A method for optimizing the selection of basis functions for RF power amplifier models

Abstract

This invention discloses a method for optimizing the selection of basis functions for RF power amplifier models. The order-wise recursive least squares method is widely used to solve various least squares problems because it avoids complex matrix inversion operations. This invention applies the order-wise recursive least squares method to the field of digital predistortion for RF power amplifiers and, based on this algorithm, uses the orthogonal projection component criterion in each step of the recursion to optimize the selection of basis functions for the power amplifier model. This effectively solves the problem of excessively large matrix condition numbers in the model coefficient solution process due to the non-orthogonal nature of basis functions in RF power amplifier models. The method proposed in this invention can simultaneously extract model coefficients and optimize basis functions in the model, significantly reducing the number of required basis functions while maintaining model accuracy, effectively reducing the resources and power consumption of the predistorter implementation. Experimental results show that the model optimized by this invention can effectively compensate for the memory effect and nonlinearity of the power amplifier.

Description

Technical Field

[0001] This invention relates to the field of digital predistortion in radio frequency power amplifiers, and more particularly to an apparatus and method for optimizing the basis functions of a radio frequency power amplifier model based on orthogonal projection criteria and order-wise recursive least squares method. Background Technology

[0002] Fifth-generation mobile communication technology (5G) has been basically deployed in my country. Compared with fourth-generation mobile communication, 5G uses wider communication bandwidth and higher carrier frequency to improve communication capacity. This poses a significant challenge to the linearity of the RF power amplifier, the most power-consuming component in a base station. Because 5G signals have a very high peak-to-average power ratio (PAPR), one solution is to back up the power amplifier power to maintain good linearity. This results in very low power amplifier efficiency, leading to significant power consumption and a major challenge to the heat dissipation of the communication system. Digital predistortion (DPD) technology has become the most popular method for improving the linearity of RF power amplifiers due to its high efficiency, high precision, and ease of integration into baseband signal processing systems. The basic principle of DPD is that the signal is pre-distorted by a module called a predistorter before being input to the power amplifier. Because the predistorter is designed to have opposite characteristics to the power amplifier, the cascaded predistorter-power amplifier system becomes a linear system for the input signal, thus enabling the RF power amplifier to output a signal without distortion relative to the original signal. Therefore, accurately establishing the RF power amplifier model is a key aspect of DPD technology. Through decades of research and exploration by scholars both domestically and internationally, various power amplifier models combining low complexity and high accuracy have been proposed and widely used, such as the memory polynomial (MP) model, the generalized memory polynomial (GMP) model, and the decomposed vector rotation (DVR) model. These models are composed of a series of basis functions of different orders, and these basis functions are often not orthogonal. This means that these basis functions may exhibit strong correlations under certain signals, which leads to two main problems. First, strong correlations between basis functions result in a large ill-conditioned number in the model matrix, leading to numerical instability during model coefficient extraction. Second, some basis functions have minimal impact. Since predistorters often operate at frequencies up to hundreds of megahertz, these insignificant basis functions still consume valuable hardware resources and power. Therefore, optimizing the selection of basis functions in the model is of great significance for reducing the power consumption and resource consumption of the DPD system and improving the robustness of the model parameter calculation process. Summary of the Invention

[0003] Technical Problem: The purpose of this invention is to provide a method for optimizing the selection of basis functions for RF power amplifier models, so as to effectively reduce the required basis functions of the model and improve the numerical stability of the parameter extraction process while maintaining predistortion performance.

[0004] Technical solution: To solve the above technical problems, the present invention provides a basis function optimization selection method applicable to RF power amplifier models, which includes: a digital predistorter, a digital-to-analog converter (DAC), an orthogonal modulator, an RF power amplifier, a coupler, an orthogonal demodulator, an analog-to-digital converter (ADC), and a basis function optimization and parameter extraction algorithm based on the orthogonal projection criterion and the order-wise recursive least squares method.

[0005] A digital predistorter is used to predistort the input digital baseband signal, generating a digital predistorted signal with the opposite distortion characteristics to the RF power amplifier. This digital predistorted signal is converted into an analog signal by a digital-to-analog converter, then modulated to the RF frequency by a quadrature modulator, and finally enters the RF power amplifier for power amplification to drive the antenna. The signal output by the RF power amplifier simultaneously enters a coupler, a quadrature demodulator, and an analog-to-digital converter (ADC) to generate the corresponding digital baseband signal output by the power amplifier. The digital baseband signals input and output by the power amplifier are fed into a basis function optimization and parameter extraction algorithm module based on the orthogonal projection criterion and the order-wise recursive least squares method to optimize the basis functions and extract the parameters of the RF power amplifier model, obtaining the parameters of the predistorter corresponding to the current distortion characteristics of the RF power amplifier. Then, these predistortion parameters are fed into the digital predistorter constructed by the model after basis function optimization.

[0006] The method specifically includes:

[0007] Step 1: Establish the generalized memoized polynomial model expression as follows:

[0008]

[0009] In formula (1), n∈[0, N-1] represents the index position of the sampling point of the digital baseband signal, and the total length of the baseband signal is N sampling points; m is the memory depth and m∈[0, M], where M is the maximum memory depth; p∈[1, P] is the nonlinear order, where P is the maximum nonlinear order; l∈[-L, L] is the depth of memory term crossover, where L is the maximum crossover depth. This is the complex input signal for the power amplifier. The output of the model is a complex signal, and || is defined as the modulo operation on the complex number. These are the model coefficients corresponding to each basis function. It can be seen that the number of coefficients and the number of basis functions in the model are K = P(M+1)(2L+1);

[0010] Step 2, Model Coefficients The solution method represents the model in matrix form as follows:

[0011] Y = HC (2)

[0012] Where Y represents the vector of the output signal, H is the model matrix, and c is the vector of model coefficients, defined as follows: H = [h1, h2, ..., h K ], T denotes the transpose operation of a vector; where h k Defined as the k-th basis function vector corresponding to different combinations of p, m, l. It is its corresponding coefficient, h k The composition can be represented by formula (3). It can be seen that the process of modeling the power amplifier is to fit the power amplifier output vector Y with a series of basis function vectors.

[0013]

[0014] The coefficients are solved using the least squares method, and the corresponding solution is expressed as follows:

[0015]

[0016] In formula (4) This represents the solved coefficient vector, (·). H Let (H) denote the conjugate transpose of a complex matrix, and (·)⁻¹ denote the inverse of the matrix; from the above derivation, it can be seen that (H) H H) -1 The prerequisite for a normal calculation is that the matrix is ​​not singular, that is, rank(H) = rank(H). H H) = K, rank(·) represents the operation of finding the rank of the matrix; since the basis functions of the RF power amplifier model are non-orthogonal, there may be correlation between the basis function vectors. When the correlation is strong, it will cause the column rank of matrix H, which is also the column rank of matrix H, to be reduced. H The rank of H is less than K, and during the process of solving for the coefficients, due to the matrix H H The numerical instability is caused by an excessively large H condition number;

[0017] Step 3: Optimization method for the basis function of the RF power amplifier model based on the orthogonal projection criterion and the order-wise recursive least squares method.

[0018] Step 3.1, Define matrix H i Let C be a matrix containing i basis function vectors. i Define the inverse matrix for its corresponding coefficient vector. Define matrix For H i P is the projection matrix of the orthogonal complement space of the space spanned by the i basis function vectors. i ⊥ x corresponds to the vector x being directed towards H. i The vector obtained by projecting the vector onto the orthogonal complement space of the space spanned by the i basis function vectors;

[0019] Step 3.2: Define a variable α k+1 The contribution of the (k+1)th basis function vector to the power amplifier modeling is:

[0020]

[0021] Its physical meaning is to calculate the (k+1)th basis function vector h. k+1 The ratio of the power of the projection vector of the orthogonal complement space spanned by the first k basis function vectors to its own power, if α k+1 If the value of H is very small, it means that most components of the (k+1)th basis function vector can be represented by the first k basis function vectors, that is, in H k Add h k+1 This did not increase the column rank, which resulted in the matrix [H] k h k+1 The pathological nature of the coefficients, coupled with the resulting enormous condition number, poses a significant challenge to the numerical stability of the coefficient calculation process. Therefore, when the contribution factor α... k+1 When the value is small, you can choose to discard its corresponding basis function.

[0022] α k+1 <δ (6)

[0023] Where δ is a threshold constant, which is a small positive number; if δ is larger, the model accuracy and model complexity will decrease simultaneously, so the value needs to take into account both model complexity and linearization performance.

[0024] Step 3.3: Recursively select basis functions and solve for their corresponding coefficients;

[0025] Step 3.3.1: Initial state H0 = φ, C0 = φ, k = 0, i = 0, where hand is represented as an empty matrix or an empty vector;

[0026] Step 3.3.2: If k = K-1, it indicates that the entire recursive process has ended, and the model matrix H optimized by the basis functions is output. i and the corresponding coefficient matrix C i Otherwise, use formula (5) to calculate α. k+1 Then proceed to step 3.3.3;

[0027] Step 3.3.3, if α k+1 If <δ holds, it means that the contribution of the basis function vector at this time is very small and can be ignored. Let k = k + 1, return to step 3.3.2 to select the next basis function. If it does not hold, select the current basis function vector and proceed to step 3.3.4.

[0028] Step 3.3.4: Update the coefficient matrix C recursively according to formulas (7) and (8).i and inverse matrix D i

[0029]

[0030]

[0031] Add the current basis function vector to the model matrix according to formula (9).

[0032] H i+1 =[H i h k+1 (9)

[0033] Let k = k+1, i = i+1, and return to step 3.3.2 to determine the next basis function vector.

[0034] Beneficial Effects: The present invention provides a device and method for optimizing the basis functions of an RF power amplifier model based on orthogonal projection criteria and order-wise recursive least squares. It offers the following advantages: Novelly, it projects new basis function vectors onto a vector space spanned by selected basis functions, then uses the projected components to measure the contribution of the new basis functions. By discarding basis functions with smaller contributions, the model is simplified, and ill-conditioned model matrices are effectively prevented. Combining this method with existing order-wise recursive least squares methods achieves the simultaneous extraction of model coefficients and optimization of model basis function selection. While maintaining predistortion performance, it effectively reduces the resource consumption and power consumption of the predistorter, while also improving the numerical stability during model coefficient calculation. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the RF power amplifier model basis function optimization device of the present invention;

[0036] Figure 2 This is a graph showing the relationship between the modeling accuracy and the condition number of the model matrix for 5G-NR signals with a bandwidth of 100MHz, as well as the number of selected basis functions.

[0037] Figure 3 This is a schematic diagram comparing the power spectrum before and after predistortion of a 5G-NR signal with a bandwidth of 100MHz, as presented in this invention. Detailed Implementation

[0038] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of a device and method for optimizing the basis functions of an RF power amplifier model based on orthogonal projection criteria and order-wise recursive least squares method.

[0039] like Figure 1As shown, the basis function optimization selection method for RF power amplifier models of the present invention includes: a digital predistorter, a digital-to-analog converter (DAC), a quadrature modulator, an RF power amplifier, a coupler, a quadrature demodulator, an analog-to-digital converter (ADC), and a basis function optimization and parameter extraction algorithm based on the orthogonal projection criterion and the order-wise recursive least squares method; wherein, the digital predistorter is used to predistort the input digital baseband signal to generate a digital predistortion signal with the opposite distortion characteristics to the RF power amplifier, the digital predistortion signal is converted into an analog signal by the DAC, and then modulated to the RF frequency by the quadrature modulator. Finally, the signal enters the RF power amplifier for power amplification to drive the antenna. The signal output from the RF power amplifier simultaneously enters the coupler, quadrature demodulator, and analog-to-digital converter (ADC) to generate the corresponding digital baseband signal output by the power amplifier. The digital baseband signals input and output by the power amplifier are fed into the basis function optimization and parameter extraction algorithm module based on the orthogonal projection criterion and the order-wise recursive least squares method to optimize the basis function of the RF power amplifier model and extract the parameters, thereby obtaining the parameters of the predistorter corresponding to the RF power amplifier with the current distortion characteristics. Then, the predistortion parameters are sent to the digital predistorter constructed by the model after basis function optimization.

[0040] The overall process of this invention is as follows: First, a suitable power amplifier model is selected; then, the model configuration parameters, such as nonlinear order and memory depth, are set; finally, the optimized basis functions and coefficients are used to model the predistorter. Specifically, a baseband signal that has not undergone predistortion is first used. The signal passes through a digital-to-analog converter, a quadrature modulator, and an RF power amplifier in sequence to obtain an analog RF signal. This analog RF signal then passes through a coupler, a quadrature demodulator, and an analog-to-digital converter in sequence to obtain the distorted digital baseband signal output by the power amplifier. Follow these steps to model the power amplifier and optimize the basis functions of the selected model (taking the Generalized Memory Polynomial (GMP) model as an example):

[0041] Step 1: Establish the generalized memoized polynomial model expression as follows:

[0042]

[0043] In formula (1), n∈[0,N-1] represents the index position of the sampling point of the digital baseband signal, and the total length of the baseband signal is N sampling points; m is the memory depth and m∈[0,M]. M is the maximum memory depth. p∈[1,P] is the nonlinear order, P is the maximum nonlinear order, l∈[-L,L] is the depth of memory term crossing, and L is the maximum crossing depth. This is the complex input signal for the power amplifier. Let || be the complex output signal of the model, and || is defined as the modulo operation on the complex number. These are the model coefficients corresponding to each basis function. It can be seen that the number of coefficients and the number of basis functions in the model are K = P(M+1)(2L+1).

[0044] Step 2: Derive the model coefficients The solution method represents the model in matrix form as follows:

[0045] Y = HC (2)

[0046] Where Y represents the vector of the output signal, H is the model matrix, and c is the vector of model coefficients, defined as follows: H = [h1, h2, ..., h K ], (·) T This represents the transpose operation of a vector. Where h k Defined as the k-th basis function vector corresponding to different combinations of p, m, l. That is its corresponding coefficient. h k The composition can be represented by formula (3). It can be seen that the process of modeling the power amplifier is to fit the power amplifier output vector Y with a series of basis function vectors.

[0047]

[0048] The coefficients are solved using the least squares method, and the corresponding solution is expressed as follows:

[0049]

[0050] In formula (4) This represents the solved coefficient vector, (·). H Let (·) denote the conjugate transpose of a complex matrix. -1 This indicates finding the inverse of a matrix; as can be seen from the above derivation, (H H H) -1 The prerequisite for a normal calculation is that the matrix is ​​not singular, that is, rank(H) H H) = K, and rank(·) represents the operation of finding the rank of the matrix. However, since the basis functions of the power amplifier model are non-orthogonal, there may be correlation between the basis function vectors. When the correlation is strong, it will affect the column rank of matrix H, which is also the column rank of matrix H. H The rank of H is less than K, and during the process of solving for the coefficients, due to the matrix H H The numerical value is unstable due to an excessively large H condition number.

[0051] Step 3: Derive the basis function optimization method for the RF power amplifier model based on the orthogonal projection criterion and the order-wise recursive least squares method:

[0052] Step 3.1, Define matrix H i Let C be a matrix containing i basis function vectors. i Define the inverse matrix for its corresponding coefficient vector. Define matrix For H i The projection matrix of the orthogonal complement space spanned by the i basis function vectors. That is, to move vector x to H i The vector obtained by projecting the vector onto the orthogonal complement space of the space spanned by the i basis function vectors.

[0053] Step 3.2: Define a variable α k+1 The contribution of the (k+1)th basis function vector to the power amplifier modeling is:

[0054]

[0055] Its physical meaning is to calculate the (k+1)th basis function vector h. k+1 The ratio of the power of the projection of the space spanned by the first k basis function vectors to its own power, if α k+1 If the value of H is very small, it means that most components of the (k+1)th basis function vector can be represented by the first k basis function vectors, that is, in H k Add h k+1 This did not increase the column rank, which resulted in the matrix [H] k h k+1 The pathological nature of the coefficients, coupled with the resulting enormous condition number, poses a significant challenge to the numerical stability of the coefficient calculation process. Therefore, when the contribution factor α... k+1 When the value is small, you can choose to discard its corresponding basis function.

[0056] α k+1 <δ (6)

[0057] Here, δ is a threshold constant, which is a small positive number. The larger δ is, the lower the model accuracy and the lower the model complexity. Therefore, the value of δ needs to be considered in light of both model complexity and linearization performance.

[0058] Step 3.3: Recursively select basis functions and solve for their corresponding coefficients.

[0059] Step 3.3.1: Initial state H0 = φ, C0 = φ, k = 0, i = 0, where φ represents an empty matrix or an empty vector.

[0060] Step 3.3.2: If k = K-1, it indicates that the entire recursive process has ended, and the model matrix H optimized by the basis functions is output. i and the corresponding coefficient matrix C i Otherwise, use formula (5) to calculate α.k+1 Then proceed to step 3.3.3.

[0061] Step 3.3.3, if α k+1 If δ is true, it means that the contribution of the basis function vector at this time is very small and can be ignored. Let k = k + 1, and return to step 3.3.2 to select the next basis function. If δ is not true, select the current basis function vector and proceed to step 3.3.4.

[0062] Step 3.3.4: Update the coefficient matrix C recursively according to formulas (7) and (8). i and inverse matrix D i

[0063]

[0064]

[0065] Add the current basis function vector to the model matrix according to formula (9).

[0066] H i+1 =[H i h k+1 (9)

[0067] Let k = k+1, i = i+1, and return to step 3.3.2 to determine the next basis function vector.

[0068] After the above optimization and recursive process of selecting basis functions, the forward model of the power amplifier can be obtained. By interchanged between the output and input positions of the power amplifier, the basis function optimization and coefficient estimation of the inverse model of the power amplifier, i.e., the predistorter, can be completed. The predistorter is updated with the finally selected basis functions and model coefficients, and then the input signal is injected into the predistorter to obtain the predistorted signal. Complete the entire pre-distortion process.

[0069] The baseband signal is a complex signal containing real and imaginary parts. The 5G-NR signal used in the test has a sampling rate of 491.52MHz, a peak-to-average power ratio of 9.5dB, and a bandwidth of 100MHz. This signal can well demonstrate the predistortion system's ability to predistort broadband signals with high peak-to-average power ratio.

[0070] In formula (1), the configuration of the generalized memory polynomial model is P=9, M=4, L=2. The total number of basis functions is 225. The method proposed in this invention is used to optimize the above basis functions. Adjusting δ in formula (6) from 0 to 0.01, the number of selected basis functions is reduced from 225 to 31. The normalized mean square error (NMSE) and model matrix H of the corresponding model are improved. H The condition number of H changes as follows Figure 2As shown, the model accuracy increases with the number of basis functions. However, when the number of basis functions exceeds 80, the rate of increase in model accuracy slows down. When the model accuracy reaches around 160, the strong correlation between basis functions leads to a sharp increase in the condition number of the model matrix (the condition number increases by approximately 10 from 80 to 225 basis functions). 29 This can cause numerical instability during the model parameter extraction process, leading to a decrease in model accuracy when the number of basis functions increases further. Therefore, the selection of δ needs to comprehensively consider both model complexity and linearization accuracy.

[0071] The following tests and comparisons show the results of using the basis function optimization method proposed in this invention with different numbers of basis functions for predistortion without predistortion. The corresponding adjacent channel leakage ratio (ACLR) results are summarized in Table 1. The power amplifier output power spectrum is also plotted, as shown below. Figure 3 As shown in the figure. A comparison reveals that after optimizing the basis functions in the model using the method proposed in this invention, only 80 basis functions are needed to obtain results with 225 coefficients similar to the original model. Combined with... Figure 3 It can be seen that this effectively compensates for the power amplifier's memory effect and nonlinearity. However, the number of basis functions and coefficients is reduced by 60%, which greatly reduces the computational load and power consumption of the predistorter, reduces the computational complexity of coefficient extraction, and improves the robustness of the calculation process.

[0072] Table 1

[0073]

[0074]

[0075] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for optimizing the selection of basis functions suitable for RF power amplifier models, characterized in that, include: The system comprises a digital predistorter, a digital-to-analog converter (DAC), a quadrature modulator, an RF power amplifier, a coupler, a quadrature demodulator, an analog-to-digital converter (ADC), and a basis function optimization and parameter extraction algorithm based on the orthogonal projection criterion and the order-wise recursive least squares method. The digital predistorter predistorts the input digital baseband signal, generating a digital predistorted signal with the opposite distortion characteristics to the RF power amplifier. This digital predistorted signal is then converted to an analog signal by the DAC, modulated to the RF frequency by the quadrature modulator, and finally amplified by the RF power amplifier. The driving antenna and the signal output from the RF power amplifier simultaneously enter the coupler, quadrature demodulator, and analog-to-digital converter (ADC) to generate the corresponding digital baseband signal output by the power amplifier. The digital baseband signals input and output by the power amplifier are fed into the basis function optimization and parameter extraction algorithm module based on the orthogonal projection criterion and the order-wise recursive least squares method to optimize the basis function of the RF power amplifier model and extract the parameters, thereby obtaining the parameters of the predistorter corresponding to the RF power amplifier with the current distortion characteristics. Then, the predistortion parameters are sent to the digital predistorter constructed by the model after basis function optimization. The method specifically includes: Step 1: Establish the generalized memoized polynomial model expression; Step 2, Model Coefficients The solution method, Step 3: Optimization method of basis function for RF power amplifier model based on orthogonal projection criterion and order-wise recursive least squares method; Step 3.1, Define matrix H i Let C be a matrix containing i basis function vectors. i Define the inverse matrix for its corresponding coefficient vector. Define matrix For H i The projection matrix of the orthogonal complement space spanned by the i basis function vectors. That is, to move vector x to H i The vector obtained by projecting the vector onto the orthogonal complement space of the space spanned by the i basis function vectors; Step 3.2: Define a variable α k+1 The contribution of the (k+1)th basis function vector to the power amplifier modeling is: Its physical meaning is to calculate the (k+1)th basis function vector h. k+1 The ratio of the power of the projection vector of the orthogonal complement space spanned by the first k basis function vectors to its own power, if α k+1 If the value of H is very small, it means that most components of the (k+1)th basis function vector can be represented by the first k basis function vectors, that is, in H k Add h k+1 This did not increase the column rank, which resulted in the matrix [H] k h k+1 The condition becomes pathological and generates a huge condition number, posing a significant challenge to the numerical stability of the coefficient solution process, especially when the contribution factor α... k+1 When the value is small, its corresponding basis function is discarded. a k+1 <d (6) Where δ is a threshold constant, which is a small positive number; if δ is larger, the model accuracy and model complexity will decrease simultaneously, so the value needs to take into account both model complexity and linearization performance. Step 3.3: Recursively select basis functions and solve for their corresponding coefficients; Step 3.3, the recursive selection of basis functions and the solution of their corresponding coefficients are as follows: Step 3.3.1: Initial state H0 = φ, C0 = φ, k = 0, i = 0, where φ represents an empty matrix or an empty vector; Step 3.3.2: If k = K-1, it indicates that the entire recursive process has ended, and the model matrix H optimized by the basis functions is output. i and the corresponding coefficient matrix C i Otherwise, use formula (5) to calculate α. k+1 Then proceed to step 3.3.3; Step 3.3.3, if α k+1 If δ is true, it means that the contribution of the basis function vector at this time is very small and can be ignored. Let k = k + 1, return to step 3.3.2 to select the next basis function. If it is not true, select the current basis function vector and proceed to step 3.3.

4. Step 3.3.4: Update the coefficient matrix C recursively according to formulas (7) and (8). i and inverse matrix D i Add the current basis function vector to the model matrix according to formula (9). H i+1 =[H i h k+1 ] (9) Let k = k+1, i = i+1, and return to step 3.3.2 to determine the next basis function vector.

2. The basis function optimization selection method applicable to RF power amplifier models according to claim 1, characterized in that, Step 1: Establish the generalized memoized polynomial model expression as follows: In formula (1), n∈[0,N-1] represents the index position of the sampling point of the digital baseband signal, and the total length of the baseband signal is N sampling points; m is the memory depth and m∈[0,M], M is the maximum memory depth, p∈[1,P] is the nonlinear order, P is the maximum nonlinear order, l∈[-L,L] is the depth of memory term intersection, L is the maximum intersection depth. This is the complex input signal for the power amplifier. Let || be the output complex signal of the model, and || be defined as the modulo operation on the complex number. These are the model coefficients corresponding to each basis function. It can be seen that the number of coefficients and the number of basis functions in the model are K = P(M+1)(2L+1).

3. The basis function optimization selection method applicable to RF power amplifier models according to claim 1, characterized in that, Step 2, Model Coefficients The solution method represents the model in matrix form as follows: Y = HC (2) Where Y represents the vector of the output signal, H is the model matrix, and c is the vector of model coefficients, defined as follows: H = [h1, h2, ..., h K ], T denotes the transpose operation of a vector; where h k Defined as the k-th basis function vector corresponding to different combinations of p, m, l. It is its corresponding coefficient, h k The composition can be represented by formula (3). It can be seen that the process of modeling the power amplifier is to fit the power amplifier output vector Y with a series of basis function vectors. The coefficients are solved using the least squares method, and the corresponding solution is expressed as follows: In formula (4) This represents the solved coefficient vector, (·). H Let (·) denote the conjugate transpose of a complex matrix. -1 This indicates finding the inverse of a matrix; as can be seen from the above derivation, (H H H) -1 The prerequisite for a normal calculation is that the matrix is ​​not singular, that is, rank(H) H H) = K, rank(·) represents the operation of finding the rank of the matrix; since the basis functions of the RF power amplifier model are non-orthogonal, there may be correlation between the basis function vectors. When the correlation is strong, it will cause the column rank of matrix H, which is also the column rank of matrix H, to be reduced. H The rank of H is less than K, and during the process of solving for the coefficients, due to the matrix H H The numerical value is unstable due to an excessively large H condition number.

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