CN113612455A - Digital predistortion system working method based on iterative learning control and principal curve analysis - Google Patents
Digital predistortion system working method based on iterative learning control and principal curve analysis Download PDFInfo
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Abstract
A digital predistortion system working method based on principal curve analysis and iterative learning control mainly relates to a digital predistortion technology in power amplifier linearization, behavior modeling of a broadband power amplifier, principal curve analysis and iterative learning control. Aiming at the problem that modeling precision is not high enough due to excessive kernel redundancy of a GMP model, the invention provides a modeling method combining main curve analysis and the GMP model, and the fitting effect of a power amplifier modeling structure provided by the F-type power amplifier is improved by about 2dB compared with the current popular TSVR and GMP algorithm model. For the Doherty power amplifier with stronger nonlinearity, the modeling accuracy of the main curve analysis model is improved by about 4dB compared with that of a TSVR model, and is improved by about 6dB compared with that of a GMP model. Compared with the ACPR of the output signal of the original power amplifier, the ACPR of the output signal of the pre-distortion structure constructed by the invention is reduced by about 19.89dB, and then the ACPR is compared with other commonly used pre-distortion structures, and the result shows that the structure provided by the invention has certain progress.
Description
Technical Field
The invention relates to the field of digital signal processing, in particular to a digital predistortion system working method based on iterative learning control and main curve analysis.
Background
In recent years, wireless communication technology has been developed vigorously, and especially in the last short decade, from the 3G era when the transmission rate is not enough at 400Kbps to the following 4G era exceeding 400Mbps, the signal transmission rate of the communication system has been improved by 1000 times, and with the gradual commercialization of the 5G communication system since 2020, it is known that the data transmission rate of the 5G system is greatly improved on the basis of 4G according to the performance index of IMT-2020 given by the International Telecommunications Union (ITU).
5G communication systems put higher demands on rate, capacity and delay. To achieve the above-mentioned goal, the method often starts with better coding and modulation, because the advanced modulation technique can better satisfy the requirements of the communication system for spectrum utilization and transmission rate, the modulation signal is a time-varying function, which brings a great challenge to the power amplifier, because this characteristic brings bandwidth expansion pressure and higher power peak-to-average ratio (PAPR). In addition to the challenges brought by signals to the power amplifier, another bigger challenge lies in the characteristics of the power amplifier itself, namely, the nonlinearity of the power amplifier, which increases the possibility of intermodulation distortion (IMD) and out-of-band spectrum spreading, thereby causing the occurrence of higher Adjacent Channel Power Ratio (ACPR) and stronger Adjacent Channel Interference (ACI), and secondly, the memory of the power amplifier, which increases the in-band error rate and Error Vector Magnitude (EVM), thereby causing the degradation of communication quality.
In wireless communication, it is generally desirable to transmit signals quickly while maintaining a low error rate, thereby achieving efficient use of information. However, these two ideal characteristics are contradictory to each other in an actual communication system, and in order to balance the two characteristics and reduce the nonlinear distortion of the power amplifier, the core task of the two technologies is achieved, so that numerous technologies for researching the linearization of the power amplifier are provided.
Disclosure of Invention
The invention provides a digital predistortion system working method based on principal curve analysis and iterative learning control, which mainly provides a new method for behavior modeling of a power amplifier and updates an iterative learning structure in a predistortion structure, and applies principal curve analysis to the field of power amplifier modeling for the first time. The method has better fitting effect on power amplifier modeling by using main curve analysis even under the condition of stronger nonlinearity. Meanwhile, the adaptive iterative learning control is applied, the algorithm has almost the same convergence effect as the general iterative learning algorithm but has higher convergence speed, and after the optimal input is obtained through the adaptive iterative learning, the predistorter is modeled through the main curve analysis, so that the power amplifier linearization is realized. The MATLAB is used for simulation analysis, the result shows that the ACPR of the output signal after the algorithm is adopted is reduced by about 19.88dB compared with the ACPR of the original power amplifier output signal, and compared with the simulation results of other common predistortion algorithms, the algorithm has certain progress. The effectiveness of the simulation result is verified by using an instrument-based predistortion verification platform, and the result shows that the ACPR of the output signal corrected by the algorithm is reduced by about 17.99dB compared with the uncorrected output signal through verification, so that the algorithm structure provided by the invention has a good correction effect on the nonlinearity of the power amplifier.
The specific technical scheme is as follows:
a digital predistortion system working method based on iterative learning control and principal curve analysis is characterized in that:
the method comprises the following steps:
s1, sending an input signal x (n) to a hardware communication system, and acquiring an output signal y (n) of the radio frequency power amplifier through a hardware feedback channel;
s2, performing autocorrelation synchronization algorithm according to the collected output signal y (n) and input signal x (n), and performing synchronization alignment processing on the input signal x (n) and the output signal y (n);
s3, after normalization processing is carried out on the input signal x (n) and the output signal y (n), power amplifier modeling is carried out by using a modeling method combining main curve analysis and a GMP model;
s4, obtaining an optimal input signal x1(n) of PA through an iterative learning control technology (ILC), constructing a predistorter based on the optimal input signal x1(n) by using a method of combining main curve analysis and GMP model, and then cascading the predistorter and a power amplifier to form a complete predistortion structure;
s5, inputting the input signal x (n) into a digital predistorter to obtain an output sequence signal z (n), and processing the output sequence signal z (n) through a power amplifier model to obtain an output sampling signal v (n);
s6, obtaining absolute error signal | e (n) | according to e (n) ═ x (n) — v (n), and determining the predistorter effect according to the magnitude of | e (n) |;
and S7, performing experimental test of digital predistortion.
To better implement the invention, the following steps can be further carried out: the S3 includes the following steps:
s3-1: solving a GMP model expression of the kernel matrix as follows:
it is written in matrix form as follows: y-H · W, where H is defined as the input data (kernel) matrix, and its expression is as follows:
Wdefined as model coefficients, the expression is shown below：
Given a dataset X ═ X1,x2,...,xn) Obtaining a kernel matrix H by the data set X through a GMP model;
s3-2: initialization of main curve order initial curve
A first principal component line of H, where a is a first linear principal component of H,
is the mean value of H, f(0)Or a random vector with a small value, and j is set to be 0;
s3-3: the first linear principal component of H is solved assuming that the kernel matrix H ═ H (H)1,…,Hd)TIs d-dimensional, R ═ E [ HHT]＝E[(H-E[H])(X-E[H])T]Covariance matrix, λ, denoted H1,...λdIs used to represent the characteristic value of R, and λ1>λ2>...>λdU1dA feature vector used to represent R;
characteristic value λ of R1Corresponding feature vector is u1Let a be u1Then the initial curve f(0)(λ) can be seen as a d-dimensional function of a single variable λ, f(0)(λ)＝(f1(λ),f2(λ),...,fd(λ))，(f1(λ),f2(λ),...,fd(λ)) is a coordinate function;
s3-4: for all H e H projections, solving
I.e. lambdaf(j)(h) A projection index λ obtained by expressing a projection index at the time of the minimum orthogonal distance between h and f (λ)1(0),λ2(0),...,λn(0) In sequence, the curve f is represented by successive projection points forming a line segment (f (λ)i),f(λi+1) A polygonal curve of);
s3-5: finding a new principal curve f(j+1)(λ)＝E[H|λf(j)(H)＝λ](the main curve satisfies the condition), a distance function D is calculated2(H,f(j+1))＝Eλf(H)E[||H-f(λf(H))||2|λf(H)]If the set threshold is greater than the expression | D2(H,f(j))-D2(H,f(j+1))|/D2(H,f(j)) Stopping, otherwise, making j equal to j +1, and going to step 3-4 to project, the distance function expression is as follows:
s3-6: the kernel matrix H is replaced by the projection coordinates of the main curve, and the H matrix can be rewritten as
And then, obtaining a model coefficient W by utilizing the G matrix, and finally obtaining model output through the G matrix and the model coefficient W: y is G.W.
Further:
the S4 obtains an optimal input signal x1(n) of PA through an iterative learning control technique (ILC), constructs a predistorter based on the optimal input signal x1(n) by using a method of combining a main curve analysis and a GMP model, and then concatenates the predistorter with a power amplifier, thereby forming a complete predistortion structure satisfying the following steps:
s4-1: setting an initial state, and giving a desired output track in advance, wherein the output track is the inverse of the output track of the power amplifier, yd(t) and the desired initial state xd(0) And setting an initial input u0(t)；
S4-2: the iteration is started, and the initial state x of the controlled system isk(0) And an initial output yk(0) Assigning and starting an iterative process;
s4-3: will uk(t) acting on the controlled system to obtain the actual output information y for each iterationk(t) recorded and stored in memory;
s4-4: at the end of each iteration, according to ek(t)＝yd(t)-yk(t) calculating the tracking error, and designing the input u at the next iteration according to the error and other informationk+1(t), obtaining the next iteration input by a PD type self-adaptive iteration learning algorithm: u. ofk+1＝uk+L(αk+1ek+βk+1Δek) Wherein Δ ek(t)＝ek(t+1)-ek(t)；αk+1,βk+1Scalar parameters corresponding to a proportional term and a differential term of the error respectively; l represents a learning gain matrix;
s4-5: setting iteration stop conditions, namely, | | y when the tracking error meets the set precisiond(t)-yk(t) | ≦ epsilon, where epsilon represents a given tracking precision, or iteration can be stopped when the iteration number reaches the upper limit of the set iteration number, and if the precision of the tracking error does not meet the above expression, the iteration process is continued, and finally the optimal input signal u (t) is obtained.
The invention has the beneficial effects that:
firstly, the modeling method combining the main curve analysis and the GMP model provided by the invention has obvious improvement in modeling precision, when F-type power amplifiers are selected, the fitting effect of the model based on the main curve analysis model is improved by about 2dB compared with that of TSVR and GMP algorithm models, and when Doherty-type power amplifiers with stronger nonlinearity, the modeling accuracy based on the main curve analysis model is improved by about 4dB compared with that of TSVR, and is improved by about 6dB compared with that of GMP model
Second, the PD-type adaptive iterative learning method proposed by the present invention has almost the same convergence accuracy but better convergence speed than the conventional iterative algorithm.
Thirdly, the Adjacent Channel Power Ratio (ACPR) of the output signal of the Doherty power amplifier is improved by 19.89dB by the digital predistortion system based on the main curve analysis and the iterative learning control. Compared with other common predistortion structures, the structure provided by the invention has certain improvement.
Drawings
FIG. 1 is a flow chart of an adaptive iterative learning algorithm for predistortion;
fig. 2 is a flow of a power amplifier modeling algorithm combining principal curve analysis and GMP;
FIG. 3 is an output power spectrum modeling a class F PA based on a master curve analysis;
FIG. 4 is an output power spectrum modeling a Doherty-type PA based on principal curve analysis;
FIG. 5 is an output power spectrum for modeling a class F PA using a dual sub-support vector machine;
FIG. 6 is an output power spectrum for a Doherty-type PA modeled using a two-sub support vector machine;
FIG. 7 output power spectrum modeled for a class F PA using GMP modeling;
FIG. 8 is an output power spectrum modeled for a Doherty-type PA using a GMP model;
FIG. 9 is a graph comparing different models of linearization effect spectra.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments 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.
The principle of digital predistortion is to introduce a predistorter module before power amplification, and its main function is to implement nonlinear complementation with power amplifier, so that the cascade connection of predistorter and power amplifier can be made into a linear system under the ideal condition. The invention adopts the predistortion technology of an iterative learning structure, and utilizes an iterative learning algorithm to obtain the optimal input of the power amplifier, and then establishes a predistorter model based on the input signal. Therefore, the exploration of a proper iterative learning algorithm and the establishment of an accurate power amplifier and predistorter model have important theoretical significance for improving the linearization effect of the power amplifier, solve the problem of signal distortion caused by the nonlinear characteristic of the power amplifier, meet the requirement of the development of a wireless communication system and have practical significance.
Specifically, a complete predistortion system is established, the system comprises a Power Amplifier (PA), a computer (PC), a Vector Signal Generator (VSG), a spectrum analyzer (VSA), a digital power supply and an attenuator, and the power amplifier used for implementing the system is a Doherty power amplifier with the working frequency band of 1.8GHz-2.4GHz and the bandwidth of 600 MHz;
the original input of the power amplifier selects an LTE signal with the bandwidth of 15M for testing, a vector signal generator is connected with a power amplifier to form a transmitting end of a digital predistortion system, and an output signal generated by the power amplifier is connected to a spectrum analyzer through an attenuator to form a feedback channel of digital predistortion;
the first step is that a vector signal generator and a spectrum analyzer are connected to a computer through a router, the vector signal generator generates a baseband signal under the control of the computer, the baseband signal is up-converted into a carrier frequency of a power amplifier working frequency, then, an up-converted radio frequency signal is amplified through a linear driving amplifier and then sent into a Doherty power amplifier needing linearization, the output of the power amplifier is attenuated through an attenuator, the down-conversion is carried out through the spectrum analyzer, the acquisition is sent to the PC, and the data of the sent and received signals are synchronously aligned.
And carrying out main curve analysis power amplifier modeling on the obtained input and output signals, wherein the specific process of the power amplifier modeling is from S3-1 to S3-6.
Meanwhile, an optimal input signal is obtained through MATLAB processing by utilizing the input and output signals, and then a predistorter model is established through the optimal input signal and the output signal, wherein the construction of the predistortion system is completed at this moment, and the predistorter model is recorded in the following S4-1 to S4-5.
From fig. 3 to fig. 8, it can be seen that the model modeling based on the main curve analysis is improved by about 2dB compared with the model modeling based on the TSVR and the GMP, and therefore, the model modeling based on the main curve analysis has higher modeling accuracy for the class F power amplifier than the other two models. For the Doherty power amplifier, the main curve analysis-based modeling is improved by about 4dB compared with the TSVR modeling, and is improved by about 6dB compared with the NMSE of the GMP model, so that the advantage of the main curve analysis-based modeling can be better embodied when the nonlinearity of the power amplifier is stronger.
And the second step is that the output signal of the original input signal input into the predistorter is sent into a vector signal generator to generate a radio frequency signal, the radio frequency signal is also required to be converted into a power amplifier working frequency, the converted signal is sent into a Doherty power amplifier which is required to be linearized, the power amplifier output is attenuated by an attenuator and then sent into a signal analyzer to obtain a digital signal, and finally the digital signal is sent back to the computer. It should be noted that the attenuators in the signal pre-distortion processing step and the attenuators used in the signal extraction should be kept the same, in order to keep the whole system unchanged.
And synchronously aligning the power amplifier output signal obtained after the processing in the second step with the original input signal data, and drawing a frequency spectrum comparison graph of different model linearization effects.
From the results of the experiments, it can be seen from FIG. 9 that: the leakage power of the main signal channel after the pre-distortion is adopted is obviously reduced, so that the pre-distortion has a certain correction effect on the nonlinear characteristic of the power amplifier. The correction effects of different predistortion models are different after the predistortion is adopted, the correction effect of an inverse structure based on a main curve analysis model is directly used in the three compared predistortion models, and the effect of the main curve analysis model and the adaptive iterative learning algorithm is the best, so that the improvement of the predistortion structure constructed by the method can be seen.
The specific process of power amplifier modeling is that S3 includes the following steps:
s3-1: solving a GMP model expression of the kernel matrix as follows:
it is written in matrix form as follows: y-H · W, where H is defined as the input data (kernel) matrix, and its expression is as follows:
Wdefined as model coefficientsThe expression is as follows:
given a dataset X ═ X1,x2,...,xn) Obtaining a kernel matrix H by the data set X through a GMP model;
s3-2: initialization of main curve order initial curve
A first principal component line of H, where a is a first linear principal component of H,
is the mean value of H, f(0)Or a random vector with a small value, and j is set to be 0;
s3-3: the first linear principal component of H is solved assuming that the kernel matrix H ═ H (H)1,…,Hd)TIs d-dimensional, R ═ E [ HHT]＝E[(H-E[H])(X-E[H])T]Covariance matrix, λ, denoted H1,...λdIs used to represent the characteristic value of R, and λ1>λ2>...>λdThen u is1,...udA feature vector used to represent R;
characteristic value λ of R1Corresponding feature vector is u1Let a be u1Then the initial curve f(0)(λ) can be seen as a d-dimensional function of a single variable λ, f(0)(λ)＝(f1(λ),f2(λ),...,fd(λ))，(f1(λ),f2(λ),...,fd(λ)) is a coordinate function;
s3-4: for all H e H projections, solving
I.e. lambdaf(j)(h) A projection index λ obtained by expressing a projection index at the time of the minimum orthogonal distance between h and f (λ)1(0),λ2(0),...,λn(0) In order, curve f is shown asThe continuous projection point forms a line segment (f (lambda)i),f(λi+1) A polygonal curve of);
s3-5: finding a new principal curve f(j+1)(λ)＝E[H|λf(j)(H)＝λ](the main curve satisfies the condition), a distance function D is calculated2(H,f(j+1))＝Eλf(H)E[||H-f(λf(H))||2|λf(H)]If the set threshold is greater than the expression | D2(H,f(j))-D2(H,f(j+1))|/D2(H,f(j)) Stopping, otherwise, making j equal to j +1, and going to step 3-4 to project, the distance function expression is as follows:
s3-6: the kernel matrix H is replaced by the projection coordinates of the main curve, and the H matrix can be rewritten as
And then, obtaining a model coefficient W by utilizing the G matrix, and finally obtaining model output through the G matrix and the model coefficient W: y is G.W.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (3)
1. A digital predistortion system working method based on iterative learning control and principal curve analysis is characterized in that:
the method comprises the following steps:
s1, sending an input signal x (n) to a hardware communication system, and acquiring an output signal y (n) of the radio frequency power amplifier through a hardware feedback channel;
s2, performing autocorrelation synchronization algorithm according to the collected output signal y (n) and input signal x (n), and performing synchronization alignment processing on the input signal x (n) and the output signal y (n);
s3, after normalization processing is carried out on the input signal x (n) and the output signal y (n), power amplifier modeling is carried out by using a modeling method combining main curve analysis and a GMP model;
s4, obtaining an optimal input signal x1(n) of PA through an iterative learning control technology (ILC), constructing a predistorter based on the optimal input signal x1(n) by using a method of combining main curve analysis and GMP model, and then cascading the predistorter and a power amplifier to form a complete predistortion structure;
s5, inputting the input signal x (n) into a digital predistorter to obtain an output sequence signal z (n), and processing the output sequence signal z (n) through a power amplifier model to obtain an output sampling signal v (n);
s6, obtaining absolute error signal | e (n) | according to e (n) ═ x (n) — v (n), and determining the predistorter effect according to the magnitude of | e (n) |;
and S7, performing experimental test of digital predistortion.
2. The working method of the digital predistortion system based on the iterative learning control and the principal curve analysis as claimed in claim 1, wherein:
the S3 includes the following steps:
s3-1: solving a GMP model expression of the kernel matrix as follows:
it is written in matrix form as follows: y-H · W, where H is defined as the input data (kernel) matrix, and its expression is as follows:
w is defined as the model coefficient, and the expression is as follows:
given a dataset X ═ X1,x2,...,xn) Obtaining a kernel matrix H by the data set X through a GMP model;
s3-2: initialization of main curve order initial curve
A first principal component line of H, where a is a first linear principal component of H,
is the mean value of H, f(0)Or a random vector with a small value, and j is set to be 0;
s3-3: the first linear principal component of H is solved assuming that the kernel matrix H ═ H (H)1,…,Hd)TIs d-dimensional, R ═ E [ HHT]＝E[(H-E[H])(X-E[H])T]Covariance matrix, λ, denoted H1,...λdIs used to represent the characteristic value of R, and λ1>λ2>...>λdThen u is1,...udA feature vector used to represent R;
characteristic value λ of R1Corresponding feature vector is u1Let a be u1Then the initial curve f(0)(λ) can be seen as a d-dimensional function of a single variable λ, f(0)(λ)＝(f1(λ),f2(λ),...,fd(λ))，(f1(λ),f2(λ),...,fd(λ)) is a coordinate function;
s3-4: for all H e H projections, solving
I.e. lambdaf(j)(h) A projection index λ obtained by expressing a projection index at the time of the minimum orthogonal distance between h and f (λ)1(0),λ2(0),...,λn(0) In sequence, the curve f is represented by successive projection points forming a line segment (f (λ)i),f(λi+1) A polygonal curve of);
s3-5: finding a new principal curve f(j+1)(λ)＝E[H|λf(j)(H)＝λ](the main curve satisfies the condition), a distance function D is calculated2(H,f(j+1))＝Eλf(H)E[||H-f(λf(H))||2|λf(H)]If the set threshold is greater than the expression | D2(H,f(j))-D2(H,f(j+1))|/D2(H,f(j)) Stopping, otherwise, making j equal to j +1, and going to step 3-4 to project, the distance function expression is as follows:
s3-6: the kernel matrix H is replaced by the projection coordinates of the main curve, and the H matrix can be rewritten as
And then, obtaining a model coefficient W by utilizing the G matrix, and finally obtaining model output through the G matrix and the model coefficient W: y is G.W.
3. The working method of the digital predistortion system based on the iterative learning control and the principal curve analysis as claimed in claim 1, wherein:
the S4 obtains an optimal input signal x1(n) of PA through an iterative learning control technique (ILC), constructs a predistorter based on the optimal input signal x1(n) by using a method of combining a main curve analysis and a GMP model, and then concatenates the predistorter with a power amplifier, thereby forming a complete predistortion structure satisfying the following steps:
s4-1: setting an initial state, and giving a desired output track in advance, wherein the output track is the inverse of the output track of the power amplifier, yd(t) and the desired initial state xd(0) And setting an initial input u0(t)；
S4-2: the iteration is started, and the initial state x of the controlled system isk(0) And an initial output yk(0) Assigning and starting an iterative process;
s4-3: will uk(t) acting on the controlled system to obtain the actual output information y for each iterationk(t) recorded and stored in memory;
s4-4: at the end of each iteration, according to ek(t)＝yd(t)-yk(t) calculating the tracking error, and designing the input u at the next iteration according to the error and other informationk+1(t), obtaining the next iteration input by a PD type self-adaptive iteration learning algorithm: u. ofk+1＝uk+L(αk+1ek+βk+1Δek) Wherein Δ ek(t)＝ek(t+1)-ek(t)；αk+1,βk+1Scalar parameters corresponding to a proportional term and a differential term of the error respectively; l represents a learning gain matrix;
s4-5: setting iteration stop conditions, namely, | | y when the tracking error meets the set precisiond(t)-yk(t) | ≦ epsilon, where epsilon represents a given tracking precision, or iteration can be stopped when the iteration number reaches the upper limit of the set iteration number, and if the precision of the tracking error does not meet the above expression, the iteration process is continued, and finally the optimal input signal u (t) is obtained.
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