Iterative Sequence Estimation Method for Underwater Acoustic Communication Based on Channel Shortening and Sphere Decoding

Abstract

The present invention discloses an iterative sequence estimation method for underwater acoustic communication based on channel shortening and sphere decoding, comprising: S1: After filtering the passband signal received by the hydrophone through a band-pass filter, it is processed by down-conversion and a matched filter. After carrier frequency offset estimation and compensation, baseband symbols are obtained through resampling; S2: Using the baseband symbols as input, channel estimation is performed to obtain the original baseband channel; S3: The original baseband channel is shortened using a channel shortening algorithm based on a minimum mean square error equalizer to reduce the number of taps; S4: Taps with concentrated energy in the underwater acoustic channel are selected for sphere decoding. The present invention uses a method combining channel shortening and iterative sphere decoding, balancing the relationship between computational complexity and demodulation performance.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic communication, and in particular to an iterative sequence estimation method for underwater acoustic communication based on channel shortening and sphere decoding. Background Art

[0002] Decision feedback equalization (hereinafter referred to as DFE) is a commonly used equalization method in underwater acoustic communication, but its performance is not optimal. In order to improve the reliability of communication, it is necessary to study a better demodulation algorithm. In the prior art, maximum likelihood sequence estimation (hereinafter referred to as MLSE) based on the Viterbi algorithm (hereinafter referred to as VA) is the optimal equalization scheme, which was first used for terrestrial wireless communication. However, since the length of the underwater acoustic channel can reach dozens or even hundreds of symbols, and the computational complexity of maximum likelihood sequence estimation increases exponentially with the increase in the number of channel taps, it is difficult to implement maximum likelihood sequence estimation equalization in an underwater acoustic channel with severe multipath effects.

[0003] In recent decades, MLSE with reduced complexity has been continuously studied and improved: M. Ghosh et al. used pre-filtering to reduce the channel length and thus reduce the number of states of VA; F. Rusek et al. introduced a method combining channel shortening and Viterbi equalization in wireless MIMO communication; M. V. Eyuboglu et al. divided the constellation diagram of high-order modulation signals into multiple subsets, reducing the modulation order, but it only reduced the modulation order of the signal, and its computational complexity is still exponentially related to the channel length; A. Duel-Hallen et al. proposed delayed decision feedback equalization to effectively reduce the number of states at each moment and eliminate inter-symbol interference at the tail through feedback, but this method will cause error propagation due to misjudged symbols; H. Vikalo et al. combined sphere decoding (hereinafter referred to as SD) with VA and dynamically deleted the paths outside the radius according to the sphere radius at each moment, greatly reducing the complexity of VA; Qu Fengchong et al. used iterative SD in the MIMO system and achieved better demodulation performance than DFE. It should be noted that the computational complexity of the SD algorithm is related to the sphere radius. If the selected radius is too large, there will be many surviving paths and the computational complexity is still very high. If the selected radius is too small, there may be no surviving paths. Selecting an appropriate sphere radius is very important in the SD algorithm.

[0004] In summary, the complexity-reduced MLSE mainly falls into three categories: the first is to reduce the channel length L; the second is to reduce the modulation order M of the signal; the third is to dynamically reduce the paths with relatively low likelihood during the sequence estimation process and retain the paths with high likelihood. However, the above methods cannot balance the relationship between computational complexity and demodulation performance. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention proposes an iterative sequence estimation method for underwater acoustic communication based on channel shortening and sphere decoding.

[0006] The specific technical solution is as follows:

[0007] An iterative sequence estimation method for underwater acoustic communication based on channel shortening and sphere decoding specifically includes the following steps:

[0008] S1: After filtering the passband signal received by the hydrophone through a band-pass filter, it is processed through down-conversion and a matched filter. After carrier frequency offset estimation and compensation, baseband symbols are obtained through resampling.

[0009] S2: Taking the baseband symbols as input, channel estimation is performed to obtain the original baseband channel.

[0010] S3: The original baseband channel is shortened using a channel shortening algorithm based on a minimum mean square error equalizer to reduce the number of taps; the specific channel shortening algorithm is: taking the original channel impulse response as input, after completing channel estimation using a pilot sequence, the original baseband channel passes through a finite impulse response filter. The finite impulse response filter is designed with the minimum mean square error between the target impulse response and the impulse response after passing through the shortening equalizer as the optimization goal, and considering the influence of noise, after passing through the minimum mean square error equalizer, the shortened baseband channel is obtained.

[0011] S4: Sphere decoding is performed on the taps with concentrated energy in the underwater acoustic channel, specifically: calculating the initial radius according to the demodulation result of the decision feedback equalizer, then selecting consecutive taps with relatively large energy for sphere decoding, searching for signals within the sphere radius, deleting paths greater than the sphere radius using sphere decoding based on the Viterbi algorithm, and finding the transmitted sequence with the highest likelihood as the demodulation result; the sphere decoding is only performed on consecutive taps with relatively large energy. To eliminate the inter-symbol interference caused by taps with relatively weak energy, before the next decoding, the received vector needs to subtract the interference amount brought by the taps with relatively weak energy, and then sphere decoding is performed to achieve iterative interference cancellation. After several iterations, the final demodulation result is obtained.

[0012] Further, in S1, for a single-input single-output system model, the expression of the baseband signal y received by the hydrophone is:

[0013] y = Hx + n

[0014] Where x is the transmitted signal with length N, H is the Toeplitz matrix of the channel vector h with length L, with dimensions (N + L - 1) × N; n is the additive white Gaussian noise with length N + L - 1, and the received signal y has length N + L - 1; the expression of matrix H is as follows:

[0015]

[0016] Furthermore, the specific implementation of S3 is achieved through the following sub - steps:

[0017] (3.1) Construct an energy window model, create an optimization problem and simplify it;

[0018] Calculate the energy of the continuous samples of the equivalent channel within the window and the energy of the continuous samples of the equivalent channel outside the window Their expressions are as follows:

[0019]

[0020]

[0021] That is, matrix matrix

[0022] where h eff in h win The expression of the continuous samples of the channel taps within the window is:

[0023]

[0024] h eff except h win The expression of the continuous samples of the channel taps outside the window is:

[0025]

[0026] In the formula, h eff represents the equivalent channel output after the convolution of the original base - band channel and the minimum mean - square error equalizer, with length L + t - 1, where t is the length of the minimum mean - square error equalizer w; h win represents a segment of window selected from h eff The channel taps within the window are the continuous v + 1 samples starting from the starting position s;

[0027] h(s) represents the channel impulse response at position s, and so on; w(0) represents the transfer function of the minimum mean - square error equalizer at position s, and so on;

[0028] Create an optimization problem: The goal of optimization is to minimize the ratio of the energy of the equivalent channel after passing through the minimum mean square error equalizer for consecutive samples within a window, denoted as \(H\), to the energy of the equivalent channel for consecutive samples outside the window when fixed, obtaining the following expression for the optimization problem: win When fixed, the energy of the equivalent channel for consecutive samples outside the window, denoted as \(H\). wall The ratio is minimized, and the expression for the optimization problem is as follows:

[0029]

[0030] In the formula, \(R\) n is the correlation matrix of the noise;

[0031] At the same time, perform a Cholesky decomposition on the matrix \(A\), and the expression is as follows:

[0032]

[0033] In the formula, \(\Delta\) is a diagonal matrix, and the diagonal elements are the eigenvalues of the matrix \(A\); \(Q\) is an orthogonal matrix composed of the eigenvectors corresponding to the eigenvalues of the matrix \(A\).

[0034] Simplify the optimization problem: Define Then the expression for the above optimization problem is simplified as follows:

[0035]

[0036] (3.2) Construct a Lagrangian function to solve the simplified optimization problem obtained in step (3.1) to obtain the optimal solution \(w\) of the minimum mean square error equalizer. This \(w\) opt is the coefficient of the finite impulse response filter for shortening the original baseband channel, and its expression is as follows: opt In the formula, \(l\)

[0037]

[0038] is the eigenvector corresponding to the minimum eigenvalue of the matrix \(C\); min

[0039] (3.3) Traverse all positions of \(h\) eff as the starting position \(s\) until the \(w\) corresponding to the minimum value of is found and taken as the optimal solution, and it is used as the coefficient of the finite impulse response filter, and the corresponding optimal starting position \(s\) opt_end is obtained, and the expression is as follows: opt

[0040]

[0041] Furthermore, the specific implementation of the S4 is as follows through the following sub-steps:

[0042] ​​(4.1) If the noise follows a zero-mean complex Gaussian distribution, the demodulation result with the minimum mean square error is the transmitted sequence corresponding to the minimum mean square error. Its expression is as follows:

[0043]

[0044] In the formula, X is the set of all possible transmitted sequences, N is the length of the transmitted sequence, y(i) represents the channel output, and x(i - l) represents the channel input;

[0045] According to the shortened baseband channel, select consecutive taps with larger energy for sphere decoding maximum likelihood sequence estimation. The mean square error expression at this time is as follows:

[0046]

[0047] In the formula, L b represents the position of the first selected tap, L f represents the position of the last selected tap, and L b to L f are consecutive;

[0048] Calculate the sphere radius at time k, specifically as follows:

[0049]

[0050] In the formula, is the demodulation result of the decision feedback equalizer;

[0051] (4.2) Iterative interference cancellation. According to the demodulation output of the (q - 1)-th iteration, eliminate the inter-symbol interference caused by taps with weaker energy, and update the received signal vector y as For the first iteration, its input is the demodulation output of step (4.1) The calculation formula for updating the received signal vector in each iteration is as follows:

[0052]

[0053] In the formula, represents the demodulation output of the (q - 1)-th iteration,

[0054] (4.3) Based on the Viterbi algorithm, use the sphere decoding algorithm to delete paths greater than the sphere radius at time k. At the last moment, search for all remaining paths using the sphere decoding combined with orthogonal triangular decomposition method to find the path corresponding to the minimum metric value as the final demodulation output, and the expression is as follows:

[0055]

[0056] (4.4) Update with the demodulation output of the previous iteration Calculate the radius at the current moment of this iteration according to the method in step (4.1); update the MSE all , calculate the demodulation output of this iteration, and the expression is as follows:

[0057]

[0058]

[0059]

[0060] In the formula, represents the demodulation output of the q-th iteration;

[0061] (4.5) Judge whether the mean square error converges. If it converges, take the output under the current iteration as the final demodulation output; if it does not converge, increment the iteration count by one, and repeat steps (4.1) and (4.4) until the mean square error of the recovered received signal converges to obtain the final demodulation output.

[0062] Furthermore, in S2, the least squares algorithm is used for channel estimation.

[0063] The beneficial effects of the present invention are as follows:

[0064] (1) The channel shortening algorithm of the present invention uses a MMSE channel shortening equalizer, takes into account the influence of noise in the environment, and has stronger environmental adaptability.

[0065] (2) The sphere decoding of the present invention is different from the traditional method. The initial radius of the sphere decoding is determined by the demodulation result of the DFE, and the paths outside the sphere radius are dynamically deleted through sphere decoding during the Viterbi equalization process, greatly reducing the computational complexity while having a demodulation performance similar to that of the Viterbi equalization.

[0066] (3) The present invention uses a method combining channel shortening and iterative sphere decoding, which greatly reduces the computational complexity compared with the Viterbi equalization, improves the demodulation performance compared with the DFE, and has good application value in underwater acoustic communication. Brief Description of the Drawings

[0067] Figure 1 is a schematic flow chart of the underwater acoustic communication iterative sequence estimation method based on channel shortening and sphere decoding of the present invention.

[0068] Figure 2 is a schematic model diagram of the MMSE equalizer.

[0069] Figure 3 is a schematic flow chart of the channel shortening step of the present invention.

[0070] Figure 4 It is a schematic flow diagram of the sphere decoding step of the present invention.

[0071] Figure 5 It is a schematic diagram of the process of reducing complexity of sphere decoding combined with Viterbi equalization in four states.

[0072] Figure 6 It is a comparison chart of bit error rate performance of sphere decoding combined with channel shortening algorithm and other equalization algorithms.

[0073] Figure 7 It is a comparison chart of calculation time of sphere decoding combined with channel shortening algorithm and other equalization algorithms.

[0074] Figure 8 It is a comparison chart of bit error rate performance of iterative sphere decoding algorithm combined with channel shortening and other equalization algorithms under different iteration times. Detailed implementation manners

[0075] The present invention will be described in detail below according to the attached drawings and preferred embodiments. The purpose and effects of the present invention will become more clear. The present invention will be further described in detail below in combination with the attached drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0076] As Figure 1 shown, an underwater acoustic communication iterative sequence estimation method based on channel shortening and sphere decoding specifically includes the following steps:

[0077] S1: Baseband processing. The received passband signal from the hydrophone is first filtered by a band-pass filter to remove out-of-band noise, and then processed by down-conversion and a matched filter. After carrier frequency offset (hereinafter referred to as CFO) estimation and compensation, baseband symbols are obtained through resampling.

[0078] For a single-input single-output system (hereinafter referred to as SISO) model, the expression of the baseband signal y received by the hydrophone is:

[0079] y = Hx + n

[0080] In the formula, x is the transmitted signal with a length of N, H is the Toeplitz matrix of the channel vector h with a length of L, and the dimension is (N + L - 1) × N; n is the additive white Gaussian noise with a length of N + L - 1, and the length of the received signal y is N + L - 1. The expression of the channel matrix H is as follows:

[0081]

[0082] S2: Channel estimation: Using the baseband symbols as the input, perform channel estimation to obtain the original baseband channel. In this embodiment, the least squares algorithm is used for channel estimation.

[0083] S3: Channel shortening. Use the channel shortening algorithm based on the minimum mean square error (MMSE) equalizer to shorten the original baseband channel and reduce the number of taps.

[0084] Channel shortening is processed in the baseband. The channel shortening algorithm is specifically as follows: Using the original channel impulse response as the input, after completing channel estimation using the pilot sequence, let the original baseband channel pass through a finite impulse response (FIR) filter. Design the FIR filter with the optimization goal of minimizing the mean square error between the target impulse response and the impulse response after passing through the shortening equalizer, and considering the influence of noise. After passing through the MMSE equalizer, obtain the shortened baseband channel. Figure 2 is the model of the MMSE equalizer. The optimal equalizer should minimize the error between the target impulse response and the equivalent impulse response after passing through the shortening equalizer.

[0085] As Figure 3 shown, S3 is specifically implemented through the following sub-steps:

[0086] (3.1) Construct an energy window model, create an optimization problem and simplify it:

[0087] Calculate the energy of the continuous samples of the equivalent channel within the window and the energy of the continuous samples of the equivalent channel outside the window The expressions are as follows:

[0088]

[0089]

[0090] That is, the matrix matrix

[0091] where, h eff in h win The expression of the channel taps of the continuous samples within the window is:

[0092]

[0093] h eff in except for h win The expression of the channel taps of the continuous samples outside the window is:

[0094]

[0095] Where h eff represents the equivalent channel output after convolution of the original baseband channel and the MMSE equalizer, with a length of L + t - 1, where t is the length of the MMSE equalizer w; h win represents eff a segment of window selected from h

[0096] h(s) represents the channel impulse response at position s, and so on; w(0) represents the transfer function of the MMSE equalizer at position s, and so on.

[0097] Create an optimization problem: The optimization objective is to minimize the ratio of the energy H of the continuous samples of the equivalent channel after passing through the MMSE equalizer within a window to the energy H of the continuous samples of the equivalent channel outside the window when H is fixed, and the expression of the optimization problem is as follows: win when H is fixed, the energy H of the continuous samples of the equivalent channel outside the window wall The ratio is minimized, and the expression of the optimization problem is as follows:

[0098]

[0099] Where R n is the correlation matrix of the noise.

[0100] At the same time, perform Cholesky decomposition on matrix A, and the expression is as follows:

[0101]

[0102] Where Δ is a diagonal matrix, and the diagonal elements are the eigenvalues of matrix A; Q is an orthogonal matrix composed of the eigenvectors corresponding to the eigenvalues of matrix A.

[0103] Simplify the optimization problem: Define Then the expression of the above optimization problem is simplified as follows:

[0104]

[0105] (3.2) Solve the simplified optimization problem obtained in step (3.1) by constructing a Lagrangian function to obtain the optimal solution w opt of the MMSE equalizer. This w opt is the coefficient of the FIR filter for shortening the original baseband channel, and its expression is as follows:

[0106]

[0107] Where l min is the eigenvector corresponding to the minimum eigenvalue of matrix C.

[0108] (3.3) Traverse all positions of h eff as the starting position s until the w corresponding to the minimum value is found opt_end as the optimal solution, use it as the coefficients of the FIR filter, and obtain the corresponding optimal starting position s opt , and the expression is as follows:

[0109]

[0110] S4: Sphere decoding. After channel shortening, the inter-symbol interference is reduced. Since the energy of the underwater acoustic channel is mainly concentrated at several tap positions, in order to further reduce the computational complexity, several main taps where the energy of the underwater acoustic channel is concentrated are selected for sphere decoding. Specifically: Calculate the initial radius according to the DFE demodulation result, then select several consecutive taps with larger energy for sphere decoding, search for the signals within the sphere radius, and use sphere decoding to delete the paths greater than the sphere radius based on the Viterbi algorithm to find the transmitted sequence with the maximum likelihood as the demodulation result; subsequent iterative interference cancellation is performed. Because sphere decoding only decodes several consecutive taps with larger energy, in order to eliminate the inter-symbol interference caused by the taps with weaker energy, before the next decoding, the received vector needs to subtract the interference amount caused by the taps with weaker energy, and then perform sphere decoding. After several iterations, the final demodulation result is obtained. S4 is specifically implemented through the following sub-steps:

[0111] (4.1) If the noise follows a zero-mean complex Gaussian distribution, the demodulation result of MMSE is the transmitted sequence corresponding to the minimum mean-square error (hereinafter referred to as MSE) Its expression is as follows:

[0112]

[0113] In the formula, X is the set of all possible transmitted sequences, N is the length of the transmitted sequence, y(i) represents the channel output, and x(i - l) represents the channel input.

[0114] According to the shortened baseband channel, select several consecutive taps with larger energy for sphere decoding MLSE. At this time, the MSE expression is as follows:

[0115]

[0116] In the formula, L b represents the position of the first selected tap, L f represents the position of the last selected tap, and L b to L f are consecutive.

[0117] Calculate the radius of the sphere at time k as follows:

[0118]

[0119] Where, is the demodulation result of the DFE.

[0120] (4.2) Iterative interference cancellation. According to the demodulation output of the (q - 1)-th iteration (i.e., the previous iteration), cancel the inter-symbol interference caused by the taps with weaker energy, and update the received signal vector y as For the first iteration, its input is the demodulation output of step (4.1). The calculation formula for updating the received signal vector in each iteration is as follows:

[0121]

[0122] Where, represents the demodulation output of the (q - 1)-th iteration,

[0123] (4.3) Based on the Viterbi algorithm, use the sphere decoding algorithm to delete the paths whose lengths are greater than the radius of the sphere at time k.

[0124] Figure 5 What is shown is how sphere decoding reduces the complexity in sequence detection. Taking quadrature phase shift keying (hereinafter referred to as QPSK) modulation as an example, at time k, there are a total of states. At this time, if the output after convolution of all possible inputs with the channel is greater than the currently calculated radius of the sphere, these paths are removed. Therefore, the number of paths finally retained at time k is less than Then at time k + 1, the number of states at this time is less than . Then use sphere decoding to delete the paths outside the radius at time k + 1, and the number of paths retained at time k + 1 is less than that at time k. As time increases, the number of retained paths becomes fewer and fewer. At the last moment, for all the retained paths, use sphere decoding combined with QR decomposition (orthogonal triangular decomposition) to search, find the path corresponding to the minimum metric value as the final demodulation output, and the expression is as follows:

[0125]

[0126] Figure 6 and Figure 7 What is shown is the simulation comparison of the channel shortening combined with the sphere decoding algorithm and other equalization algorithms in terms of bit error rate performance and computational complexity.

[0127] It can be seen from Figure 6 that the channel follows a Rayleigh fading distribution, the original channel length is 7, and within the SNR range of 6 - 22 dB, the bit error rate performance of the sphere decoding combined with channel shortening algorithm is close to that of the Viterbi equalization combined with channel shortening algorithm, indicating that the performance of the sphere decoding combined with channel shortening algorithm is close to the optimal equalization scheme. When the bit error rate is 10 -4 , the SNR required by the sphere decoding combined with channel shortening algorithm is 1 dB lower than that of RLS - DFE and CE - DFE, and 3 dB lower than that of IPNLMS - DFE; when the bit error rate is 10 -5 , the SNR required by the sphere decoding combined with channel shortening algorithm is 2 dB lower than that of RLS - DFE and CE - DFE, indicating that the sphere decoding combined with channel shortening algorithm has significantly improved demodulation performance compared with DFE, which can improve the reliability of communication.

[0128] From Figure 7 it can be seen that as the SNR increases, the normalized average calculation time of the sphere decoding combined with channel shortening algorithm continuously decreases, while the calculation time of the Viterbi equalization combined with channel shortening algorithm is independent of the SNR. When the SNR is 30 dB, the calculation time of the sphere decoding combined with channel shortening algorithm is reduced by 9 times compared with the Viterbi equalization combined with channel shortening algorithm, and the calculation complexity is only about twice that of the RLS - DFE calculation complexity. Thus, it can be seen that the sphere decoding combined with channel shortening can greatly reduce the complexity compared with the Viterbi equalization combined with channel shortening algorithm, and at the same time, the bit error rate performance is relatively close to that of the Viterbi equalization. The simulation results under the random Rayleigh fading channel prove the effectiveness of the two - step complexity - reduced maximum likelihood detection proposed in this invention.

[0129] (4.4) Update with the demodulation output of the previous iteration Calculate the radius at the current moment of this iteration according to the method in step (4.1); update MSE all , calculate the demodulation output of this iteration, and the expression is as follows:

[0130]

[0131]

[0132]

[0133] In the formula, represents the demodulation output of the q - th iteration (i.e., this iteration).

[0134] (4.5) Determine whether the MSE converges. If it converges, take the output under the current iteration as the final demodulation output; if it does not converge, increment the iteration count by one and repeat steps (4.1) and (4.4) until the MSE of the recovered received signal converges to obtain the final demodulation output.

[0135] Figure 8 The simulation comparison of the bit error rate performance between iterative sphere decoding and other equalization algorithms is shown. After the first iteration is completed, the algorithm eliminates the inter-symbol interference caused by the remaining weak taps according to the currently hard-decided symbols. In this way, after multiple iterations, the bit error rate performance will be improved. Figure 8 It shows that after the third iteration and the fifth iteration, when the bit error rate is 10 -4 the signal-to-noise ratio required by sphere decoding is 2 dB lower than that of RLS-DFE and CE-DFE. At the same time, compared with the first iteration, the signal-to-noise ratio required by the fifth iteration at a bit error rate of 10 -4 is more than 4 dB lower than that of the first iteration, thus proving the effectiveness of iterative sphere decoding.

[0136] In order to improve the demodulation performance while reducing the computational complexity, the present invention proposes a two-step complexity reduction maximum likelihood sequence detection algorithm, making it possible to apply the maximum likelihood equalization scheme in underwater acoustic communication. First, the original baseband signal is shortened through a channel shortening algorithm based on the MMSE equalizer to reduce the number of taps. Since the energy of the underwater acoustic channel is mainly concentrated at several tap positions, in order to further reduce the computational complexity, several main taps are selected for sphere decoding. Based on the Viterbi algorithm, paths greater than the sphere radius are deleted by sphere decoding, and paths with larger likelihood are retained. The hard-decided symbols obtained are then used to eliminate the inter-symbol interference caused by taps with smaller energy through an iterative method.

[0137] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, for those skilled in the art, they can still modify the technical solutions described in the foregoing examples or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims

1. A method for iterative sequence estimation of underwater acoustic communication based on channel shortening and sphere decoding, characterized in that: The specific steps include: S1: The passband signal received by the hydrophone is filtered by a bandpass filter, processed by down-mixing and matched filtering, and after carrier frequency offset estimation and compensation, the baseband symbol is obtained by resampling; S2: Take the baseband symbols as input, perform channel estimation, and obtain the original baseband channel; S3: Using a channel shortening algorithm based on a minimum mean square error equalizer to shorten the original baseband channel and reduce the number of taps; the channel shortening algorithm specifically comprises: taking the original channel impulse response as input, completing channel estimation using a pilot sequence, passing the original baseband channel through a finite impulse response filter, and designing the finite impulse response filter with the minimum mean square error between the target impulse response and the impulse response after the shortened equalizer as the optimization goal, while taking into account the influence of noise. After passing through the minimum mean square error equalizer, a shortened baseband channel is obtained; S4: Select the taps with concentrated energy in the underwater acoustic channel for sphere decoding, specifically: calculate the initial radius based on the demodulation result of the decision feedback equalizer, then select continuous taps with larger energy for sphere decoding, search for signals within the sphere radius, and use sphere decoding based on the Viterbi algorithm to delete paths larger than the sphere radius, and find the transmission sequence with the largest likelihood as the demodulation result; the sphere decoding is only performed on continuous taps with larger energy. In order to eliminate the inter-symbol interference caused by taps with weaker energy, before the next decoding, the received vector needs to subtract the interference caused by the taps with weaker energy, and then sphere decoding is performed to achieve iterative interference elimination. After several iterations, the final demodulation result is obtained; In S1, for the single-input single-output system model, the baseband signal y received by the hydrophone is expressed as: y=Hx+n Where x is the transmitted signal of length N, H is the Toplitz matrix of the channel vector h of length L, with dimensions (N + L - 1) × N, n is additive white Gaussian noise of length N + L - 1, and the received signal y has length N + L - 1. The matrix H is expressed as follows: S3 is specifically implemented through the following sub-steps: (3.1) Construct an energy window model, create an optimization problem and simplify it; Calculate the energy of the equivalent channel continuously sampled within the window and the energy of the equivalent channel continuously sampled outside the window Its expression is as follows: That is, the matrix matrix Among them, h eff Medium h win The channel tap expression for continuous sampling within the window is: h eff In addition to h win The channel tap expression for continuous sampling outside the window is: Where h eff represents the equivalent channel output after the convolution of the original baseband channel and the minimum mean square error equalizer, whose length is L+t-1, where t is the length of the minimum mean square error equalizer w; h win Indicates h eff A window is selected from , and the window contains the channel taps of v+1 consecutive samples starting at s; h(s) represents the channel impulse response at position s, and so on; w(0) represents the transfer function of the minimum mean square error equalizer at position s, and so on; Create an optimization problem: The optimization goal is to make the energy H of the equivalent channel continuously sampled in a window after the minimum mean square error equalizer win Under fixed conditions, the energy H of the equivalent channel continuously sampled outside the window is wall The ratio is the smallest, and the expression of the optimization problem is as follows: Where R n is the correlation matrix of the noise; At the same time, perform Cholesky decomposition on matrix A, and the expression is as follows: Where Δ is a diagonal matrix whose diagonal elements are the eigenvalues of matrix A; Q is an orthogonal matrix consisting of the eigenvectors corresponding to the eigenvalues of matrix A; Simplifying the Optimization Problem: Definition The above optimization problem expression is simplified as follows: (3.2) Construct a Lagrangian function to solve the simplified optimization problem obtained in step (3.1) and obtain the optimal solution w of the minimum mean square error equalizer opt , the w opt That is, the finite impulse response filter coefficient used to shorten the original baseband channel, and its expression is as follows: Where, l min is the eigenvector corresponding to the smallest eigenvalue of matrix C; (3.3) Traverse h eff All positions of as the starting position s, until you find The w corresponding to the minimum value opt_end As the optimal solution, it is used as the coefficient of the finite impulse response filter and the corresponding optimal starting position s is obtained. opt , the expression is as follows: The S4 is specifically implemented through the following sub-steps: (4.1) If the noise obeys a zero-mean complex Gaussian distribution, the demodulation result of the minimum mean square error is the corresponding transmission sequence when the mean square error is minimum Its expression is as follows: Where X is the set of all possible transmission sequences, N is the length of the transmission sequence, y(i) represents the channel output, and x(il) represents the channel input; According to the shortened baseband channel, continuous taps with larger energy are selected to perform sphere decoding maximum likelihood sequence estimation. The mean square error expression at this time is as follows: Where, L b Indicates the first selected tap position, L f Indicates the last selected tap position, and L b To L f It is continuous; Calculate the radius of the sphere at time k as follows: Where, is the demodulation result of the decision feedback equalizer; (4.2) Iterative interference elimination: According to the demodulation output of the q-1th iteration, the inter-symbol interference caused by the tap with weaker energy is eliminated, and the received signal vector y is updated as For the first iteration, its input is the demodulated output of step (4.1) The calculation formula for updating the received signal vector at each iteration is as follows: Where, represents the demodulated output of the q-1th iteration, (4.3) Based on the Viterbi algorithm, the sphere decoding algorithm is used to delete the paths with a sphere radius greater than the kth time. At the last time, all the remaining paths are searched again using the sphere decoding combined with the orthogonal triangular decomposition method to find the path with the minimum metric value as the final demodulation output. The expression is as follows: (4.4) Update the demodulated output of the previous iteration Calculate the radius of the current iteration according to the method in step (4.1); update MSE all , calculate the demodulation output of this iteration, the expression is as follows: Where, represents the demodulated output of the qth iteration; (4.5) Determine whether the mean square error converges. If so, take the output of the current iteration as the final demodulation output. If not, increase the number of iterations by one and repeat steps (4.1) and (4.4) until the mean square error of the recovered received signal converges and the final demodulation output is obtained.

2. The underwater acoustic communication iterative sequence estimation method based on channel shortening and sphere decoding according to claim 1 is characterized in that: In S2, the least squares algorithm is used to perform channel estimation.

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