Time-frequency two-dimensional soft decision feedback equalization method based on vector approximate message passing

Abstract

The invention discloses a time-frequency two-dimensional soft decision feedback equalization method based on vector approximation message passing. The method comprises the following steps: S1, dividing a time domain data block into B sub-blocks containing overlapped symbols; s2, step-by-step equalization is carried out on the bth sub-block, frequency domain equalization is carried out based on soft frequency domain equalization of vector approximation message transmission in each cycle, then time domain equalization is carried out, and b = 1, 2, 3,..., B; s3, the step S2 is executed repeatedly until step-by-step equalization of all the sub-blocks is completed, and one time of Turbo equalization iteration is completed; and S4, repeatedly executing the steps S2-S3 until a preset Turbo iteration number is reached. Through a two-stage structure of frequency domain block-level pre-equalization and time domain symbol-level fine equalization, and in combination with overlapped sub-block processing, robustness and equalization performance under a strong time-varying channel in underwater acoustic communication are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication, and in particular to a time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing. Background Technology

[0002] The variable and complex marine environment poses a severe challenge to underwater acoustic communication. The recursive least squares decision-feedback equalization (RLS-DFE) algorithm is one of the core algorithms in aquatic communication systems. It can converge quickly in adaptive filter updates, but its high computational complexity limits its application in long-delay extended channels. It is necessary to reduce the computational complexity by improving the filter structure or to reduce the order of the RLS filter by channel shortening techniques.

[0003] In recent years, approximate message passing (AMP) and its generalized form, soft equalizer (GAMP), have been proposed and widely used to improve the equalization performance of single-carrier communication systems. These methods achieve approximate minimum mean square error (MMSE) equalization through iterative message passing, exhibiting good performance under certain conditions. However, the AMP and GAMP algorithms heavily rely on the statistical properties of the linear transformation matrix, guaranteeing strict convergence only when the transformation matrix is ​​a zero-mean, small-variance Gaussian matrix. In practical underwater acoustic communication scenarios, the channel matrix rarely satisfies this assumption, leading to poor algorithm robustness, especially with significant performance degradation in highly time-varying channels. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing.

[0005] The specific technical solution is as follows: A time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing includes the following steps: S1: Divide the received time-domain data block into B sub-blocks of length N, each containing overlapping symbols. ov / 2 forward overlap region and backward overlap region; S2: Perform step-by-step equalization on the b-th sub-block, with T iterations. In each iteration, frequency domain equalization is performed first to shorten the channel, followed by time domain equalization. The head index of the current sub-block after time domain equalization coincides with the tail index of the previous sub-block after time domain equalization. b = 1, 2, 3, ..., B. The frequency domain equalization is based on soft frequency domain equalization using vector approximation message passing, and it undergoes self-iteration internally. S3: Determine whether all sub-blocks have completed step-by-step balancing. If not, proceed to the next sub-block in sequence with S2; if yes, complete one Turbo balancing iteration. S4: Determine whether the preset number of Turbo iterations has been reached. If not, repeat S2-S3. If yes, end the balancing iteration.

[0006] Furthermore, in S2, the starting index of the frequency domain equalization of the b-th sub-block in the first iteration. End of index and the starting index for time-domain equalization. End of index The expression is as follows: The starting index for frequency domain equalization in the second iteration of the b-th sub-block. End of index and the starting index for time-domain equalization. End of index The expression is as follows: The starting and ending indices for subsequent iterations are calculated in the same way as above.

[0007] Furthermore, in step S2, frequency domain equalization is achieved through soft frequency domain equalization based on vector approximation message passing, specifically through the following sub-steps: (2.1.1) Channel estimation of the received signal: The first loop of the first sub-block uses the known training sequence for channel estimation; when b≥2, if the current loop number t=1, the equalization result of the Tth loop of the (b-1)th sub-block is used to estimate the channel of the b-th sub-block, and the sub-block forgetting factor is introduced to update the channel estimate value with weight; if t≥2, the equalization result of the (t-1)th loop of the b-th sub-block is used to estimate the channel, and the sub-block forgetting factor is introduced to update the channel estimate value with weight. (2.1.2) Perform a discrete Fourier transform on the received signal to achieve frequency domain conversion; (2.1.3) Input the frequency domain converted signal into the VAMP-SFDE equalizer. The VAMP-SFDE equalizer includes an internal soft equalizer ISE and an internal soft decision unit ISS. The ISE and ISS are iterated K times to achieve frequency domain equalization. The ISE performs frequency-domain linear minimum mean square error equalization, calculating the posterior mean based on the extrinsic information parameters provided by the ISS during the k-th internal iteration, k=1,2,3,…,K. and inverse variance During the initialization of the first internal iteration, the extrinsic information parameters provided by the ISS are zero; based on the posterior mean... and inverse variance Calculate the external information parameters transmitted from ISE to ISS. and ; (2.1.4) Calculate the external prior probability based on the decoder information from the previous Turbo equalization iteration; (2.1.5) The ISS obtains the prior probability information of each symbol based on the external prior probability and the extrinsic information parameters transmitted by the ISE to the ISS during the k-th internal iteration; the prior probability information is normalized to obtain the normalized prior probability; and the posterior mean is calculated based on the normalized prior probability. and its inverse variance According to the posterior mean and its inverse variance Calculate the external information parameters transmitted from the ISS to the ISE. and ; (2.1.6) Repeat steps (2.1.3)-(2.1.5) to perform internal iterations of ISE and ISS until the number of internal iterations satisfies k=K, at which point the internal iteration ends; (2.1.7) Discard the error data of the overlapping part so that the result of the Kth internal iteration is consistent with the input of the equalizer used for time domain equalization, and obtain the pre-equalization result of VAMP-SFDE.

[0008] Further, in step (2.1.1), the expression for weighted updating of the channel estimate by introducing the sub-block forgetting factor is as follows: In the formula, This represents the weighted update value of the channel estimate for the b-th sub-block. Here, μ is the channel tap index, and μ is the sub-block forgetting factor. This represents the channel estimate for the b-th sub-block; The sub-block forgetting factor μ is based on Doppler frequency shift. The expression has been adjusted as follows: Doppler shift The expression is as follows: In the formula, ρ b-1,b This represents the channel correlation between the (b-1)th sub-block and the b-th sub-block, where N is the length of the sub-block. ov It is the sum of the lengths of the forward overlapping region and the backward overlapping region.

[0009] Furthermore, in step (2.1.3), the posterior mean and inverse variance The expression is as follows: In the formula, This represents the extrinsic information parameter transmitted from the ISS to the ISE, which is related to the posterior mean during the k-th internal iteration. (Initialization) It is a vector consisting entirely of zeros; This represents the extrinsic information parameter transferred from the ISS to the ISE related to the inverse variance during the k-th internal iteration, initialized... =0; k=1,2,3,…,K; The signal after frequency domain conversion. , It is a diagonal matrix. It is the discrete Fourier transform matrix. This is the noise vector; The external information parameters transmitted by the ISE to the ISS and The expression is as follows: In the formula, This represents the ISE information parameter related to the posterior mean at the k-th inner iteration. This represents the ISE information parameter associated with the inverse variance during the k-th internal iteration.

[0010] Furthermore, in step (2.1.4), the expression for the external prior probability is as follows: In the formula, Let M represent the i-th constellation point, and M be the number of bits corresponding to each constellation point. Representing constellation points The corresponding q-th bit, Representing data The corresponding q-th bit, This represents prior information obtained from the decoder in the previous Turbo equalization iteration; In step (2.1.5), the prior probability information expression for each symbol is: In the formula, Represents the external prior matrix The element in the nth row and i-th column; The prior probability information is normalized, and the posterior mean is calculated accordingly. and its inverse variance : In the formula, P(x n =α i ) represents the normalized prior probability; The external information parameters transmitted by the ISS to the ISE and The calculation expression is as follows: In the formula, This represents the ISS information parameter related to the inverse variance at the (k+1)th internal iteration. This represents the ISS information parameter related to the posterior mean during the (k+1)th internal iteration.

[0011] Further, in step (2.1.7), the pre-equilibrium result expression of VAMP-SFDE is as follows: In the formula, The symbol vector is obtained from frequency domain pre-equalization, and N is the length of the sub-block. ovIt is the sum of the lengths of the forward overlapping region and the backward overlapping region.

[0012] Furthermore, in S2, the time-domain equalization is implemented based on a decision feedback equalizer using the recursive least squares method, as shown in the following expression: In the formula, The symbol represents the result after time-domain equalization. This represents a portion of the symbol vector after frequency domain pre-equalization. a subset of This represents the compensation phase angle, used to compensate for Doppler frequency shift; Represents the feedforward filter coefficients. The length of the feedforward filter; Represents the feedback filter coefficients. The length of the feedback filter, Represents the set of historical decision symbols; N is the length of the sub-block, N ov It is the sum of the lengths of the forward overlap region and the backward overlap region. For phase compensation coefficients, R represents the sign-level phase rotation angle obtained through interpolation. s Indicates symbol rate, This represents the output of the phase-locked loop for the nth symbol.

[0013] A time-frequency two-dimensional soft-decision feedback equalization system based on vector approximation message passing is used to implement the time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing, comprising: an overlapping sub-block partitioning module, a VAMP-SFDE module, an RLS-DFE module, and a Turbo decoder; The overlapping sub-block partitioning module is used to divide the time-domain data into B sub-blocks containing overlapping symbols; The VAMP-SFDE module is used to implement the frequency domain equalization function in each cycle during the sub-block step equalization process; The RLS-DFE module is used to implement the time-domain equalization function in each cycle during the sub-block step-by-step equalization process; The Turbo decoder is used to provide feedback of prior information and reduce the bit error rate during iterative interaction with the VAMP-SFDE module.

[0014] The beneficial effects of this invention are: (1) The VAMP-SFDE part of the present invention achieves the optimal balance between internal and external information through self-iteration, laying a high-precision signal foundation for subsequent symbol-level equalization.

[0015] (2) The present invention uses VAMP-SFDE for block-level pre-equalization, which greatly shortens the channel length that RLS-DFE needs to process, and achieves more refined symbol-level equalization with low complexity. Attached Figure Description

[0016] Figure 1 This is a flowchart of a time-frequency two-dimensional soft decision feedback equalization method based on vector approximation message passing in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the overlapping sub-block structure and the gradual balancing process in an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram illustrating channel estimation for the b-th sub-block under different conditions in embodiments of the present invention.

[0019] Figure 4 This is a signal flow diagram of the VAMP-SFD-DFE iterative receiver in an embodiment of the present invention.

[0020] Figure 5 These are channel impulse response diagrams under different time-varying environments in embodiments of the present invention, wherein (a) is a channel impulse response diagram under a weak time-varying environment, and (b) is a channel impulse response diagram under a strong time-varying environment.

[0021] Figure 6 These are relationship curves of the error rate (BER) and signal-to-noise ratio (SNR) of different equalization algorithms under different time-varying environments in the embodiments of the present invention. Among them, (a) is the relationship curve under weak time-varying environment and (b) is the relationship curve under strong time-varying environment. Detailed Implementation

[0022] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0023] like Figure 1 As shown, a time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing (VAMP-SFD-DFE) includes the following steps: S1: Divide the received time-domain data block into B sub-blocks containing overlapping symbols. Each sub-block includes a forward overlap region and a backward overlap region. The length of each sub-block is N, and the length of the overlap with adjacent sub-blocks is also N. ov / 2, meaning that for the b-th sub-block (b=1,2,3,…,B), the length of the forward overlap region with the (b-1)-th sub-block is N. ov / 2, the length of the backward overlap region with the (b+1)th sub-block is N. ov / 2; Specifically, the first sub-block does not have a predecessor sub-block and only includes the backward overlap region.

[0024] S2: Perform step-by-step equalization on the b-th sub-block. Let T be the number of iterations for step-by-step equalization (T≥2). In the t-th iteration (t=1,2,3,…,T), frequency domain equalization is performed first, followed by time domain equalization. The head index of the b-th sub-block after time domain equalization coincides with the tail index of the (b-1)-th sub-block after time domain equalization. When t=T, the equalization of the current sub-block ends, and the equalization result of the T-th iteration is taken as the final result of the step-by-step equalization for that sub-block.

[0025] like Figure 2 As shown, since the first sub-block has no predecessor sub-block, forward interference does not need to be considered. During the iteration process, the starting index of the frequency domain equalization and the time domain equalization remains unchanged, and only the ending index is changed (the change rule is the same as below). In this embodiment, T=2 is taken, and the equalization range of the b-th sub-block in the t-th cycle is as follows: The starting index for frequency domain equalization at t=1. End of index and the starting index for time-domain equalization. End of index The expression is as follows: The starting index for frequency domain equalization at t=2. End of index and the starting index for time-domain equalization. End of index The expression is as follows: When T is greater than 2, the starting and ending indices of subsequent iterations are calculated in the same way as above.

[0026] S2 is implemented through the following sub-steps: S2.1: After converting the received signal into a frequency domain signal, perform soft frequency-domain equalizer based on the vector approximate message passing (VAMP-SFDE) on each sub-block to shorten the channel. This is achieved through the following sub-steps: (2.1.1) As Figure 3 As shown, channel estimation is performed on the received signal. In the first cycle of the first sub-block (i.e., b=1, t=1), channel estimation is performed using the known training sequence. When b≥2, if t=1, the equalization result of the Tth cycle of the previous sub-block (the (b-1)th sub-block) is used to perform channel estimation on the current sub-block (the b-th sub-block), obtaining the channel estimate value for the current sub-block. If t≥2, channel estimation is performed using the equalization result of the (t-1)th cycle of the current sub-block.

[0027] Independent channel estimation leads to a large mean square error in subsequent RLS-DFE at the beginning of each sub-block. To mitigate this inconsistency, a sub-block forgetting factor μ is introduced to weight the channel estimation for updates: In the formula, This represents the weighted update value of the channel estimate for the b-th sub-block. For channel tap index, This represents the channel estimate for the b-th sub-block.

[0028] The choice of the sub-block forgetting factor μ should be adjusted according to the Doppler frequency shift: when the Doppler frequency shift is small, a larger value is required. To ensure real-time channel tracking; conversely, a larger Doppler shift reduces channel correlation between sub-blocks, thus exacerbating inconsistencies after channel shortening. Different normalized Doppler shifts The empirical formula for the value of μ is as follows: Normalized Doppler frequency shift The channel correlation ρ between the (b-1)th sub-block and the b-th sub-block can be obtained. b-1,b The calculation yields the following formula: This invention employs overlapping block processing and introduces a sub-block forgetting factor for weighted channel estimation updates, which enhances the robustness of channel non-stationary states and reduces inconsistencies between sub-blocks. The algorithm can effectively adapt to rapid channel changes.

[0029] (2.1.2) The channel model of the received signal can be represented in matrix form: In the formula, Represents the observed signal vector. , This represents the channel matrix constructed from the channel impulse response. ; Represents the noise vector. , Represents the variance of the noise signal. Represents the identity matrix.

[0030] Channel matrix It can be decomposed into ,in It is a DFT matrix, and its first... line, number Column elements .

[0031] Performing a Discrete Fourier Transform (DFT) operation on the received signal and applying the DFT matrix F to the channel model yields the following frequency domain model: In the formula, It is The result of performing a DFT transformation; It is a diagonal matrix; It is the noise vector The result of the DFT transformation, and Follow and Same steps; Given a channel impulse response of length N, the channel impulse response is... Padding with zeros gives it a length of N.

[0032] (2.1.3) The signal after frequency domain transformation The input VAMP-SFDE equalizer consists of an inner soft equalizer (ISE) and an inner soft slicer (ISS). The ISE and ISS undergo K iterations to achieve frequency domain equalization.

[0033] The internal soft equalizer (ISE) performs frequency domain linear minimum mean square error (LMMSE) equalization and calculates the posterior mean. and inverse variance : In the formula, This represents the extrinsic information parameter (hereinafter referred to as ISS information parameter) that is related to the posterior mean at the k-th internal iteration and is transmitted from the ISS to the ISE. Initialization It is a vector consisting entirely of zeros; This represents the ISS information parameter related to the inverse variance during the k-th internal iteration, initialized... =0; k=1,2,3,…,K.

[0034] like Figure 4 As shown, the posterior mean obtained using equilibrium is... and inverse variance Calculate the extrinsic information parameters used for internal iteration, i.e., the extrinsic information parameters transmitted by the ISE to the ISS (hereinafter referred to as ISE information parameters): In the formula, This represents the ISE information parameter related to the posterior mean at the k-th internal iteration. This represents the ISE information parameter associated with the inverse variance during the k-th internal iteration.

[0035] (2.1.4) In Turbo equilibrium, the external prior probability is calculated based on the decoder information from the previous Turbo equilibrium iteration, as shown in the following expression: In the formula, This represents the i-th constellation point. The number of bits corresponding to each constellation point. Representing constellation points The corresponding q-th bit, Representing data The corresponding q-th bit, This represents prior information obtained from the decoder in the previous Turbo iteration.

[0036] Specifically, during the first Turbo balancing iteration, it is assumed that the probabilities of each constellation point are equal, and the probability of each constellation point is... .

[0037] (2.1.5) The Internal Soft Decision Controller (ISS) integrates the external prior probability and the ISE information parameters generated in the k-th internal iteration to obtain the prior probability information for each symbol: In the formula, Represents the external prior probability matrix The element in the nth row and ith column.

[0038] The prior probability information is normalized to obtain the normalized prior probability: Calculate the posterior mean based on the normalized prior probabilities. and its inverse variance : Using the posterior mean obtained from equilibrium and inverse variance Calculate the extrinsic information parameters used for internal iteration, i.e., the extrinsic information parameters transmitted from the ISS to the ISE (hereinafter referred to as ISS information parameters): In the formula, This represents the ISS information parameter related to the inverse variance during the (k+1)th (i.e., the next) internal iteration. This represents the ISS information parameter related to the posterior mean during the (k+1)th internal iteration.

[0039] (2.1.6) Repeat steps (2.1.3)-(2.1.5) to perform internal iterations of ISE and ISS until the number of internal iterations satisfies k=K, at which point the internal iteration ends.

[0040] (2.1.7) During the block equalization process, the overlapping block strategy can lead to large errors at both ends of the data block, and these erroneous data need to be discarded. Therefore, the result of the last internal iteration of VAMP-SFDE must be consistent with the input of the equalizer used for time-domain equalization in the following section. After discarding the erroneous data, the pre-equalization result of VAMP-SFDE is as follows: In the formula, This is the symbol vector obtained from frequency domain pre-equalization.

[0041] S2.2: Input the VAMP-SFDE pre-equalization result into the decision-feedback equalization based on recursive least squares (RLS-DFE) for symbol-level equalization. The specific operation is as follows: The calculation expression for the general DFE model is as follows: In the formula, The symbol represents the result after time-domain equalization. This represents a portion of the symbol vector after frequency domain pre-equalization. a subset of This represents the compensation phase angle, used to compensate for Doppler frequency shift; Represents the feedforward filter coefficients. This is the length of the feedforward filter; Represents the feedback filter coefficients. The length of the feedback filter, A set of symbols representing historical judgments.

[0042] In this embodiment, the complexity of the RLS-DFE equalization algorithm is significantly reduced after VAMP-SFDE pre-equalization. When applied to intra-block equalization, it is necessary to compensate for the phase rotation caused by Doppler frequency shift. In the general model, the feedforward equalization result is... In this embodiment, the input symbol is output based on the phase-locked loop of the first symbol. Phase shift adjustment is performed to obtain the improved feedforward equalization result. The expression is: In the formula, For phase compensation coefficients, R represents the sign-level phase rotation angle obtained through interpolation. s Indicates symbol rate, This represents the output of the phase-locked loop for the nth symbol.

[0043] The symbolic expression for the improved time-domain equalization is: .

[0044] S2.3: Repeat S2.1 and S2.2 until T loops are completed, and the step-by-step equalization of the current sub-block is completed. The equalization result is directly input to the decoder, and the decoder output is used as the final value of the equalization iteration of this sub-block (and is also part of the final value of this Turbo equalization iteration).

[0045] S3: Determine whether all sub-blocks have completed step-by-step balancing. If not, execute S2 sequentially for the next sub-block. If yes, complete one Turbo balancing iteration.

[0046] S4: Determine whether the preset number of Turbo iterations has been reached. If not, repeat S2-S3. If yes, end the balancing iteration.

[0047] To realize the above-mentioned time-frequency two-dimensional soft decision feedback equalization method based on vector approximation message passing, this embodiment also proposes a time-frequency two-dimensional soft decision feedback equalization system based on vector approximation message passing. The system includes: an overlapping sub-block partitioning module, a VAMP-SFDE module, an RLS-DFE module, and a Turbo decoder; the VAMP-SFDE module includes: an internal soft equalizer ISE and an internal soft decision equalizer ISS.

[0048] The overlapping sub-block partitioning module is used to divide time-domain data into B sub-blocks containing overlapping symbols.

[0049] The VAMP-SFDE module is used to implement frequency domain equalization in each cycle of the sub-block step equalization process.

[0050] The RLS-DFE module is used to implement time-domain equalization in each cycle of the sub-block step-by-step equalization process.

[0051] The Turbo decoder is used to provide feedback of prior information and reduce the bit error rate during iterative interaction with the VAMP-SFDE module.

[0052] like Figure 5 As shown, weak time-varying and strong time-varying environments were constructed for simulation experiments. The maximum drift velocity of the weak time-varying channel was 0.05 m / s, and the delay spread was 17.6 ms; the maximum drift velocity of the strong time-varying channel reached 0.5 m / s, and the delay spread was 26.8 ms.

[0053] Figure 6The diagram illustrates the relationship between the bit error rate (BER) and signal-to-noise ratio (SNR) of the proposed VAMP-SFD-DFE algorithm, the existing VAMP-SFDE algorithm (incorporating semi-adaptive damping, SAD, i.e., SAD-VAMP-SFDE in the figure), the SFD-DFE algorithm, and the RLS-DFE algorithm under both weakly and strongly time-varying environments. Under weakly time-varying channel conditions, the proposed VAMP-SFD-DFE algorithm significantly reduces the BER by 36.8%, 47.9%, and 85.3% compared to SFD-DFE, SAD-VAMP-SFDE, and RLS-DFE, respectively, at a SNR of 23 dB. Under highly time-varying channel conditions, the RLS-DFE algorithm exhibits a high error rate of approximately 50%, leading to the inability to correctly decode or recover transmitted information. At a signal-to-noise ratio of 23 dB, the proposed VAMP-SFD-DFE algorithm significantly reduces the error rate by 41.2% and 60.1% compared to SFD-DFE and SAD-VAMP-SFDE, respectively. These simulation results demonstrate that the proposed VAMP-SFD-DFE algorithm outperforms existing related methods in overall equalization performance, proving the effectiveness of this invention.

[0054] To address the challenges of highly time-varying underwater environments while reducing computational complexity, this invention proposes a time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing. First, a sub-block forgetting factor is introduced for weighted channel estimation updates, mitigating inconsistencies between sub-blocks and enabling the algorithm to effectively adapt to rapid channel changes. An overlapping sub-block partitioning design suppresses inter-block interference while creating conditions for progressively finer equalization. The invention innovatively constructs a time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing, utilizing VAMP-SFDE for channel shortening to reduce the partial equalization complexity of RLS-DFE. Simultaneously, a phase-locked loop is combined to compensate for phase rotation caused by Doppler frequency shift, achieving more refined symbol-level equalization.

[0055] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing, characterized in that, Includes the following steps: S1: Divide the received time-domain data block into B sub-blocks of length N, each containing overlapping symbols. ov / 2 forward overlap region and backward overlap region; S2: Perform step-by-step equalization on the b-th sub-block, with T iterations. In each iteration, frequency domain equalization is performed first to shorten the channel, followed by time domain equalization. The head index of the current sub-block after time domain equalization coincides with the tail index of the previous sub-block after time domain equalization. b = 1, 2, 3, ..., B. The frequency domain equalization is based on soft frequency domain equalization using vector approximation message passing, and it undergoes self-iteration internally. S3: Determine whether all sub-blocks have completed step-by-step balancing. If not, proceed to the next sub-block in sequence with S2; if yes, complete one Turbo balancing iteration. S4: Determine whether the preset number of Turbo iterations has been reached. If not, repeat S2-S3. If yes, end the balancing iteration.

2. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 1, characterized in that, In S2, the starting index of the frequency domain equalization of the b-th sub-block in the first iteration. End of index and the starting index for time-domain equalization. End of index The expression is as follows: The starting index for frequency domain equalization in the second iteration of the b-th sub-block. End of index and the starting index for time-domain equalization. End of index The expression is as follows: The starting and ending indices for subsequent iterations are calculated in the same way as above.

3. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 1, characterized in that, In step S2, frequency domain equalization is achieved through soft frequency domain equalization based on vector approximation message passing, specifically through the following sub-steps: (2.1.1) Channel estimation of the received signal: The first loop of the first sub-block uses the known training sequence for channel estimation; when b≥2, if the current loop number t=1, the equalization result of the Tth loop of the (b-1)th sub-block is used to estimate the channel of the b-th sub-block, and the sub-block forgetting factor is introduced to update the channel estimate value with weight; if t≥2, the equalization result of the (t-1)th loop of the b-th sub-block is used to estimate the channel, and the sub-block forgetting factor is introduced to update the channel estimate value with weight. (2.1.2) Perform a discrete Fourier transform on the received signal to achieve frequency domain conversion; (2.1.3) Input the frequency domain converted signal into the VAMP-SFDE equalizer. The VAMP-SFDE equalizer includes an internal soft equalizer ISE and an internal soft decision unit ISS. The ISE and ISS are iterated K times to achieve frequency domain equalization. The ISE performs frequency-domain linear minimum mean square error equalization, calculating the posterior mean based on the extrinsic information parameters provided by the ISS during the k-th internal iteration, k=1,2,3,…,K. and inverse variance During the initialization of the first internal iteration, the extrinsic information parameters provided by the ISS are zero; based on the posterior mean... and inverse variance Calculate the external information parameters transmitted from ISE to ISS. and ; (2.1.4) Calculate the external prior probability based on the decoder information from the previous Turbo equalization iteration; (2.1.5) The ISS obtains the prior probability information of each symbol based on the external prior probability and the external information parameters transmitted by the ISE to the ISS during the k-th internal iteration; the prior probability information is normalized to obtain the normalized prior probability. Calculate the posterior mean based on the normalized prior probability. and its inverse variance According to the posterior mean and its inverse variance Calculate the external information parameters transmitted from the ISS to the ISE. and ; (2.1.6) Repeat steps (2.1.3)-(2.1.5) to perform internal iterations of ISE and ISS until the number of internal iterations satisfies k=K, at which point the internal iteration ends; (2.1.7) Discard the error data of the overlapping part so that the result of the Kth internal iteration is consistent with the input of the equalizer used for time domain equalization, and obtain the pre-equalization result of VAMP-SFDE.

4. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 3, characterized in that, In step (2.1.1), the expression for weighted updating of the channel estimate by introducing the sub-block forgetting factor is as follows: In the formula, This represents the weighted update value of the channel estimate for the b-th sub-block. Here, μ is the channel tap index, and μ is the sub-block forgetting factor. This represents the channel estimate for the b-th sub-block; The sub-block forgetting factor μ is based on Doppler frequency shift. The expression has been adjusted as follows: Doppler shift The expression is as follows: In the formula, ρ b-1,b This represents the channel correlation between the (b-1)th sub-block and the b-th sub-block, where N is the length of the sub-block. ov It is the sum of the lengths of the forward overlapping region and the backward overlapping region.

5. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 3, characterized in that, In step (2.1.3), the posterior mean and inverse variance The expression is as follows: In the formula, This represents the extrinsic information parameter transmitted from the ISS to the ISE, which is related to the posterior mean during the k-th internal iteration. (Initialization) It is a vector consisting entirely of zeros; This represents the extrinsic information parameter transferred from the ISS to the ISE related to the inverse variance during the k-th internal iteration, initialized... =0; k=1,2,3,…,K; The signal after frequency domain conversion. , It is a diagonal matrix. It is the discrete Fourier transform matrix. This is the noise vector; The external information parameters transmitted by the ISE to the ISS and The expression is as follows: In the formula, This represents the ISE information parameter related to the posterior mean at the k-th inner iteration. This represents the ISE information parameter associated with the inverse variance during the k-th internal iteration.

6. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 3, characterized in that, In step (2.1.4), the expression for the external prior probability is as follows: In the formula, Let M represent the i-th constellation point, and M be the number of bits corresponding to each constellation point. Representing constellation points The corresponding q-th bit, Representing data The corresponding q-th bit, This represents prior information obtained from the decoder in the previous Turbo equalization iteration; In step (2.1.5), the prior probability information expression for each symbol is: In the formula, Represents the external prior matrix The element in the nth row and i-th column; The prior probability information is normalized, and the posterior mean is calculated accordingly. and its inverse variance : In the formula, P(x n =α i ) represents the normalized prior probability; The external information parameters transmitted by the ISS to the ISE and The calculation expression is as follows: In the formula, This represents the ISS information parameter related to the inverse variance at the (k+1)th internal iteration. This represents the ISS information parameter related to the posterior mean during the (k+1)th internal iteration.

7. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 3, characterized in that, In step (2.1.7), the pre-equilibrium result expression of VAMP-SFDE is as follows: In the formula, The symbol vector is obtained from frequency domain pre-equalization, and N is the length of the sub-block. ov It is the sum of the lengths of the forward overlapping region and the backward overlapping region.

8. The time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing according to claim 7, characterized in that, In S2, the time-domain equalization is implemented using a decision feedback equalizer based on the recursive least squares method, as shown in the following expression: In the formula, The symbol represents the result after time-domain equalization. This represents a portion of the symbol vector after frequency domain pre-equalization. a subset of This represents the compensation phase angle, used to compensate for Doppler frequency shift; Represents the feedforward filter coefficients. The length of the feedforward filter; Represents the feedback filter coefficients. The length of the feedback filter, Represents the set of historical decision symbols; N is the length of the sub-block, N ov It is the sum of the lengths of the forward overlap region and the backward overlap region. For phase compensation coefficients, R represents the sign-level phase rotation angle obtained through interpolation. s Indicates symbol rate, This represents the output of the phase-locked loop for the nth symbol.

9. A time-frequency two-dimensional soft-decision feedback equalization system based on vector approximation message passing, used to implement the time-frequency two-dimensional soft-decision feedback equalization method based on vector approximation message passing as described in any one of claims 1-8, characterized in that, include: Overlapping sub-block partitioning module, VAMP-SFDE module, RLS-DFE module, Turbo decoder; The overlapping sub-block partitioning module is used to divide the time-domain data into B sub-blocks containing overlapping symbols; The VAMP-SFDE module is used to implement the frequency domain equalization function in each cycle during the sub-block step equalization process; The RLS-DFE module is used to implement the time-domain equalization function in each cycle during the sub-block step-by-step equalization process; The Turbo decoder is used to provide feedback of prior information and reduce the bit error rate during iterative interaction with the VAMP-SFDE module.

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