High-precision sparse estimation method for shallow sea multipath channel

Abstract

The embodiment of the application discloses a high-precision sparse estimation method of a shallow sea multipath channel. The method is based on a coherent multipath channel model to construct a discretized channel input-output relationship, uses a sending signal to construct a measurement matrix to convert the discretized channel input-output relationship into a sparse representation model in the form of a rectangular vector, determines a target function of channel estimation according to the sparse representation model, and uses a multi-step forward search strategy to obtain a sparse solution after K iterations to estimate a more accurate channel time-domain impulse response.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of underwater acoustic communication and underwater acoustic signal processing, and in particular to a high-precision sparse estimation method for a shallow-water multipath channel. BACKGROUND

[0002] Underwater acoustic communication is currently the main way of underwater long-distance wireless communication. The underwater acoustic channel has a significant multipath effect in a shallow-water environment, which causes a large time delay spread in the received signal, thereby making the channel time-domain impulse response have a sparse characteristic. For the problem of sparse underwater acoustic channel estimation, the received signal and the known pilot signal are currently periodically trained to estimate the channel time-domain impulse response.

[0003] The traditional sparse estimation methods mainly include a matching pursuit method (MP) and an orthogonal matching pursuit method (OMP). Details of the matching pursuit algorithm can be found in Sparse channel estimation via matching pursuit with application to equalization, which was published in the journal IEEE Transactions on Communications in 2002, starting at page 374. Details of the orthogonal matching pursuit algorithm can be found in Sparse channel estimation using orthogonal matching pursuit algorithm, which was published in the international conference IEEE 60th Vehicular Technology Conference in 2004, starting at page 3880. The matching pursuit-based method has inherent redundant calculation and redundant selection characteristics of atoms, which leads to limited accuracy of the estimation result. The orthogonal matching pursuit algorithm can avoid repeated selection of the same atom, but in a noisy environment, there is a possibility of selecting an incorrect atom in the iteration process, and the estimation accuracy needs to be further improved. SUMMARY

[0004] Therefore, it is necessary to propose a high-precision sparse estimation method for a shallow-water multipath channel in view of the above problems.

[0005] The high-precision sparse estimation method for the shallow-water multipath channel comprises the following steps:

[0006] Constructing a discretized channel input-output relationship based on a coherent multipath channel model;

[0007] Constructing a measurement matrix according to a transmission signal;

[0008] transforming the discretized channel input-output relationship into a rectangular vector form according to the measurement matrix;

[0009] determining a target function of channel estimation according to the rectangular vector form;

[0010] obtaining an estimated channel time-domain impulse response by using a multi-step forward search strategy after completing all K iterations according to the target function of channel estimation.

[0011] In an example embodiment, the discretized channel input-output relationship is constructed based on the coherent multipath channel model, and specifically includes:

[0012] the discretized channel input-output relationship is m = 0, K, M-1, wherein s(m) is a sending signal, y(m) is a receiving signal, h(m) is an underwater acoustic channel time-domain impulse response, w(m) is noise, j is a discrete time, N is a length of a steady-state channel, and M is a length of an observation window.

[0013] In an example embodiment, the measurement matrix is constructed according to the sending signal, and specifically includes: wherein s(0) is a sending signal at a current time, and s(M-N) is a sending signal at the M-N time.

[0014] In an example embodiment, the discretized channel input-output relationship is transformed into a rectangular vector form according to the measurement matrix, and specifically includes:

[0015] In an example embodiment, the target function of channel estimation is determined according to the rectangular vector form, and specifically includes: wherein ||h||0 is a number of non-zero taps of a sparse underwater acoustic channel, h ∈ R N is a time-domain sparse channel response to be estimated, and a sparsity degree thereof is assumed to be K.

[0016] In an example embodiment, the estimated channel time-domain impulse response is obtained by using a multi-step forward search strategy after completing all K iterations according to the target function of channel estimation, and specifically includes:

[0017] Let h0 = 0 N ; initial residual r0 = y; initial support set initial index set initial candidate set initial iteration number k = 0; wherein the symbol denotes an empty set;

[0018] The number of multipath of the known channel is K, when k>K, the iteration is stopped, otherwise, the iteration is performed in the following way:

[0019] (1) when k≤K, the atom in the measurement matrix A corresponding to the residual r k-1 The most relevant L atoms And a candidate set is established i=1,...,L, wherein L is a search width;

[0020] (2) based on a multi-step search strategy, for each atom According to the OMP algorithm, the corresponding residual r k,i is determined by iterating forward P steps, and the atom selected in the kth iteration is selected according to the principle that the corresponding residual norm is minimum, that is λ k is the most matched atom number selected in the current matching pursuit process;

[0021] (3) according to the principle that the corresponding residual norm is minimum, the atom selected in the kth iteration is selected, that is

[0022] (4) λ k is added to the index set, that is Λ k =Λ k-1 ∪{λ k}, and is added to the support set, that is wherein denotes the λ k th column of the matrix A;

[0023] (5) the residual after the kth iteration is updated as wherein the superscript T represents matrix transposition;

[0024] (6) the iteration number is increased by 1, that is k=k+1;

[0025] When all K iterations are completed, the most matched K atoms are selected from the measurement matrix, and the estimated channel time-domain impulse response h is obtained by calculation.

[0026] In an exemplary embodiment, the estimated channel time-domain impulse response h obtained by calculation specifically comprises: obtaining the estimated channel time-domain impulse response h according to .

[0027] By adopting the embodiments of the present application, the following beneficial effects are achieved:

[0028] The algorithm proposed in the present application has the characteristics of high-precision estimation, which will be proved in the following simulation experiment. By introducing a multi-step forward search strategy in OMP, the estimation accuracy of the shallow sea multipath channel can be effectively improved by the MSF-OMP algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0030] Wherein:

[0031] Figure 1 is the sparse channel time-domain impulse response used in simulation by the method of the present application;

[0032] Figure 2 is the mean square error curve comparison result of the method of the present application and the classical method in the observation length range;

[0033] Figure 3 is the estimation performance comparison result of the method of the present application and the classical method at different observation vector lengths;

[0034] Figure 4 is the estimation performance comparison result of the method of the present application and the classical method at different received signal-to-noise ratios. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments only constitute some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0036] In one embodiment, a high-precision sparse estimation method of a shallow sea multipath channel is provided, which is realized by the following steps:

[0037] Step 101: constructing a discretized channel input-output relationship based on a coherent multipath channel model;

[0038] Specifically, the discretized channel input-output relationship is m=0, K, M-1, wherein s(m) is a transmitted signal, y(m) is a received signal, h(m) is an underwater acoustic channel time-domain impulse response, w(m) is noise, j is a discrete time, N is the length of a steady-state channel, and M is the length of an observation window.

[0039] Step 102: constructing a measurement matrix according to the transmitted signal;

[0040] Specifically, the measurement matrix A is Wherein, s(0) is the current time of the transmission signal, s(M-N) is the M-N time of the transmission signal.

[0041] Step 103: according to the measurement matrix, the discretization of the channel input-output relationship is converted into a rectangular vector form;

[0042] Specifically, the rectangular vector form is y=A h+w, wherein y is a received signal vector, A is a measurement matrix of M*N dimension, h is a channel impulse response vector, and w is a noise vector.

[0043] Step 104: according to the rectangular vector form, a target function of channel estimation is determined;

[0044] Specifically, the target function of channel estimation is Wherein, ||h||0 is the number of non-zero taps of a sparse underwater acoustic channel, h is in R N The time-domain sparse channel response to be estimated is h, and the sparsity is assumed to be K.

[0045] Step 105: according to the target function of channel estimation, the estimated channel time-domain impulse response is obtained after completing all K iterations by using a multi-step forward search strategy.

[0046] Specifically,

[0047] Let h0=0 N ; Initial residual r0=y; Initial support set Initial index set Initial candidate set Initial iteration number k=0; Wherein, symbol Indicates an empty set;

[0048] When the number of channel multipath is K, stop iteration when k>K, otherwise iterate as follows:

[0049] (1) When k≤K, select the L atoms in the measurement matrix A that are most relevant to the residual r k-1 ; And establish the candidate set I=1,...,L, wherein L is the search width;

[0050] (2) Based on the multi-step search strategy, for each atom According to the OMP algorithm, iterate forward P steps to determine the corresponding residual r k,i ;

[0051] (3) According to the principle of minimum corresponding residual norm, select the atom selected in the kth iteration, that is I=1,...,L, λ k Is the most matched atom number selected in this matching pursuit process.

[0052] (4) Add λ k to the index set, i.e. k = Λ k-1 ∪{λ k}, and update the support set as where denotes the λ k th column of matrix A.

[0053] (5) Update the residual after the kth iteration as

[0054] (6) Increase the iteration number by 1, i.e.

[0055] When all the K iterations are completed, the K atoms that best match the measurement matrix A are selected, and the estimated channel time-domain impulse response h is obtained by calculation.

[0056] According to , the estimated channel time-domain impulse response h is obtained.

[0057] wherein the index set and the support set are determined according to the multi-step forward search strategy.

[0058] The present application is directed to the problem that the existing orthogonal matching pursuit algorithm has limited estimation accuracy in sparse underwater acoustic channel estimation, and by introducing a multi-step forward search strategy into the existing OMP algorithm, a method for estimating the sparse underwater acoustic channel time-domain impulse response by using the MSF-OMP algorithm is proposed. The method of the present application reduces the possibility of selecting incorrect atoms by the existing orthogonal matching pursuit algorithm in the iteration process due to noise interference by introducing a multi-step forward search strategy, and the effectiveness of the method of the present application in the underwater acoustic sparse channel is verified through performance simulation, and further simulation verifies that the method of the present application can achieve higher channel time-domain impulse response estimation accuracy under the same parameters, and has practical application value.

[0059] The present application has the advantages of utilizing the iteration framework of the orthogonal matching pursuit and adopting the multi-step forward search strategy to update the atom selection process, thereby realizing the sequence error minimization of iteration, reducing the estimation error, and finally accurately selecting the desired atoms to constitute the basis matrix, so as to restore the time-domain impulse response of the sparse underwater acoustic channel, and under the same parameters, the present application can provide higher estimation accuracy than the orthogonal matching pursuit algorithm, and has practical application value in the underwater acoustic communication system.

[0060] Embodiment

[0061] The present application will be further described with reference to the accompanying drawings. Referring to Figure 1 ​, the BPSK (Binary Phase Shift Keying) signal is used as the baseband signal for transmission, the length of the sparse underwater acoustic multipath channel tap is 320, and 10 paths are contained in the channel length. The transmitted signal is composed of a random signal with a standard normal distribution, and the output signal is obtained by convolution of the transmitted signal and the channel impulse response. The iteration number of the OMP algorithm is set to K = 10, and the parameters of the MSF-OMP algorithm are set to the iteration number K = 10, the search width L = 4, and the forward step P = 5. In order to further compare the performance of the LS, OMP, and MSF-OMP algorithms for channel estimation, the mean square error (MSE) is used to measure the accuracy of channel estimation, and the definition of MSE is where h represents the known simulation channel CIR.

[0062] The length of the received signal is set to 720, the length of the observation vector is fixed to 70, and the length of the sliding window is set to 10. First, the MSE is used to measure the performance of each algorithm for channel estimation within the received observation length, and the results are shown in Figure 2 . The observation results show that when the number of rows of the measurement matrix is less than the number of columns, the performance of the LS algorithm is relatively poor. When the number of rows is equal to the number of columns, the performance of the LS algorithm is improved. In general, the proposed MSF-OMP algorithm exhibits smaller MSE, which indicates that the algorithm can provide higher channel estimation accuracy. In addition, the MSE curve of the MSF-OMP algorithm fluctuates less, which further proves that the proposed algorithm has better stability in channel estimation.

[0063] The received SNR is fixed at 25 dB, the sparsity is 10, the length of the observation vector is varied from 30 to 100 with an interval of 5, the MSE is taken as the average of 100 simulation estimation results, and the MSE curves of each algorithm with the change of the length of the observation vector are shown in Figure 3 . It can be seen that when the length of the observation vector is 70, the MSE corresponding to the proposed MSF-OMP algorithm is less than 10 -2 , and it can be considered that accurate estimation of the channel can be achieved at this time. The MSE corresponding to the OMP algorithm is less than 10 -2 when the length of the observation vector is 85. In addition, since the number of columns of the measurement matrix is 320, the measurement matrix used by the LS algorithm is always underdetermined within the range of the measurement length of interest, so the estimation performance of the LS algorithm is poor. Therefore, the MSF-OMP algorithm can achieve accurate estimation of the channel using a smaller observation vector length, which not only saves storage space but also has stronger channel tracking capability.

[0064] Further attention is paid to the influence of the SNR of the receiving end on the channel estimation of each algorithm. The length of the observation vector is fixed at 75, and the receiving SNR is changed from 0 to 35 dB at intervals of 5 dB. The MSE curves of each algorithm with the change of the receiving SNR are shown in Fig. 3. Figure 4 As can be seen, with the increase of the receiving SNR, the MSE curves of each algorithm present a downward trend. Obviously, when the receiving SNR is greater than 10 dB, the MSF-OMP algorithm has the smallest MSE under the same conditions, and when the SNR is greater than 15 dB, the performance of the MSF-OMP algorithm is obviously improved.

[0065] In summary, the application has obvious implementation effects in the simulation of typical parameters, estimates the time-domain impulse response of the underwater acoustic channel in a sparse multipath environment, and improves the low precision of the current underwater acoustic channel estimation algorithm.

[0066] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combinations of the technical features do not contradict, they should be considered as the scope of the present application.

[0067] The above embodiments only express several implementation manners of the present application, and the description is specific and detailed, however, it should not be understood as a limitation on the patent scope of the present application. It should be pointed out that, for ordinary skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the patent protection scope of the present application should be subject to the appended claims.

Claims

1. A high-precision sparse estimation method for a shallow sea multipath channel, characterized in that, The method comprises: constructing a discretized channel input-output relationship based on a coherent multipath channel model; constructing a measurement matrix according to a sending signal; According to the measurement matrix, the discretized channel input-output relationship is converted into a rectangular vector form, and the rectangular vector form is where y is a received signal vector, A is a measurement matrix of N dimensions, h is a channel impulse response vector, w is a noise vector, and N is the length of a stationary channel. The target function for determining the channel estimation according to the rectangular vector form specifically comprises that the target function for determining the channel estimation is wherein, is the number of non-zero taps of the sparse underwater acoustic channel, is a time-domain sparse channel response to be estimated, and the sparsity thereof is assumed to be K , N is the length of the stationary channel; According to the target function of the channel estimation, all K times of iterations are completed by using a multi-step forward search strategy, and an estimated channel time-domain impulse response is obtained K According to the target function of the channel estimation, all K times of iterations are completed by using a multi-step forward search strategy, and an estimated channel time-domain impulse response is obtained Let ; initial residual ; initial support set ; initial index set ; initial candidate set ; initial number of iterations ; where the symbol represents the empty set; The number of multipaths of the known channel is K When the iteration is stopped, otherwise it is iterated in the following way: (1) When k ≤ K , select the most relevant L atoms in the measurement matrix A to the residual and build a candidate set where L is the search width; (2) Based on the multi-step search strategy, for each atom According to the OMP algorithm to iterate forward P Step, determine the corresponding residual as ; (3) According to the principle of minimum corresponding residual norm, the atom selected in the first iteration is selected, that is, k , , the most matched atom number selected for the current matching pursuit process. (4) add to the index set , the support set , and the , the support set , where denotes the column of the matrix A; (5) the first iteration k the updated residual after the second iteration is where the superscript T denotes matrix transposition; (6) Let the iteration number be incremented by 1, i.e. ; When all is completed K After the iteration, the best match was selected from the measurement matrix. K The estimated channel time-domain impulse response h is obtained by calculating the number of atoms.

2. The method of claim 1, wherein, the step of constructing the discretized channel input-output relationship based on the coherent multipath channel model specifically comprises: The discretized channel input-output relationship is wherein, is a transmitted signal, is a received signal, is a time-domain impulse response of an underwater acoustic channel, is noise, j is a discrete time instant, N is a length of a stationary channel, M is a length of an observation window.

3. The method of claim 1, wherein, The estimated channel time-domain impulse response h is obtained by calculation, specifically comprising: The estimated channel time-domain impulse response h is obtained.

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