Time domain adaptive equalization method based on bidirectional superimposed training sequence

Abstract

The application provides a time domain adaptive equalization method based on bidirectional superimposed training sequence, which uses superimposed training sequence to improve the spectrum utilization of underwater acoustic communication and the tracking ability of time-varying underwater acoustic channel. The method uses linear superimposed structure at the transmitting end and optimizes the power distribution of training sequence and information symbol, and the receiving end uses forward and reverse adaptive time domain equalization parallel processing to construct a bidirectional iterative optimization framework. Meanwhile, the application designs a time domain symbol-by-symbol training sequence interference cancellation mechanism to eliminate the interference of superimposed training sequence on the underwater acoustic communication system. The application mainly uses superimposed training sequence to improve the spectrum utilization of the system, saves bandwidth compared with the traditional inserted training sequence mode, and uses symbol-by-symbol to eliminate the interference of superimposed training sequence on the system. The simulation results prove that the method can improve the performance of the underwater acoustic communication system.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic communication and relates to a time-domain adaptive equalization method based on bidirectional superposition training sequences. Background Technology

[0002] Underwater acoustic communication can establish reliable communication links between underwater platforms or between underwater platforms and shore-based systems, playing a crucial role in areas such as marine target localization, feature recognition, and collaborative operations. However, the underwater acoustic channel, due to its significant multipath effect, rapid time-varying characteristics, high propagation loss, and bandwidth limitations, has become a major bottleneck for improving the performance of current communication systems.

[0003] Current mainstream high-speed underwater communication technologies include Single Carrier Time Domain Equalization (SC-TDE), Single Carrier Frequency Domain Equalization (SC-FDE), and Orthogonal Frequency Division Multiplexing (OFDM). SC-TDE systems effectively suppress channel interference through multi-channel adaptive time domain equalization, and their performance has been verified in numerous sea trials. SC-FDE and OFDM transform the linear convolution of the channel into a circular convolution by inserting a cyclic prefix and use low-complexity equalization algorithms in the frequency domain to complete signal recovery. These technologies perform well in fixed-node scenarios, but their performance degrades significantly when facing rapidly time-varying channels.

[0004] Existing technologies all rely on training sequences for channel estimation or equalizer parameter training. Due to the long delay spread effect of underwater acoustic channels, relatively long training sequences are usually required to ensure estimation accuracy, but this significantly reduces the system's spectral efficiency. To address this issue, training sequence superposition techniques have been proposed in recent years. By overlaying the training sequence with information symbols during transmission, channel estimation can be achieved without additional spectral resources. For example, Zhao Junyi et al. proposed sparse channel parameter estimation based on superimposed training sequences. Combined with the generalized Akaike information theory criterion, this can significantly reduce channel estimation errors and improve system performance. FBLouza et al. proposed superimposed training for low-probability underwater communication. By superimposing the training sequence with the information sequence, equalization and synchronization are achieved. The FHT transform is used to estimate the channel and compress the training sequence energy. Then, a Wiener filter is used for channel equalization, and zero-point cancellation is used to remove interference signals. Finally, the information sequence is recovered by decompressing the sequence using inverse FHT. Yang Guang et al. proposed time-varying underwater acoustic channel estimation and equalization based on superimposed training sequences and low-complexity frequency domain Turbo equalization. Based on superimposed training sequences, time-varying underwater acoustic channel estimation and equalization are achieved.

[0005] Although the superposition training method has made progress in terms of spectral efficiency, the above studies only focus on one-way estimation or equalization, making it difficult for existing methods to simultaneously meet the dual requirements of time-varying channel tracking and communication efficiency. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a time-domain adaptive equalization method based on bidirectional superposition training sequences, which can effectively improve time-varying channel tracking and spectrum utilization.

[0007] The technical solution of this invention is as follows:

[0008] A temporal adaptive equalization method based on bidirectional superposition of training sequences includes the following steps:

[0009] Step 1: The underwater acoustic communication system transmitter transmits a transmission signal superimposed with a training sequence. In the transmission signal, the training sequence is linearly superimposed at the beginning and end of the information sequence.

[0010] Step 2: The underwater acoustic communication system receiver receives the received signal containing the training sequence and the information sequence; when the equalizer of the underwater acoustic communication system is in training mode, the forward equalizer and the reverse equalizer are trained respectively; after the training is completed, when the equalizer of the underwater acoustic communication system is in decision mode, forward adaptive channel equalization is performed on the multi-channel received signal, and after time reversal processing of the received signal, reverse adaptive channel equalization is performed; at the same time, adaptive channel estimation is performed symbol by symbol using the result of adaptive channel equalization.

[0011] Step 3: Use the channel matrix to perform superposition training sequence interference cancellation and symbol detection to obtain the forward and reverse output results; combine the forward and reverse output results bidirectionally, and combine the combined result with the equalized information sequence parts at the beginning and end to obtain the final output result;

[0012] Step 4: Decode the output obtained in Step 3 and reconstruct the decoded result to obtain the reconstructed result after bidirectional joint decoding; use the reconstructed result as input to return to Step 2 to re-perform adaptive equalization processing on the multi-channel received signal until the received signal is processed.

[0013] Furthermore, in step 1, the transmitted signal is represented as

[0014] s=γp+x

[0015] Where: x is the information sequence to be transmitted, x = [x1, x2, ..., x...] N ] T p represents the training sequence; γ represents the power ratio between the training sequence and the symbol sequence.

[0016] Furthermore, in step 2, the signal r with superimposed training sequences received by the underwater acoustic communication system receiver is represented as:

[0017] r = Hs + G

[0018] =H(γp+x)+G

[0019] =γHp+Hx+G

[0020] Where H represents the channel gain matrix and G represents the Gaussian white noise of the channel.

[0021] Furthermore, in step 2, the adaptive equalization processing of the multi-channel received signals includes two working modes: training mode and decision mode.

[0022] In the training mode, i.e., the 0 < n ≤ M stage, the forward equalizer and the reverse equalizer are trained separately.

[0023] The positive training process is as follows:

[0024] The training sequence p(n) is used as the label for the output of the forward adaptive channel equalization: for the forward feedforward filter coefficients and feedback filter coefficients at time n, the output of the forward adaptive channel equalization is obtained through the equalizer. Then, the error e(n) is obtained by combining it with the label p(n). Through the above iterative formula, the forward feedforward filter coefficients and feedback filter coefficients at time n+1 are obtained until the forward training is completed.

[0025] The reverse training process is as follows:

[0026] The training sequence after time reversal operation The labels are used as the output of the reverse adaptive channel equalization for training: For the inverse feedforward filter coefficients and feedback filter coefficients at time n, the output of the reverse adaptive channel equalization is obtained through the equalizer. Furthermore, with tags The error e(n) is obtained. The feedforward filter coefficient and the feedback filter coefficient at time n+1 are obtained by using the iterative formula of the feedforward filter coefficient and the feedback filter coefficient, until the reverse training is completed.

[0027] Furthermore, in step 2, under the decision mode, i.e., the M < n ≤ NM stage, symbol detection is performed, and simultaneously, symbol-by-symbol channel estimation is performed using the symbol detection results to obtain the channel matrix at the corresponding time. Adaptive channel equalization is also divided into forward equalization and reverse equalization. The forward equalization process is as follows: symbol detection is performed directly using the received signal based on the feedforward filter coefficients and feedback filter coefficients obtained from forward training. The reverse equalization process is as follows: the received signal is time-reversed, and then symbol detection is performed using the reversed received signal based on the feedforward filter coefficients and feedback filter coefficients obtained from reverse training.

[0028] Furthermore, the iterative formulas for the feedforward filter coefficients and the feedback filter coefficients are as follows:

[0029]

[0030] in: with w (b) These are the coefficients of the feedforward and feedback filters, respectively; μ (f) and μ (b) These are the step sizes for the feedforward and feedback filters, respectively; δ is a regularization constant to prevent the denominator from equaling 0; e * (n) is the adjoint matrix of the error e(n); V is the input signal of the feedback filter; ||u q (n)|| 2 The input signal u of the qth channel at time n q The energy of (n).

[0031] Furthermore, the specific process of using the channel matrix to superimpose training sequence interference cancellation in step 3 is as follows:

[0032] First, perform symbol-by-symbol interference removal on the training sequence at the end of the positive sequence:

[0033] Since the received signal contains superimposed training sequences, the interference of the training sequences is eliminated symbol by symbol in the time domain:

[0034] First, interference is canceled at the tail of the positive received signal, and then the information sequence at the tail is equalized; let y p For the receiving format of bidirectional superimposed training sequences, y p =y f +y r y f The received signal form of the forward-end training sequence, y r The received signal form of the reverse head training sequence, y x This is the received signal format for the information sequence, and the received signal is represented in another way as:

[0035] y = yp +y x +G

[0036] =y f +y r +y x +G

[0037] Perturbation of the training sequence at the end of positive equalization It can be represented as:

[0038]

[0039] in This represents the channel matrix corresponding to the forward channel impulse response;

[0040] The training sequence at the end of the forward equalization is eliminated using the following formula:

[0041] This achieves a positive elimination process for superimposed training sequences;

[0042] After completely eliminating the forward superimposed training sequences, symbol detection is then performed on the information symbols at NM < n ≤ N to complete the detection of all forward information symbols, resulting in...

[0043] Then, an interference cancellation process is performed using the reverse stacking of training sequences, with the training sequence being a time-reversed form of p(n). Training sequence perturbation of the reverse-equalized head Represented as:

[0044]

[0045] in This represents the channel matrix corresponding to the reverse channel impulse response;

[0046] The training sequence of the head during reverse equalization is eliminated using the following formula:

[0047]

[0048] in This is the time-reversed form of the received signal y. For y x Time reversal form, This is the time-reversed form of G; then, through information symbol detection and time-reversing the detection result, we obtain...

[0049] Furthermore, in step 3, the forward and reverse outputs are combined bidirectionally, and the combined result is then combined with the balanced information sequence at the beginning and end to obtain the final output.

[0050] Will and The process of combining the outputs employs a weighted combination of the forward adaptive equalization output and the reverse adaptive equalization output:

[0051]

[0052] Where: n=1,…,N; α is a weighting factor, 0≤α≤1; It is the output signal of positive adaptive equalization; It is a time-reversed form of the inverse adaptive equalization output signal;

[0053] Then Combining this with the balanced information sequence at the beginning and end, the final result is:

[0054]

[0055] in and These are the information sequence parts that are superimposed on the head and tail of the training sequence, respectively.

[0056] Furthermore, in step 4, the output result z obtained in step 3 is decoded, and the decoded result is reconstructed to obtain the reconstructed result after bidirectional joint decoding. by As input, return to step 2 to re-perform adaptive equalization processing of the multi-channel received signal, wherein the forward training process in the training phase is based on... The labels used as the output of the positive adaptive channel equalization are used for training, and the reverse training process is as follows: The labels used as the output of the reverse adaptive channel equalization are used for training; where for A time-reversed sequence.

[0057] Furthermore, in step 4, Turbo iterative equalization is applied to the adaptive equalization of the bidirectional superimposed training sequences to further improve the performance of the underwater acoustic communication system.

[0058] Beneficial effects

[0059] This invention proposes a time-domain adaptive equalization method based on bidirectional superimposed training sequences for SC-TDE systems. This invention utilizes superimposed training sequences to improve the spectral efficiency and tracking capability of time-varying underwater acoustic channels. Furthermore, the method employs a linear superposition structure at the transmitter and optimizes the power allocation between the training sequences and information symbols. At the receiver, it uses parallel processing of forward and reverse adaptive time-domain equalization to construct a bidirectional iterative optimization framework. Simultaneously, this invention designs a time-domain symbol-by-symbol interference cancellation mechanism to eliminate interference from the superimposed training sequences on the underwater acoustic communication system.

[0060] This invention primarily utilizes superimposed training sequences to improve the spectral efficiency of the system, saving bandwidth compared to the traditional insertion-based training sequence method. Furthermore, it employs symbol-by-symbol elimination to remove interference from the superimposed training sequences. Simulation results confirm that the proposed method can improve the performance of underwater acoustic communication systems.

[0061] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0062] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0063] Figure 1 It is the frame structure of the transmitted signal in an underwater acoustic communication system;

[0064] Figure 2 It is a frame structure diagram of bidirectionally superimposed training sequences;

[0065] Figure 3 This is a block diagram of the overall structure of a two-way DFE;

[0066] Figure 4 This is the bit error rate result corresponding to the superimposed power ratio;

[0067] Figure 5 This is a comparison of the bit error rate between the traditional method and the superposition training method under the condition of weak channel time-varying characteristics;

[0068] Figure 6 This is a comparison of the bit error rate between the traditional method and the superposition training method under the condition of strong channel time-varying characteristics;

[0069] Figure 7 This is the impulse response result of a time-varying channel under conditions where the channel's time-varying nature is weak;

[0070] Figure 8 It is the impulse response result of a time-varying channel under the condition of strong time-varying channel characteristics;

[0071] Figure 9It compares the bit error rate at different iteration numbers. Detailed Implementation

[0072] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0073] The basic principle of the time-domain adaptive equalization method based on bidirectional superposition training sequences proposed in this embodiment is:

[0074] In the underwater acoustic communication system, a linear superposition structure is adopted at the transmitting end, and the power allocation between the training sequence and information symbols is optimized. At the receiving end, a bidirectional iterative optimization framework is constructed through parallel processing of forward and reverse adaptive time-domain equalization. Simultaneously, a time-domain symbol-by-symbol interference cancellation mechanism is designed: firstly, preliminary channel estimation is performed based on the adaptive equalization results; after system convergence, the time-varying channel impulse response is tracked in real time, and a channel matrix is ​​constructed to eliminate training sequence interference; subsequently, the soft symbol information after forward and reverse decoding is fed back to the channel estimation module to further improve estimation accuracy, and Turbo iterative equalization is used to achieve coordinated optimization of equalization and estimation.

[0075] Specifically, the following steps are included:

[0076] Step 1: The underwater acoustic communication system transmitter transmits a transmission signal superimposed with a training sequence. In the transmission signal, the training sequence is linearly superimposed at the beginning and end of the information sequence.

[0077] In this embodiment, the structure of the transmitted signal frame of the underwater acoustic communication system is as follows: Figure 1 As shown, a training sequence of length M is superimposed on both ends of the information sequence. For ease of description, the transmitted signal s can be represented as...

[0078] s=γp+x

[0079] Where: x is the information sequence to be transmitted, x = [x1, x2, ..., x...] N ] T N is the length of the information sequence;

[0080] p is a training sequence that satisfies p n =0, M+1≤n≤NM;

[0081] γ is the power ratio of the training sequence to the symbol sequence.

[0082] In this embodiment, 1 / 2 convolutional coding and QPSK mapping are used, N=1024, M=256, the power ratio of the training sequence to the information sequence is 1:0.6, and the underwater acoustic communication system adopts single-carrier modulation.

[0083] Step 2: The underwater acoustic communication system receiver receives the received signal containing the training sequence and the information sequence; when the equalizer of the underwater acoustic communication system is in training mode, the forward equalizer and the reverse equalizer are trained respectively; after the training is completed, when the equalizer of the underwater acoustic communication system is in decision mode, forward adaptive channel equalization is performed on the multi-channel received signal, and after time reversal processing of the received signal, reverse adaptive channel equalization is performed; at the same time, adaptive channel estimation is performed symbol by symbol using the result of adaptive channel equalization.

[0084] In this embodiment, the signal r with superimposed training sequences received by the underwater acoustic communication system receiver is represented as:

[0085] r = Hs + G

[0086] =H(γp+x)+G

[0087] =γHp+Hx+G

[0088] Where H represents the channel gain matrix and G represents the Gaussian white noise of the channel.

[0089] Then, adaptive equalization processing is performed on the multi-channel received signals:

[0090] In a conventional multi-channel decision feedback equalizer (DFE), the DFE first performs forward filtering on the received signals from multiple channels to eliminate preamble interference (ISI). Then, the output signal of the feedforward filter is combined with the decision and feedback filter to eliminate residual interference caused by subsequent symbols in the current signal.

[0091] The specific process is as follows: Assume that in the DFE... Let w be the feedforward filter coefficient for the q-th channel. (b) For the feedback filter coefficients, the output of the q-th channel of the feedforward filter at time n is expressed as:

[0092]

[0093] Where: r n The received signal at time n; Let Q be the symbol that has been decided at time n, and let Q be the number of channels.

[0094] The core of adaptive equalization lies in minimizing the error between the received signal and the desired transmitted signal by dynamically adjusting the filter coefficients. Traditionally, the equalizer coefficients are updated using the Least Mean Square (LMS) algorithm. The iterative formula for the LMS algorithm is:

[0095]

[0096] Where: w(n) represents the filter coefficient vector at time n; μ is a fixed step size parameter. The gradient term is represented as:

[0097]

[0098] Where u(n) is the input signal; e(n) is the error between the expected value and the estimated value.

[0099] e * (n)u(n) instead of E[e * The recursive formula for the LMS algorithm is obtained from [(n)u(n)].

[0100]

[0101] The convergence rate in the formula is controlled by the step size μ, and it is usually required that:

[0102]

[0103] Where: λ max It is the largest eigenvalue of the autocorrelation matrix R of the input signal.

[0104] Although the LMS algorithm is simple to implement, the convergence rate and steady-state error of the traditional LMS algorithm are greatly affected by the step size μ. Considering the time-varying nature and strong multipath interference of underwater acoustic channels, this invention further employs the Normalized Minimum Mean Square Error (NLMS) algorithm. This algorithm dynamically adjusts the step size to balance convergence and stability. The iterative formulas for the feedforward filter coefficients and feedback filter coefficients of the NLMS algorithm are as follows:

[0105]

[0106] in: with w (b) These are the coefficients of the feedforward and feedback filters, respectively; μ (f) and μ (b) These are the step sizes for the feedforward and feedback filters, respectively; δ is a regularization constant to prevent the denominator from equaling 0; e * (n) is the adjoint matrix of the error e(n); V is the input signal of the feedback filter; ||u q (n)|| 2 The input signal u of the qth channel at time n q The energy of (n).

[0107] Based on the NLMS algorithm proposed above, adaptive equalization processing is performed on the multi-channel received signals:

[0108] The adaptive equalization process is divided into two working modes: training mode and decision mode.

[0109] In the training mode, i.e., the 0 < n ≤ M stage, the forward equalizer and the reverse equalizer are trained separately.

[0110] The positive training process is as follows:

[0111] The training sequence p(n) is used as the label for the output of the forward adaptive channel equalization: for the forward feedforward filter coefficients and feedback filter coefficients at time n, the output of the forward adaptive channel equalization is obtained through the equalizer. Then, the error e(n) is obtained by combining it with the label p(n). Through the above iterative formula, the forward feedforward filter coefficients and feedback filter coefficients at time n+1 are obtained until the forward training is completed.

[0112] The reverse training process is as follows:

[0113] The training sequence after time reversal operation The labels are used as the output of the reverse adaptive channel equalization for training: For the inverse feedforward filter coefficients and feedback filter coefficients at time n, the output of the reverse adaptive channel equalization is obtained through the equalizer. Furthermore, with tags The error e(n) is obtained, and the feedforward filter coefficients and feedback filter coefficients at time n+1 are obtained through the above iterative formula until the reverse training is completed.

[0114] In the decision mode, i.e., the M < n ≤ NM stage, adaptive channel equalization (i.e., symbol detection) is performed. Simultaneously with symbol detection, symbol-by-symbol channel estimation is performed using the symbol detection results to obtain the channel matrix at the corresponding time. Adaptive channel equalization is further divided into forward equalization and reverse equalization. The forward equalization process involves directly using the received signal and performing symbol detection based on the feedforward and feedback filter coefficients obtained through forward training. The reverse equalization process involves time reversing the received signal and then using the reversed received signal to perform symbol detection based on the feedforward and feedback filter coefficients obtained through reverse training.

[0115] The following example, using the forward direction, details the symbol detection and symbol-by-symbol channel estimation process:

[0116] For the q-th channel, the output of its feedforward filter can be expressed as:

[0117]

[0118] Where: w f,q For the positive q-th channel, (·) H Indicates the complex conjugate transpose; This represents the input of the feedforward filter at time n for the q-th channel.

[0119] The output of the feedback filter is expressed as:

[0120]

[0121] The total output of the filter is expressed as:

[0122]

[0123] Next, the desired response is calculated for the filter output. Perform symbolic decision to obtain the symbolic result. The error is Since this invention performs channel equalization and channel estimation symbol by symbol, the equalization result... Symbol-by-symbol estimation will be used for channel estimation, i.e.: Here Input for adaptive channel estimation:

[0124]

[0125] Where: w q The weights for channel estimation; (·) T Indicates transpose; for L symbols in the text.

[0126] Obtain from the received signal of the q-th channel but The error is The weights are then updated using the proportionally normalized NLMS algorithm:

[0127]

[0128] Where: k l ζ is a diagonal proportional matrix; α is a sparsity control parameter, when α = -1, IPNLMS degenerates into the NLMS algorithm; ζ is a regularization constant to prevent division by zero.

[0129] Next, the channel impulse response is updated:

[0130]

[0131] in: The positive channel impulse response of the q-th channel at time n is given, and the channel matrix corresponding to the q-th channel at time n is obtained.

[0132] Step 3: Use the channel matrix to perform superposition training sequence interference cancellation and symbol detection to obtain the forward and reverse output results; combine the forward and reverse output results bidirectionally, and combine the combined result with the equalized information sequence parts at the beginning and end to obtain the final output result.

[0133] First, perform symbol-by-symbol interference removal on the training sequence at the end of the positive sequence:

[0134] When NM<n≤N, in this stage, interference cancellation and symbol detection are performed by superimposing training sequences, and the channel estimation result from the previous time step is used to replace the current channel.

[0135] Let the underwater acoustic channel be L is the order of the underwater acoustic channel, and H is the channel matrix corresponding to the channel impulse response.

[0136]

[0137] Since the received signal contains superimposed training sequences, the interference of the training sequences is then eliminated symbol by symbol in the time domain:

[0138] First, interference is canceled at the tail of the positive received signal, and then the information sequence at the tail is equalized. Let y p For the receiving format of bidirectional superimposed training sequences, y p =y f +y r y f The received signal form of the forward-end training sequence, y r The received signal form of the reverse head training sequence, y x This is the received signal format for the information sequence, and the received signal is represented in another way as:

[0139] y = y p +y x +G

[0140] =y f +y r +y x +G

[0141] The training sequence perturbation at the end of the positive equalization can be expressed as:

[0142]

[0143] The training sequence at the end of the forward equalization is eliminated using the following formula:

[0144]

[0145] This achieves a positive elimination process for superimposed training sequences.

[0146] After completely eliminating the forward superimposed training sequences, symbol detection is then performed on the information symbols at positions NM < n ≤ N. This completes the detection of all forward information symbols, yielding the desired result.

[0147] Figure 2 This is a frame structure diagram of bidirectionally superimposed training sequences. Taking forward adaptive equalization as an example, the training sequence at the beginning of the frame structure is used to train the equalizer, while the training sequence at the end of the frame structure is the interference part that needs to be eliminated in forward equalization. The information sequence part is used for adaptive channel estimation. The diagram also shows the result after interference elimination of the training sequence after forward equalization.

[0148] Then, a reverse stacking training sequence interference removal process is performed. The removal process is similar to the forward process, except that the training sequence used is a time-reversed form of p(n). The training sequence perturbation of the reverse-equalized head can be represented as:

[0149]

[0150] The training sequence of the head during reverse equalization is eliminated using the following formula:

[0151]

[0152] The above equation illustrates the elimination process of the head training sequence in reverse equalization, where This is the time-reversed form of the received signal y. For y x Time reversal form, This is the time-reversed form of G. Through this method, ... Figure 2 The training sequence in the middle head is eliminated, and then information symbol detection is performed. The detection results are then time-reversed to obtain...

[0153] Next, and Perform joint generation of the bidirectional joint result Furthermore, sequences with M < n ≤ NM are combined with the already balanced information sequences at the head and tail. Let... and The information sequence portions, which are the head, tail, and training sequence superimposed respectively, result in the following final result:

[0154]

[0155] Among them and The process of combining the outputs employs a weighted combination of the forward adaptive equalization output and the reverse adaptive equalization output:

[0156]

[0157] Where: n=1,…,N; α is a weighting factor, 0≤α≤1; It is the output signal of positive adaptive equalization; It is a time-reversed form of the inverse adaptive equalization output signal.

[0158] Step 4: Decode z and reconstruct the decoded result to obtain the reconstructed result after bidirectional joint decoding. by As input, return to step 2 to re-perform adaptive equalization processing of the multi-channel received signal, wherein the forward training process in the training phase is based on... The labels used as the output of the positive adaptive channel equalization are used for training, and the reverse training process is as follows: The labels used as the output of the reverse adaptive channel equalization are used for training; where for A time-reversed sequence.

[0159] The reason for using the reconstruction result here is As input, we return to step 2 to re-perform adaptive equalization of the multi-channel received signal because during the first equalization, due to the lack of prior information, we cannot use the reconstruction of information symbols and the soft information results of Turbo equalization to improve the accuracy of channel estimation and interference cancellation. After obtaining the reconstruction results, we can use the reconstruction results to further improve the accuracy of channel estimation, and send the soft symbols into the equalizer. Then, combined with the channel matrix obtained from channel estimation, we can perform interference cancellation on the superimposed training sequence. Through iteration, we can gradually improve the accuracy of channel estimation.

[0160] This embodiment also applies Turbo iterative equalization to the adaptive equalization of bidirectional superimposed training sequences, further improving the performance of the underwater acoustic communication system. The bidirectional joint result is demapped, and the extrinsic information L is obtained using Bayes' theorem. e (b n,j Subtract the prior LLR from the posterior log-likelihood ratio (LLR):

[0161]

[0162] External Information L e (b n,j The two parameters in ) can be solved in the following way:

[0163]

[0164] in:

[0165]

[0166] The external mean and variance are:

[0167]

[0168] in: for A firm verdict.

[0169] By combining the above equations, we can obtain the expression for the external information. Then, we deinterweave the external information to obtain the soft information result L. D (b i',j' Then, through interleaving, L(b) is obtained. i,j Finally, L(b) i,j The symbol is mapped to a soft symbol and used as input for the next iteration.

[0170] Figure 1 and Figure 2 These are the frame structure diagrams of the transmitted signal of the underwater acoustic communication system and the frame structure diagram of the bidirectional superimposed training sequence. Figure 1 The bidirectional superimposed training sequence in the transmission signal frame structure is that a training sequence of length M is superimposed on both ends of the information sequence. Figure 2 Taking forward adaptive equalization as an example, the training sequence at the beginning of the frame structure is used to train the equalizer, while the training sequence at the end of the frame structure is the interference part that needs to be eliminated in forward equalization, and the information sequence part is used for adaptive channel estimation. The figure also shows the result after interference elimination of the training sequence after forward equalization.

[0171] Figure 3 This is a block diagram of the overall structure of a two-way DFE (Digital Equalization Module). This structure combines time reversal technology with adaptive equalization technology, and includes two equalization modules: one for forward and one for reverse. Figure 3 Positive adaptive equalization module ( Figure 3 The lower part performs routine processing on the received signal; the reverse adaptive equalization module ( Figure 3 The system first performs a time-reversal operation on the received signal, followed by equalization. Then, the results of the bidirectional equalization are jointly processed, and the joint output is demapped, deinterleaved, and decoded. Afterward, the reconstructed signal is used to further optimize the system through an iterative mechanism. This bidirectional joint processing and iterative mechanism can improve the anti-interference performance and transmission reliability of the underwater acoustic communication system.

[0172] Figure 4 The result shows the bit error rate corresponding to the power ratio of the information sequence and the training sequence. The horizontal axis represents the power ratio from 0 to 1, and the vertical axis represents the bit error rate. The results show that the power ratio decreases from 0 to 0.6, and the bit error rate drops to 0 when the power ratio of the information sequence to the training sequence is 0.6, 0.7, and 0.8.

[0173] Figure 5 and Figure 6 The comparison of bit error rates between the traditional method and the superposition training method is shown under the conditions of weak channel time-varying and strong channel time-varying, respectively. Figure 5 The example shown is for underwater acoustic channels with weak time-varying characteristics (e.g., the channel's impulse response). Figure 7 As shown in the figure, the bit error rate of the traditional insertion training sequence method and the superposition training sequence method are compared. As can be seen from the figure, the bit error rate of the bidirectional superposition training sequence method is lower than that of the traditional insertion training sequence method. The underwater acoustic communication performance is significantly better than that of the traditional method, and the bit error rate of the bidirectional superposition training sequence method shows a downward trend. Figure 6 For underwater acoustic channels with strong time-varying characteristics (e.g., the channel's impulse response), Figure 8 As shown in the figure, the bit error rate comparison between the traditional insertion training sequence and the superposition training sequence method is presented. Even with the strong time-varying nature of the underwater acoustic channel, the superposition training sequence method still exhibits better communication performance. Simulation results demonstrate the effectiveness of the proposed algorithm.

[0174] Figure 9 To compare the bit error rate (BER) results for different iteration counts, the simulation was set up with three iterations (iter=1, iter=2, iter=3). As shown in the figure, the BER decreases with increasing iteration count, reaching its lowest value when the iteration count is 3. This demonstrates that using signal reconstruction techniques for channel estimation combined with receiver Turbo iterative equalization can effectively improve the transmission performance of underwater acoustic communication systems.

[0175] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A time-domain adaptive equalization method based on bidirectional superposition of training sequences, characterized in that: Includes the following steps: Step 1: The underwater acoustic communication system transmitter transmits a transmission signal superimposed with a training sequence. In the transmission signal, the training sequence is linearly superimposed at the beginning and end of the information sequence. Step 2: The underwater acoustic communication system receiver receives the received signal containing the training sequence and the information sequence; when the equalizer of the underwater acoustic communication system is in training mode, the forward equalizer and the reverse equalizer are trained respectively. After training, when the equalizer of the underwater acoustic communication system is in decision mode, it performs forward adaptive channel equalization on the received signals of multiple channels, and performs time reversal processing on the received signals before performing reverse adaptive channel equalization; at the same time, it uses the result of adaptive channel equalization to perform adaptive channel estimation symbol by symbol. Step 3: Use the channel matrix to perform superposition training sequence interference cancellation and symbol detection to obtain the forward and reverse output results; combine the forward and reverse output results bidirectionally, and combine the combined result with the equalized information sequence parts at the beginning and end to obtain the final output result; The specific process of using the channel matrix to superimpose training sequence interference cancellation is as follows: First, perform symbol-by-symbol interference removal on the training sequence at the end of the positive sequence: Since the received signal contains superimposed training sequences, the interference of the training sequences is eliminated symbol by symbol in the time domain: First, interference is canceled at the tail of the positive received signal, and then the information sequence at the tail is equalized; assuming This is a receiving format for bidirectional superimposed training sequences. , This is the received signal form of the forward-ending training sequence. This is the received signal format of the reverse head training sequence. This is the received signal format for the information sequence, and the received signal is represented in another way as: Where G is the Gaussian white noise of the channel; Perturbation of the training sequence at the end of positive equalization It can be represented as: in This represents the channel matrix corresponding to the forward channel impulse response; Represents the training sequence; The training sequence at the end of the forward equalization is eliminated using the following formula: This achieves a positive elimination process for superimposed training sequences; After completely eliminating the positively stacked training sequences, then... The information symbols at each location are subjected to symbol detection. This completes the detection of all positive information symbols, resulting in... ; Then, an inverse stacking training sequence interference cancellation process is performed, using the following training sequence: Time Reversal Form Training sequence interference of the reverse-equalized head Represented as: in This represents the channel matrix corresponding to the reverse channel impulse response; The training sequence of the head during reverse equalization is eliminated using the following formula: in To receive signals Time reversal form, for Time reversal form, for The time-reversed form; then, through information symbol detection, and time-reversing the detection result, we obtain... ; Step 4: Decode the output obtained in Step 3 and reconstruct the decoded result to obtain the reconstructed result after bidirectional joint decoding; use the reconstructed result as input to return to Step 2 to re-perform adaptive equalization processing on the multi-channel received signal until the received signal is processed.

2. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 1, characterized in that: In step 1, the transmitted signal is represented as in: For the sequence of information to be transmitted, ; For training sequences; This represents the power ratio between the training sequence and the symbol sequence.

3. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 2, characterized in that: In step 2, the underwater acoustic communication system receiver receives a signal with superimposed training sequences. Represented as: in: Represents the channel gain matrix. This represents the Gaussian white noise of the channel.

4. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 1, characterized in that: Step 2 involves adaptive equalization processing of the multi-channel received signals, which includes two working modes: training mode and decision mode. In training mode, i.e. In this phase, the forward equalizer and the reverse equalizer are trained separately. The positive training process is as follows: With training sequences The labels are used as the output of the positive adaptive channel equalization for training: For The forward feedforward filter coefficients and feedback filter coefficients at time 1 are used to obtain the output of the forward adaptive channel equalization through an equalizer. And thus with tags Obtaining error By using iterative formulas for the feedforward filter coefficients and the feedback filter coefficients, we obtain... The forward and feedback filter coefficients are updated continuously until the forward training is complete; The reverse training process is as follows: The training sequence after time reversal operation The labels are used as the output of the reverse adaptive channel equalization for training: for The inverse feedforward filter coefficients and feedback filter coefficients at time 1 are used to obtain the output of the inverse adaptive channel equalization through an equalizer. And thus with tags Obtaining error By using iterative formulas for the feedforward filter coefficients and the feedback filter coefficients, we obtain... The feedforward filter coefficients and feedback filter coefficients are reversed at every moment until reverse training is completed; The iterative formulas for the feedforward filter coefficients and the feedback filter coefficients are as follows: in: and These are the coefficients of the feedforward and feedback filters, respectively. and These are the step sizes for the feedforward and feedback filters, respectively. This is a regularization constant to prevent the denominator from being equal to 0; For error The adjoint matrix; This is the input signal to the feedback filter; For time n, the first... Each channel input signal Energy.

5. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 4, characterized in that: In step 2, under the decision mode, that is In the next stage, symbol detection is performed, and while the symbol detection is completed, the symbol-by-symbol channel estimation is performed using the symbol detection results to obtain the channel matrix at the corresponding time. Adaptive channel equalization is further divided into forward equalization and reverse equalization; The forward equalization process involves directly using the received signal to perform symbol detection based on the feedforward filter coefficients and feedback filter coefficients obtained through forward training. The reverse equalization process involves performing a time reversal operation on the received signal, and then using the reversed received signal to perform symbol detection based on the feedforward filter coefficients and feedback filter coefficients obtained through reverse training.

6. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 5, characterized in that: In step 3, the forward and reverse outputs are combined bidirectionally, and the combined result is then combined with the balanced information sequence at the beginning and end to obtain the final output. Will and The process of combining the outputs employs a weighted combination of the forward adaptive equalization output and the reverse adaptive equalization output: in: ; It is a weighting factor. ; It is the output signal of positive adaptive equalization; It is a time-reversed form of the inverse adaptive equalization output signal; Then Combining this with the balanced information sequence at the beginning and end, the final result is: in and These are the information sequence parts that are superimposed on the head and tail of the training sequence, respectively.

7. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 6, characterized in that: In step 4, the output results obtained in step 3 are processed. Decode the code and reconstruct the result to obtain the reconstructed result of the bidirectional joint decoding. ;by As input, return to step 2 to re-perform adaptive equalization processing of the multi-channel received signal, wherein the forward training process in the training phase is based on... The labels used as the output of the positive adaptive channel equalization are used for training, and the reverse training process is as follows: The labels used as the output of the reverse adaptive channel equalization are used for training; where for A time-reversed sequence.

8. The time-domain adaptive equalization method based on bidirectional superposition training sequences according to claim 1, characterized in that: In step 4, Turbo iterative equalization is also applied to the adaptive equalization of the bidirectional superimposed training sequences to further improve the performance of the underwater acoustic communication system.

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