Compressive sensing shallow water acoustic channel estimation method based on atomic threshold and backtracking

Abstract

The application discloses a compressed sensing shallow sea acoustic channel estimation method based on an atom threshold and backtracking, and relates to the technical field of underwater communication. The application improves the gOMP algorithm by setting a reasonable atom screening threshold, introducing a backtracking thought and an iteration stopping condition based on noise, and applies the improved gOMP algorithm to a compressed sensing channel estimation framework of an underwater acoustic orthogonal frequency division multiplexing system, and proposes a gOMP channel estimation method based on an atom threshold and backtracking. The method performs secondary atom screening by setting a reasonable atom threshold, introduces a backtracking step and sets an iteration condition under noise, and is applied to a sparse shallow channel OFDM system. Experiments show that the method improves channel estimation accuracy, shortens estimation time by reducing algorithm calculation amount, and improves spectrum utilization rate by using fewer pilots.

Description

Technical Field

[0001] This invention relates to the field of underwater communication technology, specifically to a compressed sensing method for shallow water acoustic channel estimation based on atomic thresholds and backtracking. Background Technology

[0002] As humanity continues to develop and utilize the ocean, underwater communication technology has also been continuously improved. Underwater acoustic communication is the only way to achieve high-speed, high-reliability data transmission underwater. Today, it is widely used in scientific research, military, and commercial fields, such as seabed data collection, national security defense, and remote control of offshore oil operations. Underwater acoustic channels are considered the most complex channels. Shallow water acoustic channels are greatly affected by boundary conditions (sea surface and seabed) and seawater temperature distribution, making the shallow water channel environment even more complex and a typical multipath propagation channel with significant time delay. The prerequisite for achieving underwater acoustic communication in complex shallow water environments is obtaining accurate Channel State Information (CSI) through channel estimation. Channel estimation is also key to adaptive modulation at the transmitter, channel equalization techniques, and receiver design. Furthermore, it is the foundation for high-quality signal recovery and an important indicator for measuring the performance of underwater communication systems.

[0003] OFDM systems employ multi-carrier modulation to improve spectral efficiency and multipath interference resistance, thus they are widely used in underwater acoustic communication. However, due to the time-varying and high-noise characteristics of underwater channels, traditional channel estimation methods such as Least Square (LS) and Minimum Mean Square Error (MMSE) require a large number of subcarriers to transmit pilot information to ensure the accuracy of channel estimation, which seriously occupies spectrum resources. Furthermore, interpolation-based channel estimation methods cannot effectively eliminate the influence of frequency-selective fading caused by multipath, and cannot accurately estimate the channel frequency response at the data point, resulting in poor estimation performance.

[0004] Underwater acoustic channels are sparse channels with a large number of zero taps in their time-domain response. Compressed sensing algorithms can fully utilize this sparsity, achieving better channel estimation results with fewer pilots. The essence of compressed sensing algorithm reconstruction of sparse signals is an L0-norm optimization problem, which is an NP-hard non-convex optimization problem. The Basic Pursuit (BP) algorithm and the Least Absolute Shrinkage and Selection Operator (LASSO) algorithm replace the L0-norm with the L1-norm, transforming the problem into a more easily solvable convex optimization problem. These two algorithms improve estimation accuracy, but have high computational complexity and do not fully consider the impact of noise. The Basis Pursuit Denoising (BPDN) algorithm is an improvement on the BP algorithm in noisy conditions. It reconstructs the original signal by solving a perturbation linear programming problem. However, its algorithm complexity is greatly affected by the multipath delay of the channel, and its long running time makes it unsuitable for timely and effective estimation of complex and variable underwater acoustic channels. Greedy iterative algorithms are widely used in underwater acoustic channel estimation due to their high estimation accuracy, fast computation speed, simple hardware implementation, and robustness to noise. The Matching Pursuit (MP) algorithm, the earliest proposed classic greedy algorithm, approximates the original signal through multiple iterations. If the residual is not orthogonal after perpendicular projection onto the selected atoms, the optimal solution cannot be obtained in each iteration. The Orthogonal Matching Pursuit (OMP) algorithm, an improvement on the MP algorithm, guarantees the orthogonality of the residual and the selected atoms, thus avoiding the repeated selection of the same atoms, thereby improving estimation accuracy and convergence speed.

[0005] In existing technologies, several algorithms based on improvements to OMP have been proposed. Compressive Sampling Matching Pursuit (CoSaMP) and Regularized Orthogonal Matching Pursuit (ROMP) select multiple atoms in each iteration. CoSaMP employs a backtracking approach, while ROMP uses regularization criteria for secondary selection of atoms. Both algorithms offer improvements in estimation accuracy and speed compared to OMP. gOMP also selects multiple atoms in each iteration to reduce computation time and outperforms OMP in noise-free environments. However, its estimation performance is poor in underwater acoustic channels with high noise levels and low signal-to-noise ratios (SNR).

[0006] In summary, existing technologies have poor performance in estimating acoustic channels in shallow water, and there are still shortcomings in terms of estimation accuracy, running time, and spectrum saving. Summary of the Invention

[0007] The purpose of this invention is to provide a compressed sensing method for shallow water acoustic channel estimation based on atomic thresholds and backtracking. By improving gOMP from multiple perspectives through TB-gOMP, it can effectively estimate shallow water acoustic channels and has significant advantages over comparative algorithms in terms of estimation accuracy, running time, and spectrum saving.

[0008] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0009] A compressed sensing method for shallow water acoustic channel estimation based on atomic thresholds and backtracking is proposed. In the compressed sensing channel estimation framework of underwater acoustic orthogonal frequency division multiplexing system, a reasonable atomic threshold is proposed based on the gOMP algorithm to finely select atoms. The backtracking idea is introduced to eliminate the misselected atoms in the gOMP algorithm. A noise-based iterative stopping condition is set for shallow water acoustic channel estimation.

[0010] A compressed sensing method for shallow water acoustic channel estimation based on atomic thresholds and backtracking includes the following steps:

[0011] S0: Initialization, let r0 = Y p , t = 1;

[0012] Where the subscript "0" represents the initial value before the iteration, Let r represent the residual vector, r0 represent the initial value of r, and P represent the number of pilot subcarriers. This represents the received signal containing pilot data, i.e., the measurement vector; Λ represents the support set; and Λ0 represents the initial support set of Λ. Represents the empty set;

[0013] S1: Calculate the inner product and take its absolute value;

[0014] Where, m j Let the j-th column of matrix M be... Let r represent the sensing matrix, 1≤j≤L, r t-1 Let represent the residual vector of the (t-1)th iteration. Indicates r t-1 With m j The vector obtained by taking the inner product and its absolute value, u t Let represent the inner product vector of the t-th iteration, where "<·,·>" indicates the inner product operation and "|·|" indicates the absolute value operation.

[0015] S2: Selecting atoms: Choosing u tThe top S largest values ​​in M ​​are used to form a set C corresponding to column indices i in M. t ;

[0016] Where S is the atomic selection number, and i is the u t The S largest values ​​in M ​​correspond to column indices of M, and C is the set of column indices i. t Let be the set of column indices in the t-th iteration;

[0017] S3: Calculate the atomic threshold value α t ;

[0018] S4: Perform a second screening of atoms;

[0019] S5: Expanded support set;

[0020] S6: Estimate the channel using least squares operations;

[0021] S7: Backtracking: When length(h) t When ) > K, from h t The column indices corresponding to the K items with the largest absolute values ​​are selected from the set, and denoted as the set. Update support set And through support set updates and Otherwise, proceed directly to step S8;

[0022] S8: Update residuals:

[0023] S9: Determine whether the condition t > min(K, P / S) or ||r is met. t If ||2≤ε, proceed to step S10; otherwise, let t=t+1 and return to step S1.

[0024] S10: Output the final estimated sparse channel impulse response.

[0025] Furthermore, S3 calculates the atomic threshold value α. t :

[0026]

[0027] in, and Let u be the inner product vector in the t-th iteration. t The first and second maximum values, μ represents the trade-off factor parameter, which is generally taken as [0.2, 0.4];

[0028] S4 performs a secondary screening of atoms:

[0029] J t ={i|ut (i)>α t};

[0030] Among them, u t (i) is the inner product value corresponding to column index i, and J is the inner product value u corresponding to i. t (i) Greater than the atomic threshold α t The set of column indices, J t Let J be the set in the t-th iteration;

[0031] The S5 expansion support set:

[0032] Λ t =Λ t-1 ∪J t .,

[0033] Where ∪ represents the union, and Λ represents the support set Λ of the (t-1)th iteration. t-1 With J in the t-th iteration t Merged into the support set Λ of the t-th iteration t ; and These represent the sensing matrix M corresponding to the set Λ respectively. t-1 J t Λ t A matrix composed of column vectors;

[0034] S6 estimates the channel using least squares operations:

[0035]

[0036] Right now:

[0037]

[0038] The superscript "H" indicates the conjugate transpose of the matrix, and the superscript "-1" indicates the inverse operation of the matrix. t This represents the estimated channel impulse response;

[0039] Furthermore, the S7 backtracking:

[0040] When length(h) t When ) > K, from h t The column indices corresponding to the K items with the largest absolute values ​​are selected from the set, and denoted as the set. Update support set And through support set updates and Otherwise, proceed directly to step S8;

[0041] Here, length(·) represents the length of the vector.

[0042] Furthermore, S9 determines whether the condition t > min(K, P / S) or ||r is met. t If ||2≤ε, proceed to step S10; otherwise, let t=t+1 and return to step S1.

[0043] Where min(·,·) denotes the minimum function, ||·||2 denotes the L2 norm of the vector, and ε takes the value of ||G p ||2,G p This represents the frequency domain noise at the pilot frequency.

[0044] The beneficial effects of this invention are:

[0045] This invention improves the generalized orthogonal matching pursuit (gOMP) algorithm by setting reasonable atomic screening thresholds, introducing backtracking, and using noise-based iterative stopping conditions. It then applies this improvement to the compressed sensing channel estimation framework of an underwater acoustic orthogonal frequency division multiplexing (OFDM) system, proposing a gOMP channel estimation method based on atomic thresholds and backtracking, named TB-gOMP.

[0046] This invention proposes TB-gOMP, which improves upon gOMP from multiple perspectives. First, it proposes a reasonable atomic threshold for fine-tuning atomic selection, improving the reliability of the support set. The reduced number of atoms lowers the computational cost of least squares, relatively increasing the computational speed. Furthermore, the secondary atomic selection reduces the impact of the number of atoms selected (S) on algorithm performance. Second, the TB-gOMP algorithm incorporates backtracking to eliminate misselected atoms found in the gOMP algorithm. Finally, the iteration conditions are carefully designed to account for noise factors, improving the overall performance of the algorithm. Multiple experimental results demonstrate that the proposed algorithm can effectively estimate shallow sea acoustic channels and exhibits significant advantages over comparative algorithms in terms of estimation accuracy, running time, and spectral efficiency.

[0047] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0048] Figure 1 This is a flowchart of the compressed sensing shallow water acoustic channel estimation method based on atomic threshold and backtracking as described in an embodiment of the present invention;

[0049] Figure 2 This is a sound velocity profile of a certain sea area as described in an embodiment of the present invention;

[0050] Figure 3This is the impulse response diagram of the underwater acoustic channel simulated by BELLHOP according to an embodiment of the present invention;

[0051] Figure 4 NMSE of different channel estimation methods described in the embodiments of the present invention;

[0052] Figure 5 BER of different channel estimation methods described in the embodiments of the present invention;

[0053] Figure 6 The NMSE of channel estimation with different pilot numbers described in the embodiments of the present invention. Detailed Implementation

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings.

[0055] A compressed sensing method for shallow water acoustic channel estimation based on atomic thresholds and backtracking is proposed. In the compressed sensing channel estimation framework of underwater acoustic orthogonal frequency division multiplexing system, a reasonable atomic threshold is proposed based on the gOMP algorithm to finely select atoms. The backtracking idea is introduced to eliminate the misselected atoms in the gOMP algorithm. A noise-based iterative stopping condition is set for shallow water acoustic channel estimation.

[0056] The present invention will now be described in conjunction with specific embodiments:

[0057] Example 1

[0058] In this embodiment:

[0059] The published method is an improved underwater acoustic channel estimation method based on the gOMP algorithm:

[0060] In underwater acoustic communication, the impulse response of a time-varying underwater acoustic channel is generally defined as follows:

[0061]

[0062] Consider an OFDM system with N subcarriers, and assume that the channel coherence time is much longer than the OFDM symbol period, during which the channel response is time-invariant. Then the formula can be written as:

[0063]

[0064] The input data stream undergoes modulation, serial-to-parallel conversion, and inverse fast Fourier transform to obtain a time-domain signal x(n), which is then transmitted through an underwater acoustic channel.

[0065] y(n) = x(n) * h(n) + g(n)

[0066] Here, h(n) is the time-domain channel impulse response after discretization of h(τ). After convolving x(n) and h(n), Gaussian white noise g(n) is added to finally obtain the output signal y(n). To avoid inter-symbol interference, a cyclic prefix (CP) is added before the OFDM symbol. The length of the CP is greater than the maximum delay spread τ. max .

[0067] After removing the CP and performing an N-point Fast Fourier Transform on y(n), we obtain:

[0068]

[0069] The frequency domain received signal is:

[0070] Y = XH + G = XDh + G

[0071] Where X = diag(X0, X1…X) N-1 ) represents the useful data and pilot data carried in the OFDM symbol, with a dimension of N×N. H is the N×1 channel frequency domain response, which is obtained by performing an N-point Discrete Fourier Transform (DFT) on the time-domain channel impulse response. Specifically, it is expressed as H = Dh, which is the product of the DFT matrix D and the time-domain channel impulse response h.

[0072] In the compressed sensing OFDM framework, P pilot subcarriers, known to both the transmitter and receiver, are first obtained using the pilot localization matrix R, and then the complete channel impulse response is recovered using these subcarriers. The formula can then be written as:

[0073] Y P =X P D P h+G P

[0074] Among them, Y P =RY is the received signal containing pilot data, referred to here as the measurement vector, X P =RXR T For the transmitted signal containing pilot data, the sparse matrix D p It is a DFT matrix of dimension P×L, G P =RG is the noise signal at the pilot frequency, let the sensing matrix M = X p ×D p Then the formula can be written as:

[0075] Y P =Mh+G P

[0076] To ensure that the formula yields a unique sparse solution, M should satisfy the Restricted Isometry Property (RIP):

[0077]

[0078] Where δ 2k It is a constant related to the sparsity K, if δ 2k If M << 1, then M has a relatively high probability of stably reconstructing the sparse signal h from K.

[0079] Based on the above theory, this invention proposes the following three improvements to the gOMP algorithm:

[0080] In this embodiment, the atomic screening threshold is as follows:

[0081] Calculate the inner product vector of the residual and each column of the sensing matrix:

[0082] u t =|<r t-1 ,m j >|

[0083] Where, m j Let the j-th column of matrix M be... Let r represent the sensing matrix, 1≤j≤L, r t-1 Let represent the residual vector of the (t-1)th iteration. Indicates r t-1 With m j The vector obtained by taking the inner product and its absolute value, u t Let represent the inner product vector of the t-th iteration, where "<·,·>" indicates the inner product operation and "|·|" indicates the absolute value operation.

[0084] Select u t The top S largest values ​​in M ​​are used to form a set C corresponding to column indices i in M. t Choose the inner product vector u t First maximum value Second maximum value Calculate the atomic sieving threshold α t :

[0085]

[0086] Where μ is the trade-off factor parameter, typically taking values ​​[0.2, 0.4], and is determined by using a threshold α. t For set C t Secondary screening:

[0087] J t ={i|u t (i)>α t}

[0088] Among them, u t (i) is the inner product value corresponding to column index i, and J is the inner product value u corresponding to i. t (i) Greater than the atomic threshold α t The set of column indices, J t Let J be the set in the t-th iteration. Through secondary selection, the atomic selection becomes more precise, computational complexity is reduced, and the stability of the algorithm is improved.

[0089] In this embodiment, backtracking is added as follows:

[0090] Use the filtered set J t For the original support set Λ t-1 Expand capacity:

[0091] Λ t =Λ t-1 ∪J t

[0092] Where ∪ represents the union, and Λ represents the support set Λ of the (t-1)th iteration. t-1 With J in the t-th iteration t Merged into the support set Λ of the t-th iteration t And obtain the matrix of column combinations corresponding to the sensing matrix through the support set:

[0093]

[0094] in, and These represent the sensing matrix M corresponding to the set Λ respectively. t-1 J t Λ t A matrix composed of column vectors.

[0095] The channel impulse response is solved using the least squares method:

[0096]

[0097] The formula can be used to solve for h. t As shown in the following formula:

[0098]

[0099] Then, using the backtracking approach to filter atoms, when h t When the length is greater than the sparsity K, from h t The column indices corresponding to the K items with the largest absolute values ​​are selected from the set, and denoted as the set. Update support set And through support set updates and Improve the reliability of sparse solutions by backtracking.

[0100] In this embodiment, the iteration stopping condition is set as follows:

[0101] The residuals are updated using the following formula:

[0102]

[0103] Considering that the formula recovers the channel impulse response from noise, the L2 norm of the noise is used as the stopping condition for iteration, i.e.:

[0104] ||r t ||2≤ε

[0105] Where ||·||2 represents the L2 norm of the vector, and ε takes the value of ||G p ||2,G p This represents the frequency domain noise at the pilot. Based on the gOMP algorithm, the iteration stopping condition of this invention can be set as follows: when t ≥ min(K, P / S) or ||r t Stop iteration when ||2≤ε.

[0106] In this embodiment, a compressed sensing shallow sea acoustic channel estimation method based on atomic thresholds and backtracking is used, such as... Figure 1 As shown:

[0107] include:

[0108] S0: Initialization, let r0 = Y p , t = 1;

[0109] Where the subscript "0" represents the initial value before the iteration, Let r represent the residual vector, r0 represent the initial value of r, and P represent the number of pilot subcarriers. This represents the received signal containing pilot data, i.e., the measurement vector; Λ represents the support set; and Λ0 represents the initial support set of Λ. Represents the empty set;

[0110] S1: Calculate the inner product and take its absolute value: u t =|<r t-1 ,m j >|;

[0111] Where, m j Let the j-th column of matrix M be... Let r represent the sensing matrix, 1≤j≤L, r t-1 Let represent the residual vector of the (t-1)th iteration. Indicates r t-1 With m j The vector obtained by taking the inner product and its absolute value, u tLet represent the inner product vector of the t-th iteration, where "<·,·>" indicates the inner product operation and "|·|" indicates the absolute value operation.

[0112] S2: Selecting atoms: Choosing u t The top S largest values ​​in M ​​are used to form a set C corresponding to column indices i in M. t ;

[0113] Where S is the atomic selection number, and i is the u t The S largest values ​​in M ​​correspond to column indices of M, and C is the set of column indices i. t Let be the set of column indices in the t-th iteration;

[0114] S3: Calculate the atomic threshold value α t :

[0115]

[0116] in, and Let u be the inner product vector in the t-th iteration. t The first and second maximum values, μ represents the trade-off factor parameter, which is generally taken as [0.2, 0.4];

[0117] S4: Perform a second screening of atoms:

[0118] J t ={i|u t (i)>α t};

[0119] Among them, u t (i) is the inner product value corresponding to column index i, and J is the inner product value u corresponding to i. t (i) Greater than the atomic threshold α t The set of column indices, J t Let J be the set in the t-th iteration;

[0120] S5: Expanded Support Set:

[0121] Λ t =Λ t-1 ∪J t .,

[0122] Where ∪ represents the union, and Λ represents the support set Λ of the (t-1)th iteration. t-1 With J in the t-th iteration t Merged into the support set Λ of the t-th iteration t ; and These represent the sensing matrix M corresponding to the set Λ respectively. t-1 Jt Λ t A matrix composed of column vectors;

[0123] S6: Estimate the channel using least squares operations:

[0124]

[0125] Right now:

[0126]

[0127] The superscript "H" indicates the conjugate transpose of the matrix, and the superscript "-1" indicates the inverse operation of the matrix. t This represents the estimated channel impulse response;

[0128] S7: Backtracking: When length(h) t When ) > K, from h t The column indices corresponding to the K items with the largest absolute values ​​are selected from the set, and denoted as the set. Update support set And through support set updates and Otherwise, proceed directly to step S8;

[0129] Here, length(·) represents the length of the vector.

[0130] S8: Update residuals:

[0131] S9: Determine whether the condition t > min(K, P / S) or ||r is met. t If ||2≤ε, proceed to step S10; otherwise, let t=t+1 and return to step S1.

[0132] Where min(·,·) denotes the minimum function, ||·||2 denotes the L2 norm of the vector, and ε takes the value of ||G p ||2,G p This refers to the frequency domain noise at the pilot frequency.

[0133] S10: Output the final estimated sparse channel impulse response.

[0134] Example 2

[0135] To verify the performance of the proposed method, we conducted simulation experiments.

[0136] The OFDM symbol used in the experiment contained 512 subcarriers and was modulated using 16QAM. Since the power spectrum of OFDM signals is the sum of many frequency-shifted sinc functions, it has significant out-of-band power, which can cause adjacent channel interference. Virtual carriers (i.e., unused carriers at both ends of the transmission bandwidth) can suppress adjacent channel interference. Considering spectral efficiency, a total of 52 unused carriers were used at both ends of the OFDM symbol in this experiment. Pilot data was randomly inserted into the signal subcarriers using a comb-like method. To avoid inter-symbol interference, the CP length was greater than the channel length.

[0137] In this experiment, the Bellhop underwater acoustic channel model was used to simulate the impulse response of a sparse underwater acoustic channel. One sound source and one receiver were used at depths of 12 meters and 15 meters respectively, with a distance of 1000 meters between the source and receiver. The grazing angle of the sound ray ranged from -80° to 80°. Figure 2 The sound velocity profile in the figure is based on measured data at a depth of 60 meters in a shallow sea area. The underwater acoustic channel impulse response with a sparsity of 12 was simulated under the above environment. After normalization and removal of impulses with amplitudes less than 0.1, the following result was obtained: Figure 3 The channel shown has a sparsity K of 8. This channel is used for simulation. The horizontal axis represents relative delay, and the vertical axis represents normalized amplitude. Figure 3 It can be seen that the underwater acoustic channel has obvious sparsity.

[0138] To verify the effectiveness of the method of this invention, we compared ROMP, gOMP, and CoSaMP algorithms for estimation. Figure 2 The channel impulse response is shown. In the experiments, Normalized Mean Square Error (NMSE) and Bit Error Ratio (BER) were used to evaluate the algorithm's performance. Lower NMSE and BER values ​​indicate more accurate estimations. The formula for calculating NMSE is as follows:

[0139]

[0140] Where T represents the number of simulations at each signal-to-noise ratio. In this experiment, each algorithm underwent 1000 simulations, with a signal-to-noise ratio range of 0–20 dB, pilot number P set to 34, atom selection number S set to 3, and tradeoff factor parameter μ set to 0.3. The NMSE and BER under different algorithms are shown below. Figure 4 and Figure 5 As shown. By Figure 4 and Figure 5It can be seen that compressed sensing algorithms can recover the entire channel from noise with fewer pilots, and the NMSE and BER curves show basically the same trend. The NMSE and BER of the four algorithms decrease with increasing signal-to-noise ratio. In comparison, the simulation results of the TB-gOMP method of this invention are superior to the other algorithms in both metrics. Furthermore, under the same conditions, the running times of ROMP, gOMP, CoSaMP, and the TB-gOMP method of this invention are 6.97 seconds, 16.94 seconds, 23.72 seconds, and 9.57 seconds, respectively. It can be seen that the running time of TB-gOMP is nearly 1.8 times less than gOMP and nearly 2.5 times less than CoSaMP, showing a significant improvement in time efficiency.

[0141] In addition, we compared and analyzed the impact of the number of pilots on the estimation results. Simulation experiments were conducted using gOMP with 44 pilots and TB-gOMP with 24, 34, and 44 pilots respectively. The NMSE results are as follows: Figure 6 As shown in the figure, the number of pilots is noted after the algorithm name in the legend. It can be seen that the more pilots, the better the estimation performance. Furthermore, TB-gOMP achieves better results than gOMP with fewer pilots. Compared to gOMP with 44 pilots, TB-gOMP with only 34 pilots performs 3-5 dB better throughout the estimation process. Moreover, at low SNR levels below 10 dB, TB-gOMP with 44 pilots can achieve a 5 dB performance gain. The performance gain increases with increasing SNR; at an SNR of 20 dB, TB-gOMP can achieve a 10 dB gain. Even when TB-gOMP uses only 24 pilots (approximately 5% of the carriers), it still outperforms gOMP with 44 pilots at low SNR levels below 4 dB. Therefore, the TB-gOMP method of this invention has a greater advantage in spectrum conservation.

[0142] This invention addresses the problems of low correlation, excessive misselection of atoms, and lack of consideration for noise in the gOMP algorithm. It proposes a TB-gOMP channel estimation method, which performs secondary atom selection by setting reasonable atom thresholds, introduces a backtracking step, and sets iterative conditions under noise. Applied to sparse shallow-sea OFDM systems, experiments show that this method improves channel estimation accuracy, shortens estimation time by reducing algorithm computation, and improves spectral efficiency by using fewer pilots.

[0143] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A compressed sensing method for shallow sea acoustic channel estimation based on atomic thresholds and backtracking, characterized in that: In the compressed sensing channel estimation framework of underwater acoustic orthogonal frequency division multiplexing system, a reasonable atomic threshold pair for fine screening of atoms is proposed based on the gOMP algorithm. It also introduces the backtracking concept to eliminate misselected atoms in the gOMP algorithm; Set a noise-based iterative stopping condition for shallow water acoustic channel estimation; Specifically, the following steps are included: S0: Initialization, let , , ; Among them, the subscript " " represents the initial value before iteration, Represents the residual vector. This indicates that the matrix is ​​a complex matrix with a size of . , express initial value, Indicates the number of pilot subcarriers. This represents the received signal containing pilot data, i.e., the measurement vector. Represents the support set, express The initial support set, Represents the empty set; S1: Calculate the inner product and take its absolute value: ; in, For matrix The List, Represents the sensing matrix, This indicates that the matrix is ​​a complex matrix and its size is . , , Indicates the first The residual vector of the next iteration express and The vector obtained by taking the absolute value of the inner product. This indicates that the matrix is ​​a real matrix and its size is . , Indicates the first The inner product vector of the next iteration, "Indicates performing an inner product operation," " indicates the absolute value operation; S2: Selecting Atoms: Choosing The largest front This value, Each value corresponds to Column number Form a set ; in, For the atomic selection number, for The largest Each value corresponds to Column number, For column number The set constituted For the first The set formed by the column indices in each iteration; S3: Calculate atomic threshold values ; S4: Perform a second screening of atoms; S5: Expanded support set; S6: Estimate the channel using least squares operations; S7: Backtracking: When At that time, from Select the one with the largest absolute value The column index corresponding to each item is denoted as the set. Update support set And through support set updates and Otherwise, proceed directly to step S8; S8: Update residuals: ; S9: Determine if the condition is met. or If yes, proceed to step S10; otherwise, let And return to step S1; S10: Output the final estimated sparse channel impulse response. ; S3 calculates the atomic threshold value. : ； in, and The first In the next iteration, the inner product vector The first and second maximum values, This represents the trade-off factor parameter, with values ​​in the range [0.2, 0.4]. S4 performs a secondary screening of atoms: ； in, For the corresponding column number The inner product value, for The corresponding inner product value Greater than the atomic threshold The set of column indices at time, For the first The set in the next iteration ; The S5 expansion support set: ， ； in, Represents the union, and the first set is the first set. Support set of the next iteration With the The next iteration merged into the first Support set of the next iteration ; , and Representing the sensing matrix respectively Corresponding to sets , , A matrix composed of column vectors; S6 estimates the channel using least squares operations: ； Right now: The superscript " " represents the conjugate transpose operation of a matrix, with the superscript " " represents the inverse operation of a matrix. This represents the estimated channel impulse response.

2. The compressed sensing shallow sea acoustic channel estimation method based on atomic thresholds and backtracking as described in claim 1, characterized in that, The S7 backtracking: when At that time, from Select the one with the largest absolute value The column index corresponding to each item is denoted as the set. Update support set And through support set updates and Otherwise, proceed directly to step S8; in, This indicates the length of the vector.

3. The compressed sensing shallow sea acoustic channel estimation method based on atomic thresholds and backtracking as described in claim 1, characterized in that, S9 determines when the condition is met. or If yes, proceed to step S10; otherwise, let And return to step S1; in, This represents the function that takes the minimum value. Describes the L2 norm of a vector. Values , This represents the frequency domain noise at the pilot frequency.

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