High-precision sparse estimation method for shallow sea multipath channel

Abstract

The embodiment of the invention discloses a high-precision sparse estimation method for a shallow sea multipath channel, and the method comprises the steps: constructing a discretized channel input and output relation based on a coherent multipath channel model, constructing a measurement matrix through employing a transmitted signal, and converting the discretized channel input and output relation into a sparse representation model in a rectangular vector form; according to the method, in the process of solving the sparse solution of the target function for the first time, a multi-step forward search strategy is utilized to carry out all K iterations, and then the sparse solution is obtained, so that more accurate channel time domain impulse response is obtained through estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic communication and underwater acoustic signal processing, and in particular to a high-precision sparse estimation method for shallow-water multipath channels. Background Art

[0002] Underwater acoustic communication is the main mode of underwater long-distance wireless communication. Underwater acoustic channels have obvious multipath effects in shallow water environments, which causes large delay spread in the received signal, making the channel time domain impulse response sparse. To solve the problem of sparse underwater acoustic channel estimation, the received signal and the known pilot signal are often used for periodic training to estimate the channel time domain impulse response.

[0003] Traditional sparse estimation methods mainly include Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP). For details of the matching pursuit algorithm, see "Sparse channel estimation via matching pursuit with application to equalization", which was published in the 50th issue of the journal "IEEE Transactions on Communications" in 2002, starting on page 374; for details of the orthogonal matching pursuit algorithm, see "Sparse channel estimation using orthogonal matching pursuit algorithm", which was published in the international conference "IEEE 60th Vehicular Technology Conference" in 2004, starting on page 3880. The matching pursuit-based method has inherent redundant calculations and redundant selection characteristics of atoms, resulting in limited accuracy of the estimation results of this method; the orthogonal matching pursuit algorithm can avoid repeated selection of the same atom, however, in a noisy environment, this method has the possibility of selecting wrong atoms during the iteration process, and its estimation accuracy needs to be further improved. Summary of the invention

[0004] Based on this, it is necessary to propose a high-precision sparse estimation method for shallow sea multipath channels to address the above problems.

[0005] The high-precision sparse estimation method of the shallow sea multipath channel includes:

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

[0007] Constructing a measurement matrix based on the transmitted signal;

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

[0009] Determine the objective function of channel estimation according to the rectangular vector form;

[0010] According to the objective function of the channel estimation, after completing all K iterations using a multi-step forward search strategy, an estimated channel time domain impulse response is obtained.

[0011] In an exemplary implementation, constructing a discretized channel input-output relationship based on a coherent multipath channel model specifically includes:

[0012] The discretized channel input-output relationship is: m=0,K,M-1, where s(m) is the transmitted signal, y(m) is the received signal, h(m) is the time domain impulse response of the underwater acoustic channel, w(m) is the noise, j is the discrete moment, N is the length of the steady-state channel, and M is the length of the observation window.

[0013] In an exemplary implementation, constructing a measurement matrix according to the transmitted signal specifically includes: the measurement matrix A is Among them, s(0) is the sending signal at the current moment, and s(MN) is the sending signal at the MNth moment.

[0014] In an exemplary embodiment, the discretized channel input-output relationship is converted into a rectangular vector form according to the measurement matrix, specifically including: the rectangular vector form is y=Ah+w, wherein y is the received signal vector, A is the M×N dimensional measurement matrix, h is the channel impulse response vector, and w is the noise vector.

[0015] In an exemplary embodiment, determining the objective function of channel estimation according to the rectangular vector form specifically includes: the objective function of channel estimation is Where ||h||0 is the number of non-zero taps in the sparse water acoustic channel, h∈R N is the time-domain sparse channel response to be estimated, and its sparsity is assumed to be K.

[0016] In an exemplary implementation, the objective function of the channel estimation is used to complete all K iterations using a multi-step forward search strategy to obtain an estimated channel time domain impulse response, specifically including:

[0017] Let h0 = 0 N ; Initial residual r0 = y; Initial support set Initial index set Initial candidate set The initial number of iterations k = 0; where the symbol represents the empty set;

[0018] The number of multipaths in a known channel is K. When k>K, the iteration stops. Otherwise, the iteration is performed as follows:

[0019] (1) When k≤K, select the measurement matrix A with the residual r k-1 The most relevant L atoms And build a candidate set i=1,...,L, where L is the search width;

[0020] (2) Based on the multi-step search strategy, for each atom According to the OMP algorithm, iterate forward P steps and determine the corresponding residual as r k,i ;

[0021] (3) According to the principle of minimum corresponding residual norm, select the atom selected in the kth iteration, that is, λ k The best matching atom number selected for this matching pursuit process;

[0022] (4) k Add the index set Λ k =Λ k-1 ∪{λ k},Will Adding support set in represents the λth k List;

[0023] (5) The updated residual after the kth iteration is The superscript T indicates the matrix transpose;

[0024] (6) Let the number of iterations increase by 1, that is, k = k + 1;

[0025] When all K iterations are completed, the most matching 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 includes: Get the estimated channel time domain impulse response h.

[0027] The embodiments of the present invention have the following beneficial effects:

[0028] The algorithm proposed in the present invention has the characteristics of high-precision estimation, which will be proved in the following simulation experiments. By introducing a multi-step forward search strategy in OMP, the MSF-OMP algorithm can effectively improve the estimation accuracy of shallow water multipath channels. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0030] in:

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

[0032] Figure 2 It is the comparison result of mean square error curve between the method of the present invention and the classical method within the observation length range;

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

[0034] Figure 4 This is the result of comparing the estimation performance between the method of the present invention and the classical method under different received signal-to-noise ratios. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] In one embodiment, a high-precision sparse estimation method for a shallow-water multipath channel is provided, and the method is implemented 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, where s(m) is the transmitted signal, y(m) is the received signal, h(m) is the time domain impulse response of the underwater acoustic channel, w(m) is the noise, j is the discrete moment, N is the length of the steady-state channel, and M is the length of the observation window.

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

[0040] Specifically, the measurement matrix A is Among them, s(0) is the sending signal at the current moment, and s(MN) is the sending signal at the MNth moment.

[0041] Step 103: converting the discretized channel input-output relationship into a rectangular vector form according to the measurement matrix;

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

[0043] Step 104: determining an objective function of channel estimation according to the rectangular vector form;

[0044] Specifically, the objective function of the channel estimation is: Where ||h||0 is the number of non-zero taps in the sparse water acoustic channel, h∈R N is the time-domain sparse channel response to be estimated, and its sparsity is assumed to be K.

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

[0046] Specifically,

[0047] Let h0 = 0 N ; Initial residual r0 = y; Initial support set Initial index set Initial candidate set The initial number of iterations k = 0; where the symbol represents the empty set;

[0048] The number of multipaths in a known channel is K. When k>K, the iteration stops. Otherwise, the iteration is performed as follows:

[0049] (1) When k≤K, select the measurement matrix A with the residual r k-1 The most relevant L atoms And build a candidate set i=1,...,L, where 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 and determine the corresponding residual as 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 The best matching atom number selected for this matching pursuit process;

[0052] (4) k Add the index set Λ k =Λ k-1 ∪{λ k},Will Adding support set in represents the λth k List;;

[0053] (5) The updated residual after the kth iteration is

[0054] (6) Let the number of iterations increase by 1, that is, k = k + 1;

[0055] After all K iterations are completed, the most matching K atoms are selected from the measurement matrix A, and the estimated channel time domain impulse response h is obtained by calculation.

[0056] according to Get the estimated channel time domain impulse response h.

[0057] Among them, the index set and support set are determined according to the proposed multi-step forward search strategy.

[0058] The present invention aims at the problem of limited estimation accuracy of the existing orthogonal matching pursuit algorithm in sparse water acoustic channel estimation. By introducing a multi-step forward search strategy into the existing OMP algorithm, a method for estimating the time domain impulse response of a sparse water acoustic channel using the MSF-OMP algorithm is proposed. The method of the present invention reduces the possibility of the existing orthogonal matching pursuit algorithm being interfered by noise and selecting wrong atoms during the iteration process by introducing a multi-step forward search strategy, and verifies the effectiveness of the method of the present invention in a sparse water acoustic channel through performance simulation. Further, through simulation, it is confirmed that the method of the present invention can achieve higher channel time domain impulse response estimation accuracy under the same parameters, and has practical application value.

[0059] The advantages of the present invention are that it utilizes the iterative framework of orthogonal matching pursuit and adopts a multi-step forward search strategy to update the atom selection process, thereby minimizing the iterative sequence error, reducing the estimation error, and ultimately accurately selecting the desired atoms to form the basis matrix, thereby restoring the time domain impulse response of the sparse underwater acoustic channel and being able to provide higher estimation accuracy than the orthogonal matching pursuit algorithm under the same parameters. It has practical application value in underwater acoustic communication systems.

[0060] Example

[0061] The present invention will now be further described with reference to the accompanying drawings. Figure 1The simulation uses BPSK (Binary PhaseShift Keying, BPSK) signal as the transmitted baseband signal. The tap length of the sparse underwater acoustic multipath channel is 320, and the channel length contains 10 multipaths. The transmitted signal is composed of a random signal with a standard normal distribution, and the output signal is obtained by convolving the transmitted signal with the channel impulse response. The number of iterations of the OMP algorithm is set to K=10, and the parameters of the MSF-OMP algorithm are set to the number of iterations K=10, the search width L=4, and the forward step length P=5. In order to further compare the performance of LS, OMP and MSFOMP algorithms for channel estimation, the mean square error MSE can be used to measure the accuracy of channel estimation. Here, MSE is defined as Where h is the known CIR of the simulated channel.

[0062] The received signal length is set to 720, the observation vector length is fixed to 70, and the sliding window length is set to 10. First, the MSE is used to measure the performance of each algorithm for channel estimation within the received observation length. The results are as follows Figure 2 As shown in the figure. The observation results show that when the number of rows in the measurement matrix is ​​less than the number of columns, the performance of the LS algorithm is relatively poor. When the number of rows and columns is equal, the performance of the LS algorithm is improved. In general, the proposed MSF-OMP algorithm shows a smaller mean square error, 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 is more stable in channel estimation.

[0063] The received SNR is fixed at 25dB, the sparsity is 10, the observation vector length is changed from 30 to 100 with an interval of 5, and the MSE is taken as the average of 100 simulation estimation results. The MSE curves of each algorithm with the change of observation vector length are shown in Figure 3 As shown in Figure 2, it can be seen that when the observation vector length is 70, the MSE corresponding to the proposed MSF-OMP algorithm is already less than 10. -2 , it can be considered that the channel can be accurately estimated at this time. When the length of the observation vector of the OMP algorithm is 85, its corresponding MSE is less than 10 -2 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 measurement length range of interest, so the estimation performance of the LS algorithm is very poor. Therefore, the MSF-OMP algorithm can use a smaller observation vector length to achieve accurate channel estimation, which not only saves storage space but also has stronger channel tracking capabilities.

[0064] Further focus on the impact of the signal-to-noise ratio (SNR) at the receiving end on the channel estimation of each algorithm. The length of the observation vector is fixed at 75, and the received SNR is varied from 0 to 35 dB at intervals of 5 dB. The MSE curves of each algorithm as a function of the received SNR are as shown in Figure 4 Figure []. Here, the MSE curves corresponding to the LS algorithm when the number of rows of the measurement matrix is much smaller than the number of columns (M < N) and when the number of rows is equal to the number of columns (M = N) are calculated respectively. It can be seen that as the received SNR increases, the MSE curves of each algorithm show a downward trend. Obviously, when the received SNR is greater than 10 dB, the proposed MSF-OMP algorithm has the smallest MSE under the same conditions. Moreover, when the SNR exceeds 15 dB, the performance of the proposed MSF-OMP algorithm improves significantly.

[0065] In summary, the present invention has achieved obvious implementation effects in the simulation of typical parameters, estimated the time-domain impulse response of the underwater acoustic channel in a sparse multipath environment, and improved the deficiency of low accuracy in the current underwater acoustic channel estimation algorithms.

[0066] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0067] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A high-precision sparse estimation method for shallow-water multipath channels, characterized in that: The method is: Construct a discretized channel input-output relationship based on the coherent multipath channel model; Constructing a measurement matrix based on the transmitted signal; Converting the discretized channel input-output relationship into a rectangular vector form according to the measurement matrix; Determine the objective function of channel estimation according to the rectangular vector form; According to the objective function of the channel estimation, after completing all K iterations using a multi-step forward search strategy, an estimated channel time domain impulse response is obtained.

2. The high-precision sparse estimation method for shallow sea multipath channels according to claim 1, characterized in that: The constructing of a discretized channel input-output relationship based on a coherent multipath channel model specifically includes: The discretized channel input-output relationship is: m=0,K,M-1, where s(m) is the transmitted signal, y(m) is the received signal, h(m) is the time domain impulse response of the underwater acoustic channel, w(m) is the noise, j is the discrete moment, N is the length of the steady-state channel, and M is the length of the observation window.

3. The high-precision sparse estimation method for shallow sea multipath channels according to claim 1 or 2, characterized in that: The constructing of the measurement matrix according to the transmitted signal specifically includes: the measurement matrix A is Among them, s(0) is the sending signal at the current moment, and s(MN) is the sending signal at the MNth moment.

4. The high-precision sparse estimation method for shallow-water multipath channels according to claim 3 is characterized in that: The method of converting the discretized channel input-output relationship into a rectangular vector form according to the measurement matrix specifically includes: the rectangular vector form is y=Ah+w, wherein y is the received signal vector, A is the M×N dimensional measurement matrix, h is the channel impulse response vector, and w is the noise vector.

5. The high-precision sparse estimation method for shallow sea multipath channels according to claim 4 is characterized in that: Determining the objective function of channel estimation according to the rectangular vector form specifically includes: the objective function of channel estimation is Where ||h||0 is the number of non-zero taps in the sparse water acoustic channel, h∈R N is the time-domain sparse channel response to be estimated, and its sparsity is assumed to be K.

6. The high-precision sparse estimation method for shallow-water multipath channels according to claim 5, characterized in that: The objective function of the channel estimation is used to complete all K iterations using a multi-step forward search strategy to obtain an estimated channel time domain impulse response, which specifically includes: Let h0 = 0 N ; Initial residual r0 = y; Initial support set Initial index set Initial candidate set The initial number of iterations k = 0; where the symbol represents the empty set; The number of multipaths in a known channel is K. When k>K, the iteration stops. Otherwise, the iteration is performed as follows: (1) When k≤K, select the measurement matrix A with the residual r k-1 The most relevant L atoms 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, iterate forward P steps and determine the corresponding residual as r k,i ; (3) According to the principle of minimum corresponding residual norm, select the atom selected in the kth iteration, that is, λ k The best matching atom number selected for this matching pursuit process; (4) k Add the index set Λ k =Λ k-1 ∪{λ k }, a λk Adding support set in represents the λth k List; (5) The updated residual after the kth iteration is The superscript T indicates the matrix transpose; (6) Let the number of iterations increase by 1, that is, k = k + 1; When all K iterations are completed, the most matching K atoms are selected from the measurement matrix, and the estimated channel time domain impulse response h is obtained by calculation.

7. The high-precision sparse estimation method for shallow sea multipath channels according to claim 6, characterized in that: The estimated channel time domain impulse response h obtained by calculation specifically includes: Get the estimated channel time domain impulse response h.

Images