Underwater sound OFDM (Orthogonal Frequency Division Multiplexing) impulse noise elimination method based on orthogonal subspace

Abstract

The invention discloses an underwater acoustic OFDM impulse noise elimination method based on an orthogonal subspace, and relates to underwater acoustic communication. Aiming at the problem that the performance of an OFDM underwater acoustic communication system is reduced due to the interference of impulse noise, an orthogonal projection matrix is constructed, and a received signal is projected to an orthogonal subspace corresponding to a channel component, so that the impulse noise and the channel are decomposed and coupled. The sparse characteristic of impulse noise is utilized, impulse noise estimation is carried out in the orthogonal subspace by adopting a compressed sensing algorithm, then time domain impulse noise is eliminated, and finally signals are restored through channel estimation, signal equalization and symbol detection. The problems of nonlinear distortion and error propagation in a traditional method are avoided, and the robustness and performance of an OFDM underwater acoustic communication system in an impulse noise interference environment are remarkably improved. Through comparison simulation experiments, under the condition of different signal-to-noise ratios and signal-to-pulse ratios, the method is superior to a traditional method in performance indexes such as pulse noise estimation mean square error, channel estimation mean square error and output signal-to-noise ratio.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic communication, and particularly to an underwater acoustic OFDM impulse noise cancellation method based on orthogonal subspaces, which is used to improve the performance of an OFDM underwater acoustic communication system in an impulse noise interference environment. Background Art

[0002] Orthogonal frequency division multiplexing (OFDM) is considered to be one of the most competitive systems in underwater acoustic communication. It uses multiple carriers for data transmission and has high spectral efficiency. However, in the actual underwater acoustic communication environment, natural or man-made impulse noise will cause serious distortion of the received signal, and the broadband characteristics of impulse noise will cause serious interference to all subcarriers in the OFDM system. The impulse noise interference greatly reduces the robustness of the OFDM underwater acoustic communication system.

[0003] The concept of orthogonal subspaces is usually used in signal processing applications for signal-to-noise separation. By using eigenvalue decomposition or singular value decomposition, the signal and noise are decomposed into different subspaces, thereby effectively separating the signal and noise. It has been widely used in wireless communication fields such as multiple-input multiple-output channel estimation, symbol detection, and multi-user communication, and has important practical application value. Impulse noise has the characteristics of short duration in the time domain and wide frequency band in the frequency domain, so it will contaminate all subcarriers in the OFDM system. This contamination has an adverse impact on various processes in the OFDM communication system, including CFO estimation, channel estimation, etc., resulting in a significant decline in the performance of the OFDM underwater acoustic communication system. Therefore, research on impulse noise cancellation methods for OFDM underwater acoustic communication systems must be carried out.

[0004] Currently, for the problem of impulse noise interference in OFDM, there are generally two types of methods. The first type is to identify impulse noise by using the high amplitude and short duration characteristics of impulse noise, and eliminate the impulse noise by means of clipping or zeroing. However, this type of method will cause nonlinear distortion. The second type is to use the compressive sensing joint estimation method. By using the sparse characteristics of impulse noise and multipath channels, joint estimation is performed through the compressive sensing algorithm. However, this type of method will have the problem of error propagation. The first type of method uses clipping or zeroing, which will cause nonlinear distortion and affect the performance of the OFDM underwater acoustic communication system. The second type of method uses the compressive sensing joint estimation method. Due to the mutual coupling between impulse noise and multipath interference, error propagation occurs in the joint estimation, reducing the estimation accuracy. Both types of methods have a certain effect on impulse noise cancellation, but due to the problems of nonlinear distortion or error propagation, they will still affect all subcarriers in the frequency domain of the OFDM communication signal.

[0005] Chinese Patent CN202111657692.3 discloses a method for processing received signals in underwater acoustic OFDM communication based on message passing for impulse noise cancellation. The time-domain impulse noise is modeled as a sparse vector, and through null carrier measurement, the channel and impulse noise are jointly estimated. After carrier frequency offset compensation and impulse noise interference cancellation, based on factor graph design, an approximate message passing algorithm is designed to achieve joint channel estimation, symbol detection, and channel decoding. Chinese Patent CN202011501650.6 discloses a method for suppressing impulse noise using GAMPSBL and realizing underwater acoustic channel estimation. (1) Input the baseband received signal, dictionary matrix, iteration termination condition, and initial values of relevant parameters; (2) Use GAMP-SBL to estimate impulse noise; (3) Subtract the impulse noise estimation result from the baseband received signal; (4) Use GAMP-SBL for underwater acoustic channel estimation; Utilize the sparsity of impulse noise in the time domain, estimate the impulse noise, and subtract it from the baseband signal to suppress impulse noise, which can reduce the damage to the signal structure and improve the impulse noise suppression performance. However, the above technical solutions cannot solve the error propagation problem in joint estimation.

[0006] In traditional OFDM underwater acoustic communication systems, the methods of clipping or zeroing will cause nonlinear distortion and affect the performance of the OFDM underwater acoustic communication system. In traditional OFDM underwater acoustic communication systems, the method of joint estimation using compressive sensing has error propagation in joint estimation due to the mutual coupling between impulse noise and multipath interference, reducing the estimation accuracy.

[0007] Therefore, in order to improve the robustness of the OFDM underwater acoustic communication system in an underwater impulse noise interference environment, the present invention proposes a method for impulse noise cancellation based on orthogonal subspaces, which avoids nonlinear distortion and error propagation problems and improves the system performance. Summary of the Invention

[0008] The purpose of the present invention is to solve the limitations faced by two existing types of impulse cancellation methods, improve the robustness of the OFDM underwater acoustic communication system in an underwater impulse noise interference environment, and provide an underwater acoustic OFDM impulse noise cancellation method based on orthogonal subspaces that avoids nonlinear distortion and error propagation problems and improves the system performance, effectively solving the key problem of system performance degradation caused by impulse noise interference in underwater acoustic communication, and significantly enhancing the robustness of the OFDM underwater acoustic communication system in an impulse noise interference environment.

[0009] To achieve the above invention purpose, the present invention provides the following technical solutions.

[0010] An underwater acoustic OFDM impulse noise cancellation method based on orthogonal subspaces, comprising the following steps:

[0011] 1) Time-domain baseband signal: Obtain the OFDM time-domain baseband signal after Doppler compensation;

[0012] 2) Frequency-domain pilot signal: Convert the time-domain baseband signal to a frequency-domain baseband signal through Fourier transform, and extract the pilot signal;

[0013] 3) Construct an orthogonal projection matrix: Construct an orthogonal projection matrix according to the pilot information and the channel length to eliminate the interference of the channel component on the impulse noise estimation;

[0014] 4) Project onto the orthogonal subspace: Use the orthogonal projection matrix constructed in step 3) to project the frequency-domain pilot signal onto a specific orthogonal subspace corresponding to the channel component;

[0015] 5) Sparse reconstruction of impulse noise: Based on the projected signal, use the compressive sensing algorithm to perform sparse reconstruction of the time-domain impulse noise using the sparse characteristics of the impulse noise;

[0016] 6) Eliminate impulse noise in the time-domain signal: Directly subtract the estimated time-domain impulse noise from the original time-domain signal to obtain the signal after interference cancellation. Perform channel estimation and frequency-domain equalization on the signal after interference cancellation to recover the pilot and data information in the OFDM symbol, and finally complete data decoding through symbol detection.

[0017] In step 1), the obtaining of the OFDM time-domain baseband signal after Doppler compensation has the following expression:

[0018]

[0019] where r represents the OFDM time-domain baseband signal after Doppler compensation, represents the inverse discrete Fourier transform matrix, S represents the modulated OFDM information, F [:,0:L-1] represents the submatrix formed by all rows and the first L columns of the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1,..., h L-1 represents the channel impulse response, α = [α0, α1,..., α K-1 represents the time-domain impulse noise, w = [w0, w1,..., w K-1 represents the time-domain Gaussian noise.

[0020] In step 2), the frequency-domain baseband signal can be expressed as:

[0021]

[0022] where y represents the OFDM frequency-domain baseband signal after Doppler compensation, represents the inverse discrete Fourier transform matrix, r represents the OFDM time-domain baseband signal after Doppler compensation, S represents the modulated OFDM information, F[:,0:L-1] denotes the sub - matrix formed by all rows and the first L columns of the discrete Fourier transform matrix, where L represents the channel length, h = [h0, h1, …, h L-1 represents the channel impulse response, F K denotes the discrete Fourier transform matrix, α = [α0, α1, …, α K-1 represents the time - domain impulse noise, w = [w0, w1, …, w K-1 represents the time - domain Gaussian noise; the corresponding pilot information can be expressed as:

[0023] y p = P p SF [:,0:L-1] h + P p F K α + P p F K w

[0024] = Φ h h + Φ α α + Φ w w

[0025] where, Φ h = P p SF [:,0:L-1] Φ α = P p F K α, Φ w = P p F K w, y p represents the OFDM frequency - domain pilot signal after Doppler compensation, S represents the modulated OFDM information, F [:,0:L-1] denotes the sub - matrix formed by all rows and the first L columns of the discrete Fourier transform matrix, where L represents the channel length, h = [h0, h1, …, h L-1 represents the channel impulse response, F K denotes the discrete Fourier transform matrix, α = [α0, α1, …, α K-1 represents the time - domain impulse noise, w = [w0, w1, …, w K-1 represents the time - domain Gaussian noise. In step 3), the orthogonal projection matrix is defined as:

[0026]

[0027] where, Π represents the orthogonal projection matrix, I represents the identity matrix, Φ h = P p SF [:,0:L-1] and satisfies (·) -1 represents matrix inversion.

[0028] In step 4), for the projection onto the orthogonal subspace, in the orthogonal subspace specific to the channel components, there is:

[0029]

[0030] where 0 represents the unit zero matrix; thus, in the orthogonal subspace of the channel components, the OFDM symbol can be expressed as:

[0031] y o = Πy p = Π(Φ h h + Φ α α + Φ w w) = ΠΦ α α + ΠΦ w w

[0032] where Φ α = P p F K α, Φ w = P p F K w, y o represents the signal in the projected orthogonal subspace, y p represents the frequency-domain pilot signal before projection, Π represents the orthogonal projection matrix, Φ h = P p SF [:,0:L-1] and satisfies α = [α0, α1, …, α K-1 represents the time-domain impulse noise, w = [w0, w1, …, w K-1 represents the time-domain Gaussian noise.

[0033] It can be seen that after projection onto the orthogonal subspace, the channel component ΠΦ h h = 0 is eliminated, and the channel component is decoupled from the impulse noise component.

[0034] In step 5), for the sparse reconstruction of the impulse noise, since the impulse noise has a sparse property, assuming the sparsity is χ, a compressive sensing algorithm is used for impulse noise estimation, that is, solving the cost function:

[0035]

[0036] where Φ α = P p F K α, y o represents the signal in the projected orthogonal subspace, Π represents the orthogonal projection matrix, Φ h = P p SF [:,0:L-1] and satisfies α = [α0, α1, …, αK-1 denotes the time-domain impulse noise, ||·||0 and ||·||2 denote the l0 and l2 norms respectively, and arg min(·) denotes taking the minimum value.

[0037] In step 6), the elimination of the time-domain signal impulse noise obtains the time-domain impulse noise estimation through the compressive sensing algorithm After that, the original time-domain OFDM signal is subjected to impulse noise elimination, that is:

[0038]

[0039] where denotes the time-domain signal after impulse noise interference elimination, r denotes the OFDM time-domain baseband signal after Doppler compensation, denotes the inverse discrete Fourier transform matrix, S denotes the modulated OFDM information, F [:,0:L-1] denotes the submatrix formed by all rows and the first L columns in the discrete Fourier transform matrix, L denotes the channel length, h = [h0, h1, …, h L-1 denotes the channel impulse response, w = [w0, w1, …, w K-1 denotes the time-domain Gaussian noise, denotes the impulse noise estimation error; and then the information modulated in the OFDM symbol is restored through channel estimation, signal equalization and symbol detection.

[0040] Compared with the prior art, the present invention has the following outstanding technical effects and advantages:

[0041] 1. Solving coupling and error propagation: The present invention constructs a subspace orthogonal to the channel and effectively separates the channel component and the impulse noise component by using the orthogonal property. In traditional joint estimation, due to their coupling, an error in one place during the estimation process is likely to trigger a chain reaction, resulting in a large deviation in the final result. However, this method decouples them, blocks the error propagation path at the source, avoids inaccurate estimation caused by coupling, and improves the stability and reliability of the overall estimation.

[0042] 2. Avoiding non-linear distortion: Traditional non-linear methods such as joint estimation of clipping, zeroing, and compressive sensing are likely to cause irreversible distortion to the signal during the processing. The present invention adopts the orthogonal subspace strategy and does not introduce non-linear operations when estimating the impulse noise and the channel. Through comparison of actual performance indicators, the present invention is superior to the traditional method in terms of impulse noise mean square error, channel mean square error, and output signal-to-noise ratio.

[0043] 3. Achieve component separation: Aiming at the problem that the performance of the OFDM underwater acoustic communication system deteriorates due to underwater impulse noise interference, the present invention projects the time-domain signal skillfully onto a specific orthogonal subspace corresponding to the channel components. According to the properties of the orthogonal subspace, the channel components in this subspace will be eliminated, thereby realizing the accurate separation of the impulse noise components and the channel components. Improving the accuracy of impulse noise estimation, providing purer data after eliminating impulse noise interference for signal processing, and contributing to improving the performance of the communication system in complex underwater environments.

[0044] 4. Eliminate the interference of channel components: The present invention makes full use of a specific subspace orthogonal to the channel, so that when estimating impulse noise in this subspace, the interference of channel components is completely eliminated. In previous methods, the interference of channel components often caused bias in impulse noise estimation. And through this ingenious subspace design of the present invention, it is ensured that the estimation process only targets impulse noise, and thus accurate impulse noise can be obtained, laying a solid foundation for subsequent noise cancellation work. Brief Description of the Drawings

[0045] Figure 1 It is a flowchart of an underwater acoustic OFDM impulse noise cancellation method based on orthogonal subspace proposed by the present invention.

[0046] Figure 2 It is a schematic diagram of Gaussian mixture noise common in underwater acoustic communication signals in complex shallow sea environments.

[0047] Figure 3 It is the mean square error of impulse noise at different SNRs.

[0048] Figure 4 It is the mean square error of the channel at different SNRs.

[0049] Figure 5 It is the output signal-to-noise ratio at different SNRs.

[0050] Figure 6 It is the mean square error of impulse noise at different SIRs.

[0051] Figure 7 It is the mean square error of channel estimation at different SIRs.

[0052] Figure 8 It is the output signal-to-noise ratio at different SIRs.

[0053] In Figure 3-8 , BI represents the zeroing nonlinear method, CI represents the clipping nonlinear method, JIC represents the joint impulse noise and channel estimation method, and PIC represents the present invention. Detailed Embodiment

[0054] The following embodiments will further illustrate the present invention in conjunction with the drawings.

[0055] An embodiment of the present invention relates to an underwater acoustic OFDM impulse noise cancellation method based on an orthogonal subspace. The specific process is as follows Figure 1 shown. By using the orthogonal subspace theory, the impulse noise component and the channel component are separated to avoid error propagation, including constructing an orthogonal subspace matrix, projecting the time-domain signal onto a specific orthogonal subspace corresponding to the channel component, using a compressive sensing algorithm to sparsely reconstruct the impulse noise based on the sparse characteristics of the impulse noise, and canceling the impulse noise in the time-domain signal.

[0056] 1 Gaussian mixture noise model

[0057] As Figure 2 shown, in OFDM underwater acoustic communication in a complex shallow sea environment, not only the Gaussian noise of the background environment needs to be considered, but also the impulse noise generated naturally or artificially needs to be considered. Moreover, the characteristics of high amplitude and wide frequency band of the impulse noise seriously restrict the performance of the OFDM underwater acoustic communication system.

[0058] Considering an additive Gaussian mixture noise model, it can be expressed as:

[0059]

[0060] where represents the complex Gaussian distribution function, δ α represents the probability of the impulse noise occurrence, and represent the additive Gaussian noise variance and the impulse noise variance respectively. The signal-to-noise ratio and the signal-to-impulse ratio can be defined as:

[0061]

[0062] where represents the signal variance.

[0063] 2 Underwater acoustic OFDM impulse noise cancellation method based on orthogonal subspace

[0064] Considering an OFDM symbol with a total number of subcarriers K and an index position sequence p, it contains K p pilot subcarriers and K d data subcarriers, and the corresponding index position sequences are p p and p d . The frequency corresponding to the k-th subcarrier is located at

[0065] f k = kf Δ , k = 0, 1,..., K - 1

[0066] where f Δ represents the subcarrier spacing. Assume there is a length of K dThe data sequence s d and the data sequence s p with length K p , based on the index position sequence p p and p d , the data sequence and the pilot sequence together form the frequency-domain information sequence s of an OFDM symbol. Therefore, an OFDM time-domain baseband symbol can be expressed as:

[0067]

[0068] wherein, denotes the inverse discrete Fourier transform matrix and can be defined as: Since the present invention focuses on OFDM underwater acoustic communication between fixed two points and considers perfect Doppler compensation, that is, only considers the separation of the coupling between the impulse noise and the channel, the received time-domain signal can be expressed as:

[0069]

[0070] wherein, r represents the OFDM time-domain baseband signal after Doppler compensation, denotes the inverse discrete Fourier transform matrix, S represents the modulated OFDM information, F [:,0:L-1] represents the sub-matrix formed by all rows and the first L columns in the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1,..., h L-1 represents the channel impulse response, α = [α0, α1,..., α K-1 represents the time-domain impulse noise, w = [w0, w1,..., w K-1 represents the time-domain Gaussian noise. The frequency-domain signal can be expressed as:

[0071]

[0072] wherein, y represents the OFDM frequency-domain baseband signal after Doppler compensation, r represents the OFDM time-domain baseband signal after Doppler compensation, denotes the inverse discrete Fourier transform matrix, S represents the modulated OFDM information, F [:,0:L-1] represents the sub-matrix formed by all rows and the first L columns in the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1,..., h L-1 represents the channel impulse response, F K represents the discrete Fourier transform matrix, α = [α0, α1,..., α K-1 represents the time-domain impulse noise, w = [w0, w1,..., w K-1 represents the time-domain Gaussian noise.

[0073] Therefore, the pilot information of an OFDM symbol can be expressed as:

[0074] y p = P p SF [:,0:L-1] h + P p F K α + P p F K w

[0075] = Φ h h + Φ α α + Φ w w

[0076] where Φ h = P p SF [:,0:L-1] ,Φ α = P p F K α,Φ w = P p F K w,y p represents the OFDM frequency - domain pilot signal after Doppler compensation, S represents the modulated OFDM information, F [:,0:L-1] represents the sub - matrix composed of all rows and the first L columns in the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1, …, h L-1 represents the channel impulse response, F K represents the discrete Fourier transform matrix, α = [α0, α1, …, α K-1 represents the time - domain impulse noise, w = [w0, w1, …, w K-1 represents the time - domain Gaussian noise. It can be seen that the channel component Φ h h and the impulse - noise component Φ α α are mutually coupled, and traditional joint - estimation methods will cause error - propagation problems during estimation. Therefore, it is considered to separate the channel component and the impulse - noise component by using the concept of orthogonal sub - spaces, that is, projecting the base - band signal of time - domain OFDM onto the orthogonal sub - space corresponding to the channel component through the orthogonal projection matrix constructed based on Φ h to estimate the impulse - noise in a specific orthogonal sub - space and eliminate the interference of the channel component, avoiding the error - propagation problem. Based on the orthogonal - projection theory, the channel component h is eliminated in its corresponding orthogonal sub - space, that is, an orthogonal projection matrix is constructed such that ΠΦ h h = 0. Therefore, the orthogonal projection matrix can be defined as:

[0077]

[0078] where I represents the identity matrix, Φ h satisfies The pilot information and the channel length are respectively reflected in Φ h= P p SF [:,0:L-1] in P of p S and F [:,0:L-1] in, (·) -1 represents matrix inversion. Therefore, in the orthogonal subspace specific to the channel components, there is:

[0079]

[0080] where 0 represents the unit zero matrix. Therefore, in the orthogonal subspace of the channel components, the OFDM symbol can be expressed as:

[0081] y o = ΠΦ α α + ΠΦ w w

[0082] where Φ α = P p F K α, Φ w = P p F K w, y o represents the orthogonal subspace signal after projection, y p represents the frequency-domain pilot signal before projection, Π represents the orthogonal projection matrix, Φ h = P p SF [:,0:L-1] and satisfies α = [α0, α1, …, α K-1 represents the time-domain impulse noise, w = [w0, w1, …, w K-1 represents the time-domain Gaussian noise.

[0083] It can be seen that after projection onto the orthogonal subspace, the channel component ΠΦ h h = 0 is eliminated, and the channel component is decoupled from the impulse noise component. Since the impulse noise has sparse characteristics, assuming the sparsity is χ, a compressive sensing algorithm is used for impulse noise estimation, that is, solving the cost function:

[0084]

[0085] where Φ α = P p F K α, y o represents the orthogonal subspace signal after projection, Π represents the orthogonal projection matrix, Φ h = P p SF [:,0:L-1] and satisfies α = [α0, α1, …, α K-1represents time-domain impulse noise, ||·||0 and ||·||2 represent the l0 and l2 norms respectively, and arg min(·) represents taking the minimum value.

[0086] The time-domain impulse noise estimation is obtained through the compressive sensing algorithm After that, the original time-domain OFDM signal is subjected to impulse noise cancellation, that is:

[0087]

[0088] Among them, represents the time-domain signal after impulse noise interference cancellation, r represents the OFDM time-domain baseband signal after Doppler compensation, represents the inverse discrete Fourier transform matrix, S represents the modulated OFDM information, F [:,0:L-1] represents the sub-matrix formed by all rows and the first L columns in the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1,..., h L-1 ] represents the channel impulse response, w = [w0, w1,..., w K-1 ] represents the time-domain Gaussian noise, represents the impulse noise estimation error. Then the information modulated in the OFDM symbol is restored through channel estimation, signal equalization, and symbol detection.

[0089] To verify the effectiveness of the proposed method, the present invention conducts comparative simulation experiments. The methods of setting to zero (reference: Xiaoyan Kuai, Haixin Sun, Shengli Zhou, and En Cheng. Impulsive noise mitigation in underwater acoustic OFDM systems. IEEE Transactions on Vehicular Technology, 65(10): 8190 - 8202, 2016.), clipping (reference: Xiaoyan Kuai, Haixin Sun, Shengli Zhou, and En Cheng. Impulsive noise mitigation in underwater acoustic OFDM systems. IEEE Transactions on Vehicular Technology, 65(10): 8190 - 8202, 2016.), and the joint estimation algorithm of compressive sensing (reference: Peng Chen, Yue Rong, Sven Nordholm, Zhiqiang He, and Alexander J Duncan. Joint channel estimation and impulsive noise mitigation in underwater acoustic OFDM communication systems. IEEE Transactions on Wireless Communications, 16(9): 6165 - 6178, 2017.) are selected as comparative methods. The methods of setting to zero, clipping, and the joint estimation algorithm of compressive sensing are respectively labeled as BI, CI, and JIC, while the method of the present invention is labeled as PIC. Taking the mean square error of impulsive noise estimation, the mean square error of channel estimation, and the output signal - to - noise ratio as evaluation metrics, which involve the estimated channel, the estimated impulsive noise, and the equalized symbols. In the simulation experiment, a single - input single - output OFDM system is adopted. The total number of sub - carriers of the OFDM signal is 1024, the bandwidth is 4800 Hz, the sampling rate is 96 kHz, the QPSK constellation mapping method is used, the sparsity of impulsive noise is set to 10, the sparsity of the channel is 8. The orthogonal matching pursuit algorithm with a sparsity setting of 15 is used for channel estimation in CI, BI, and PIC. The joint sparsity of the channel and impulsive noise in the JIC method is set to 30. The orthogonal matching pursuit algorithm with a sparsity setting of 15 is used for impulsive noise estimation in PIC. The equalizer uses a linear zero - forcing equalizer.

[0090] Define the evaluation parameters including the mean square error of impulsive noise estimation, the mean square error of channel estimation, and the output signal - to - noise ratio:

[0091]

[0092] Among them, respectively represent the estimated channel, the estimated impulse noise, and the equalized symbols. Simulation experiments are carried out and verified respectively under different signal-to-noise ratios and signal-to-impulse ratios, and the experimental results are as Figures 3-8 shown. In Figure 3-8 , under different signal-to-noise ratios and signal-to-impulse ratios, both BI and CI directly set the impulse noise to zero and clip it using non-linear methods, resulting in non-linear distortion, and leading to lower performance in terms of the mean square error of impulse noise estimation, the mean square error of channel estimation, and the output signal-to-noise ratio than the proposed PIC method. The JIC algorithm jointly estimates the impulse noise and the channel, but due to the problem of error propagation, the channel estimation and the impulse noise estimation affect each other, affecting the estimation performance, and leading to lower performance in terms of the mean square error of impulse noise estimation, the mean square error of channel estimation, and the output signal-to-noise ratio than the proposed PIC method. However, the method proposed in the present invention overcomes the problems of error propagation and non-linear distortion in the joint estimation process by using the orthogonal subspace to solve the coupling between the channel component and the impulse noise component. In different signal-to-noise ratio and signal-to-impulse ratio scenarios, its performance in terms of the mean square error of impulse noise estimation, the mean square error of channel estimation, and the output signal-to-noise ratio is superior to the traditional methods of clipping, zeroing, and compressive sensing joint estimation, comprehensively verifying the effectiveness of the subspace-based impulse noise cancellation method proposed in the present invention.

[0093] Aiming at the problem of the performance degradation of the OFDM underwater acoustic communication system in the underwater impulse noise interference environment, the present invention uses the concept of orthogonal subspace to project the time-domain signal into a specific orthogonal subspace corresponding to the channel component, where the channel component is eliminated in the orthogonal subspace, thereby realizing the separation of the impulse noise component and the channel component, solving the problems of non-linear distortion or error propagation caused by traditional methods, and improving the accuracy of impulse noise estimation.

[0094] The above embodiments are only preferred embodiments of the present invention and cannot be considered as limiting the scope of implementation of the present invention. All equivalent changes and improvements made within the scope of the application of the present invention shall still fall within the scope covered by the patent of the present invention.

Claims

1. An underwater acoustic OFDM impulse noise cancellation method based on orthogonal subspaces, characterized in that Including the following steps: 1) Time-domain baseband signal: Obtain the OFDM time-domain baseband signal after Doppler compensation; 2) Frequency-domain pilot signal: Convert the time-domain baseband signal into a frequency-domain baseband signal through Fourier transform, and extract the pilot signal; 3) Construct an orthogonal projection matrix: According to the pilot information and the channel length, construct an orthogonal projection matrix to eliminate the interference of the channel component on the impulse noise estimation; 4) Project onto the orthogonal subspace: Project the frequency-domain pilot signal onto the specific orthogonal subspace corresponding to the channel component through the orthogonal projection matrix constructed in step 3) to obtain the projected signal; 5) Sparse reconstruction of impulse noise: Based on the projected signal, use the compressed sensing algorithm to sparsely reconstruct the time-domain impulse noise by utilizing the sparse characteristics of the impulse noise; 6) Elimination of impulse noise in the time-domain signal: Directly subtract the estimated time-domain impulse noise from the original time-domain signal to obtain the signal after interference elimination. Perform channel estimation and frequency-domain equalization on the signal after interference elimination to recover the pilot and data information in the OFDM symbol, and finally complete data decoding through symbol detection.

2. The method for eliminating underwater acoustic OFDM impulse noise based on orthogonal subspace according to claim 1, characterized in that In step 1), the expression for obtaining the OFDM time-domain baseband signal after Doppler compensation is: where r represents the OFDM time-domain baseband signal after Doppler compensation, denotes the inverse discrete Fourier transform matrix, S represents the modulated OFDM information, and F [:,0:L-1] represents the submatrix formed by all rows and the first L columns of the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1, …, h L-1 represents the channel impulse response, α = [α0, α1, …, α K-1 represents the time-domain impulse noise, and w = [w0, w1, …, w K-1 represents the time-domain Gaussian noise.

3. The method for eliminating underwater acoustic OFDM impulse noise based on orthogonal subspaces according to claim 1, wherein In step 2), the frequency-domain baseband signal is expressed as: Among them, y represents the OFDM frequency-domain baseband signal after Doppler compensation, represents the inverse discrete Fourier transform matrix, r represents the OFDM time-domain baseband signal after Doppler compensation, S represents the modulated OFDM information, F [:,0:L-1] represents the submatrix formed by all rows and the first L columns of the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1, …, h L-1 ] represents the channel impulse response, F K represents the discrete Fourier transform matrix, α = [α0, α1, …, α K-1 ] represents the time-domain impulse noise, w = [w0, w1, …, w K-1 ] represents the time-domain Gaussian noise; the corresponding pilot information is expressed as: y p = P p SF [:,0:L-1] h + P p F K α + P p F K w = Φ h h + Φ α α + Φ w w Among them, Φ h = P p SF [:,0:L-1] , Φ α = P p F K α, Φ w = P p F K w, y p represents the OFDM frequency-domain pilot signal after Doppler compensation, S represents the modulated OFDM information, F [:,0:L-1] represents the sub-matrix formed by all rows and the first L columns in the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1,..., h L-1 represents the channel impulse response, F K represents the discrete Fourier transform matrix, α = [α0, α1,..., α K-1 represents the time-domain impulse noise, w = [w0, w1,..., w K-1 represents the time-domain Gaussian noise.

4. The method for eliminating underwater acoustic OFDM impulse noise based on orthogonal subspaces as claimed in claim 1, wherein In step 3), the orthogonal projection matrix is defined as: where Π represents an orthogonal projection matrix, I represents an identity matrix, and Φ h = P p SF [:,0:L-1] and satisfies (·) -1 represents matrix inversion.

5. The method for eliminating underwater acoustic OFDM impulse noise based on orthogonal subspaces according to claim 1, wherein In step 4), for the projection onto the orthogonal subspace, in the specific orthogonal subspace of the channel component, there is: where 0 represents the unit zero matrix; therefore, in the orthogonal subspace of the channel component, the OFDM symbol is expressed as: y o = Πy p = Π(Φ h h + Φ α α + Φ w w) = ΠΦ α α + ΠΦ w w Among them, Φ α = P p F K α, Φ w = P p F K w, y o represents the projected orthogonal subspace signal, and y p represents the frequency-domain pilot signal before projection, Π represents the orthogonal projection matrix, and Φ h = P p SF [:,0:L-1] and satisfies α = [α0, α1, …, α K-1 represents the time-domain impulse noise, and w = [w0, w1, …, w K-1 represents the time-domain Gaussian noise; After projecting onto the orthogonal subspace, the channel component ΠΦ h h = 0 is eliminated, and the channel component is decoupled from the impulse noise component.

6. The method for eliminating underwater acoustic OFDM impulse noise based on orthogonal subspaces according to claim 1, wherein In step 5), for the sparse reconstruction of impulse noise, since the impulse noise has sparse characteristics, assuming the sparsity is χ, use the compressed sensing algorithm to estimate the impulse noise, that is, solve the cost function: where, Φ α = P p F K α, y o represents the orthogonal subspace signal after projection, Π represents the orthogonal projection matrix, Φ h = P p SF [:,0:L-1] and satisfies α = [α0, α1, …, α K-1 represents the time-domain impulse noise, ||·||0 and ||·||2 represent the l0 and l2 norms respectively, and argmin(·) represents taking the minimum value.

7. The method for eliminating underwater acoustic OFDM impulse noise based on orthogonal subspaces according to claim 1, wherein In step 6), for the elimination of the time-domain signal pulse noise, an estimation of the time-domain pulse noise is obtained through a compressive sensing algorithm. After that, pulse noise elimination is performed on the original time-domain OFDM signal, that is: Among them, represents the time-domain signal after pulse noise interference cancellation, r represents the OFDM time-domain baseband signal after Doppler compensation, represents the inverse discrete Fourier transform matrix, S represents the modulated OFDM information, F [:,0:L-1] represents the submatrix formed by all rows and the first L columns in the discrete Fourier transform matrix, L represents the channel length, h = [h0, h1, …, h L-1 represents the channel impulse response, w = [w0, w1, …, w K-1 represents the time-domain Gaussian noise, represents the pulse noise estimation error; and then the information modulated in the OFDM symbol is restored through channel estimation, signal equalization, and symbol detection.

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