Low-frequency underwater acoustic channel estimation method based on time-frequency analysis

Abstract

The invention provides a low-frequency underwater acoustic channel estimation method based on time-frequency analysis. The method comprises the following steps: firstly, applying matched filtering to a signal received by a single hydrophone so as to optimize a time-frequency structure and ensure that the time-frequency structure meets application conditions of time-domain warping transformation; and then the matched signal is converted into a linear combination of a plurality of single-frequency single-mode signals by using time domain warping transformation, and a nonlinear time-frequency structure caused by mode group delay is compensated, so that mode decomposition is easier to perform. After decomposition, the inter-modal frequency dispersion effect is significantly weakened, and the effective length of a channel is shortened. At the moment, the LS method is adopted to estimate each single-mode channel, so that the estimation precision can be effectively improved. And finally, a more accurate global channel estimation result is obtained through channel reconstruction. The method is suitable for a single hydrophone receiving system, channel estimation errors can be effectively reduced, a receiving end can recover original information more accurately, and therefore the reliability of shallow sea low-frequency underwater acoustic communication is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic communication, and in particular to a low-frequency underwater acoustic channel estimation method based on time-frequency analysis. Background Art

[0002] Underwater acoustic communication technology, as an important means of underwater information transmission, plays a vital role in the exploration and development of marine resources and monitoring of the marine environment. However, the complexity of underwater acoustic channels, particularly the significant multimodality and modal dispersion in shallow, low-frequency underwater acoustic channels, can cause varying degrees of time delay in underwater signal propagation, leading to severe inter-symbol interference (ISI), posing significant challenges to signal transmission. In such a complex channel environment, obtaining accurate channel estimation is crucial for improving the performance of underwater acoustic communication systems and reducing bit error rates.

[0003] In the process of implementing the embodiments of the present invention, the following defects are found in the prior art: (1) The traditional least squares (LS) channel estimation algorithm is sensitive to noise and interference, and it is difficult to provide high-precision channel estimation in a complex underwater acoustic channel environment, resulting in a decrease in communication performance; (2) Delay spread causes the channel impulse response length to increase, making the channel estimation method based on optimization theory highly computationally complex and having limited stability; (3) The existing sparsity-based channel estimation method has significant limitations in shallow water low-frequency underwater acoustic channels, mainly because the sparsity assumption may be destroyed in this environment, and such methods fail to fully consider the modal dispersion characteristics unique to shallow water low-frequency channels, making it difficult to achieve effective targeted processing. Summary of the Invention

[0004] The purpose of the present invention is to provide a low-frequency underwater acoustic channel estimation method based on time-frequency analysis to overcome the influence of inter-modal and intra-modal dispersion in shallow water low-frequency acoustic channels on the accuracy of traditional channel estimation, so as to solve the problems of impaired channel sparsity in shallow water low-frequency environments and the decreased accuracy of traditional least squares (LS) channel estimation algorithms in such channel environments.

[0005] The present invention is implemented by the following technical solution. The present invention proposes a low-frequency underwater acoustic channel estimation method based on time-frequency analysis, which includes the following steps:

[0006] Step 1: Apply matched filtering to the single hydrophone received signal to optimize its time-frequency structure and ensure that it meets the applicable conditions of time domain warping transform;

[0007] Step 2: Use time domain warping transform to convert the matched signal into a linear combination of multiple single-frequency single-mode signals to compensate for nonlinear frequency changes;

[0008] Step 3: Separate and extract the single-modal signal by time-frequency mask filtering, and restore the single-modal signal to the original time domain by inverse warping transformation;

[0009] Step 4: Use the LS method to estimate each single-mode channel separately, and finally obtain a more accurate global channel estimation result through channel reconstruction.

[0010] Furthermore, in step 1, the signal passes through the shallow sea low-frequency underwater acoustic channel, and the received signal passing through the channel is specifically expressed as:

[0011] y(t)=h(t)*s(t)+n(t) (1)

[0012] Where * represents the convolution operation, h(t) is the channel impulse response, n(t) is the channel noise, and s(t) is the transmitted signal.

[0013] Furthermore, in step 1, before performing time domain warping on the signal, it is necessary to perform matched filtering on the received signal; the signal after filtering is:

[0014] r(t)=y(t)*h mf (t) (2)

[0015] Among them, h mf (t) is the impulse response of the matched filter, which is taken as the conjugate inverse of the known signal s(t):

[0016] h mf (t) = s * (-t) (3)

[0017] Therefore, the formula for matched filtering can be written as:

[0018] r(t)=y(t)*s * (-t) (4)

[0019] According to the normal wave theory, r(t) can be expressed as:

[0020]

[0021] where r m (t) represents the m-th order single-mode signal, which is specifically expressed as:

[0022]

[0023] Let f m (t) is the instantaneous frequency of the m-th order single-mode signal, then:

[0024]

[0025] Where f om=(2m-1)c / 4H, c is the speed of sound in the waveguide, H is the water depth, t0=r / c, r is the propagation distance.

[0026] Furthermore, in step 2, a time domain warping transform is performed on the matched filtered signal, and the transform formula is:

[0027]

[0028] In the formula Ensures the energy conservation of the signal before and after the transformation; w -1 It represents the inverse function of the function w(t'), which maps the original time t to the new time axis t'; the transformed signal is:

[0029]

[0030] Where t' is the time variable after warping transformation; is a composite function operator, specifically expressed as The transformed signal is expressed as the sum of single-mode signals, and the instantaneous frequency of each single-mode signal is:

[0031] f wm (t') = f om (10)

[0032] That is, the transformed signal can be regarded as a linear superposition of a series of dispersion-free single-mode signals with the modal cutoff frequency as the fundamental frequency.

[0033] Furthermore, in step 3, the time-frequency mask filtering is used to separate and extract the single-modal signal, specifically:

[0034] Perform time-frequency transform: Perform short-time Fourier transform (STFT) on the warping-transformed time-domain signal to map the multimodal signal to the time-frequency domain and obtain its time-frequency representation:

[0035] R w (t',f')=∫ r w (τ')ω(τ'-t')e -j2πf'τ' dτ' (11)

[0036] Where ω(t') is the analysis window function;

[0037] Define time-frequency mask: Define the time-frequency mask based on the modal cutoff frequency:

[0038]

[0039] Where Q is the region in the time-frequency domain corresponding to the single-order mode to be extracted;

[0040] Modal filtering: Use the defined time-frequency mask to filter the multimodal signal and extract the single-modal signal to achieve modal decomposition:

[0041] R wm (t',f')=R w (t',f')M(t',f') (13)

[0042] Perform inverse time-frequency transform: Use inverse short-time Fourier transform (ISTFT) to reconstruct the filtered signal and obtain the time domain representation of the separated single-mode signal:

[0043]

[0044] where A is the normalization factor and v(t') is the synthesis window function, which is associated with the analysis window ω(t').

[0045] Furthermore, the inverse warping transform restores the single-modal signal to the original time domain, and the formula is:

[0046]

[0047] In the formula Indicates the inverse time domain coordinate transformation of the signal;

[0048] In order to facilitate the subsequent single-mode channel estimation, r m (t) Perform discrete sampling to obtain observation data r in the form of discrete vectors m ; This discrete process can be expressed as:

[0049] r m =[r m (t1),r m (t2),…,r m (t N )] T (16)

[0050] Among them, t n is the sampling time, and N is the number of sampling points.

[0051] Furthermore, the LS method is used to estimate each single-mode channel separately, and the formula is:

[0052]

[0053] in is the matrix of the probe signal after matched filtering; the estimation result at this time is Channels corresponding to only a single modality.

[0054] Furthermore, the channel reconstruction is specifically as follows: repeating steps 3-4 to obtain the estimation results of each single-mode channel respectively; after all single-mode channels are estimated, these independently obtained channel estimation results are reconstructed:

[0055]

[0056] At this time, the obtained is the estimation result of the multimodal global channel.

[0057] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the low-frequency underwater acoustic channel estimation method based on time-frequency analysis are implemented.

[0058] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the low-frequency underwater acoustic channel estimation method based on time-frequency analysis.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] The present invention provides an innovative low-frequency underwater acoustic channel estimation method based on time-frequency analysis. This method first uses matched filtering to preprocess the received signal of a single hydrophone, ensuring that it meets the applicable conditions for time-domain warping transform. A time-domain warping transform is then used to convert a multimodal signal with nonlinear time-frequency characteristics into a linear combination of single-modal signals with linear time-frequency characteristics. Intra-modal dispersion is compensated, making modal decomposition easier. Mask filtering is then performed in the time-frequency domain to effectively separate the different modal components in the signal without relying on detailed ocean environment data or a multi-element hydrophone array. The inter-modal dispersion effect is significantly reduced, thereby shortening the channel extension length and improving the output signal-to-noise ratio. Furthermore, the LS channel estimation method is combined to independently estimate the single-modal channel, effectively improving the estimation accuracy. Channel reconstruction is then performed based on the physical characteristics of the shallow-water low-frequency acoustic channel, resulting in a more accurate global channel estimation result. This series of improvements significantly enhances the accuracy of shallow-water low-frequency acoustic channel estimation, providing a more robust and efficient solution for shallow-water low-frequency underwater acoustic communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0062] Figure 1 This is a flow chart of a low-frequency underwater acoustic channel estimation method based on time-frequency analysis described in the present invention.

[0063] Figure 2 This is a schematic diagram showing the comparison results of the normalized mean square error (NMSE) curves between the TW-MD-LS channel estimation algorithm proposed in the present invention and the traditional LS channel estimation algorithm. DETAILED DESCRIPTION

[0064] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0065] The method described in the present invention introduces the time-domain warping-assisted modal decomposition (TW-MD) technology and proposes a LS-based TW-MD (TW-MD-LS) channel estimation algorithm. The method first applies matched filtering to the single hydrophone received signal to optimize its time-frequency structure and ensure that it meets the applicable conditions of the time-domain warping transform. The time-domain warping transform is then used to convert the matched signal into a linear combination of multiple single-frequency single-modal signals, compensating for the nonlinear time-frequency structure caused by the modal group delay, making it easier to perform modal decomposition. After decomposition, the inter-modal dispersion effect is significantly weakened, and the effective length of the channel is shortened. At this time, the LS method is used to estimate each single-modal channel separately, which can effectively improve the estimation accuracy. Finally, a more accurate global channel estimation result is obtained through channel reconstruction. The present invention is applicable to a single-hydrophone receiving system, can effectively reduce the channel estimation error, and enable the receiving end to more accurately restore the original information, thereby improving the reliability of shallow water low-frequency underwater acoustic communication.

[0066] Specifically, combined Figure 1-Figure 2 The present invention proposes a low-frequency underwater acoustic channel estimation method based on time-frequency analysis, which includes the following steps:

[0067] Step 1: Apply matched filtering to the single hydrophone received signal to optimize its time-frequency structure and ensure that it meets the applicable conditions of time domain warping transform;

[0068] In step 1, the signal passes through the shallow sea low-frequency underwater acoustic channel, and the received signal through the channel is specifically expressed as:

[0069] y(t)=h(t)*s(t)+n(t) (1)

[0070] Where * represents the convolution operation, h(t) is the channel impulse response, n(t) is the channel noise, and s(t) is the transmitted signal.

[0071] Before performing time domain warping on the signal, the received signal needs to be matched filtered; the signal after filtering is:

[0072] r(t)=y(t)*h mf (t) (2)

[0073] Among them, h mf (t) is the impulse response of the matched filter, which is taken as the conjugate inverse of the known signal s(t):

[0074] h mf (t) = s * (-t) (3)

[0075] Therefore, the formula for matched filtering can be written as:

[0076] r(t)=y(t)*s * (-t) (4)

[0077] According to the normal wave theory, r(t) can be expressed as:

[0078]

[0079] where r m (t) represents the m-th order single-mode signal, which is specifically expressed as:

[0080]

[0081] Let f m (t) is the instantaneous frequency of the m-th order single-mode signal, then:

[0082]

[0083] Where f om =(2m-1)c / 4H, c is the speed of sound in the waveguide, H is the water depth, t0=r / c, r is the propagation distance.

[0084] It can be seen that the instantaneous frequency of each order simple normal wave changes nonlinearly with time, and it is difficult to directly separate the single mode signal r from r(t). m (t), so the nonlinear frequency conversion needs to be compensated.

[0085] Step 2: Use time domain warping transform to convert the matched signal into a linear combination of multiple single-frequency single-mode signals to compensate for nonlinear frequency changes;

[0086] In step 2, the time domain warping transform is performed on the matched filtered signal. The transform formula is:

[0087]

[0088] In the formula Ensures the energy conservation of the signal before and after the transformation; w -1 It represents the inverse function of the function w(t'), which maps the original time t to the new time axis t'; the transformed signal is:

[0089]

[0090] Where t' is the time variable after warping transformation; is a composite function operator, specifically expressed as The transformed signal is expressed as the sum of single-mode signals, and the instantaneous frequency of each single-mode signal is:

[0091] f wm (t') = f om (10)

[0092] That is, the transformed signal can be regarded as a linear superposition of a series of dispersion-free single-mode signals with the modal cutoff frequency as the fundamental frequency.

[0093] Step 3: Separate and extract the single-modal signal by time-frequency mask filtering, and restore the single-modal signal to the original time domain by inverse warping transformation;

[0094] In step 3, the time-frequency mask filtering is used to separate and extract the single-modal signal, specifically:

[0095] Perform time-frequency transform: Perform short-time Fourier transform (STFT) on the warping-transformed time-domain signal to map the multimodal signal to the time-frequency domain and obtain its time-frequency representation:

[0096] R w (t',f')=∫ r w (τ')ω(τ'-t')e -j2πf'τ' dτ' (11)

[0097] Where ω(t') is the analysis window function;

[0098] Define time-frequency mask: Define the time-frequency mask based on the modal cutoff frequency:

[0099]

[0100] Where Q is the region in the time-frequency domain corresponding to the single-order mode to be extracted;

[0101] Modal filtering: Use the defined time-frequency mask to filter the multimodal signal and extract the single-modal signal to achieve modal decomposition:

[0102] R wm (t',f')=R w (t',f')M(t',f') (13)

[0103] Perform inverse time-frequency transform: Use inverse short-time Fourier transform (ISTFT) to reconstruct the filtered signal and obtain the time domain representation of the separated single-mode signal:

[0104]

[0105] where A is the normalization factor and v(t') is the synthesis window function, which is associated with the analysis window ω(t').

[0106] The inverse warping transform restores the single-modal signal to the original time domain, and the formula is:

[0107]

[0108] In the formula Indicates the inverse time domain coordinate transformation of the signal;

[0109] In order to facilitate the subsequent single-mode channel estimation, r m (t) Perform discrete sampling to obtain observation data r in the form of discrete vectors m ; This discrete process can be expressed as:

[0110] r m =[r m (t1),r m (t2),…,r m (t N )] T (16)

[0111] Among them, t n is the sampling time, and N is the number of sampling points.

[0112] Step 4: Use the LS method to estimate each single-mode channel separately, and finally obtain a more accurate global channel estimation result through channel reconstruction.

[0113] The LS method is used to estimate each single-mode channel separately, and the formula is:

[0114]

[0115] in is the matrix of the probe signal after matched filtering; the estimation result at this time is Channels corresponding to only a single modality.

[0116] Channel reconstruction is as follows: repeat steps 3-4 to obtain the estimation results of each single-mode channel respectively; after all single-mode channels are estimated, these independently obtained channel estimation results are reconstructed:

[0117]

[0118] At this time, the obtained is the estimation result of the multimodal global channel.

[0119] Example

[0120] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0121] The embodiment of the present invention provides a low-frequency underwater acoustic channel estimation method based on time-frequency analysis. Figure 1 As shown, the specific steps include:

[0122] 1. Generate a send signal.

[0123] Channel estimation is performed using a probe signal. The probe signal consists of a pseudo-random m-sequence. By organizing the m-sequence into a Toeplitz matrix, a probe signal with a special structure is generated. Specifically, each column of the Toeplitz matrix X consists of a cyclically shifted version of the m-sequence.

[0124] 2. The signal passes through the shallow sea low-frequency underwater acoustic channel.

[0125] In practical applications, signals propagate through shallow, low-frequency underwater acoustic channels. To effectively estimate the channel, the first step is to establish the correlation between the probe signal input and output, and then, through matrix transformation, express the output as a parameter vector to be estimated. Specifically, the received signal is expressed as:

[0126] y=Xh+n

[0127] Where h is the discrete impulse response of the channel to be estimated, and n is the noise of the channel.

[0128] 3. Perform matched filtering on the received signal.

[0129] In practice, the received signal is first preprocessed, a key step of which is to apply matched filtering technology to make it meet the applicable conditions of the time domain warping transform. Specifically, the matched filter matrix is multiplied with the received signal to obtain the filtered vector r:

[0130] r=Cy

[0131] Where C is the matched filter matrix, which is designed based on the known probe signal matrix. In practical applications, it can be expressed as:

[0132] C=X H

[0133] 4. Perform time domain warping transformation to compensate for nonlinear frequency changes.

[0134] Perform time domain warping transform on the matched filtered signal:

[0135]

[0136] Where M represents the modal order contained in the channel.

[0137] The transformed signal is converted into a linear superposition of a series of dispersion-free single-mode signals, and the center frequency is the cutoff frequency of the mode.

[0138] 5. Binary mask filtering is used to separate and extract single-modal signals.

[0139] Use binary mask filtering to split the transformed signal into multiple components:

[0140] Step 5-1: Perform time-frequency transform: Apply short-time Fourier transform (STFT) to the signal processed by warping transform to generate its corresponding time-frequency matrix R w .

[0141] Step 5-2: Define a binary mask: Based on the prior knowledge of the modal cutoff frequency, define a binary mask matrix M in the time-frequency domain:

[0142]

[0143] The elements of the mask matrix take values of 0 or 1, where the elements with a value of 1 correspond to the region range Q corresponding to the single-order mode to be extracted, and the elements with a value of 0 correspond to other non-target mode regions.

[0144] Step 5-3: Signal filtering: Use the binary mask matrix defined in step 5-2 to perform element-by-element multiplication with the time-frequency matrix obtained in step 5-1 to achieve filtering. This operation only retains the signal components corresponding to the desired single mode, thus obtaining the time-frequency matrix of the single-mode signal:

[0145] R wm =R w Mm is the order corresponding to the extracted mode.

[0146] Step 5-4: Perform inverse time-frequency transform: Convert the time-frequency matrix of the single-modal signal obtained in step 5-3 back to the time domain through inverse short-time Fourier transform (ISTFT) to obtain the separated single-modal signal r hm .

[0147] 6. The inverse warping transform restores the single-modal signal to the original time domain.

[0148] The obtained single-mode signal is processed using the warping inverse transformation function.

[0149]

[0150] The r obtained after processing m The original single-mode signal in the time domain is successfully separated into modes.

[0151] 7. Use LS to estimate the single-mode channel.

[0152] Construct the probe signal matrix after matched filtering, denoted as

[0153]

[0154] For the LS problem, the goal is to minimize the sum of squared errors between the received signal and the model output. By solving the partial derivative of the objective function with respect to the channel parameter vector and setting it equal to zero, we can obtain an estimate of the channel parameter vector. The specific expression is:

[0155]

[0156] When C=X H When , the channel estimation result can be expressed as:

[0157]

[0158] When X is full rank, the channel estimation result can be further simplified as:

[0159]

[0160] The estimated results at this time Channels corresponding to only a single modality.

[0161] 8. Channel reconstruction.

[0162] For each unimodal channel, follow the method of steps 5-7 to obtain its estimation results. After all unimodal channels are estimated, these independently obtained channel estimation results are reconstructed to obtain the estimated value of the global channel:

[0163]

[0164] Where M is the total number of single-mode channels. is the final channel estimation result.

[0165] The proposed TW-MD-LS channel estimation method based on time-frequency analysis is compared with the traditional LS method. Simulations are performed in a shallow sea low-frequency environment with the following parameters: water depth H = 50 m, average underwater sound speed c = 1500 m / s, propagation distance r = 20 km, the sound source and hydrophone are both located on the seabed, and the channel contains the first five modes. The resulting NMSE curve is shown in Figure 2. Figure 2 shown.

[0166] Compared to the traditional LS method, this method significantly reduces channel estimation error, providing a performance gain of approximately 5dB, demonstrating its effectiveness in improving estimation accuracy. Furthermore, the method is simple in structure and easy to implement, suitable for single-hydrophone systems, and can further enhance the overall performance of underwater acoustic communication systems.

[0167] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the low-frequency underwater acoustic channel estimation method based on time-frequency analysis are implemented.

[0168] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the low-frequency underwater acoustic channel estimation method based on time-frequency analysis.

[0169] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. The non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DRRAM). It should be noted that the memory of the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0170] In the above embodiments, all or part of the embodiments may be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments may be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated therein. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a high-density digital video disc (DVD)), or a semiconductor medium (eg, a solid state disc (SSD)).

[0171] During implementation, each step of the above method can be completed by an integrated logic circuit of the hardware in the processor or by instructions in the form of software. The steps of the method disclosed in conjunction with the embodiments of the present application can be directly embodied as being executed by a hardware processor, or can be executed by a combination of hardware and software modules in the processor. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it will not be described in detail here.

[0172] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiment can be completed by an integrated logic circuit of the hardware in the processor or by instructions in the form of software. The above processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component. The various methods, steps, and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The steps of the method disclosed in the embodiments of the present application can be directly embodied as being executed by a hardware decoding processor, or can be executed by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium mature in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0173] The above is a detailed introduction to the low-frequency underwater acoustic channel estimation method based on time-frequency analysis proposed in the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A low-frequency underwater acoustic channel estimation method based on time-frequency analysis, characterized in that: The method comprises the following steps: Step 1: Apply matched filtering to the single hydrophone received signal to optimize its time-frequency structure and ensure that it meets the applicable conditions of time domain warping transform; Step 2: Use time domain warping transform to convert the matched signal into a linear combination of multiple single-frequency single-mode signals to compensate for nonlinear frequency changes; Step 3: Separate and extract the single-modal signal by time-frequency mask filtering, and restore the single-modal signal to the original time domain by inverse warping transformation; Step 4: Use the LS method to estimate each single-mode channel separately, and finally obtain a more accurate global channel estimation result through channel reconstruction.

2. The method according to claim 1, characterized in that In step 1, the signal passes through the shallow sea low-frequency underwater acoustic channel, and the received signal through the channel is specifically expressed as: y(t)=h(t)*s(t)+n(t) (1) Where * represents the convolution operation, h(t) is the channel impulse response, n(t) is the channel noise, and s(t) is the transmitted signal.

3. The method according to claim 2, characterized in that In step 1, before performing time domain warping on the signal, the received signal needs to be matched filtered; the signal after filtering is: r(t)=y(t)*h mf (t) (2) Among them, h mf (t) is the impulse response of the matched filter, which is taken as the conjugate inverse of the known signal s(t): h mf (t)=s * (-t) (3) Therefore, the formula for matched filtering can be written as: r(t)=y(t)*s * (-t) (4) According to the normal wave theory, r(t) can be expressed as: where r m (t) represents the m-th order single-mode signal, which is specifically expressed as: Let f m (t) is the instantaneous frequency of the m-th order single-mode signal, then: Where f om =(2m-1)c / 4H, c is the speed of sound in the waveguide, H is the water depth, t0=r / c, r is the propagation distance.

4. The method according to claim 3, characterized in that In step 2, the time domain warping transform is performed on the matched filtered signal. The transform formula is: In the formula Ensures the energy conservation of the signal before and after the transformation; w -1 It represents the inverse function of the function w(t'), which maps the original time t to the new time axis t'; the transformed signal is: Where t' is the time variable after warping transformation; is a composite function operator, specifically expressed as The transformed signal is expressed as the sum of single-mode signals, and the instantaneous frequency of each single-mode signal is: f wm (t')=f om (10) That is, the transformed signal can be regarded as a linear superposition of a series of dispersion-free single-mode signals with the modal cutoff frequency as the fundamental frequency.

5. The method according to claim 4, characterized in that In step 3, the time-frequency mask filtering is used to separate and extract the single-modal signal, specifically: Perform time-frequency transform: Perform short-time Fourier transform (STFT) on the warping-transformed time-domain signal to map the multimodal signal to the time-frequency domain and obtain its time-frequency representation: R w (t',f')=∫ r w (t')ω(t'-t')e -j2πf'τ' dt' (11) Where ω(t') is the analysis window function; Define time-frequency mask: Define the time-frequency mask based on the modal cutoff frequency: Where Q is the region in the time-frequency domain corresponding to the single-order mode to be extracted; Modal filtering: Use the defined time-frequency mask to filter the multimodal signal and extract the single-modal signal to achieve modal decomposition: R wm (t',f')=R w (t',f')M(t',f') (13) Perform inverse time-frequency transform: Use inverse short-time Fourier transform (ISTFT) to reconstruct the filtered signal and obtain the time domain representation of the separated single-mode signal: where A is the normalization factor and v(t') is the synthesis window function, which is associated with the analysis window ω(t').

6. The method according to claim 5, characterized in that The inverse warping transform restores the single-modal signal to the original time domain, and the formula is: In the formula Indicates the inverse time domain coordinate transformation of the signal; In order to facilitate the subsequent single-mode channel estimation, r m (t) Perform discrete sampling to obtain observation data r in the form of discrete vectors m ; This discrete process can be expressed as: r m =[r m (t1),r m (t2),…,r m (t N )] T (16) Among them, t n is the sampling time, and N is the number of sampling points.

7. The method according to claim 6, characterized in that The LS method is used to estimate each single-mode channel separately, and the formula is: in is the matrix of probe signals after matched filtering; the estimation result at this time is Channels corresponding to only a single modality.

8. The method according to claim 7, characterized in that Channel reconstruction is as follows: repeat steps 3-4 to obtain the estimation results of each single-mode channel respectively; after all single-mode channels are estimated, these independently obtained channel estimation results are reconstructed: At this time, the obtained is the estimation result of the multimodal global channel.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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