CN109861937B - Underwater acoustic channel estimation method and system based on MSASSWOMP algorithm - Google Patents

Underwater acoustic channel estimation method and system based on MSASSWOMP algorithm Download PDF

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CN109861937B
CN109861937B CN201910219808.1A CN201910219808A CN109861937B CN 109861937 B CN109861937 B CN 109861937B CN 201910219808 A CN201910219808 A CN 201910219808A CN 109861937 B CN109861937 B CN 109861937B
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underwater acoustic
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张秀再
赵慧
蒋闯
刘思成
沈嘉程
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses an underwater acoustic channel estimation method based on MSASSWOMP algorithm, which comprises the following steps: (1) constructing a frequency division multiplexing system, obtaining a received pilot signal Y according to the data symbol of the subcarrier, and establishing an underwater acoustic channel compression sensing equation; (2) adding a weak selection of a threshold value into signal residual matching of an MSAMP algorithm, adding backtracking screening after the weak selection of the threshold value for iterative optimization, updating a support set, and further realizing estimation of a underwater acoustic channel vector. The invention adopts a threshold value weak selection method, backtracking screening is added after threshold value weak selection, atoms selected through the threshold value weak selection are taken as candidate atoms in a backtracking stage, and in the backtracking screening stage, the size of an atom support set selected through the threshold value weak selection at the moment is compared with an initial support set K0And the channel estimation performance can be effectively improved by using less pilot frequency resources.

Description

Underwater acoustic channel estimation method and system based on MSASSWOMP algorithm
Technical Field
The invention relates to the field of underwater acoustic channel estimation, in particular to an underwater acoustic channel estimation method and system based on an MSASSWOMP algorithm.
Background
At present, the method for resisting the multipath interference and the time-varying problem of the underwater acoustic channel, accurately estimating the channel state information and effectively tracking the rapidly-varying underwater acoustic channel becomes the important work of an underwater acoustic communication system. For underwater acoustic Orthogonal Frequency Division Multiplexing (OFDM) communication, a common channel estimation method is that both a least square method (LS) and a Minimum Mean Square Error (MMSE) are optimal estimates based on an L2 norm, and a channel is taken as a dense channel, which cannot reflect sparsity of the channel. Research shows that the inherent sparsity of the underwater acoustic channel is a prerequisite condition for channel estimation by using a compression theory framework, and after an OFDM signal passes through the sparse underwater acoustic channel, the time domain impulse response of the channel can be reconstructed by using a small amount of pilot frequency information of a transmitting terminal, and meanwhile, the interference caused by noise can be reduced.
The Generalized Orthogonal Matching Pursuit (gOMP) algorithm proposed by Jianan W et al simply sets a proper fixed value S as the number of atoms selected iteratively, and the algorithm has a great improvement in reconstruction accuracy and speed compared with the OMP algorithm. The Subspace tracking (SP) algorithm proposed by miltenkovic et al introduces a backtracking idea, adds atoms in each iteration process, simultaneously rejects some non-optimal atoms, and only reserves a limited number of atoms with high reliability. An improved generalized orthogonal matching pursuit algorithm (MgOMP) proposed by Zhao L et al, whose backtracking concept starts backtracking only when the number of indexes supporting concentrated atoms reaches the sparsity K when matching atoms are selected, avoids backtracking errors and excessive calculation costs caused by too few correct atoms in the initial stage of iteration.
Several greedy algorithms, described above, all require that the sparsity K of the signal be known. In practical applications, sparsity is unknown. Aiming at the situation, an improved sparsity self-adaptive matching pursuit algorithm (MSAMP) proposed by Zhuyanwan et al solves the problems of under-estimation and over-estimation caused by a large amount of calculation and a fixed step length of SAMP under a large sparsity condition to a certain extent, realizes accurate reconstruction when the sparsity of a signal is unknown, but consumes more pilot frequency resources.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the prior art, the invention provides an underwater acoustic channel estimation method based on an MSASSWOMP algorithm, which solves the problem of excessive pilot frequency resource consumption, and also provides an underwater acoustic channel estimation system based on the MSASSWOMP algorithm.
The technical scheme is as follows: on one hand, the underwater acoustic channel estimation method based on the MSASSWOMP algorithm comprises the following steps:
(1) constructing a frequency division multiplexing system, obtaining a received pilot signal Y according to the data symbol of the subcarrier, and establishing an underwater acoustic channel compression sensing equation Y;
(2) adding a weak selection of a threshold value into signal residual matching of an MSAMP algorithm, adding backtracking screening after the weak selection of the threshold value for iterative optimization, updating a support set, and further realizing estimation of a underwater acoustic channel vector.
Preferably, in the step (2), a threshold weak selection is added to the signal residual matching of the MSAMP algorithm, and specifically includes:
select signal residual match gkThe value greater than threshold th in generates set VkAnd stores the corresponding atom subscript index into the set JkSaid signal residuals are matched gk＝|<AT，rk-1>Where a is XF, r represents white gaussian noise which is independently and identically distributed, with a mean of 0 and a variance of w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix.
Preferably, the weak selection threshold th ═ α · max (abs (g)), where 0 is set<α<1，
Figure BDA0002003213910000025
Denotes rounding up, g ═ noncash<AT，y>And | is signal residual matching, and | is inner product calculation.
Preferably, in the step (2), a backtracking screening is added after the threshold value is weakly selected for iterative optimization, and the support set is updated, which specifically includes:
if | | Jk||0Size, from the set VkThe largest size element is selected and the corresponding element J is foundkAdding indexes in the set to the set Ck，Fk＝Fk-1∪CkWherein the initial support set length size is K0，K0Sparsity of the underwater acoustic channel vector, FkA support set corresponding to the kth iteration;
otherwise, let Fk＝Fk-1∪Jk。
Preferably, in step (2), the estimating of the underwater acoustic channel vector includes:
(21) calculating a signal residual matching value gk＝|<AT，rk-1>|；
(22) The estimate of the underwater acoustic channel is formulated as:
Figure BDA0002003213910000021
then the residual is updated:
Figure BDA0002003213910000022
(23) if it is
Figure BDA0002003213910000023
Go to step (24), otherwise go to step (25);
(24) if it is
Figure BDA0002003213910000024
Stopping the iteration, otherwise go to (26), where ε1And ε2Are both parameters for controlling the sparsity step size and algorithm termination iteration and are1>ε2；
(25) If rk||2>||rk-1||2Then, the size is set to size + step1,
Figure BDA0002003213910000031
returning to the step (21);
otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the procedure returns to step (21), wherein the step size of the initialization stage is set as the step size
Figure BDA0002003213910000035
step is sparsity estimation step length, and the initialization stage is 1;
(26) if rk||2>||rk-1||2If so, the stage is stage +1,
Figure BDA0002003213910000036
size＝size+step1，
Figure BDA0002003213910000032
returning to the step (21); otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the process returns to step (21).
On the other hand, the invention also provides an underwater acoustic channel estimation system based on the MSASSWOMP algorithm, which comprises the following components: the frequency division multiplexing system construction module is used for constructing a frequency division multiplexing system, obtaining a received pilot signal Y according to the data symbol of the subcarrier and establishing an underwater acoustic channel compression sensing equation Y;
and the underwater acoustic channel vector estimation module is used for adding a weak threshold selection in signal residual matching of the MSAMP algorithm, adding backtracking screening after the weak threshold selection for iterative optimization, updating the support set and further realizing the estimation of the underwater acoustic channel vector.
Preferably, the underwater acoustic channel vector estimation module comprises a threshold weak selection unit for selecting the signal residual matching gkThe value greater than threshold th in generates set VkAnd stores the corresponding atom subscript index into the set JkSaid signal residuals are matched gk＝|<AT，rk-1>Where a is XF, r represents white gaussian noise which is independently and identically distributed, with a mean of 0 and a variance of w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix.
Preferably, the weak selection threshold th ═ α · max (abs (g)), where 0 is set<α<1，
Figure BDA0002003213910000037
Denotes rounding up, g ═ noncash<AT，y>And | is signal residual matching, and | is inner product calculation.
Preferably, the underwater acoustic channel vector estimation module further includes a backtracking screening unit, configured to update the proppant on the basis of the threshold weak selection unit, if | | Jk||0Size, from the set VkThe largest size element is selected and the corresponding element J is foundkAdding indexes in the set to the set Ck，Fk＝Fk-1∪CkWherein the initial support set length size is K0，K0Sparsity of the underwater acoustic channel vector, FkA support set corresponding to the kth iteration; otherwise, let Fk＝Fk-1∪Jk。
Preferably, the underwater acoustic channel vector estimation module further includes a channel vector estimation unit, configured to implement calculation of an underwater acoustic channel vector estimation value, and includes:
(1) calculating a signal residual matching value gk＝|<AT，rk-1>|；
(2) The estimate of the underwater acoustic channel is formulated as:
Figure BDA0002003213910000033
then the residual is updated:
Figure BDA0002003213910000034
(3) if it is
Figure BDA0002003213910000041
Turning to the step (4), otherwise, turning to the step (5);
(4) if it is
Figure BDA0002003213910000042
Stopping the iteration, otherwise go to (6), where ε1And ε2Are both parameters for controlling the sparsity step size and algorithm termination iteration and are1>ε2；
(5) If rk||2>||rk-1||2Then, the size is set to size + step1,
Figure BDA0002003213910000043
returning to the step (1);
otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the procedure returns to step (1), wherein the step size of the initialization stage is
Figure BDA0002003213910000045
step is sparsity estimation step length, and the initialization stage is 1;
(6) if rk||2>||rk-1||2If so, the stage is stage +1,
Figure BDA0002003213910000046
size＝size+step1，
Figure BDA0002003213910000044
returning to the step (1); otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the procedure returns to the step (1).
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: 1. the method determines whether the current sparsity is suitable or not by judging whether the estimated sparsity meets the finite equidistant constraint (RIP), solves the problems of underestimation and overestimation caused by large operation amount and fixed step length under the condition of large sparsity in the prior art, and well realizes the accurate reconstruction when the sparsity of the unknown signal is unknown; 2. the invention adopts a threshold value weak selection method, backtracking screening is added after threshold value weak selection, atoms which are weakly selected through the threshold value are taken as candidate atoms in a backtracking stage, and in the backtracking screening stage, the size of an atom support set which is weakly selected through the threshold value at the moment is compared with an initial support set K0And the channel estimation performance can be effectively improved by using less pilot frequency resources.
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FIG. 1 is an underwater acoustic OFDM communication system model;
FIG. 2 is a flow chart of a method according to the present invention;
FIG. 3 is a schematic diagram of the system of the present invention;
FIG. 4 is a normalized impulse response of a simulation channel;
FIG. 5 is a graph showing the output SNR of the sensing matrix A at different row numbers m;
FIG. 6 is NPA channel mean square error curve of 6 estimation algorithms when the mean square error curve is 50;
FIG. 7 is NPChannel mean square error plots for the 6 estimation algorithms 80.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
Example 1
The invention provides an algorithm flow chart of underwater acoustic channel estimation based on MSASSWOMP algorithm, the MSASSWOMP algorithm used in the method is an improvement of the MSAMP algorithm, and the specific steps are as follows, as shown in figure 1:
step1, building an underwater acoustic OFDM system as shown in fig. 2, assuming that all subcarriers are orthogonal, that is, there is no inter-carrier interference (ICI), the data symbols X of N subcarriers may be represented in a matrix form, and the data carrier positions are set to zero.
Figure BDA0002003213910000051
Where X [ i ] denotes a pilot signal on the ith subcarrier, i ═ 0,1, 2.
After passing through the underwater acoustic channel, performing Fourier transform to obtain a received pilot signal Y:
Figure BDA0002003213910000052
h is an underwater acoustic channel frequency domain matrix and is Fourier transform of an underwater acoustic channel impulse response H; f is a Fourier transform (DFT) matrix; and Z is an ambient noise matrix.
Step 2, establishing an underwater acoustic channel compressed sensing equation:
Figure BDA0002003213910000053
wherein the content of the first and second substances,
Figure BDA0002003213910000054
representing the underwater sound time domain impulse response to be estimated, wherein Y is equivalent to the frequency domain form of a received pilot frequency Y, the dimension of the Y is Mx 1, and M represents the number of elements for receiving the pilot frequency; a is composed of XF, and the dimension of the XF is M multiplied by N; r represents independent and identically distributed white Gaussian noise with mean 0 and variance w2；
Step 3, utilizing improved sparsity self-adaptive weak selection matching pursuit calculationThe method carries out channel estimation to obtain the final iterative underwater acoustic channel vector estimation value
Figure BDA0002003213910000055
The method comprises the following specific steps:
(1) initializing sparsity K0Initializing as 1
Figure BDA0002003213910000056
Sparsity estimation step size>0, supporting set F0Is an empty set;
(2) calculating signal residual matching g ═ Y<AT，y>I, the top K to be the largest0Storing subscript indexes corresponding to items into a support set F0Wherein, | is an inner product calculation;
(3) if:
Figure BDA0002003213910000057
then K is0＝K0+ step, go to (2); otherwise if
Figure BDA0002003213910000058
Then
Figure BDA0002003213910000068
K0＝K0+ step, go to (2); if it is
Figure BDA0002003213910000061
Turning to (4), whereinKE (0,1), representing constants that make matrix A satisfy a finite equidistant constraint (RIP); /a2Represents a 2 norm;
(4) calculating the initial residual r0＝y-AF0(AT F0AF0)-1y, initial set of index values F0Temporary set Jk，CkFor the empty set, the initialization stage is 1, the initialization iteration number k is 1, and the initialization stage step length
Figure BDA0002003213910000069
Initial support set length size K0；
(5) Computing signal residual match gk＝|<AT，rk-1>|；
(6) Weak selection of a threshold value: selection of gkThe value greater than threshold th in generates set VkAnd store the corresponding atom subscript index into Jk；
(7) Backtracking and screening: if | | Jk||0Size from VkThe largest size element is selected and the corresponding element J is foundkAddition of indexes in the set to Ck，Fk＝Fk-1∪Ck(ii) a If | | Jk||0<size, then Fk＝Fk-1∪Jk；
(8) Underwater acoustic channel estimation:
Figure BDA0002003213910000062
and (3) residual error updating:
Figure BDA0002003213910000063
(9) if it is
Figure BDA0002003213910000064
Then go to (10), otherwise go to (11);
(10) if it is
Figure BDA0002003213910000065
Stopping the iteration, otherwise, turning to (12);
(11) if/rk∥2>∥rk-1∥2Then, the size is set to size + step1,
Figure BDA0002003213910000066
turning to (5); otherwise Fk+1＝Fk，rk+1＝rkK +1 goes to (5);
(12) if/rk∥2>∥rk-1∥2If so, the stage is stage +1,
Figure BDA00020032139100000610
size＝size+step1，
Figure BDA0002003213910000067
turning to (5); otherwise Fk+1＝Fk，rk+1＝rkK +1 goes to (5).
The steps (1) to (4) complete the initial estimation of sparsity and the initialization of residual error and support set; (5) and (12) fusing weak selection and backtracking screening for iterative optimization under the framework of an MSAMP algorithm. Wherein the weak selection threshold th ═ α · max (abs (g)), 0<α<1；
Figure BDA00020032139100000611
Represents rounding up; (9) and (10) ε in step (a)1And ε2For controlling sparsity step size and algorithm termination iteration and epsilon1>ε2。
Example 2
On the other hand, the present invention further provides an underwater acoustic channel estimation system based on the msasswomp algorithm, as shown in fig. 3, including:
the frequency division multiplexing system building module 1 is configured to build a frequency division multiplexing system, obtain a received pilot signal Y according to a data symbol of a subcarrier, and build an underwater acoustic channel compressive sensing equation Y, and includes:
the pilot signal calculation unit 11 firstly establishes an underwater acoustic OFDM system; assuming that all sub-carriers are orthogonal, i.e. there is no inter-carrier interference (ICI), the data symbols X for N sub-carriers can be represented in matrix form with the data carrier positions zeroed out.
Figure BDA0002003213910000071
Where X [ i ] denotes a pilot signal on the ith subcarrier, i ═ 0,1, 2.
Secondly, calculating a pilot signal Y; after passing through the underwater acoustic channel, performing Fourier transform to obtain a received pilot signal Y:
Figure BDA0002003213910000072
h is an underwater acoustic channel frequency domain matrix and is Fourier transform of an underwater acoustic channel impulse response H; f is a Fourier transform (DFT) matrix; and Z is an ambient noise matrix.
The compressed sensing equation building unit 12 is configured to build an underwater acoustic channel compressed sensing equation:
Figure BDA0002003213910000073
wherein the content of the first and second substances,
Figure BDA0002003213910000074
representing the underwater sound time domain impulse response to be estimated, wherein Y is equivalent to the frequency domain form of a received pilot frequency Y, the dimension of the Y is Mx 1, and M represents the number of elements for receiving the pilot frequency; a is composed of XF, and the dimension of the XF is M multiplied by N; r represents independent and identically distributed white Gaussian noise with mean 0 and variance w2。
The underwater acoustic channel vector estimation module 2 is configured to add a weak threshold selection in signal residual matching of the MSAMP algorithm, add backtracking screening after the weak threshold selection for iterative optimization, update a support set, and further realize estimation of an underwater acoustic channel vector, and specifically includes:
the sparsity judging unit 21 is configured to judge whether the estimated sparsity satisfies a finite equidistant constraint (RIP) to determine whether the current sparsity is suitable, and specifically includes the following implementation steps:
(211) initializing sparsity K0Initializing as 1
Figure BDA0002003213910000075
Sparsity estimation step size>0, supporting set F0Is an empty set;
(212) calculating signal residual matching g ═ Y<AT，y>I, the top K to be the largest0Storing subscript indexes corresponding to items into a support set F0Wherein, | is an inner product calculation;
(213) if:
Figure BDA0002003213910000081
then K is0＝K0+ step, go to (212); otherwise if
Figure BDA0002003213910000082
Then
Figure BDA0002003213910000089
K0＝K0+ step, go to (212); if it is
Figure BDA0002003213910000083
Turning to (214), whereinKE (0,1), representing constants that make matrix A satisfy a finite equidistant constraint (RIP); /a2Represents a 2 norm;
(214) calculating the initial residual r0＝y-AF0(AT F0AF0)-1y, initial set of index values F0Temporary set Jk，CkFor the empty set, the initialization stage is 1, the initialization iteration number k is 1, and the initialization stage step length
Figure BDA00020032139100000810
Initial support set length size K0；
(215) Computing signal residual match gk＝|<AT，rk-1>|；
A threshold weak selection unit 22 for selecting a signal residual match gkThe value greater than threshold th in generates set VkAnd stores the corresponding atom subscript index into the set JkSaid signal residuals are matched gk＝|<AT，rk-1>Where a is XF, r represents white gaussian noise which is independently and identically distributed, with a mean of 0 and a variance of w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix.
The weak selection threshold th ═ α · max (abs (g)), where 0<α<1，
Figure BDA00020032139100000811
Denotes rounding up, g ═ noncash<AT，y>And | is signal residual matching, and | is inner product calculation.
A backtracking screening unit 23 for updating the proppant on the basis of the weak selection unit of the threshold value, if | | Jk||0Size, from the set VkThe largest size element is selected and the corresponding element J is foundkAdding indexes in the set to the set Ck，Fk＝Fk-1∪CkWherein the initial support set length size is K0，K0Sparsity of the underwater acoustic channel vector, FkA support set corresponding to the kth iteration; otherwise, let Fk＝Fk-1∪Jk。
A channel vector estimation unit 24, configured to implement calculation of an underwater acoustic channel vector estimation value according to units 21 and 22, including the following implementation steps:
(241) underwater acoustic channel estimation:
Figure BDA0002003213910000084
and (3) residual error updating:
Figure BDA0002003213910000085
(242) if it is
Figure BDA0002003213910000086
Go to (243), otherwise go to (244);
(243) if it is
Figure BDA0002003213910000087
Stopping the iteration, otherwise go to (245);
(244) if/rk∥2>∥rk-1∥2Then, the size is set to size + step1,
Figure BDA0002003213910000088
go to the sparsity determination unit 21Step (215); otherwise Fk+1＝Fk，rk+1＝rkA step (215) of shifting to the sparsity determination unit 21 when k +1 is reached;
(245) if/rk∥2>∥rk-1∥2If so, the stage is stage +1,
Figure BDA0002003213910000092
size＝size+step1，
Figure BDA0002003213910000091
a step (215) of proceeding to the sparsity determination unit 21; otherwise Fk+1＝Fk，rk+1＝rkThe process proceeds to step (215) in the sparsity determining unit 21 when k +1 is reached.
The sparsity judging unit 21 completes initial estimation of sparsity and initialization of residual errors and a support set; the threshold weak selection unit 22, the backtracking screening unit 23 and the channel vector estimation unit 24 are used for performing iterative optimization by fusing weak selection and backtracking screening in the framework of the MSAMP algorithm. Wherein the weak selection threshold th ═ α · max (abs (g)), 0<α<1；
Figure BDA0002003213910000093
Represents rounding up; epsilon of steps (243) and (244) in channel vector estimation unit 241And ε2Are all used for controlling sparsity step length and algorithm termination iteration and epsilon1>ε2。
According to the underwater acoustic channel estimation method and system based on the MSASSWOMP algorithm, simulation experiments are carried out.
First, the sparsity of the underwater acoustic channel is simulated. In order to verify the effectiveness of the invention, bellhop underwater acoustic channel simulation software is adopted to construct a sparse underwater acoustic channel, a transmitting source and a receiving end are arranged, the depth is respectively set to be 10m and 20m, the horizontal distance is 1000m, the water depth is 150m, and the sound velocity is uniform (the simulation environment is representative). The transmitting signal adopts QPSK modulation, the transmitting source transmits uncorrelated random code element sequence with the symbol rate of 4ksymbols/s and superimposed Gaussian white noise. Fig. 4 shows the normalized impulse response absolute value of the simulation channel.
Second, the number of rows m of the sensing matrix A. To verify the estimated performance of the present invention, FIG. 5 shows the experimental results comparing SP, gOMP, MgOMP, SAMP, MSAMP and the present invention, the algorithm described herein is referred to as MSASSWOMP. When the signal length n is 256, the sparsity K is 12, and the input signal-to-noise ratio SNR is 20dB, the number of rows m of the perceptual matrix a is set from 20 to 200 at a transform pitch of 20. Each estimation algorithm independently runs for 100 times every time a set value is taken, and when the Output signal-to-noise ratio (Output SNR) of the estimated channel exceeds 20dB, the channel estimation precision is high. As can be seen from FIG. 5, when the number m of rows of the sensing matrix A is 40-60, the Output SNR obtained by the invention and the SAMP algorithm is approximately equal and superior to those of other algorithms; when the row number m of the sensing matrix A is larger than 60, the method can keep better estimation performance, and the SAMP algorithm increases the iteration times along with the increase of the row number m, so that the over-estimation of sparsity occurs, the output signal-to-noise ratio is gradually reduced, and the estimation performance is deteriorated. Therefore, the invention can obtain better estimation performance with less rows m. In the underwater acoustic channel OFDM system, the number of the pilot frequency determines the row number of the sensing matrix A, namely, the invention can utilize less pilot frequency resources and obtain better channel estimation effect.
And finally, simulating OFDM underwater sound channel estimation. Under the parameter condition of the experiment simulation system, the pilot frequency number N is selected in the experimentPGaussian noise level ranges from 0dB to 30dB of channel estimate at 50, 80. The estimation algorithm runs 100 times independently for each setting taken.
The MSE curves of the present invention, which are respectively matched with the channel estimation of the SAMP, MSAMP, giomp, MgOMP (S ═ 3) algorithms, are shown in fig. 6 (N)P50), fig. 7 (N)P80) is shown. As can be seen from fig. 6, when NP is 50, the number of pilots is small, and in combination with the simulation experiment result shown in fig. 5, the SAMP algorithm at this time has a better estimation effect than the MSAMP, giomp, and MgOMP (S is 3) algorithms, and as the signal-to-noise ratio increases, the estimation performance of the present invention is better than that of the SAMP algorithm; as can be seen from FIG. 7, when N is presentPAt 80, the number of pilots increases, the SAMP algorithm estimation effect becomes worse, and the MSAMP and MgOMP (S ═ 3) algorithm estimation effect increases. Wherein, MgOMP (S)3) the algorithm approaches the estimation effect of the present invention. Therefore, the MSASSWOMP algorithm can utilize less pilot frequency resources and obtain better channel estimation effect.
In summary, the estimation performance of the present invention is better than the SP, giomp, MgOMP (S ═ 3), SAMP, and MSAMP algorithms.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (8)

1. An underwater acoustic channel estimation method based on MSASSWOMP algorithm is characterized by comprising the following steps:
(1) constructing a frequency division multiplexing system, obtaining a received pilot signal Y according to the pilot signal inserted by the subcarrier, and establishing an underwater acoustic channel compression sensing equation;
(2) adding a weak selection of a threshold value into signal residual matching of an MSAMP algorithm, adding backtracking screening after the weak selection of the threshold value for iterative optimization, and updating a support set so as to realize estimation of a underwater acoustic channel vector;
in the step (2), the estimating of the underwater acoustic channel vector includes:
(21) calculating a signal residual matching value gk＝|<AT，rk-1>L, |; wherein, A is XF, r represents independent and same distributed white Gaussian noise, the mean value is 0, and the variance is w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix;
(22) the estimate of the underwater acoustic channel is formulated as:
Figure FDA0002976790500000011
then the residual is updated:
Figure FDA0002976790500000012
wherein Y is an underwater acoustic channel compressive sensing equation which is a frequency domain form of the received pilot signal Y;
(23) if it is
Figure FDA0002976790500000013
Go to step (24), otherwise go to step (25);
(24) if it is
Figure FDA0002976790500000014
Stopping the iteration, otherwise go to (26), where ε1And ε2Are both parameters for controlling the sparsity step size and algorithm termination iteration and are1>ε2；
(25) If rk||2>||rk-1||2Then, the size is set to size + step1,
Figure FDA0002976790500000015
returning to the step (21);
otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the procedure returns to step (21), wherein the step size of the initialization stage is set as the step size
Figure FDA0002976790500000018
step is sparsity estimation step length, and the initialization stage is 1;
(26) if rk||2>||rk-1||2If so, the stage is stage +1,
Figure FDA0002976790500000019
size＝size+step1，
Figure FDA0002976790500000016
returning to the step (21); otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the process returns to step (21).
2. The method for estimating an underwater acoustic channel based on an msasmop algorithm as claimed in claim 1, wherein in said step (2), a threshold weak selection is added to the signal residual matching of the MSAMP algorithm, specifically comprising:
select signal residual match gkThe value greater than threshold th in generates set VkAnd stores the corresponding atom subscript index into the set JkSaid signal residuals are matched gk＝|<AT，rk-1>Where a is XF, r represents white gaussian noise which is independently and identically distributed, with a mean of 0 and a variance of w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix.
3. The method of claim 2, wherein the weak selection threshold th ═ α -max (abs (g)), where 0 is set to be 0<α<1，
Figure FDA0002976790500000017
Denotes rounding up, g ═ noncash<AT，y>I is signal residual matching, | - | is inner product calculation, and y is an underwater sound channel compression sensing equation;
the underwater acoustic channel compressed sensing equation y is as follows:
Figure FDA0002976790500000021
wherein the content of the first and second substances,
Figure FDA0002976790500000022
an estimate representing the underwater acoustic time domain impulse response h, a is made of XF, with dimensions mxn,
and, the received pilot signal Y is represented as:
Figure FDA0002976790500000023
h is an underwater acoustic channel frequency domain matrix and is Fourier transform of an underwater acoustic channel impulse response H; f is a Fourier transform (DFT) matrix; z is the ambient noise matrix, and thus the underwater acoustic channel compressive sensing equation Y is the frequency domain form of the received pilot signal Y.
4. The method for estimating an underwater acoustic channel based on an msasswomp algorithm as claimed in claim 2, wherein in the step (2), a backtracking screening is added after the threshold value is weakly selected for iterative optimization, and the support set is updated, specifically including:
if | | Jk||0Size, from the set VkThe largest size element is selected and the corresponding element J is foundkAdding indexes in the set to the set Ck，Fk＝Fk-1∪CkWherein the initial support set length size is K0，K0Sparsity of the underwater acoustic channel vector, FkA support set corresponding to the kth iteration;
otherwise, let Fk＝Fk-1∪Jk。
5. An estimation system implemented by the underwater acoustic channel estimation method based on the MSASSWOMP algorithm according to any one of claims 1 to 4, comprising:
the frequency division multiplexing system construction module is used for constructing a frequency division multiplexing system, obtaining a received pilot signal Y according to the pilot signal inserted in the subcarrier and establishing an underwater acoustic channel compression sensing equation;
the underwater acoustic channel vector estimation module is used for adding a threshold weak selection in signal residual matching of an MSAMP algorithm, adding backtracking screening after the threshold weak selection for iterative optimization, updating a support set and further realizing the estimation of an underwater acoustic channel vector;
the underwater acoustic channel vector estimation module comprises a channel vector estimation unit, is used for realizing the calculation of the underwater acoustic channel vector estimation value, and comprises:
(1) computingSignal residual matching value gk＝|<AT，rk-1>L, |; wherein, A is XF, r represents independent and same distributed white Gaussian noise, the mean value is 0, and the variance is w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix;
(2) the estimate of the underwater acoustic channel is formulated as:
Figure FDA0002976790500000031
then the residual is updated:
Figure FDA0002976790500000032
wherein Y is an underwater acoustic channel compressive sensing equation which is a frequency domain form of the received pilot signal Y;
(3) if it is
Figure FDA0002976790500000033
Turning to the step (4), otherwise, turning to the step (5);
(4) if it is
Figure FDA0002976790500000034
Stopping the iteration, otherwise go to (6), where ε1And ε2Are both parameters for controlling the sparsity step size and algorithm termination iteration and are1>ε2；
(5) If rk||2>||rk-1||2Then, the size is set to size + step1,
Figure FDA0002976790500000035
returning to the step (1);
otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the procedure returns to step (1), wherein the step size of the initialization stage is
Figure FDA00029767905000000311
step is sparsity estimation step length, and initialization stage is 1；
(6) If rk||2>||rk-1||2If so, the stage is stage +1,
Figure FDA00029767905000000310
size＝size+step1，
Figure FDA0002976790500000036
returning to the step (1); otherwise Fk+1＝Fk，rk+1＝rkAnd k is k +1, the procedure returns to the step (1).
6. The MSASHOMP algorithm based underwater acoustic channel estimation system of claim 5, wherein the underwater acoustic channel vector estimation module comprises a threshold weak selection unit for selecting signal residual matching gkThe value greater than threshold th in generates set VkAnd stores the corresponding atom subscript index into the set JkSaid signal residuals are matched gk＝|<AT，rk-1>Where a is XF, r represents white gaussian noise which is independently and identically distributed, with a mean of 0 and a variance of w2K is the iteration number of the algorithm, X is the matrix form corresponding to the data symbols X of the N subcarriers, and F is a Fourier transform matrix.
7. The MSASHOMP algorithm based hydroacoustic channel estimation system of claim 6 wherein the weak selection threshold th ═ α max (abs (g)), where 0<α<1，
Figure FDA0002976790500000037
Denotes rounding up, g ═ noncash<AT，y>I is signal residual matching, | - | is inner product calculation, and y is an underwater sound channel compression sensing equation;
the underwater acoustic channel compressed sensing equation y is as follows:
Figure FDA0002976790500000038
wherein the content of the first and second substances,
Figure FDA0002976790500000039
an estimate representing the underwater acoustic time domain impulse response h, a is made of XF, with dimensions mxn,
and, the received pilot signal Y is represented as:
Figure FDA0002976790500000041
h is an underwater acoustic channel frequency domain matrix and is Fourier transform of an underwater acoustic channel impulse response H; f is a Fourier transform (DFT) matrix; z is the ambient noise matrix, and thus the underwater acoustic channel compressive sensing equation Y is the frequency domain form of the received pilot signal Y.
8. The system of claim 6, wherein the underwater acoustic channel vector estimation module further comprises a backtracking filtering unit for updating the support set based on the weak threshold selection unit, if Jk||0Size, from the set VkThe largest size element is selected and the corresponding element J is foundkAdding indexes in the set to the set Ck，Fk＝Fk-1∪CkWherein the initial support set length size is K0，K0Sparsity of the underwater acoustic channel vector, FkA support set corresponding to the kth iteration; otherwise, let Fk＝Fk-1∪Jk。
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