A traveling wave tube non-linear simulation method applied to a wireless channel simulator

Abstract

The application provides a traveling wave tube nonlinear simulation method applied to a wireless channel simulator and relates to the technical field of signal processing. The application obtains suitable error functions and conversion functions through a transformation formula selection step; the error functions are selected: according to amplitude / phase nonlinear transformation, logarithmic / linear forms are respectively adopted; the conversion functions are selected: according to amplitude / phase nonlinear transformation, full-order forms are uniformly adopted; the targeted error functions and conversion functions can make fitting errors to be extremely small. A transformation formula iteration step: through fitting parameters of local optimal solutions, simulation of nonlinear transformation curves is completed, so that excellent fitting results are obtained. In addition, when the fitting error does not meet the requirements, the highest order of the numerator of the nonlinear amplitude / phase conversion function can be raised to 2 orders, the highest order of the denominator can be raised to 3 orders, and fitting is performed again, so that the fitting precision is improved.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a traveling wave tube nonlinear simulation method for use in wireless channel simulators. Background Technology

[0002] When simulating satellite-to-ground communication using a wireless channel simulator, it is necessary not only to simulate the wireless channel between the satellite and the ground, but also to simulate the satellite's payload characteristics. As part of the satellite transponder, the power characteristic curve of a traveling wave tube amplifier includes an amplification region and a saturation region. Due to the limitations of the satellite's operating environment, its power is usually very restricted, causing the traveling wave tube amplifier to generally operate near the saturation point. This inevitably introduces nonlinear distortion into the satellite-to-ground wireless channel.

[0003] When simulating the nonlinear characteristics of traveling wave tube (TWT) amplifiers, the amplitude conversion effect (AM / AM) and amplitude-phase conversion effect (AM / PM) proposed by Salah are generally used. However, since the conversion coefficients are fixed values, only fixed nonlinear characteristics can be simulated. If users need to specify the nonlinear characteristics of the TWT according to the characteristics of their own equipment, Salah's method cannot match arbitrary nonlinear transformation curves due to the fixed parameters, lacking flexibility. Therefore, existing technologies cannot simulate arbitrary nonlinear transformation curves well and cannot meet the nonlinear simulation requirements of wireless channel simulators for TWTs.

[0004] Therefore, it is necessary to provide a traveling wave tube nonlinear simulation method for wireless channel simulators to solve the above-mentioned technical problems. Summary of the Invention

[0005] To address one of the aforementioned technical problems, this invention provides a nonlinear simulation method for traveling wave tubes applied to a wireless channel simulator, comprising: a transformation formula selection step and a transformation formula iteration step; wherein: Transformation formula selection steps: For the simulation of nonlinear transformation curves, select the corresponding transformation formula according to the amplitude / phase transformation type; this includes selecting the error function and the conversion function; for error function selection: logarithmic form is used for amplitude nonlinear transformation; linear form is used for phase nonlinear transformation; for conversion function selection: full-order form is uniformly used for both amplitude and phase nonlinear transformations, and the amplitude and phase conversion functions are selected accordingly. The transformation formula iterative steps are as follows: Based on the amplitude / phase nonlinear transformation, select the corresponding error function and transformation function; iterate the fitting parameters in the transformation function through iterative logic; obtain the fitting parameters that satisfy the local optimum in the transformation function through iteration; and complete the simulation of the nonlinear transformation curve using the fitting parameters of the local optimum.

[0006] As a further solution, a logarithmic error function is used when performing the amplitude nonlinear transformation: in, This is the nonlinear magnitude transformation function that needs to be fitted; The amplitude conversion value input by the user.

[0007] As a further solution, a nonlinear amplitude transformation function is used when performing the nonlinear amplitude transformation: Both the numerator and denominator are expressed in full order. , , and These are the amplitude fitting parameters.

[0008] As a further solution, a linear error function is used when performing phase nonlinear transformation: in, The nonlinear phase transition function to be fitted; The phase conversion value input by the user.

[0009] As a further solution, a nonlinear phase transformation function is used when performing phase nonlinear transformation: Both the numerator and denominator are expressed in full order. , , , and These are the phase fitting parameters.

[0010] As a further solution, the formula iteration steps are transformed: Step 1: For the function to be fitted Given an initial value ; Step 2: Begin iteration, for the ... Next iteration: Step 2.1: Calculate the current Jacobian matrix. and ; Step 2.2: Solve the corresponding and ; Step 2.2: Using the formula Solve ; Step 2.3: Determine Is it small enough? like If it is small enough, stop iterating; Otherwise, let Return to step 2 and execute the next step. +1 iterations; Step 3: Output the fitted parameters obtained through iteration to obtain the fitted parameters of the local optimum.

[0011] As a further solution, when performing a nonlinear amplitude transformation, the Jacobian matrix corresponding to the nonlinear amplitude transformation function is: in, .

[0012] As a further solution, when performing a phase nonlinear transformation, the Jacobian matrix corresponding to the nonlinear phase transformation function is: in, .

[0013] As a further solution, utilizing the formula Solve ;in: , ; Indicates to Find the partial derivative and represent the Jacobian matrix in the multivariate case; For the function to be fitted, Relative to The minute change.

[0014] As a further solution, when the fitting error does not meet the requirements, an order-scaling method is adopted to increase the highest order of the numerator of the nonlinear amplitude / phase conversion function to the second order and the highest order of the denominator to the third order, and then the fitting is performed again.

[0015] Compared with related technologies, the traveling wave tube nonlinear simulation method for wireless channel simulators provided by this invention has the following advantages: This invention obtains suitable error and transformation functions through a transformation formula selection step. The error function is selected by using logarithmic or linear forms based on the amplitude / phase nonlinear transformation. The transformation function is selected by uniformly using the full-order form based on the amplitude / phase nonlinear transformation. These targeted error and transformation functions minimize fitting errors, allowing for different fitting methods to meet the needs of nonlinear simulation. The transformation formula iterative step simulates the nonlinear transformation curve using fitting parameters from local optima, resulting in excellent fitting results. Furthermore, when the fitting error is insufficient, an order-increasing method can be used, raising the highest order of the numerator of the nonlinear amplitude / phase transformation function to 2 and the highest order of the denominator to 3, and then refitting, thereby improving fitting accuracy. Attached Figure Description

[0016] Figure 1 This is a preferred flowchart illustrating a traveling wave tube nonlinear simulation method for a wireless channel simulator, as provided in an embodiment of the present invention. Figure 2 This is an example diagram of the Saleh amplitude-phase conversion model provided in an embodiment of the present invention; Figure 3 A comparison diagram of amplitude nonlinear transformation and Saleh amplitude transformation in DVB-S2X provided in the embodiments of the present invention; Figure 4 This is a comparison diagram of fitting methods provided in the embodiments of the present invention, wherein: Method 1: Fitting using the amplitude variation and logarithmic error function proposed by Salah; Method 2: Fitting using the amplitude variation and logarithmic error function proposed in the example; Method 3: Fitting using the amplitude variation and linear error function proposed in the example; Figure 5 A comparison diagram of phase nonlinear fitting provided for embodiments of the present invention. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] like Figure 1 As shown in the figure, this embodiment provides a nonlinear simulation method for traveling wave tubes applied to a wireless channel simulator, including: a transformation formula selection step and a transformation formula iteration step; wherein: Transformation formula selection steps: For the simulation of nonlinear transformation curves, select the corresponding transformation formula according to the amplitude / phase transformation type; this includes selecting the error function and the conversion function; for error function selection: logarithmic form is used for amplitude nonlinear transformation; linear form is used for phase nonlinear transformation; for conversion function selection: full-order form is uniformly used for both amplitude and phase nonlinear transformations, and the amplitude and phase conversion functions are selected accordingly. The transformation formula iterative steps are as follows: Based on the amplitude / phase nonlinear transformation, select the corresponding error function and transformation function; iterate the fitting parameters in the transformation function through iterative logic; obtain the fitting parameters that satisfy the local optimum in the transformation function through iteration; and complete the simulation of the nonlinear transformation curve using the fitting parameters of the local optimum.

[0019] It should be noted that the nonlinear characteristics of traditional satellite traveling wave tube amplifiers generally employ the amplitude conversion effect (AM / AM) and amplitude-phase conversion effect (AM / PM) proposed by Salah; the formula for the amplitude-phase conversion model is as follows: (1) In the above table, corresponding and In formula (1) and ; corresponding and In formula (1) and These parameters have no particular physical meaning; they merely represent the coefficients of their respective variables. Each set of parameters in the Saleh amplitude conversion model is obtained from numerous statistical experiments using different measurement data, and can only simulate fixed nonlinear characteristics, such as... Figure 2 As shown. Meanwhile, in formula (1)... For example, its numerator only contains order 1, and the denominator only contains order 0 and order 2. The use of fixed orders for the numerator and denominator in the Saleh transformation formula will also limit the accuracy of the fitting error.

[0020] Because its conversion coefficient is a fixed value, it can only simulate fixed nonlinear characteristics; if the user needs to specify the nonlinear characteristics of the traveling wave tube according to the characteristics of their own equipment, it cannot match arbitrary nonlinear transformation curves, lacking flexibility. Figure 3As shown, the Ka-band single-carrier transmission nonlinearity based on DVB-S2X (Digital Video Broadcasting-Second Generation Satellite Extensuons) is found to be mismatched with Saleh's amplitude conversion model by comparison, and thus cannot meet the fitting requirements.

[0021] Therefore, this embodiment proposes a nonlinear simulation method for traveling wave tubes applied to wireless channel simulators. It achieves full order by modifying the transformation formula and adopts different fitting methods according to the amplitude and phase characteristics specified by the user to meet the requirements of nonlinear simulation.

[0022] As a further solution, a logarithmic error function is used when performing the amplitude nonlinear transformation: (9) in, This is the nonlinear magnitude transformation function that needs to be fitted; The amplitude conversion value input by the user.

[0023] It should be noted that the amplitude conversion model in formula (1) is expressed as a linear value, assuming that the amplitude conversion value input by the user is... (dB value), the error function has two forms, namely linear form and logarithmic form; considering that the input signal power (dB value) is negative, the fitting error of the linear form is large. In order to reduce the fitting error, the error function adopts the form of formula (9).

[0024] As a further solution, a nonlinear amplitude transformation function is used when performing the nonlinear amplitude transformation: (10) Both the numerator and denominator are expressed in full order. , , and These are the amplitude fitting parameters.

[0025] It should be noted that: considering that the highest order of the numerator in the amplitude conversion formula (1) is 1, and the 0th order is missing, and the highest order of the denominator is 2, and the 1st order is missing, in order to maximize the accuracy of the fitting, the numerator and denominator in the fitting conversion function are both of full order; that is, the amplitude conversion formula (1) can be considered as a special case of formula (10).

[0026] As a further solution, a linear error function is used when performing phase nonlinear transformation: (8) in, The nonlinear phase transition function to be fitted; The phase conversion value input by the user.

[0027] As a further solution, a nonlinear phase transformation function is used when performing phase nonlinear transformation: (12) Both the numerator and denominator are expressed in full order. , , , and These are the phase fitting parameters.

[0028] As a further solution, the formula iteration steps are transformed: Step 1: For the function to be fitted Given an initial value ; Step 2: Begin iteration, for the ... Next iteration: Step 2.1: Calculate the current Jacobian matrix. and ; Step 2.2: Solve the corresponding and ; Step 2.2: Using the formula Solve ; Step 2.3: Determine Is it small enough? like If it is small enough, stop iterating; Otherwise, let Return to step 2 and execute the next step. +1 iterations; Step 3: Output the fitted parameters obtained through iteration to obtain the fitted parameters of the local optimum.

[0029] It should be noted that: assuming For the function to be fitted, exist Using Taylor series expansion and taking its first-order approximation, we obtain: (2) in, Relative to A tiny change, express First derivative, Indicates to Find the partial derivative (representing the Jacobian matrix in multivariate time).

[0030] The squared error of formula (2) can be written as: (3) To minimize the error in formula (2), i.e., to adjust formula (3) as follows: Take the derivative and set it to zero: (4) Rearranging formula (4), we get: (5) make , Formula (5) can be written as: (6) As can be seen from the above, formula (6) can make formula (2) satisfy the iteration condition: make Formula (2) can be rewritten as: (7) Among them, when Enough hours , That is, a local optimum.

[0031] As a further solution, when performing the amplitude nonlinear transformation, the Jacobian matrix corresponding to the nonlinear amplitude transformation function can be obtained according to formula (9): (11) in, .

[0032] It should be noted that: according to formula (11) And the matrix can be calculated using formula (9). and And through multiple iterations, the local optimal solution in formula (10) can be achieved. , , and .

[0033] like Figure 4 As shown below, the iterative fitting result of a specific embodiment is as follows: Table 1. DVB-S2X Amplitude-Phase Nonlinear Transformation Table Table 2 Fitting results for nonlinear amplitude variation Based on Table 1, draw the nonlinear conversion diagram of DVB-S2X input power; for Figure 4 A comparison of Method 1 and Method 2 shows that for fitting nonlinear changes, using Method 2 (full-order method) can significantly reduce errors. Figure 4 A comparison of Method 2 and Method 3 shows that, due to the negative dB input power, the accuracy of linear fitting using Method 3 is difficult to guarantee for smaller powers (-20 dB). Simulation results demonstrate the rationality of using a full-order logarithmic error function for fitting, as mentioned in this paper, when dealing with nonlinear amplitude transformations.

[0034] As a further solution, when performing the phase nonlinear transformation, the Jacobian matrix corresponding to the nonlinear phase transformation function can be obtained from the linear error function of formula (8): (13) in, .

[0035] It should be noted that: according to formula (13) And the matrix can be calculated using formula (8). and And through multiple iterations, the local optimal solution in formula (12) can be achieved. , , , and .

[0036] Table 3. Fitting results of phase nonlinear variation like Figure 5 The fitting comparison shown demonstrates that a linear error function can effectively represent the user-specified nonlinear phase change. Furthermore, simulation results demonstrate the rationality of using a full-order linear error function for fitting nonlinear phase transformations, as mentioned in this paper.

[0037] As a further solution, utilizing the formula Solve ;in: , ; Indicates to Find the partial derivative and represent the Jacobian matrix in the multivariate case; For the function to be fitted, Relative to The minute change.

[0038] As a further solution, when the fitting error does not meet the requirements, an order-scaling method is adopted to increase the highest order of the numerator of the nonlinear amplitude / phase conversion function to the second order and the highest order of the denominator to the third order, and then the fitting is performed again.

[0039] The above are merely embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A nonlinear simulation method for traveling wave tubes applied to a wireless channel simulator, characterized in that, include: The transformation formula selection steps and the transformation formula iteration steps; where: Transformation formula selection steps: For the simulation of nonlinear transformation curves, select the corresponding transformation formula according to the amplitude / phase transformation type; this includes selecting the error function and the conversion function; for error function selection: logarithmic form is used for amplitude nonlinear transformation; linear form is used for phase nonlinear transformation; for conversion function selection: full-order form is uniformly used for both amplitude and phase nonlinear transformations, and the amplitude and phase conversion functions are selected accordingly. The transformation formula iterative steps are as follows: Based on the amplitude / phase nonlinear transformation, select the corresponding error function and transformation function; iterate the fitting parameters in the transformation function through iterative logic; obtain the fitting parameters that satisfy the local optimum in the transformation function through iteration; and complete the simulation of the nonlinear transformation curve using the fitting parameters of the local optimum. When performing amplitude nonlinear transformation, a logarithmic error function is used: in, This is the nonlinear magnitude transformation function that needs to be fitted; The amplitude conversion value input by the user; When performing phase nonlinear transformation, a linear error function is used: in, The nonlinear phase transition function to be fitted; The phase conversion value input by the user.

2. The traveling wave tube nonlinear simulation method applied to a wireless channel simulator according to claim 1, characterized in that, When performing nonlinear amplitude transformation, a nonlinear amplitude transformation function is used: Both the numerator and denominator are expressed in full order. , , and These are the amplitude fitting parameters.

3. The traveling wave tube nonlinear simulation method applied to a wireless channel simulator according to claim 1, characterized in that, When performing phase nonlinear transformation, a nonlinear phase transformation function is used: Both the numerator and denominator are expressed in full order. , , , and These are the phase fitting parameters.

4. A traveling wave tube nonlinear simulation method for a wireless channel simulator according to any one of claims 1 to 3, characterized in that, Iterative steps for the transformation formula: Step 1: For the function to be fitted Given an initial value ; Step 2: Begin iteration, for the ... Next iteration: Step 2.1: Calculate the current Jacobian matrix. and ; Step 2.2: Solve the corresponding and ; Step 2.3: Using the formula Solve ; Step 2.4: Judgment Is it small enough? like If it is small enough, stop iterating; Otherwise, let Return to step 2 and execute the next step. +1 iterations; Step 3: Output the fitting parameters obtained through iteration to obtain the fitting parameters of the local optimum.

5. The traveling wave tube nonlinear simulation method applied to a wireless channel simulator according to claim 4, characterized in that, When performing a nonlinear amplitude transformation, the Jacobian matrix corresponding to the nonlinear amplitude transformation function is: in, 。 6. The traveling wave tube nonlinear simulation method applied to a wireless channel simulator according to claim 4, characterized in that, When performing a phase nonlinear transformation, the Jacobian matrix corresponding to the nonlinear phase transformation function is: in, 。 7. The traveling wave tube nonlinear simulation method applied to a wireless channel simulator according to claim 4, characterized in that, Using formula Solve ;in: , ; Indicates to Find the partial derivative and represent the Jacobian matrix in the multivariate case; For the function to be fitted, Relative to The minute change.

8. The traveling wave tube nonlinear simulation method applied to a wireless channel simulator according to claim 4, characterized in that, If the fitting error does not meet the requirements, the order is increased to the highest order of the numerator of the nonlinear amplitude / phase conversion function to the second order and the highest order of the denominator to the third order, and then the fitting is performed again.

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