A channel equalization method for OFDM underwater acoustic communication under fast time-varying conditions

Abstract

The present invention discloses a method for equalizing OFDM underwater acoustic communication channels under fast time-varying conditions. For OFDM underwater acoustic communication systems, the method mainly addresses the contradiction between channel equalization performance and complexity under fast time-varying conditions. The method comprises the following steps: 1) obtaining time-varying channel parameter estimates based on pilot symbols; 2) obtaining a frequency domain channel matrix based on the estimated channel parameters; and 3) implementing data symbol detection using the Expectation Maximization-Vector Approximate Message Passing (EM-VAMP) algorithm. The EM-VAMP-based equalization method proposed in the present invention has moderate computational complexity, superior performance to existing equalization methods, and high practical application value.

Description

Technical Field

[0001] The present invention belongs to the field of OFDM underwater acoustic communication, and in particular relates to an OFDM underwater acoustic communication channel equalization method under fast time-varying conditions. Background Art

[0002] The underwater acoustic channel is characterized by large delay spread and rapid variations. It is a typical time-frequency dual-selective fading channel. Therefore, OFDM underwater acoustic communication faces severe inter-carrier interference (ICI). Accurately characterizing and suppressing ICI is the key to OFDM underwater acoustic communication.

[0003] A propagation path-based underwater acoustic communication channel model is currently widely used in the literature. This model effectively characterizes the characteristics of the underwater acoustic channel and, therefore, accurately describes ICI. In this case, the frequency domain system model can be expressed as z = Hs + w. Due to ICI, the frequency domain channel H is a non-diagonal matrix. The goal of channel equalization is to estimate the transmitted symbol vector s based on the observed z and the above system model.

[0004] There are various methods for symbol estimation. Ideal estimation schemes include maximum a posteriori probability (MAP) equalization and minimum mean squared error (MMSE) equalization, but their complexity is too high to be used in practical systems. Suboptimal equalization methods include the classic least squares (LS) method and the linear minimum mean square error (LMMSE) method. Because ICI primarily occurs between adjacent subcarriers, H can be approximated as a banded matrix. In this case, the complexity of LS / LMMSE equalization is moderate. However, their performance still lags significantly behind the ideal MAP / MMSE equalization.

[0005] Equalization methods based on the Approximate Message Passing (AMP) algorithm are currently receiving considerable attention. They can achieve superior performance to LMMSE equalization while maintaining comparable complexity. Equalization based on the Generalized Approximate Message Passing (GAMP) algorithm has been applied to OFDM underwater acoustic communications. However, GAMP equalization only achieves satisfactory performance when the elements of the channel matrix H satisfy an independent and identically distributed Gaussian distribution, limiting its practical application. Summary of the Invention

[0006] The present invention aims to provide an OFDM underwater acoustic communication channel equalization method under fast time-varying conditions, so as to solve the technical problem of the contradiction between complexity and performance faced by OFDM underwater acoustic communication channel equalization under fast time-varying conditions.

[0007] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0008] A method for equalizing an OFDM underwater acoustic communication channel under fast time-varying conditions, characterized by comprising the following steps:

[0009] Step 1: Determine the number of transmitter transducers N and the center carrier frequency f c , transmission bandwidth B, number of OFDM subcarriers K, where K D are data subcarriers, K P are pilot subcarriers, so K=K D +K P , subcarrier spacing Δf; let the transducer number be n, and determine the pilot symbol vector It is defined as a column vector of length K, but its value is non-zero only at the pilot subcarrier position and zero at other positions;

[0010] Step 2: Determine the number M of hydrophones at the receiving end, perform Doppler preprocessing on the received signal, and obtain the input-output relationship of the N×M MIMO system;

[0011] Step 3: Using the Orthogonal Matching Pursuit (OMP) algorithm based on the pilot symbols to estimate the multiple-input multiple-output (MIMO) channel parameters, and further obtaining the frequency domain channel matrix H based on the estimated parameters;

[0012] Step 4: Use the Expectation Maximization-Vector Approximate Message Passing (EM-VAMP) equalization algorithm to obtain the estimated value of the data symbol vector

[0013] Furthermore, in step 2, the specific steps for obtaining the system input-output relationship are as follows: For the above-mentioned N×M MIMO system consisting of N transducers and M hydrophones, the bandpass signal sent by the nth transducer is writing:

[0014]

[0015] Where t represents time, is the transmission symbol of the nth transducer, fk =(k-1-K / 2)Δf is the k-th baseband subcarrier frequency, g(t) is the shaping filter;

[0016] For the sub-channel between the nth transducer and the mth hydrophone, the following path-based underwater acoustic communication channel model is adopted:

[0017]

[0018] Where t represents time, τ represents delay, is the u-th order Taylor expansion coefficient of the p-th path amplitude, τ p,m,n is the initial delay of the path, α p,m,n represents the Doppler scaling factor of the path, and δ represents the Dirac function; therefore, the passband received signal of the mth hydrophone is:

[0019]

[0020] Where u! represents the factorial of u, represents the passband noise on the mth hydrophone;

[0021] remember is the estimated value of the Doppler scaling factor, The estimated value of carrier frequency offset CFO is obtained by resampling, carrier demodulation and carrier frequency offset CFO compensation of the above passband received signal to obtain the following baseband received signal:

[0022]

[0023] where ω m (t) is the baseband noise;

[0024] to r m (t) is sampled at a sampling rate of 1 / B, and then a discrete Fourier transform is performed to obtain the following frequency domain input and output relationship:

[0025]

[0026] in represents the residual Doppler of each path, w m [l] is the noise after sampling; H m,n [l,k] is called the ICI coefficient, which reflects the contribution of the symbol transmitted on the kth subcarrier to the received signal on the lth subcarrier;

[0027] In the 5th move Written as a column vector z m ; Written as a column vector s n ; Written as a column vector w m , we get the system input-output relationship in vector form:

[0028]

[0029] in is the subchannel matrix between the nth transducer and the mth hydrophone, expressed as follows

[0030]

[0031] in is a diagonal matrix, and its kth diagonal element is is a banded matrix with half-bandwidth D, where half-bandwidth represents the maximum distance between the non-zero elements of the matrix and the main diagonal; Γ (u) (b p,m,n ) is [Γ (u) (b p,m,n )] l,k =G (u) (β l,k (b p,m,n )), where G (u) (·) represents the u-order derivative of the Fourier transform of g(·); From Equation 7, we can see that H m,n Is a parameter group nonlinear function.

[0032] Furthermore, in step 3, in order to realize the multi-input multi-output MIMO channel parameter estimation based on the orthogonal matching pursuit OMP algorithm, firstly replace the s on the right side of the equation 6 with n Decompose into in is the pilot part, is the data part, so Equation 6 is rewritten as:

[0033]

[0034] in represents the equivalent noise composed of observation noise and data symbol interference. The last equation in Equation 8 uses the relationship in Equation 7;

[0035] Then, Equation 8 is equivalent to a dictionary-based representation, and the delay candidate set is defined as and the residual Doppler factor candidate set b p ∈{-b max ,-b max +Δb,...,b max}, delay candidate set The size is Residual Doppler factor candidate set b p ∈{-b max ,-b max +Δb,...,b max The size of} is N b =2b max / Δb+1; Set the possible delays and Doppler factors of all sub-channels to fall into the above two candidate sets, that is, the channel delay-Doppler pair falls into The delay-Doppler grid is represented as follows:

[0036]

[0037] in

[0038] Equation 9 can be written in a more concise form

[0039] z m =Aξ m +v m Formula 10,

[0040] in:

[0041]

[0042]

[0043]

[0044]

[0045] In formula 10, A is called the dictionary, which is known, and the problem to be solved is ξ m , thus transforming the nonlinear problem of Equation 8 into a linear problem; for ξ m Elements in Only when the channel is in the aforementioned delay-Doppler grid If the point exists, its value is non-zero, otherwise it is zero, so ξ m is a sparse vector, which is solved by the orthogonal matching pursuit OMP algorithm; once ξ is determined m The non-zero elements in can determine the corresponding delay and Doppler, thereby obtaining the channel estimation

[0046] Get channel estimate After that, data symbol detection can be performed. First, the interference of the pilot symbol on the data symbol in Equation 6 is eliminated, and we can get in because The value at the pilot symbol position is zero, so the system model is further simplified as in Only by The non-zero data symbols in for Keep only the part of the column where the data symbol is located; Combine into column vector Combine into column vector Combine into column vector Will Combined into MIMO channel matrix The frequency domain input and output relationship of the MIMO system is obtained:

[0047] z=Ηs+w Formula 15.

[0048] Furthermore, in step 4, the Expectation Maximization-Vector Approximate Message Passing (EM-VAMP) equalization algorithm consists of three parts: an inner soft equalizer (ISS), an inner soft slicer (ISE), and an EM-based signal-to-noise ratio estimator. The "-" in the Expectation Maximization-Vector Approximate Message Passing algorithm and other nouns mentioned below represents a connector, indicating that it is composed of a combination or union of two parts.

[0049] The following describes the VAMP equalization process based on the idea of ​​the Sum-Product (SP) algorithm based on Equation 15. The noise is set to obey the Gaussian distribution and its accuracy is γ w , then the joint probability density function of the received signal and the symbol to be estimated is:

[0050]

[0051] Where I is the identity matrix;

[0052] To obtain the factor graph representation, decompose s into s1=s2, and then Equation 16 is rewritten as:

[0053]

[0054] Where s1 and s2 are variable nodes, p(s1), δ(s1-s2) and is a factor node;

[0055] Next, we describe the VAMP equilibrium based on the factor graph. Gaussian approximation is used in the message passing process, so multiple rounds of iteration are required. The following is the message passing between ISS (corresponding to variable node s1) and ISE (corresponding to variable node s2); in the kth round of iteration, ISS is based on the external information from ISE. and prior distribution p(s1), according to the message passing rule, obtain the SP belief of s1 The corresponding posterior probability b app (s1) is approximately a complex Gaussian distribution The posterior mean vector is The posterior variance is in is the symbol prior variance; after completing the above steps, the external information passed by ISS to ISE is According to the following Gaussian distribution division equation

[0056]

[0057] Obtain The external mean vector external variance

[0058] Then, ISE is based on the external information from ISS and the likelihood of the observed data Calculate the SP belief of s2 The corresponding posterior probability is The posterior mean s 2,k =(γ w,k H H H+γ 2,k I) -1 (γ w,k H H z+γ 2,k r 2,k ), posterior variance After completing the above steps, the external verification information transmitted by ISE to ISS is expressed as in

[0059] The above completes a round of information transmission between ISS and ISE. Assume that the equalizer starts iterating from ISS and initializes the external mean vector to r 1,0 =0, the external variance is set to

[0060] The EM algorithm is used to estimate the noise accuracy, which is divided into E step and M step. In the E step, the following conditional expectation is calculated

[0061]

[0062] above The posterior probability obtained using ISE You can also use the posterior probability b of ISS app(s1); in the M step, the noise accuracy is obtained by the following formula:

[0063]

[0064] Taking the derivative of Equation 19 and setting it equal to zero, we obtain the noise accuracy estimate as follows:

[0065]

[0066] This estimate will be used in the next iteration;

[0067] After R rounds of iteration, the final symbol estimate is obtained

[0068] The OFDM underwater acoustic communication channel equalization method under fast time-varying conditions of the present invention has the following advantages: the EM-VAMP equalization proposed in the present invention has better performance than the traditional LMMSE equalization on the one hand, and its complexity is much lower than the ideal MAP equalization on the other hand, achieving a good compromise in terms of complexity and performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is an overall block diagram of the present invention;

[0070] Figure 2 is the factor graph corresponding to the VAMP equalizer of the present invention;

[0071] Figure 3 This is a block diagram of the EM-VAMP equalizer of the present invention;

[0072] Figure 4 This is a step diagram of the EM-VAMP equalization algorithm of the present invention;

[0073] Figure 5 is the local (H 1,1 ) display diagram;

[0074] Figure 6 This is a comparison diagram of estimated symbols under different iteration times of the EM-VAMP equalizer of the present invention;

[0075] Figure 7 This is a comparison chart of the bit error numbers of the EM-VAMP equalization and the LMMSE equalization of the present invention. DETAILED DESCRIPTION

[0076] In order to better understand the purpose, structure and function of the present invention, the following further describes in detail an OFDM underwater acoustic communication channel equalization method under fast time-varying conditions of the present invention in conjunction with the accompanying drawings.

[0077] The specific technical solutions of the present invention are as follows:

[0078] Step 1: Determine the number of transmitter transducers N and the center carrier frequency f c , transmission bandwidth B, number of OFDM subcarriers K, where K D are data subcarriers, K P are pilot subcarriers, so K=K D +K P , subcarrier spacing Δf. Let the transducer number be n, and determine the pilot symbol vector It is defined as a column vector of length K, but its value is non-zero only at the pilot subcarrier position and zero at other positions;

[0079] Step 2: Determine the number M of hydrophones at the receiving end, perform Doppler preprocessing on the received signal, and obtain the system input-output relationship;

[0080] Step 3: Based on the pilot symbols, the orthogonal matching pursuit (OMP) algorithm is used to estimate the multiple-input multiple-output (MIMO) channel parameters, and the frequency domain channel matrix H is further obtained based on the estimated parameters.

[0081] Step 4: Use the expectation maximization-vector approximate message passing EM-VAMP equalization algorithm to obtain the estimated value of the data symbol vector

[0082] In step 2, the specific steps for obtaining the input-output relationship of the MIMO system are as follows: For an N×M MIMO system consisting of N transducers and M hydrophones, the bandpass signal sent by the nth transducer is writing:

[0083]

[0084] Where t represents time, is the transmission symbol of the nth transducer, f k =(k-1-K / 2)Δf is the k-th baseband subcarrier frequency, g(t) is the shaping filter;

[0085] For the sub-channel between the nth transducer and the mth hydrophone, the following path-based underwater acoustic communication channel model is adopted:

[0086]

[0087] Where t represents time, τ represents delay, is the u-th order Taylor expansion coefficient of the p-th path amplitude, τ p,m,n is the initial delay of the path, α p,m,n represents the Doppler scaling factor of the path, and δ represents the Dirac function; therefore, the passband received signal of the mth hydrophone is:

[0088]

[0089] Where u! represents the factorial of u, represents the passband noise on the mth hydrophone;

[0090] remember is the estimated value of the Doppler scaling factor, The estimated value of carrier frequency offset CFO is obtained by resampling, carrier demodulation and carrier frequency offset CFO compensation of the above passband received signal to obtain the following baseband received signal:

[0091]

[0092] where ω m (t) is the baseband noise;

[0093] to r m (t) is sampled at a sampling rate of 1 / B, and then a discrete Fourier transform is performed to obtain the following frequency domain input and output relationship:

[0094]

[0095] in represents the residual Doppler of each path, w m [l] is the noise after sampling; H m,n [l,k] is called the ICI coefficient, which reflects the contribution of the symbol transmitted on the kth subcarrier to the received signal on the lth subcarrier;

[0096] In the 5th move Written as a column vector z m ; Written as a column vector s n ; Written as a column vector w m , we get the system input-output relationship in vector form:

[0097]

[0098] in is the subchannel matrix between the nth transducer and the mth hydrophone, expressed as follows:

[0099]

[0100] in is a diagonal matrix, and its kth diagonal element is is a banded matrix with half-bandwidth D, where half-bandwidth represents the maximum distance between the non-zero elements of the matrix and the main diagonal; Γ (u) (b p,m,n ) is [Γ (u) (b p,m,n )] l,k =G (u) (β l,k (b p,m,n )), where G (u) (·) represents the u-order derivative of the Fourier transform of g(·); From Equation 7, we can see that H m,n Is a parameter group nonlinear function.

[0101] In step 3, in order to realize the multi-input multi-output MIMO channel parameter estimation based on the orthogonal matching pursuit OMP algorithm, first replace the s on the right side of Equation 6 with n Decompose into in is the pilot part, is the data part, so Equation 6 is rewritten as:

[0102]

[0103] in represents the equivalent noise composed of observation noise and data symbol interference. The last equation in Equation 8 uses the relationship in Equation 7;

[0104] Then, Equation 8 is equivalent to a dictionary-based representation, and the delay candidate set is defined as and the residual Doppler factor candidate set b p ∈{-b max ,-b max +Δb,…,b max}, delay candidate set The size is Residual Doppler factor candidate set b p ∈{-b max ,-b max +Δb,...,b max The size of} is N b =2b max / Δb+1; Set the possible delays and Doppler factors of all sub-channels to fall into the above two candidate sets, that is, the channel delay-Doppler pair falls into The delay-Doppler grid is represented as follows:

[0105]

[0106] in

[0107] Equation 9 can be written in a more concise form

[0108] z m =Aξ m +v m Formula 10,

[0109] in:

[0110]

[0111]

[0112]

[0113]

[0114] In formula 10, A is called the dictionary, which is known, and the problem to be solved is ξ m , thus transforming the nonlinear problem of Equation 8 into a linear problem; for ξ m Elements in Only when the channel is in the aforementioned delay-Doppler grid If the point exists, its value is non-zero, otherwise it is zero, so ξ m is a sparse vector, which is solved by the orthogonal matching pursuit OMP algorithm; once ξ is determined m The non-zero elements in can determine the corresponding delay and Doppler, thereby obtaining the channel estimation

[0115] Get channel estimate After that, data symbol detection can be performed. First, the interference of the pilot symbol on the data symbol in Equation 6 is eliminated, and we can get in because The value at the pilot symbol position is zero, so the system model is further simplified as in Only by The non-zero data symbols in for Keep only the part of the column where the data symbol is located; Combine into column vector Combine into column vector Combine into column vector Will Combined into MIMO channel matrix The frequency domain input and output relationship of the MIMO system is obtained:

[0116] z=Ηs+w Formula 15.

[0117] In step 4, the expectation maximization-vector approximate message passing EM-VAMP equalization algorithm consists of three parts: internal soft equalizer, internal soft slicer, and EM-based signal-to-noise ratio estimator;

[0118] The following describes the VAMP equalization process based on the idea of ​​the sum-product SP algorithm based on Equation 15, setting the noise to obey the Gaussian distribution and its accuracy to γ w , then the joint probability density function of the received signal and the symbol to be estimated is:

[0119]

[0120] Where I is the identity matrix;

[0121] To obtain the factor graph representation, decompose s into s1=s2, and then Equation 16 is rewritten as:

[0122]

[0123] Where s1 and s2 are variable nodes, p(s1), δ(s1-s2) and is a factor node;

[0124] Gaussian approximation is used in the message passing process, so multiple rounds of iteration are required. The following is the message passing between the variable node s1 corresponding to the ISS and the variable node s2 corresponding to the ISE; in the kth round of iteration, the ISS is based on the external information from the ISE. and prior distribution p(s1), according to the message passing rule, obtain the SP belief of s1 The corresponding posterior probability b app (s1) is approximately a complex Gaussian distribution The posterior mean vector is The posterior variance is in is the symbol prior variance; after completing the above steps, the external information passed by ISS to ISE is According to the following Gaussian distribution division equation:

[0125]

[0126] Obtain The external mean vector external variance

[0127] Then, ISE is based on the external information from ISS and the likelihood of the observed data Calculate the SP belief of s2 The corresponding posterior probability is The posterior mean s 2,k =(γ w,k H H H+γ 2,k I) -1 (γ w,k H H z+γ 2,k r 2,k ), posterior variance After completing the above steps, the external verification information transmitted by ISE to ISS is expressed as in

[0128] The above completes a round of information transmission between ISS and ISE. Assume that the equalizer starts iterating from ISS and initializes the external mean vector to r 1,0 =0, the external variance is set to

[0129] The EM algorithm is used to estimate the noise accuracy, which is divided into E step and M step. In the E step, the following conditional expectation is calculated:

[0130]

[0131] above The posterior probability obtained using ISE You can also use the posterior probability b of ISS app (s1); in the M step, the noise accuracy is obtained by the following formula:

[0132]

[0133] Taking the derivative of Equation 19 and setting it equal to zero, we obtain the noise accuracy estimate as follows:

[0134]

[0135] This estimate will be used in the next iteration;

[0136] After R rounds of iteration, the final symbol estimate is obtained

[0137] The method of the present invention was verified using experimental data. The experiment involved a 1×4 multi-channel OFDM underwater acoustic communication system, using QPSK modulation and a convolutional code with a code rate of r = 1 / 2. Other system parameters are given in Table 1, where the pilot subcarriers are evenly distributed. The received signal's signal-to-noise ratio was approximately 10 dB. First, the received signal was preprocessed in the time domain: the estimated Doppler scaling factor was used. The signal is resampled and then the estimated CFO compensation is performed, and finally the received signal after Doppler preprocessing is subjected to discrete Fourier transform to obtain the frequency domain signal. The received signals mentioned below are all preprocessed frequency domain signals.

[0138] Table 1 OFDM underwater acoustic communication system parameters

[0139]

[0140] Figure 1 The overall block diagram of the present invention is given, which is mainly composed of the OMP channel estimation module and the EM-VAMP equalization module. For OMP channel estimation, the sparsity is set to S = 40, the highest order of the channel amplitude Taylor series expansion is U = 1, and the maximum possible channel delay τ max = 80 symbol periods, with a resolution of common points; residual Doppler scaling factor range -0.0003 to 0.0003, resolution 0.00001, total N b = 61 points. After obtaining the estimated channel parameters, the frequency domain channel matrix H is calculated, and the ICI depth D is limited to 3.

[0141] Figure 3 The block diagram of the EM-VAMP equalizer is given. The equalizer consists of ISE, ISS and EM-based noise power estimation modules. Figure 4 The specific process of EM-VAMP equalization is given, in which the initial noise variance It can be estimated from the signal power within the guard interval of the time domain received signal. The maximum number of iterations is set to R = 5. To improve the robustness of the equalizer, a damping factor ρ = 0.9 is introduced.

[0142] The beneficial effects of the present invention are described below in conjunction with the test results.

[0143] The coefficient vector obtained in the channel estimation stage The non-zero elements of are clustered in the delay-Doppler domain, and the residual Doppler factors of each path are roughly 5×10 -5 and -1.9×10 -4 The frequency domain channel matrix obtained according to equations 7 and 8 is the center dispersion. Composed of 4 sub-channel matrices composition. Figure 5 Subchannel H is presented 1,1 From the local magnified image, we can see that due to the influence of the residual Doppler factor and the time-varying channel amplitude, the channel matrix is ​​not a diagonal matrix, but a strip matrix, and the half-bandwidth D is within 3.

[0144] Figure 6The data symbol estimation output of the 1st, 3rd, and 5th iterations of the EM-VAMP equalizer is shown. It can be seen that the performance of the symbol estimation improves with the number of iterations. Figure 7 The comparison of bit errors for 12 OFDM symbol blocks detected by the EM-VAMP equalization of the present invention and the classic LMMSE equalization is shown. Both equalizations use OMP channel estimation. It can be seen that the equalization performance of the present invention is better than that of the LMMSE equalization.

[0145] It will be understood that the present invention is described by way of some embodiments, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be protected by the present invention.

Claims

1. A method for equalizing OFDM underwater acoustic communication channels under fast time-varying conditions, characterized in that: The steps include: Step 1: Determine the number of transmitter transducers N and the center carrier frequency f c , transmission bandwidth B, number of OFDM subcarriers K, where K D are data subcarriers, K P are pilot subcarriers, so K=K D +K P , subcarrier spacing Δf; let the transducer number be n, and determine the pilot symbol vector It is defined as a column vector of length K, but its value is non-zero only at the pilot subcarrier position and zero at other positions; Step 2: Determine the number M of hydrophones at the receiving end, perform Doppler preprocessing on the received signal, and obtain the input-output relationship of the N×M MIMO system; Step 3: Based on the pilot symbols, the orthogonal matching pursuit (OMP) algorithm is used to estimate the multiple-input multiple-output (MIMO) channel parameters, and the frequency domain channel matrix H is further obtained based on the estimated parameters. Step 4: Use the expectation maximization-vector approximate message passing EM-VAMP equalization algorithm to obtain the estimated value of the data symbol vector In step 2, the specific steps for obtaining the input-output relationship of the MIMO system are as follows: For an N×M MIMO system consisting of N transducers and M hydrophones, the bandpass signal sent by the nth transducer is writing: Where t represents time, is the transmission symbol of the nth transducer, f k =(k-1-K / 2)Δf is the k-th baseband subcarrier frequency, g(t) is the shaping filter; For the sub-channel between the nth transducer and the mth hydrophone, the following path-based underwater acoustic communication channel model is adopted: Where t represents time, τ represents delay, is the u-th order Taylor expansion coefficient of the p-th path amplitude, τ p,m,n is the initial delay of the path, α p,m,n represents the Doppler scaling factor of the path, and δ represents the Dirac function; therefore, the passband received signal of the mth hydrophone is: Where u! represents the factorial of u, represents the passband noise on the mth hydrophone; remember is the estimated value of the Doppler scaling factor, The estimated value of carrier frequency offset CFO is obtained by resampling, carrier demodulation and carrier frequency offset CFO compensation of the above passband received signal to obtain the following baseband received signal: where ω m (t) is the baseband noise; to r m (t) is sampled at a sampling rate of 1 / B, and then a discrete Fourier transform is performed to obtain the following frequency domain input and output relationship: in represents the residual Doppler of each path, w m [l] is the noise after sampling; H m,n [l,k] is called the ICI coefficient, which reflects the contribution of the symbol transmitted on the kth subcarrier to the received signal on the lth subcarrier; In the 5th move Written as a column vector z m ; Written as a column vector s n ; Written as a column vector w m , we get the system input-output relationship in vector form: in is the subchannel matrix between the nth transducer and the mth hydrophone, expressed as follows: in is a diagonal matrix, and its kth diagonal element is is a banded matrix with half-bandwidth D, where half-bandwidth represents the maximum distance between the non-zero elements of the matrix and the main diagonal; Γ (u) (b p,m,n ) is [Γ (u) (b p,m,n )] l,k =G (u) (β l,k (b p,m,n )), where G (u) (·) represents the u-order derivative of the Fourier transform of g(·); From Equation 7, we can see that H m,n Is a parameter group nonlinear function.

2. The OFDM underwater acoustic communication channel equalization method under fast time-varying conditions according to claim 1 is characterized in that: In step 3, in order to realize the multi-input multi-output MIMO channel parameter estimation based on the orthogonal matching pursuit OMP algorithm, first replace the s on the right side of Equation 6 with n Decompose into in is the pilot part, is the data part, so Equation 6 is rewritten as: in represents the equivalent noise composed of observation noise and data symbol interference. The last equation in Equation 8 uses the relationship in Equation 7; Then, Equation 8 is equivalent to a dictionary-based representation, and the delay candidate set is defined as and the residual Doppler factor candidate set b p ∈{-b max ,-b max +Δb,...,b max }, delay candidate set The size is Residual Doppler factor candidate set b p ∈{-b max ,-b max +Δb,...,b max The size of} is N b =2b max / Δb+1; Set the possible delays and Doppler factors of all sub-channels to fall into the above two candidate sets, that is, the channel delay-Doppler pair falls into The delay-Doppler grid is represented as follows: in Equation 9 can be written in a more concise form z m = Aξ m + v m Equation 10 in: In formula 10, A is called the dictionary, which is known, and the problem to be solved is ξ m , thus transforming the nonlinear problem of Equation 8 into a linear problem; for ξ m Elements in Only when the channel is in the aforementioned delay-Doppler grid If the point exists, its value is non-zero, otherwise it is zero, so ξ m is a sparse vector, which is solved by the orthogonal matching pursuit OMP algorithm; once ξ is determined m The non-zero elements in can determine the corresponding delay and Doppler, thereby obtaining the channel estimation Get channel estimate After that, data symbol detection can be performed. First, the interference of the pilot symbol on the data symbol in Equation 6 is eliminated, and we can get in because The value at the pilot symbol position is zero, so the system model is further simplified as in Only by The non-zero data symbols in for Keep only the part of the column where the data symbol is located; Combine into column vector Combine into column vector Combine into column vector Will Combined into MIMO channel matrix The frequency domain input and output relationship of the MIMO system is obtained: z=Ηs+w Formula 15.

3. The OFDM underwater acoustic communication channel equalization method under fast time-varying conditions according to claim 1, characterized in that: In step 4, the expectation maximization-vector approximate message passing EM-VAMP equalization algorithm consists of three parts: internal soft equalizer, internal soft slicer, and EM-based signal-to-noise ratio estimator; The following describes the VAMP equalization process based on the idea of ​​the sum-product SP algorithm based on Equation 15, setting the noise to obey the Gaussian distribution and its accuracy to γ w , then the joint probability density function of the received signal and the symbol to be estimated is: Where I is the identity matrix; To obtain the factor graph representation, decompose s into s1=s2, and then Equation 16 is rewritten as: Where s1 and s2 are variable nodes, p(s1), δ(s1-s2) and is a factor node; Gaussian approximation is used in the message passing process, so multiple rounds of iteration are required. The following is the message passing between the variable node s1 corresponding to the ISS and the variable node s2 corresponding to the ISE; in the kth round of iteration, the ISS is based on the external information from the ISE. and prior distribution p(s1), according to the message passing rule, obtain the SP belief of s1 The corresponding posterior probability b app (s1) is approximately a complex Gaussian distribution The posterior mean vector is The posterior variance is in is the symbol prior variance; after completing the above steps, the external information passed by ISS to ISE is According to the following Gaussian distribution division equation: Obtain The external mean vector external variance Then, ISE is based on the external information from ISS and the likelihood of the observed data Calculate the SP belief of s2 The corresponding posterior probability is The posterior mean s 2,k =(γ w,k H H H+γ 2,k I) -1 (γ w,k H H z+γ 2,k r 2,k ), posterior variance After completing the above steps, the external verification information transmitted by ISE to ISS is expressed as in The above completes a round of information transmission between ISS and ISE. Assume that the equalizer starts iterating from ISS and initializes the external mean vector to r 1,0 =0, the external variance is set to The EM algorithm is used to estimate the noise accuracy, which is divided into E step and M step. In the E step, the following conditional expectation is calculated: above The posterior probability obtained using ISE You can also use the posterior probability b of ISS app (s1); in the M step, the noise accuracy is obtained by the following formula: Taking the derivative of Equation 19 and setting it equal to zero, we obtain the noise accuracy estimate as follows: This estimate will be used in the next iteration; After R rounds of iteration, the final symbol estimate is obtained

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