CN112737702B - MIMO underwater acoustic channel estimation method under sparse interference background - Google Patents

MIMO underwater acoustic channel estimation method under sparse interference background Download PDF

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CN112737702B
CN112737702B CN202011508369.5A CN202011508369A CN112737702B CN 112737702 B CN112737702 B CN 112737702B CN 202011508369 A CN202011508369 A CN 202011508369A CN 112737702 B CN112737702 B CN 112737702B
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殷敬伟
葛威
韩笑
生雪莉
李爽
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Harbin Engineering University
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Abstract

The invention provides a MIMO underwater sound channel estimation method under a sparse interference background, and belongs to the field of underwater sound signal processing. The invention utilizes the variational Bayes inference theory to respectively estimate the pulse interference and the sparsity of the channel, and simultaneously fully utilizes the spatial correlation of the channel to obtain the processing gain. Compared with the existing underwater acoustic channel estimation method, the method has higher estimation precision and lower calculation complexity.

Description

MIMO underwater acoustic channel estimation method under sparse interference background
Technical Field
The invention relates to a MIMO underwater sound channel estimation method under a sparse interference background, belonging to the field of underwater sound signal processing.
Background
The underwater acoustic communication is the most effective means for underwater information transmission at present, and the acquisition of more accurate underwater acoustic channel information is of great importance to the improvement of the underwater acoustic communication quality. The traditional underwater acoustic channel estimation method such as a least square method, a sparse channel estimation method based on compressed sensing and the like assumes additive white gaussian noise as background noise, however, abundant impulse noise is distributed in the real marine environment, and the impulse noise may come from krill, ice cover extrusion and rupture, sonar emission artificial signals and the like, so that the performance of the traditional underwater acoustic channel estimation method is reduced. In recent years, a channel and impulse noise joint estimation method based on a Bayesian estimation theory appears, however, the method ignores the difference between the sparsity of an underwater acoustic channel and the sparsity of impulse noise, so that theoretical performance loss exists, and meanwhile, the joint estimation causes the improvement of the computational complexity.
Disclosure of Invention
The invention aims to provide a MIMO underwater acoustic channel estimation method under a sparse interference background.
The purpose of the invention is realized as follows: the method comprises the following steps:
the method comprises the following steps: building a MIMO underwater acoustic communication system, and receiving a plurality of pilot signals received by a hydrophone;
step two: initializing parameters; setting t to 1, initializing
Figure BDA0002845585740000011
μh,Σh,μe,ΣeThe sum of the values of ε, B and δ,
Figure BDA0002845585740000012
for estimating the resulting channel, muhIs the mean value of the channel vector ∑hIs the channel vector variance, mueAs the mean of impulse noise vectors, sigmaeThe variance of the impulse noise vector is shown, epsilon is a hyper-parameter representing sparsity, B is a space correlation matrix, and delta is a preset threshold;
step three: iterative computation, updating according to a joint distribution function, comprising:
updating
Figure BDA0002845585740000013
Figure BDA0002845585740000014
Updating muhSum-sigmah：
Figure BDA0002845585740000015
Figure BDA0002845585740000016
Updating mueSum-sigmae：
Figure BDA0002845585740000017
Figure BDA0002845585740000018
Updating epsilon0:L-1(underwater acoustic channel sparsity) and B:
Figure BDA0002845585740000021
Figure BDA0002845585740000022
updating
Figure BDA0002845585740000023
(impulse noise sparsity):
Figure BDA0002845585740000024
let T be T +1, if T is T or
Figure BDA0002845585740000025
Then output
Figure BDA0002845585740000026
Otherwise, continuing the iteration;
step four: outputting the result of the channel estimation, and outputting,
Figure BDA0002845585740000027
the invention also includes such structural features:
1. the received signal model is:
ym≈Xhm+em+wm
wherein the content of the first and second substances,
Figure BDA0002845585740000028
is the received signal of the mth hydrophone, NpIs the pilot sequence length, and L is the channel length;
Figure BDA0002845585740000029
Figure BDA00028455857400000210
is the l-th tap of the channel between the nth transmitting transducer and the mth hydrophone, N being the total number of transmitting transducers;
Figure BDA00028455857400000211
is defined as:
Figure BDA00028455857400000212
wherein the content of the first and second substances,
Figure BDA00028455857400000213
is a known pilot sequence;
Figure BDA00028455857400000214
in order to be the term of the impulse noise,
Figure BDA00028455857400000215
is an independent identically distributed complex gaussian noise vector with zero mean variance σ.
Compared with the prior art, the invention has the beneficial effects that: the invention separates the sparsity of the underwater acoustic channel from the sparsity of the impulse noise, namely, dividing the hyper-parameter epsilon into epsilon0:L-1And
Figure BDA00028455857400000216
and the estimation is respectively carried out, so that the performance loss caused by simultaneous estimation of sparsity in general Bayesian joint estimation is avoided, and the estimation precision is higher. In addition, inIn the channel and impulse noise joint estimation method based on the Bayes estimation theory, the vector variance sigma needs to be calculated by utilizing a matrix containing a parameter epsilon for inversion, and epsilon is respectively utilized in the method0:L-1And ε0:L-1Inversion is carried out, the matrix dimension is smaller, and the calculation complexity is lower. And considering the spatial correlation B, more processing gains are obtained, and the estimation precision is further improved.
Drawings
FIG. 1 is a flow chart of an iterative update distribution function;
fig. 2 is an analog noise time-domain waveform, q is 0.002, INR is 30;
fig. 3(a) and (b) are curves of channel estimation MSE with SNR: fig. 3(a) transducer No. 2 (strong spatial correlation), noise model GMM, p is 0.03, INR is 20dB, training sequence is 300 symbols long; fig. 3(b) transducer No. 2 (weak spatial correlation), noise model GMM, p is 0.03, INR is 20dB, training sequence is 300 symbols long;
fig. 4(a) and (b) are the variation curves of channel estimation MSE with SNR of transducer No. 2 (strong spatial correlation): fig. 4(a) shows the noise model as GMM, p is 0.01, INR is 20dB, and the training sequence is 300 symbols long; the noise model in fig. 4(b) is GMM, p is 0.01, INR is 25dB, and the training sequence is 300 symbols long.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The steps of the invention are as follows with reference to the attached drawings:
(1) and (4) building a MIMO underwater acoustic communication system, and receiving the multipath pilot signals received by the hydrophone. The received signal is modeled as
ym≈Xhm+em+wm
Wherein the content of the first and second substances,
Figure BDA0002845585740000031
is the received signal of the mth hydrophone, NpIs the pilot sequence length, L is the channel length, hm,l＝[hm,1(l) hm,2(l)…hm,N(l)]T∈cN×1，
Figure BDA0002845585740000032
Is the l-th tap of the channel between the nth transmitting transducer and the mth hydrophone, and N is the total number of transmitting transducers.
Figure BDA0002845585740000033
Figure BDA0002845585740000034
Is defined as:
Figure BDA0002845585740000035
wherein the content of the first and second substances,
Figure BDA0002845585740000036
is a known pilot sequence.
Figure BDA0002845585740000037
In order to be the term of the impulse noise,
Figure BDA0002845585740000038
is an independent identically distributed complex gaussian noise vector with zero mean variance σ.
(2) And initializing parameters. Setting t to 1, initializing
Figure BDA0002845585740000041
μh,Σh,μe,Σeε, B and δ. Wherein, the first and second guide rollers are arranged in a row,
Figure BDA0002845585740000042
for estimating the resulting channel, muhIs the mean value of the channel vector ∑hIs the channel vector variance, mueAs the mean of impulse noise vectors, sigmaeThe variance of the impulse noise vector is shown, epsilon is a hyper-parameter representing sparsity, B is a space correlation matrix, and delta is a preset threshold;
(3) and (5) performing iterative computation.
Updating
Figure BDA0002845585740000043
Figure BDA0002845585740000044
Updating muhSum-sigmah：
Figure BDA0002845585740000045
Figure BDA0002845585740000046
Updating mueSum-sigmae：
Figure BDA0002845585740000047
Figure BDA0002845585740000048
Updating epsilon0:L-1(underwater acoustic channel sparsity) and B:
Figure BDA0002845585740000049
Figure BDA00028455857400000410
updating
Figure BDA00028455857400000411
(impulse noise sparsity):
Figure BDA00028455857400000412
t is T +1, if T is T or
Figure BDA00028455857400000413
Then output
Figure BDA00028455857400000414
Otherwise, the iteration is continued.
(4) And outputting a channel estimation result.
Figure BDA00028455857400000415
In the implementation, considering the spatial correlation of the MIMO channel, we define hmA priori likelihood function
Figure BDA00028455857400000416
Wherein the content of the first and second substances,
Figure BDA00028455857400000519
denotes a Gaussian distribution, RmComprises hmSparsity epsilon of vector0:L-1And a spatial correlation matrix B, which is defined as
Rm＝diag{ε0B0,…,εL-1BL-1}
Figure BDA0002845585740000051
To determine the covariance of the spatial correlation of the ith tap of the sparse channel. Due to BiSubject to a uniform distribution, we describe all B using one positive definite matrix Bi. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002845585740000052
emhas a prior likelihood function of
Figure BDA0002845585740000053
In this section, we use variational Bayesian inference fitting
Figure BDA0002845585740000054
(is defined as
Figure BDA0002845585740000055
). To separate h in Bayesian inferencemAnd emWe will
Figure BDA0002845585740000056
The limitation is to factorize as follows:
Figure BDA0002845585740000057
the basic idea of variational Bayesian inference is to find the way to minimize
Figure BDA0002845585740000058
And
Figure BDA0002845585740000059
best factorization of KL divergence between
Figure BDA00028455857400000510
Namely, it is
Figure BDA00028455857400000511
Let Ψ ═ h for simplicity of representationm,emAnd epsilon, sigma represents the hyper-parameter that needs to be estimated. The optimal factorization should satisfy the following formula
Figure BDA00028455857400000512
Therein ΨiIs the i-th element of Ψ,
Figure BDA00028455857400000513
is that
Figure BDA00028455857400000514
Obviously, all q · (Ψ)i) Are interdependent. Therefore, the above formula hardly yields a closed solution, but we can update every q [ (/ ] by iterationi) To solve. In particular, q (σ), q (h)m)，q(em) And q (ε) can be iterated as follows:
Figure BDA00028455857400000515
Figure BDA00028455857400000516
Figure BDA00028455857400000517
Figure BDA00028455857400000518
wherein q isnew(. cndot.) represents the updated distribution function that will replace the previously updated distribution function q (-). Thus the joint distribution function can be expressed as
Figure BDA0002845585740000061
The following can be derived:
qnew(σ)＝γ(σ；c-Np,dσ)
Figure BDA00028455857400000610
Figure BDA00028455857400000611
Figure BDA0002845585740000062
Figure BDA0002845585740000063
where γ (·) represents the gamma distribution. Fig. 1 depicts a process for iteratively updating a distribution function. The invention uses the distribution function of the sparsity of the underwater acoustic channel
Figure BDA0002845585740000064
And impulse noise distribution function qnewAnd (epsilon (i)) are respectively estimated, so that the underwater acoustic channel estimation precision is higher. Taking spatial correlation into account simultaneously
Figure BDA0002845585740000065
The underwater acoustic channel estimation precision can be further improved.
Simulation study of the invention:
simulation conditions are as follows:
the impulse noise is constructed here using a two-component Gaussian Mixture Model (GMM) whose signal form is
v[n]＝w[n]+e[n]
Where w [ n ] is a Gaussian noise component, e [ n ] is an impulse noise component, and v [ n ] has a probability density function of
Figure BDA0002845585740000066
Wherein the content of the first and second substances,
Figure BDA00028455857400000612
is a complex gaussian distribution model, which is,
Figure BDA0002845585740000067
is the variance of an additive white gaussian noise component,
Figure BDA0002845585740000068
q is the probability of occurrence of impulse noise in a segment of a signal, being the variance of the impulse noise component. Meanwhile, a Signal-to-noise Ratio (SNR), a Signal-to-interference Ratio (SIR), an interference-to-noise Ratio (INR) are defined:
Figure BDA0002845585740000069
fig. 2 is a time-domain waveform of analog noise.
The MIMO underwater acoustic channel is generated through Bellhop acoustic simulation software, and the parameters are as follows: the water depth is 250m, the transceiving distance is 5km, the transmitting end is a 2-array-element transducer array, the transducer 1 is 100m away from the water surface, the transducer 2 is 101m (strong spatial correlation) and 103m (weak spatial correlation) away from the water surface, the receiving hydrophone is 100m away from the water surface, and the simulation frequency is 12 kHz. There are several comparative channel estimation methods: least square method (LS), orthogonal matching tracking method (OMP), Bayesian channel estimation method (SBL) under the assumption of Gaussian noise, Bayesian channel estimation (ISBL) under the assumption of sparse interference, channel estimation method (VSBL) without considering spatial correlation in the invention, and channel estimation method (IVSBL) with considering spatial correlation in the invention.
Fig. 3(a) and fig. 3(b) are graphs showing Mean Square Error (MSE) of channel estimation results of transducer No. 2 (strong spatial correlation) and transducer No. 2 (weak spatial correlation) respectively as a function of SNR. Compared with the traditional channel estimation algorithm (LS, OMP, SBL) under the white noise background assumption, the channel estimation algorithm (ISBL, VSBL, IVSBL) under the sparse impulse noise background assumption has better performance. Meanwhile, the variational Bayesian method can separate sparsity hyper-parameters of the channel and impulse noise, so that the VSBL and the IVSBL have more accurate channel estimation capability. Comparing fig. 3 and fig. 4, it can be seen that the IVSBL algorithm has a greater performance advantage than the VSBL algorithm when the channel spatial correlation is strong, and the performance of the two algorithms is close to each other when the channel spatial correlation is weak.
As shown in fig. 3(a) and fig. 4(a), when the GMM impulse noise model p is 0.03 and p is 0.01, respectively, the channel estimation result MSE is a curve that varies with the SNR. The larger the p value is, the larger the probability of pulse occurrence in the background noise is, i.e. the more serious the pulse interference is. As can be seen from the figure, the performance of the conventional channel estimation algorithm (LS, OMP, SBL) under the white noise background assumption is worse than that of p 0.01 when p is 0.03, i.e. these algorithms are greatly affected by impulse background noise, while the channel estimation algorithm (ISBL, VSBL, IVSBL) under the sparse impulse noise background assumption is less affected.
As shown in fig. 4(a) and fig. 4(b), when the GMM impulse noise model INR is 20dB and INR is 25dB, respectively, the channel estimation result MSE is a curve varying with SNR. The change of INR has a large influence on the traditional channel estimation algorithm (LS, OMP, SBL) under the assumption of white noise background, and the influence of ISBL, VSBL and IVSBL is small.
In summary, the present invention provides a method for estimating a MIMO underwater acoustic channel under a sparse interference background, and belongs to the field of underwater acoustic signal processing. The invention utilizes the variational Bayes inference theory to respectively estimate the pulse interference and the sparsity of the channel, and simultaneously fully utilizes the spatial correlation of the channel to obtain the processing gain. Compared with the existing underwater acoustic channel estimation method, the method has higher estimation precision and lower calculation complexity.

Claims (1)

1. A MIMO underwater sound channel estimation method under a sparse interference background is characterized in that: the method comprises the following steps:
the method comprises the following steps: building a MIMO underwater acoustic communication system, and receiving a plurality of pilot signals received by a hydrophone;
the received signal model is:
ym≈Xhm+em+wm
wherein the content of the first and second substances,
Figure FDA0003510584650000011
is the received signal of the mth hydrophone, NpIs the pilot sequence length, and L is the channel length;
Figure FDA0003510584650000012
hm,l＝[hm,1(l) hm,2(l)…hm,n(l)…hm,N(l)]T∈cN×1，，
Figure FDA0003510584650000013
is the l-th tap of the channel between the nth transmitting transducer and the mth hydrophone, N being the total number of transmitting transducers;
Figure FDA0003510584650000014
Figure FDA0003510584650000015
is defined as:
Figure FDA0003510584650000016
wherein the content of the first and second substances,
Figure FDA0003510584650000017
known pilot sequence;
Figure FDA0003510584650000018
in order to be the term of the impulse noise,
Figure FDA0003510584650000019
is a complex Gaussian noise vector with zero mean variance of sigma which is independent and identically distributed;
step two: initializing parameters; setting t to 1, initializing
Figure FDA00035105846500000110
μh,∑h,μe,∑eThe sum of the values of ε, B and δ,
Figure FDA00035105846500000111
for estimating the resulting channel, muhIs the channel vector mean, ΣhIs the channel vector variance, mueIs the mean value of impulse noise vector, sigmaeThe variance of the impulse noise vector is shown, epsilon is a hyper-parameter representing sparsity, B is a space correlation matrix, and delta is a preset threshold;
step three: iterative computation, updating according to a joint distribution function, comprising:
updating
Figure FDA00035105846500000112
Figure FDA00035105846500000113
Updating muhSum Σh：
Figure FDA00035105846500000114
Figure FDA00035105846500000115
Updating mueSum Σe：
Figure FDA0003510584650000021
Figure FDA0003510584650000022
Updating the sparsity epsilon of the underwater acoustic channel0:L-1And B:
Figure FDA0003510584650000023
Figure FDA0003510584650000024
updating impulse noise sparsity
Figure FDA0003510584650000025
Figure FDA0003510584650000026
Let T be T +1, if T is T or
Figure FDA0003510584650000027
Then output
Figure FDA0003510584650000028
Otherwise, continuing the iteration;
step four: outputting the result of the channel estimation, and outputting,
Figure FDA0003510584650000029
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