Underwater acoustic channel parametric modeling method based on variable parameter autoregression model

Abstract

The invention discloses an underwater acoustic channel parametric modeling method based on a variable parameter autoregression model, which comprises the following steps of: constructing a variable parameter autoregression model of an underwater acoustic channel based on a frequency-related model coefficient and a model invariant coefficient; carrying out model coefficient solving on the constructed variable parameter autoregression model to obtain a model pole related to the frequency; and according to the frequency-related model poles, obtaining a frequency-related underwater acoustic channel multipath structure and statistical distribution parameters. According to the method, the multipath cluster is described by adopting the pole parameter of the variable parameter autoregression model, the pole can be regarded as the cluster characteristic parameter of the underwater acoustic channel, and compared with a time delay-amplitude and emergence angle-arrival angle mode, the number of the parameters is greatly reduced because the pole with larger amplitude corresponds to one cluster of multipath, and the birth and death characteristics of scattering multipath do not need to be considered. In addition, the variable parameter autoregression model can be used for describing multipath structures corresponding to different frequencies, and a fine and visual channel characteristic representation method is provided.

Description

Technical Field

[0001] The present invention belongs to the field of underwater communication technology, relates to underwater acoustic channel modeling technology, and specifically relates to an underwater acoustic channel parameterized modeling method based on a variable parameter autoregressive model. Background Art

[0002] The underwater acoustic channel model can facilitate the analysis of the impact of the marine environment on the propagation law of underwater acoustic communication signals, support the development of underwater acoustic communication simulation tools, and be used to guide the design of underwater acoustic communication systems and the optimization of algorithms.

[0003] Based on the parameter types of the underwater acoustic channel model, underwater acoustic channel modeling methods can be divided into delay-amplitude and departure-angle-arrival methods. Since the sound velocity profile varies with seawater depth, according to the law of refraction, sound waves propagate in directions with lower sound velocity. Furthermore, the seabed and surface reflect sound waves. Furthermore, scatterers in the seawater environment, such as a dynamic sea surface, rough seabed, and tiny particles, cause sound waves to scatter. Due to refraction and reflection, the underwater acoustic channel exhibits a complex multipath structure. Further scattering, the arrival paths of refraction and reflection are accompanied by relatively small-amplitude scattered paths, representing the multipath clustering characteristic of the underwater acoustic channel. Using delay-amplitude and departure-angle-arrival methods to describe multipath clustering often requires a large number of parameters, and given the birth and death characteristics of multipath, the number of parameters also varies over time. Furthermore, channel models based on delay-amplitude and departure-angle-arrival methods are often unfavorable for the random generation of underwater acoustic channels. In addition, considering the frequency differences of underwater acoustic channels, that is, the multipath structures corresponding to different frequencies are different, the number of parameters required will increase greatly when using delay-amplitude and departure angle-arrival angle. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a parametric modeling method for underwater acoustic channels based on a variable parameter autoregressive model is provided.

[0005] Technical solution: To achieve the above-mentioned purpose, the present invention provides a method for parameterized modeling of an underwater acoustic channel based on a variable parameter autoregressive model, comprising the following steps:

[0006] S1: Construct a variable parameter autoregressive model of the underwater acoustic channel based on the frequency-related model coefficients and the model invariant coefficients;

[0007] S2: Solve the model coefficients of the constructed variable parameter autoregressive model to obtain the frequency-related model poles;

[0008] S3: Obtain the frequency-dependent underwater acoustic channel multipath structure and statistical distribution parameters based on the frequency-dependent model poles.

[0009] Furthermore, the construction of the variable parameter autoregressive model of the underwater acoustic channel in step S1 includes:

[0010] A1: Transmission function H(f n ) is represented by a variable parameter autoregressive model:

[0011]

[0012] Among them, H(n) is the nth frequency point f n The corresponding frequency response, f n Represents the nth frequency point of the underwater acoustic channel, A p (f n ) represents the frequency f n The corresponding model coefficient, E(f n ) represents complex noise, P is the model order, which can be estimated using the Bayesian Information Criterion; in the field of channel research, the frequency response is also called the transfer function;

[0013] A2: Using Q Fourier basis functions G q (n) Decomposition to obtain frequency-related model coefficients;

[0014] A3: Construct a solution equation for the model's invariant coefficients.

[0015] Furthermore, the frequency-related model coefficients in step A2 are expressed as:

[0016]

[0017] G q (n) = e -i2π(q-1)n / N

[0018] Among them, the superscript T represents the transpose, vector G(n) and A p G(n)=[G1(n),...,G Q (n)] T and A p =[A p,1 ,...,A p,Q ] T , A p,q is the coefficient A related to the pth frequency p (n) is the qth invariant coefficient after decomposition, and the decomposition order Q is estimated based on the decreasing trend of the variance of the complex noise.

[0019] Furthermore, the solution equation for the model invariant coefficient in step A3 is:

[0020] H=Π·A+E

[0021] Where H, π, A and E are as follows:

[0022] H=[H(1) H(2) LH(N)] T

[0023] Π=[H G (1) -H G (2) L-H G (N)] T

[0024] E=[E(1) E(2) LE(N)] T

[0025]

[0026] Among them, H, A and E are the transfer function vector, model coefficient vector and complex noise vector respectively, π is the matrix used to solve the model coefficient, which is the vector H constructed by the basis function and the transfer function G (n) obtained.

[0027] Furthermore, the step S2 specifically includes:

[0028] B1: Use least squares to estimate the invariant parameters of the model as follows:

[0029]

[0030] B2: Solve the frequency-related model coefficients based on the Fourier basis, as shown below:

[0031]

[0032] B3: Perform Z-transform on the frequency-dependent model coefficients to obtain the frequency-dependent model pole parameters.

[0033] Furthermore, the Z transform in step B3 is expressed as follows:

[0034]

[0035] in, is the frequency f n The corresponding pole parameters.

[0036] Furthermore, the acquisition of the frequency-related underwater acoustic channel multipath structure in step S3 includes:

[0037] C1: Frequency-dependent pole The frequency-dependent Z-transform form of the underwater acoustic channel is obtained as follows:

[0038]

[0039] C2: According to the relationship between frequency and time delay, which are Fourier transforms, substitute z = exp(-i2πτ) into h(f n ,z), the frequency-related underwater acoustic channel multipath structure is obtained as follows:

[0040]

[0041] Furthermore, the amplitude and phase distribution characteristics of the extreme points of the statistical model in step S3 are fitted using different probability density functions to obtain frequency-related statistical distribution parameters.

[0042] The method of the present invention innovatively utilizes a variable-parameter autoregressive model. During the underwater acoustic channel modeling process, the model's variable parameters are treated as model parameters, and their variation is frequency-dependent. This yields model parameters at different frequencies, enabling more detailed channel characteristics. During the channel modeling process, the discrete transfer function is treated as a non-stationary sequence suitable for processing with a variable-parameter autoregressive model, where the variable parameters are the frequency-dependent model coefficients. To solve for the variable parameters, basis functions are used to decompose the variable coefficients into frequency-independent coefficients, i.e., invariant parameters. These coefficients are then solved using the least squares method and synthesized again using the basis functions to obtain the frequency-dependent coefficients. Based on the relationship between the model coefficients and the poles, frequency-dependent poles are determined. Compared to the channel parameters of delay-amplitude and departure-angle-arrival angle, poles can more concisely describe the characteristics of multipath clusters, and their number is slightly greater than the number of multipath clusters. Based on the frequency-dependent poles, frequency-dependent multipath channels can be easily obtained, thus enabling the variable-parameter autoregressive model to reflect more frequency variability. Treating the model poles as channel parameters and fitting them using a probability distribution function yields a frequency-dependent statistical model that conforms to the frequency variability characteristic of the underwater acoustic channel.

[0043] Beneficial effects: Compared with the prior art, the present invention uses the pole parameters of the variable parameter autoregressive model to describe the multipath cluster. The poles can be regarded as cluster characteristic parameters of the underwater acoustic channel. Compared with the delay-amplitude and departure angle-arrival angle methods, since the poles with larger amplitudes correspond to a cluster of multipaths, there is no need to describe each scattered micropath, so the number of parameters is greatly reduced. In addition, the scattered multipaths in the multipath cluster have birth and death characteristics, but the multipath cluster exists stably. Therefore, using the poles as channel parameters does not require considering the birth and death characteristics of the scattered multipaths. In addition, the variable parameter autoregressive model can be used to describe the multipath structure corresponding to different frequencies, providing a sophisticated and intuitive channel characteristic representation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the process of the present invention;

[0045] Figure 2The fourth-order pole distribution related to the frequencies of 4.2, 4.7, 5.2, 5.7, 6.2, 6.7, 7.2 and 7.7 kHz obtained by the method of the present invention;

[0046] Figure 3 The fourth-order pole amplitude distribution related to the frequencies of 4.7, 5.7, 6.7 and 7.7 kHz obtained by the method of the present invention;

[0047] Figure 4 The phase distribution of the fourth-order poles related to the frequencies of 4.7, 5.7, 6.7 and 7.7 kHz obtained by the method of the present invention;

[0048] Figure 5 The pole amplitude and phase distribution parameters and the change of mean and variance with frequency obtained by the method of the present invention;

[0049] Figure 6 The frequency-related multipath structure of the underwater acoustic channel obtained by the method of the present invention. DETAILED DESCRIPTION

[0050] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0051] Example 1:

[0052] like Figure 1 As shown, this embodiment provides a method for parameterized modeling of an underwater acoustic channel based on a variable parameter autoregressive model, comprising the following steps:

[0053] S1: Construct a variable parameter autoregressive model of the underwater acoustic channel based on the frequency-dependent model coefficients and the model invariant coefficients. The specific process includes:

[0054] A1: Transmission function H(f n ) is represented by a variable parameter autoregressive model:

[0055]

[0056] Among them, H(n) is the nth frequency point f n The corresponding frequency response, f n Represents the nth frequency point of the underwater acoustic channel, A p (f n ) represents the frequency f n The corresponding model coefficient, E(f n ) represents complex noise, P is the model order, and can be estimated using the Bayesian Information Criterion;

[0057] A2: Using Q Fourier basis functions G q (n) Decompose to obtain frequency-related model coefficients:

[0058]

[0059] G q (n) = e -i2π(q-1)nN

[0060] Among them, the superscript T represents the transpose, vector G(n) and A p G(n)=[G1(n),...,G Q (n)] T and A p =[A p,1 ,...,A p,Q ] T , A p,q is the coefficient A related to the pth frequency p (n) The qth invariant coefficient after decomposition, the decomposition order Q is estimated based on the decreasing trend of the variance of the complex noise;

[0061] A3: Construct the solution equation of the model's invariant coefficients:

[0062] H=Π·A+E

[0063] Where H, π, A and E are as follows:

[0064] H=[H(1)H(2)LH(N)] T

[0065] Π=[-H G (1) -H G (2) L-H G (N)] T

[0066] E=[E(1) E(2) LE(N)] T

[0067]

[0068] Among them, H, A and E are the transfer function vector, model coefficient vector and complex noise vector respectively, π is the matrix used to solve the model coefficient, which is the vector H constructed by the basis function and the transfer function G (n) obtained;

[0069] S2: Solve the model coefficients of the constructed variable parameter autoregressive model to obtain the frequency-related model poles; specifically, it includes:

[0070] B1: Use least squares to estimate the invariant parameters of the model as follows:

[0071]

[0072] B2: Solve the frequency-related model coefficients based on the Fourier basis, as shown below:

[0073]

[0074] B3: Perform Z transform on the frequency-dependent model coefficients to obtain the frequency-dependent model pole parameters, which are expressed as follows:

[0075]

[0076] in, is the frequency f n The corresponding pole parameters.

[0077] S3: Obtain frequency-dependent underwater acoustic channel multipath structure and statistical distribution parameters based on frequency-dependent model poles;

[0078] The acquisition of frequency-dependent underwater acoustic channel multipath structure includes:

[0079] C1: Frequency-dependent pole The frequency-dependent Z-transform form of the underwater acoustic channel is obtained as follows:

[0080]

[0081] C2: According to the relationship between frequency and time delay, z can be exp(-i2pt), and z = exp(-i2πτ) is substituted into h(f n ,z), the frequency-related underwater acoustic channel multipath structure is obtained as follows:

[0082]

[0083] C3: The amplitude and phase distribution characteristics of the statistical model poles are fitted using different probability density functions to obtain frequency-related statistical distribution parameters.

[0084] Example 2:

[0085] To verify the effectiveness of the modeling method of the present invention, this embodiment was verified with measured data. The relevant parameters of the underwater acoustic channel are as follows:

[0086] 1. The channel measurement frequency range is 4 to 8 kHz, the sampling rate is 8 kHz, and the measured channel has been downsampled to baseband;

[0087] 2. A total of 4,000 measured underwater acoustic channels;

[0088] 3. The model order P is 4 and the decomposition order is 50.

[0089] For the frequency-dependent pole magnitude and phase, Rician and Weibull distributions are used, respectively, as shown below:

[0090]

[0091] Where s and σ are the non-centrality parameter and scale parameter of the Rician distribution, a and b are the scale and shape parameters of the Weibull distribution, and I0(xs / σ 2 ) is the 0th-order modified Bessel function of the first kind.

[0092] The local scattering function is used to extract the root mean square delay and root mean square Doppler shift corresponding to different frequencies. The Ricean distribution is used to describe the statistical distribution laws of the root mean square delay and root mean square Doppler shift at different frequencies. The changes of the Ricean distribution parameters (non-center parameter and scale parameter) of the measured channel and the playback channel with frequency are compared.

[0093] Figure 2 The fourth-order pole distributions related to the frequencies of 4.2, 4.7, 5.2, 5.7, 6.2, 6.7, 7.2 and 7.7 kHz obtained by the modeling method of the present invention correspond to Figure 2 In (a)-(f), as the frequency increases, the distribution of the four poles becomes concentrated, which shows that the pole distribution of the model has obvious frequency differences. At the same time, the higher the order, the more concentrated the pole distribution.

[0094] Figure 3 The amplitude distribution of the fourth-order poles related to the frequencies of 4.7, 5.7, 6.7 and 7.7 kHz obtained by the modeling method of the present invention. The first to fourth order poles correspond to Figure 3 From (a1)-(a4), (b1)-(b4), (c1)-(c4), and (d1)-(d4), we can see that the amplitude distribution of each order pole becomes more concentrated as frequency increases. Furthermore, the first- through third-order poles correspond to three clusters of multipath in the time domain, respectively. Therefore, the first-order pole has the largest mean, and the amplitude mean gradually decreases as the order increases. Compared to the delay-amplitude and departure-angle-arrival equations, a single pole can describe a cluster of multipath, demonstrating the simplicity of the pole parameters.

[0095] Figure 4 The phase distribution of the fourth-order poles related to the frequencies of 4.7, 5.7, 6.7 and 7.7 kHz obtained by the modeling method of the present invention. The first to fourth order poles correspond to Figure 4In (a1)-(a4), (b1)-(b4), (c1)-(c4), and (d1)-(d4), the phase of the pole is linearly related to the multipath cluster delay. The three clusters of multipath and the corresponding poles gradually increase, indicating that the multipath cluster can reflect the time variability of the multipath cluster;

[0096] Figure 5 The pole amplitude and phase distribution parameters and the change of mean and variance with frequency obtained by the modeling method of the present invention are as follows: Figure 5 (a1) and (a2) are the noncentral parameter and scale parameter of the pole amplitude distribution, respectively; (b1) and (b2) are the scale parameter and shape parameter of the pole phase distribution, respectively. The mean of the dotted pole amplitude or phase, the noncentral parameter of the Rician distribution, and the scale parameter of the Weibull distribution can respectively reflect the change of the pole amplitude and phase mean with frequency; the scale parameter of the Rician distribution and the shape parameter of the Weibull distribution also reflect that the pole distribution is more concentrated with frequency; the change of the statistical parameters with frequency also verifies that the proposed parameterized model can accurately reflect the frequency variability of the underwater acoustic channel.

[0097] Figure 6 The frequency-related multipath structure of the underwater acoustic channel obtained by the modeling method of the present invention is as follows: Figure 6 (a) is the time-varying impulse response of the underwater acoustic channel, (b) is the impulse response slice, (c) is the transfer function, and (d) is the frequency-dependent multipath structure of the underwater acoustic channel. It can be seen that the multipath delay and multipath amplitude corresponding to different frequencies are significantly different, that is, the channel structure has frequency correlation.

Claims

1. A parametric modeling method for underwater acoustic channels based on a variable parameter autoregressive model, characterized in that: The steps include: S1: Construct a variable parameter autoregressive model of the underwater acoustic channel based on the frequency-related model coefficients and the model invariant coefficients; S2: Solve the model coefficients of the constructed variable parameter autoregressive model to obtain the frequency-related model poles; S3: Obtain the frequency-dependent underwater acoustic channel multipath structure and statistical distribution parameters based on the frequency-dependent model poles.

2. The method for parameterized modeling of an underwater acoustic channel based on a variable parameter autoregressive model according to claim 1, characterized in that: The construction of the variable parameter autoregressive model of the underwater acoustic channel in step S1 includes: A1: Transmission function H(f n ) is represented by a variable parameter autoregressive model: Among them, H(n) is the nth frequency point f n The corresponding frequency response, f n Represents the nth frequency point of the underwater acoustic channel, A p (f n ) represents the frequency f n The corresponding model coefficient, E(f n ) represents complex noise, P is the model order, and can be estimated using the Bayesian Information Criterion; A2: Using Q Fourier basis functions G q (n) Decomposition to obtain frequency-related model coefficients; A3: Construct a solution equation for the model's invariant coefficients.

3. The method for parameterized modeling of underwater acoustic channels based on a variable parameter autoregressive model according to claim 2, characterized in that: The frequency-related model coefficients in step A2 are expressed as: G q (n)=e -i2π(q-1)n / N Among them, the superscript T represents the transpose, vector G(n) and A p G(n)=[G1(n),...,G Q (n)] T and A p =[A p,1 ,...,A p,Q ] T , A p,q is the coefficient A related to the pth frequency p (n) is the qth invariant coefficient after decomposition, and the decomposition order Q is estimated based on the decreasing trend of the variance of the complex noise.

4. The method for parameterized modeling of underwater acoustic channels based on a variable parameter autoregressive model according to claim 3 is characterized in that: The solution equation for the model invariant coefficient in step A3 is: H=Π·A+E Where H, π, A and E are as follows: H=[H(1) H(2) L H(N)] T Π=[-H G (1) -H G (2) L-H G (N)] T E=[E(1) E(2) LE(N)] T Among them, H, A and E are the transfer function vector, model coefficient vector and complex noise vector respectively, π is the matrix used to solve the model coefficient, which is the vector H constructed by the basis function and the transfer function G (n) obtained.

5. The method for parameterized modeling of underwater acoustic channels based on a variable parameter autoregressive model according to claim 4 is characterized in that: The step S2 specifically includes: B1: Use least squares to estimate the invariant parameters of the model as follows: B2: Solve the frequency-related model coefficients based on the Fourier basis, as shown below: B3: Perform Z-transform on the frequency-dependent model coefficients to obtain the frequency-dependent model pole parameters.

6. The method for parameterized modeling of underwater acoustic channels based on a variable parameter autoregressive model according to claim 5, characterized in that: The Z transform in step B3 is expressed as follows: in, is the frequency f n The corresponding pole parameters.

7. The method for parameterized modeling of underwater acoustic channels based on a variable parameter autoregressive model according to claim 6, characterized in that: The acquisition of the frequency-related underwater acoustic channel multipath structure in step S3 includes: C1: Frequency-dependent pole The frequency-dependent Z-transform form of the underwater acoustic channel is obtained as follows: C2: According to the relationship between frequency and time delay, which are Fourier transforms, substitute z = exp(-i2πτ) into h(f n ,z), the frequency-related underwater acoustic channel multipath structure is obtained as follows:

8. The method for parameterized modeling of underwater acoustic channels based on a variable parameter autoregressive model according to claim 1, characterized in that: The amplitude and phase distribution characteristics of the extreme points of the statistical model in step S3 are fitted using different probability density functions to obtain frequency-related statistical distribution parameters.

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