An Off-Network Block Sparse Orthogonal Matching Pursuit Method for Underwater Acoustic Delay Doppler Domain Channel Estimation

Abstract

This invention discloses an off-grid, block-sparse orthogonal matched pursuit (OMP) underwater acoustic time-delay Doppler domain channel estimation method, belonging to the field of underwater acoustic channel estimation technology. This invention solves the problems of traditional OMP-based channel estimation methods being unable to estimate frequency shift parameters at non-grid points and having high computational complexity. First, this invention obtains the channel parameters at integer grid points based on the BOMP algorithm, and then further refines the estimation of residual Doppler factors at non-grid points using maximum likelihood fitting. This addresses the limitation of traditional OMP channel estimation methods in underwater OTFS communication, which can only estimate channel parameters at grid points. By estimating frequency shift parameters at non-grid points, this invention further improves the estimation accuracy of channel frequency shift parameters; simultaneously, it avoids establishing a fractional-order dictionary during the channel parameter estimation process, thereby reducing system complexity to some extent. This method can be applied to underwater acoustic time-delay Doppler domain channel estimation.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic channel estimation technology, specifically relating to an off-network block sparse orthogonal matching pursuit underwater acoustic delay Doppler domain channel estimation method. Background Technology

[0002] The exploration and utilization of underwater communication technology is one of the most cutting-edge technologies in the field of marine research today. In recent years, with the continuous development of underwater motion platform units such as carrier / unmanned underwater vehicles and underwater robots in my country, one of the current challenges is how to improve the transmission rate and stability of underwater motion platform units in highly mobile scenarios to meet diverse and high-quality communication and collaboration needs. Due to the severe time delay Doppler spread effect of platform movement on the underwater acoustic channel, coupled with 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 has become one of the mainstream solutions for underwater acoustic communication in recent years. However, in the context of mobile communication, the orthogonality between subcarriers in OFDM systems is destroyed, leading to severe inter-carrier interference and a subsequent performance degradation. Currently, time-delay Doppler domain communication technology, also known as Orthogonal Time-Frequency Space (OTFS) communication technology, is considered a highly reliable communication method for high-speed mobile scenarios. OTFS shifts signal processing and analysis from the time-frequency domain to the time-delay Doppler domain, effectively utilizing the time-invariant and sparsity characteristics of the time-delay Doppler domain channel to combat inter-carrier crosstalk caused by Doppler frequency offset. More importantly, relying on two-dimensional orthogonal transformation, each time-delay Doppler domain symbol can undergo a complete time-frequency domain channel, resulting in time-frequency diversity gain and robustness against external sudden interference, effectively enhancing communication reliability.

[0004] Currently, most underwater OTFS channel estimation problems follow wireless channel models or carrier frequency offset schemes from the wireless communication field. Based on this, the derived dual-extended underwater acoustic channel exhibits sparsity in the time-delay Doppler domain. Therefore, channel estimation in the time-delay Doppler domain is a common approach in current mobile communication receiver technologies. Since narrowband channel models are used or it is assumed that the Doppler effect is completely eliminated after resampling, a solution to the channel estimation problem is proposed based on the channel input-output model in the time-delay Doppler domain. The generalized message passing algorithm achieves expectation maximization to learn path sparsity and noise variance. Compressed sensing techniques optimize the combination of multiple paths in the fractional-order dictionary. Deep learning is used to build a neural network for noise reduction, thereby estimating parameters such as Doppler frequency shift, time delay, and channel gain.

[0005] In practice, when the variance of the Doppler factor across all paths in an underwater acoustic channel is small, the residual Doppler of the received signal after resampling can be considered a uniform frequency shift. In this case, it is reasonable to borrow the frequency offset estimation method and channel model from the narrowband model. However, considering that the actual underwater acoustic received signal will still have a certain residual Doppler factor after resampling, resulting in a non-uniform frequency shift, it is necessary to adopt a unique broadband Doppler estimation method to achieve reliable communication in underwater mobile scenarios, i.e., to overcome the off-grid effect. Compressed sensing theory can effectively utilize the multipath sparsity characteristics of underwater acoustic channels to achieve channel estimation. However, the traditional Orthogonal Matching Pursuit (OMP) estimation method for overcoming the off-grid effect requires a fractional dictionary matrix. As the fractional matrix is ​​refined, its size increases, which in turn increases the computational complexity of the time-delay Doppler domain channel estimation system. Moreover, the channel estimation method based on traditional OMP can only estimate parameters at grid points and cannot estimate frequency shift parameters at non-grid points. Summary of the Invention

[0006] The purpose of this invention is to address the problems of traditional orthogonal matched pursuit channel estimation methods being unable to estimate frequency shift parameters at non-grid points and having high computational complexity. Therefore, this invention proposes an off-grid block sparse orthogonal matched pursuit underwater acoustic time delay Doppler domain channel estimation method.

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

[0008] Step 1: Modulate the signal x(k,l) to be transmitted by the underwater motion platform using OTFS 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. The receiving end resamples the received signal and then performs down-conversion processing on the resampled signal to obtain the down-converted signal.

[0011] Step 4: Discretize the down-conversion signal, and then demodulate the discretized signal using OTFS to obtain the demodulated signal y(k,l).

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

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

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

[0015] Where k is the Doppler index of the time-delay Doppler domain grid. Let l represent the set of integers from 0 to N-1, where l is the time delay index of the time delay Doppler domain grid. Let n represent the 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 signal after the up-conversion process for:

[0018]

[0019] in, Indicates up-conversion processing, g tx (·) is the pulse shaping function at the transmitting end, t is time, T is the symbol period, e is the base of the natural logarithm, j is the imaginary unit, and f m Let m represent the frequency point of the m-th subcarrier, 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 Let α represent the channel gain and delay of the p-th path, respectively. p Let p represent the Doppler factor of the p-th path, where 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 denoted by , where represents the relative velocity between the moving units of the underwater platform, and c represents the speed of sound propagation underwater.

[0026] Furthermore, the OTFS demodulation of the discretized signal specifically involves:

[0027] Step 41: The discretized signal is processed by the pulse shaping function g at the receiving end. rx Then, after passing through the pulse shaping function g rx The signal is then subjected to an FFT transformation to obtain the FFT-transformed signal.

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

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

[0030] Step 51: Establish the compressed sensing matrix X based on the pilot component of the signal x(k,l) to be transmitted by the underwater motion platform. P The observation vector y is obtained from the pilot component of the signal y(k,l);

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

[0032] Step 52, based on r p-1 and X P Calculate the atomic index λ with the strongest matching in the p-th iteration. p ;

[0033] Step 53, based on λ p Update index set ξ p ;

[0034]

[0035] Step 54, according to ξ p Updated support set:

[0036] Λ p =Λ p-1 ∪ξ p

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

[0038] Step 55: Based on the support set Λ p Estimating sparse vectors:

[0039]

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

[0041] Steps 5 and 6: Obtain the time delay and Doppler factor at the grid point of the p-th path based on the sparse vector obtained in the p-th iteration, and then determine the channel gain at the grid point of the p-th path based on the time delay and Doppler factor at the grid point of the p-th path.

[0042] Step 57: Based on the channel gain at the grid points obtained in the p-th iteration, calculate the residual Doppler factor b of the p-th path after resampling. p ;

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

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

[0045] If p < P, then proceed to step 59;

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

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

[0048]

[0049] Where <·> denotes the calculation of the inner product, X P,j X represents P The j-th column in the array, j = 1, 2, ..., L, where L represents X P The total number of columns in the array, where |·| represents taking the absolute value.

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

[0051] The atomic index λ with the strongest matching pFor the center grid point of the p-th path, extend ω grid points to the left of the center grid point, and then extend ω grid points to the right of the center grid point. Use the maximum likelihood criterion to fit the equivalent index and channel gain corresponding to the center grid point and each extended grid point of the p-th path:

[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 p-th path p for:

[0055]

[0056] Here, frac(.) means extracting the fractional part within the parentheses.

[0057] Furthermore, the specific process of step 59 is as follows:

[0058]

[0059] The beneficial effects of this invention are:

[0060] This invention addresses the block-sparse nature of the time-delay Doppler domain input-output relationship in underwater OTFS communication. It proposes an off-network, block-sparse orthogonal matched pursuit channel estimation algorithm combining maximum likelihood fitting. First, channel parameters at integer grid points are obtained using the BOMP algorithm. Then, the residual Doppler factors at non-grid points are further refined using maximum likelihood fitting. This solves the problem that traditional OMP channel estimation methods in underwater OTFS communication can only estimate channel parameters at grid points. By estimating frequency shift parameters at non-grid points, this invention further improves the estimation accuracy of channel frequency shift parameters. Simultaneously, it avoids establishing a fractional-order dictionary during the channel parameter estimation process, thereby reducing system complexity to some extent. Attached Figure Description

[0061] Figure 1 This is a flowchart of the signal transmission and reception process of an underwater motion platform;

[0062] Figure 2 This is a flowchart of channel estimation;

[0063] Figure 3 This is a comparison chart of the minimum mean square estimation error between the channel estimation method of this invention and the traditional OMP estimation method;

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

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

[0066] Step 1: Modulate the signal x(k,l) to be transmitted by the underwater motion platform using OTFS 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, the signal reaches the receiving end (which can be a stationary or moving underwater platform). The receiving end resamples the received bandpass time domain signal and then performs down-conversion processing on the resampled signal to obtain the down-converted signal.

[0069] Step 4: Discretize the down-conversion signal, and then demodulate the discretized signal using OTFS to obtain the demodulated signal y(k,l).

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

[0071] The method of the present invention further includes a sixth step, which involves performing time-frequency domain MMSE equalization on the data portion of the demodulated signal y(k,l) based on the estimation result of the fifth step, to recover the signal transmitted by the underwater platform.

[0072] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the specific process of OTFS modulation is as follows:

[0073] Step 11: Perform ISFFT (Inverse Symmetric Finite Fourier Transform) on the signal x(k,l) to be transmitted 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 time-delay Doppler domain grid. Let l represent the set of integers from 0 to N-1, where l is the time delay index of the time delay Doppler domain grid. Let n represent the 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 result, and use the pulse-shaped signal s(t) as the OTFS modulated signal.

[0076] The other steps and parameters are the same as in Specific Implementation Method 1.

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

[0078] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method 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 transmitting end, t is time, T is the symbol period, e is the base of the natural logarithm, j is the imaginary unit, and f m Let m represent the frequency point of the m-th subcarrier, t∈(0,T).

[0081] Other steps and parameters are the same as in specific implementation method one or two.

[0082] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three 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, it is a multipath channel model), and h p and τ p Let α represent the channel gain and delay of the p-th path, respectively.p Let p represent the Doppler factor of the p-th path, where p = 1, 2, ..., P.

[0085] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0086] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the Doppler factor (reflecting the Doppler effect caused by the motion of the underwater platform) for the p-th path is:

[0087] α p =v p / c

[0088] Among them, v p denoted by , where represents the relative velocity between the moving units of the underwater platform, and c represents the speed of sound propagation underwater.

[0089] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0090] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the OTFS demodulation of the discretized signal is specifically as follows:

[0091] Step 41: The discretized signal is processed by the pulse shaping function g at the receiving end. rx (Same as the pulse shaping function at the transmitting end), then the pulse shaping function g rx The signal is then subjected to an FFT (Fast Fourier Transform) to obtain the FFT-transformed signal.

[0092] Step 4.2: Perform SFFT (Symplocantative Finite Fourier Transform) on the signal after FFT transformation, and use the SFFT transformed signal as the demodulated signal y(k,l).

[0093] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0094] Specific implementation method seven: Combination Figure 2 This embodiment is described below. The difference between this embodiment and any one of specific embodiments one through six is ​​that the specific process of step five is as follows:

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

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

[0097] Step 52, based on r p-1 and X P Calculate the atomic index λ with the strongest matching in the p-th iteration. p ;

[0098] Step 53, based on λ p Update index set ξ p ;

[0099]

[0100] Step 54, according to ξ p Updated support set:

[0101] Λ p =Λ p-1 ∪ξ p

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

[0103] Step 55: Based on the support set Λ p Estimating sparse vectors:

[0104]

[0105] in, Let X represent the sparse vector obtained in the p-th iteration. P (Λ p ) represents the support set Λ p In X P The matrix composed of the corresponding column vectors (i.e., using the support set Λ) p The index in X P The corresponding column vectors form a matrix), y(Λ) p ) represents the support set Λ p The vector formed by the corresponding elements in y (i.e., using the support set Λ) p The index in y corresponds to the element in y, which forms a vector. The superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix.

[0106] Steps 5 and 6: Obtain the time delay and Doppler factor at the grid point of the p-th path based on the sparse vector obtained in the p-th iteration, and then determine the channel gain at the grid point of the p-th path based on the time delay and Doppler factor at the grid point of the p-th path.

[0107] Step 57: Based on the channel gain at the grid points obtained in the p-th iteration, calculate the residual Doppler factor b of the p-th path after resampling. p ;

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

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

[0110] If p < P, then proceed to step 59;

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

[0112] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

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

[0114] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step five-two is as follows:

[0115]

[0116] Where <·> denotes the calculation of the inner product, X P,j X represents P The j-th column in the array, j = 1, 2, ..., L, where L represents X P The total number of columns in the array, where |·| represents taking the absolute value.

[0117] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0118] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the specific process of step five and seven is as follows:

[0119] The atomic index λ with the strongest matching pFor the center grid point of the p-th path, extend ω grid points to the left of the center grid point, and then extend ω grid points to the right of the center grid point. Use the maximum likelihood criterion to fit the equivalent index and channel gain corresponding to the center grid point and each extended grid point of the p-th path:

[0120]

[0121] Where q represents the equivalent index (the path block of the p-th path is composed of the center grid point and the extended grid points, 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 p-th path p for:

[0123]

[0124] Here, frac(.) means extracting the fractional part within the parentheses.

[0125] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0126] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the specific process of step five nine is as follows:

[0127]

[0128] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

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

[0130] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An off-network block sparse orthogonal matching pursuit underwater acoustic delay Doppler domain channel estimation method, characterized in that, The method specifically includes the following steps: Step 1: Modulate the signal x(k,l) to be transmitted by the underwater motion platform using OTFS 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. The receiving end resamples the received signal and then performs down-conversion processing on the resampled signal to obtain the down-converted signal. Step 4: Discretize the down-conversion signal, and then demodulate the discretized signal using OTFS to obtain the demodulated signal y(k,l). Step 5: Estimate the time delay, channel gain, and residual Doppler factor of each path on each grid point in the channel based on the demodulated signal y(k,l) to obtain the channel estimation result; The specific process of step five is as follows: Step 51: Establish the compressed sensing matrix X based on the pilot component of the signal x(k,l) to be transmitted by the underwater motion platform. P The observation vector y is obtained from the pilot component of the signal y(k,l); The signal sparsity is initialized to P, the constant ω is initialized, the residual r0 = y is initialized, and the support set is initialized. Initialize the number of iterations p = 1; Step 52, based on r p-1 and X P Calculate the atomic index λ with the strongest matching in the p-th iteration. p ; Step 53, based on 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 Updated support set: L p =L p-1 ∪ξ p Among them, Λ p This represents the support set after the p-th iteration update; Step 55: Based on the support set Λ p Estimating sparse vectors: in, Let X represent the sparse vector obtained in the p-th iteration. P (Λ p ) represents the support set Λ p In X P The matrix formed by the corresponding column vectors in y(Λ) p ) represents the support set Λ p The vector formed by the corresponding elements in y, where the superscript T represents the transpose of the matrix and the superscript -1 represents the inverse of the matrix; Steps 5 and 6: Obtain the time delay and Doppler factor at the grid point of the p-th path based on the sparse vector obtained in the p-th iteration, and then determine the channel gain at the grid point of the p-th path based on the time delay and Doppler factor at the grid point of the p-th path. Step 57: Based on the channel gain at the grid points obtained in the p-th iteration, calculate the residual Doppler factor b of the p′-th path after resampling. p′ ; Step 58: Determine whether p = P is satisfied; If p = P, then the estimation ends; If p < P, then proceed to step 59; Step 59, according to Calculate the updated residual error r p Then set p = p + 1 and return to step 52.

2. The method for estimating the Doppler domain channel of off-network block sparse orthogonal matching pursuit underwater acoustic delay according to claim 1, characterized in that, The specific process of OTFS modulation is as follows: Step 11: Perform ISFFT transformation on the signal x(k,l) to be transmitted by the underwater motion platform to obtain the time-frequency domain data X[n,m] after ISFFT transformation; Where k is the Doppler index of the time-delay Doppler domain grid. Let l represent the set of integers from 0 to N-1, where l is the time delay index of the time delay Doppler domain grid. Let n represent the 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 method for estimating the Doppler domain channel of off-network block sparse orthogonal matching pursuit underwater acoustic delay according to claim 2, characterized in that, The signal after upconversion for: in, Indicates up-conversion processing, g tx (·) is the pulse shaping function at the transmitting end, t is time, T is the symbol period, e is the base of the natural logarithm, j is the imaginary unit, and f m Let m represent the frequency point of the m-th subcarrier, t∈(0,T).

4. The method for estimating the Doppler domain channel of off-network block sparse orthogonal matching pursuit underwater acoustic delay 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′ Let α represent the channel gain and delay of the p-th path, respectively. p′ Let p' represent the Doppler factor of the p-th path, where p' = 1, 2, ..., P'.

5. The method for estimating the underwater acoustic delay in the Doppler domain using off-network block sparse orthogonal matching pursuit as described in claim 4, characterized in that... The Doppler factor of the p′-th path is: a p′ =v p / c Among them, v p denoted by , where represents the relative velocity between the moving units of the underwater platform, and c represents the speed of sound propagation underwater.

6. The method for estimating the Doppler domain channel of off-network block sparse orthogonal matching pursuit underwater acoustic delay 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 processed by the pulse shaping function g at the receiving end. rx Then, after passing through the pulse shaping function g rx The signal is then subjected to an FFT transformation to obtain the FFT-transformed signal. Step 42: Perform SFFT transformation on the signal after FFT transformation, and use the SFFT transformed signal as the demodulated signal y(k,l).

7. The method for estimating the Doppler domain channel of off-network block sparse orthogonal matching pursuit underwater acoustic delay according to claim 6, characterized in that, The specific process of step 52 is as follows: λ p =argmax j＝1,2,...,L |<r p-1 ,X P,j >| Where <·> denotes the calculation of the inner product, X P,j X represents P The j-th column in the array, j = 1, 2, ..., L, where L represents X P The total number of columns in the array, where |·| represents taking the absolute value.

8. The method for estimating the underwater acoustic delay in the Doppler domain using off-network block sparse orthogonal matching pursuit as described in claim 7, is characterized in that... The specific process of step five or seven is as follows: The atomic index λ with the strongest matching p For the center grid point of the p′-th path, extend ω grid points to the left of the center grid point, and then extend ω grid points to the right of the center grid point. Use the maximum likelihood criterion to fit the equivalent index and channel gain corresponding to the center grid point and each extended grid point of the p′-th path: 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 p′-th path p′ for: Here, frac(.) means extracting the fractional part within the parentheses.

9. The method for estimating the Doppler domain channel of off-network block sparse orthogonal matching pursuit underwater acoustic delay according to claim 8, characterized in that, The specific process of step 59 is as follows:

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