CN112104580B - Sparse underwater acoustic channel estimation method based on generalized approximate message transfer-sparse Bayesian learning - Google Patents
Sparse underwater acoustic channel estimation method based on generalized approximate message transfer-sparse Bayesian learning Download PDFInfo
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Abstract
The invention provides a sparse underwater sound channel estimation method based on generalized approximate message transfer-sparse Bayesian learning, and belongs to the field of underwater sound signal processing. To a channel estimation method combining Generalized Approximate Messaging (GAMP) with Sparse Bayesian Learning (SBL). (1) Inputting frequency domain baseband receiving signals, dictionary matrixes, iteration termination conditions and related parameter initial values; (2) Calculating channel impulse response by using GAMP under the framework of SBL; (3) updating the noise variance and the channel super-parameters; (4) Judging the iteration termination condition, and outputting a channel estimation result if the iteration termination condition is met. The invention has the advantages that: the impulse response of the underwater sound channel is calculated by utilizing an approximate message transmission mode under the framework of the SBL, and the calculation complexity of the SBL is reduced and the running time of an algorithm is shortened under the condition of basically no performance loss.
Description
Technical Field
The invention relates to a method for processing underwater sound signals, in particular to a sparse underwater sound channel estimation method based on generalized approximate message transfer (GAMP) -Sparse Bayesian Learning (SBL).
Background
In underwater acoustic communication, a complex and changeable underwater acoustic channel has a great influence on the underwater acoustic communication, and in order to improve the communication quality, the state of the channel needs to be estimated. The underwater acoustic channel has remarkable sparsity, the sparse Bayesian learning has good reconstruction performance on sparse signals, and the sparse Bayesian learning is stable in scenes with poor partial conditions, so that more and more attention is paid. However, when the problem dimension becomes larger, the computation complexity of SBL will increase, which is unfavorable for real-time processing of data. Under the framework of SBL, the generalized approximate message transfer-sparse Bayesian learning (GAMP-SBL) utilizes GAMP to calculate channel impulse response in an iterative manner, and converts vector operation into scalar operation, so that the calculation complexity of SBL is effectively reduced and the stability of SBL is maintained under the condition of basically no performance loss.
Disclosure of Invention
The invention aims to provide a sparse underwater acoustic channel estimation method based on generalized approximate message transfer-sparse Bayesian learning.
The purpose of the invention is realized in the following way: the method comprises the following steps:
step one: inputting frequency domain baseband receiving signals, dictionary matrixes, iteration termination conditions and related parameter initial values;
step two: calculating channel impulse response by using GAMP under the framework of SBL;
step three: updating the noise variance and the channel super-parameters;
step four: judging the iteration termination condition, if yes, outputting a channel estimation result, otherwise, returning to the step two.
The invention also includes such structural features:
1. the parameters in the first step are specifically as follows: received signal Y at pilot position p Dictionary matrix phi p Let s= |Φ p | 2 In GAMP |. | 2 Refers to squaring in units of elements; assume that the channel obeys a Gaussian independent same distribution with mean value of 0 and variance of super-parameter gamma, and gamma= [ gamma ] 1 ,γ 2 ,…,γ L ] T L is the channel length; let Γ=diag (γ); for a pair ofγ 0 Assignment, typically a vector greater than 0, wherein +.>Variance of channel estimation result; let the initial noise variance (sigma) 2 ) 0 A constant greater than 0; s is(s) 0 ,/>h 0 Is a 0 vector, where h is the channel, s and τ s First-order and second-order Taylor expansion coefficients for transmitting messages from the factor node to the variable node, respectively,>for recording the value of s when the GAMP converges and assigning an initial value to s in the next round of GAMP iteration; SBL maximum cycle number K max Maximum number of cycles M of GAMP algorithm max The method comprises the steps of carrying out a first treatment on the surface of the GAMP algorithm stop condition ε gamp SBL stop condition ε sbl The method comprises the steps of carrying out a first treatment on the surface of the k=1, m=1, k and m record the number of iterations of SBL and GAMP, respectively.
2. Step two, specifically, using GAMP to perform channel estimation:
order theμ m＝1 ＝h k-1 ，/>
If [ mu ] m+1 -μ m || 2 ＜ε gamp Or m=m max Stopping GAMP iteration, otherwise returning to G1;
let h k ＝μ m+1 ，
3. The method is characterized in that: step three SBL parameter update
If it isOr k=k max The iteration is terminated, otherwise step two is returned.
4. Step four output channel impulse responseThe specific form of the two scalar estimation functions and their derivatives are:
compared with the prior art, the invention has the beneficial effects that: the GAMP-SBL method is expanded to the underwater sound field, and the GAMP is utilized to replace the SBL matrix inversion step under the SBL framework, so that vector operation is converted into scalar operation, and the calculation complexity of the SBL is effectively reduced under the condition of basically no performance loss.
Specifically:
aiming at the problem of high SBL calculation complexity in sparse underwater sound channel estimation, the invention introduces a GAMP-SBL channel estimation method. The invention uses GAMP to iteratively calculate channel impulse response in message transmission mode, and converts the original vector operation into scalar calculation by two scalar estimation functions. Compared with SBL, GAMP-SBL reduces the computation complexity of SBL without performance loss, and improves the convergence rate.
Drawings
FIG. 1 is a schematic diagram of GAMP-SBL sparse underwater acoustic channel estimation;
FIG. 2 is a graph showing the comparison of error rate performance of each channel estimation method at a test distance 1440m of the pine pollen lake underwater acoustic communication;
FIG. 3 is a graph showing the comparison of SBL and GAMP-SBL calculation times at a test distance 1440m of the pine lake underwater sound communication.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The invention is realized in the following way:
(1) The receiving end demodulates the received passband signal into a frequency domain baseband complex signal;
(2) Calculating channel impulse response by using GAMP under the framework of SBL;
(3) Updating the noise variance and the channel super-parameters;
(4) And if the iteration termination condition is met, outputting a channel estimation result.
Namely, the invention combines SBL and GAMP to realize sparse underwater acoustic channel estimation; solving the channel impulse response, converting the vector operation into a scalar operation. The combination of SBL and GAMP is realized by using GAMP to estimate channel impulse response under SBL framework. The solving of the channel impulse response converts vector operation into scalar operation through two scalar estimation functions in GAMP.
The invention is described in more detail below in connection with fig. 1:
(1) Inputting parameters: received signal Y at pilot position p Dictionary matrix phi p Let s= |Φ p | 2 In GAMP |. | 2 Refers to squaring in units of elements; assume that the channel obeys a Gaussian independent same distribution with mean value of 0 and variance of super-parameter gamma, and gamma= [ gamma ] 1 ,γ 2 ,…,γ L ] T L is the channel length; let Γ=diag (γ); for a pair ofγ 0 Assignment, typically a vector greater than 0, wherein +.>Can be understood as the variance of the channel estimation result; let the initial noise variance (sigma) 2 ) 0 A constant greater than 0; s is(s) 0 ,/>h 0 Is a 0 vector, where h is the channel, s and τ s First-order and second-order Taylor expansion coefficients for transmitting messages from the factor node to the variable node, respectively,>for recording the value of s when the GAMP converges and assigning an initial value to s in the next round of GAMP iteration; SBL maximum cycle number K max Maximum number of cycles M of GAMP algorithm max The method comprises the steps of carrying out a first treatment on the surface of the GAMP algorithm stop condition ε gamp SBL stop condition ε sbl The method comprises the steps of carrying out a first treatment on the surface of the k=1, m=1, k and m record the iteration number of SBL and GAMP, respectively;
(2) Channel estimation using GAMP:
order theμ m＝1 ＝h k-1 ，/>
If [ mu ] m+1 -μ m || 2 ＜ε gamp Or m=m max Stopping GAMP iteration, otherwise returning to G1;
let h k ＝μ m+1 ，
(3) SBL parameter update
If it isOr k=k max Terminating the iteration, otherwise returning to the GAMP;
(4) Output channel impulse response
The specific form of the two scalar estimation functions and their derivatives are:
in the algorithm flow, the multiplication between vectors or matrixes is carried out by taking elements as units, and theta s ,θ h ∈(0,1]Is a damping factor, and is used for reducing the iteration speed and improving the algorithm convergence. p, τ p ,r,τ r To calculate intermediate variables used in the transfer of messages between nodes.
2. Experimental study
The GAMP-SBL sparse underwater acoustic channel estimation algorithm is verified by using pine lake communication test data. In the test, the transmission signal consisted of a chirp signal and a QPSK modulated OFDM signal, wherein the chirp signal was used to synchronize the reception signal. The frequency band range of the OFDM signal is 9 kHz-15 kHz, the center frequency is 12kHz, 1024 subcarriers are used, and 244 pilot subcarriers are used; a total of 12 data frames, 8 symbols per frame; the sampling rate is 96kHz and the communication distance is 1.44km.
The LS, OMP, BPDN, SBL algorithm is used to compare with the GAMP-SBL algorithm, and FIG. 2 is a bit error rate comparison of the algorithm. It can be seen that: (1) The LS algorithm has higher error rate and poorer channel estimation performance; (2) OMP algorithms with different sparsity parameters show different performances, which verifies the sensitivity of the algorithm to the sparsity parameters; (3) The performance of the BPDN algorithm with different regularization parameters is different, and the fact that the regularization parameters have a certain influence on the BPDN algorithm is verified. Average bit error rates of SBL, GAMP-SBL, BPDN (λ=0.2), OMP (k=96) are respectively: the average error rate of 1.47%, 1.83%, 1.56% and 2.78% of OMP is higher than that of the other three algorithms, the performance of the BPDN algorithm with regularization parameter of 0.2 is relatively close to that of SBL and GAMP-SBL, but the sparsity and regularization parameters of the two Bayesian algorithms are not required to be set, the calculation complexity of the BPDN algorithm is very high, and the running time is far longer than that of the Bayesian algorithm. Based on the above analysis, SBL and GAMP-SBL algorithms are more advantageous.
FIG. 3 is a comparison of the calculation times of GAMP-SBL and SBL. As can be seen, the GAMP-SBL has a significantly smaller run time than SBL. GAMP-SBL is superior to SBL in computational complexity.
In summary, the invention provides an underwater acoustic channel estimation method based on generalized approximate message transfer-sparse Bayesian learning (GAMP-SBL). The invention belongs to the field of underwater acoustic signal processing. To a channel estimation method combining Generalized Approximate Messaging (GAMP) with Sparse Bayesian Learning (SBL). (1) Inputting frequency domain baseband receiving signals, dictionary matrixes, iteration termination conditions and related parameter initial values; (2) Calculating channel impulse response by using GAMP under the framework of SBL; (3) updating the noise variance and the channel super-parameters; (4) Judging the iteration termination condition, and outputting a channel estimation result if the iteration termination condition is met. The invention has the advantages that: the impulse response of the underwater sound channel is calculated by utilizing an approximate message transmission mode under the framework of the SBL, and the calculation complexity of the SBL is reduced and the running time of an algorithm is shortened under the condition of basically no performance loss.
Claims (1)
1. The sparse underwater acoustic channel estimation method based on generalized approximate message transfer GAMP-sparse Bayesian learning SBL is characterized by comprising the following steps of: the method comprises the following steps:
step one: inputting frequency domain baseband receiving signals, dictionary matrixes, iteration termination conditions and related parameter initial values;
the parameters in the first step are specifically as follows: received signal Y at pilot position p Dictionary matrix phi p Let s= |Φ p | 2 In GAMP |. | 2 Refers to squaring in units of elements; assume that the channel obeys a Gaussian independent same distribution with mean value of 0 and variance of super-parameter gamma, and gamma= [ gamma ] 1 ,γ 2 ,…,γ L ] T L is the channel length; let Γ=diag (γ); for a pair ofγ 0 A vector assigned to be greater than 0, wherein +.>Variance of channel estimation result; let the initial noise variance (sigma) 2 ) 0 A constant greater than 0; s is(s) 0 ,/>h 0 Is a 0 vector, where h is the channel, s and τ s First-order and second-order Taylor expansion coefficients for transmitting messages from the factor node to the variable node, respectively,>for recording the value of s when the GAMP converges and assigning an initial value to s in the next round of GAMP iteration; SBL maximum cycle number K max Maximum number of cycles M of GAMP algorithm max The method comprises the steps of carrying out a first treatment on the surface of the GAMP algorithm stop condition ε gamp SBL stop condition ε sbl The method comprises the steps of carrying out a first treatment on the surface of the k and m record the iteration times of SBL and GAMP respectively, and the initial values of k and m are 1;
step two: calculating channel impulse response by using GAMP under the framework of SBL;
step two, specifically, using GAMP to perform channel estimation:
order theμ m＝1 ＝h k-1 ，/>
If [ mu ] m+1 -μ m || 2 ＜ε gamp Or m=m max Stopping GAMP iteration, otherwise returning to G1;
let h k ＝μ m+1 ，
Step three: updating noise variance and channel super parameters, specifically:
if it isOr k=k max Ending the iteration, otherwise returning to the step two;
step four: judging iteration termination conditions, if yes, outputting a channel estimation result, otherwise, returning to the step two;
output channel impulse responseThe specific form of the two scalar estimation functions and their derivatives are:
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