Generalized linear dual-mode blind equalization method based on Volterra model

Abstract

Aiming at the problem of signal nonlinear distortion caused by nonlinear characteristics of a power amplifier in satellite communication, the invention provides a generalized linear dual-mode switching blind equalization algorithm based on a third-order truncated Volterra structure, and the technical scheme and the application effect are expanded according to the following steps S1 to S3: S1: initializing parameters of a generalized linear blind equalizer based on the third-order Volterra structure; s2, taking a modified constant modulus algorithm and a decision-oriented least mean square algorithm in the linear blind equalization field as theoretical basis, combining signal processing characteristics of a third-order truncated Volterra nonlinear model, deriving to obtain two generalized linear equalizer tap updating formulas suitable for the nonlinear model, and providing algorithm support for a dual-mode equalization mechanism; s3, adopting a staged adaptive equalization strategy to construct a switching mechanism: in an equalization initial stage, using a generalized linear correction constant modulus algorithm of a nonlinear channel, and utilizing a rapid convergence characteristic of the algorithm to realize rapid reduction of a mean square error; and when the equalization process reaches a preset judgment condition, automatically switching to a generalized linear judgment guide algorithm of a nonlinear channel, further reducing the steady-state error through judgment feedback, and considering both the convergence speed and the equalization precision.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of nonlinear channel blind equalization in satellite communication signal processing, and relates to a generalized linear dual-mode blind equalization method based on a Volterra model. BACKGROUND

[0002] With the rapid development of space technology, satellite communication has become an important means of modern data transmission. In order to realize long-distance transmission, satellite systems usually rely on power amplifiers to amplify signals. However, the inherent nonlinear characteristics of power amplifiers will cause distortion to the amplitude and phase of the modulated signal, resulting in constellation distortion. In particular, in the case of high-order multi-mode modulation signals, the nonlinear distortion has a particularly serious impact on system performance, and the demodulation accuracy and communication reliability of the receiver are significantly reduced.

[0003] In the prior art, researchers have proposed a variety of nonlinear equalization methods to compensate for the nonlinear distortion of satellite channels. Traditional equalization methods based on Volterra structure and LMS algorithm can improve the equalization performance to a certain extent, but there are still the following shortcomings in the satellite communication environment: on the one hand, the long delay characteristics of satellite links result in the use of a large amount of bandwidth resources by equalization methods relying on training sequences; on the other hand, the complex and variable satellite channel environment makes it difficult for traditional equalization algorithms to track and converge stably in real time. In addition, although the Volterra equalizer has advantages in modeling nonlinearity, its high computational complexity limits its practical deployment. In contrast, blind equalization technology does not require training sequences and can save bandwidth and adapt to channel changes, but the existing blind equalization methods still have contradictions between convergence speed, steady-state error and computational complexity, and it is difficult to balance them. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a generalized linear dual-mode blind equalization method based on a Volterra model to solve the problems of difficulty in compensating for nonlinear distortion, slow algorithm convergence and large steady-state error in satellite communication. The present application first derives the tap update formula of the generalized linear equalizer based on a third-order truncated Volterra structure; then a dual-mode switching mechanism is designed: in the initial equalization stage, a modified constant modulus algorithm based on generalized linearity is used to achieve rapid reduction of mean square error; when the decision condition is met, switch to a generalized linear decision-directed algorithm to reduce the mean square steady-state error. This method balances convergence speed and complexity while ensuring equalization performance, and can effectively improve the equalization performance and transmission reliability of high-order multi-mode modulation signals in satellite communication systems.

[0005] To achieve the above purpose, the present application provides the following technical solutions:

[0006] A generalized linear dual-mode blind equalization method based on the Volterra model for nonlinear distortion compensation includes the following steps:

[0007] S1: Initialize the parameters of the generalized linear blind equalizer based on the third-order Volterra structure;

[0008] S2: Based on the modified constant modulus algorithm and decision-oriented minimum mean square algorithm in the field of linear blind equalization, and combined with the signal processing characteristics of the third-order truncated Volterra nonlinear model, two generalized linear equalizer tap update formulas applicable to this nonlinear model are derived, providing algorithmic support for the dual-mode equalization mechanism.

[0009] S3: A phased adaptive equalization strategy is adopted to construct a switching mechanism: In the initial stage of equalization, the generalized linear corrected constant modulus algorithm of the nonlinear channel is used to achieve a rapid decrease in mean square error by taking advantage of its fast convergence characteristics; when the equalization process reaches the preset decision condition, it automatically switches to the generalized linear decision-guided algorithm of the nonlinear channel to further reduce the steady-state error through decision feedback, taking into account both convergence speed and equalization accuracy.

[0010] Furthermore, the parameters of the generalized linear blind equalizer based on the third-order Volterra structure mentioned in step S1 include: x(n) is the input signal of the equalizer, y(n) is the input signal of the equalizer, and the linear and nonlinear parts of the Volterra nonlinear equalizer are respectively... Error function e(n), nonlinear satellite channel memory depth N, cost function J of the generalized linear correction constant modulus algorithm for nonlinear channels. NCWL-MCMA The cost function J of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels. NCWL-DD .

[0011] Furthermore, the two generalized linear equalizer tap update formulas applicable to this nonlinear model in step S2 are as follows:

[0012]

[0013] Among them, J NCWL-MCMA J is the cost function of the generalized linear modified constant modulus algorithm for nonlinear channels. NCWL-DD Let be the cost function of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels, w be the kernel coefficient of the Volterra nonlinear equalizer, and G(n) and Z(n) be the tap update coefficients of the linear and nonlinear parts of the generalized linear modified constant modulus algorithm for nonlinear channels, respectively. The linear cost function J NCWL-MCMA The instantaneous gradient of (G), The nonlinear cost function J NCWL-MCMAThe instantaneous gradient of (Z), L(n) and K(n) are the tap update coefficients of the linear and nonlinear parts of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels. The cost function J NCWL-DD (L) Instantaneous gradient of the linear part, The cost function J NCWL-DD (K) Instantaneous gradient of the nonlinear part, μ1 is the step size parameter for updating the taps of the linear part, μ3 is the step size parameter for updating the taps of the nonlinear part, y(n) is the output of the third-order truncated Volterra equalizer, the linear part output is y1(n), the nonlinear part output is y3(n), y R (n) is the real part of y(n), y I (n) is the imaginary part of y(n), r R and r I This was calculated statistically from the transmitted signals; where:

[0014]

[0015]

[0016] s R (n) and s I (n) represents the real and imaginary parts of the transmitted signal, which are independent of the instantaneous values ​​of the training sequence; It is the signal corresponding to the ideal constellation point obtained by making a decision based on the equalizer output, and therefore it is also unrelated to the instantaneous value of the training sequence.

[0017] Furthermore, the updating of the tap coefficients of the two algorithm equalizers and the determination of the algorithm switching time mentioned in step S3 specifically include the following steps:

[0018] The determination is based on the distance between the equalizer output point and the ideal constellation point. When y(n)∈D, the generalized linear modified constant modulus algorithm for nonlinear channels is used for reliability assessment to achieve fast convergence. k When switching to a generalized linear decision-guided minimum mean square error algorithm for a nonlinear channel, better steady-state performance is achieved. Here, y(n) is the equalizer output, and D... k Let be a circle with radius d near the modulation point.

[0019] Furthermore, the updating of the tap coefficients of the two algorithm equalizers and the determination of the algorithm switching time mentioned in step S3 specifically include the following steps:

[0020] S31: In the initial stage of equalization, due to inaccurate selection of the step size and the number of equalizer orders, equalization cannot be performed well, and the equalizer output point may be far from the ideal constellation point. Initial equilibrium is first achieved using the tap coefficients of the generalized linear modified constant modulus algorithm.

[0021] S32: Determine whether the algorithm switching condition y(n)∈D is met. k When the algorithm switching condition is met, proceed to step S33. If the condition is not met, determine whether the maximum number of iterations has been reached, i.e. whether all sampling points have been used. If so, the iteration ends; otherwise, return to S31.

[0022] S33: After the decision condition is met, the algorithm is replaced with the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels with smaller steady-state residuals. Since the data is already relatively reliable when using the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels, there is no need to make a reliability decision. This can achieve better steady-state performance while achieving fast convergence.

[0023] The beneficial effects of this invention are as follows: Addressing the performance degradation of high-order multimode modulated signals due to nonlinear distortion of power amplifiers in satellite communication, a generalized linear dual-mode switching blind equalization method based on a third-order truncated Volterra structure is proposed. This method employs a generalized linear modified constant modulus algorithm in the initial equalization stage to rapidly reduce the mean square error. Once the decision condition is met, it switches to a generalized linear decision-guided algorithm to reduce the mean square steady-state error. Compared to traditional adaptive equalization methods, this invention eliminates the need for training sequences, saves bandwidth, and adaptively handles complex time-varying channel environments. Furthermore, combining the advantages of fast convergence and low steady-state error, it achieves nonlinear distortion compensation for high-order multimode modulated signals, improving the equalization performance and transmission reliability of satellite communication systems.

[0024] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0026] Figure 1 This is a structural diagram of the generalized linear dual-mode blind equalization communication system based on the Volterra model described in this invention.

[0027] Figure 2 This is a flowchart of the generalized linear dual-mode blind equalization method based on the Volterra model described in this invention.

[0028] Figure 3The bit error rate curves of different methods of the generalized linear dual-mode blind equalization method based on the Volterra model described in this invention are shown.

[0029] Figure 4 The graph shows the residual inter-symbol interference (ISI) curves for different methods of the Volterra model-based generalized linear dual-mode blind equalization method described in this invention. Detailed Implementation

[0030] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0031] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0032] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0033] This invention provides a generalized linear dual-mode blind equalization method based on the Volterra model, considering the transmission scenarios of actual satellite communication systems, such as... Figure 1 As shown, the overall communication block diagram of the generalized linear dual-mode blind equalization method based on the Volterra model is as follows: signal source, nonlinear satellite channel, noise signal v(n), Volterra filter, generalized linear adaptive filter, error estimate e(n); the signal source transmits radio frequency information; after passing through the Wiener nonlinear satellite channel, the nonlinear distortion generated by the power amplifier is simulated; the generalized linear adaptive filter updates the equalizer tap coefficients using the generalized linear corrected constant modulus algorithm and the generalized linear decision-guided minimum mean square error algorithm respectively; the Volterra filter realizes the equalization of the nonlinear part.

[0034] likeFigure 2 As shown, this method specifically includes the following steps:

[0035] S1: Initialize the parameters of the generalized linear blind equalizer based on the third-order Volterra structure;

[0036] Preferably, the parameters of the generalized linear blind equalizer based on the third-order Volterra structure include: x(n) is the input signal of the equalizer, and the linear and nonlinear parts of the Volterra nonlinear equalizer are respectively... Error function e(n), nonlinear satellite channel memory depth N, cost function J of the generalized linear correction constant modulus algorithm for nonlinear channels. NCWL-MCMA The cost function J of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels. NCWL-DD .

[0037] S2: Based on the modified constant modulus algorithm and decision-oriented minimum mean square algorithm in the field of linear blind equalization, and combined with the signal processing characteristics of the third-order truncated Volterra nonlinear model, two generalized linear equalizer tap update formulas applicable to this nonlinear model are derived, providing algorithmic support for the dual-mode equalization mechanism.

[0038] The two generalized linear equalizer tap update formulas for the Volterra nonlinear model, derived from the traditional dual-mode linear blind equalization, are as follows:

[0039]

[0040] Among them, J NCWL-MCMA J is the cost function of the generalized linear modified constant modulus algorithm for nonlinear channels. NCWL-DD Let be the cost function of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels, w be the kernel coefficient of the Volterra nonlinear equalizer, and G(n) and Z(n) be the tap update coefficients of the linear and nonlinear parts of the generalized linear modified constant modulus algorithm for nonlinear channels, respectively. The linear cost function J NCWL-MCMA The instantaneous gradient of (G), The nonlinear cost function J NCWL-MCMA The instantaneous gradient of (Z), L(n) and K(n) are the tap update coefficients of the linear and nonlinear parts of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels. The cost function J NCWL-DD (L) Instantaneous gradient of the linear part, The cost function J NCWL-DD(K) Instantaneous gradient of the nonlinear part, μ1 is the step size parameter for updating the taps of the linear part, μ3 is the step size parameter for updating the taps of the nonlinear part, y(n) is the output of the third-order truncated Volterra equalizer, the linear part output is y1(n), the nonlinear part output is y3(n), y R (n) is the real part of y(n), y I (n) is the imaginary part of y(n), r R and r I This was calculated statistically based on the transmitted signals; where:

[0041]

[0042] Among them, s I (n) and s R (n) represents the real and imaginary parts of the transmitted signal, which are independent of the instantaneous values ​​of the training sequence; It is the signal corresponding to the ideal constellation point obtained by making a decision based on the equalizer output, and therefore it is also unrelated to the instantaneous value of the training sequence.

[0043] S3: A phased adaptive equalization strategy is adopted to construct a switching mechanism: In the initial stage of equalization, the generalized linear corrected constant modulus algorithm of the nonlinear channel is used to achieve a rapid decrease in mean square error by taking advantage of its fast convergence characteristics; when the equalization process reaches the preset decision condition, it automatically switches to the generalized linear decision-guided algorithm of the nonlinear channel to further reduce the steady-state error through decision feedback, taking into account both convergence speed and equalization accuracy.

[0044] The determination is based on the distance between the equalizer output point and the ideal constellation point. When y(n)∈D, the generalized linear modified constant modulus algorithm for nonlinear channels is used for reliability assessment to achieve fast convergence. k When switching to a generalized linear decision-guided minimum mean square error algorithm for a nonlinear channel, better steady-state performance is achieved. Here, y(n) is the equalizer output, and D... k Let be a circle with radius d near the modulation point.

[0045] S4: In the initial stage of equalization, due to inaccurate selection of the step size and the number of equalizer orders, equalization cannot be performed well, and the equalizer output point may be far from the ideal constellation point. Initial equilibrium is first achieved using the tap coefficients of the generalized linear modified constant modulus algorithm.

[0046] S5: Determine if the algorithm switching condition y(n)∈D is met. k When the algorithm switching condition is met, proceed to step S6. If the condition is not met, determine whether the maximum number of iterations has been reached, i.e., whether all sampling points have been used. If so, the iteration ends; otherwise, return to S4.

[0047] S6: After the decision condition is met, the algorithm is replaced with the generalized linear decision-guided minimum mean square error algorithm of the nonlinear channel with smaller steady-state residual. Since the data is already relatively reliable when using the generalized linear decision-guided minimum mean square error algorithm of the nonlinear channel, there is no need to make a reliability decision. While achieving fast convergence, it can further achieve better steady-state performance.

[0048] The application effects of this invention will be described in detail below with reference to simulation.

[0049] The simulation uses a medium-high Earth orbit satellite with an altitude of 18,000 km. 16APSK modulation is currently the modulation method with the highest communication quality and transmission efficiency among multi-amplitude multi-phase modulation methods for satellite communication signals; therefore, 16APSK modulation is used in the simulation. The upsampling and downsampling rates are both 8x, and both the shaping filter and the matched filter are raised cosine roll-off filters with a length of 64 bits and a roll-off factor of 0.25. In the satellite communication system, the length of the transmitted discrete signal is 50,000 symbols. The satellite channel uses a nonlinear Wiener model for the power amplifier.

[0050] In this embodiment, Figure 3 The bit error rate curves for different methods in this example are given. Figure 4 The graphs of residual inter-symbol interference for different methods in this example are given.

[0051] Among them, by Figure 3It can be seen that the traditional Modified Constant Modulus Algorithm (MCMA) and Decision-Directed Least Mean Square (DD-LMS) algorithms maintain a high bit error rate (BER) across the entire signal-to-noise ratio (SNR) range, indicating that these algorithms cannot effectively eliminate power amplifier distortion and reduce the BER. The Nonlinear Channel Wideband Linear-Decision-Directed (NCWL-DD) algorithm gradually decreases the BER with increasing SNR, but the decrease is slow, reaching a BER of 0.1% at an SNR of 25dB. This indicates that the algorithm can compensate for nonlinear distortion to some extent, but the effect is not significant. The Nonlinear Channel Wideband Linear-Modified Constant Modulus (NCWL-MCMA) algorithm shows a faster BER decrease than the NCWL-DD algorithm, and at an SNR of 25dB, the BER is only about 0.01%. This indicates that the algorithm outperforms NCWL-DD and provides better compensation for nonlinear distortion, but there is still room for improvement. Finally, the generalized linear dual-mode blind equalization algorithm NCWL-MCMA-DD for nonlinear channels exhibits the fastest decrease in bit error rate, achieving a bit error rate of approximately 10% at a signal-to-noise ratio of 25dB. -4 Furthermore, under the same signal-to-noise ratio, its bit error rate is always the lowest, indicating that the algorithm has the best performance. Figure 4 Among the results, the MCMA-DD algorithm exhibits the highest residual inter-symbol interference (ISI), indicating its inability to effectively compensate for nonlinear distortion. The NCWL-DD algorithm shows a lower steady-state error compared to the MCMA-DD algorithm, but its effect on nonlinear distortion compensation remains limited. The NCWL-MCMA algorithm generally has lower ISI than both the MCMA-DD and NCWL-DD algorithms, and its convergence speed is faster, demonstrating better nonlinear distortion compensation. The NCWL-MCMA-DD algorithm curve shows a rapid decline in the initial segment. It has the fastest convergence speed and the lowest final ISI, representing a nearly 15dB performance improvement over the MCMA-DD algorithm. This indicates that the NCWL-MCMA-DD algorithm has the strongest ability to suppress ISI, quickly and effectively reducing it and achieving nonlinear distortion compensation.

[0052] In the above embodiments, the reference to "this embodiment" in the specification indicates that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily all refer to the same embodiment.

[0053] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0054] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0055] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A generalized linear dual-mode blind equalization method based on the Volterra model for nonlinear distortion compensation, characterized in that: Includes the following steps: S1: Initialize the parameters of the generalized linear blind equalizer based on the third-order Volterra structure; S2: Based on the modified constant modulus algorithm and decision-oriented minimum mean square algorithm in the field of linear blind equalization, and combined with the signal processing characteristics of the third-order truncated Volterra nonlinear model, two generalized linear equalizer tap update formulas applicable to this nonlinear model are derived, providing algorithmic support for the dual-mode equalization mechanism. S3: A phased adaptive equalization strategy is adopted to construct a switching mechanism: In the initial stage of equalization, the generalized linear corrected constant modulus algorithm of the nonlinear channel is used to achieve a rapid decrease in mean square error by taking advantage of its fast convergence characteristics; when the equalization process reaches the preset decision condition, it automatically switches to the generalized linear decision-guided algorithm of the nonlinear channel to further reduce the steady-state error through decision feedback, taking into account both convergence speed and equalization accuracy.

2. The generalized linear dual-mode blind equalization method based on the Volterra model according to claim 1, characterized in that: The parameters of the generalized linear blind equalizer based on the third-order Volterra structure mentioned in step S1 include: x(n) is the input signal of the equalizer, and the linear and nonlinear parts of the Volterra nonlinear equalizer are respectively... Error function e(n), nonlinear satellite channel memory depth N, cost function J of the generalized linear correction constant modulus algorithm for nonlinear channels. NCWL-MCMA The cost function J of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels. NCWL-DD .

3. The Volterra model-based generalized linear dual-mode blind equalization method for nonlinear distortion compensation according to claim 1, characterized in that: The two generalized linear equalizer tap update formulas applicable to this nonlinear model in step S2 provide algorithmic support for the dual-mode equalization mechanism: Among them, J NCWL-MCMA J is the cost function of the generalized linear modified constant modulus algorithm for nonlinear channels. NCWL-DD Let be the cost function of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels, w be the kernel coefficient of the Volterra nonlinear equalizer, and G(n) and Z(n) be the tap update coefficients of the linear and nonlinear parts of the generalized linear modified constant modulus algorithm for nonlinear channels, respectively. The linear cost function J NCWL-MCMA The instantaneous gradient of (G), The nonlinear cost function J NCWL-MCMA The instantaneous gradient of (Z), L(n) and K(n) are the tap update coefficients of the linear and nonlinear parts of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels. The cost function J NCWL-DD (L) Instantaneous gradient of the linear part, The cost function J NCWL-DD (K) Instantaneous gradient of the nonlinear part, μ1 is the step size parameter for updating the taps of the linear part, μ3 is the step size parameter for updating the taps of the nonlinear part, y(n) is the output of the third-order truncated Volterra equalizer, the linear part output is y1(n), the nonlinear part output is y3(n), y R (n) is the real part of y(n), y I (n) is the imaginary part of y(n), r R and r I This was calculated statistically from the transmitted signals; where: s I (n) and s R (n) represents the real and imaginary parts of the transmitted signal, which are independent of the instantaneous values ​​of the training sequence; It is the signal corresponding to the ideal constellation point obtained by making a decision based on the equalizer output, and therefore it is also unrelated to the instantaneous value of the training sequence.

4. The generalized linear dual-mode blind equalization method based on the Volterra model according to claim 1, characterized in that: Step S3 involves performing a handover equalization algorithm based on the decision criteria, specifically including the following steps: The determination is based on the distance between the equalizer output point and the ideal constellation point. When y(n)∈D, the generalized linear modified constant modulus algorithm for nonlinear channels is used for reliability assessment to achieve fast convergence. k When switching to a generalized linear decision-guided minimum mean square error algorithm for a nonlinear channel, better steady-state performance is achieved. Here, y(n) is the equalizer output, and D... k Let be a circle with radius d near the modulation point.

5. The generalized linear dual-mode blind equalization method based on the Volterra model according to claim 4, characterized in that: The update of the tap coefficients of the two algorithm equalizers and the determination of the algorithm switching time mentioned in step S3 specifically include the following steps: S31: In the initial stage of equalization, due to inaccurate selection of the step size and the number of equalizer orders, equalization cannot be performed well, and the equalizer output point may be far from the ideal constellation point. Initial equilibrium is first achieved using the tap coefficients of the generalized linear modified constant modulus algorithm. S32: Determine whether the algorithm switching condition y(n)∈D is met. k When the algorithm switching condition is met, proceed to step S33. If the condition is not met, determine whether the maximum number of iterations has been reached, i.e. whether all sampling points have been used. If so, the iteration ends; otherwise, return to S31. S33: After the decision condition is met, the algorithm is replaced with the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels with smaller steady-state residuals. Since the data is already relatively reliable when using the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels, there is no need to make a reliability decision. This can achieve better steady-state performance while achieving fast convergence.

6. The generalized linear dual-mode blind equalization method based on the Volterra model according to claim 5, characterized in that: The expression for calculating the tap coefficients of the generalized linear modified constant modulus algorithm in step S31 is as follows: Where G(n) and Z(n) are the tap update coefficients of the linear and nonlinear parts of the generalized linear correction constant modulus algorithm for the nonlinear channel, respectively.

7. The generalized linear dual-mode blind equalization method based on the Volterra model according to claim 6, characterized in that: In step S32, the expression for calculating the decision condition is: y(n)∈D k Where y(n) is the output of the equalizer, which determines the distance to the nearest ideal constellation point. If the distance is less than d, the switching condition is considered to be met.

8. The generalized linear dual-mode blind equalization method based on the Volterra model according to claim 7, characterized in that: The expression for calculating the tap coefficients of the generalized linear modified constant modulus algorithm in step S33 is as follows: Where L(n) and K(n) are the tap update coefficients of the linear and nonlinear parts of the generalized linear decision-guided minimum mean square error algorithm for nonlinear channels.

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