Joint symbol and sparse channel bayesian estimation method based on superimposed training sequences

Abstract

The application discloses a kind of based on superimposed training sequence joint symbol and sparse channel bayesian estimation method, device, electronic equipment and storable medium.This application constructs hierarchical bayesian model using the characteristics of superimposed training sequence not occupying extra time slot, adopts variational bayesian inference to jointly process channel state and data interference, realizes the outer information circulation exchange between equalizer and decoder through Turbo equalization architecture, and optimizes detection performance.Compared with traditional time division multiplex pilot estimation, this application not only improves spectral efficiency and information throughput through superimposed training, but also effectively separates signal interference by virtue of variational inference, while ensuring high bandwidth efficiency, optimizes channel estimation accuracy, bit error rate performance and transmission reliability.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic communication technology, specifically relating to a joint symbol and sparse channel Bayesian estimation method, apparatus, electronic device and storage medium based on superimposed training sequences. Background Technology

[0002] The underwater acoustic environment is extremely complex, characterized by severe multipath effects, rapid time-varying features, and bandwidth constraints, posing significant challenges to reliable communication. Traditional underwater acoustic communication systems typically employ time-division multiplexing to insert training sequences for channel estimation. However, this consumes substantial time slot resources, reducing the effective information transmission rate of the underwater acoustic communication system, which is particularly detrimental in bandwidth-constrained underwater channels. Therefore, improving bandwidth efficiency while ensuring the accuracy of channel estimation is a critical issue that urgently needs to be addressed in the field of underwater acoustic communication.

[0003] To improve spectral efficiency, existing technologies employ superimposed training sequence techniques, which save time-domain resources by superimposing known sequences with transmitted symbols before transmission. However, this approach introduces mutual interference between data and sequences, significantly increasing the difficulty for the receiver in channel estimation and signal separation. Although current Turbo equalization structures can iteratively obtain coding gain, under the superimposed training system, traditional linear estimators struggle to achieve effective estimation in the presence of data interference, thus limiting the bit error rate performance of underwater acoustic communication systems. Therefore, how to effectively suppress superimposed interference and achieve accurate estimation and signal detection in complex underwater acoustic channels while ensuring high bandwidth efficiency is a critical technical problem that urgently needs to be solved in the field of underwater acoustic communication.

[0004] Furthermore, underwater acoustic channels typically exhibit sparse structural characteristics, and existing techniques for receiving superimposed training sequences often fail to fully exploit and utilize this prior information, resulting in insufficient robustness of channel estimation in environments with severe sparse multipath interference. Simultaneously, the lack of a deep joint modeling mechanism for channel state and unknown data interference makes it difficult for the receiver to achieve a good balance between suppressing interference and improving estimation accuracy. This further limits the effective throughput and transmission reliability of underwater acoustic communication systems in complex underwater acoustic environments. Summary of the Invention

[0005] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences to improve the transmission efficiency and performance of underwater acoustic communication.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences, the estimation method comprising the following steps:

[0008] S1. Receive the transmitted signal with the superimposed training sequence in the underwater acoustic channel, and obtain the received data vector after sampling. ;

[0009] S2, Based on received data vector Constructing a channel impulse response Unknown transmission symbol Superimposed on the transmitted symbol Training sequences on Channel power vector and channel noise power The joint probability model, in which, For the first Send sub-symbols, , Indicates the total number of sent sub-symbols;

[0010] S3. Initialize each parameter to be estimated and the variational Bayes algorithm iteration control variables. The parameters to be estimated and the variational Bayes algorithm iteration control variables include: the first... Send sub-symbols Corresponding posterior soft symbol The decoder feeds back the prior information of the input equalizer, log-likelihood ratio , Indicates the first Send sub-symbols The Middle bits, , Represents the total number of bits in a transmit sub-symbol mapping, and the number of Turbo equalization iterations. The maximum number of Turbo equilibrium iterations is ;

[0011] S4. Initialize the number of iterations in the inner loop of the variational Bayes algorithm. Set the maximum number of iterations for variational Bayes to 0. ;

[0012] S5. Iteratively estimate the channel impulse response using the variational Bayesian algorithm. Expected vector and the Send sub-symbols Corresponding equalizer symbol Based on the parameters obtained from variational estimation in the current iteration round, the channel power vector is then updated. Channel noise power ,and Determine if the inner loop of the variational Bayesian algorithm terminates; if so, the iteration count... Then the iteration ends and step S6 is executed; otherwise, step S5 is repeated to complete the next iteration of the variational Bayesian algorithm inner loop.

[0013] S6. Iterate through the various equilibrium subsymbols output by the variational Bayes algorithm. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output ,right Deinterleaving is performed to obtain the prior information log-likelihood ratio of the input decoder. ,Will The input is decoded by a decoder, and the updated prior information log-likelihood ratio of the input equalizer is obtained from the decoder. ;

[0014] S7. Log-likelihood ratio of prior information input to the equalizer over the entire symbol period. Perform a hard decision and verify whether the bit sequence after the hard decision has been successfully decoded: if the verification is successful, the transmission signal is successfully recovered and the decoding result is output; if the verification fails, continue to execute the operation.

[0015] Furthermore, in step S1, the receiving end of the underwater acoustic communication system first acquires a received data vector. Data length Corresponding to the size of a single symbol block, Reference 1-dimensional complex field column vector Then the receiving end is at the 1st Complex sampled signals captured at discrete moments, This represents the transpose operation. At the signal transmitting end, a known training sequence was designed and introduced for this scheme. ,in This represents the training sequence at time [time]. The specific symbols transmitted. Meanwhile, the effective information that the underwater acoustic communication system actually needs to transmit and that needs to be estimated is defined as the transmitted symbols. The symbol uses Modulation method. The known training sequence... With unknown transmitted symbols to be estimated The working principle of superposition transmission aims to utilize a known sequence as an observation benchmark to provide a reliable reference for subsequent joint channel estimation and signal detection, thereby improving communication rate and demodulation success rate under adverse channel conditions. Underwater acoustic communication systems define the channel impulse response as... Using the total length and the Complex gain coefficients of each channel tap This is used to characterize the delay distribution and fading features of multipath channels. Accompanying the ambient noise floor, a channel noise vector is defined. ,in Reflects the first Instantaneous noise interference at any given moment. Based on the construction of the above physical quantities, the data vector obtained by the receiving end... Able to use the expression: ,

[0016] Provide a complete description. It is worth noting that in this equation... Based on channel impulse response Constructed 3D circular convolution matrix.

[0017] Furthermore, in step S2, a probability model based on Bayes' theorem is used for signal processing. The specific design idea is to transform signal distortion and noise interference during transmission into a probability and statistics problem. The entire joint probability model is divided into three main parts: the received data vector... Likelihood probability, channel noise vector The statistical distribution of the channel impulse response. The prior distribution. First, receive the data vector. The likelihood probability density function (i.e., marginal likelihood probability). Specifically, it is expressed as follows:

[0018] ,

[0019] Meanwhile, we set the channel noise to follow a Gaussian distribution, therefore the noise vector Statistical distribution Represented as:

[0020] ,

[0021] Indicates channel noise power Given the noise vector The conditional probability. In the formula... Indicates that the variable x follows the mean. variance is The complex Gaussian distribution, and It is the size of The identity matrix. The working principle of this part mainly uses statistical laws to describe the deviation between the received signal and the ideal signal. Furthermore, practical underwater acoustic channels typically exhibit sparse characteristics. Based on this physical characteristic, this scheme provides the channel impulse response. A prior sparse distribution was designed: ,

[0022] in, Represented in the channel power vector Given the channel impulse response The conditional probability, Indicates the first The channel power of each tap. This design, which introduces a sparse prior distribution, achieves good technical results: the underwater acoustic communication system assigns an independent complex Gaussian distribution to each channel tap and uses hyperparameters... The variance is dynamically controlled, thereby reducing noise interference.

[0023] Furthermore, in step S3, to ensure the stable convergence of the variational Bayes algorithm, the underwater acoustic communication system needs to reasonably initialize the various parameters to be estimated and the iterative control variables. In the early stages of the computation, lacking prior information, the underwater acoustic communication system will... Send sub-symbols Corresponding posterior soft symbol Initialize all values ​​to 0, and simultaneously input the prior information log-likelihood ratio to the equalizer. It is also initialized to 0. This neutral initial setting avoids the algorithm from making incorrect estimations in the initial stage. For practical channel environments, underwater acoustic communication systems utilize the silent intervals in the received signal to pre-estimate the initial value of the channel noise power. Based on this, the channel noise power Initialize to Meanwhile, in order to effectively control computing resources and time, the maximum number of Turbo balancing iterations is explicitly initialized to an upper limit. To address the energy distribution of multipath channels, underwater acoustic communication systems use channel power vectors. all elements All are initialized to a preset channel power reference value. Furthermore, the derivation involved in this step... For size is The identity matrix.

[0024] Furthermore, in step S4, the number of iterations in the inner loop of the variational Bayes algorithm is initialized. Set the maximum number of iterations for variational Bayes to 0. ;

[0025] Furthermore, in step S5, to recover the damaged signal amidst complex interference, this scheme establishes a joint inference mechanism based on the variational Bayes theorem. The design idea is to jointly process channel estimation and signal equalization, alternately updating channel parameters and symbol information in the inner loop, allowing them to mutually correct each other and gradually approach the true value. In the variational Bayes algorithm... In this iteration, the underwater acoustic communication system first updates the channel impulse response vector. The statistical characteristics. Specifically, the expected vector. Posterior covariance matrix and channel power vector The Power of each tap Calculate using the following formulas in sequence:

[0026] ,

[0027] ,

[0028] ,

[0029] Here It is composed of training sequences The dictionary matrix formed, This utilizes the posterior soft sign from the previous round of estimation. The constructed Toplitz signal matrix has the following specific structure:

[0030] ,

[0031] at the same time, This represents the covariance matrix of the received channel. This represents the autocorrelation matrix of the transmitted signal. and These represent the conjugate transpose and inverse operations, respectively. It is by The diagonal matrix formed and These represent the diagonal elements of the matrix and the corresponding elements of the vector, respectively. This is achieved by introducing a matrix containing prior information. The underwater acoustic communication system can effectively control error fluctuations during the channel estimation process. Subsequently, the underwater acoustic communication system adjusts the channel noise power... Perform adaptive updates to dynamically match the current channel state:

[0032] ,

[0033] ,

[0034] ,

[0035] In the formula, This indicates the construction of a diagonal matrix. This represents finding the trace of a matrix. It measures the average variance of the current soft sign estimate, reflecting the uncertainty of the sign estimate; This is a diagonal matrix constructed based on this variance. The principle behind using this uncertainty to dynamically correct noise power and improve the algorithm's robustness in varying environments is as follows.

[0036] After the channel parameters are updated, the underwater acoustic communication system updates the parameters sequentially. Send sub-symbols Equalizer symbol and posterior variance :

[0037] ,

[0038] ,

[0039] The channel autocorrelation matrix involved in the above process is: ,

[0040] And the channel estimation error equivalent noise matrix is ,

[0041] Choose a vector for the position. Based on the expected vector The cyclic channel matrix is ​​constructed. Here, the interference vector with the current symbol position hollowed out is constructed, i.e. and It is used to achieve interference cancellation.

[0042] Achieve balanced output Subsequently, the underwater acoustic communication system further updated the time domain... posterior soft symbol at each position So that it can be used in the next iteration:

[0043] ,

[0044] in, The corresponding symbol in the preset modulation constellation diagram. The probability density of the transmitted symbol mapped to this constellation point is calculated as follows: ,

[0045] here The normalization constant is The bit value represents the constellation symbol after bipolar mapping (+1 when it is 0, and -1 when it is 1). The posterior log-likelihood ratio is calculated by fusing prior information from the input equalizer. External information output by the equalizer The calculation shows that: ,

[0046] in This represents the operation of taking the real part. This full interaction of soft information can improve the error correction capability of underwater acoustic communication systems. After completing all the above updates, the iteration counter is incremented by 1 (i.e., The underwater acoustic communication system will determine whether the inner loop has reached the maximum number of iterations. If the condition is met, the iteration ends and step S6 is executed; if not, the process returns to the beginning of step S5 to continue the next round of updates. The technical effect of this alternating optimization mechanism is to reduce error propagation problems in complex channels and improve the overall demodulation and detection accuracy of the receiver without increasing additional pilot overhead.

[0047] Furthermore, in step S6, the design concept of the underwater acoustic communication system is to convert the complex symbols output by the equalizer into "soft bit" probability information that the decoder can directly process. Specifically, the underwater acoustic communication system iteratively outputs each equalized sub-symbol using the variational Bayes algorithm. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output The calculation formula is as follows: ,

[0048] The formula works by utilizing the real part of the balancer symbol. and posterior variance The reliability of this bit information is quantitatively assessed. A smaller variance indicates a higher confidence level in the soft information. After acquiring external information, in order to mitigate the sudden, continuous errors common in underwater acoustic channels, the underwater acoustic communication system will... Perform deinterleaving operation uniformly. The log-likelihood ratio obtained after deinterleaving. This information is input as prior information into the channel decoder. The decoder then performs decoding using error-correcting code rules and feeds back the updated soft information, namely the log-likelihood ratio of the prior information input to the equalizer. Through the above demapping and deinterleaving process, the underwater acoustic communication system connects the equalizer and decoder into a closed-loop feedback structure.

[0049] Furthermore, in step S7, the underwater acoustic communication system needs to convert the soft information output by the decoder into the final binary bits and control the termination of the entire iterative process. First, the posterior information output by the decoder... Hard decision is performed. Its working principle is to directly determine the bit value based on the sign of the log-likelihood ratio. ,

[0050] Obtain the binary sequence of hard decision Subsequently, the underwater acoustic communication system verifies its correctness. If the verification fails, it further determines the current number of Turbo equalization iterations. Has the maximum limit been reached? If the upper limit has been reached, it means that the error can no longer be corrected under the current conditions, and the loop is forcibly terminated; if it has not been reached, then... Then, proceed to step S4 for the next round of Turbo balancing iteration.

[0051] Secondly, the present invention provides a joint symbol and sparse channel Bayesian estimation device based on superimposed training sequences, used to perform the above-mentioned joint symbol and sparse channel Bayesian estimation method, the estimation device comprising:

[0052] The signal receiving module is used to receive the transmitted signal with the superimposed training sequence in the underwater acoustic channel, and obtain the received data vector through sampling. ;

[0053] The model building module is based on the received data vector. Constructing a channel impulse response Unknown transmission symbol Superimposed on the transmitted symbol Training sequences on Channel power vector and channel noise power The joint probability model, in which, For the first Send sub-symbols, , Indicates the total number of sent sub-symbols;

[0054] The first initialization module is used to initialize each parameter to be estimated and the variational Bayesian algorithm iteration control variables, wherein the parameters to be estimated and the variational Bayesian algorithm iteration control variables include: Send sub-symbols Corresponding posterior soft symbol The decoder feeds back the prior information of the input equalizer, log-likelihood ratio , Indicates the first Send sub-symbols The Middle bits, , Represents the total number of bits in a transmit sub-symbol mapping, and the number of Turbo equalization iterations. The maximum number of Turbo equilibrium iterations is ;

[0055] The second initialization module is used to initialize the number of iterations in the inner loop of the variational Bayes algorithm. Set the maximum number of iterations for variational Bayes to 0. ;

[0056] The estimation and update module uses the variational Bayesian algorithm to iteratively estimate the channel impulse response. Expected vector and the Send sub-symbols Corresponding equalizer symbol Based on the parameters obtained from variational estimation in the current iteration round, the channel power vector is then updated. Channel noise power ,and Determine if the inner loop of the variational Bayesian algorithm terminates; if so, the iteration count... If the iteration ends, the decoding module is executed; otherwise, the estimation and update module is returned to repeat the inner loop of the variational Bayes algorithm.

[0057] The decoding module is used to process the various equalization sub-symbols output iteratively by the variational Bayesian algorithm. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output ,right Deinterleaving is performed to obtain the prior information log-likelihood ratio of the input decoder. ,Will The input is decoded by a decoder, and the updated prior information log-likelihood ratio of the input equalizer is obtained from the decoder. ;

[0058] The decision verification module is used to calculate the log-likelihood ratio of the prior information input to the equalizer throughout the entire symbol period. Perform a hard decision and verify whether the bit sequence after the hard decision has been successfully decoded: if the verification is successful, determine that the transmission signal has been successfully recovered, terminate the loop and output the decoding result; if the verification fails, determine the number of iterations. :like If the condition is met, the loop will be forcibly terminated and the current decoding result will be output; otherwise, the loop will be terminated and the current decoding result will be output. The log-likelihood ratio of prior information to the input equalizer Intertwined and mapped to the first Send sub-symbols posterior soft symbol Then, proceed to the second initialization module to continue execution.

[0059] Thirdly, the present invention provides an electronic device, including a processor and a memory for storing a processor-executable program, wherein when the processor executes the program stored in the memory, it implements the above-mentioned joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences.

[0060] Fourthly, the present invention provides a storage medium storing a program that, when executed by a processor, implements the above-described joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences.

[0061] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0062] (1) This invention adopts a signal structure based on superimposed training sequences and gradually updates symbol priors through information interaction between the equalizer and the decoder. During the processing, no additional independent pilots need to be inserted into the data frame, thereby saving time and frequency resource overhead, improving data transmission throughput and effective bandwidth utilization, and realizing the improvement of communication efficiency.

[0063] (2) This invention establishes a joint probability model, placing channel impulse response, channel power, channel noise, and transmitted symbols under the same framework for joint estimation. Under this alternating optimization mechanism, channel estimation can utilize extrinsic information from decoding feedback to capture sparse multipath taps, while decoding and equalization can reduce the decision error rate based on more accurate channel parameters. This joint processing method avoids the error superposition problem caused by traditional step-by-step estimation, effectively improving the accuracy of underwater acoustic channel estimation and the final data recovery performance. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 This is a flowchart of the steps of a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this invention.

[0066] Figure 2 This is a schematic diagram of the transmission frame structure of a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this invention.

[0067] Figure 3 This is a schematic diagram of the received frame structure of a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this invention.

[0068] Figure 4 This is a simulation diagram of the iterative performance of the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this invention when the signal-to-noise ratio is 10dB.

[0069] Figure 5 This is a simulation comparison of the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this invention under different signal-to-noise ratios.

[0070] Figure 6 This is a simulation comparison of different signal power ratios under the measured channel of Wanlv Lake using a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this invention.

[0071] Figure 7 This is a structural block diagram of a joint symbol and sparse channel Bayesian estimation device based on superimposed training sequences in Embodiment 4 of the present invention.

[0072] Figure 8 This is a structural block diagram of the electronic device in Embodiment 5 of the present invention. Detailed Implementation

[0073] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0074] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0075] Example 1

[0076] This embodiment discloses a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences. To facilitate understanding of the subsequent estimation method, a brief description of the signal model of the communication system to which this estimation method is applied is provided first. The signal model of the communication system used in this embodiment is as follows: Information bits After encoding, interleaving, modulation, and generation, unknown transmission symbols are generated. Unknown transmission symbol and training sequence The transmitted sequence is obtained by superposition, such as Figure 2 The diagram shown is a schematic representation of the signal transmission frame structure in this embodiment. For unknown transmission symbols... This embodiment employs QPSK modulation. The superimposed transmission sequence is sent to the baseband channel, the signal passes through a multipath channel, and the received baseband symbol is obtained at the receiving end. .

[0077] This embodiment discloses a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences, which is applied to the aforementioned signal model. The receiver obtains the received baseband symbols. Its structure is as follows Figure 3 As shown, it includes Send symbol and training sequences After passing through the channel, the values ​​of each parameter in this embodiment are as follows:

[0078] , and The power ratio is 5:1. Maximum channel length. The actual number of taps is 20. The channel impulse response is generated according to the Rayleigh distribution. The channel coding rate is 1 / 4. Training sequence Randomly generated QPSK symbols are used for channel estimation.

[0079] This embodiment discloses a joint symbolic and sparse channel Bayesian estimation method based on superimposed training sequences. During the processing, it analyzes the data... Joint channel estimation and demodulation are performed to eliminate interference from superimposed training sequences and obtain the transmitted information.

[0080] like Figure 1 As shown, the flowchart of the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in this embodiment is presented, specifically including the following steps:

[0081] S1. In an underwater acoustic communication system, the transmitting end superimposes the training sequence with the transmitted symbols before sending. The receiving end first performs front-end processing such as down-conversion and sampling on the underwater acoustic signal transmitted through the multipath channel to obtain the original received data vector containing the superimposed training sequence. ;

[0082] S2, Based on the received data vector obtained in step S1 Constructing a channel impulse response Unknown transmission symbol Superimposed on the transmitted symbol Training sequences on Channel power vector and channel noise power The joint probability model, in which, For the first Send sub-symbols, In this embodiment Indicates the total number of sent sub-symbols;

[0083] S3. Initialize the parameters to be estimated and the iteration control variables required for the variational Bayes algorithm. These parameters to be estimated and the iteration control variables for the variational Bayes algorithm include: [The remaining text appears to be incomplete and requires further context.] Send sub-symbols Corresponding posterior soft symbol The decoder feeds back the prior information of the input equalizer, log-likelihood ratio , Indicates the first Send sub-symbols The Middle bits, , Represents the total number of bits in a transmit sub-symbol mapping, and the number of Turbo equalization iterations. The maximum number of Turbo equilibrium iterations is ;

[0084] S4. Set the loop variable inside the variational Bayes algorithm and initialize the number of inner loop iterations. Set the maximum number of iterations for variational Bayes to 0. ;

[0085] S5. Use the variational Bayesian algorithm for iterative iteration, estimating the channel impulse response in each iteration. Expected vector and the Send sub-symbols Corresponding equalizer symbol Subsequently, the channel power vector is updated based on the estimated values ​​obtained from the current iteration. Channel noise power In the variational Bayes algorithm, the first... In each iteration, the channel impulse response vector Expected vector Posterior covariance matrix and channel power vector The Channel power of each tap Iteratively update using the following formula:

[0086] ,

[0087] ,

[0088] ,

[0089] in, Indicates the training sequence The dictionary matrix formed, Indicates by posterior soft symbols The constructed Toeplitz signal matrix is: ,

[0090] in addition, This represents the covariance matrix of the received underwater acoustic channel. This represents the autocorrelation matrix of the transmitted signal. Represents a diagonal matrix. The elements on the diagonal are composition, Represents the covariance matrix of the received underwater acoustic channel The diagonal of One element, The expectation vector representing the channel estimation The One element;

[0091] Update channel noise power :

[0092] ,

[0093] ,

[0094] ,

[0095] in This represents the mean variance of the posterior soft sign. The mean variance of the posterior soft sign represents the variance of the posterior soft sign. The diagonal matrix formed;

[0096] In each variational Bayes iteration, in sequence Update one by one Send sub-symbols Equalizer symbol and posterior variance The updated formula is:

[0097] ,

[0098] ,

[0099] in,

[0100] ,

[0101] ,

[0102] To select a vector, Indicates size is The row vector, Represents the channel autocorrelation matrix. This represents the equivalent noise matrix of the channel estimation error. Represents the expectation vector estimated by the channel. The constructed cyclic channel estimation matrix, at the same time, , , No. One equalizer symbol After calculation and output, the time domain is updated using the following formula. posterior soft symbol at each position ,

[0103] ,

[0104] in, Indicates preset The first in the modulated constellation diagram A modulated constellation symbol, Indicates sending sub-symbols Mapped to constellation symbols The probability density function is calculated using the following formula:

[0105] ,

[0106] in, A constant that makes the sum of normalized probabilities equal to 1. constellation symbols The corresponding number The value of a binary bit after bipolar mapping; if the bit is 0, then... If the value of this bit is 1, then ; Indicates the first The posterior variance of each transmitted sub-symbol. Indicates the first Send sub-symbols The The posterior log-likelihood ratio for each bit is calculated using the following formula: ,

[0107] in, This represents the log-likelihood ratio of the prior information input to the equalizer. The log-likelihood ratio of the extrinsic information output by the equalizer is expressed by the following formula: ,in, This indicates the operation of taking the real part of a complex number;

[0108] After completing the above updates, Determine if the inner loop of the variational Bayesian algorithm terminates; if so, the iteration count... If so, exit the inner loop and proceed to step S6; otherwise, return to step S5 to execute the next inner loop iteration.

[0109] S6. Iterate over each equalization subsymbol of the variational Bayes algorithm output. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output ,right Deinterleaving is performed to obtain the prior information log-likelihood ratio of the input decoder. ,Will The input is decoded by the decoder, and then further processed by the decoder to obtain the updated prior information log-likelihood ratio fed back to the equalizer from the decoder. ;

[0110] S7. Log-likelihood ratio of prior information input to the equalizer over the entire symbol period. Perform a hard decision and verify whether the bit sequence after the hard decision has been successfully decoded; if the verification is successful, determine that the transmission signal has been successfully recovered, terminate the loop and output the decoding result; if the verification fails, then... ;like If the condition is met, the loop will be forcibly terminated and the current decoding result will be output; otherwise, the log-likelihood ratio of the prior information of the input equalizer will be calculated. Intertwined and mapped to the first Send sub-symbols posterior soft symbol Proceed to step S4.

[0111] The above embodiment discloses a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences. This embodiment uses a one-transmitter-one-receiver simulated communication structure. First, at the transmitting end, the QPSK modulated baseband symbols and training sequences are superimposed at a power ratio of 5:1. The signal passes through a multipath sparse channel with a maximum length of 120, an actual number of taps of 20, and follows a Rayleigh distribution. This channel can simulate the multipath fading environment in communication. After obtaining the received data vector at the receiving end, a probabilistic model of its channel impulse response and noise is constructed. Subsequently, at the receiving end, an initial channel noise power estimate is performed through a blank segment. Using an iterative formula based on the variational Bayesian principle, the expected vector, power vector parameters, noise variance, and equalization sub-symbols of the sparse channel are alternately and sequentially updated. After iteration, the extrinsic information is demapped and output. Then, the extrinsic information is sent to the decoder for 1 / 4 code rate decoding and feedback of the posterior and extrinsic information. The loop ends by decision verification or reaching the maximum Turbo iteration count; otherwise, the extrinsic information fed back by the decoder is interleaved and returned to the variational Bayesian equalizer for the next round of iteration. The estimation accuracy is higher than that of traditional algorithms. Through this joint estimation and demodulation process, the co-frequency interference caused by superimposed training sequences can be effectively eliminated. In the bit error rate results of experimental data, the bit error rate performance and convergence speed of this invention are improved compared with traditional algorithms without joint iteration. Figure 4 The graph shows a comparison of the bit error rate performance of the variational Bayesian channel estimation and equalization method proposed in this embodiment with that of the traditional sparse Bayesian-based channel estimation algorithm at different iteration numbers. Figure 4As can be seen, with the increase of the number of iterations, the bit error rate of both algorithms shows a decreasing trend and tends to converge. The traditional sparse Bayes-based channel estimation algorithm eventually stabilizes at a bit error rate of around 0.105; while the variational Bayesian channel estimation and equalization method used in this embodiment converges to a lower bit error rate after about 5 iterations, verifying that the present invention has better convergence performance and a lower bit error rate after joint iterative processing, and the system performance is improved.

[0112] Example 2

[0113] This embodiment further discloses a joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences, which uses a single-transmitter, single-receiver communication structure. This method is based on the steps of the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in Embodiment 1.

[0114] In this embodiment, the modulation method is the same as in Embodiment 1, both employing QPSK modulation. The modulated symbols are collected by the receiver after passing through a real superimposed training sequence physical channel. Symbol demodulation and sparse channel impulse response estimation operations based on variational Bayesian joint iteration are then performed on the received data vector. The transmit frame structure and receive frame structure in this embodiment are the same as in Embodiment 1: the transmit frame consists of unknown transmit symbols. and training sequence The data is obtained by superposition; the receiving end then processes the received data vector. Perform joint processing.

[0115] A single test transmitted 10 frames of data, each of which underwent targeted processing after synchronization was completed. In the algorithm estimation process, the maximum channel length was set to... The actual number of taps is 20 to simulate the typical sparse multipath fading characteristics in underwater acoustic communication. The system integrates a sparse Bayesian learning algorithm and the joint estimation algorithm of this invention for parallel comparison. The maximum number of iterations for the overall Turbo equalization and external information interaction is set to... The maximum number of Turbo equalization iterations is set to 8, balancing convergence performance and computational complexity, and adapting to the low-power, near-real-time application requirements of underwater acoustic communication. In the actual iterative solution, this method uses variational Bayesian principles to alternately update the channel expectation and posterior soft symbol extrinsic information, and performs decision verification through a 1 / 4 code rate decoding feedback mechanism, ensuring that the receiver can use the soft decision information to perform more accurate recursive optimization of the channel. In the specific joint estimation and demodulation processing flow, the receiver algorithm uses variational Bayesian principles to alternately execute channel expectation vector updates and posterior soft symbol information updates in each iteration. This processing method can effectively eliminate interference caused by the superposition of training sequences, thereby improving the system's signal recognition capability in channel fading environments through decoder feedback information. Experimental results show that this invention exhibits better bit error rate convergence performance than traditional algorithms within a limited number of iterations, can reproduce the multipath fading pattern in underwater acoustic environments, and has higher engineering practical value. Figure 5 The figure shows the bit error rate performance curves of the proposed variational Bayesian channel estimation and equalization method and the traditional sparse Bayesian-based channel estimation algorithm under different signal-to-noise ratios when the number of iterations is 5. Figure 5 As can be clearly seen, the bit error rate of both algorithms decreases as the signal-to-noise ratio (SNR) gradually increases. At lower SNRs (8-11 dB), their performance is similar; however, as the SNR further increases (when it exceeds 11 dB), the advantages of the variational Bayesian channel estimation and equalization method used in this embodiment become increasingly apparent. Especially at an SNR of 13 dB, the bit error rate of the method in this invention drops to 10%. -4 The bit error rate is lower than that of traditional sparse Bayes-based channel estimation algorithms, verifying that the present invention can exhibit better bit error rate performance under different signal-to-noise ratio environments and has higher engineering practical value.

[0116] Example 3

[0117] This embodiment further discloses a joint symbolic and sparse channel Bayesian estimation method based on superimposed training sequences. This method uses a shipborne underwater acoustic communication structure and was tested in the Wanlv Lake area, with a line-of-sight communication distance of 4700 meters between the transmitting and receiving ends. This method is based on the steps of the joint symbolic and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in Embodiment 1.

[0118] In this embodiment, the modulation method is the same as in Embodiment 1, both employing QPSK modulation. The modulated symbols are collected by the receiver after passing through a superimposed training sequence underwater acoustic experimental channel obtained from measured data of Wanlv Lake. The transmitter transducer is positioned 8 meters below the water surface, and the receiver uses an array of four transducers spaced 60 cm vertically, with the uppermost transducer 6 meters above the water surface. The two boats float on the water with a relative speed of approximately 0.2~0.4 m / s. The receiver performs symbol demodulation and sparse channel impulse response estimation operations on the received data vector based on variational Bayesian joint iteration. The transmit and receive frame structures in this embodiment are the same as in Embodiment 1: the transmit frame contains HFM signals and data segments used for synchronization and Doppler estimation, obtained by superimposing unknown transmit symbols and training sequences. Each frame contains 2336 baseband symbols with a baseband symbol sampling rate of 6 kHz and a bandpass signal sampling rate of 96 kHz. The receiver then performs joint processing on the received data vector.

[0119] In the algorithm estimation process, the maximum channel length is set to... The actual number of taps is 20. The experimental channel was obtained by inverting measured data from Wanlv Lake using a matching pursuit algorithm and stored as a four-dimensional channel matrix. The baseband sampling rate is 6kHz, and each moment corresponds to 256 baseband delays (42.67ms in duration), of which 64 taps have responses to reproduce the real sparse multipath fading characteristics in underwater acoustic communication. The system integrates a sparse Bayesian learning algorithm and the joint estimation algorithm of this invention for parallel comparison. The maximum number of iterations for the overall Turbo equalization and extrinsic information interaction is set to a certain value. In the actual iterative solution, this method uses the variational Bayesian principle to alternately update the channel expectation and posterior soft symbol extrinsic information, and uses a 1 / 4 code rate decoding feedback mechanism for decision verification to ensure that the receiver can use the soft decision information to perform more accurate recursive optimization of the channel.

[0120] In the specific joint estimation and demodulation process, the receiver algorithm utilizes the variational Bayesian principle to alternately update the channel expectation vector and the posterior soft symbol information in each iteration. This approach effectively eliminates interference caused by the superposition of training sequences, thereby improving the system's signal recognition capability under the measured underwater acoustic channel fading environment at Wanlv Lake through the information fed back from the decoder.

[0121] Experimental results show that this invention exhibits superior bit error rate convergence performance compared to traditional sparse Bayesian learning algorithms within a limited number of iterations, and can reproduce the real multipath fading patterns in the underwater acoustic environment of Wanlv Lake, demonstrating higher engineering practical value in long-distance mobile underwater acoustic communication scenarios. Figure 6The figure shows a comparison of the bit error rate performance of the Joint Estimation Algorithm (JCED) and the traditional Sparse Bayesian Learning Algorithm (SBL) as the signal-to-noise ratio changes under different power ratios of transmitted symbols to training sequences (2:1 and 3:1). Figure 6 It can be clearly seen that the bit error rate decreases under all test conditions as the signal-to-noise ratio (SNR) increases. Under the same power ratio configuration, the bit error rate of the JCED algorithm in this embodiment is consistently lower than that of the traditional SBL algorithm: when the power ratio is 2:1, the system achieves good communication quality at a lower SNR, and the bit error rate of the JCED algorithm drops to 10⁻ when the SNR is 6dB. 4 When the power ratio is 3:1, although the overall bit error rate curve shifts to the right, the bit error rate of the JCED algorithm decreases to approximately 5 × 10⁻⁻⁴ when the SNR is 9 dB. 5 This outperforms the SBL algorithm. This further verifies that our method maintains superior anti-interference capability and convergence performance in long-distance mobile underwater acoustic communication scenarios and under different power ratio configurations.

[0122] Example 4

[0123] Reference Figure 7 This embodiment provides a joint symbol and sparse channel Bayesian estimation device based on superimposed training sequences, used to execute the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences disclosed in the above embodiment. The estimation device includes a signal receiving module 701, a model building module 702, a first initialization module 703, a second initialization module 704, an estimation and update module 705, a decoding operation module 706, and a decision verification module 707, connected in sequence.

[0124] Signal receiving module 701 is used to receive the transmitted signal with the superimposed training sequence in the underwater acoustic channel, and obtain the received data vector by sampling. ;

[0125] Model building module 702, based on received data vector Constructing a channel impulse response Unknown transmission symbol Superimposed on the transmitted symbol Training sequences on Channel power vector and channel noise power The joint probability model, in which, For the first Send sub-symbols, , Indicates the total number of sent sub-symbols;

[0126] The first initialization module 703 is used to initialize each parameter to be estimated and the variational Bayes algorithm iteration control variables, wherein the parameters to be estimated and the variational Bayes algorithm iteration control variables include: Send sub-symbols Corresponding posterior soft symbol The decoder feeds back the prior information of the input equalizer, log-likelihood ratio , Indicates the first Send sub-symbols Middle bits, and ,in Represents the total number of bits in a transmit sub-symbol mapping, and the number of Turbo equalization iterations. The maximum number of Turbo equilibrium iterations is ;

[0127] The second initialization module 704 is used to initialize the number of iterations in the inner loop of the variational Bayes algorithm. Set the maximum number of iterations for variational Bayes to 0. ;

[0128] The estimation and update module 705 uses the variational Bayesian algorithm to iteratively estimate the channel impulse response. Expected vector and the Send sub-symbols Corresponding equalizer symbol Based on the parameters obtained from variational estimation in the current iteration round, the channel power vector is then updated. Channel noise power ,and Determine if the inner loop of the variational Bayesian algorithm terminates; if so, the iteration count... If the iteration ends, the decoding module is executed; otherwise, the estimation and update module is returned to repeat the inner loop of the variational Bayes algorithm.

[0129] The decoding module 706 is used to process the various equalization sub-symbols output iteratively by the variational Bayes algorithm. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output ,right Deinterleaving is performed to obtain the prior information log-likelihood ratio of the input decoder. ,Will The input is decoded by a decoder, and the updated prior information log-likelihood ratio of the input equalizer is obtained from the decoder. ;

[0130] The decision verification module 707 is used to perform a log-likelihood ratio calculation on the prior information of the input equalizer over the entire symbol period. Perform a hard decision and verify whether the bit sequence after the hard decision has been successfully decoded: if the verification is successful, determine that the transmission signal has been successfully recovered, terminate the loop, and output the decoding result; if the verification fails, determine the number of iterations. :like If the condition is met, the loop will be forcibly terminated and the current decoding result will be output; otherwise, the loop will be terminated and the current decoding result will be output. The log-likelihood ratio of prior information to the input equalizer Intertwined and mapped to the first Send sub-symbols posterior soft symbol Then, proceed to the second initialization module to continue execution.

[0131] Example 5

[0132] This embodiment provides an electronic device, which can be a computer, such as... Figure 8 As shown, it is connected via a system bus 801 to a processor 802, a memory, an input device 803, a display 804, and a network interface 805. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 806 and an internal memory 807. The non-volatile storage medium 806 stores an operating system, computer programs, and a database. The internal memory 807 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 802 executes the computer program stored in the memory, it implements the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences proposed in Embodiment 1 above. Specifically, refer to steps S1 to S7 in Embodiment 1.

[0133] Example 6

[0134] This embodiment provides a storage medium, which is a computer-readable and storable medium that stores a computer program. When the computer program is executed by a processor, it implements the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences proposed in Embodiment 1 above. Specifically, refer to steps S1 to S7 in Embodiment 1.

[0135] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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, they should be considered to be within the scope of this specification.

[0136] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A joint symbolic and sparse channel Bayesian estimation method based on superimposed training sequences, characterized in that, The estimation method includes the following steps: S1. Receive the transmitted signal with the superimposed training sequence in the underwater acoustic channel, and obtain the received data vector by sampling. ; S2, Based on received data vector Constructing a channel impulse response Unknown transmission symbol Superimposed on the transmitted symbol Training sequences on Channel power vector and channel noise power The joint probability model, in which, For the first Send sub-symbols, , Indicates the total number of sent sub-symbols; S3. Initialize each parameter to be estimated and the variational Bayes algorithm iteration control variables. The parameters to be estimated and the variational Bayes algorithm iteration control variables include: the first... Send sub-symbols Corresponding posterior soft symbol The decoder feeds back the prior information of the input equalizer, log-likelihood ratio , Indicates the first Send sub-symbols The Middle bits, , Represents the total number of bits in a transmit sub-symbol mapping, and the number of Turbo equalization iterations. The maximum number of Turbo equilibrium iterations is ; S4. Initialize the number of iterations in the inner loop of the variational Bayes algorithm. Set the maximum number of iterations for variational Bayes to 0. ; S5. Iteratively estimate the channel impulse response using the variational Bayesian algorithm. Expected vector and the Send sub-symbols Corresponding equalizer symbol Based on the parameters obtained from variational estimation in the current iteration round, the channel power vector is then updated. Channel noise power ,and Determine if the inner loop of the variational Bayesian algorithm terminates; if so, the iteration count... Then the iteration ends and step S6 is executed; otherwise, step S5 is repeated to complete the next iteration of the variational Bayesian algorithm inner loop. S6. Iterate through the various equilibrium subsymbols output by the variational Bayes algorithm. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output ,right Deinterleaving is performed to obtain the prior information log-likelihood ratio of the input decoder. ,Will The input is decoded by a decoder, and the updated prior information log-likelihood ratio of the input equalizer is obtained from the decoder. ; S7. Log-likelihood ratio of prior information input to the equalizer over the entire symbol period. Perform a hard decision and verify whether the bit sequence after the hard decision has been successfully decoded: if the verification is successful, the transmission signal is successfully recovered and the decoding result is output; if the verification fails, continue to execute the operation.

2. The joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences according to claim 1, characterized in that, In step S1, the received data vector is obtained. ,in Indicates size is A column vector of the complex field of dimension 1. The data length of a single symbol block. This is represented as a transpose operation. Indicates the receiver is at the 1st The training sequence is defined by the complex sampled signal received at each time step. , Indicates the sending end is at the 1st Time-based training sequence The symbol, the transmitted symbol to be estimated The modulation method is Order modulation, and simultaneously, defining the channel impulse response. , , indicating the first Complex gain coefficients of each channel tap Define the channel noise vector as the channel impulse response length. , Indicates the first The channel noise at a given time is then the received data vector The expression is as follows: , in, Based on channel impulse response Constructed 3D circular convolution matrix.

3. The joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences according to claim 1, characterized in that, In step S2, the joint probability model is based on Bayes' theorem, and the probability density function structure of the joint probability model includes the received data vector. Likelihood probability density function, channel noise vector Channel noise statistical distribution and channel impulse response The channel prior is sparsely distributed, where the received data vector Likelihood probability density function The expression is as follows: , Channel noise vector Channel noise statistical distribution The expression is as follows: , Channel impulse response Channel prior sparse distribution The expression is as follows: , in Represents the received data vector The conditional likelihood probability density function, Indicates that x follows the mean of variance is The complex Gaussian distribution; Indicates channel noise power Given the channel noise vector The conditional probability; Represents the channel power vector Channel impulse response under known conditions The conditional probability, Indicates the first Channel power per tap, Indicates size is The identity matrix.

4. The joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences according to claim 1, characterized in that, In step S3, the parameters to be estimated and the control variables for the variational Bayes algorithm iteration are initialized as follows: Send sub-symbols Corresponding posterior soft symbol All are initialized to 0, and the prior information log-likelihood ratio of the input equalizer is... All values ​​are initialized to 0, using the initial channel noise power estimated from the blank segments of the received signal. Channel noise power Initialize to The maximum number of Turbo balancing iterations is initialized to Channel power vector All elements Initialize to ,in The preset channel power, Indicates size is The identity matrix.

5. The joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences according to claim 1, characterized in that, In step S5, the channel impulse response vector is derived based on the variational Bayes theorem and the joint probability model established in S2. Channel noise power Send sub-symbols The update formula, in the variational Bayes algorithm, is... In each iteration, the channel impulse response vector Expected vector Posterior covariance matrix and channel power vector The Channel power of each tap Iteratively update using the following formula: ， ， ， in, Indicates the training sequence The dictionary matrix formed, Indicates by posterior soft symbols The constructed Toplitz signal matrix, i.e. , in, This represents the covariance matrix of the received underwater acoustic channel. This represents the autocorrelation matrix of the transmitted signal. This is represented as the conjugate transpose operation. This is represented as the inverse operation. The calculation of the 2-norm of a vector. Represents a diagonal matrix. The elements on the diagonal are composition, Represents the covariance matrix of the received underwater acoustic channel The first diagonal One element, The expectation vector representing the channel estimation The One element; Update the channel noise power in each iteration : ， ， ， in, This indicates that the elements in parentheses are used to construct a diagonal matrix. Represents the trace operation of a matrix. This represents the mean variance of the posterior soft sign. The mean variance of the posterior soft sign represents the variance of the posterior soft sign. The diagonal matrix formed; In each iteration, in order Update one by one Send sub-symbols Equalizer symbol and posterior variance The updated formula is: ， ， in, ， ， To select a vector, Indicates size is The row vector, Represents the channel autocorrelation matrix. This represents the equivalent noise matrix of the channel estimation error. Represents the expectation vector estimated by the channel. The constructed cyclic channel estimation matrix, at the same time, , , No. One equalizer symbol After calculation and output, the time domain is updated using the following formula. posterior soft symbol at each position , , in, Indicates preset The first in the modulated constellation diagram A modulated constellation symbol, Indicates sending sub-symbols Mapped to constellation symbols The probability density function is calculated using the following formula: ， in, A constant that makes the sum of normalized probabilities equal to 1. constellation symbols The corresponding number The value of a binary bit after bipolar mapping; if the bit is 0, then... If the value of this bit is 1, then ; Indicates the first The posterior variance of each transmitted sub-symbol. Indicates the first Send sub-symbols The The posterior log-likelihood ratio for each bit is calculated using the following formula: ， in, This represents the log-likelihood ratio of the prior information input to the equalizer. The log-likelihood ratio of the extrinsic information output by the equalizer is expressed by the following formula: ,in, This indicates the operation of taking the real part of a complex number; After completing the above updates, it will be possible to Determine if the inner loop of the variational Bayes algorithm has terminated; if so, the iteration count... If the iteration ends, proceed to step S6; otherwise, return to the beginning of step S5 and continue executing the next iteration of the variational Bayesian algorithm's inner loop.

6. The joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences according to claim 1, characterized in that, In step S6, the various equilibrium sub-symbols output by the variational Bayes algorithm are iterated. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output The calculation formula is: ， The Perform deinterleaving to obtain the log-likelihood ratio of the prior information of the deinterleaved input decoder. ,Will The input is decoded by a decoder, and the updated prior information log-likelihood ratio of the input equalizer is obtained from the decoder. .

7. The joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences according to claim 1, characterized in that, In step S7, the a posteriori information output by the decoder is processed. A hard decision is made, and the hard decision process is as follows: ， Simultaneous verification The correctness of the check is verified; if the verification fails, the number of iterations is determined. :when If the loop terminates, the current decoding result will be output. otherwise The log-likelihood ratio of prior information to the input equalizer Intertwined and mapped to the first Send sub-symbols posterior soft symbol Then, proceed to step S4 for the next round of Turbo balancing iteration.

8. A joint symbolic and sparse channel Bayesian estimation device based on superimposed training sequences, used to execute the joint symbolic and sparse channel Bayesian estimation method based on superimposed training sequences as described in any one of claims 1 to 7, characterized in that, The estimation device includes: The signal receiving module is used to receive the transmitted signal with the superimposed training sequence in the underwater acoustic channel, and obtain the received data vector through sampling. ; The model building module is based on the received data vector. Constructing a channel impulse response Unknown transmission symbol Superimposed on the transmitted symbol Training sequences on Channel power vector and channel noise power The joint probability model, in which, For the first Send sub-symbols, , Indicates the total number of sent sub-symbols; The first initialization module is used to initialize each parameter to be estimated and the variational Bayesian algorithm iteration control variables, wherein the parameters to be estimated and the variational Bayesian algorithm iteration control variables include: Send sub-symbols Corresponding posterior soft symbol The decoder feeds back the prior information of the input equalizer, log-likelihood ratio , Indicates the first Send sub-symbols The Middle bits, , Represents the total number of bits in a transmit sub-symbol mapping, and the number of Turbo equalization iterations. The maximum number of Turbo equilibrium iterations is ; The second initialization module is used to initialize the number of iterations in the inner loop of the variational Bayes algorithm. Set the maximum number of iterations for variational Bayes to 0. ; The estimation and update module uses the variational Bayesian algorithm to iteratively estimate the channel impulse response. Expected vector and the Send sub-symbols Corresponding equalizer symbol Based on the parameters obtained from variational estimation in the current iteration round, the channel power vector is then updated. Channel noise power ,and Determine if the inner loop of the variational Bayesian algorithm terminates; if so, the iteration count... If the iteration ends, the decoding module is executed; otherwise, the estimation and update module is returned to repeat the inner loop of the variational Bayes algorithm. The decoding module is used to process the various equalization sub-symbols output iteratively by the variational Bayesian algorithm. Demapping to the log-likelihood ratio of the extrinsic information of the equalizer output ,right Deinterleaving is performed to obtain the prior information log-likelihood ratio of the input decoder. ,Will The input is decoded by a decoder, and the updated prior information log-likelihood ratio of the input equalizer is obtained from the decoder. ; The decision verification module is used to calculate the log-likelihood ratio of the prior information input to the equalizer throughout the entire symbol period. Perform a hard decision and verify whether the bit sequence after the hard decision has been successfully decoded: if the verification is successful, the transmission signal is successfully recovered and the decoding result is output; if the verification fails, continue to execute the operation.

9. An electronic device comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences as described in any one of claims 1 to 7.

10. A storable medium storing a program, characterized in that, When the program is executed by the processor, it implements the joint symbol and sparse channel Bayesian estimation method based on superimposed training sequences as described in any one of claims 1 to 7.

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