Random orthogonal precoding method and system for underwater acoustic communication

Abstract

This application discloses a random orthogonal precoding underwater acoustic communication method and system. The transmitting end generates a real Gaussian matrix based on a shared seed, obtains a fixed orthogonal matrix through symbol-normalized QR decomposition, orthogonally spreads the modulation symbols along the effective subcarrier dimension, inserts pilots, and completes OFDM modulation, cyclic prefix, up-conversion, and alternating up-down linear frequency modulation synchronization header framing. The receiving end completes synchronization, wideband Doppler scale estimation and resampling, timing refinement, pilot channel estimation, carrier-by-carrier LMMSE equalization, and orthogonal transpose despreading. Without increasing occupied bandwidth, pilots, or redundancy, the dependence of a single symbol on deeply fading subcarriers is distributed across the entire bandwidth, improving frequency selectivity and reception reliability in time-varying underwater acoustic channels, while remaining compatible with existing OFDM transceivers.

Description

Technical Field

[0001] This invention relates to the field of communications, and more particularly to a random orthogonal precoding underwater acoustic communication method and system. Background Technology

[0002] Underwater acoustic channels are characterized by narrow usable bandwidth, long propagation time, significant sparse multipath propagation, and wideband Doppler scale variations caused by motion. Traditional OFDM loads information symbols onto each subcarrier, which reduces equalization complexity, but symbols falling into deep fading still exhibit low reliability; adding pilots, retransmissions, or channel coding typically incurs additional overhead. Two-dimensional transforms such as OTFS can achieve diversity in the time-delay-Doppler domain, but grid construction, two-dimensional estimation, and detection are highly complex. Summary of the Invention

[0003] The following is an overview of the topics described in detail in this article.

[0004] The purpose of this application is to at least partially solve one of the technical problems existing in the related technologies. The embodiments of this application provide a random orthogonal precoding underwater acoustic communication method and system, and provide a low-complexity reliable transmission scheme that does not change the existing OFDM frame resources and is suitable for underwater acoustic broadband Doppler compensation.

[0005] An embodiment of the first aspect of this application provides a random orthogonal precoding underwater acoustic communication method, comprising:

[0006] The transmitter maps the data to be transmitted into a data matrix containing effective subcarriers and data symbols;

[0007] A fixed real orthogonal matrix is ​​generated based on the shared seed and the matrix dimension. The data matrix is ​​then multiplied by the fixed real orthogonal matrix along the effective subcarrier dimension to obtain the frequency domain extended matrix.

[0008] The frequency domain extension matrix and pilot are mapped to OFDM frequency domain symbols, IFFT, cyclic prefix insertion and upconversion are performed, and the underwater acoustic transmission frame is formed by framing with the linear frequency modulation synchronization segment.

[0009] The transmitting end transmits the underwater acoustic transmission frame to the receiving end, and the receiving end receives the underwater acoustic transmission frame.

[0010] The receiver uses the linear frequency modulation synchronization segment to determine the frame start point and broadband Doppler scale, performs resampling compensation on the received sampled data of the underwater acoustic transmission frame, and refines the timing and residual frequency offset using the cyclic prefix and pilot.

[0011] Pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization are performed on the effective subcarriers to obtain the equalization matrix;

[0012] The equalization matrix is ​​multiplied along the effective subcarrier dimension by the transpose of the fixed real orthogonal matrix to recover the transmitted data.

[0013] According to certain embodiments of the first aspect of this application, generating a fixed real orthogonal matrix based on a shared seed and matrix dimension includes:

[0014] Generate an independent and identically distributed real Gaussian matrix G of size K×K using a shared seed;

[0015] Perform QR decomposition on an independent and identically distributed real Gaussian matrix G into matrices U and R;

[0016] Construct a diagonal matrix D, where the k-th diagonal element of D is the sign of the k-th diagonal element of matrix R;

[0017] The transpose of the product of matrix U and diagonal matrix D yields a fixed real orthogonal matrix Q, such that the product of the transpose of Q and Q equals the K-dimensional identity matrix.

[0018] Where K is the number of effective subcarriers, and the transmitter and receiver use the same seed, K value, random number generator and subcarrier sorting.

[0019] According to certain embodiments of the first aspect of this application, the fixed real orthogonal matrix operates only on the effective subcarrier dimension and remains unchanged between data symbol time slots in one or more frames; the symbol energy before and after precoding remains unchanged, and it does not occupy additional time slots or frequency bands.

[0020] According to certain embodiments of the first aspect of this application, the linear frequency modulation synchronization segment includes a frequency-up linear frequency modulation signal and a frequency-down linear frequency modulation signal;

[0021] The receiver jointly estimates the frame start point and scale factor by using the peak values ​​of the up-frequency linear frequency modulated signal and the down-frequency linear frequency modulated signal, as well as the candidate Doppler scale search, and then resamples and compensates the entire frame of received sampled data or data segments in the received sampled data according to the scale factor.

[0022] According to certain embodiments of the first aspect of this application, pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization are performed on effective subcarriers, including:

[0023] The receiver obtains the effective subcarrier channel response at each pilot symbol, performs phase expansion, and then interpolates in the time and / or frequency dimensions.

[0024] For the k-th subcarrier, the sum of the conjugate of the estimated channel coefficient divided by its squared modulus and the regularization parameter is used as the LMMSE equalization weight, and the residual common phase error is compensated by the cyclic prefix correlation or pilot phase slope.

[0025] According to certain embodiments of the first aspect of this application, the equalized output complex data symbol of the k-th subcarrier and the m-th data symbol is:

[0026]

[0027] In the formula, The equalized output complex data symbol for the k-th subcarrier and the m-th data symbol. The channel coefficients at the data time are obtained by phase expansion interpolation of the effective subcarrier channel response at the pilot position. The regularization parameter is determined based on noise power or channel power. This refers to the received frequency domain complex data before equalization on the k-th effective subcarrier at the m-th data symbol time. Indicates complex conjugation. The channel coefficient represents the power gain, k is the effective subcarrier index, and m is the data symbol index.

[0028] According to certain embodiments of the first aspect of this application, the same information block can be repeatedly transmitted in different frames; during the process of recovering transmitted data, the receiving end performs synchronization, scale compensation, channel estimation, equalization and orthogonal despreading on each frame respectively, and then performs soft combining according to the weight determined by channel quality, noise variance or peak value, and then performs constellation decision and bit recovery.

[0029] According to certain embodiments of the first aspect of this application, the variance of the error of the i-th symbol after despreading is:

[0030]

[0031] In the formula, Let be the variance of the error of the i-th symbol after despreading. For the first Error variance after subcarrier equalization The number of effective subcarriers, is the element in the k-th row and i-th column of the fixed real orthogonal matrix Q; i is the despread symbol index, and k is the effective subcarrier index.

[0032] According to a second aspect of this application, a random orthogonal precoding underwater acoustic communication system is provided, which applies the random orthogonal precoding underwater acoustic communication method described in the first aspect of this application. The system includes a transmitting device and a receiving device. The transmitting device includes a bit mapping module, a fixed orthogonal matrix generation module, a subcarrier-dimensional orthogonal expansion module, a pilot insertion module, a multi-carrier modulation module, a linear frequency modulation framing module, and an underwater acoustic transmission module. The receiving device includes a linear frequency modulation synchronization module, a wideband Doppler estimation and resampling module, a timing and frequency offset correction module, a pilot channel estimation module, an LMMSE equalization module, an orthogonal transpose despreading module, and a data decision module.

[0033] According to a third aspect of this application, a non-transitory computer-readable storage medium stores a program thereon that, when executed by a processor of an underwater acoustic communication device, causes the underwater acoustic communication device to implement the random orthogonal precoding underwater acoustic communication method as described in the first aspect of this application.

[0034] The above-mentioned solution has at least the following beneficial effects:

[0035] Orthogonal transformation preserves the total energy and dimension of the transmitted symbols without increasing bandwidth, cyclic prefix, pilot, or explicit spreading code overhead;

[0036] Each information symbol is carried by multiple effective subcarriers, and the impact of deep fading is changed from local concentration to full bandwidth weighted average, thus improving the reliability distribution.

[0037] The OFDM per-subcarrier LMMSE equalization is retained, and the new processing is only a fixed matrix multiplication, which is convenient for offline generation, parallel computing and upgrading of existing equipment.

[0038] LFM broadband scale correction, phase-aware pilot interpolation and transpose despreading form a closed-loop receiving link to adapt to underwater acoustic motion, multipath and residual frequency offset;

[0039] Without increasing effective bandwidth, data slots, and pilot load, the dominance of frequency-selective deep fading on individual modulation symbols is reduced, while maintaining a single-tap equalization structure suitable for engineering implementation. Attached Figure Description

[0040] The accompanying drawings are used to provide a further understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.

[0041] Figure 1 This is a flowchart illustrating the steps of a random orthogonal precoding underwater acoustic communication method.

[0042] Figure 2 This is a step diagram illustrating the process of generating a fixed real orthogonal matrix based on a shared seed and matrix dimension.

[0043] Figure 3 This is a flowchart illustrating the steps of performing pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization on effective subcarriers.

[0044] Figure 4 This is a flowchart of the overall process of transmission, channel propagation, and reception processing in the random orthogonal precoding underwater acoustic communication method.

[0045] Figure 5 This is a structural diagram of the launching equipment;

[0046] Figure 6 This is a structural diagram of the receiving device. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0048] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, or the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0049] Underwater acoustic channels are characterized by narrow usable bandwidth, long propagation time, significant sparse multipath propagation, and wideband Doppler scale variations caused by motion. Traditional OFDM loads information symbols onto each subcarrier, which reduces equalization complexity, but symbols falling into deep fading still exhibit low reliability; adding pilots, retransmissions, or channel coding typically incurs additional overhead. Two-dimensional transforms such as OTFS can achieve diversity in the time-delay-Doppler domain, but grid construction, two-dimensional estimation, and detection are highly complex.

[0050] To address the above problems, embodiments of this application provide a random orthogonal precoding underwater acoustic communication method and system.

[0051] Based on: S = QX, Q T Q = I K Where X, S, and Z are the modulation symbol matrix, orthogonal expansion matrix, and equalization matrix, respectively, and Q is a K-order fixed real orthogonal matrix.

[0052] Before OFDM modulation, the transmitter performs energy-preserving spreading on all valid subcarrier symbols in the same time slot using a reproducible fixed real orthogonal matrix. The receiver first corrects the broadband scale based on the LFM synchronization header, then performs pilot-assisted LMMSE equalization, and finally despreads using the transpose of the orthogonal matrix. The matrix does not change randomly with the symbols, so there is no need to transmit the matrix index frame by frame; the random seed is used for reproducible basis generation and does not serve as a cryptographic key.

[0053] The embodiments of this application will be further described below with reference to the accompanying drawings.

[0054] Reference Figure 1 A random orthogonal precoding underwater acoustic communication method includes the following steps:

[0055] Step S1: The transmitter maps the data to be transmitted into a data matrix containing effective subcarriers and data symbols;

[0056] Step S2: Generate a fixed real orthogonal matrix based on the shared seed and matrix dimension, and multiply the data matrix along the effective subcarrier dimension by the fixed real orthogonal matrix to obtain the frequency domain extended matrix;

[0057] Step S3: Map the frequency domain extension matrix and pilot to OFDM frequency domain symbols, perform IFFT, cyclic prefix insertion and upconversion, and frame with the linear frequency modulation synchronization segment to form an underwater acoustic transmission frame;

[0058] Step S4: The transmitter sends an underwater acoustic transmission frame to the receiver.

[0059] Step S5: The receiving end receives the underwater acoustic transmission frame;

[0060] Step S6: The receiver uses the linear frequency modulation synchronization segment to determine the frame start point and broadband Doppler scale, performs resampling compensation on the received sampled data of the underwater acoustic transmission frame, and refines the timing and residual frequency offset using the cyclic prefix and pilot.

[0061] Step S7: Perform pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization on the effective subcarriers to obtain the equalization matrix;

[0062] Step S8: Multiply the equalization matrix along the effective subcarrier dimension by the transpose of the fixed real orthogonal matrix to recover the transmitted data.

[0063] Reference Figure 4 The overall process of transmission, channel propagation, and reception processing in this method is as follows:

[0064] Bit to QPSK mapping → ORAND orthogonal spread → OFDM / LFM frame transmission → underwater acoustic channel → synchronization and Doppler correction → LMMSE equalization → transpose despreading and decision.

[0065] For step S1, the transmitter converts the data to be transmitted (such as images, text, or sensor data) into a bit sequence, performs channel coding, scrambling, and interleaving as needed, then completes QPSK mapping, and follows the steps outlined in step S1. One effective subcarrier and The data slots are arranged as follows:

[0066] ;

[0067] Each column corresponds to one OFDM data symbol.

[0068] For example, take , Of course, other values ​​can be used in other embodiments.

[0069] Reference Figure 2 For step S2, generating a fixed real orthogonal matrix based on the shared seed and matrix dimension includes the following steps:

[0070] Step S21: Generate an independent and identically distributed real Gaussian matrix G of size K×K using a shared seed;

[0071] Step S22: Perform QR decomposition on the independent and identically distributed real Gaussian matrix G into matrix U and matrix R;

[0072] Step S23: Construct a diagonal matrix D, where the k-th diagonal element of the diagonal matrix D is the sign of the k-th diagonal element of matrix R;

[0073] Step S24: Obtain a fixed real orthogonal matrix Q by transposing the product of matrix U and diagonal matrix D, such that the product of the transpose of Q and Q is equal to the K-dimensional identity matrix.

[0074] Where K is the number of effective subcarriers, and the transmitter and receiver use the same seed, K value, random number generator and subcarrier sorting.

[0075] in accordance with Perform QR decomposition on an independent and identically distributed real Gaussian matrix G into matrices U and R.

[0076] in accordance with The fixed real orthogonal matrix Q is obtained by transposing the product of matrix U and diagonal matrix D.

[0077] The fixed real orthogonal matrix operates only on the effective subcarrier dimension and remains unchanged between data symbol time slots in one or more frames; the symbol energy remains unchanged before and after precoding, and does not occupy additional time slots or frequency bands.

[0078] The product of the transpose of Q and Q equals the K-dimensional identity matrix, expressed by the formula: .

[0079] Multiplying the data matrix along the effective subcarrier dimension by a fixed real orthogonal matrix yields the frequency domain extension matrix. Here, subcarrier-dimensional extension is performed only on the data symbols, resulting in:

[0080] .

[0081] This step distributes a single information symbol across multiple effective subcarriers while maintaining data dimensionality and total energy, without increasing bandwidth, time slots, or pilot overhead. Q-fixed multiplexing eliminates the need for frame-by-frame matrix transmission.

[0082] For step S3, the frequency domain extension matrix and pilot are mapped to OFDM frequency domain symbols, IFFT, cyclic prefix insertion and upconversion are performed, and the underwater acoustic transmission frame is formed by framing with the linear frequency modulation synchronization segment.

[0083] Specifically, the expanded data symbols and the unprocessed ones will be... The transformed known pilots are loaded onto effective subcarriers, and after IFFT, cyclic prefix insertion, resampling, and upconversion, a real passband OFDM signal is generated. This signal is then framed and transmitted according to the sequence "LFM synchronization segment – ​​guard interval – OFDM data segment – ​​guard interval". Pilots are used for subcarrier-by-subcarrier channel estimation, cyclic prefixes are used to reduce inter-symbol interference caused by multipath propagation, and LFM is used for frame synchronization and wideband Doppler scale estimation.

[0084] For steps S4 and S5, the transmitting end transmits underwater acoustic transmission frames to the receiving end; the receiving end receives underwater acoustic transmission frames.

[0085] For step S6, the linear frequency modulation synchronization segment includes an up-frequency linear frequency modulation signal and a down-frequency linear frequency modulation signal; the receiver jointly estimates the frame start point and scale factor by searching the peak values ​​of the up-frequency linear frequency modulation signal and the down-frequency linear frequency modulation signal and the candidate Doppler scale, and resamples the entire frame of received sampled data or the data segments in the received sampled data according to the scale factor, and refines the timing and residual frequency offset using the cyclic prefix and pilot.

[0086] Furthermore, the receiver uses the peak detection frame start point of the up-frequency linear frequency modulated (RFFM) signal and the down-frequency RFFM signal to estimate the dominant common Doppler scale through a two-level coarse and fine scale search, and then resamples the received data; subsequently, it refines the OFDM start point by combining the cyclic prefix correlation and pilot coherence, and uses the cyclic prefix phase to estimate the residual carrier frequency offset.

[0087] This step reduces inter-carrier interference caused by timing errors and broadband scale mismatch.

[0088] Reference Figure 3 For step S7, pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization are performed on the effective subcarriers, including the following steps:

[0089] Step S71: The receiver obtains the effective subcarrier channel response at each pilot symbol, performs phase expansion, and then interpolates in the time dimension and / or frequency dimension.

[0090] Step S72: For the k-th subcarrier, the sum of the conjugate of the estimated channel coefficient divided by its squared modulus and the regularization parameter is used as the LMMSE equalization weight, and the residual common phase error is compensated by cyclic prefix correlation or pilot phase slope.

[0091] The equalized output complex data symbol for the k-th subcarrier and the m-th data symbol is:

[0092]

[0093] In the formula, The equalized output complex data symbol for the k-th subcarrier and the m-th data symbol. The channel coefficients at the data time are obtained by phase expansion interpolation of the effective subcarrier channel response at the pilot position. The regularization parameter is determined based on noise power or channel power. This refers to the received frequency domain complex data before equalization on the k-th effective subcarrier at the m-th data symbol time. Indicates complex conjugation. The channel coefficient represents the power gain, k is the effective subcarrier index, and m is the data symbol index.

[0094] LMMSE equalization can limit noise amplification on deep fading subcarriers and stabilize subsequent orthogonal despreading.

[0095] For step S8, the equalization matrix is ​​multiplied along the effective subcarrier dimension by the transpose of the fixed real orthogonal matrix to recover the transmitted data.

[0096] The same information block can be repeatedly transmitted in different frames. During the process of recovering transmitted data, the receiver performs synchronization, scale compensation, channel estimation, equalization and orthogonal despreading on each frame, and then performs soft combining according to the weights determined by channel quality, noise variance or peak value, and then performs constellation decision and bit recovery.

[0097] After subcarrier-by-subcarrier equalization, orthogonal transpose despreading is performed in the reverse order of the transmitting end, which can be expressed by the following formula: .

[0098] Under ideal conditions, This ensures that the original symbols are recoverable; in actual channels, this processing is mainly used to equalize the equivalent reliability of different symbols.

[0099] The variance of the error of the i-th symbol after despreading is:

[0100]

[0101] In the formula, Let be the variance of the error of the i-th symbol after despreading. For the first Error variance after subcarrier equalization The number of effective subcarriers, Let be the element in the k-th row and i-th column of the fixed real orthogonal matrix Q; i is the despread symbol index, and k is the effective subcarrier index, both i and k ranging from 1 to K. For dense random orthogonal matrices, Usually close to Therefore, the effects of local deep fading are distributed from a single symbol to multiple symbols.

[0102] An embodiment of this application provides a random orthogonal precoding underwater acoustic communication system, applying the above-described random orthogonal precoding underwater acoustic communication method; the system includes a transmitting device and a receiving device; refer to Figure 5 The transmitting device includes a bit mapping module, a fixed orthogonal matrix generation module, a subcarrier orthogonal extension module, a pilot insertion module, a multi-carrier modulation module, a linear frequency modulation framing module, and an underwater acoustic transmission module; (Refer to...) Figure 6 The receiving equipment includes a linear frequency modulation synchronization module, a broadband Doppler estimation and resampling module, a timing and frequency offset correction module, a pilot channel estimation module, an LMMSE equalization module, an orthogonal transpose despreading module, and a data decision module.

[0103] An embodiment of this application provides a non-transitory computer-readable storage medium storing a program thereon, which, when executed by a processor of an underwater acoustic communication device, causes the underwater acoustic communication device to implement the above-described random orthogonal precoding underwater acoustic communication method.

[0104] Taking a sea trial prototype as an example, the transmission sampling rate is 96 kHz, the underwater acoustic operating frequency band is 8 kHz to 16 kHz, and the center frequency is 12 kHz; the OFDM IFFT length is 1024, the cyclic prefix length is 512, and the effective subcarrier number K is 512. Each frame includes 24 pilot symbols and 48 data symbols, using QPSK mapping; the synchronization segment uses alternating up-frequency and down-frequency LFM, with each segment lasting 1 s, and a 0.4 s guard interval is set before and after the data segment. The information block formed by the 96×96 grayscale image is carried by two frames.

[0105] During initialization, both the transmitter and receiver generate a 512-order real Gaussian matrix G using the same random seed, perform G=UR, and correct U according to the diagonal sign of R to obtain the transpose of Q=(UD). For each data time slot, the 512-dimensional QPSK column vector is left-multiplied by Q and then loaded into the effective subcarrier. After IFFT, cyclic prefix, and real passband upconversion, it is concatenated with the LFM synchronization segment and transmitted by the transducer. This Q is fixedly multiplexed in all data time slots and between repeated frames, so the receiver only needs to store the seed and parameters.

[0106] The receiver first uses matched filtering to search for rising and falling LFM correlation peaks, performs a coarse-to-fine Doppler scale candidate search, and resamples. Then, it refines the OFDM starting point using cyclic prefix correlation and pilot correlation to estimate the carrier frequency offset and common phase. After removing the cyclic prefix and FFT, channel estimation and interpolation with phase expansion are performed at the pilot, and LMMSE equalization is performed per subcarrier using w[k]=h*[k] / (|h[k]|²+α). The resulting matrix Z is left-multiplied by the transpose of Q to compensate for the residual phase and complete the QPSK soft decision. When duplicate frames exist, they can be weighted and combined according to the estimated signal-to-noise ratio.

[0107] During sea trials, the prototype successfully completed real-passband waveform transmission, reception synchronization, Doppler compensation, equalization, orthogonal despreading, and image restoration, verifying the feasibility of the complete link. It should be noted that the role of orthogonal precoding is to redistribute the equivalent reliability of each information symbol, rather than unconditionally increasing Shannon capacity under any channel. The specific matrix order, modulation scheme, pilot density, LFM duration, and carrier frequency can be adjusted according to the transducer bandwidth and communication distance, all falling within the scope of this application.

[0108] This solution has the following beneficial effects:

[0109] Orthogonal transformation preserves the total energy and dimension of the transmitted symbols without increasing bandwidth, cyclic prefix, pilot, or explicit spreading code overhead;

[0110] Each information symbol is carried by multiple effective subcarriers, and the impact of deep fading is changed from local concentration to full bandwidth weighted average, thus improving the reliability distribution.

[0111] The OFDM per-subcarrier LMMSE equalization is retained, and the new processing is only a fixed matrix multiplication, which is convenient for offline generation, parallel computing and upgrading of existing equipment.

[0112] LFM broadband scale correction, phase-aware pilot interpolation and transpose despreading form a closed-loop receiving link to adapt to underwater acoustic motion, multipath and residual frequency offset;

[0113] Without increasing effective bandwidth, data slots, and pilot load, the dominance of frequency-selective deep fading on individual modulation symbols is reduced, while maintaining a single-tap equalization structure suitable for engineering implementation.

[0114] The above is a detailed description of the preferred embodiments of this application, but this application is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A random orthogonal precoding underwater acoustic communication method, characterized in that, include: The transmitter maps the data to be transmitted into a data matrix containing effective subcarriers and data symbols; A fixed real orthogonal matrix is ​​generated based on the shared seed and the matrix dimension. The data matrix is ​​then multiplied by the fixed real orthogonal matrix along the effective subcarrier dimension to obtain the frequency domain extended matrix. The frequency domain extension matrix and pilot are mapped to OFDM frequency domain symbols, IFFT, cyclic prefix insertion and upconversion are performed, and the underwater acoustic transmission frame is formed by framing with the linear frequency modulation synchronization segment. The transmitting end transmits the underwater acoustic transmission frame to the receiving end, and the receiving end receives the underwater acoustic transmission frame. The receiver uses the linear frequency modulation synchronization segment to determine the frame start point and broadband Doppler scale, performs resampling compensation on the received sampled data of the underwater acoustic transmission frame, and refines the timing and residual frequency offset using the cyclic prefix and pilot. Pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization are performed on the effective subcarriers to obtain the equalization matrix; The equalization matrix is ​​multiplied along the effective subcarrier dimension by the transpose of the fixed real orthogonal matrix to recover the transmitted data.

2. The random orthogonal precoding underwater acoustic communication method according to claim 1, characterized in that, Generate a fixed real orthogonal matrix based on a shared seed and matrix dimension, including: Generate an independent and identically distributed real Gaussian matrix G of size K×K using a shared seed; Perform QR decomposition on an independent and identically distributed real Gaussian matrix G into matrices U and R; Construct a diagonal matrix D, where the k-th diagonal element of D is the sign of the k-th diagonal element of matrix R; The transpose of the product of matrix U and diagonal matrix D yields a fixed real orthogonal matrix Q, such that the product of the transpose of Q and Q equals the K-dimensional identity matrix. Where K is the number of effective subcarriers, and the transmitter and receiver use the same seed, K value, random number generator and subcarrier sorting.

3. The random orthogonal precoding underwater acoustic communication method according to claim 1, characterized in that, The fixed real orthogonal matrix operates only on the effective subcarrier dimension and remains unchanged between data symbol time slots in one or more frames; the symbol energy remains unchanged before and after precoding, and does not occupy additional time slots or frequency bands.

4. The random orthogonal precoding underwater acoustic communication method according to claim 1, characterized in that, The linear frequency modulation synchronization section includes an up-frequency linear frequency modulation signal and a down-frequency linear frequency modulation signal; The receiver jointly estimates the frame start point and scale factor by using the peak values ​​of the up-frequency linear frequency modulated signal and the down-frequency linear frequency modulated signal, as well as the candidate Doppler scale search, and then resamples and compensates the entire frame of received sampled data or data segments in the received sampled data according to the scale factor.

5. The random orthogonal precoding underwater acoustic communication method according to claim 1, characterized in that, Perform pilot-assisted channel estimation and carrier-by-carrier linear minimum mean square error equalization on the effective subcarriers, including: The receiver obtains the effective subcarrier channel response at each pilot symbol, performs phase expansion, and then interpolates in the time and / or frequency dimensions. For the k-th subcarrier, the sum of the conjugate of the estimated channel coefficient divided by its squared modulus and the regularization parameter is used as the LMMSE equalization weight, and the residual common phase error is compensated by the cyclic prefix correlation or pilot phase slope.

6. The random orthogonal precoding underwater acoustic communication method according to claim 5, characterized in that, The equalized output complex data symbol for the k-th subcarrier and the m-th data symbol is: In the formula, The equalized output complex data symbol for the k-th subcarrier and the m-th data symbol. The channel coefficients at the data time are obtained by phase expansion interpolation of the effective subcarrier channel response at the pilot position. The regularization parameter is determined based on noise power or channel power. This refers to the received frequency domain complex data before equalization on the k-th effective subcarrier at the m-th data symbol time. Indicates complex conjugation. The channel coefficient represents the power gain, k is the effective subcarrier index, and m is the data symbol index.

7. The random orthogonal precoding underwater acoustic communication method according to claim 1, characterized in that, The same information block can be repeatedly transmitted in different frames. During the process of recovering transmitted data, the receiver performs synchronization, scale compensation, channel estimation, equalization and orthogonal despreading on each frame, and then performs soft combining according to the weights determined by channel quality, noise variance or peak value, and then performs constellation decision and bit recovery.

8. The random orthogonal precoding underwater acoustic communication method according to claim 7, characterized in that, The variance of the error of the i-th symbol after despreading is: In the formula, Let be the variance of the error of the i-th symbol after despreading. For the first Error variance after subcarrier equalization The number of effective subcarriers, is the element in the k-th row and i-th column of the fixed real orthogonal matrix Q; i is the despread symbol index, and k is the effective subcarrier index.

9. A random orthogonal precoding underwater acoustic communication system, characterized in that, The system employs the random orthogonal precoding underwater acoustic communication method as described in any one of claims 1 to 8; the system includes a transmitting device and a receiving device; the transmitting device includes a bit mapping module, a fixed orthogonal matrix generation module, a subcarrier-dimensional orthogonal expansion module, a pilot insertion module, a multi-carrier modulation module, a linear frequency modulation framing module, and an underwater acoustic transmission module; the receiving device includes a linear frequency modulation synchronization module, a wideband Doppler estimation and resampling module, a timing and frequency offset correction module, a pilot channel estimation module, an LMMSE equalization module, an orthogonal transpose despreading module, and a data decision module.

10. A non-transitory computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor of the underwater acoustic communication device, the underwater acoustic communication device implements the random orthogonal precoding underwater acoustic communication method as described in any one of claims 1 to 8.

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