Multi-channel underwater acoustic OFDM (Orthogonal Frequency Division Multiplexing) communication method and system based on joint optimization sparse channel estimation

Abstract

The invention relates to the technical field of underwater acoustic communication, in particular to a multi-channel underwater acoustic OFDM (Orthogonal Frequency Division Multiplexing) communication method and system based on joint optimization sparse channel estimation. Selecting sparse signals and designing a measurement matrix; a step of performing dimension reduction on the original signal by using a compressed sensing technology; a step of performing sparse recovery on the observation signal and the measurement matrix by using an orthogonal matching pursuit algorithm, including a step of performing sparsity detection by using global approximate message passing GAMP; based on a high-probability support set output by the GAMP, accurate reconstruction is carried out through a local orthogonal matching pursuit LOMP algorithm, sparse optimization is carried out on signals, and multi-channel underwater acoustic OFDM communication based on joint optimization sparse channel estimation is achieved. According to the method, the traditional channel estimation process is simplified by utilizing the sparse characteristic of the channel, and the performance and efficiency of an underwater acoustic communication system are greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic communication technology, and in particular to a multi-channel underwater acoustic OFDM communication method and system based on jointly optimized sparse channel estimation. Background Art

[0002] Underwater acoustic communication, as an important means of underwater information exchange, has extensive application requirements in the fields of marine resource exploration, seabed observation, marine scientific research, etc. By researching and implementing a Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) underwater acoustic communication system, the development of underwater communication technology can be promoted, providing a more advanced and reliable communication solution for related fields. Since the propagation speed of sound waves in water is very slow, and there are severe multipath effects in the underwater channel, which leads to severe inter-symbol interference. Moreover, in the case of unchanged channel parameters, inter-code interference will increase with the increase of the symbol rate. Severe inter-code interference will cause the receiving end to be unable to correctly demodulate and recover the original signal, and thus effective information cannot be obtained. In addition, the underwater acoustic channel often exhibits sparsity, and the performance of traditional channel estimation methods is poor in this environment, and the original signal cannot be accurately recovered.

[0003] Based on the above, the following defects exist in the prior art: (1) In the underwater acoustic communication system, the channel shows sparsity in both the time domain and the frequency domain. The traditional Least Square (LS) channel estimation method usually cannot provide sufficiently accurate channel estimation when facing a highly sparse channel due to ignoring the influence of noise; (2) A single channel estimation algorithm has limitations. Summary of the Invention

[0004] The present invention provides a multi-channel underwater acoustic OFDM communication method and system based on jointly optimized sparse channel estimation. Aiming at the problems of low channel estimation accuracy, waste of pilot resources, and high computational complexity in underwater communication due to complex multipath propagation and significant noise interference, the sparse characteristics of the channel are used to simplify the traditional channel estimation process, greatly improving the performance and efficiency of the underwater acoustic communication system.

[0005] In contrast, the other three master's theses mainly perform channel sparse modeling based on the compressed sensing theory and use a single recovery algorithm for estimation, failing to implement the joint optimization strategy of global coarse estimation and local refinement, resulting in certain limitations when dealing with complex underwater communication environments.

[0006] The present invention is realized through the following technical solutions:

[0007] A multi-channel underwater acoustic OFDM communication method based on joint optimization sparse channel estimation, the method is as follows:

[0008] Steps of selecting a sparse signal and designing a measurement matrix;

[0009] Steps of dimension reduction of the original signal by using compressive sensing technology;

[0010] Steps of sparse recovery of the observed signal and the measurement matrix by using the orthogonal matching pursuit algorithm, including steps of sparse detection by using the global approximate message passing GAMP;

[0011] Steps of precise reconstruction by using the local orthogonal matching pursuit LOMP algorithm based on the high-probability support set output by GAMP to optimize the sparsity of the signal, realizing multi-channel underwater acoustic OFDM communication based on joint optimization sparse channel estimation.

[0012] Furthermore, the selection of the sparse signal and the design of the measurement matrix are specifically as follows:

[0013] Signal sparse representation: Select a suitable sparse basis such that the signal is sparse under this basis, satisfying h = Ψs, where is a sparse vector, that is, most of the non-zero elements are zero or close to zero, and only K significant non-zero elements;

[0014] Design of the measurement matrix: That is, for all sparse vectors s, there exists a constant δ K ∈(0, 1) such that:

[0015]

[0016] Furthermore, the dimension reduction of the original signal by using compressive sensing technology is specifically as follows: The high-dimensional original signal h is dimension-reduced and sampled by the measurement matrix X, satisfying:

[0017] y = Xh + w (2)

[0018] where is the low-dimensional observed signal, is Gaussian white noise.

[0019] Furthermore, combining the compressive sensing theory and the channel sparse characteristics,

[0020] The sparse detection by using the global approximate message passing GAMP is specifically as follows: The approximate message passing algorithm AMP is used for global sparse estimation of the compressed observed signal; AMP is used to solve the following compressive sensing problem:

[0021] y = Cx + w (3)

[0022] Among them, is the observation vector, is the measurement matrix, is the sparse signal to be estimated, and w is Gaussian noise;

[0023] Furthermore, the AMP iteration steps are as follows:

[0024] Steps for initializing the signal estimation and the residual;

[0025] Signal estimation y = Cx + w (4)

[0026] Residual r (0) = y (5)

[0027] Steps for updating the residual with the Onsager correction term and updating the signal;

[0028] Residual update

[0029] Among them, η(·; τ 2 ) is the Bayesian threshold function:

[0030] Soft threshold function η(μ; θ) = sign(u)·max(|u| - θ, 0) (7)

[0031] Among them, θ is adaptively adjusted according to the noise level, and η'(·) is its derivative.

[0032] Signal update

[0033] Steps for realizing state evolution based on the residual update and the signal update, that is, for predicting the error distribution after each round of iteration:

[0034]

[0035] Steps for realizing global sparse support detection based on state evolution, that is, through continuous iteration, AMP can output the probabilistic information of each dimension in the signal being non - zero; assuming the estimated vector is obtained after the iteration termination, a support score can be constructed:

[0036]

[0037] The positions of the top K components with the highest scores are formed into the candidate support set ∧.

[0038] Furthermore, the high-probability support set output based on GAMP is accurately reconstructed by the local orthogonal matching pursuit (LOMP) algorithm. The specific sparse optimization of the signal is as follows: Based on the ∧ set provided by AMP, the orthogonal matching pursuit (OMP) algorithm is used to perform local accurate reconstruction within this high-confidence region, realizing the collaborative optimization from sparse detection to sparse reconstruction.

[0039] Furthermore, steps for initializing the residuals and support set of OMP;

[0040] Residual r (0) = y (11)

[0041] Support set

[0042] Steps for each iteration of OMP;

[0043] Select the atom with the maximum correlation

[0044] Update the support set Γ←Γ∪{j t} (14)

[0045] Least squares solution

[0046] Update the residual

[0047] The termination condition for each iteration is to reach the set number of iterations or for the residual to converge;

[0048] Steps for fusing the final output of OMP: The global rough estimate result output by AMP and the local compensation result of OMP are superimposed to obtain the final estimate:

[0049] Update the residual

[0050] A multi-channel underwater acoustic OFDM communication system based on jointly optimized sparse channel estimation. The system uses the multi-channel underwater acoustic OFDM communication method based on jointly optimized sparse channel estimation as described above. The system includes:

[0051] Measurement matrix design module: Select sparse signals and design the measurement matrix;

[0052] Dimensionality reduction acquisition module: Use compressive sensing technology to perform dimensionality reduction acquisition on the original signal;

[0053] Sparse recovery module: Use the orthogonal matching pursuit algorithm for sparse recovery of the observed signal and the measurement matrix, including using the global approximate message passing (GAMP) for sparsity detection;

[0054] Based on the high-probability support set output by GAMP, precise reconstruction is performed through the local orthogonal matching pursuit (LOMP) algorithm, enabling sparse optimization of the signal and realizing multi-channel underwater acoustic OFDM communication based on jointly optimized sparse channel estimation.

[0055] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned method is implemented.

[0056] A computer-readable storage medium stores a computer program therein. When the computer program is executed by a processor, the above-mentioned method is implemented.

[0057] The beneficial effects of the present invention are as follows:

[0058] The present invention can more accurately reflect the true characteristics of the channel, thereby improving the accuracy of channel estimation, and further enabling more accurate recovery of the original information at the receiving end.

[0059] By combining MIMO-OFDM technology with compressive sensing algorithms, the present invention significantly improves the performance and efficiency of underwater communication. The system utilizes the sparse characteristics of the underwater acoustic channel in the time domain and frequency domain, and the method of joint optimization of LOMP and GAMP to achieve high-precision and low-complexity channel estimation. The LOMP algorithm quickly locates the non-zero elements of the sparse signal through greedy iteration, while the GAMP algorithm further refines the estimation result through Bayesian inference and Gaussian approximation, and introduces the Onsager correction term to reduce the computational complexity. This joint optimization strategy overcomes the defects of traditional least squares estimation being sensitive to noise and having high sampling requirements, and at the same time solves the problem of high computational complexity of the matching pursuit algorithm. This system improvement significantly improves the spectral efficiency, reduces the number of channel samplings, enhances the anti-multipath interference ability, reduces the bit error rate, improves the robustness of the algorithm in scenarios with unknown sparsity through sparse prior modeling and adaptive parameter estimation, reduces the hardware cost and power consumption, is applicable to systems with resource constraints or equipped with multiple hydrophones, and can make full use of the space-time-frequency sparsity to improve the estimation accuracy and anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a flowchart of the method of the present invention.

[0061] Figure 2 Comparison diagram of mean square errors of different channel estimation algorithms.

[0062] Figure 3 Comparison diagram of the true sparse channel and the joint estimation result of GAMP-LOMP.

[0063] Figure 4Schematic diagram of the throughput performance of a 2×2 MIMO-OFDM system based on GAMP-LOMP estimation. Detailed implementation manners

[0064] In the following description, specific details such as specific system architectures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0065] It should be understood that when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, wholes, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0066] It should also be understood that the terms used in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the specification of the present application and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" are intended to include the plural forms.

[0067] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings of the present application specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the scope of protection of the present application.

[0068] Many specific details are set forth in the following description in order to provide a thorough understanding of the present application, but the present application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar generalizations without departing from the spirit of the present application. Therefore, the present application is not limited by the specific embodiments disclosed below.

[0069] Embodiment 1

[0070] This embodiment provides a multi-channel underwater acoustic OFDM communication method based on jointly optimized sparse channel estimation, as Figure 1As shown in the figure, the communication model fully considers the characteristics of the underwater acoustic channel and the constraints of hardware implementation during the design process. The system uses 1,024 subcarriers to implement orthogonal frequency division multiplexing, and the distribution of pilot subcarriers adopts a non-uniform interval strategy. By dynamically configuring 256 pilot positions with an interval coefficient of 4, this design strictly controls the pilot overhead within 25% while ensuring the accuracy of channel estimation. To overcome the delay spread caused by underwater multipath effects, the system sets the length of the cyclic prefix to one-fourth of the symbol period. The system adopts a 2-transmit and 2-receive antenna architecture, combining spatial diversity and multiplexing transmission modes. The receiving end realizes the equalization optimization of interference suppression and signal separation through a Minimum Mean Square Error (MMSE) detector. The method is as follows,

[0071] Steps of selecting a sparse signal and designing a measurement matrix;

[0072] Steps taken to reduce the dimension of the original signal using compressive sensing technology;

[0073] Steps of sparse recovery of the observed signal and the measurement matrix using the orthogonal matching pursuit algorithm, including steps of performing sparsity detection using global approximate message passing GAMP (Global Approximate Message Passing);

[0074] Based on the high-probability support set output by GAMP, perform precise reconstruction through the local orthogonal matching pursuit LOMP (Local Orthogonal Matching Pursuit) algorithm to optimize the sparsity of the signal, and realize multi-channel underwater acoustic OFDM communication based on jointly optimized sparse channel estimation.

[0075] Furthermore, the specific steps of selecting a sparse signal and designing a measurement matrix are as follows,

[0076] Signal sparse representation: Select a suitable sparse basis such that the signal is sparse under this basis, satisfying h = Ψs, where, is a sparse vector, that is, most of the non-zero elements are zero or close to zero, and only K significant non-zero elements (K << n, n is the length of the original signal);

[0077] Design a measurement matrix: The elements of the measurement matrix X follow the restricted isometry property to ensure that the signal can be accurately recovered; that is, for all sparse vectors s, there exists a constant δ K ∈(0,1) such that:

[0078]

[0079] Further, the dimensionality reduction of the original signal using compressive sensing technology is specifically achieved by performing dimensionality reduction sampling on the high-dimensional original signal h through the measurement matrix X, satisfying:

[0080] y = Xh + w (2)

[0081] where, is the low-dimensional observation signal, is Gaussian white noise.

[0082] Further, combining compressive sensing theory with the sparse characteristics of the channel, a two-stage hybrid estimation architecture called GAMP-LOMP (Global AMP with Local OMP refinement) is proposed to improve the modeling accuracy and recovery performance of underwater acoustic channels in complex environments. This method utilizes the ability of GAMP to quickly identify potential sparse structures in the entire signal domain and combines the fine reconstruction advantage of LOMP in high-confidence regions, thereby achieving efficient modeling and accurate estimation of complex underwater acoustic channels.

[0083] The specific process of using the global approximate message passing GAMP for sparsity detection is to perform global sparse estimation on the compressed observation signal using the global approximate message passing algorithm. AMP is used to solve the following compressive sensing problem:

[0084] y = Cx + w (3)

[0085] where, is the observation vector, is the measurement matrix, is the sparse signal to be estimated, and w is Gaussian noise;

[0086] AMP is derived from the belief propagation of factor graphs and can effectively perform approximate posterior estimation in large-scale signal scenarios through Gaussian approximation and the central limit theorem.

[0087] Further, the AMP iteration steps are as follows:

[0088] Steps for initializing the signal estimation and the residual;

[0089] Signal estimation y = Cx + w (4)

[0090] Residual r (0) = y (5)

[0091] Steps for updating the residual with the Onsager correction term and updating the signal;

[0092] Residual update

[0093] where, η(·; τ 2) is the Bayesian threshold function, often approximated in the form of a soft threshold function:

[0094] The soft threshold function η(μ;θ) = sign(u)·max(|u| - θ, 0) (7)

[0095] where θ is adaptively adjusted according to the noise level, and η'(·) is its derivative.

[0096] Signal update

[0097] Steps to implement state evolution based on residual update and signal update, i.e., used to predict the error distribution after each iteration:

[0098]

[0099] Steps to implement global sparse support detection based on state evolution, i.e., through continuous iteration, AMP can output the probabilistic information of each dimension in the signal being non - zero; assume the estimated vector obtained after the iteration terminates A support score can be constructed:

[0100]

[0101] The positions of the top K components with the highest scores are formed into a candidate support set ∧; this step reflects the "global signal screening" function of AMP.

[0102] Furthermore, for the high - probability support set output based on GAMP, it is precisely reconstructed through the local orthogonal matching pursuit LOMP algorithm. Specifically, for sparse optimization of the signal, based on the ∧ set provided by AMP, the orthogonal matching pursuit algorithm OMP is used to perform local precise reconstruction within this high - confidence region, realizing the collaborative optimization from sparse detection to sparse reconstruction.

[0103] Furthermore, steps to initialize the residual and support set of the orthogonal matching pursuit algorithm OMP;

[0104] Residual r (0) = y (11)

[0105] Support set

[0106] Steps for each iteration of the orthogonal matching pursuit algorithm OMP;

[0107] Select the atom with the maximum correlation

[0108] Update the support set Γ ← Γ ∪ {j t} (14)

[0109] Least - squares solution

[0110] Updated residual

[0111] The termination condition for each iteration is to reach the set number of iteration steps or residual convergence;

[0112] Steps for finally fusing the output of the orthogonal matching pursuit algorithm OMP: The globally rough estimated result output by AMP And the local compensation result of OMP Are superimposed to obtain the final estimate:

[0113] Updated residual

[0114] Specific embodiments formed according to the present invention are as follows:

[0115] 1. System composition and parameter setting

[0116] The communication system of the present invention is based on the MIMO - OFDM architecture and adopts a multi - antenna configuration of 2 transmit and 2 receive (i.e., 2×2 MIMO). Both the transmitter and the receiver are set as underwater acoustic transducer arrays commonly used in underwater environments. The system uses a total of 1,024 sub - carriers for orthogonal frequency - division multiplexing (OFDM). The pilot sub - carriers are arranged using a non - uniform spacing strategy. By dynamically configuring 256 pilot positions with a spacing coefficient of 4, the pilot overhead is controlled within 25%. A cyclic prefix with a length of 1 / 4 of the symbol period is added to each OFDM symbol period to resist underwater multipath effects.

[0117] The receiver is configured with a Minimum Mean Square Error (MMSE) detector to achieve interference suppression, decoupling, and equalization processing of multi - channel signals. The system design fully considers the sparsity and time - variability of the underwater channel, combines the compressed sensing theory, and effectively improves the channel estimation accuracy and system performance.

[0118] 2. Channel modeling and sparse signal construction

[0119] The underwater channel is modeled using a sparse impulse response model. The length of the channel impulse response is set to L = 12, where the number of non - zero taps K actually present is usually much smaller than the total length, for example, K = 10 - 20. The position of each non - zero tap follows a uniform distribution within [0, L - 1], and its complex amplitude conforms to an independent complex Gaussian distribution to reflect the multipath fading characteristics in the real underwater acoustic environment.

[0120] Through an appropriate sparse transform basis (such as the discrete Fourier transform DFT or the discrete cosine transform DCT), the original signal can be represented as a sparse vector With only a few significant non - zero components, and the rest approaching zero.

[0121] 3. Compressed Sensing Observation Generation

[0122] To reduce the observation dimension and sampling overhead, a compressed sensing framework is introduced to obtain the observation signal. A measurement matrix is designed to satisfy the restricted isometry property to ensure the reconstructability of the sparse signal. Common design methods include random Gaussian matrices, partial Fourier matrices, or sparse binary matrices with random perturbations added.

[0123] Channel Observation Signal is generated as follows:

[0124] y = Φx + n

[0125] where n is Gaussian white noise. This process is realized by projecting the pilot signal at the transmitter and the compressed observation signal is sent.

[0126] 4. Using the GAMP Algorithm for Global Support Detection

[0127] At the receiver, the GAMP (Global Approximate Message Passing) algorithm is first used to perform a preliminary sparse estimation of the compressed signal to identify the high-probability positions where non-zero components may exist in the signal.

[0128] 4-1. Initialization:

[0129] The initial signal estimate value is set to

[0130] The initial residual r (0) = y

[0131] 4-2. Iterative Update (t-th round):

[0132] Residual Update (including the Onsager term):

[0133] Signal Estimate Update: where η(·) is a soft threshold function with noise-adaptive adjustment:

[0134] η(x) = sign(x)·max(|x| - θ, 0)

[0135] State Evolution: Used to evaluate the evolution of the estimation error and control the iteration termination condition.

[0136] 4-3. Support Set Scoring and Extraction: The top K terms with the largest magnitudes in the final estimated vector are used as the candidate sparse support set S ANP to provide guidance for the next-stage accurate reconstruction.

[0137] 5. Using the LOMP Algorithm for Local Fine Reconstruction

[0138] Within the candidate support set extracted by AMP, the local orthogonal matching pursuit algorithm is further used for the accurate reconstruction of sparse signals;

[0139] The steps of the LOMP algorithm are as follows:

[0140] 5-1. Initialization:

[0141] Residual r (0) = y

[0142] Support set

[0143] The maximum number of iterations is set to T max

[0144] 5-2. Each round of iteration:

[0145] Calculate the correlation between the residual and each column in the measurement matrix:

[0146] Add to the support set

[0147] Estimate the sparse signal coefficients using the least squares method:

[0148] Update the residual:

[0149] If the residual modulus is less than the threshold or the maximum number of iterations is reached, terminate.

[0150] 5-3. Output the reconstruction result: Obtain the signal estimate accurately reconstructed at the sparse positions

[0151] 6. Fusion of GAMP and LOMP results

[0152] The rough estimate result obtained in the GAMP stage and the LOMP fine reconstruction result are weighted and fused to obtain the final sparse channel estimate: λ1 + λ2 = 1, which can be determined according to the channel environment or system training.

[0153] 7. Demodulation and performance optimization

[0154] 7-1. According to the estimated sparse channel impulse response, use a frequency domain equalizer and an MMSE detector to demodulate the OFDM signal.

[0155] 7-2. The system introduces an adaptive modulation mechanism based on SNR estimation:

[0156] When the SNR is lower than 5dB, use BPSK modulation;

[0157] When the SNR is higher than 10 dB, switch to QPSK modulation to improve the spectral efficiency.

[0158] 7-3. Add a digital predistortion module to compensate for the nonlinear distortion of the power amplifier and effectively reduce the error vector magnitude.

[0159] As Figure 2 shown, it shows the mean square error performance of different channel estimation algorithms at each SNR. The GAMP-LOMP algorithm of the present invention maintains the lowest error throughout the SNR range, with obvious advantages. At a high SNR of 30 dB, the algorithm of the present invention reduces the MSE to 10 -5 , and the accuracy is leading among other methods. In contrast, the MSE of OMP is still in the order of 10 -4 , and the difference between the two is one order of magnitude; this shows that the GAMP-LOMP algorithm of the present invention has a stronger sparse recovery ability, especially excellent performance under high SNR conditions. The LS algorithm maintains a high error at any SNR, indicating that it cannot effectively model the sparse channel structure.

[0160] In comparison, the GAMP-LOMP algorithm of the present invention better combines noise suppression and utilization of channel sparsity and is one of the optimal solutions.

[0161] As Figure 3 shown, it shows the comparison between the real channel and the estimated result of the GAMP-LOMP algorithm of the present invention in the time-delay tap domain. The outer AMP effectively suppresses the false path response caused by noise through probabilistic message passing. The inner OMP iteratively corrects the residual and accurately locks the position and amplitude of the main path.

[0162] In the main path estimation (time delays 0, 15, 25), the amplitude error of the joint algorithm is less than 3%.

[0163] For the weak path tap (such as time delay 5), the estimated value is 0.6 and the real value is 0.5, and the error is reduced by 42% compared with OMP.

[0164] The overall positioning accuracy of non-zero taps reaches 92.3%, which is improved by 67.8% compared with the LS method.

[0165] The present invention realizes the fine modeling of the impulse response by jointly optimizing the sparse structure and observation fitting. The results in the figure show that the GAMP-LOMP algorithm of the present invention not only maintains accuracy in the main path but also improves the perception ability of weak path signals.

[0166] As Figure 4As shown, it presents the curve of the throughput of a 2×2 MIMO-OFDM system estimated by the GAMP-LOMP algorithm based on the present invention varying with SNR. It can be seen that when the SNR increases from 5 dB to 10 dB, the throughput jumps from 6.5 kbps to 15.5 kbps, and the modulation mode of the system switches from BPSK to QPSK. This jump is driven by a significant improvement in channel estimation accuracy: the GAMP-LOMP algorithm of the present invention reduces the phase error by 58%, increasing the confidence level of constellation demodulation to 92%, thus supporting the stable demodulation of higher-order modulation. This joint estimation scheme realizes cross-layer optimization by enhancing the underlying channel sensing ability, and the spectral efficiency is increased by 1.38 times without increasing the transmit power, fully demonstrating the advantage of the GAMP-LOMP structure in throughput optimization.

[0167] Embodiment 2

[0168] This embodiment provides a multi-channel underwater acoustic OFDM communication system based on jointly optimized sparse channel estimation. The system uses the multi-channel underwater acoustic OFDM communication method based on jointly optimized sparse channel estimation as described in Embodiment 1. The system is

[0169] Measurement matrix design module: Select sparse signals and design the measurement matrix;

[0170] Dimensionality reduction acquisition module: Use compressive sensing technology to perform dimensionality reduction acquisition on the original signal;

[0171] Sparse recovery module: Use the orthogonal matching pursuit algorithm to perform sparse recovery on the observed signal and the measurement matrix, including using the global approximate message passing GAMP (Global Approximate Message Passing) for sparsity detection;

[0172] Based on the high-probability support set output by GAMP, perform precise reconstruction through the local orthogonal matching pursuit LOMP (Local Orthogonal Matching Pursuit, LOMP) algorithm to optimize the sparsity of the signal and achieve multi-channel underwater acoustic OFDM communication based on jointly optimized sparse channel estimation.

[0173] As can be seen from the above, the embodiment of the present invention utilizes the sparse characteristics of the channel to simplify the traditional channel estimation process, greatly improving the performance and efficiency of the underwater acoustic communication system. Experimental results show that this method improves the accuracy of channel estimation, and thus can more accurately recover the original information at the receiving end.

[0174] Embodiment 3

[0175] An embodiment of the present invention provides an electronic device. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. Among them, the memory is used to store software programs and modules. The processor executes various functional applications and data processing by running the software programs and modules stored in the memory. The memory and the processor are connected by a bus. Specifically, when the processor runs the computer program stored in the memory, any step in the first embodiment is implemented.

[0176] It should be understood that in the embodiment of the present invention, the so-called processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0177] The memory may include a read-only memory, a flash memory, and a random access memory, and provide instructions and data to the processor. A part or all of the memory may also include a non-volatile random access memory.

[0178] As can be seen from the above, the electronic device provided by the embodiment of the present invention can implement the multi-channel underwater acoustic OFDM communication method as described in the first embodiment by running a computer program, and obtain a two-stage hybrid estimation architecture called GAMP-LOMP (Global AMP with Local OMP refinement) for improving the modeling accuracy and recovery performance of the underwater acoustic channel in a complex environment.

[0179] It should be understood that if the above integrated modules / units are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, to implement all or part of the processes in the above-described implementation manners of the present invention, it can also be completed by a computer program instructing related hardware. The above computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above various method embodiments can be implemented. Among them, the above computer program includes computer program code, and the above computer program code can be in the form of source code, object code, executable file or some intermediate form, etc. The above computer-readable medium can include: any entity or device that can carry the above computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the above computer-readable storage medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0180] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

[0181] Those skilled in the art can clearly understand that for the convenience and brevity of description, only the above division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the above device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiments can be integrated into a processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of the present invention. The specific working processes of the units and modules in the above system can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0182] It should be noted that the methods and their detailed examples provided in the above embodiments can be combined with the devices and equipment provided in the embodiments and referred to each other, and will not be elaborated here.

[0183] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed in this article can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present invention.

[0184] In the embodiments provided by the present invention, it should be understood that the disclosed devices / terminal devices and methods can be implemented in other ways. For example, the device / equipment embodiments described above are only illustrative. For example, the above division of modules or units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0185] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A multi-channel underwater acoustic OFDM communication method based on jointly optimized sparse channel estimation, characterized in that The method is as follows: Steps of selecting a sparse signal and designing a measurement matrix; Steps of dimension reduction of the original signal using compressive sensing technology; Steps of sparse recovery of the observed signal and the measurement matrix using the orthogonal matching pursuit algorithm, including steps of sparse detection using the global approximate message passing GAMP; Steps of precise reconstruction using the local orthogonal matching pursuit LOMP algorithm based on the high-probability support set output by GAMP to perform sparse optimization on the signal, realizing multi-channel underwater acoustic OFDM communication based on jointly optimized sparse channel estimation.

2. The method according to claim 1, wherein The specific steps of selecting a sparse signal and designing a measurement matrix are as follows: Sparse representation of signals: Selecting an appropriate sparse basis such that the signal is sparse under this basis, satisfying h = Ψs, where is a sparse vector, that is, most of the non-zero elements are zero or close to zero, and only K significant non-zero elements; Design measurement matrix: That is, for all sparse vectors s, there exists a constant δ K ∈(0, 1) such that:

3. The method according to claim 1, wherein The specific steps of dimension reduction of the original signal using compressive sensing technology are as follows: the high-dimensional original signal h is dimension-reduced and sampled by the measurement matrix X, satisfying: y = Xh + w (2) Among them, is a low-dimensional observation signal, is Gaussian white noise.

4. The method according to claim 1, wherein The specific steps of sparse detection using the global approximate message passing GAMP are as follows: the approximate message passing algorithm AMP is used for global sparse estimation of the compressed observed signal. AMP is used to solve the following compressive sensing problem: y = Cx + w (3) wherein, is the observation vector, is the measurement matrix, is the sparse signal to be estimated, and w is Gaussian noise.

5. The method according to claim 4, wherein The AMP iteration steps are as follows: Steps of initializing the signal estimation and the residual; Signal estimation y = Cx + w (4) Residual r (0) = y(5) Steps of updating the residual with the Onsager correction term and updating the signal; Residual update where η(·; τ 2 ) is the Bayesian threshold function: Soft threshold function η(μ; θ) = sign(u)·max(|u| - θ, 0) (7) where θ is adaptively adjusted according to the noise level, and η'(·) is its derivative. Signal update Steps of realizing state evolution based on the residual update and the signal update, that is, used to predict the error distribution after each iteration: Steps for realizing global sparse support detection based on state evolution, that is, through continuous iteration, AMP can output the probabilistic information of each dimension in the signal being non-zero; assume that the estimated vector is obtained after the iteration ends A support score can be constructed: The positions of the top K components with the highest scores are used to form the candidate support set ∧.

6. The method according to claim 1, wherein The specific steps of precise reconstruction using the local orthogonal matching pursuit LOMP algorithm based on the high-probability support set output by GAMP to perform sparse optimization on the signal are as follows: based on the ∧ set provided by AMP, the orthogonal matching pursuit algorithm OMP is used for local precise reconstruction within this high-confidence region, realizing the collaborative optimization from sparse detection to sparse reconstruction.

7. The method according to claim 6, wherein Steps of initializing the residual and the support set of OMP; Residual r (0) = y(11) Support set Steps of each iteration of OMP; Select the most relevant atom Update the support set Γ ← Γ ∪ {j t} (14) Least squares solution Updated residual The termination condition for each iteration is to reach the set number of iteration steps or the residual converges; Steps for fusing the final output of OMP: The globally roughly estimated result output by AMP is superimposed with the locally compensated result of OMP to obtain the final estimate: Updated residual .

8. A multi-channel underwater acoustic OFDM communication system based on jointly optimized sparse channel estimation, characterized in that The system uses the multi-channel underwater acoustic OFDM communication method based on jointly optimized sparse channel estimation as described in any one of claims 1-7. The system is as follows: Measurement matrix design module: selects a sparse signal and designs a measurement matrix; Dimension reduction module: performs dimension reduction on the original signal using compressive sensing technology; Sparse recovery module: performs sparse recovery on the observed signal and the measurement matrix using the orthogonal matching pursuit algorithm, including sparse detection using the global approximate message passing GAMP; Based on the high-probability support set output by GAMP, precise reconstruction is performed using the local orthogonal matching pursuit LOMP algorithm to perform sparse optimization on the signal, realizing multi-channel underwater acoustic OFDM communication based on jointly optimized sparse channel estimation.

9. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method described in any one of claims 1-7 is implemented.

10. A computer-readable storage medium, characterized in that, A computer program is stored in the computer-readable storage medium. When the computer program is executed by the processor, the method described in any one of claims 1-7 is implemented.

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