Off-network block sparse orthogonal matching pursuit underwater acoustic time delay Doppler domain channel estimation method

Abstract

The invention discloses an off-network block sparse orthogonal matching pursuit underwater acoustic time delay Doppler domain channel estimation method, and belongs to the technical field of underwater acoustic channel estimation. The method solves the problems that a channel estimation method based on traditional orthogonal matching pursuit cannot estimate frequency shift parameters on non-grid points and is high in calculation complexity. According to the method, channel parameters of integer grid points are obtained based on a BOMP algorithm, and then residual Doppler factors on non-grid points are subjected to further fine estimation based on maximum likelihood criterion fitting. The problem that a traditional OMP channel estimation method in underwater OTFS communication can only estimate channel parameters on grid points is solved, and the estimation precision of channel frequency shift parameters is further improved by estimating frequency shift parameters on non-grid points; and meanwhile, a fractional order dictionary is prevented from being established in a channel parameter process, so that the system complexity is reduced to a certain extent. The method can be applied to underwater sound time delay Doppler domain channel estimation.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic channel estimation, and in particular relates to an off-grid block sparse orthogonal matching pursuit underwater acoustic delay Doppler domain channel estimation method. Background Art

[0002] The exploration and utilization of underwater communication technology is one of the most cutting-edge technologies in the field of ocean research today. In recent years, with the continuous development of underwater motion platform units such as manned / unmanned submersibles and underwater robots in my country, one of the challenges currently faced is how to improve the transmission rate and stability of underwater motion platform units in high-mobility scenarios to meet the diverse and high-quality communication and collaboration needs. Due to the serious delay Doppler spread effect of the water acoustic channel caused by platform movement, coupled with factors such as limited bandwidth and low sound speed, underwater communication lags far behind the rapidly developing radio communication in terms of quality and efficiency.

[0003] Orthogonal frequency division modulation (OFDM) technology is one of the mainstream solutions for underwater acoustic communication in recent years. However, in the context of mobile communication, the orthogonality between subcarriers of the OFDM system is destroyed, resulting in serious interference between subcarriers, and the performance is also reduced. At present, the delay-Doppler domain communication technology, also known as the orthogonal time-frequency space (OTFS) communication technology, is considered to be a high-reliability communication method in high-speed mobile scenarios. OTFS migrates signal processing and analysis from the time-frequency domain to the delay-Doppler domain, effectively utilizing the time-invariant and sparse characteristics of the delay-Doppler domain channel to combat the inter-carrier crosstalk caused by Doppler frequency deviation. More importantly, relying on two-dimensional orthogonal transformation, each delay-Doppler domain symbol can experience the complete time-frequency domain channel, bringing time-frequency diversity gain, being robust to external burst interference, and effectively enhancing communication reliability.

[0004] At present, the channel estimation problem of underwater OTFS mostly follows the wireless channel model or the carrier frequency deviation scheme in the field of wireless communication. On this basis, the derived double-extended underwater acoustic channel is sparse in the delay-Doppler domain. Therefore, channel estimation in the delay-Doppler domain is a common means of key technology in the current mobile communication receiving end. Since the narrowband channel model is used or it is believed that the influence of Doppler is completely eliminated after resampling, a solution to the channel estimation problem is proposed based on the channel input-output model in the delay-Doppler domain. The generalized message passing algorithm realizes the expected maximization of learning path sparsity and noise variance. The compressed sensing method optimally combines multiple paths in the fractional-order dictionary. Deep learning is used to build a neural network for denoising, and then estimate Doppler frequency shift, delay, channel gain and other parameter information.

[0005] In fact, when the variance of the Doppler factors of each path in the underwater acoustic channel is small, the residual Doppler of the received signal after resampling can be considered as a consistent frequency shift. In this case, it is reasonable to borrow the frequency offset estimation method and channel model of the narrowband model. However, considering that the actual underwater acoustic received signal will still have a certain residual Doppler factor after resampling, which will bring about non-uniform frequency offset, it is necessary to adopt a unique broadband Doppler estimation method to achieve reliable communication in underwater mobile scenarios, that is, to break through the off-grid effect. Compressed sensing theory can effectively utilize the multipath sparse characteristics of the underwater acoustic channel to achieve channel estimation, but the traditional orthogonal matching pursuit (OMP) estimation needs to be based on a fractional-order dictionary matrix to break through the off-grid effect. As the fraction is refined, the size of the dictionary matrix will also increase, and the computational complexity of the delay Doppler domain channel estimation system will also increase. Moreover, the channel estimation method based on the traditional orthogonal matching pursuit can only estimate the parameters on the grid points, and cannot estimate the frequency shift parameters on non-grid points. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the channel estimation method based on traditional orthogonal matching pursuit cannot estimate the frequency shift parameters at non-grid points and has high computational complexity, and propose an off-grid block sparse orthogonal matching pursuit underwater acoustic delay Doppler domain channel estimation method.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: an off-grid block sparse orthogonal matching pursuit underwater acoustic delay Doppler domain channel estimation method, the method specifically comprising the following steps:

[0008] Step 1: Perform OTFS modulation on the signal x(k, l) to be sent by the underwater motion platform to obtain the OTFS modulated signal s(t);

[0009] Step 2: Up-convert the signal s(t) to obtain the up-converted signal

[0010] Step 3: Signal After passing through the underwater acoustic channel, the signal reaches the receiving end, where the receiving end resamples the received signal and then performs down-conversion processing on the resampled signal to obtain a down-converted signal;

[0011] Step 4: discretize the signal after down-conversion processing, and then perform OTFS demodulation on the discretized signal to obtain a demodulated signal y(k,l);

[0012] Step 5: Estimate the time delay of the grid points on each path in the channel, the channel gain, and the residual Doppler factor on each path according to the demodulated signal y(k,l) to obtain the channel estimation result.

[0013] Furthermore, the specific process of the OTFS modulation is:

[0014] Step 11: Perform ISFFT transformation on the signal x(k,l) to be sent by the underwater motion platform to obtain time-frequency domain data X[n,m] after ISFFT transformation;

[0015] where k is the Doppler index of the delay-Doppler domain grid, represents a set of integers from 0 to N-1, l is the delay index of the delay-Doppler domain grid, represents a set of integers from 0 to M-1, where n is the time index of the time-frequency domain grid. m is the frequency domain subcarrier index of the time-frequency domain grid,

[0016] Step 1 and 2: perform IFFT transformation on the time-frequency domain data X[n,m], then perform pulse shaping on the IFFT transformation result, and use the pulse-shaped signal s(t) as the OTFS modulated signal.

[0017] Furthermore, the up-converted signal for:

[0018]

[0019] in, Indicates up-conversion processing, g tx (·) is the pulse shaping function at the transmitter, t is time, T is the symbol period, e is the base of the natural logarithm, j is the imaginary unit, and f m Represents the mth subcarrier frequency, t∈(0,T).

[0020] Furthermore, the channel response h(t) of the underwater acoustic channel is:

[0021]

[0022] Where P is the total number of paths in the channel, δ(·) represents the underwater acoustic channel model, and h p and τ p denote the channel gain and delay of the pth path, α p represents the Doppler factor of the pth path, p=1,2,…,P.

[0023] Furthermore, the Doppler factor of the p-th path is:

[0024] α p =v p / c

[0025] Among them, v p represents the relative speed between the underwater platform motion units, and c represents the speed of sound propagation underwater.

[0026] Furthermore, the discretized signal is subjected to OTFS demodulation, specifically:

[0027] Step 41: The discretized signal is passed through the pulse shaping function g at the receiving end. rx , and then after the pulse shaping function g rx Perform FFT transformation on the signal after FFT transformation to obtain the signal after FFT transformation;

[0028] Step 42: Perform SFFT transformation on the signal after FFT transformation, and use the signal after SFFT transformation as the demodulated signal y(k,l).

[0029] Furthermore, the specific process of step five is as follows:

[0030] Step 51: Establish a compressed sensing matrix X according to the pilot part of the signal x(k,l) to be sent by the underwater motion platform P , obtain the observation vector y according to the pilot part of the signal y(k,l);

[0031] Initialize the signal sparsity to P, initialize the constant ω, initialize the residual r0 = y, and initialize the support set Initialize the number of iterations p = 1;

[0032] Step 52: According to r p-1 and X P Calculate the most matching atomic index λ at the pth iteration p ;

[0033] Step 53: According to λ p Update index set ξ p ;

[0034]

[0035] Step 54: According to ξ p Update support set:

[0036] Λ p =Λ p-1 ∪ξ p

[0037] Among them, Λ p represents the support set after the pth iteration update;

[0038] Step 55: According to the support set Λ p Estimate a sparse vector:

[0039]

[0040] in, represents the sparse vector obtained in the pth iteration, X P (Λ p ) represents the support set Λ p In X P The matrix composed of the corresponding column vectors in y(Λ p ) represents the support set Λ p The vector of corresponding elements in y, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix;

[0041] Step 56: Obtain the time delay at the grid point of the p-th path and the Doppler factor at the grid point according to the sparse vector obtained in the p-th iteration, and then determine the channel gain at the grid point of the p-th path according to the time delay at the grid point of the p-th path and the Doppler factor at the grid point;

[0042] Step 57: Calculate the residual Doppler factor b of the pth path after resampling based on the channel gain at the grid point obtained in the pth iteration. p ;

[0043] Step 58: Determine whether p=P is satisfied;

[0044] If p = P, the estimation ends;

[0045] If p<P, execute step 59;

[0046] Step 59: According to Calculate the updated residual error r p , and set p=p+1, and return to execute step 52.

[0047] Furthermore, the specific process of step 52 is as follows:

[0048]

[0049] Among them, <·> means calculating the inner product, X P,j Represents X P The jth column in , j = 1, 2, ..., L, L represents X P The total number of columns in , |·| means taking the absolute value.

[0050] Furthermore, the specific process of step five seven is:

[0051] Index λ with the atom that matches best pis the central grid point of the p-th path, expand ω grid points to the left of the central grid point, and then expand ω grid points to the right of the central grid point, and use the maximum likelihood criterion to fit the equivalent index and channel gain corresponding to the central grid point of the p-th path and each extended grid point:

[0052]

[0053] Where q represents the equivalent index, r(q) represents the channel gain corresponding to the equivalent index q, and κ represents the fractional frequency shift of the received signal on the Doppler domain grid;

[0054] Then the residual Doppler factor b of the pth path is p for:

[0055]

[0056] Among them, frac(.) means to take out the fractional part in the brackets.

[0057] Furthermore, the specific process of step fifty-nine is as follows:

[0058]

[0059] The beneficial effects of the present invention are:

[0060] Based on the characteristics of the block sparse form of the input-output relationship of the delay-Doppler domain of underwater OTFS communication, the present invention proposes an off-grid block sparse orthogonal matching pursuit channel estimation algorithm combined with maximum likelihood fitting. First, the channel parameters of integer grid points are obtained based on the BOMP algorithm, and then the residual Doppler factors on non-grid points are further refined based on the maximum likelihood criterion fitting. The problem that the traditional OMP channel estimation method in underwater OTFS communication can only estimate the channel parameters on grid points is solved. The present invention further improves the estimation accuracy of the channel frequency shift parameters by estimating the frequency shift parameters on non-grid points; at the same time, the establishment of a fractional-order dictionary is avoided in the channel parameter process, thereby reducing the system complexity to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of the process of sending and receiving signals from an underwater motion platform;

[0062] Figure 2 is a flow chart of channel estimation;

[0063] Figure 3 It is a comparison diagram of the minimum mean square estimation error between the channel estimation method of the present invention and the traditional OMP estimation method;

[0064] Figure 4It is a comparison chart of the original bit error rate performance of the signal OTFS modulation scheme of the present invention and the traditional OFDM modulation scheme at the same communication rate. DETAILED DESCRIPTION

[0065] Specific implementation method 1: Combination Figure 1 This embodiment describes an off-grid block sparse orthogonal matching pursuit underwater acoustic delay Doppler domain channel estimation method, the method specifically comprising the following steps:

[0066] Step 1: Perform OTFS modulation on the signal x(k,l) to be sent by the underwater motion platform to obtain the OTFS modulated signal s(t);

[0067] Step 2: Up-convert the signal s(t) to obtain the up-converted signal

[0068] Step 3: Signal After passing through the underwater acoustic channel, it reaches the receiving end (which can be a stationary or moving underwater platform), and the receiving end resamples the received bandpass time domain signal, and then down-converts the resampled signal to obtain a down-converted signal;

[0069] Step 4: discretize the signal after down-conversion processing, and then perform OTFS demodulation on the discretized signal to obtain a demodulated signal y(k,l);

[0070] Step 5: Estimate the time delay of the grid points on each path in the channel, the channel gain, and the residual Doppler factor on each path according to the demodulated signal y(k,l) to obtain the channel estimation result.

[0071] The method of the present invention also includes step six, performing time-frequency domain MMSE equalization on the data part of the demodulated signal y(k, l) according to the estimation result of step five, and restoring the signal sent by the underwater platform.

[0072] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the specific process of the OTFS modulation is as follows:

[0073] Step 11: Perform ISFFT (Symplectic Inverse Fourier Transform) on the signal x(k,l) to be sent by the underwater motion platform to obtain the time-frequency domain data X[n,m] after ISFFT transformation;

[0074] where k is the Doppler index of the delay-Doppler domain grid, represents a set of integers from 0 to N-1, l is the delay index of the delay-Doppler domain grid, represents a set of integers from 0 to M-1, where n is the time index of the time-frequency domain grid. m is the frequency domain subcarrier index of the time-frequency domain grid,

[0075] Step 1 and 2: perform IFFT (inverse fast Fourier transform) on the time-frequency domain data X[n,m], then perform pulse shaping on the IFFT transform result, and use the pulse-shaped signal s(t) as the OTFS modulated signal.

[0076] The other steps and parameters are the same as those in the first embodiment.

[0077] The amplitude and phase of the symbols in the set {1+j,-1+j,1-j,-1-j} carry the effective information of the communication (including the text information and voice information of the underwater motion platform). The symbols are then encoded and mapped into a bit stream, and the mapped bit stream is used as the modulated signal x(k,l)∈C, where C represents the complex domain and the Doppler index Latency Index Arranged on the grid Λ={(k / NT,l / MΔf)} in the delay-Doppler domain, the delay-Doppler domain data x(k,l) is mapped to the grid Λ of the time-frequency domain data X[n,m] through the two-dimensional transform ISFFT ⊥ ={(nT,mΔf)}.

[0078] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the signal after up-conversion processing for:

[0079]

[0080] in, Indicates up-conversion processing, g tx (·) is the pulse shaping function (i.e., rectangular window function) at the transmitter, t is time, T is the symbol period, e is the base of the natural logarithm, j is the imaginary unit, and f m Represents the mth subcarrier frequency, t∈(0,T).

[0081] The other steps and parameters are the same as those in the first or second embodiment.

[0082] Specific implementation mode 4: This implementation mode is different from any one of specific implementation modes 1 to 3 in that the channel response h(t) of the underwater acoustic channel is:

[0083]

[0084] Where P is the total number of paths in the channel, δ(·) represents the underwater acoustic channel model (in this invention, the multipath channel model), and h p and τ p denote the channel gain and delay of the pth path, αp represents the Doppler factor of the pth path, p=1,2,…,P.

[0085] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0086] Specific implementation method 5: This implementation method is different from any one of the specific implementation methods 1 to 4 in that the Doppler factor of the p-th path (reflecting the Doppler effect caused by the motion of the underwater platform) is:

[0087] α p =v p / c

[0088] Among them, v p represents the relative speed between the underwater platform motion units, and c represents the speed of sound propagation underwater.

[0089] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0090] Specific implementation method 6: This implementation method is different from any one of specific implementation methods 1 to 5 in that OTFS demodulation is performed on the discretized signal, specifically:

[0091] Step 41: The discretized signal is passed through the pulse shaping function g at the receiving end. rx (same as the pulse shaping function at the transmitter), and then rx The signal after FFT transformation (Fast Fourier Transform) is performed to obtain the signal after FFT transformation;

[0092] Step 42: Perform SFFT transformation (Symphotic Finite Fourier Transform) on the signal after FFT transformation, and use the signal after SFFT transformation as the demodulated signal y(k,l).

[0093] The other steps and parameters are the same as those in Specific Implementations 1 to 5.

[0094] Specific implementation method seven: Combination Figure 2 This embodiment is different from the first to sixth embodiments in that the specific process of step five is as follows:

[0095] Step 51: Establish a compressed sensing matrix X according to the pilot part of the signal x(k,l) to be sent by the underwater motion platform P (All elements in the matrix are integers), and the observation vector y is obtained according to the pilot part of the signal y(k,l);

[0096] Initialize the signal sparsity to P, initialize the constant ω (the specific value can be selected according to the moving speed of the underwater moving platform and the time-varying degree of the underwater acoustic channel, which can generally be set to 5), use the block approximation processing parameter ω as the input parameter of the channel estimator, initialize the residual r0 = y, and initialize the support set Initialize the number of iterations p = 1;

[0097] Step 52: According to r p-1 and X P Calculate the most matching atomic index λ at the pth iteration p ;

[0098] Step 53: According to λ p Update index set ξ p ;

[0099]

[0100] Step 54: According to ξ p Update support set:

[0101] Λ p =Λ p-1 ∪ξ p

[0102] Among them, Λ p represents the support set after the pth iteration update;

[0103] Step 55: According to the support set Λ p Estimate a sparse vector:

[0104]

[0105] in, represents the sparse vector obtained in the pth iteration, X P (Λ p ) represents the support set Λ p In X P The matrix composed of the corresponding column vectors in (that is, using the support set Λ p The index in X P The corresponding column vectors in the matrix), y(Λ p ) represents the support set Λ p The vector composed of the corresponding elements in y (that is, using the support set Λ p The indices in y correspond to the elements in y forming a vector), the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix;

[0106] Step 56: Obtain the time delay at the grid point of the p-th path and the Doppler factor at the grid point according to the sparse vector obtained in the p-th iteration, and then determine the channel gain at the grid point of the p-th path according to the time delay at the grid point of the p-th path and the Doppler factor at the grid point;

[0107] Step 57: Calculate the residual Doppler factor b of the pth path after resampling based on the channel gain at the grid point obtained in the pth iteration. p ;

[0108] Step 58: Determine whether p=P is satisfied;

[0109] If p = P, the estimation ends;

[0110] If p<P, execute step 59;

[0111] Step 59: According to Calculate the updated residual error r p , and set p=p+1, and return to execute step 52.

[0112] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0113] The average value of the Doppler factor is eliminated by resampling, and the delay-Doppler domain is obtained by discretization and OTFS demodulation. Since the input-output relationship in the delay-Doppler domain is block-sparse, this embodiment proposes a BOMP-ML channel estimation method in the delay-Doppler domain, and obtains the channel parameters of integer grid points based on the BOMP algorithm (steps 51 to 56 and steps 58 to 59), and further implements fine estimation based on maximum likelihood criterion fitting.

[0114] Specific implementation eight: This implementation differs from specific implementations one to seven in that the specific process of step five-two is as follows:

[0115]

[0116] Among them, <·> means calculating the inner product, X P,j Represents X P The jth column in , j = 1, 2, ..., L, L represents X P The total number of columns in , |·| means taking the absolute value.

[0117] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0118] Specific implementation method 9: This implementation method is different from specific implementation methods 1 to 8 in that the specific process of step 57 is as follows:

[0119] Index λ with the atom that matches best pis the central grid point of the p-th path, expand ω grid points to the left of the central grid point, and then expand ω grid points to the right of the central grid point, and use the maximum likelihood criterion to fit the equivalent index and channel gain corresponding to the central grid point of the p-th path and each extended grid point:

[0120]

[0121] Wherein, q represents the equivalent index (the central grid point and the extended grid point constitute the path block of the pth path, and the equivalent index is the index of each grid point on the path block along the Doppler domain grid), r(q) represents the channel gain corresponding to the equivalent index q, and κ represents the fractional frequency shift of the received signal on the Doppler domain grid;

[0122] Then the residual Doppler factor b of the pth path is p for:

[0123]

[0124] Among them, frac(.) means to take out the fractional part in the brackets.

[0125] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0126] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the specific process of step 59 is as follows:

[0127]

[0128] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0129] like Figure 3 and Figure 4 As shown in the figure, the experimental results show that compared with the traditional OMP channel estimation method, the BOMP-MLE channel estimation algorithm proposed in the present invention achieves higher estimation accuracy and lower computational complexity under the same channel conditions. Compared with the OFDM modulation method, the OTFS algorithm has certain advantages in underwater mobile communication scenarios. In the field of underwater acoustic mobile communications, the present invention can achieve faster and more robust communications.

[0130] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. An off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method, characterized in that: The method specifically comprises the following steps: Step 1: Perform OTFS modulation on the signal x(k, l) to be sent by the underwater motion platform to obtain the OTFS modulated signal s(t); Step 2: Up-convert the signal s(t) to obtain the up-converted signal Step 3: Signal After passing through the underwater acoustic channel, the signal reaches the receiving end, where the receiving end resamples the received signal and then performs down-conversion processing on the resampled signal to obtain a down-converted signal; Step 4: discretize the signal after down-conversion processing, and then perform OTFS demodulation on the discretized signal to obtain a demodulated signal y(k,l); Step 5: Estimate the time delay of the grid points on each path in the channel, the channel gain, and the residual Doppler factor on each path according to the demodulated signal y(k,l) to obtain the channel estimation result.

2. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 1, characterized in that: The specific process of the OTFS modulation is: Step 11: Perform ISFFT transformation on the signal x(k,l) to be sent by the underwater motion platform to obtain time-frequency domain data X[n,m] after ISFFT transformation; where k is the Doppler index of the delay-Doppler domain grid, represents a set of integers from 0 to N-1, l is the delay index of the delay-Doppler domain grid, represents a set of integers from 0 to M-1, where n is the time index of the time-frequency domain grid. m is the frequency domain subcarrier index of the time-frequency domain grid, Step 1 and 2: perform IFFT transformation on the time-frequency domain data X[n,m], then perform pulse shaping on the IFFT transformation result, and use the pulse-shaped signal s(t) as the OTFS modulated signal.

3. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 2, characterized in that: The up-converted signal for: in, Indicates up-conversion processing, g tx (·) is the pulse shaping function at the transmitter, t is time, T is the symbol period, e is the base of the natural logarithm, j is the imaginary unit, and f m Represents the mth subcarrier frequency, t∈(0,T).

4. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 3, characterized in that: The channel response h(t) of the underwater acoustic channel is: Where P is the total number of paths in the channel, δ(·) represents the underwater acoustic channel model, and h p and τ p denote the channel gain and delay of the pth path, α p represents the Doppler factor of the pth path, p=1,2,…,P.

5. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 4, characterized in that: The Doppler factor of the pth path is: a p =v p / c Among them, v p represents the relative speed between the underwater platform motion units, and c represents the speed of sound propagation underwater.

6. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 5, characterized in that: The OTFS demodulation of the discretized signal is specifically performed as follows: Step 41: The discretized signal is passed through the pulse shaping function g at the receiving end. rx , and then after the pulse shaping function g rx Perform FFT transformation on the signal after FFT transformation to obtain the signal after FFT transformation; Step 42: Perform SFFT transformation on the signal after FFT transformation, and use the signal after SFFT transformation as the demodulated signal y(k,l).

7. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 6, characterized in that: The specific process of step five is as follows: Step 51: Establish a compressed sensing matrix X according to the pilot part of the signal x(k,l) to be sent by the underwater motion platform P , obtain the observation vector y according to the pilot part of the signal y(k,l); Initialize the signal sparsity to P, initialize the constant ω, initialize the residual r0 = y, and initialize the support set Initialize the number of iterations p = 1; Step 52: According to r p-1 and X P Calculate the most matching atomic index λ at the pth iteration p ; Step 53: According to λ p Update index set ξ p ; x p ={λ p -oh,l p -ω+1,...,λ p +ω} Step 54: According to ξ p Update support set: L p =L p-1 ∪ξ p Among them, Λ p represents the support set after the pth iteration update; Step 55: According to the support set Λ p Estimate a sparse vector: in, represents the sparse vector obtained in the pth iteration, X P (Λ p ) represents the support set Λ p In X P The matrix composed of the corresponding column vectors in y(Λ p ) represents the support set Λ p The vector of corresponding elements in y, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix; Step 56: Obtain the time delay at the grid point of the p-th path and the Doppler factor at the grid point according to the sparse vector obtained in the p-th iteration, and then determine the channel gain at the grid point of the p-th path according to the time delay at the grid point of the p-th path and the Doppler factor at the grid point; Step 57: Calculate the residual Doppler factor b of the pth path after resampling based on the channel gain at the grid point obtained in the pth iteration. p ; Step 58: Determine whether p=P is satisfied; If p = P, the estimation ends; If p<P, execute step 59; Step 59: According to Calculate the updated residual error r p , and set p=p+1, and return to execute step 52.

8. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 7, characterized in that: The specific process of step 52 is as follows: l p =arg max j＝1,2,...,L | <r p-1 ,X P,j >| Among them, <·> means calculating the inner product, X P,j Represents X P The jth column in , j = 1, 2, ..., L, L represents X P The total number of columns in , |·| means taking the absolute value.

9. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 8, characterized in that: The specific process of step five seven is: Index λ with the atom that matches best p is the central grid point of the p-th path, expand ω grid points to the left of the central grid point, and then expand ω grid points to the right of the central grid point, and use the maximum likelihood criterion to fit the equivalent index and channel gain corresponding to the central grid point of the p-th path and each extended grid point: Where q represents the equivalent index, r(q) represents the channel gain corresponding to the equivalent index q, and κ represents the fractional frequency shift of the received signal on the Doppler domain grid; Then the residual Doppler factor b of the pth path is p for: Among them, frac(.) means to take out the fractional part in the brackets.

10. The off-grid block sparse orthogonal matching pursuit underwater acoustic delay-Doppler domain channel estimation method according to claim 9, characterized in that: The specific process of step fifty-nine is as follows:

Images