Decision feedback equalization method and device for matching pursuit, equipment and storage medium

Abstract

The invention belongs to the technical field of underwater acoustic communication, and relates to a matching pursuit decision feedback equalization method, device and equipment and a storage medium, and the method comprises the steps: initializing system parameters; constructing a training data matrix, and reorganizing the receiving signals of the time sequence and the known training symbols into a matrix form; global information required in the iteration process is pre-calculated and stored according to the training data matrix; carrying out rapid matching pursuit iteration solution, gradually selecting an atom, namely an equalizer tap, which is most related to the current residual error from the dictionary in an iteration mode, and updating the coefficient and the residual error until sparseness constraint is met; mapping a solution obtained on the normalized augmented system back to an original physical equalizer coefficient, and initializing the state of the equalizer; and performing continuous equalization and demodulation on unknown data symbols by using the filter coefficient obtained in the training stage, and recursively eliminating inter-symbol interference. And the stability and the overall performance of the underwater acoustic communication receiver under a complex channel condition are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater acoustic communication, and in particular to a decision feedback equalization method based on matching pursuit, a device, an apparatus and a storage medium. BACKGROUND

[0002] The underwater acoustic channel is a typical frequency selective channel, which has long multipath delay, strong inter-symbol interference (ISI) and time variability. The traditional decision feedback equalization (DFE) relies heavily on accurate channel estimation and lengthy training sequences, which has large computational overhead and poor environmental adaptability. Although the existing sparse matching pursuit algorithm can take advantage of channel sparsity, it often has high computational complexity and is difficult to achieve a good balance between convergence speed and equalization accuracy. SUMMARY

[0003] To solve the above technical problems, the present application provides a decision feedback equalization method based on matching pursuit, which adopts the following technical solution, including the following steps:

[0004] According to the modulation mode adopted by the communication system, the system parameters are initialized;

[0005] A training data matrix is constructed, and the time-series received signal and the known training symbol are reorganized into a matrix form;

[0006] According to the training data matrix, the global information required in the iteration process is pre-calculated and stored;

[0007] According to the global information, fast matching pursuit iteration is solved, that is, in an iterative manner, the atom most related to the current residual error is selected from the dictionary, that is, the equalizer tap, and its coefficient and residual error are updated until the sparsity constraint is met;

[0008] The solution obtained by fast matching pursuit on the normalized augmented system is mapped back to the original physical equalizer coefficient, and the state of the equalizer is initialized;

[0009] The filter coefficient obtained in the training stage is used to continuously equalize and demodulate the unknown data symbol, and the decided symbol is fed back to recursively eliminate the inter-symbol interference.

[0010] Preferably, the step of initializing the system parameters according to the modulation mode adopted by the communication system specifically includes:

[0011] According to the modulation mode adopted by the communication system, the modulation parameters are defined;

[0012] The equalizer structure parameters are configured;

[0013] The sparsity, regularization and training scale parameters are set.

[0014] Preferably, the step of constructing the training data matrix, reorganizing the time-ordered received signal and known training symbols into a matrix form, specifically comprises:

[0015] Constructing input vectors, extracting vectors from the received signal sequence and the decision symbol sequence respectively at each time point n;

[0016] Assembling the training matrix and the target vector, stacking the joint input vectors of multiple time points into the training data matrix, and composing the target symbols of the corresponding time into the target vector;

[0017] Performing system augmentation and regularization.

[0018] Preferably, the step of pre-computing and storing the global information required in the iterative process according to the training data matrix specifically comprises:

[0019] Normalizing each column of the augmented matrix;

[0020] Computing the Gram matrix of the normalized dictionary;

[0021] Computing the initial correlation vector;

[0022] Storing the Gram matrix and the initial correlation vector.

[0023] Preferably, the step of performing fast matching pursuit iteration solution according to the global information, selecting the atom, i.e. the equalizer tap, most relevant to the current residual from the dictionary in an iterative manner, and updating its coefficient and residual until the sparsity constraint is met, specifically comprises:

[0024] Performing atom selection, finding the component with the largest absolute value in the current correlation vector in each iteration;

[0025] Performing coefficient update and residual calculation, re-computing the optimal coefficients of all selected atoms using the least square method, and updating the residual;

[0026] Using the pre-computed Gram matrix and the current residual to quickly update the correlation vector for use in the next iteration.

[0027] Preferably, the step of mapping the solution obtained by fast matching pursuit on the normalized augmented system back to the original physical equalizer coefficients, and initializing the state of the equalizer, specifically comprises:

[0028] Converting the solution on the normalized dictionary back to the solution on the original augmented system;

[0029] Decomposing the joint coefficient vector obtained from the augmented system into feedforward and feedback two parts, separating the feedforward and feedback filter coefficients;

[0030] Initialize the filter state, fill the initial values for the shift registers of the feedforward and feedback filters.

[0031] Preferably, the step of using the filter coefficients obtained in the training phase to continuously equalize and demodulate the unknown data symbols, feeding back the decided symbols, and recursively eliminating the intersymbol interference comprises:

[0032] At each symbol time, perform feedforward filtering and feedback filtering, and combine the results;

[0033] Perform hard decision on the equalizer output, and estimate the transmitted symbols;

[0034] Update the state registers of the feedforward and feedback filters in a sliding window manner.

[0035] To solve the above technical problems, the application further provides a decision feedback equalization device based on matching pursuit, which adopts the following technical scheme and comprises:

[0036] An initialization module is configured to initialize system parameters according to a modulation mode adopted by a communication system;

[0037] A construction module is configured to construct a training data matrix, and reorganize the time-series received signals and known training symbols into a matrix form;

[0038] A pre-computation module is configured to pre-compute and store global information required in an iterative process according to the training data matrix;

[0039] An iteration module is configured to perform fast matching pursuit iteration solving according to the global information, and gradually select an atom most relevant to a current residual error from a dictionary and update the coefficient and the residual error of the atom in an iterative manner until a sparsity constraint is met;

[0040] A mapping module is configured to map a solution obtained by the fast matching pursuit on a normalized augmented system back to original physical equalizer coefficients, and initialize a state of the equalizer;

[0041] A recursion module is configured to use filter coefficients obtained in a training phase to continuously equalize and demodulate unknown data symbols, feed back decided symbols, and recursively eliminate intersymbol interference.

[0042] To solve the above technical problems, the application further provides a device, which adopts the following technical scheme and comprises a memory and a processor, the memory stores computer readable instructions, and the processor implements the steps of the decision feedback equalization method based on matching pursuit when executing the computer readable instructions.

[0043] To solve the above technical problems, the application further provides a computer readable storage medium, which adopts the technical scheme as follows, the computer readable storage medium stores computer readable instructions, and the computer readable instructions are executed by a processor to realize the steps of the matching pursuit decision feedback equalization method.

[0044] Compared with the prior art, the application has the following beneficial effects:

[0045] (1) Reducing the computational complexity: through the Gram matrix pre-computation and the correlation vector incremental update two core technologies, the complexity of each iteration of the matching pursuit is reduced from O(NL) to O(L), avoiding large-scale matrix operation, and significantly improving the computing efficiency.

[0046] (2) High precision and fast convergence: the regularized least square method and the accurate least square coefficient update (rather than simple greedy coefficient accumulation) are adopted, so that each iteration is optimal, thereby achieving higher fitting precision and faster convergence speed within the sparsity budget.

[0047] (3) Reducing the training overhead: the unified training matrix is used to optimize the feedforward and feedback filters at one time, so that the limited training samples are fully utilized, and the dependence on the long training sequence is reduced.

[0048] (4) Improving the performance: the method finally forms a closed-loop decision feedback equalizer in the data stage, which can effectively resist the serious ISI in the frequency selective underwater acoustic channel, realizes reliable communication with low error rate and low delay, and significantly improves the stability and overall performance of the underwater acoustic communication system. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the scheme in the application, the drawings needed in the description of the embodiments of the application will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0050] Figure 1 is a flowchart of an embodiment of the matching pursuit decision feedback equalization method of the application;

[0051] Figure 2 shows the time consumption distribution diagram of each block of the CEDFE series equalizer under different algorithms (LSQR, OMP, CoSaMP and MP);

[0052] Figure 3 gives the constellation distribution diagram of the CEDFE series equalizer under the LSQR, OMP, CoSaMP and MP algorithms;

[0053] Figure 4 The CEDFE series equalizer is shown in a block BER (Bit Error Rate) distribution diagram in different error rate intervals.

[0054] Figure 5 is a structural schematic diagram of an embodiment of the matching pursuit decision feedback equalization device of the present application.

[0055] Figure 6 is a structural schematic diagram of an embodiment of the device of the present application. DETAILED DESCRIPTION

[0056] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used in the description herein is for describing particular embodiments only and is not intended to be limiting of the application; the description herein and the claims of the application and the above description of the drawings herein is not intended to be complete descriptions of all features of the application; the terminology used herein is intended to be interpreted in accordance with reasonably acceptable dictionary categories, as appropriate for the purposes of description and claims. The terms "comprising", "having", "including", and "containing" are to be construed as open-ended terms (i.e., meaning "including, but not limited to") unless otherwise noted. The terms "first", "second" and the like, as used herein do not have any specific meaning, and are used only to distinguish one element from another.

[0057] Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. The appearances of the phrase "in an embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily all directed to the same embodiment, or to a single alternative embodiment. It is explicitly contemplated that embodiments described herein can be combined with each other in their individual aspects.

[0058] In order to make the technical personnel in the art better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings.

[0059] It should be noted that the matching pursuit decision feedback equalization method provided by the embodiments of the present application is generally executed by a server / terminal device, and accordingly, the matching pursuit decision feedback equalization device is generally arranged in the server / terminal device.

[0060] It should be understood that the number of terminal devices, networks and servers is only illustrative. Any number of terminal devices, networks and servers can be provided according to the implementation needs.

[0061] Embodiment one

[0062] Please refer to Figure 1, shows a flow chart of one embodiment of the matched tracking decision feedback equalization method of the present application. The matched tracking decision feedback equalization method comprises the following steps:

[0063] Step S1, initialize system parameters according to the modulation mode adopted by the communication system.

[0064] In this embodiment, the electronic device (such as a server / terminal device) on which the matched tracking decision feedback equalization method runs can receive the matched tracking decision feedback equalization request through wired connection or wireless connection. It should be noted that the wireless connection can include but is not limited to 3G / 4G / 5G connection, WiFi connection, Bluetooth connection, WiMAX connection, Zigbee connection, UWB (ultra wideband) connection, and other now known or future developed wireless connection modes.

[0065] Step S1 sets the framework and boundary conditions for the entire equalization algorithm, ensures that the algorithm runs in the correct configuration, and is the basis for achieving low complexity and high performance equalization.

[0066] In this embodiment, step S1, initializing system parameters according to the modulation mode adopted by the communication system, can specifically include the following steps:

[0067] S11, define modulation parameters according to the modulation mode adopted by the communication system.

[0068] Set the modulation order M. For example, if QPSK modulation is used, M = 4; if 16-QAM is used, M = 16.

[0069] Calculate the number of bits per symbol m = log2(M). The number of bits per symbol m is used for subsequent data processing and symbol-to-bit mapping.

[0070] By using step S11, the signal modulation format is determined, which is a prerequisite for the receiver to correctly demodulate and decode.

[0071] S12, configure equalizer structure parameters.

[0072] The key length parameters of the equalizer can be set according to prior knowledge or estimation of channel delay spread, such as setting the feedback filter length L b . For example, L b = 10 means that the equalizer uses the last 10 decided symbols to offset ISI.

[0073] Set the feedforward filter length L f . It can follow the empirical rule or be self-defined, for example, set L f = 2L bto ensure enough degrees of freedom to handle the forward interference.

[0074] Total filter length L total = L f + L b .

[0075] Step S12 determines the complexity of the equalizer and the ability to eliminate ISI. A suitable length can balance performance and complexity.

[0076] S13, set the parameters of sparsity, regularization and training scale.

[0077] Set the number of effective training samples N train = L training sequence - L total + 1. Where L training sequence is the total length of the transmitted training sequence. This formula ensures that there is no overflow when constructing the training matrix.

[0078] Set the Tikhonov regularization parameter λ, which takes the value range λ∈[10 -8 ,10 -4 ].

[0079] Set the sparsity budget K. According to the estimation of the sparsity of the channel (such as the number of multipath paths), set a value much smaller than L total .

[0080] N train determines the amount of data used for training, affecting the accuracy of the estimate. The Tikhonov regularization parameter λ is used to prevent overfitting and improve the numerical stability of the solution process. The sparsity budget K directly controls the number of iterations of the fast matching pursuit algorithm and the sparsity of the final solution, and is the key to reducing computational complexity.

[0081] In specific implementation, the equalizer parameters can be initialized according to the Doppler time-varying characteristics of the underwater acoustic channel, combined with specific modulation methods (such as QPSK, OFDM, etc.), considering the time-varying range of the channel and the multipath delay distribution.

[0082] Step S2, construct the training data matrix, and reorganize the time-series received signal and known training symbols into a matrix form.

[0083] Reorganize the time-series received signal and known training symbols into a matrix form, convert the equalizer coefficient solving problem into a linear model fitting problem, and lay a data foundation for subsequent sparse solving.

[0084] In this embodiment, the step S2 of constructing the training data matrix, reorganizing the time-series received signal and the known training symbols into a matrix form, can specifically include the steps of:

[0085] S21, constructing an input vector, at each time point n, extracting a vector from the received signal sequence and the decision symbol sequence respectively.

[0086] Constructing a feedforward input vector (FF Input Vector), which is a vector composed of consecutive received sampling points: x f (n) = [y(n), y(n-1), …, y(n-L f +1)] T , where y(n) represents the received sampling signal at time point n.

[0087] Constructing a feedback input vector (FB Input Vector), which is a vector composed of previously decided symbols:

[0088] In the training phase, replaced by the known training symbols s(n).

[0089] Concatenating the feedforward and feedback vectors into a joint input vector:

[0090] The function of the step S21 is to combine the current received signal and the historical decision information into a complete feature vector as the input of the linear predictor.

[0091] S22, assembling the training matrix and the target vector, stacking the joint input vectors of multiple time points into a training data matrix, and assembling the target symbols at the corresponding time points into a target vector.

[0092] Assembling the training matrix A (also called dictionary or atom set): The size of the matrix is N train ×L total .

[0093] Assembling the target vector b (also called observation vector): b = [s(n), s(n-1), …, s(n-N train +1)] T , where s(n) is the known transmitted training symbol at time point n.

[0094] The function of the step S22 is to construct a complete linear system Aw≈b, where w is the equalizer coefficient vector to be solved. The goal is to solve the optimal equalizer coefficient vector w from the system.

[0095] S23, system augmentation and regularization.

[0096] To avoid directly solving the ill-conditioned problem and introduce sparsity constraints, the original least squares problem is converted into a regularized least squares problem.

[0097] Construct the augmented matrix and augmented vector: where I is the L total ×L total identity matrix and 0 is a zero vector of corresponding length.

[0098] The objective is converted to solving the following regularized least squares problem: This is equivalent to:

[0099]

[0100] The role of step S23 is: This term is called the L2 regularization term (ridge regression term), which prevents overfitting by penalizing excessively large coefficient values, especially when A T A is approximately singular, which provides numerical stability. It provides a numerically stable base system for subsequent sparse solution.

[0101] In implementation, in a long multipath underwater acoustic environment, the time series received signal and the known training symbol can be reorganized into a matrix according to the multipath time delay extension, while preserving the channel space-time coupling characteristics.

[0102] Step S3: According to the training data matrix, pre-compute and store the global information required in the iteration process.

[0103] Pre-compute and store the global information (Gram matrix G and related vector d) required in the iteration process, to avoid repeated and high complexity matrix multiplication in the main loop of the matching pursuit.

[0104] In this embodiment, step S3, according to the training data matrix, pre-compute and store the global information required in the iteration process can specifically include the steps of:

[0105] S31: Normalize each column of the augmented matrix.

[0106] Calculate the normalization coefficient, for each column atom φ j (jth column of the augmented matrix Φ), calculate its norm: g j = ||φ j ||2.

[0107] Generate the normalized dictionary: ψ j = φ j / g j .

[0108] All normalized columns form the normalized dictionary matrix Ψ.

[0109] The role of step S31 is: fair atomic selection can be performed, ensuring that the matching pursuit algorithm does not produce deviation when selecting atoms due to different energy (norm) of the atoms themselves, and all atoms compete under the same conditions; calculation can be simplified, and the norm of the atom after normalization is 1, so that the term involving the norm in subsequent calculation can be simplified.

[0110] S32, calculate the Gram matrix of the normalized dictionary.

[0111] The definition of the Gram matrix G is: G = Ψ T Ψ, the element G i,j <ψ i , ψ j > is the inner product of atom i and atom j. Where G is a L total ×L total symmetric matrix.

[0112] The role of step S32 is: in the matching pursuit iteration, the inner product of the residual and all atoms needs to be frequently calculated. By precomputing the Gram matrix G, the inner product required in the subsequent iteration can be quickly obtained by table lookup and vector operation, avoiding the high-cost matrix-vector multiplication, and greatly reducing the computational complexity.

[0113] S33, calculate the initial correlation vector.

[0114] The initial correlation vector is calculated by calculating the inner product of the initial residual (i.e. the augmented target vector z) and all normalized atoms.

[0115] The initial residual r0 = z.

[0116] Calculate the initial correlation vector d0: d0 = Ψ T r0 = Ψ T z. The jth component d0(j) of the initial correlation vector d0 = <ψ j , z> indicates the correlation of atom j with the initial residual.

[0117] The role of step S33 is: it provides the starting point of the algorithm iteration, and in the first iteration, the atom with the largest |d0(j)| is selected; it provides the initial value for the subsequent correlation vector increment update strategy, which allows the correlation vector d to be updated only by a small amount of calculation after each iteration, instead of recalculating the entire Ψ T r.

[0118] S34, store the Gram matrix and the initial correlation vector.

[0119] In implementation, the channel covariance matrix, sparse basis dictionary and other global information required for iteration can be pre-computed based on statistical characteristics of the underwater acoustic channel (such as Doppler spread, number of multipaths), so as to reduce real-time computation complexity.

[0120] In step S4, fast matching pursuit iteration is performed according to the global information, and in an iterative manner, the atom (equalizer tap) most relevant to the current residual is selected from the dictionary, and the coefficient and residual thereof are updated, until the sparsity constraint is met.

[0121] This process efficiently fits the most important taps of the joint feedforward-feedback filter.

[0122] In the embodiment, in step S4, fast matching pursuit iteration is performed according to the global information, and in an iterative manner, the atom (equalizer tap) most relevant to the current residual is selected from the dictionary, and the coefficient and residual thereof are updated, until the sparsity constraint is met, which can specifically include the following steps:

[0123] In step S41, atom selection is performed, and in each iteration, the component with the largest absolute value is found from the current correlation vector.

[0124] Search index: Wherein Λ k-1 is the index set of the atoms (called support set) selected in the first k-1 iterations. The selected atom index j k is added to the support set: Λ k = Λ k-1 ∪{j k}. In each iteration k, the component with the largest absolute value is found from the current correlation vector d k-1 .

[0125] Step S41 functions to identify the filter tap (coefficient) that currently makes the largest contribution to reducing the residual.

[0126] In step S42, coefficient update and residual calculation are performed, and the optimal coefficients of all selected atoms are recalculated using the least square method, and the residual is updated.

[0127] The selected atom refers to the atom corresponding to the support set Λ k .

[0128] Let be the submatrix formed by the columns corresponding to the support set Λ k .

[0129] Solve the constrained least square problem: The solution is

[0130] Update the residual:

[0131] The role of step S42 is to find a set of optimal coefficients on the selected atom set, so that the fitting error of the current model to the target vector is minimized. This is more accurate than simply accumulating the correlation coefficients, and can accelerate the convergence speed.

[0132] S43, using the pre-computed Gram matrix and the current residual, quickly update the correlation vector for the next iteration.

[0133] The standard correlation vector calculation is d k = Ψ T r k .

[0134] The fast method uses the formula: where is the j k th column of the Gram matrix G, and c k (j k ) is the value of the coefficient vector c k after this update, corresponding to the newly selected atom j k .

[0135] The new correlation d k is equal to the old correlation d k-1 minus the coefficient of the new atom j k multiplied by its correlation vector with all other atoms This cleverly eliminates the part of the energy that the new atom has already explained from the correlation.

[0136] That is, using the pre-computed Gram matrix G and the current residual r k , quickly update the correlation vector d k for the next iteration.

[0137] The iteration termination condition is: when the iteration number k reaches the preset sparsity budget K, the iteration stops.

[0138] The role of step S43 is to avoid the O(NL total ) complexity operation of calculating Ψ T r k each time, and instead use a vector subtraction with only O(L total ) complexity, greatly improving the calculation efficiency; and provide a basis for the selection of atoms for the next iteration.

[0139] In specific implementation, under the sparsity constraint, the equalizer taps most related to the current residual can be selected from the over-complete dictionary (considering Doppler shift compensation), and the coefficients and the residual are iteratively updated to adapt to the channel time-varying characteristics.

[0140] Step S5 maps the solution obtained by fast matching pursuit on the normalized augmented system back to the original physical equalizer coefficients and initializes the state of the equalizer.

[0141] In the present embodiment, the step S5 of mapping the solution obtained by fast matching pursuit on the normalized augmented system back to the original physical equalizer coefficients and initializing the state of the equalizer can specifically include the steps of:

[0142] S51 converts the solution on the normalized dictionary back to the solution on the original augmented system.

[0143] A vector w total of length L aug is created with support set Λ K and values c final / g j at the positions of the atoms (where g j is the original norm of the jth atom) and 0 elsewhere.

[0144] Mathematically:

[0145] The function of the step S51 is to reverse the normalization operation in the step S31 to obtain the sparse solution w aug in the sense of the original regularized least squares problem.

[0146] S52 decomposes the joint coefficient vector obtained from the augmented system into two parts of feedforward and feedback, and separates the feedforward and feedback filter coefficients.

[0147] The feedforward filter coefficients w f are composed of the first L f elements of w aug :

[0148]

[0149] The feedback filter coefficients w b are composed of the last L b elements of w aug :

[0150]

[0151] The function of the step S52 is to obtain two independent filter tap weight vectors that can be used for filtering operation in the data stage.

[0152] S53 initializes the filter state, and fills the initial values for the shift registers of the feedforward and feedback filters.

[0153] The feedforward filter state S f : is filled with the last L fThe initialization is performed for each received sample point.

[0154] Feedback filter state S b initialized with the last L b training symbols (or initial decision values).

[0155] The function of step S53 is to ensure that when switching from training mode to data mode, the filter has the correct history data to perform the first filtering and decision operation, avoiding the initial transient effect.

[0156] In implementation, the normalized augmented system can be demapped back to physical equalizer coefficients, and the equalizer state is initialized to match long multipath delay.

[0157] Step S6, using the filter coefficients obtained in the training phase, performs successive equalization and demodulation on unknown data symbols, and feeds back the decided symbols to recursively eliminate intersymbol interference.

[0158] In the embodiment, step S6, using the filter coefficients obtained in the training phase, performs successive equalization and demodulation on unknown data symbols, and feeds back the decided symbols to recursively eliminate intersymbol interference can specifically include steps of:

[0159] S61, at each symbol time, performs feedforward filtering and feedback filtering, and combines the results.

[0160] Collect current feedforward input: x f (n) = [y(n), y(n-1),..., y(n-L f +1)] T .

[0161] Collect current feedback input:

[0162] Calculate equalizer output z(n):

[0163] Feedforward part is responsible for processing current and future interference (and noise), and feedback part is responsible for subtracting ISI components estimated based on past decided symbols.

[0164] The function of step S61 is to generate a clean signal z(n) that eliminates most of the ISI, for the detector to make decisions.

[0165] S62, perform hard decision on the equalizer output to estimate the transmitted symbols.

[0166] According to the modulation mode, map the complex output z(n) to the nearest constellation point:

[0167]

[0168] For example, under QPSK, the signs of the real and imaginary parts of z(n) are determined.

[0169] The function of step S62 is to generate the symbol estimate value of the current time This value is the final output and will also be used for feedback filtering in the subsequent time, forming a closed loop.

[0170] S63, the state register of the feedforward and feedback filter is updated in a sliding window manner.

[0171] The feedforward state S f is updated: the oldest sample y(n-L f +1) is discarded and the new sample y(n+1) is incorporated.

[0172] The feedback state S b is updated: the oldest symbol is discarded and the new decision symbol

[0173] The function of step S63 is to prepare for processing the next symbol n+1, ensuring that the filter state always contains the latest L f samples and L b decided symbols. This recursive process enables continuous equalization.

[0174] Using the filter coefficients in the training phase, unknown data symbols are continuously equalized and demodulated, and inter-symbol interference (ISI) is eliminated through decision feedback recursion, especially for the long memory characteristics of the underwater acoustic channel.

[0175] Figure 2 The time distribution diagram of each block of the CEDFE series equalizer under different algorithms (LSQR, OMP, CoSaMP, MP) is shown. As shown in the figure, the horizontal axis is the processing block sequence, and the vertical axis is the corresponding time consumption (seconds). This figure intuitively reflects the calculation efficiency difference of each algorithm when processing the same signal data, providing a basis for selecting an efficient equalization method. Figure 2

[0176] The constellation diagram distribution of the CEDFE series equalizer under LSQR, OMP, CoSaMP, and MP algorithms is given. As shown in the figure, the horizontal axis is the in-phase component (In-Phase), and the vertical axis is the quadrature component (Quadrature). By comparing the signal point aggregation degree and distribution form under different algorithms, the signal recovery quality and noise resistance performance of the equalizer can be intuitively evaluated. Figure 3 Figure 3

[0177] Figure 4 ​​The CEDFE series equalizer is shown in the block BER (Bit Error Rate) distribution diagram in different error rate intervals. As shown in Figure 4 the horizontal axis is different error rate ranges, and the vertical axis is the block proportion (%) in the range. The graph reflects the error rate performance of each algorithm under different channel conditions, providing a reference for performance optimization of equalization algorithms in engineering applications.

[0178] The analysis of the three graphs Figure 2 , Figure 3 and Figure 4 concludes that the CEDFE series algorithm based on sparse reconstruction introduced in the equalization of the underwater acoustic channel effectively improves the computational efficiency and signal recovery accuracy of the equalizer. The experimental results show that this method significantly reduces the single block processing time while ensuring constellation aggregation and low error rate, balancing operation speed, estimation accuracy, and operation reliability, and is particularly suitable for real-time high-speed communication in complex time-varying underwater acoustic channels, providing strong support for stable and efficient operation of underwater acoustic communication systems.

[0179] The implementation of this embodiment has the following advantages:

[0180] (1) Reduces computational complexity: Through Gram matrix pre-computation and related vector incremental update, the complexity of each iteration of the matching pursuit is reduced from O(NL) to O(L), avoiding large-scale matrix operations and significantly improving computational efficiency.

[0181] (2) High precision and fast convergence: Regularized least squares and accurate least squares coefficient update (instead of simple greedy coefficient accumulation) are used to ensure that each iteration is optimal, resulting in higher fitting accuracy and faster convergence within the sparsity budget.

[0182] (3) Reduces training overhead: The unified training matrix optimizes the feedforward and feedback filters at once, making full use of limited training samples and reducing dependence on lengthy training sequences.

[0183] (4) Improves performance: The method ultimately forms a closed-loop decision feedback equalizer in the data stage, effectively combating severe ISI in frequency-selective underwater acoustic channels, achieving low error rate, low delay, and reliable communication, and significantly improving the stability and overall performance of the underwater acoustic communication system.

[0184] The application is operational with numerous general purpose or special purpose computing system environments or configurations. Examples of well- known computing systems, environments, and / or configurations that can be suitable for use with the application include personal computers, server computers, handheld or laptop devices, tablet devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like. The application can be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and the like, that perform particular tasks or implement particular abstract data types. The application can also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules can be located in both local and remote computer storage media including memory storage devices.

[0185] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing relevant hardware through computer readable instructions, and the computer readable instructions can be stored in a computer readable storage medium. When the program is executed, the processes of the above-mentioned embodiment methods can be included. The storage medium can be a non-volatile storage medium such as a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0186] It should be understood that although each step in the flowchart of the accompanying drawings is displayed in sequence according to the direction of the arrow, these steps are not necessarily executed in sequence according to the direction of the arrow. Unless otherwise stated herein, the execution of these steps is not strictly limited in sequence, and they can be executed in other sequences. Moreover, at least part of the steps in the flowchart of the accompanying drawings can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution sequence is not necessarily sequential, but can be alternately or alternately executed with at least part of other steps or sub-steps or stages of other steps.

[0187] Embodiment two

[0188] Further reference Figure 5 to the method described above Figure 1 , the application provides an embodiment of a matching tracking decision feedback equalization device, which corresponds to the method embodiment shown in Figure 1 , and the device can be applied to various electronic devices.

[0189] AsFigure 5 As shown in the figure, the decision feedback equalization device 70 of the matching pursuit in the embodiment comprises an initialization module 71, a construction module 72, a pre-computation module 73, an iteration module 74, a mapping module 75 and a recursion module 76. Among them:

[0190] The initialization module 71 is used for initializing system parameters according to the modulation mode adopted by the communication system;

[0191] The construction module 72 is used for constructing a training data matrix, and reorganizing the time-series received signal and the known training symbol into a matrix form;

[0192] The pre-computation module 73 is used for pre-computing and storing global information required in the iteration process according to the training data matrix;

[0193] The iteration module 74 is used for solving the fast matching pursuit iteration according to the global information, selecting the atom most related to the current residual error from the dictionary, i.e. the equalizer tap, in an iterative manner, and updating the coefficient and the residual error of the atom, until the sparsity constraint is met;

[0194] The mapping module 75 is used for mapping the solution obtained by the fast matching pursuit on the normalized augmented system back to the original physical equalizer coefficient, and initializing the state of the equalizer;

[0195] The recursion module 76 is used for continuously equalizing and demodulating the unknown data symbol by using the filter coefficient obtained in the training stage, feeding back the decided symbol, and recursively eliminating the inter-symbol interference.

[0196] In some optional implementation manners of the embodiment, the initialization module 71 further comprises:

[0197] The definition module 711 is used for defining the modulation parameter according to the modulation mode adopted by the communication system;

[0198] The configuration module 712 is used for configuring the equalizer structure parameter;

[0199] The setting module 713 is used for setting the parameters of sparsity, regularization and training scale.

[0200] In some optional implementation manners of the embodiment, the construction module 72 further comprises:

[0201] The construction module 721 is used for constructing an input vector, and extracting the vector from the received signal sequence and the decided symbol sequence at each time point n, respectively;

[0202] The assembly module 722 is used for assembling the training matrix and the target vector, stacking the joint input vectors at multiple time points into the training data matrix, and assembling the target symbol at the corresponding time into the target vector;

[0203] Augmentation module 723 for system augmentation and regularization.

[0204] In some optional implementations of the embodiment, the pre-computation module 73 further comprises:

[0205] Normalization module 731 for normalizing each column of the augmented matrix;

[0206] Computation module 732 for computing the Gram matrix of the normalized dictionary;

[0207] Vector module 733 for computing the initial correlation vector.

[0208] In some optional implementations of the embodiment, the iteration module 74 further comprises:

[0209] Search module 741 for atom selection, finding the component with the largest absolute value from the current correlation vector in each iteration;

[0210] Update module 742 for coefficient update and residual computation, re-computing the optimal coefficients of all selected atoms using least squares method and updating the residual;

[0211] Update module 743 for fast updating the correlation vector using the pre-computed Gram matrix and the current residual for use in the next iteration.

[0212] In some optional implementations of the embodiment, the mapping module 75 further comprises:

[0213] Conversion module 751 for converting the solution on the normalized dictionary back to the solution on the original augmented system;

[0214] Decomposition module 752 for decomposing the joint coefficient vector obtained from the augmented system into two parts of feedforward and feedback, separating the feedforward and feedback filter coefficients;

[0215] Padding module 753 for initializing the filter states, padding the initial values for the shift registers of the feedforward and feedback filters.

[0216] In some optional implementations of the embodiment, the recursion module 76 further comprises:

[0217] Combination module 761 for performing feedforward filtering and feedback filtering at each symbol time and combining the results;

[0218] Hard decision module 762 for performing hard decision on the equalizer output to estimate the transmitted symbols;

[0219] Sliding window module 763 is used to update the state registers of the feedforward and feedback filters in a sliding window manner.

[0220] The embodiment has the beneficial effects that:

[0221] (1) The computational complexity is reduced: By the two core technologies of Gram matrix pre-computation and correlation vector incremental update, the complexity of each iteration of the matching pursuit is reduced from O(NL) to O(L), avoiding large-scale matrix operations and significantly improving the computational efficiency.

[0222] (2) High precision and fast convergence can be achieved: The regularized least squares method and accurate least squares coefficient update (rather than simple greedy coefficient accumulation) are used to ensure that each step of iteration is optimal, thereby achieving higher fitting precision and faster convergence speed within the sparsity budget.

[0223] (3) Training overhead can be reduced: The unified training matrix is used to optimize the feedforward and feedback filters at one time, fully utilizing the limited training samples and reducing the dependence on long training sequences.

[0224] (4) Performance is improved: The method ultimately forms a closed-loop decision feedback equalizer in the data stage, which can effectively combat severe ISI in the frequency-selective underwater acoustic channel, realize reliable communication with low bit error rate and low delay, and significantly improve the stability and overall performance of the underwater acoustic communication system.

[0225] Embodiment Three

[0226] To solve the above technical problems, the embodiment of the present application also provides a device. For details, please refer to Figure 6 , Figure 6 The device of the present embodiment is a basic structure block diagram.

[0227] The device 8 described above includes a memory 81, a processor 82, and a network interface 83 connected to each other through a system bus. It should be noted that the device 8 in the figure only shows components such as the memory 81, the processor 82, and the network interface 83, but it should be understood that not all the components shown are required, and more or fewer components can be implemented instead. Among them, those skilled in the art can understand that the device here is a device that can automatically perform numerical calculation and / or information processing according to pre-set or stored instructions, and its hardware includes but is not limited to microprocessors, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0228] The device can be a desktop computer, a notebook computer, a palm computer, a cloud server, or the like. The device can interact with a user through a keyboard, a mouse, a remote controller, a touchpad, a voice control device, or the like.

[0229] The memory 81 can include at least one type of readable storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory (e.g., an SD or DX memory, or the like), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, or the like. In some embodiments, the memory 81 can be an internal storage unit of the device 8, such as a hard disk or a memory of the device 8. In other embodiments, the memory 81 can also be an external storage device of the device 8, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, or the like. Of course, the memory 81 can include both an internal storage unit and an external storage device of the device 8. In this embodiment, the memory 81 is generally used to store an operating system and various application software installed in the device 8, such as computer readable instructions of the decision feedback equalization method based on matching pursuit, or the like. In addition, the memory 81 can also be used to temporarily store various data that has been output or will be output.

[0230] The processor 82 can be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments. The processor 82 is generally used to control the overall operation of the device 8. In this embodiment, the processor 82 is used to run computer readable instructions or process data stored in the memory 81, such as computer readable instructions of the decision feedback equalization method based on matching pursuit.

[0231] The network interface 83 can include a wireless network interface or a wired network interface, and is generally used to establish a communication connection between the device 8 and other electronic devices.

[0232] By implementing this embodiment, the following beneficial effects can be achieved:

[0233] (1) Reducing the computational complexity: By using the two core technologies of Gram matrix pre-computation and correlation vector incremental update, the complexity of each iteration of the matching pursuit is reduced from O(NL) to O(L), avoiding large-scale matrix operations and significantly improving the computational efficiency.

[0234] (2) High precision and fast convergence: Regularized least squares and exact least squares coefficient update (rather than simple greedy coefficient accumulation) are used to ensure that each iteration is optimal, thereby achieving higher fitting accuracy and faster convergence speed within the sparsity budget.

[0235] (3) Reduced training overhead: A unified training matrix is used to optimize the feedforward and feedback filters at one time, making full use of limited training samples and reducing dependence on lengthy training sequences.

[0236] (4) Improved performance: The method ultimately forms a closed-loop decision feedback equalizer in the data stage, which can effectively combat severe ISI in the frequency-selective underwater acoustic channel, achieve low error rate and low delay reliable communication, and significantly improve the stability and overall performance of the underwater acoustic communication system.

[0237] Embodiment Four

[0238] The application also provides another embodiment, that is, a computer readable storage medium storing computer readable instructions, which can be executed by at least one processor to make the at least one processor execute the steps of the matching pursuit decision feedback equalization method as described above.

[0239] The implementation of this embodiment has the following beneficial effects:

[0240] (1) Reduced computational complexity: Gram matrix pre-computation and related vector incremental update are two core technologies that reduce the complexity of each iteration of matching pursuit from O(NL) to O(L), avoiding large-scale matrix operations and significantly improving computational efficiency.

[0241] (2) High precision and fast convergence: Regularized least squares and exact least squares coefficient update (rather than simple greedy coefficient accumulation) are used to ensure that each iteration is optimal, thereby achieving higher fitting accuracy and faster convergence speed within the sparsity budget.

[0242] (3) Reduced training overhead: A unified training matrix is used to optimize the feedforward and feedback filters at one time, making full use of limited training samples and reducing dependence on lengthy training sequences.

[0243] (4) Improved performance: The method ultimately forms a closed-loop decision feedback equalizer in the data stage, which can effectively combat severe ISI in the frequency-selective underwater acoustic channel, achieve low error rate and low delay reliable communication, and significantly improve the stability and overall performance of the underwater acoustic communication system.

[0244] Those skilled in the art can clearly understand the above-mentioned embodiment method can be realized by means of software and necessary general hardware platform, of course, also can be realized by hardware, but in many cases, the former is a better embodiment. Based on such understanding, the technical solutions of the present application can be embodied in the form of software product, and the computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), including a plurality of instructions to make a terminal device (may be a mobile phone, computer, server, air conditioner, or network device, etc.) execute the various embodiment methods of the present application.

[0245] Obviously, the above-described embodiments are only a part of the embodiments of the present application, rather than all the embodiments, and the preferred embodiments of the present application are given in the drawings, but do not limit the patent scope of the present application. The present application can be realized in many different forms, and conversely, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing specific embodiments, or make equivalent replacements to some technical features. Any equivalent structure made by using the content of the present application specification and drawings, directly or indirectly applied to other related technical fields, is also within the patent protection scope of the present application.

Claims

1. A decision feedback equilibrium method for matching pursuit, characterized in that, Includes the following steps: Initialize the system parameters according to the modulation scheme used by the communication system; Construct a training data matrix by reorganizing the time-series received signals and known training symbols into a matrix form; Based on the training data matrix, pre-compute and store the global information required during the iteration process; Based on the global information, a fast matching and tracking iterative solution is performed. In an iterative manner, the atoms most relevant to the current residual, i.e. equalizer taps, are selected from the dictionary step by step, and their coefficients and residuals are updated until the sparsity constraint is met. The solution obtained by fast matching tracing on the normalized augmented system is mapped back to the original physical equalizer coefficients, and the state of the equalizer is initialized. Using the filter coefficients obtained during the training phase, continuous equalization and demodulation are performed on the unknown data symbols, and the decided symbols are fed back to recursively eliminate inter-symbol interference.

2. The matching pursuit decision feedback equilibrium method according to claim 1, characterized in that, The steps for initializing system parameters according to the modulation scheme used by the communication system specifically include: Define the modulation parameters according to the modulation method used by the communication system; Configure equalizer structure parameters; Set parameters for sparsity, regularization, and training size.

3. The matching pursuit decision feedback equilibrium method according to claim 1, characterized in that, The step of constructing the training data matrix, which reorganizes the time-series received signals and known training symbols into matrix form, specifically includes: Construct an input vector, and at each time point n, extract the vector from the received signal sequence and the decision symbol sequence respectively; Assemble the training matrix and the target vector, stack the joint input vectors from multiple time points into a training data matrix, and combine the target symbols at the corresponding time points into a target vector; Perform system augmentation and regularization.

4. The matching pursuit decision feedback equilibrium method according to claim 3, characterized in that, The step of pre-calculating and storing the global information required during the iteration process based on the training data matrix specifically includes: Normalize each column of the augmented matrix; Calculate the Gram matrix of the normalized dictionary; Calculate the initial correlation vector; Store the Gram matrix and the initial correlation vector.

5. The matching pursuit decision feedback equilibrium method according to claim 4, characterized in that, The step of performing fast matching and tracking iterative solution based on the global information, and iteratively selecting the atoms (equalizer taps) most relevant to the current residual from the dictionary and updating their coefficients and residuals until the sparsity constraint is satisfied, specifically includes: Perform atomic selection, and in each iteration, find the component with the largest absolute value from the current relevant vector; Perform coefficient updates and residual calculations, recalculate the optimal coefficients of all selected atoms using the least squares method, and update the residuals; Using the pre-computed Gram matrix and the current residual, the relevant vectors are quickly updated for use in the next iteration.

6. The matching pursuit decision feedback equilibrium method according to claim 1, characterized in that, The steps of mapping the solution obtained by fast matching tracking on the normalized augmented system back to the original physical equalizer coefficients and initializing the state of the equalizer specifically include: Transform the solutions from the normalized dictionary back to the solutions from the original augmented system; The joint coefficient vector obtained from the augmented system is decomposed into two parts: feedforward and feedback, and the coefficients of the feedforward and feedback filters are separated. Initialize the filter state by filling the shift registers of the feedforward and feedback filters with initial values.

7. The matching pursuit decision feedback equilibrium method according to any one of claims 1 to 6, characterized in that, The steps of using the filter coefficients obtained during the training phase to continuously equalize and demodulate unknown data symbols, feeding back the decided symbols, and recursively eliminating inter-symbol interference specifically include: At each symbol time, feedforward filtering and feedback filtering are performed, and the results are combined. Perform a hard decision on the equalizer output to estimate the transmitted symbol; The state registers of the feedforward and feedback filters are updated using a sliding window method.

8. A decision feedback equalization device for matching pursuit, characterized in that, include: The initialization module is used to initialize system parameters according to the modulation scheme used by the communication system. The building module is used to construct the training data matrix, which reorganizes the time-series received signals and known training symbols into a matrix form; The pre-computation module is used to pre-compute and store the global information required during the iteration process based on the training data matrix; The iteration module is used to perform fast matching and tracking iterative solution based on the global information. In an iterative manner, it selects the atoms most relevant to the current residual, i.e. equalizer taps, from the dictionary and updates their coefficients and residuals until the sparsity constraint is met. The mapping module is used to map the solution obtained by fast matching tracing on the normalized augmented system back to the original physical equalizer coefficients and initialize the state of the equalizer. The recursive module is used to continuously equalize and demodulate unknown data symbols using the filter coefficients obtained during the training phase, and feed back the decided symbols to recursively eliminate inter-symbol interference.

9. A device, characterized in that, The system includes a memory and a processor, wherein the memory stores computer-readable instructions, and the processor executes the computer-readable instructions to implement the steps of the matching pursuit decision feedback equilibrium method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-readable instructions that, when executed by a processor, implement the steps of the matching tracking decision feedback equilibrium method as described in any one of claims 1 to 7.

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