic shifts to provide orthogonal multiplexing sub-channels, denoted as: ; wherein, represents the cyclic matrix; represents the complex domain; Each column of the cyclic matrix corresponds to the ZC root sequence with incremental cyclic shift.

[0025] S12. According to equal cyclic shift intervals , the transmitter performs zero padding on the data to be modulated to form a data vector, and divides it into multiple multiplexing symbols according to the data length corresponding to each symbol, and then performs differential modulation on the data vector corresponding to each multiplexing symbol.

[0026] Specifically, the data to be modulated is denoted as , wherein represents the total length of the original data; the data to be modulated is zero-padded as: ; wherein, represents the index of the modulated data after zero padding; The original data is allocated to each multiplexing symbol according to , and the number of enabled sub-channels is predetermined as , wherein the first sub-channel is used as the differential reference of the next sub-channel, and the number of multiplexing symbols required is Information modulated in a single multiplexed symbol For example, the transmitter adopts differential modulation within a symbol, i.e. the information modulated in each sub-channel is the difference between the previous sub-channel with modulated information.

[0027] S13. For each multiplexed symbol, the transmitter adopts fast FFT transformation to perform matrix multiplication between the data vector and the circulant matrix, to modulate the data onto each sub-channel of the multiplexed waveform and superimpose.

[0028] Specifically, the transmitter finally calculates the actual transmission sequence, i.e. the sequence with zero padding and matrix multiplication with the circulant matrix ; in order to reduce the computational complexity, the circulant matrix is first subjected to eigenvalue decomposition, and then fast matrix multiplication is performed through Fourier transformation, to modulate the to-be-transmitted sequence onto each sub-channel, and the formula is as follows: ; wherein represents the modulated to-be-transmitted sequence; and respectively represent an N-point discrete Fourier transform (DFT) matrix and an inverse discrete Fourier transform (IDFT) matrix; and respectively represent fast Fourier transform (FFT) operation and inverse fast Fourier transform (IFFT) operation; represents the eigenvalue vector corresponding to the root sequence generated by the transmitter and the circulant matrix; represents taking a diagonal matrix.

[0029] S14. For each multiplexed symbol, in order to mitigate inter-symbol interference in the multipath channel, the transmitter adds a CP (Cyclic Prefix) with a length of to the front of the signal.

[0030] Specifically, the transmission sequence with the CP is defined as: ; wherein the superscript represents taking a transpose.

[0031] S15. The transmitter combines the signals of all multiplexed symbols, adds a preamble, performs pulse shaping, and up-converts to the acoustic frequency band to transmit the signal.

[0032] Specifically, the preamble is composed of two chirp signals for wake-up and two repeated ZC root sequences (root index ).

[0033] S21. The receiver adopts a sliding correlator to realize two-stage frame synchronization, which includes signal detection and user matching.

[0034] Specifically, the receiver first performs frame detection, uses a sliding correlator to detect the chirp signal in the passband, and after detecting the chirp signal, it performs down-conversion and matched filtering on the subsequent signal. It uses ZC root sequence sliding correlators corresponding to multiple users to perform cross-correlation operation on the passband baseband signal until the corresponding user is reached, retains the potential correlation peak position and its corresponding root index, and determines the starting position of the data symbol.

[0035] S22. Using Fast Fourier Transform to Calculate Cyclic Correlation Spectrum and Extract Multipath Weights: After the receiver identifies the start position of each multiplexed symbol during frame synchronization, it uses Fast Fourier Transform to calculate the cyclic correlation spectrum. A soft-decision decoding algorithm based on multipath diversity is adopted. By traversing multiple peak positions in the cyclic correlation spectrum, the amplitude and phase information of each path are extracted. Combined with inter-channel differential demodulation, soft-decision information and hard-decision results are output.

[0036] Specifically, for a single multiplexed symbol received by the receiver After finding the starting position of the multiplexed symbol, the cyclic correlation spectrum is calculated using the ZC root sequence. This calculation is the inverse of the matrix multiplication operation performed in S12 using Fourier transform. Finally, the receiver obtains the cyclic correlation spectrum. The absolute value is: ;in, The complex conjugate of the eigenvectors of the cyclic matrix constructed from the ZC root sequence; To calculate the weights of each path, a multipath weight vector is defined. Calculate the cyclic displacement interval starting from different offsets. The cumulative correlation energy of the sliding window is given by the following formula: ;in, Indicates the displacement interval along the cycle. The index used during traversal.

[0037] S23. Solving symbol likelihood probability based on multipath weights: In order to utilize the extracted multipath weights, a soft-decision decoding method based on the cyclic correlation spectrum of multiple equally spaced cyclic shift sequences is proposed. The specific steps are as follows: based on the multipath peak weights, traverse multiple potential peaks, retain the amplitude and phase solution of these peaks, and give the unnormalized likelihood probability of the modulated data on the sub-channel.

[0038] Specifically, for those that have already been calculated Receivers with multipath peak weighting, the first The data modulated on each subchannel is The unnormalized likelihood probability is calculated as follows: ; wherein, represents the index of the multipath weight; is an indicator function, i.e. its value is 1 when the equation in the brackets is true, otherwise 0; represents the base number; , respectively represent the estimation results of the phase on the first , the first sub-channel, corresponding to the intra-symbol differential modulation mentioned in S12; represents the index of the multi-base symbol. The calculated likelihood result can be directly used for symbol hard decision, and can also be used as the input of channel soft decoding when similar low-density parity-check code is used.

[0039] The key points of the present application include but are not limited to: (1) Based on the low cross-correlation characteristics of the ZC sequence, different ZC root sequences are allocated to different users to support random asynchronous access without the need for coordination overhead to support multi-user networking; (2) Based on the zero autocorrelation characteristics of the ZC sequence, a cyclic ZC sequence is used to construct orthogonal sub-channels, and modulation is performed on multiple sub-channels to improve the communication rate; (3) The modulation mode of sub-channel equal interval zero padding is used to reduce the influence of the multipath channel on demodulation and improve the communication reliability; (4) The intra-symbol differential modulation between sub-channels is used to reduce the influence of the time-varying channel on demodulation and improve the communication reliability.

[0040] Therefore, the orthogonal sequence multiplexing modulation and demodulation method based on the ZC sequence proposed by the present application can solve the following problems with low overhead: (I) the signal interference problem of different users in the random concurrent access of the underwater acoustic network; (II) the high communication rate problem in the dynamic multipath underwater acoustic channel; (III) the high communication reliability problem in the dynamic multipath underwater acoustic channel. (I) The method proposed utilizes the low cross-correlation characteristics of the ZC sequence, and the corresponding waveform can whiten the multi-user interference; (II) The method proposed utilizes the zero cross-correlation characteristics of the ZC sequence to construct multiple orthogonal sub-channels for data transmission; (III) The method proposed utilizes the zero padding and intra-symbol differential modulation characteristics. The differential modulation ensures low implementation complexity.

[0041] Reference Figure 3 , Figure 4 indicates two specific embodiments of the present application.

[0042] wherein, Figure 3 is an embodiment of the present application in which the transmitter uses to send a signal, and the receiver calculates a cyclic correlation spectrum. Due to the zero padding design in S12, the multipath in the calculated cyclic correlation spectrum There is almost no overlap; at the same time, Figure 4 The transmitter of this invention adopts An example of transmitting a signal and the receiver extracting multipath weights shows that the extracted multipath and channel responses are very similar.

[0043] refer to Figure 5 As shown, actual simulation and experimental results demonstrate that, compared to traditional CSS modulation, OFDM modulation based on interpolation or differential modulation, and direct-sequence spread spectrum-CDMA modulation, this invention exhibits a significant performance gain at the same energy-to-noise power spectral density ratio (Eb / N0). For example, when Eb / N0 = 6 dB, the present invention... The bit error rate is 10 -3 Order of magnitude, ( The bit error rate is 10 -2 The bit error rates of all waveforms are orders of magnitude better than those of the CSS waveform, while the bit error rates of all other waveforms are within 10. -1 Or higher. Furthermore, compared to other waveforms, the error level of this invention is significantly lower in bit error rate.

[0044] The above embodiments and figures are not intended to limit the product form and style of the present invention. Any appropriate changes or modifications made by those skilled in the art should be considered as not departing from the patent scope of the present invention.

Claims

1. A high-speed modulation and demodulation method for dynamic underwater acoustic networks, characterized in that, Includes the following steps: S11. The transmitter assigns a unique root sequence to each user and constructs multiplexed subchannels based on ZC sequences through cyclic shifting, with each subchannel used to carry information; S12. According to equal cyclic displacement intervals The transmitter zero-padding the data to be modulated to form a data vector, and divides it into multiple multiplexed symbols according to the data length corresponding to each symbol, and then differentially modulates the data vector corresponding to each multiplexed symbol. S13. For each multiplexed symbol, the transmitter uses a fast FFT transform to perform matrix multiplication between the data vector and the cyclic matrix, modulates the data onto each sub-channel of the multiplexed waveform, and superimposes them; S14. For each multiplexed symbol, the transmitter adds a length of [length missing] before the signal. CP; S15. The transmitter merges the signals of all multiplexed symbols, adds a preamble, performs pulse shaping, and upconverts the signal to the acoustic frequency band to transmit the signal; S21. The receiver uses a sliding correlator to achieve two-stage frame synchronization, which includes signal detection and user matching; S22. Using Fast Fourier Transform to calculate the cyclic correlation spectrum and extract multipath weights: After the receiver identifies the start position of each multiplexed symbol during frame synchronization, it uses Fast Fourier Transform to calculate the cyclic correlation spectrum. A soft-decision decoding algorithm based on multipath diversity is adopted. By traversing multiple peak positions in the cyclic correlation spectrum, the amplitude and phase information of each path are extracted. Combined with inter-channel differential demodulation, soft-decision information and hard-decision results are output. S23. Solving symbol likelihood probability based on multipath weights: In order to utilize the extracted multipath weights, a soft-decision decoding method based on the cyclic correlation spectrum of multiple equally spaced cyclic shift sequences is proposed. The specific steps are as follows: based on the multipath peak weights, traverse multiple potential peaks, retain the amplitude and phase solution of these peaks, and give the unnormalized likelihood probability of the modulated data on the sub-channel.

2. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 1, characterized in that, S11 specifically refers to: For those who have allocated a root index For users, their root sequence is defined as: ;in, Indicates the ZC sequence index; Represents the base of the natural logarithm function; Represents the imaginary unit; Indicates the length of the ZC sequence; Based on the zero autocorrelation property of the ZC sequence, the transmitter constructs a cyclic matrix using a series of root sequences with different cyclic shifts to provide orthogonal multiplexed sub-channels, denoted as: ;in, Represents a circular matrix; Represents the field of complex numbers; Each column of the cyclic matrix corresponds to a ZC root sequence with incremental cyclic displacement.

3. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 2, characterized in that, S12 specifically refers to: The data to be modulated is denoted as ,in Indicates the total length of the original data; Zero-padding the modulated data: ;in, Indicates the index of the modulated data after zero padding; The original data is according to They are assigned to various multiplexing symbols, and the number of enabled sub-channels is predetermined. The first sub-channel serves as the differential reference for the next sub-channel, requiring a number of multiplexing symbols. .

4. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 3, characterized in that, S13 specifically refers to: The transmitter calculates the actual transmitted sequence and performs zero-padding. With circular matrix Matrix multiplication; first, eigenvalue decomposition is performed on the circular matrix, then matrix multiplication is performed quickly using Fourier transform to modulate the sequence to be transmitted onto each sub-channel. The formula is: ;in, This indicates that the sequence has been modulated and is ready to be transmitted; and These represent the N-point Discrete Fourier Transform (DFT) matrix and the Inverse Discrete Fourier Transform (IDFT) matrix, respectively. and These represent the Fast Fourier Transform (FFT) operation and the Inverse Fast Fourier Transform (FFT) operation, respectively. This represents the eigenvalue vector corresponding to the cyclic matrix generated by the root sequence of the transmitter; This indicates taking a diagonal matrix.

5. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 4, characterized in that: In S14, the transmission sequence with CP is defined as follows: ; where superscript This indicates taking the transpose.

6. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 5, characterized in that: In S15, the preamble consists of two chirp signals for wake-up and two repeated ZC root sequences.

7. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 6, characterized in that, S21 specifically refers to: The receiver first performs frame detection, using a sliding correlator to detect the chirp signal in the passband. After detecting the chirp signal, it performs down-conversion and matched filtering on the subsequent signal. It uses ZC root sequence sliding correlators corresponding to multiple users to perform cross-correlation operation on the passband baseband signal until it traverses to the corresponding user, retains the potential correlation peak positions and their corresponding root indices, and determines the starting position of the data symbol.

8. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 7, characterized in that, S22 specifically refers to: For a single multiplexed symbol received by the receiver Once the starting position of the multiplexed symbol is found, the cyclic correlation spectrum is calculated using the ZC root sequence. The calculation process is the inverse of the matrix multiplication operation performed by Fourier transform in S12. Finally, the receiver obtains the cyclic correlation spectrum. The absolute value is: ;in, The complex conjugate of the eigenvectors of the cyclic matrix constructed from the ZC root sequence; To calculate the weights of each path, a multipath weight vector is defined. Calculate the cyclic displacement interval starting from different offsets. The cumulative correlation energy of the sliding window is given by the following formula: ;in, Indicates the displacement interval along the cycle. The index used during traversal.

9. The high-speed modulation and demodulation method for dynamic underwater acoustic networks as described in claim 8, characterized in that, S23 specifically refers to: For those that have already been calculated Receivers with multipath peak weighting, the first The data modulated on each subchannel is The unnormalized likelihood probability is calculated as follows: ;in, This indicates a multipath weighted traversal index; This is an indicator function, meaning its value is 1 if the equation within the brackets is true, and 0 otherwise. Represents the number base; , They represent the first The, the The estimation results of the phase on each sub-channel; This represents the traversal index for multi-base symbols.

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