A method for estimating a multi-carrier underwater acoustic communication channel under time-delay and scale dual expansion

Abstract

The application discloses a kind of multi-carrier underwater acoustic communication channel estimation methods under time delay-scale double expansion, for general multi-carrier underwater acoustic channel model, the influence of insufficient characterization of Doppler effect, and the precision of traditional channel estimation method is limited, it is proposed to utilize time delay-scale double expansion channel model to characterize the influence of Doppler effect on multi-carrier underwater acoustic communication system, and utilize orthogonal matching pursuit algorithm to separate multipath signal, and the delay and size parameter estimation results of each path of channel are corrected using Newton method, while realizing off-grid channel estimation, reduce algorithm complexity.The characterization of the present application to Doppler effect is more in line with the real scene, and realizes off-grid channel estimation and low complexity algorithm, so that the channel estimation result is more accurate.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication, and in particular to a method for estimating multi-carrier underwater acoustic communication channels under time delay-scale dual extension. Background Technology

[0002] Multicarrier communication, with its advantages of high spectral efficiency, high communication rate, and strong resistance to multipath interference, has become a key technology in underwater acoustic communication. However, the relative motion between the transmitter and receiver in underwater acoustic channels easily introduces significant Doppler effects, causing inter-carrier interference and severely degrading the performance of multicarrier systems. Especially in high-speed mobile scenarios, underwater acoustic channels exhibit broadband characteristics, and traditional time-delay-Doppler spread models are insufficient to accurately describe their response characteristics. In contrast, channel modeling methods based on time-delay-scale dual spread more closely approximate the actual propagation mechanism. Therefore, research on channel estimation based on this model has significant theoretical and applied value.

[0003] Achieving robust multi-carrier underwater acoustic communication in channels with both delay and scale extension has become a pressing computational challenge. Currently, traditional channel estimation methods, such as orthogonal matched pursuit (ORP), rely on discretized grids for sparse reconstruction. In practical underwater acoustic environments, grid mismatch can easily lead to decreased estimation accuracy, making it difficult to meet the demands of high-precision communication. ORP, however, adds a Newton correction step, effectively achieving high-precision estimation of the parameters to be estimated. Although ORP has been applied to many parameter estimation problems, it still lacks systematic adaptation and optimization in multi-carrier underwater acoustic communication scenarios, requiring further research and application. Summary of the Invention

[0004] To address the problem of severe inter-carrier interference caused by signal compression and broadening due to the Doppler effect in multi-carrier systems, this invention proposes a channel estimation method for multi-carrier underwater acoustic communication under time-delay-scale dual-expansion, starting from the time-delay-scale dual-expansion channel model of multi-carrier systems and utilizing Newton's correction and cyclic correction. This method more accurately characterizes the impact of the Doppler effect on multi-carrier communication and performs de-grid correction on the estimation results of delay and size parameters for each path of the channel, achieving off-grid channel estimation and low algorithm complexity, enabling robust communication of multi-carrier systems in high-speed mobile scenarios.

[0005] The specific technical solution is as follows:

[0006] A method for estimating multi-carrier underwater acoustic communication channels under time-delay-scale dual spread includes the following steps:

[0007] S1: Acquire the received signal, downsample it to obtain the symbol rate passband signal, multiply each multicarrier symbol by the receive matrix to obtain the demodulated baseband symbol;

[0008] S2: Establish a time-delay-scale dual-spread channel model with discrete time-delay grids and scale grids, and construct a discrete atom dictionary matrix in the two-dimensional parameter space of time-delay and scale coefficients based on pilot and received pilot symbols.

[0009] S3: Perform a coarse search on the discrete atom dictionary matrix on the discrete time delay grid and scale grid to initially estimate the parameters of the strongest path. Then subtract the energy of the estimated path to obtain the residual of the remaining path energy. Continue to estimate the parameters of the current strongest path. Repeat the above operation until the coarse estimation of all path parameters is completed.

[0010] S4: Calculate the residual for each path, and use the Newton-Raphson iteration method to correct the parameters of each path multiple times to improve the estimation accuracy of time delay and scale; then, based on the channel parameters corrected by Newton, recalculate the residual for each path; repeat the above operation to iteratively correct the parameters of each path.

[0011] S5: Output the parameter estimation results for all paths, including complex amplitude, time delay and scaling coefficient, and construct the estimated channel matrix.

[0012] Further, step S1 includes the following sub-steps:

[0013] S1.1: Obtain the received signal from the receiver;

[0014] S1.2: Downsample the received signal at preset time intervals to obtain the symbol rate passband signal;

[0015] S1.3: Multiply each multicarrier symbol by a receive matrix to obtain the demodulated baseband symbol.

[0016] Further, step S2 includes the following sub-steps:

[0017] S2.1: Based on the length N of the pilot sequence q Extract the first N from the demodulated baseband symbols q One symbol, to obtain the received pilot symbol;

[0018] S2.2: Based on the pilot sequence and the received pilot symbols, establish a time-delay-scale dual-spread channel model:

[0019] S2.3: Construct a time-delay grid and a scale grid as an atomic dictionary, and construct a discrete atomic dictionary matrix.

[0020] Furthermore, step S3 includes the following sub-steps:

[0021] S3.1: First, initialize the path number p=0, and the residual e p Equal to pilot symbol y q And give the number of multipaths P;

[0022] S3.2: Traverse the discrete atom dictionary and select the scale α and time delay that maximize the normalized modulus of the product of the discrete atom dictionary matrix and the sparse coefficient vector. These are used as coarse estimates of the p+1th path scale and time delay, respectively. and ;

[0023] S3.3: Update p=p+1, and roughly estimate the residual e p ;

[0024] S3.4: Determine if p is greater than P. If yes, complete the coarse estimation of all paths. If no, return to S3.2.

[0025] Further, step S4 includes the following sub-steps:

[0026] S4.1: First, initialize the number of cycles r for the loop correction. c =1, and given the number of multipaths P and the total number of Newton corrections R. s and the total number of iterations R c , and the initial values ​​of the scale parameters, time delay, and complex amplitude for each path;

[0027] S4.2: Re-record the scale parameter and time delay estimate of each path as initial values ​​and form them into a column vector; initialize the index k=1 of the path to be optimized;

[0028] S4.3: Initialize the round r of Newton's correction s =1;

[0029] S4.4: Calculate the precise residual of the k-th path. And for α and in the cost function Find the first and second derivatives to obtain the gradient matrix and Hansen matrix of the cost function;

[0030] S4.5: Substitute the current estimates of the k-th path scale parameter and time delay into the gradient matrix and Hansen matrix of the cost function, calculate the correction step size, perform a Newton correction, and update r. s =r s +1;

[0031] S4.6: Determine r s Is it greater than R? s If so, then complete the Newton correction for the k-th path scale parameter and time delay, obtain the corrected value for the complex amplitude of the k-th path, and update k=k+1, letting r s =1, execute S4.7; otherwise, return to S4.4;

[0032] S4.7: Determine if k is greater than P. If so, complete the Newton correction for all path parameters and update r. c =r c +1, execute S4.8; otherwise, return to S4.3;

[0033] S4.8: Determine r c Is it greater than R? c If yes, then complete the iterative correction of all path parameters; otherwise, return to S4.2.

[0034] Furthermore, the preset time interval is Where m is the current subcarrier index, M is the number of subcarriers, and T S The period of a multi-carrier symbol.

[0035] Furthermore, the discrete atom dictionary matrix in S2.3 is composed of... It consists of column vectors, where... M is the number of delay grids. α The number of scale grids; each column vector of the discrete atom dictionary matrix is ​​represented as ,in, It is a matrix formed by performing the Kronecker product between an identity matrix of dimension 1 (length of the pilot symbol) and the pilot symbols; To be consistent with scale The relevant matrices, This is a matrix related to time delay.

[0036] A multi-carrier underwater acoustic communication channel estimation system under time-delay-scale dual extension includes one or more processors for implementing the multi-carrier underwater acoustic communication channel estimation method under time-delay-scale dual extension.

[0037] An electronic device, comprising:

[0038] One or more processors;

[0039] A storage device for storing one or more programs, which, when executed by the electronic device, enable the electronic device to implement a multi-carrier underwater acoustic communication channel estimation method under delay-scale dual extension.

[0040] A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements a method for estimating multi-carrier underwater acoustic communication channels under delay-scale dual extension.

[0041] The beneficial effects of this invention are as follows:

[0042] (1) This invention uses a time delay-scale dual extended channel model to describe the impact of the Doppler effect on multicarrier communication, making its characterization of the Doppler effect more consistent with real-world scenarios.

[0043] (2) By introducing Newton correction and cyclic correction methods, this invention achieves low complexity of off-grid channel estimation and algorithm, making the channel estimation results more accurate. Attached Figure Description

[0044] Figure 1 This is a flowchart of a multi-carrier underwater acoustic communication channel estimation method under time-scale dual extension according to an embodiment of the present invention.

[0045] Figure 2 This is a flowchart of the coarse estimation part in an embodiment of the present invention.

[0046] Figure 3 This is a flowchart of the Newton correction and cyclic correction parts in an embodiment of the present invention.

[0047] Figure 4 This is a comparison chart of the root mean square error of different channel estimation results of the OFDM system in this embodiment of the invention.

[0048] Figure 5 This is a comparison chart of the root mean square error of different channel estimation results of the OCDM system in this embodiment of the invention. Detailed Implementation

[0049] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0050] like Figure 1 As shown, the multi-carrier underwater acoustic communication channel estimation method under time delay-scale dual extension of the present invention includes the following steps S1 to S5.

[0051] S1: Obtain the signal r(t) from the receiver, downsample it to obtain the symbol rate passband signal R, and then process the signal for each multicarrier symbol r. n Multiply by a receiver matrix G H The demodulated baseband symbol y is obtained. n .

[0052] S1 is implemented through the following sub-steps:

[0053] S1.1: Obtain the received signal r(t) from the receiver.

[0054] Receiver matrix G H It is the conjugate transpose of the transmission matrix G, which transposes each modulated symbol x consisting of M original symbols. nModulated into a multi-carrier symbol s n ,Right now Then N multicarrier symbols s n The transmitted signal s(t) is obtained after upsampling and pulse shaping, where n represents the nth multicarrier symbol and M represents the number of subcarriers.

[0055] The transmit matrix G is an M×M matrix, and its specific values ​​depend on the modulation scheme. For example, in an orthogonal frequency division multiplexing (OFDM) system,

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Where F is the discrete Fourier transform matrix, F i,j f represents the element in the i-th row and j-th column of F. i T is the center frequency of the i-th subcarrier, where i and j range from 1 to M; s G represents the period of a multicarrier symbol; F It is a pulse-shaping diagonal matrix, g tx (t) represents the pulse shaping filter, and β represents the roll-off factor.

[0063] In an orthogonal chirp division multiplexing (OCDM) system, the emission matrix G is represented as:

[0064]

[0065]

[0066]

[0067] in, It is a discrete Fresnel transformation matrix. express The element in the i-th row and j-th column, where i and j range from 1 to M. For subcarrier diagonal matrix, This is the center frequency of the total frequency band.

[0068] S1.2: For the received signal r(t) at intervals of... The time interval is downsampled to obtain the passband signal R of the symbol rate, that is: the symbol of the m-th subcarrier in the n-th received multicarrier symbol. Each M sampling points constitutes one multicarrier symbol, and the nth received multicarrier symbol is denoted as r. n T S The period of a multicarrier symbol is represented by m, where m represents the m-th subcarrier, and there are a total of M subcarriers.

[0069] S1.3: For each multicarrier symbol r n Multiply by a receiver matrix G H The demodulated baseband symbol y is obtained. n ,Right now .

[0070] S2: Establish a time-delay-scale dual-spread channel model with discrete time-delay grids and scale grids, and construct a discrete atomic dictionary matrix in the two-dimensional parameter space of time-delay and scale coefficients based on pilot and received pilot symbols.

[0071] S2 includes the following sub-steps:

[0072] S2.1: Based on pilot x q Length N q Extract the first N bits from the demodulated baseband symbol y. q The received pilot symbol y is obtained from the given symbols. q .

[0073] S2.2: Based on pilot x q and the received pilot symbol y q Establish a time-delay-scale dual-spread channel model:

[0074]

[0075] in,

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Among them, X q For dimension N qunit array and The matrix formed by performing the Kronecker product; P is the number of multipaths, η p Let p be the complex amplitude of the p-th path; α is the time delay of the p-th path; p Let A(α) be the scale parameter of the p-th diameter. p ) is the matrix related to the scale parameter of the p-th path; To be with α p The relevant intermediate variables have no specific physical meaning; for The element in the i-th row and j-th column; f j It is the center frequency of the j-th subcarrier; the values ​​of i and j range from 1 to M. A vector related to time delay; f1 ~ f M is the center frequency of the corresponding subcarrier, and w is noise.

[0082] S2.3: Constructing a Delay Mesh And the scale grid α is used as the atomic dictionary, and the elements in the time delay grid τ are... Uniformly selected within the interval The value, the element in the scale grid α, is in [1 / α]. max , α max Take M uniformly within the interval α 1 value; construct a discrete atom dictionary matrix The discrete atom dictionary matrix is ​​composed of It consists of column vectors, each column vector Represented as , where are elements in the α-scale grid α. It is an element in the time-delay grid τ.

[0083] S3: Perform a coarse search on the discrete atom dictionary matrix across the discrete time-delay grid τ and scale grid α to initially estimate the parameters of the strongest path. Then subtract the energy of the estimated path to obtain the residual e of the remaining path energy. p Continue to estimate the parameters of the current strongest path; repeat the above operation until a coarse estimate of all path parameters is completed.

[0084] like Figure 2 As shown, S3 is implemented through the following sub-steps:

[0085] S3.1: First, initialize the path number p=0 and the residual e p =y q And give the number of multipaths P.

[0086] S3.2: Traverse the discrete atom dictionary matrix and select those that make... The largest values ​​of α and τ are used as coarse estimates of the path scaling parameter and time delay of the (p+1)th path, respectively. and ,Right now Rough estimate of the corresponding complex amplitude ;

[0087] S3.3: Update p=p+1, and roughly estimate the residuals. ;

[0088] S3.4: Determine if p is greater than P. If yes, complete the coarse estimation of all paths. If no, return to S3.2.

[0089] S4: Calculate the residual r for each path. k The parameters of each path are corrected multiple times using the Newton-Raphson iterative method to improve the estimation accuracy of time delay and scale. Then, based on the channel parameters corrected by Newton, the residual r corresponding to each path is recalculated. k Repeat the above operation to iteratively correct the parameters for each path.

[0090] like Figure 3 As shown, S4 is implemented through the following sub-steps:

[0091] S4.1: First, initialize the number of cycles r for the loop correction. c =1, and given the number of multipaths P and the total number of Newton corrections R. s and the total number of iterations R c And the initial values ​​of the scale parameters, time delay, and complex amplitude for each path. , , ;

[0092] S4.2: Re-record the scale parameters and time delay estimates for each path as follows: , and form them into column vectors , and initialize the index k=1 for the path to be optimized;

[0093] S4.3: Initialize the round r of Newton's correction s =1;

[0094] S4.4: Calculate the precise residual of the k-th path. and the cost function α and Find the first and second derivatives to obtain the gradient matrix. and Hansen matrix ,in:

[0095]

[0096]

[0097] .

[0098] S4.5: The current estimated values ​​of the k-th path scale parameter and time delay. and Bring into and H In the middle, calculate the correction step size Perform a Newtonian correction. , update r s =r s +1.

[0099] S4.6: Determine r s Is it greater than R? s If so, then complete the Newton correction for the k-th radius scale parameter and time delay to obtain the value of the k-th radius complex amplitude correction. And update k=k+1, let r s =1, execute S4.7; otherwise, return to S4.4.

[0100] S4.7: Determine if k is greater than P. If so, complete the Newton correction for all path parameters and update r. c =r c +1, execute S4.8; otherwise, return to S4.3.

[0101] S4.8: Determine r c Is it greater than R? c If so, then complete the iterative correction of all path parameters, and record the estimated values ​​of the complex amplitude, time delay, and scale parameter of the final P-path as follows: , and If not, return to S4.2.

[0102] S5: Output the parameter estimation results for all paths, including complex magnitudes. Delay and scaling factor Construct the estimated channel matrix :

[0103]

[0104]

[0105] in, and These are the transmit matrix and the receive matrix, respectively. It is the discrete Fourier transform matrix. Therefore Let be a diagonal matrix with diagonal elements, where This represents the center frequency of the m-th subcarrier.

[0106] Corresponding to the aforementioned embodiments of the multi-carrier underwater acoustic communication channel estimation method under delay-scale dual extension, the present invention also provides an embodiment of a multi-carrier underwater acoustic communication channel estimation system under delay-scale dual extension.

[0107] The present invention provides a multi-carrier underwater acoustic communication channel estimation system under time-delay-scale dual extension, comprising one or more processors for implementing the multi-carrier underwater acoustic communication channel estimation method under time-delay-scale dual extension in the above embodiments.

[0108] The embodiment of the multi-carrier underwater acoustic communication channel estimation system under delay-scale dual extension of the present invention can be applied to any device with data processing capabilities, such as a computer or other similar device. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical system, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 5 The diagram shown is a hardware structure diagram of any device with data processing capabilities in which the multi-carrier underwater acoustic communication channel estimation system under the time delay-scale dual extension of the present invention is located. In addition to the processor, memory, network interface and non-volatile memory, the device with data processing capabilities in the embodiment may also include other hardware depending on the actual function of the device with data processing capabilities, which will not be described in detail here.

[0109] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0110] For the system embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0111] This invention also provides a computer-readable storage medium storing a program that, when executed by a processor, implements the multi-carrier underwater acoustic communication channel estimation method under time-delay-scale dual extension described in the above embodiments.

[0112] The computer-readable storage medium can be an internal storage unit of any data processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0113] To verify the performance of the method of the present invention, corresponding performance simulation experiments were conducted, and the following two examples illustrate this in detail.

[0114] Example 1: To verify the effectiveness of the channel estimation method under delay-scale spread in the present invention in an OFDM system, the parameters of this example are set as follows: communication frequency band of 2kHz-3kHz, signal bandwidth of 1kHz, number of subcarriers of 20, BPSK symbol mapping, and OFDM modulation. The received signal is affected by marine environmental noise simulated by Gaussian white noise, as well as by three multipaths: direct path, sea surface reflection path, and seabed reflection path. The maximum delay is 20ms, and the maximum scale change is 1.001, which is approximately equivalent to the three-segment Doppler effect at the moving speed.

[0115] The specific parameter settings are shown in Table 1 below.

[0116] Table 1. Specific parameters for OFDM underwater acoustic communication channel estimation under delay-scale spread.

[0117]

[0118] Under these simulation parameters, the proposed channel estimation algorithm has 3 Newton corrections and 3 cyclic corrections. 100 Monte Carlo experiments were conducted at different signal-to-noise ratios (SNRs). The root mean square error (RMS) of channel estimation within the SNR range of 0–20 dB was compared with that of the traditional orthogonal matching pursuit algorithm. Figure 3 As shown. By Figure 4 It can be seen that the channel estimation method proposed in this invention has a much higher estimation accuracy for OFDM delay-scale dual-spread channel parameters than the traditional orthogonal matching pursuit algorithm.

[0119] Example 2: To verify the effectiveness of the channel estimation method under delay-scale spread in the present invention in an OCDM system, the parameters of this example are set as follows: communication frequency band of 2kHz-3kHz, signal bandwidth of 1kHz, number of subcarriers of 20, BPSK symbol mapping, and OCDM modulation. The received signal is affected by marine environmental noise simulated by Gaussian white noise, as well as by three multipaths: direct path, sea surface reflection path, and seabed reflection path. The maximum delay is 20ms, and the maximum scale change is 1.001, which is approximately equivalent to the three-segment Doppler effect at the moving speed.

[0120] The specific parameter settings are shown in Table 2 below.

[0121] Table 2 Specific parameters for OCDM underwater acoustic communication channel estimation under delay-scale spread

[0122]

[0123] Under these simulation parameters, the proposed channel estimation algorithm has 3 Newton corrections and 3 cyclic corrections. 100 Monte Carlo experiments were conducted at different signal-to-noise ratios (SNRs). The root mean square error (RMS) of channel estimation within the SNR range of 0–20 dB was compared with that of the traditional orthogonal matching pursuit algorithm. Figure 5 As shown in the figure, the channel estimation method proposed in this invention has a much higher estimation accuracy for OCDM delay-scale dual-spread channel parameters than the traditional orthogonal matching pursuit algorithm.

[0124] In summary, this invention proposes a channel estimation method for multi-carrier underwater acoustic communication under time-delay and scale dual-spreading based on Discrete Fourier Transform and Newton's orthogonal matched pursuit algorithm. This method can achieve high-precision channel estimation for multi-carrier communication systems in high-speed motion scenarios at both the transceiver and receiver, thereby ensuring high-speed communication between high-speed underwater mobile platforms.

[0125] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for channel estimation of multi-carrier underwater acoustic communication under time-delay and scale dual expansion, characterized in that, Includes the following steps: S1: Acquire the received signal, downsample it to obtain the symbol rate passband signal, multiply each multicarrier symbol by the receive matrix to obtain the demodulated baseband symbol; the receive matrix is ​​the conjugate transpose of the transmit matrix G, which is expressed as: ； ； ； in, It is a discrete Fresnel transformation matrix. express The element in the i-th row and j-th column, where i and j range from 1 to M; For subcarrier diagonal matrix, T is the center frequency of the total frequency band; s Indicates the period of a multicarrier symbol; S2: Establish a time-delay-scale dual-spread channel model with discrete time-delay grids and scale grids, and construct a discrete atom dictionary matrix in the two-dimensional parameter space of time-delay and scale coefficients based on pilot and received pilot symbols. S2 includes the following sub-steps: S2.1: Based on pilot x q Length N q Extract the first N bits from the demodulated baseband symbol y. q The received pilot symbol y is obtained from the given symbols. q ; S2.2: Based on pilot x q and the received pilot symbol y q Establish a time-delay-scale dual-spread channel model: ； in, ； ； ； ； ； Among them, X q For dimension N q unit array and The matrix formed by performing the Kronecker product; P is the number of multipaths, η p Let p be the complex amplitude of the p-th path; α is the time delay of the p-th path; p Let A(α) be the scale parameter of the p-th diameter. p ) is the matrix related to the scale parameter of the p-th path; To be with α p The relevant intermediate variables have no specific physical meaning; for The element in the i-th row and j-th column; f j It is the center frequency of the j-th subcarrier; the values ​​of i and j range from 1 to M. A vector related to time delay; f1 ~ f M is the center frequency of the corresponding subcarrier, and w is noise; S2.3: Constructing a Delay Mesh And the scale grid α is used as the atomic dictionary, and the elements in the time delay grid τ are... Uniformly selected within the interval The value, the element in the scale grid α, is in [1 / α]. max , α max Take M uniformly within the interval α 1 value; construct a discrete atom dictionary matrix The discrete atom dictionary matrix is ​​composed of It consists of column vectors, each column vector Represented as Where α is an element in the scale grid α, It is an element in the time-delay grid τ; S3: Perform a coarse search on the discrete atom dictionary matrix on the discrete time delay grid and scale grid to initially estimate the parameters of the strongest path. Then subtract the energy of the estimated path to obtain the residual of the remaining path energy. Continue to estimate the parameters of the current strongest path. Repeat the above operation until the coarse estimation of all path parameters is completed. S4: Calculate the residual corresponding to each path, and use the Newton-Raphson iteration method to correct the parameters of each path multiple times to improve the estimation accuracy of time delay and scale; then, based on the channel parameters corrected by Newton, recalculate the residual corresponding to each path; repeat the above operation to iteratively correct the parameters of each path; S4 includes the following sub-steps: S4.1: First initialize the round r of loop correction c = 1, and given the number of multipaths P, the total number of Newton corrections R s and the total number of loop corrections R c and the initial values of the scale parameter, time delay and complex amplitude of each path; S4.2: Re-record the scale parameter and time delay estimate of each path as initial values ​​and form them into a column vector; initialize the index k=1 of the path to be optimized; S4.3: Initialization of the round r of Newton's correction s = 1; S4.4: Calculate the precise estimation residual r of the k-th path. k , And for α and in the cost function Find the first and second derivatives to obtain the gradient matrix and Hansen matrix of the cost function; S4.5: Substitute the current estimate of the kth diameter parameter and the time delay into the gradient matrix and Hessian matrix of the cost function, calculate the correction step, make one Newton correction, and update r s = r s + 1; S4.6: Determine r s Is it greater than R? s If so, then complete the Newton correction for the k-th path scale parameter and time delay, obtain the corrected value for the complex amplitude of the k-th path, and update k=k+1, letting r s =1, execute S4.7; otherwise, return to S4.4; S4.7: Determine if k is greater than P. If so, complete the Newton correction for all path parameters and update r. c =r c +1, execute S4.8; otherwise, return to S4.3; S4.8: Determine if r c is greater than R c , if so, complete the loop correction of all path parameters; if not, return to S4.2; S5: Output the parameter estimation results for all paths, including complex amplitude, time delay and scaling coefficient, and construct the estimated channel matrix.

2. The method of claim 1, wherein, Step S1 includes the following sub-steps: S1.1: Obtain the received signal from the receiving end; S1.2: Downsample the received signal at preset time intervals to obtain the symbol rate passband signal; S1.3: Multiply each multicarrier symbol by a receive matrix to obtain the demodulated baseband symbol.

3. The multi-carrier underwater acoustic communication channel estimation method under time-delay-scale dual spread as described in claim 1, characterized in that, S3 includes the following sub-steps: S3.1: First, initialize the path number p=0, and the residual e p Equal to pilot symbol y q And give the number of multipaths P; S3.2: iterate over the discrete atom dictionary matrix, select the scale a and the delay t that maximize the normalized modulus of the product of the discrete atom dictionary matrix and the sparse coefficient vector respectively as a coarse estimate of the p+1 st radial dimension and the delay and ; S3.3: Update p = p + 1, coarse estimate residual e p ; S3.4: Determine if p is greater than P. If yes, complete the coarse estimation of all paths. If no, return to S3.

2.

4. The method of claim 2, wherein, The preset time interval is wherein m is the serial number of the current subcarrier, M is the number of subcarriers, T S is the period of one multicarrier symbol.

5. A system for estimating a multi-carrier underwater acoustic communication channel under time-delay and scale dual expansion, characterized in that, It includes one or more processors for implementing the multi-carrier underwater acoustic communication channel estimation method under time delay-scale dual extension as described in any one of claims 1 to 4.

6. An electronic device, comprising: include: One or more processors; A storage device for storing one or more programs, which, when executed by the electronic device, cause the electronic device to implement the delay-scale dual-spread multicarrier underwater acoustic communication channel estimation method as described in any one of claims 1 to 4.

7. A computer readable storage medium characterized in that, It stores a program that, when executed by a processor, implements the multi-carrier underwater acoustic communication channel estimation method under time delay-scale dual extension as described in any one of claims 1 to 4.

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