CN110784423A - Underwater acoustic channel estimation method based on sparse constraint - Google Patents

Underwater acoustic channel estimation method based on sparse constraint Download PDF

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CN110784423A
CN110784423A CN201911086673.2A CN201911086673A CN110784423A CN 110784423 A CN110784423 A CN 110784423A CN 201911086673 A CN201911086673 A CN 201911086673A CN 110784423 A CN110784423 A CN 110784423A
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training sequence
tap coefficient
channel tap
channel
error
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梁仕杰
王彪
何呈
李晓曼
张岑
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Jiangsu University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods

Abstract

The invention discloses an underwater acoustic channel estimation method based on sparse constraint, which increases the norm term of a channel tap coefficient in a cost function of a traditional RLS algorithm to constrain the norm term so as to improve the precision of sparse channel estimation, and then processes the cost function in a sliding window mode to reduce the calculation amount of the algorithm. On the basis, the method introduces a binary coordinate descent algorithm to search a solution which minimizes the cost function in a single iteration, further reduces the complexity of the algorithm, and has certain superiority in precision and complexity compared with the existing algorithm.

Description

Underwater acoustic channel estimation method based on sparse constraint
Technical Field
The invention relates to the technical field of underwater acoustic channels, in particular to an underwater acoustic channel estimation method based on sparse constraint.
Background
Compared with wireless channels on land, underwater acoustic channels have many different places, especially in shallow sea, and face the characteristics of strong multipath effect, ocean surface reflection, rapid time-varying effect caused by environments such as internal wave and the like, available bandwidth is narrow, signal attenuation is serious and the like, and the underwater acoustic channel is one of the most complicated wireless communication channels, so that the development of underwater acoustic communication is limited.
At present, the sparse channel estimation problem is generally solved by a compressed sensing algorithm or an adaptive filtering algorithm. Although channel impulse responses can be estimated by signal reconstruction according to a small amount of information, compressed sensing-based channel estimation methods such as Orthogonal Matching Pursuit (OMP), Regularized Orthogonal Matching Pursuit (ROMP), and the like require a priori information of channel sparsity, which limits the development of such methods.
The adaptive filtering algorithm mainly utilizes the filter parameters obtained at the previous moment, and automatically adjusts the parameters at the current moment according to the estimation error, so that a certain cost function reaches the minimum, and the optimal filtering is realized. The least mean square error (LMS) algorithm, Least Square (LS) algorithm and least recursive quadratic (RLS) algorithm are mainly used, the LMS algorithm is based on the LMS algorithm, and the filter coefficient estimated by the LMS algorithm is related to the statistical characteristic of data, so the convergence speed is low. And the LS algorithm is applied to estimate the channel, so that the convergence speed is high. The related literature provides a channel estimation method based on RLS, wherein a forgetting factor is introduced into an RLS algorithm, and corresponding weights are given according to the distance from an error to an n moment, so that observation data in a certain period of time in the past are ensured to be forgotten, and a filter can work in a stable state. Although the performance of the LS algorithm is improved, the norm constraint on the coefficients is not carried out, so that pseudo peaks generally appear at zero tap coefficients of a channel during estimation, and the effect of the LS algorithm on sparse channel estimation is severely limited.
Disclosure of Invention
The invention provides an underwater acoustic channel estimation method based on sparse constraint, which aims to solve the technical problems of poor effect, high complexity and low convergence speed of underwater acoustic channel calculation in the prior art.
The invention provides an underwater acoustic channel estimation method based on sparse constraint, which comprises the following steps:
step 1: initializing values of all parameters of the channel estimation algorithm, and executing an iterative process from step 2 to step 6;
step 2: calculating an autocorrelation matrix of the training sequence;
and step 3: calculating an error value between the output of the training sequence under the channel tap coefficient and the corresponding expected signal, wherein the channel tap coefficient is the channel tap coefficient estimated in the previous iteration;
and 4, step 4: calculating error values between outputs of training sequences with a plurality of lengths lagging the current training sequence under channel tap coefficients and corresponding expected signals, wherein the channel tap coefficients are estimated by previous iteration;
and 5: calculating a residual value under a channel tap coefficient according to the error value obtained in the step 3, the error value obtained in the step 4 and a residual value of a previous iteration, wherein the channel tap coefficient is a channel tap coefficient estimated in the previous iteration;
step 6: and (2) obtaining the minimum value of the cost function by applying a binary coordinate descent normative search method, adding the minimum value of the cost function and the channel tap coefficient of the previous iteration to obtain the current channel tap coefficient, updating the residual value obtained in the step (5) according to a formula for obtaining the residual value in the step (5), and stopping iteration and outputting the channel tap coefficient when the mean square error of the estimated channel tap coefficient and the actual channel tap coefficient reaches the preset requirement of channel estimation precision.
Further, the parameters in step 1 include: original training sequence x (n), receiving sequence y (n) corresponding to the original training sequence, channel tap coefficient:
Figure BDA0002265621950000021
residual error: c (0|0) ═ 0 NR (0) η I as initial value of training sequence autocorrelation matrix NWherein "0 N"represents an N × 1 vector; "I N"denotes an N × N identity matrix," η "denotes constants of very small values.
Further, the recursive formula for calculating the autocorrelation matrix of the training sequence in step 2 is as follows:
R(n)＝R(n-1)+x(n)x H(n)-x(n-M)x H(n-M)
wherein "n" represents the current iterative process; "M" is the length of the sliding window; "x (n)" represents the training sequence of the current iteration; "x (n-M)" represents a training sequence M lengths behind the current training sequence; "x H(n) "denotes the Hermite conjugate transpose of x (n).
Further, the formula for calculating the error value between the output of the training sequence under the channel tap coefficient and the corresponding desired signal in step 3 is as follows:
e(n)＝d(n)-y(n)
wherein "n" represents the current iterative process;
Figure BDA0002265621950000032
representing the channel tap coefficients estimated in the previous iteration; "x (n)" represents the training sequence of the current iteration; "d (n)" represents the desired signal corresponding to x (n); "y (n)" represents the output corresponding to x (n); "e (n)" represents the error between the output corresponding to x (n) and the desired signal.
Further, the formula for calculating the error value between the output of the training sequence with several lengths lagging the current training sequence and the corresponding expected signal under the channel tap coefficient in step 4 is as follows:
Figure BDA0002265621950000033
e M(n)＝d(n-M)-y M(n)
wherein "n" represents the current iterative process;
Figure BDA0002265621950000034
representing the channel tap coefficients estimated in the previous iteration; "x (n-M)"represents a training sequence that lags the current training sequence by M lengths; "d (n-M)" represents the desired signal for x (n-M); "y" is M(n) "represents the output corresponding to x (n-M); "e M(n) "represents the error of the output corresponding to x (n-M) from the desired signal.
Further, in step 5, according to the error value obtained in step 3, the error value obtained in step 4, and the residual value of the previous iteration, a formula for calculating the residual value under the channel tap coefficient is as follows:
Figure BDA0002265621950000035
wherein "n" represents the current iterative process;
Figure BDA0002265621950000036
representing the residual value of the previous iteration; "b (n)" represents the cross-correlation vector of the taken training sequence and its corresponding expected signal; "e *(n) "represents the complex conjugate of e (n).
The invention has the beneficial effects that:
the underwater acoustic channel estimation method based on sparse constraint increases the norm term of the channel tap coefficient in the cost function of the traditional RLS algorithm to constrain the cost function, thereby improving the precision of sparse channel estimation, and then reduces the calculation amount of the algorithm by processing the cost function in a sliding window mode. On the basis, the method introduces a binary coordinate descent algorithm to search a solution which minimizes the cost function in a single iteration, further reduces the complexity of the algorithm, and has certain superiority in precision and complexity compared with the existing algorithm.
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The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and not to be construed as limiting the invention in any way, and in which:
FIG. 1 is a flow chart of an underwater acoustic channel estimation method based on sparse constraint according to the present invention;
FIG. 2 is a graph comparing the estimated performance of different penalty functions according to an embodiment of the present invention;
FIG. 3 is a comparison graph of the impact of penalty function on the estimation result according to an embodiment of the present invention;
FIG. 4 is a graph of normalized mean square error comparison for different channel estimation algorithms in an embodiment of the present invention;
FIG. 5 is a comparison graph of CPU running times of different channel estimation algorithms in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a sparse constraint-based underwater acoustic channel estimation method, where a penalty function term is added on the basis of a minimum recursive two-times algorithm cost function to improve sparse channel estimation accuracy, and the complexity of the algorithm is further reduced by using a sliding window processing method and a binary coordinate descent method (DCD), so as to obtain an underwater acoustic channel, where the method specifically includes the following steps:
step 1: initializing the parameters of the channel estimation algorithm comprises the following steps: original training sequence x (n), receiving sequence y (n) corresponding to the original training sequence, channel tap coefficient:
Figure BDA0002265621950000041
residual error: c (0|0) ═ 0 NR (0) η I as initial value of training sequence autocorrelation matrix NWherein "0 N"represents an N × 1 vector; "I NAfter the parameters are set, the iterative process from the step 2 to the step 6 is executed until the estimation precision of the underwater acoustic channel meets the requirement;
step 2: calculating an autocorrelation matrix R of the training sequence, specifically by the following recursive equation:
R(n)＝R(n-1)+x(n)x H(n)-x(n-M)x H(n-M)
wherein "n" represents the current iterative process; "M" is the length of the sliding window; "x (n)" represents the training sequence of the current iteration; "x (n-M)" represents a training sequence M lengths behind the current training sequence; "x H(n) "denotes the Hermite conjugate transpose of x (n);
and step 3: calculating an error value between an output of the training sequence under the channel tap coefficient and a corresponding expected signal, wherein the channel tap coefficient is estimated in the previous iteration, and a specific formula is as follows:
e(n)＝d(n)-y(n)
wherein "n" represents the current iterative process;
Figure BDA0002265621950000052
representing the channel tap coefficients estimated in the previous iteration; "x (n)" represents the training sequence of the current iteration; "d (n)" represents the desired signal corresponding to x (n); "y (n)" represents the output corresponding to x (n); "e (n)" represents the error between the output corresponding to x (n) and the desired signal;
and 4, step 4: calculating error values between outputs of training sequences with a plurality of lengths lagging the current training sequence under channel tap coefficients and corresponding expected signals, wherein the channel tap coefficients are estimated by previous iteration, and the specific formula is as follows:
e M(n)＝d(n-M)-y M(n)
wherein "n" represents the current iterative process;
Figure BDA0002265621950000054
representing the channel tap coefficients estimated in the previous iteration; "x (n-M)" represents a training sequence M lengths behind the current training sequence; "d (n-M)" represents the desired signal for x (n-M); "y" is M(n) "represents the output corresponding to x (n-M); "e M(n) "represents the error of the output corresponding to x (n-M) with the desired signal;
and 5: calculating a residual value under a channel tap coefficient according to the error value obtained in the step 3, the error value obtained in the step 4 and a residual value of a previous iteration, wherein the channel tap coefficient is a channel tap coefficient estimated in the previous iteration, and a specific formula is as follows:
Figure BDA0002265621950000055
wherein "n" represents the current iterative process;
Figure BDA0002265621950000056
representing the residual value of the previous iteration; "b (n)" represents the cross-correlation vector of the taken training sequence and its corresponding expected signal; "e *(n) "represents the complex conjugate of e (n);
step 6: obtaining a minimum value delta h of a cost function by applying a DCD linear search method, adding the minimum value of the cost function and a channel tap coefficient of the previous iteration to obtain a current channel tap coefficient, updating the residual value obtained in the step 5 according to a formula of the residual value calculated in the step 5, and stopping iteration when the normalized mean square error of the tap coefficient of the estimated channel and the actual channel tap coefficient meets the preset requirement of channel estimation precision, wherein the specific process comprises the following steps:
step 61: inputting parameters: c (n | n-1), R ═ R (n),
Figure BDA0002265621950000061
H,M b,N u；
step 62, initializing parameters, wherein δ is H, α is δ [1, -1, j, -j ], m is 0, and u is 0;
and step 63: when M is less than M b，u＜N uWhen s is 1…, N and q are 1, …,4
Figure BDA0002265621950000062
Minimum s, q value, wherein
Let s ═ p, q ═ k;
step 64: judgment of
Figure BDA0002265621950000063
And 0 when Δ J minWhen < 0, h p＝h p+α k、c＝c-α kR (p)U +1, and returning to step 63;
otherwise
Figure BDA0002265621950000064
m is m +1 and returns to step 63
Wherein H is a power of 2; m bIs the number of bits of the term of the solution vector; n is a radical of uIs the upper limit of the number of successful iterations, α is the direction matrix of solution vector change, M and n are M bAnd N uAn initial value of (1); r s,sRepresents the row s and column s elements of the matrix R; c. C sThe s-th element representing a residual vector;
Figure BDA0002265621950000065
representing the operation of the real part; r (p)Representing the pth column of the matrix R.
In each iteration, only the p-th element of the solution vector will be updated to Δ h + α e pα is a scalar quantity of complex values, e pIs the p-th column of the identity matrix, the only condition for solution vector update is a decreasing cost function,
ΔJ＝J Δ(Δh+αe p)-J Δ(Δh)＜0
since the solution vector is complex valued, 4 possible directions on the complex plane need to be considered to update each coordinate: 1, -1, j and-j, wherein
Figure BDA0002265621950000071
Wherein α is δ [1, -1, j, -j ═ j]。
In the next DCD iteration, all s 1, …, N and q 1, …,4 need to be found to find the s and q values that minimize the cost function increment. Comparing the minimum value with 0 after finding, and conforming to the updating principle of the solution vector when the minimum value is less than 0; and when the compression parameter is larger than 0, continuously searching until the delta h when the cost function obtains the minimum value is obtained, and adding the delta h with the h obtained in the previous iteration to obtain the h of the current iteration.
FIG. 2 compares the estimated performances of three different penalty functions, wherein a broken line DCD slipping-ElasticNet in the figure represents that the penalty function is an elastic net function; a broken line DCD Sliding-Lasso represents that the penalty function is a Lasso function; the polyline DCDSliding-ridge represents that the penalty function is a ridge function. The length of the Gaussian training sequence is 7000, the number of channel sampling points is 2000, the number of iterations is 5000, and the signal-to-noise ratio is 25 dB. The abscissa is shown as the iteration number, the ordinate is the normalized mean square error, and the figure shows that the estimated performance of the lasso penalty function is the best after 5000 iterations, because the lasso penalty function uses l 1The norm constrains the channel tap coefficients, setting the regression coefficient of the argument with smaller absolute value or smaller influence factor to 0, which makes it more suitable for sparse channel estimation.
As shown in fig. 3, the length of the selected gaussian training sequence is 7000, the number of channel sampling points is 2000, the sampling frequency is 128kHz, the iteration is 5000 times, and the signal-to-noise ratio is 25 dB. FIG. 3 is a comparison graph of the calculation result of the method of the present invention and the estimation result of the existing RLS algorithm, wherein the vertical axis is the difference between the estimation value and the actual value, and the horizontal axis is the number of sampling points. The broken line with square points in the figure represents the amplitude difference between the channel tap coefficient estimated by the dcdsliking-Lasso method and the actual channel tap coefficient, and the broken line with cross points represents the amplitude difference between the channel tap coefficient estimated by the RLS method and the actual channel tap coefficient. As can be seen from the figure, the RLS algorithm is similar to the method of the invention in the estimation precision of the non-zero tap coefficient of the channel, and the error can be controlled at 10 -2An order of magnitude. However, the estimation result of the RLS algorithm generally fluctuates at the position of the channel zero coefficient, so that the result of the RLS algorithm on sparse channel estimation is poor. The method carries out the channel tap coefficientNorm constraint is achieved, and sparse channel estimation accuracy is higher.
FIG. 4 is a graph comparing the performance of the proposed algorithm with the conventional channel estimation algorithm, where the broken line with the star shape is the normalized mean square error of the estimated channel and the actual channel obtained by the least square algorithm; the fold line with the fork shape is the normalized mean square error of an estimated channel and an actual channel obtained by applying an OMP algorithm in compressed sensing; the broken line with the square is the normalized mean square error of the estimated channel and the actual channel obtained by the minimum recursive quadratic multiplication algorithm; the polygonal line with triangles is the normalized mean square error of the estimated channel and the actual channel obtained by the method. The signal-to-noise ratio varies between 5dB and 30dB with a 5dB variation interval. In the LS channel estimation process, a pilot is inserted every 8 subcarriers for 256 subcarriers. The OMP algorithm employs random pilots. The RLS algorithm and the method of the invention insert a Gaussian training sequence with the length of 1000 through a time domain, and the sampling point number of a sparse channel is 100. As can be seen from fig. 4, the normalized mean square error of all algorithms decreases with the increase of the signal-to-noise ratio, and the estimation performance of the LS algorithm is much lower than that of the other three algorithms, because the LS algorithm is most affected by noise when estimating a sparse channel, so the performance is the worst. The performance difference between the OMP algorithm and the RLS algorithm is small, and the method disclosed by the invention has the optimal performance in the four channel estimation algorithms.
Fig. 5 analyzes the complexity of the different channel estimation algorithms by CPU run time. The ordinate of the graph shows the running time of the CPU, the abscissa shows the sparsity of the channel, and the broken line with the star shape in the graph shows the running time of the CPU when the channel estimation is carried out by using an OMP algorithm in compressed sensing; the broken line with the square is the CPU running time when the minimum recursive quadratic multiplication algorithm is used for channel estimation; the broken line with triangle is the CPU running time when the method of the invention is used for channel estimation; the broken line with the crosses is the CPU running time when channel estimation is performed with the least square method. The simulation signal-to-noise ratio is 15dB, the iteration times of the channel estimation method based on the compressed sensing are related to the channel sparsity, so that the OMP algorithm is greatly influenced by the sparsity, and the higher the sparsity is, the higher the complexity is. The method of the invention uses a sliding window method to process and uses a DCD algorithm to search an optimal solution, thereby reducing the complexity of the algorithm. Compared with the LS algorithm, the method adds the norm constraint term in the cost function, thereby increasing the complexity to a certain degree, so the complexity is slightly higher than the LS algorithm, but the channel estimation precision is far higher than the LS algorithm.
Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope defined by the appended claims.

Claims (6)

1. An underwater acoustic channel estimation method based on sparse constraint is characterized by comprising the following steps:
step 1: initializing values of all parameters of the channel estimation algorithm, and executing an iterative process from step 2 to step 6;
step 2: calculating an autocorrelation matrix of the training sequence;
and step 3: calculating an error value between the output of the training sequence under the channel tap coefficient and the corresponding expected signal, wherein the channel tap coefficient is the channel tap coefficient estimated in the previous iteration;
and 4, step 4: calculating error values between outputs of training sequences with a plurality of lengths lagging the current training sequence under channel tap coefficients and corresponding expected signals, wherein the channel tap coefficients are estimated by previous iteration;
and 5: calculating a residual value under a channel tap coefficient according to the error value obtained in the step 3, the error value obtained in the step 4 and a residual value of a previous iteration, wherein the channel tap coefficient is a channel tap coefficient estimated in the previous iteration;
step 6: and (2) obtaining the minimum value of the cost function by applying a binary coordinate descent normative search method, adding the minimum value of the cost function and the channel tap coefficient of the previous iteration to obtain the current channel tap coefficient, updating the residual value obtained in the step (5) according to a formula for obtaining the residual value in the step (5), and stopping iteration and outputting the channel tap coefficient when the mean square error of the estimated channel tap coefficient and the actual channel tap coefficient reaches the preset requirement of channel estimation precision.
2. The sparse constraint-based underwater acoustic channel estimation method of claim 1, wherein the parameters in the step 1 comprise: original training sequence x (n), receiving sequence y (n) corresponding to the original training sequence, channel tap coefficient:
Figure FDA0002265621940000011
residual error: c (0|0) ═ 0 NR (0) η I as initial value of training sequence autocorrelation matrix NWherein "0 N"represents an N × 1 vector; "I N"denotes an N × N identity matrix," η "denotes constants of very small values.
3. The sparse constraint-based underwater acoustic channel estimation method of claim 1, wherein the recursive formula for calculating the autocorrelation matrix of the training sequence in the step 2 is as follows:
R(n)＝R(n-1)+x(n)x H(n)-x(n-M)x H(n-M)
wherein "n" represents the current iterative process; "M" is the length of the sliding window; "x (n)" represents the training sequence of the current iteration; "x (n-M)" represents a training sequence M lengths behind the current training sequence; "x H(n) "denotes the Hermite conjugate transpose of x (n).
4. The sparse constraint-based underwater acoustic channel estimation method of claim 1, wherein the formula for calculating the error value between the output of the training sequence under the channel tap coefficient and the corresponding desired signal in the step 3 is as follows:
Figure FDA0002265621940000021
e(n)＝d(n)-y(n)
wherein "n" represents the current iterative process;
Figure FDA0002265621940000022
representing the channel tap coefficients estimated in the previous iteration; "x (n)" represents the training sequence of the current iteration; "d (n)" represents the desired signal corresponding to x (n); "y (n)" represents the output corresponding to x (n); "e (n)" represents the error between the output corresponding to x (n) and the desired signal.
5. The sparse constraint-based underwater acoustic channel estimation method of claim 1, wherein the formula for calculating the error value between the output of the training sequence lagging the current training sequence by several lengths under the channel tap coefficient and the corresponding expected signal in the step 4 is as follows:
e M(n)＝d(n-M)-y M(n)
wherein "n" represents the current iterative process;
Figure FDA0002265621940000024
representing the channel tap coefficients estimated in the previous iteration; "x (n-M)" represents a training sequence M lengths behind the current training sequence; "d (n-M)" represents the desired signal for x (n-M); "y" is M(n) "represents the output corresponding to x (n-M); "e M(n) "represents the error of the output corresponding to x (n-M) from the desired signal.
6. The sparse constraint-based underwater acoustic channel estimation method of claim 1, wherein the formula for calculating the residual value under the channel tap coefficient according to the error value obtained in step 5, the error value obtained in step 4 and the residual value of the previous iteration is as follows:
wherein "n" represents the current iterative process;
Figure FDA0002265621940000026
representing the residual value of the previous iteration; "b (n)" represents the cross-correlation vector of the taken training sequence and its corresponding expected signal; "e *(n) "represents the complex conjugate of e (n).
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Application publication date: 20200211