CN115396274A - Digital predistortion model simplification method based on Greville method - Google Patents

Digital predistortion model simplification method based on Greville method Download PDF

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CN115396274A
CN115396274A CN202211087523.5A CN202211087523A CN115396274A CN 115396274 A CN115396274 A CN 115396274A CN 202211087523 A CN202211087523 A CN 202211087523A CN 115396274 A CN115396274 A CN 115396274A
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李怡然
李浩天
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CETC 54 Research Institute
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Abstract

The invention discloses a digital predistortion model simplification method based on a Greville method, and belongs to the technical field of digital predistortion. The invention comprises the following steps: collecting baseband signals input and output by a power amplifier; converting the model coefficient simplification problem into a signal reconstruction problem; constructing an observation matrix; and completing the model coefficient simplification process. The method can simplify the coefficients of the Volterra series model, is suitable for different modulation signals and application scenes, can greatly reduce the model coefficients on the basis of ensuring the modeling precision and the predistortion effect, enhances the system stability and the model simplification flexibility, and provides a new solution for the problem of simplifying the digital predistortion power amplifier model. Meanwhile, the method does not contain matrix inversion operation, reduces hardware implementation difficulty and has engineering significance.

Description

Digital predistortion model simplification method based on Greville method
Technical Field
The invention relates to the technical field of digital predistortion, in particular to a digital predistortion model simplification method based on a Greville method.
Background
The wireless communication technology is developing towards high-order modulation, broadband and the like, the problems of high peak-to-average power ratio and the like of the wireless communication technology put higher requirements on the linearity of the power amplifier, and therefore, the power amplifier linearization technology becomes one of the key technologies for promoting the development of the wireless communication system. The digital predistortion technology has become a research hotspot due to strong stability and good linearization effect. The accurate establishment of the power amplifier model is the key of the digital predistortion technology, and the VS model is widely applied because of good fitting effect of power amplifier nonlinearity and memory effect, and is the most common model in the field of digital predistortion. However, VS models have the problems that the size of the model rapidly increases along with the increase of the order and the memory depth, redundancy exists among the basis function vectors and the like, and the problems that the coefficient solving is unstable and the applicability of the model is poor are easily caused. Therefore, how to effectively simplify the VS-like model is one of the important points in the digital predistortion technology research.
The method for simplifying the VS models by using the Compressed Sensing (CS) algorithm is a common method, can flexibly trim the VS models, can effectively reduce the number of coefficients on the premise of ensuring the modeling precision and the predistortion effect, and realizes power amplifier linearization. However, the time for applying the compressive sensing algorithm to the digital predistortion model simplification field is short, and the effect verification of the simplified model mainly focuses on computer simulation or instrument platform verification, and the hardware implementation of the digital predistortion simplified model based on the compressive sensing algorithm is not seen at present. The main reasons are two reasons: firstly, some algorithms improve the reconstruction precision by utilizing modes such as regularization, backtracking and the like, but the complexity of the algorithms is also increased; and secondly, matrix inversion operation often exists in the compressed sensing algorithm, and hardware implementation difficulty is high.
Disclosure of Invention
The invention aims to simplify the coefficient of a digital predistortion model by utilizing a compressed sensing idea, solve two problems of a VS power amplifier model, simplify the flow of an algorithm and reduce the complexity of the algorithm. Therefore, the method for simplifying the digital predistortion model based on the Greville method can greatly simplify the power amplifier model coefficient on the basis of ensuring the model precision and the predistortion effect, enhances the system stability, is suitable for VS models, adaptively prunes the model coefficient according to different modulation signals and application scenes, and has high flexibility. In addition, the method has simple flow and does not need matrix inversion, thereby reducing the hardware realization difficulty of the algorithm and having high engineering realization value.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a digital predistortion model simplification method based on a Greville method comprises the following steps:
(1) Acquiring an input baseband signal and an output baseband signal of a power amplifier;
(2) Converting the model coefficient simplification problem into a signal reconstruction problem;
(3) Constructing an observation matrix;
(4) And completing the model coefficient simplification process.
Further, the observation matrix constructed in the step (3) is a model basis function matrix formed by the input signals.
Further, the step (4) specifically comprises the following steps:
(401) Inputting an observation matrix X, an observation vector y and a termination condition, and setting an output model coefficient estimated value as
Figure BDA0003835765790000021
Index set index;
(402) Initialization residual r 0 = y, supporting set
Figure BDA0003835765790000022
Index set
Figure BDA0003835765790000023
The number of iterations k =1;
(403) Calculating the inner product u = | X of the observation matrix and the residual H ·r 0 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S 1 The corresponding positions form a set J 1 (ii) a Superscript H denotes conjugate transpose;
(404) Updating support set F 1 ＝F 0 ∪S 1 Index set index 1 ＝index 0 ∪J 1 ；
(405) Updating generalized inverse matrix T 1 ＝(F 1 H ·F 1 ) -1 ·F 1 H Coefficient of
Figure BDA0003835765790000024
Residual error
Figure BDA0003835765790000025
The number of iterations k =2;
Figure BDA0003835765790000026
representing a least square solution in the first iteration, wherein the superscript-1 represents matrix inversion, and the superscript ^ represents an estimated value;
(406) Judging whether a termination condition is met, if so, exiting, and if not, entering an iteration process;
(407) Starting iteration: calculating the inner product u = | X of the observation matrix and the residual H ·r k-1 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S k The corresponding positions form a set J k ；
(408) Updating support set F k ＝F k-1 ∪S k Index set index k ＝index k-1 ∪J k ；
(409) Setting an intermediate variable d k ＝T k-1 ·S k ，c k ＝S k -F k-1 ·d k ；
(410) If c is k If =0, the intermediate variable b is updated k H ＝(1+d k H ·d k ) -1 ·d k H ·T k-1 If c is a k Not equal to 0, the intermediate variable b is updated k H ＝(c k H ·c k ) -1 ·c k H ；
(411) Updating generalized inverse matrices
Figure BDA0003835765790000027
Determining the estimated value of the coefficient
Figure BDA0003835765790000028
Updating residual errors
Figure BDA0003835765790000029
Figure BDA00038357657900000210
Represents the least squares solution at the kth iteration;
(412) Exiting iteration and outputting when the termination condition is met or the number of the coefficient estimation values is larger than the maximum coefficient of the model
Figure BDA00038357657900000211
Index set index, otherwise update k = k +1, continue iteration.
The invention adopts the technical scheme to produce the beneficial effects that:
1. the invention simplifies the number of coefficients of the VS type model by utilizing a compressed sensing technology, completes the sparse process of the model coefficients by utilizing the sparsity of the model and reduces the number of the coefficients.
2. The model simplification method can be applied to all VS type polynomial models, and has strong applicability. Meanwhile, the model coefficient can be greatly reduced on the basis of ensuring the modeling precision and the predistortion effect, and the coefficient solving stability is improved.
3. The model simplification method has the advantages of simple flow, no need of matrix inversion, small hardware realization difficulty and high value for technical engineering.
Drawings
Fig. 1 is a flowchart of a method (hereinafter referred to as GOMP algorithm, namely Greville Orthogonal Matching Pursuit based on Greville method) according to an embodiment of the present invention.
FIG. 2 is a table of predistortion effects for an MP-GOMP model in an embodiment of the present invention.
FIG. 3 is a comparison graph of AMAM curves before and after simplified model predistortion in an embodiment of the present invention.
FIG. 4 is a comparison of AMPM curves before and after simplified model pre-distortion in an embodiment of the present invention.
FIG. 5 is a graph of a comparison of the frequency spectrum before and after the simplified model pre-distortion in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings and examples, but the embodiments described below are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A digital predistortion model simplification method based on a Greville method is characterized in that a base band input signal of a power amplifier is used for constructing a basis function matrix according to a power amplifier model, model coefficients are simplified by using a model simplification algorithm to obtain a simplified model, and finally, the number of the model coefficients can be greatly reduced on the basis of ensuring modeling precision and predistortion effect through testing and verifying of an instrument end platform.
The method comprises the following specific steps:
(1) Acquiring an input baseband signal and an output baseband signal of a power amplifier;
(2) Converting the model coefficient simplification problem into a signal reconstruction problem;
(3) Constructing an observation matrix;
(4) And completing the model coefficient simplification process.
Wherein, the step (4) comprises the following steps:
(401) Inputting an observation matrix X, an observation vector y and a termination condition, and setting an output model coefficient estimated value as
Figure BDA0003835765790000031
Index set index;
(402) Initialization residual r 0 = y, supporting set
Figure BDA0003835765790000032
Index set
Figure BDA0003835765790000033
The number of iterations k =1;
(403) Calculating the inner product u = | X of the observation matrix and the residual H ·r 0 Taking out the maximum value in u, and the vector of the corresponding position in X forms a set S 1 The corresponding positions form a set J 1 ；
(404) Updating support set F 1 ＝F 0 ∪S 1 Index set index 1 ＝index 0 ∪J 1 ；
(405) Updating generalized inverse T 1 ＝(F 1 H ·F 1 ) -1 ·F 1 H Coefficient of
Figure BDA0003835765790000041
Residual error
Figure BDA0003835765790000042
The number of iterations k =2;
(406) Judging whether a termination condition is met or not, exiting if the termination condition is met, and entering an iteration process if the termination condition is not met;
(407) Starting iteration: calculating the inner product u = | X of the observation matrix and the residual H ·r k-1 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S k The corresponding positions form a set J k ；
(408) Updating support set F k ＝F k-1 ∪S k Index set index k ＝index k-1 ∪J k ；
(409)d k ＝T k-1 ·S k ，c k ＝S k -F k-1 ·d k ；
(410) If c is k ＝0，b k H ＝(1+d k H ·d k ) -1 ·d k H ·T k-1 If c is a k ≠0，b k H ＝(c k H ·c k ) -1 ·c k H ；
(411) Updating generalized inverse
Figure BDA0003835765790000043
Determining the estimated value of the coefficient
Figure BDA0003835765790000044
Updating residual errors
Figure BDA0003835765790000045
(412) Exiting iteration and outputting when the termination condition is met or the number of the coefficient estimation values is larger than the maximum coefficient of the model
Figure BDA0003835765790000046
And if the index set index is not satisfied, updating k = k +1, and continuing iteration.
The following is a more specific example:
a digital predistortion model simplification method based on a Greville method mainly comprises the following steps:
(1) Collecting baseband signals input and output by a power amplifier:
(2) The model coefficient simplification problem is converted into a signal reconstruction problem:
the expression of the VS class model can be expressed as follows
y＝X·a
Wherein, y, X, a represent the model basis function matrix and model coefficient that output signal, input signal of the power amplifier formed respectively. Because the coefficients of the VS-class model are often different from each other, this indicates that the contribution degrees of the nonlinear basis functions corresponding to different coefficients to model building are different, and if the basis function with the large contribution degree is retained, the basis function with the small contribution degree is removed, that is, the value of the model coefficient which tends to zero is set to zero, and the loss to the modeling precision is very small. On this basis, the coefficient vector can be considered to contain zeros, i.e., to be sparse. Therefore, the simplification of the model coefficient a can be regarded as a signal reconstruction problem in compressed sensing, and the number of the model coefficients can be reduced by using a reconstruction algorithm.
(3) Constructing an observation matrix:
the coefficient a can be considered to be sparse and can be obtained by VS type model expression, the output signal y is an observation vector, the model basis function matrix X formed by the input signal is an observation matrix, and the structure of X depends on the selected VS simplified model.
(4) And (3) completing a model coefficient simplification process:
and reconstructing the signal by using a GOMP algorithm, namely completing a model coefficient simplification process, wherein a flow chart is shown in figure 1. The GOMP algorithm updates the support set through greedy thought each time of iteration, continuously approaches to an original signal, does not need to know coefficient sparsity in advance, sets a termination condition, and can adaptively output a result meeting the condition; meanwhile, the generalized inverse of the matrix can be solved by utilizing finite iterations in the Greville method, matrix inversion is not needed, and hardware implementation difficulty is reduced. The algorithm steps are as follows:
(401) Inputting an observation matrix X, an observation vector y and a termination condition, and setting an output model coefficient estimated value as
Figure BDA0003835765790000051
Index set index;
(402) Initialization residual r 0 = y, supporting set
Figure BDA0003835765790000052
Index set
Figure BDA0003835765790000053
The number of iterations k =1;
(403) Calculating the inner product u = | X of the observation matrix and the residual H ·r 0 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S 1 The corresponding positions form a set J 1 ；
(404) Updating support set F 1 ＝F 0 ∪S 1 Index set index 1 ＝index 0 ∪J 1 ；
(405) Updating generalized inverse T 1 ＝(F 1 H ·F 1 ) -1 ·F 1 H Coefficient of
Figure BDA0003835765790000054
Residual error
Figure BDA0003835765790000055
The number of iterations k =2;
(406) Judging whether a termination condition is met, exiting if the termination condition is met, and entering an iteration process if the termination condition is not met;
(407) Starting iteration: calculating the inner product u = | X of the observation matrix and the residual H ·r k-1 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S k The corresponding positions form a set J k ；
(408) Updating support set F k ＝F k-1 ∪S k Index set index k ＝index k-1 ∪J k ；
(409)d k ＝T k-1 ·S k ，c k ＝S k -F k-1 ·d k ；
(410) If c is k ＝0，b k H ＝(1+d k H ·d k ) -1 ·d k H ·T k-1 If c is k ≠0，b k H ＝(c k H ·c k ) -1 ·c k H ；
(411) Updating generalized inverse
Figure BDA0003835765790000056
Determining the estimated value of the coefficient
Figure BDA0003835765790000057
Updating residual errors
Figure BDA0003835765790000058
(412) When the termination condition is met or the number of the coefficient estimation values is larger than the maximum coefficient of the model, the iteration is exited and output
Figure BDA0003835765790000061
And if the index set index is not satisfied, updating k = k +1, and continuing iteration.
(5) Test verification
And verifying the validity of the GOMP algorithm by using an instrument platform, wherein the verification work uses an MP full coefficient model as comparison. Generating a 16QAM signal with a peak-to-average ratio of 7.8dB and a bandwidth of 25MHz by using a computer, and downloading the signal to a vector signal source; then the signal is amplified through a gallium arsenide power amplifier, and then data is acquired through an attenuator by a real-time signal analyzer; and finally, sending the data back to the computer for signal time delay calibration, model coefficient extraction and predistortion signal generation.
Model coefficients, modeling accuracy and predistortion effects of the MP full coefficient model are shown in FIG. 2, the number of the coefficients of the SDDR model after the GOMP algorithm simplification is 7, and is reduced by 84% compared with 45 coefficients of the SDDR full coefficient model, and the comparison of AMAM curves, AMPM curves and Adjacent Channel Power Ratios (ACPR) before and after the digital predistortion of the simplified model is shown in FIGS. 3, 4 and 5, so that the MP model can still ensure the predistortion effects equivalent to the full coefficient model after the GOMP algorithm coefficient simplification.
In conclusion, the method can simplify coefficients of a Volterra Series (VS) model, is suitable for different modulation signals and application scenes, can greatly reduce the model coefficients on the basis of ensuring the modeling precision and the predistortion effect, enhances the system stability and the model simplification flexibility, simultaneously does not need matrix inversion, reduces the hardware realization difficulty, has stronger engineering application value, and provides a new solution for the digital predistortion power amplifier model simplification problem and the hardware realization problem.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown above but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
The principle and the implementation mode of the invention are explained by applying specific embodiments in the invention, and the description of the embodiments is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (3)

1. A digital predistortion model simplification method based on a Greville method is characterized by comprising the following steps:
(1) Collecting an input baseband signal and an output baseband signal of a power amplifier;
(2) Converting the model coefficient simplification problem into a signal reconstruction problem;
(3) Constructing an observation matrix;
(4) And completing the model coefficient simplification process.
2. The method for simplifying the digital predistortion model based on the Greville method as set forth in claim 1, wherein the observation matrix constructed in the step (3) is a model basis function matrix formed by the input signals.
3. The method for simplifying the digital predistortion model based on the Greville method as claimed in claim 1, wherein the step (4) comprises the following steps:
(401) Inputting an observation matrix X, an observation vector y and a termination condition, and setting an output model coefficient estimated value as
Figure FDA0003835765780000011
Index set index;
(402) Initialization residual r 0 = y, supporting set
Figure FDA0003835765780000012
Index set
Figure FDA0003835765780000013
The number of iterations k =1;
(403) Calculating the inner product u = | X of the observation matrix and the residual H ·r 0 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S 1 The corresponding positions form a set J 1 (ii) a Superscript H denotes conjugate transpose;
(404) Updating support set F 1 ＝F 0 ∪S 1 Index set index 1 ＝index 0 ∪J 1 ；
(405) Updating generalized inverse matrix T 1 ＝(F 1 H ·F 1 ) -1 ·F 1 H Coefficient of
Figure FDA0003835765780000014
Residual error
Figure FDA0003835765780000015
The number of iterations k =2;
Figure FDA0003835765780000016
representing a least square solution in the first iteration, wherein the superscript-1 represents matrix inversion, and the superscript ^ represents an estimated value;
(406) Judging whether a termination condition is met, if so, exiting, and if not, entering an iteration process;
(407) Starting iteration: calculating the inner product u = | X of the observation matrix and the residual H ·r k-1 L, taking out the maximum value in u, the vector of the corresponding position in X forms a set S k The corresponding positions form a set J k ；
(408) Updating support set F k ＝F k-1 ∪S k Index set index k ＝index k-1 ∪J k ；
(409) Setting an intermediate variable d k ＝T k-1 ·S k ，c k ＝S k -F k-1 ·d k ；
(410) If c is k If =0, the intermediate variable b is updated k H ＝(1+d k H ·d k ) -1 ·d k H ·T k-1 If c is a k Not equal to 0, the intermediate variable b is updated k H ＝(c k H ·c k ) -1 ·c k H ；
(411) Updating generalized inverse matrices
Figure FDA0003835765780000017
Determining the estimated value of the coefficient
Figure FDA0003835765780000018
Updating residual errors
Figure FDA0003835765780000021
Figure FDA0003835765780000022
Represents the least squares solution at the kth iteration;
(412) Exiting iteration and outputting when the termination condition is met or the number of the coefficient estimation values is larger than the maximum coefficient of the model
Figure FDA0003835765780000023
Index set index, otherwise update k = k +1, continue iteration.
CN202211087523.5A 2022-09-07 2022-09-07 Digital predistortion model simplification method based on Greville method Pending CN115396274A (en)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020034394A1 (en) * 2018-08-13 2020-02-20 南京邮电大学 Compressed sensing-based large scale mimo channel feedback reconstruction algorithm
CN111030954A (en) * 2019-12-04 2020-04-17 辽宁工程技术大学 Multichannel sampling broadband power amplifier predistortion method based on compressed sensing
CN113987788A (en) * 2021-10-26 2022-01-28 中国电子科技集团公司第五十四研究所 Digital predistortion model simplification method based on compressed sensing technology

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020034394A1 (en) * 2018-08-13 2020-02-20 南京邮电大学 Compressed sensing-based large scale mimo channel feedback reconstruction algorithm
CN111030954A (en) * 2019-12-04 2020-04-17 辽宁工程技术大学 Multichannel sampling broadband power amplifier predistortion method based on compressed sensing
CN113987788A (en) * 2021-10-26 2022-01-28 中国电子科技集团公司第五十四研究所 Digital predistortion model simplification method based on compressed sensing technology

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