CN116319202A - Basis function optimization selection method suitable for radio frequency power amplifier model - Google Patents
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Abstract
The invention discloses a base function optimization selection method suitable for a radio frequency power amplifier model. The order recursive least square method is widely applied to solving various least square problems because complex matrix inversion operation can be avoided. The invention applies the order recursive least square method to the field of digital predistortion of the radio frequency power amplifier, and based on the algorithm, an orthogonal projection component criterion is used in each step of recursive process to optimally select the basis function of the power amplifier model, thereby effectively solving the problem of overlarge matrix condition number in the process of solving the model coefficient due to the non-orthogonal characteristic of the basis function in the radio frequency power amplifier model. The method provided by the invention can simultaneously extract the model coefficients and optimize the basis functions in the model, can obviously reduce the number of the required basis functions while maintaining the model precision, and effectively reduces the resources and the power consumption of the predistorter implementation. The actual measurement result shows that the model after the basis function is optimized by the invention can effectively compensate the memory effect and nonlinearity of the power amplifier.
Description
Technical Field
The invention belongs to the field of digital predistortion of radio frequency power amplifiers, and particularly relates to a device and a method for optimizing a base function of a radio frequency power amplifier model based on an orthogonal projection criterion and a step-by-step recursive least square method.
Background
The fifth generation mobile communication technology (5G) has basically completed deployment in China, and compared with the fourth generation mobile communication technology, the 5G uses a wider communication bandwidth and a higher carrier frequency in order to improve the communication capacity, which brings great challenges to the linearity degree of the highest power consumption device in the base station, namely the radio frequency power amplifier. Because the 5G signal has a very high peak-to-average power ratio (PAPR), one solution is to maintain good linearity of the power back-off of the power amplifier, which can result in very low efficiency of the power amplifier, resulting in a large amount of power consumption and also a great challenge to heat dissipation of the communication system. Digital Predistortion (DPD) technology has become the most popular method for improving the radio frequency power amplifier due to its high efficiency, high accuracy, ease of integration in baseband signal processing systems, and the like. The basic principle of DPD is that a signal is predistorted by a module called predistorter and then input to a power amplifier, and as the predistorter is designed to have the opposite characteristic to the power amplifier, the cascade system of predistorter-power amplifier becomes a linear system for the input signal, so that the radio frequency power amplifier can output a signal which is undistorted relative to the original signal. Therefore, the accurate establishment of the model of the radio frequency power amplifier is a key of the DPD technology, and through research and exploration of students at home and abroad for decades, various power amplifier models with low complexity and high precision are proposed and widely used, such as a Memory Polynomial (MP) model, a Generalized Memory Polynomial (GMP) model, a Decomposition Vector Rotation (DVR) model, and the like. These models are composed of a series of basis functions of different orders, and these basis functions are often not orthogonal, that is, these basis functions may show strong correlation under certain signals, which brings about two major problems, firstly, the strong correlation between the basis functions causes the condition number of the model matrix to become large, which causes the numerical instability in the extraction of the model coefficients. Secondly, some basic functions have small effects, and because predistorters often work at frequencies up to hundreds of megahertz, the basic functions with small effects still occupy valuable hardware resources and power consumption, so the selection of the basic functions in the optimization model has great significance for reducing the power consumption and resource consumption of a DPD system and improving the robustness of the model parameter calculation process.
Disclosure of Invention
Technical problems: the invention aims to provide a base function optimization selection method suitable for a radio frequency power amplifier model, so that the problem that the base function required by the model can be effectively reduced and the numerical stability in the parameter extraction process can be improved on the premise of keeping the predistortion performance is solved.
The technical scheme is as follows: in order to solve the technical problems, the basis function optimization selection method suitable for the radio frequency power amplifier model comprises the following steps: a digital predistorter, a digital-to-analog converter (DAC), a quadrature modulator, a radio frequency power amplifier, a coupler, a quadrature demodulator, an analog-to-digital converter (ADC), a basis function optimization and parameter extraction algorithm based on a quadrature projection criterion and a step-wise recursive least square method;
the digital predistorter is used for predistortion processing an input digital baseband signal to generate a digital predistortion signal with opposite distortion characteristics to the radio frequency power amplifier, the digital predistortion signal is converted into an analog signal through the digital-to-analog converter, the analog signal is modulated to the radio frequency through the quadrature modulator, finally the digital predistortion signal enters the radio frequency power amplifier to be amplified in power so as to drive an antenna, the signal output by the radio frequency power amplifier simultaneously enters the coupler, and the quadrature demodulator and the analog-to-digital converter (ADC) generate a digital baseband signal output by the corresponding power amplifier; and the digital baseband signals input and output by the power amplifier are respectively sent to a basis function optimization and parameter extraction algorithm module based on orthogonal projection criteria and a step-by-step recursive least square method for performing basis function optimization and parameter extraction of a radio frequency power amplifier model to obtain parameters of a predistorter corresponding to the radio frequency power amplifier with current distortion characteristics, and then the predistortion parameters are sent to the digital predistorter formed by the model after the basis function optimization.
The method specifically comprises the following steps:
step 1, establishing a generalized memory polynomial model expression as follows:
n E [0, N-1 ] in formula (1)]The index position of the sampling point of the digital baseband signal is represented, and the total length of the baseband signal is N sampling points; m is memory depth and m is 0, M]M is the maximum memory depth, p E [1, P]For nonlinear order, P is the maximum nonlinear order, l.e [ -L, L]To memorize the depth of the item crossing, L is the maximum crossing depth,
input complex signal for power amplifier, +.>
For the output complex signal of the model, I is defined as modulo-manipulation of complex numbers,/->
The coefficient number and the number of the base functions in the model are known as K=P (M+1) (2L+1);
Y＝HC (2)
Wherein Y represents the vector of the output signal, H is the model matrix, c is the model coefficient vector, respectively defined as
H＝[h 1 ，h 2 ，…，h K ]，/>
T represents the transpose operation of the vector; wherein h is k Defined as the difference between the different p, m,the corresponding kth basis function vector under the combination +.>
Is the corresponding coefficient, h k The constitution of (2) can be represented by the formula (3), and it can be seen that the modeling process of the power amplifier is a process of fitting the output vector Y of the power amplifier by using a series of basis function vectors
Solving coefficients using least squares, the corresponding solution being expressed as
In the formula (4)
Representing the solved coefficient vector, (-) H Representing the conjugate transpose of the complex matrix, (-) -1 representing the inverse of the matrix; from the above derivation, (H) H H) -1 The premise that can be normally found is that the matrix is nonsingular, namely rank (H H H) =k, rank (·) represents the operation of solving the matrix rank; since the basis functions of the radio frequency power amplifier model are non-orthogonal, there may be correlation between the basis function vectors, which when strong, may result in a column rank of the matrix H, i.e., the matrix H H H has a rank less than K, and is determined by matrix H H Numerical instability caused by an excessive number of H conditions;
step 3, a radio frequency power amplifier model base function optimization method based on orthogonal projection criteria and a step-by-step recursive least square method,
step 3.1, defining a matrix H i As a matrix containing i basis function vectors, C i For its corresponding coefficient vector, an inverse matrix is defined
Definition matrix->
Is H i Projection matrix of orthogonal complement space of space formed by i basis function vectors, P i ⊥ x is the corresponding handle vector x to H i Vectors obtained after orthogonal complementary space projection of the space formed by the i basis function vectors;
step 3.2, defining a variable alpha k+1 The contribution to power amplifier modeling for measuring the k+1th basis function vector 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 to the power of itself in the orthogonal complement space of the space spanned by the first k basis function vectors, if α k+1 If the value of (1) is small, it means that most of the components of the k+1 th basis function vector can be represented by the first k basis function vectors, i.e., at H k Adding h into k+1 The column rank is not increased, which results in matrix H k h k+1 ]Becomes ill-conditioned and generates a huge condition number, which brings great challenges to the numerical stability in the coefficient solving process, so when the contribution factor alpha k+1 Smaller time may choose to discard its corresponding basis function
α k+1 ＜δ (6)
Wherein delta is a threshold constant, which is a small positive number; if delta is obtained more, the model precision and the model complexity are synchronously reduced, so that the value needs to comprehensively consider the model complexity and linearization performance;
step 3.3, recursively selecting the basis functions and solving the corresponding coefficients;
step 3.3.1, initial State H 0 ＝φ，C 0 =Φ, k=0, i=0, where the hand is represented as a null matrix or null vector;
step 3.3.2, if k=k-1, indicates that the whole recursion process has completedBeam, output model matrix H optimized by basis function i And corresponding coefficient matrix C i Otherwise, alpha is calculated using equation (5) k+1 And enter step 3.3.3;
step 3.3.3, if alpha k+1 If < delta is met, the contribution of the basis function vector at the moment is small and can be ignored, k=k+1 is returned to the step 3.3.2 to select the next basis function, if not, the current basis function vector is selected, and the step 3.3.4 is entered;
step 3.3.4, recursively updating coefficient matrix C according to formulas (7) and (8) i And inverse matrix D i
Adding the current basis function vector to the model matrix according to equation (9)
H i+1 ＝[H i h k+1 ] (9)
Let k=k+1, i=i+1, go back to step 3.3.2 to make the next basis function vector determination.
The beneficial effects are that: the device and the method for optimizing the basis function of the radio frequency power amplifier model based on the orthogonal projection criterion and the order recursive least square method have the following advantages: the novel model is simplified and model matrix morbidity is effectively prevented by spatially projecting new basis function vectors to vectors formed by selected basis functions, and then measuring the contribution of the new basis functions by projection components, and by discarding basis functions with smaller contributions. The method is combined with the existing order recursive least square method, so that the effects of simultaneously extracting model coefficients and optimizing model base function selection can be achieved. On the premise of keeping the predistortion performance, the resource consumption and the power consumption of the predistorter can be effectively reduced, and meanwhile, the numerical stability in the model coefficient calculation process is improved.
Drawings
FIG. 1 is a schematic diagram of a basic function optimizing device of a radio frequency power amplifier model according to the present invention;
FIG. 2 is a graph of modeling accuracy for a 5G-NR signal having a bandwidth of 100MHz versus condition number of a model matrix with the number of basis functions selected in accordance with the present invention;
FIG. 3 is a graph showing the power spectrum before and after predistortion of a 5G-NR signal with a bandwidth of 100MHz in accordance with the present invention;
Detailed Description
In order to better understand the purpose, structure and function of the invention, the invention provides a radio frequency power amplifier model base function optimizing device and method based on orthogonal projection criteria and a step-by-step recursive least square method, which are described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for optimizing and selecting the basis function applicable to the radio frequency power amplifier model comprises the following steps: a digital predistorter, a digital-to-analog converter (DAC), a quadrature modulator, a radio frequency power amplifier, a coupler, a quadrature demodulator, an analog-to-digital converter (ADC), a basis function optimization and parameter extraction algorithm based on a quadrature projection criterion and a step-wise recursive least square method; the digital predistorter is used for predistortion processing an input digital baseband signal to generate a digital predistortion signal with opposite distortion characteristics to a radio frequency power amplifier, the digital predistortion signal is converted into an analog signal through a digital-to-analog converter, the analog signal is modulated to a radio frequency through a quadrature modulator, finally the radio frequency power amplifier is entered to carry out power amplification to drive an antenna, a signal output by the radio frequency power amplifier simultaneously enters a coupler, and the quadrature demodulator and an analog-to-digital converter (ADC) generate a digital baseband signal corresponding to the power amplifier output; and the digital baseband signals input and output by the power amplifier are respectively sent to a basis function optimization and parameter extraction algorithm module based on orthogonal projection criteria and a step-by-step recursive least square method for performing basis function optimization and parameter extraction of a radio frequency power amplifier model to obtain parameters of a predistorter corresponding to the radio frequency power amplifier with current distortion characteristics, and then the predistortion parameters are sent to the digital predistorter formed by the model after the basis function optimization.
The overall flow of the invention is that firstly, a proper power amplifier model is selected, and then, the used model is setAnd finally, modeling the predistorter by using the optimized and selected basis functions and coefficients. In particular, a baseband signal without predistortion is used first
Sequentially passing through a digital-to-analog converter, a quadrature modulator and a radio frequency power amplifier to obtain an analog radio frequency signal, and sequentially passing through a coupler, a quadrature demodulator and an analog-to-digital converter to obtain a distorted digital baseband signal corresponding to the power amplifier output>
Modeling the power amplifier and optimizing the basis functions of the selected model (exemplified by Generalized Memory Polynomial (GMP) model) according to the following steps:
step 1, establishing a generalized memory polynomial model expression as follows:
n E [0, N-1 ] in formula (1)]The index position of the sampling point of the digital baseband signal is represented, and the total length of the baseband signal is N sampling points; m is memory depth and m is 0, M]. M is the maximum memory depth. P is E [1, P]For nonlinear order, P is the maximum nonlinear order, l.e [ -L, L]To memorize the depth of the item intersection, L is the maximum intersection depth.
Input complex signal for power amplifier, +.>
For the output complex signal of the model, || is defined as operating on complex modulo values. />
Is the model coefficient corresponding to each basis function. The number of coefficients and the number of basis functions in the model are known as k=p (m+1) (2l+1)
Y＝HC (2)
Wherein Y represents the vector of the output signal, H is the model matrix, c is the model coefficient vector, respectively defined as
H＝[h 1 ,h 2 ,…,h K ]，/>
(·) T Representing the transpose operation of the vector. Wherein h is k Defined as the corresponding kth basis function vector under different combinations of p, m, l,/and/or->
Is its corresponding coefficient. h is a k The composition of (2) can be expressed by formula (3). It can be seen that the modeling process of the power amplifier is a process of fitting the output vector Y of the power amplifier by using a series of basis function vectors
Solving coefficients using least squares, the corresponding solution being expressed as
In the formula (4)
Representing the solved coefficient vector, () H Representing the conjugate transpose of the complex matrix, (-) -1 Representing an inverse of the matrix; from the above derivation, (H) H H) -1 The premise that can be normally found is that the matrix is nonsingular, namely rank (H H H) =k, rank (·) represents the operation of solving the matrix rank. However, since the basis functions of the power amplifier model are non-orthogonal, there may be correlation between the basis function vectors, which when strong, may result in a column rank of the matrix H, i.e., the matrix H H H has a rank less than K, and is determined by matrix H H An excessively large H condition number results in unstable values.
Step 3, deducing a radio frequency power amplifier model base function optimization method based on an orthogonal projection criterion and a step-by-step recursive least square method:
step 3.1, defining a matrix H i As a matrix containing i basis function vectors, C i For its corresponding coefficient vector, an inverse matrix is defined
Definition matrix->
Is H i Projection matrix of orthogonal complement space of space spanned by i basis function vectors,/i>
I.e. corresponding vector x to H i The vector obtained after the orthogonal complementary space projection of the space formed by the i basis function vectors.
Step 3.2, defining a variable alpha k+1 The contribution to power amplifier modeling for measuring the k+1th basis function vector is:
its physical meaning is to calculate the (k+1) th basis function vector h k+1 The ratio of the projected power to the own power of the orthogonal complement of the space spanned by the first k basis function vectors, if alpha k+1 Is very smallThe majority of the components showing the k+1 th basis function vector can be represented by the first k basis function vectors, i.e., at H k Adding h into k+1 The column rank is not increased, which results in matrix H k h k+1 ]Becomes ill-conditioned and generates a huge condition number, which brings great challenges to the numerical stability in the coefficient solving process, so when the contribution factor alpha k+1 Smaller time may choose to discard its corresponding basis function
α k+1 <δ (6)
Where δ is a threshold constant and is a small positive number. If delta is obtained more, the model accuracy and the model complexity are synchronously reduced, so that the value needs to comprehensively consider the model complexity and the linearization performance.
And 3.3, recursively selecting the basis functions and solving the corresponding coefficients.
Step 3.3.1, initial State H 0 ＝φ，C 0 =Φ, k=0, i=0, where Φ is denoted as a null matrix or null vector.
Step 3.3.2, if k=k-1, indicating that the whole recursive process is finished, and outputting the model matrix H optimized by the basis function i And corresponding coefficient matrix C i Otherwise, alpha is calculated using equation (5) k+1 And proceeds to step 3.3.3.
Step 3.3.3, if alpha k+1 <Delta is true, which means that the contribution of the basis function vector at this time is negligible, let k=k+1, and return to step 3.3.2 to select the next basis function. If not, selecting the current basis function vector, and entering step 3.3.4.
Step 3.3.4, recursively updating coefficient matrix C according to formulas (7) and (8) i And inverse matrix D i
Adding the current basis function vector to the model matrix according to equation (9)
H i+1 ＝[H i h k+1 ] (9)
Let k=k+1, i=i+1, go back to step 3.3.2 to make the next basis function vector determination.
Through the processes of optimizing and selecting the basis functions and recursion, a forward model for building a power amplifier can be obtained, the output and input positions of the power amplifier are exchanged, the basis function optimization and coefficient estimation of an inverse power amplifier model, namely a predistorter can be completed, the finally selected basis functions and model coefficients are updated for the predistorter, and then an input signal is injected into the predistorter to obtain a signal after predistortion
The whole predistortion process is completed.
The baseband signal is a complex signal containing a real part and an imaginary part, the sampling rate is 491.52MHz, the peak-to-average ratio is 9.5dB, and the bandwidth is 5G-NR signal of 100MHz, and the predistortion processing capability of a predistortion system to broadband signals with peak-to-average ratio can be well reflected.
The configuration of the corresponding generalized memory polynomial model in equation (1) is p= 9,M = 4.L =2. The number of all corresponding basis functions is 225, and the basis functions are optimized by using the method provided by the invention. Adjusting delta in formula (6) from 0 to 0.01, reducing the number of selected basis functions from 225 to 31, and Normalizing Mean Square Error (NMSE) and model matrix H of the corresponding model H The change in condition number of H is shown in fig. 2. It can be seen that the model accuracy increases with increasing number of basis functions, but the model accuracy slows down when the number of basis functions increases above 80, and a steep increase in condition number of the model matrix due to strong correlation between basis functions (about 10 increase in condition number from 80 basis functions to 225 basis function matrices) can be seen when the model accuracy is as high as about 160 29 Multiple), which causes a phenomenon of unstable values in the process of extracting model parameters, resulting in a decrease in model accuracy when the basis functions are further increased. Therefore, the model needs to be comprehensively considered in selecting deltaComplexity and linearization accuracy.
The following tests respectively compare the results of predistortion performed by selecting different numbers of basis functions by using the basis function optimization method provided by the invention under the condition of not performing predistortion, and the corresponding Adjacent Channel Leakage Ratio (ACLR) results are summarized in table 1. And the power amplifier output power spectrum is plotted as shown in fig. 3. It can be seen from comparison that after the basis functions in the model are optimized by using the method provided by the invention, the results with 225 similar coefficients of the original model can be obtained by using only 80 basis functions, and the memory effect and nonlinearity of the power amplifier can be effectively compensated by combining with the results shown in fig. 3. But the number of the basis functions and the coefficients is reduced by 60%, the calculated amount and the power consumption of the predistorter are greatly reduced, the calculation complexity of coefficient extraction is reduced, and the robustness of the calculation process is improved.
TABLE 1
It will be understood that the invention has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (6)
1. The basis function optimization selection method suitable for the radio frequency power amplifier model is characterized by comprising the following steps of: a digital predistorter, a digital-to-analog converter (DAC), a quadrature modulator, a radio frequency power amplifier, a coupler, a quadrature demodulator, an analog-to-digital converter (ADC), a basis function optimization and parameter extraction algorithm based on a quadrature projection criterion and a step-wise recursive least square method; the digital predistorter is used for predistortion processing an input digital baseband signal to generate a digital predistortion signal with opposite distortion characteristics to a radio frequency power amplifier, the digital predistortion signal is converted into an analog signal through a digital-to-analog converter, the analog signal is modulated to a radio frequency through a quadrature modulator, finally the radio frequency power amplifier is entered to carry out power amplification to drive an antenna, a signal output by the radio frequency power amplifier simultaneously enters a coupler, and the quadrature demodulator and an analog-to-digital converter (ADC) generate a digital baseband signal corresponding to the power amplifier output; and the digital baseband signals input and output by the power amplifier are respectively sent to a basis function optimization and parameter extraction algorithm module based on orthogonal projection criteria and a step-by-step recursive least square method for performing basis function optimization and parameter extraction of a radio frequency power amplifier model to obtain parameters of a predistorter corresponding to the radio frequency power amplifier with current distortion characteristics, and then the predistortion parameters are sent to the digital predistorter formed by the model after the basis function optimization.
2. The method for optimized selection of the basis function applicable to the radio frequency power amplifier model according to claim 1, which is characterized by comprising the following steps:
step 1, establishing a generalized memory polynomial model expression;
step 2, model coefficients
Is used for solving the problem of the prior art,
and 3, optimizing the basis function of the radio frequency power amplifier model based on the orthogonal projection criterion and the order recursive least square method.
3. The method for optimized selection of basis functions for a radio frequency power amplifier model as set out in claim 1, wherein,
step 1, establishing a generalized memory polynomial model expression as follows:
n E [0, N-1 ] in formula (1)]The index position of the sampling point of the digital baseband signal is represented, and the total length of the baseband signal is N sampling points; m is memory depth and m is 0, M]M is the maximum memory depth, p E [1, P]For nonlinear order, P is the maximum nonlinear order, l.e [ -L, L]To memorize the depth of the item crossing, L is the maximum crossing depth,
input complex signal for power amplifier, +.>
For the output complex signal of the model, I is defined as modulo-manipulation of complex numbers,/->
The number of coefficients and the number of basis functions in the model are known as k=p (m+1) (2l+1), which are model coefficients corresponding to each basis function.
4. The method for optimized selection of basis functions for a radio frequency power amplifier model as set out in claim 1, wherein,
step 2, model coefficients
Representing the model as a matrix form
Y＝HC (2)
Wherein Y represents the vector of the output signal, H is the model matrix, c is the model coefficient vector, respectively defined as
H＝[h 1 ,h 2 ,…,h K ]，/>
T represents the transpose operation of the vector; wherein h is k Defined as the corresponding kth basis function vector under different combinations of p, m, l,/and/or->
Is the corresponding coefficient, h k The constitution of (2) can be represented by the formula (3), and it can be seen that the modeling process of the power amplifier is a process of fitting the output vector Y of the power amplifier by using a series of basis function vectors
Solving coefficients using least squares, the corresponding solution being expressed as
In the formula (4)
Representing the solved coefficient vector, (-) H Representing the conjugate transpose of the complex matrix, (-) -1 Representing an inverse of the matrix; from the above derivation, (H) H H) -1 The premise that can be normally found is that the matrix is nonsingular, namely rank (H H H) =k, rank (·) represents the operation of solving the matrix rank; since the basis functions of the radio frequency power amplifier model are non-orthogonal, there may be correlation between the basis function vectors, which when strong, may result in a column rank of the matrix H, i.e., the matrix H H H has a rank less than K, and is determined by matrix H H An excessively large H condition number results in unstable values.
5. The method for optimized selection of basis functions for a radio frequency power amplifier model as set out in claim 1, wherein,
step 3, a radio frequency power amplifier model base function optimization method based on orthogonal projection criteria and a step-by-step recursive least square method,
step 3.1, defining a matrix H i As a matrix containing i basis function vectors, C i For its corresponding coefficient vector, an inverse matrix is defined
Definition matrix->
Is H i Projection matrix of orthogonal complement space of space spanned by i basis function vectors,/i>
I.e. corresponding vector x to H i Vectors obtained after orthogonal complementary space projection of the space formed by the i basis function vectors;
step 3.2, defining a variable alpha k+1 The contribution to power amplifier modeling for measuring the k+1th basis function vector 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 to the power of itself in the orthogonal complement space of the space spanned by the first k basis function vectors, if α k+1 If the value of (1) is small, it means that most of the components of the k+1 th basis function vector can be represented by the first k basis function vectors, i.e., at H k Adding h into k+1 The column rank is not increased, which results in matrix H k h k+1 ]Becomes ill-conditioned and generates a huge condition number, which brings great challenges to the numerical stability in the coefficient solving process, so when the contribution factor alpha k+1 Smaller time may choose to discard its corresponding basis function
α k+1 <δ (6)
Wherein delta is a threshold constant, which is a small positive number; if delta is obtained more, the model precision and the model complexity are synchronously reduced, so that the value needs to comprehensively consider the model complexity and linearization performance;
and 3.3, recursively selecting the basis functions and solving the corresponding coefficients.
6. The method for optimizing and selecting the basis function applicable to the radio frequency power amplifier model according to claim 1, wherein the step 3.3 of recursively selecting the basis function and solving the corresponding coefficients is specifically as follows:
step 3.3.1, initial State H 0 ＝φ，C 0 =Φ, k=0, i=0, where Φ is represented as a null matrix or null vector;
step 3.3.2, if k=k-1, indicating that the whole recursive process is finished, and outputting the model matrix H optimized by the basis function i And corresponding coefficient matrix C i Otherwise, alpha is calculated using equation (5) k+1 And enter step 3.3.3;
step 3.3.3, if alpha k+1 <If delta is established, the contribution of the basis function vector at the moment is small and can be ignored, k=k+1 is returned to the step 3.3.2 to select the next basis function, if not, the current basis function vector is selected, and the step 3.3.4 is entered;
step 3.3.4, recursively updating coefficient matrix C according to formulas (7) and (8) i And inverse matrix D i
Adding the current basis function vector to the model matrix according to equation (9)
H i+1 ＝[H i h k+1 ](9) Let k=k+1, i=i+1, return to step 3.And 3.2, judging the next basis function vector.
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