CN113868994A - Threshold value optimization method suitable for power amplifier model based on CPWL function - Google Patents
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Abstract
The invention discloses a threshold value optimization method suitable for a power amplifier model based on a CPWL function. On a simplified second-order DDR model based on a CPWL function, the invention uses a sign function to enable the threshold value of the model and the output of the model to be approximately linear relation, and an optimized value of the threshold is searched out through iteration. On the premise of keeping the predistortion performance, the method reduces the number of threshold values and coefficients required in the model, and reduces resources and power consumption required by the model. The test result shows that the model after threshold optimization can well compensate the nonlinearity and the memory effect of the radio frequency power amplifier.
Description
Technical Field
The invention belongs to the field of radio frequency power amplifier digital predistortion, and particularly relates to a threshold value optimization method suitable for a power amplifier model based on a CPWL function.
Background
In modern wireless communication systems, in order to obtain a large communication rate, a modulation scheme with a large communication bandwidth and a high modulation order, such as Orthogonal Frequency Division Multiplexing (OFDM) technology and Quadrature Amplitude Modulation (QAM) technology, is often adopted. This results in a signal with a high peak-to-average ratio (PARP), which puts high demands on the linearity of the rf power amplifier. If the power amplifier is biased in a linear region state during the operation when the peak power of the signal is injected, the average power is far lower than the peak power, which causes the efficiency of the power amplifier to be very low, and brings a large amount of power consumption and a great challenge to the heat dissipation of a communication system. The Digital Predistortion (DPD) technology is widely applied to solve the problem, and the basic principle of the DPD is that a module which is called a predistorter and has the opposite characteristic with a power amplifier is used before a signal is injected into the power amplifier, so that a primary connection system of the predistorter and the power amplifier becomes a linear system, and the nonlinear distortion of a final output signal of the radio frequency power amplifier is eliminated. Therefore, accurate modeling of power amplifier characteristics is the core of DPD technology. For a long time, various power amplifier models based on the Volterra series have been proposed and widely used, such as a Memory Polynomial (MP) model, etc. The basic idea of the model is to use an exponential function to fit the nonlinear characteristic of the power amplifier, which inevitably results in the generation of high-order terms, so that the model consumes a large amount of multiplier resources in hardware implementation. Recently, a new power amplifier model based on a piecewise linear (CPWL) function has been proposed and is widely researched and focused, such as DVR model, which has the idea of segmenting the nonlinear characteristic of the power amplifier in amplitude and then fitting a straight line for each segment. It generally appears that a polyline is used in fitting the curve for non-linear correspondence. The use of absolute value operation in CPWL replaces the high order terms in the Volterra series, whereas absolute value operation consumes far less resources in hardware implementation than multipliers. The power amplifier model of the CPWL function class has very low complexity.
Disclosure of Invention
The invention aims to provide a threshold value optimization method suitable for a power amplifier model based on a CPWL function, so as to solve the technical problems of overlarge resources and power consumption required by the model on the premise of keeping the predistortion performance.
In order to solve the technical problems, the specific technical scheme of the invention is as follows:
a threshold value optimization method suitable for a power amplifier model based on a CPWL function comprises the following steps:
step 1, establishing a simplified second-order DDR power amplifier model expression based on a CPWL function:
n belongs to [0, N-1] in the formula (1), represents the index position of the sampling point, and has N sampling points; i.e. i
Is memory depth and i ∈ [0, M]M is the maximum memory depth;
is an input complex signal of the power amplifier,
for the output complex signal of the power amplifier, | | is defined as taking the module value of the complex number and taking the absolute value of the real number to operate ")*Defining as conjugate operation for complex number; k is the number of segments for the nonlinear fit interval, K ∈ [1, K]Denoted as the k-th segment thereof; beta is akIs the k-th section threshold value;
is the model coefficient corresponding to the first term,
is the model coefficient corresponding to the second term,
is the model system corresponding to the third termThe number of the first and second groups is,
is the model coefficient corresponding to the fourth term; the subscript ki represents the model coefficient corresponding to the kth section and the memory depth i; when the model is used, one item or a plurality of items are used in combination according to the power amplifier used and the requirement on linearization of the power amplifier, so that the model has flexibility; in order to simplify the expression without losing generality, all the following deductions are based on a scene only using a model 1 order item, and corresponding items and coefficients in the formula (1) only need to be added into the formulas (3) - (6) under the condition of using multiple items, and are not described again; the condition that a plurality of items can be used by expanding the device;
step 2, deriving model coefficients
The model is expressed in matrix form as
Y＝Hc (2)
Wherein Y represents a vector of the output signal, H is a model matrix, and c is a model coefficient vector, each defined as
H＝[h10，…，hKM]，
(·)TA transpose operation representing a vector; wherein h iskiDefined as the kth segment, and the memory depth is the model item corresponding to i, expressed as
Solving the coefficients using a least squares method, the corresponding solution being expressed as
In the formula (4)
Representing the solved coefficient vector (·)HConjugate transpose of complex matrix representation, (.)-1Representing the inverse of the matrix;
step 3, deriving a threshold optimization method:
step 3.1, mixing
Expressed in the form of the addition of real and imaginary parts
Wherein [. ]]rRepresenting the real part of a complex number [ ·]iRepresents the imaginary part of the complex number; j is the unit imaginary number;
step 3.2, define Φki(n) is
Then
Is represented by the real part of
Wherein sgn (. cndot.) is a sign function defined as
Step 3.3, if coefficient
Is an optimal solution, an optimized threshold tableShown as
The desired output corresponding to the optimized threshold is
Its real part is expressed as
Order to
Definition of
Current output
And desired output
The real part of the error is obtained by subtraction and is defined as
Expression of formula (11) in matrix form
Er＝-ΨΔβ (12)
E in formula (12)rAs an error vector, Ψ is a threshold matrix, and Δ β is a threshold update vector, each defined as Ψ [ [ ψ [ ]10(0),…,ψ10(N-1)]T,…,[ψKM(0),…,ψKM(N-1)]T]，
(·)TA transpose operation representing a vector; Δ β ═ Δ β1，…，Δβk]T(ii) a Solving for a least squares solution of Δ β, defined as
Step 3.4, solving the difference between the current threshold value and the optimized threshold value through multiple iterative approximation to the optimized threshold value, thereby indirectly obtaining the optimized value of the threshold, wherein the multiple iterative approximation to the optimized threshold value is expressed as
In the formula
The number of iterations is indicated;
and 4, updating the obtained optimization threshold and model coefficients to the predistorter to complete the whole predistortion process.
Further, the specific iterative process in step 3.4 is as follows:
step 3.4.1, searching to obtain ideal output of the predistorter by using an iterative learning control method
Selecting the initial threshold as uniformly distributed, beta1＝[1/K，2/K，…，1]TSetting a variable representing the number of iterations
3.4.2 outputting the ideal output
Threshold (THD)
And input
Substituting the model coefficient into formula (4) to solve the model coefficient corresponding to the iteration, and recording the model coefficient as
Step 3.4.3, treating
And input
Substituting formula (2) to calculate the current coefficient and the corresponding model output under the threshold, and recording the current coefficient and the corresponding model output as
Computing
And ideal output
If the error meets the requirement, the modeling is finished, and the iteration is ended; otherwise, entering the next step;
step 3.4.4, treating
And
the update values of the thresholds calculated by substituting equations (11) to (14) are recorded
Setting the number of iterations
Then step 3.4.2 is entered to start the next iteration process.
The threshold value optimization method applicable to the power amplifier model based on the CPWL function has the following advantages:
the invention separates the threshold of the CPWL function from the absolute value symbol by using the symbol function, so that the updated value and the output of the threshold value can be approximately regarded as a linear relation, and the updated value of the threshold is solved by using a least square method. And then, an optimized threshold is gradually searched out by an iterative method, and the number of sections of the CPWL can be reduced on the premise of not reducing the model precision after optimization. The number of coefficients and the consumption of computing resources are reduced, the scale of the model is reduced, and the power consumption is reduced. Meanwhile, the scale of the model is reduced, so that the requirement on the time sequence of a digital circuit is relieved, and the predistortion system can operate at higher frequency.
Drawings
Fig. 1 is a schematic structural diagram of a power amplifier digital predistortion device of the invention;
FIG. 2 is a flow chart of a digital predistortion modeling method of the present invention;
FIG. 3 is a diagram of a power spectrum of a 5G-NR signal with a bandwidth of 100MHz after digital pre-distortion by using an initial threshold and an optimized threshold when a system sampling frequency is 500 MHz.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, the following describes a threshold value optimization method of a power amplifier model based on a CPWL function in detail with reference to the accompanying drawings.
As shown in fig. 1, the power amplifier digital predistortion device of the invention includes a digital predistorter, an analog-to-digital converter, a digital-to-analog converter, an orthogonal modulator, an orthogonal demodulator, a radio frequency power amplifier, a coupler, iterative learning control, coefficient estimation and threshold update based on a simplified second-order DDR model of a CPWL function.
The general flow chart of the invention is shown in FIG. 2, and first iterative learning control is usedThe expected output of the predistorter is searched, then the used model items, the number of thresholds and the memory depth are set, the optimized thresholds and the optimized coefficients are iterated through the threshold optimization method provided by the invention, and finally the optimized thresholds and the optimized coefficients are used for modeling the predistorter. In particular, first a baseband signal without predistortion is used
The method comprises the steps of sequentially obtaining an analog radio frequency signal through a digital predistorter, a digital-to-analog converter, an orthogonal modulator and a radio frequency power amplifier of a simplified second-order DDR model based on a CPWL function, sequentially obtaining a distorted digital baseband signal corresponding to the output of the power amplifier through the coupler, the orthogonal demodulator and the analog-to-digital converter, and then searching a linear signal, namely a linear signal output by the power amplifier, of the power amplifier through iterative learning control
Input signal corresponding to time power amplifier
I.e. the ideal output signal of the predistorter.
The CPWL function-based digital predistorter input end external digital baseband complex input signal
And ideal output
As is known, the following steps are performed to iteratively search out the optimized threshold and coefficient and update the predistorter:
step 1, establishing a simplified second-order DDR power amplifier model expression based on a CPWL function:
n is belonged to [0, N-1] in formula (1)]Index bit representing sample pointSetting N sampling points in total; i is the memory depth and i belongs to [0, M ]]And M is the maximum memory depth.
Is an input complex signal of the power amplifier,
for the output complex signal of the power amplifier, | | is defined as taking the module value of the complex number and taking the absolute value of the real number to operate ")*Defined as the conjugate operation on a complex number. K is the number of segments for the nonlinear fit interval, K ∈ [1, K]Denoted as the kth segment therein. Beta is akIs the k-th section threshold value;
is the model coefficient corresponding to the first term,
is the model coefficient corresponding to the second term,
is the model coefficient corresponding to the third term,
is the model coefficient corresponding to the fourth term; the subscript ki represents the model coefficient corresponding to the kth segment and the memory depth i. When the model is used, one item or a plurality of items can be used in combination according to the power amplifier actually used and the requirement on linearization of the power amplifier, and the model has high flexibility. In order to simplify the expression without losing generality, all the following deductions are based on a scene only using a model 1 order item, and corresponding items and coefficients in the formula (1) only need to be added into the formulas (3) - (6) under the condition of using multiple items, and are not described again; it is easy to expand to cases where multiple terms are used.
Step 2, deriving model coefficients
The method of solving, model tableShown in matrix form as
Y＝Hc (2)
Wherein Y represents a vector of the output signal, H is a model matrix, and c is a model coefficient vector, each defined as
H＝[h10，…，hKM]，
(·)TRepresenting a transpose operation of the vector. Wherein h iskiDefining as the k-th section, and memorizing the model item corresponding to the depth i. Can be expressed as
The coefficients are solved using a least squares method, and the corresponding solution can be expressed as
In the formula (4)
Representing the solved coefficient vector (·)HConjugate transpose of complex matrix representation, (.)-1Representing the inverse of the matrix;
step 3, deducing a threshold optimization method;
step 3.1, mixing
Expressed in the form of the addition of real and imaginary parts
Wherein [. ]]rRepresenting the real part of a complex number [ ·]iRepresentsThe imaginary part of the complex number; j is the unit imaginary number;
step 3.2, to simplify the expression, define Φki(n) is
Then
Is represented by the real part of
Wherein sgn (. cndot.) is a sign function defined as
Step 3.3, assume the coefficients at this time
Already the optimal solution, the threshold of optimization is expressed as
The desired output corresponding to the optimized threshold is
Its real part is expressed as
In general, the difference between the optimized threshold and the current threshold is small, and we can make the following assumptions
Definition of
Current output
And desired output
The real part of the error is obtained by subtraction and is defined as
Expression of formula (11) in matrix form
Er＝-ΨΔβ(12)
E in formula (12)rAs an error vector, Ψ is a threshold matrix, and Δ β is a threshold update vector, each defined as Ψ [ [ ψ [ ]10(0),…,ψ10(N-1)]T,…,[ψKM(0),…,ψKM(N-1)]T]，
Δβ＝[Δβ1，…，Δβk]T(ii) a A least squares solution of Δ β can be solved, defined as
Step 3.4, as can be seen from the derivation process, although the optimal value of the threshold cannot be directly solved, the difference between the current threshold value and the optimal threshold value can be solved, so as to indirectly obtain the optimal value of the threshold, and when the process is actually implemented, the optimal threshold needs to be approached through multiple iterations, which is expressed as the optimal threshold
In the formula
The number of iterations is indicated. The specific iterative process is as follows:
step 3.4.1, obtaining ideal output of the predistorter by searching through an iterative learning control method (ILC)
Selecting the initial threshold as uniformly distributed, beta1＝[1/K，2/K，…，1]TSetting a variable representing the number of iterations
3.4.2 outputting the ideal output
Threshold (THD)
And input
Substituting the model coefficient into formula (4) to solve the model coefficient corresponding to the iteration, and recording the model coefficient as
Step 3.4.3, treating
And input
Substituting formula (2) to calculate the current coefficient and the corresponding model output under the threshold, and recording the current coefficient and the corresponding model output as
Computing
And ideal output
If the error meets the requirement, the modeling is finished, and the iteration is finished. Otherwise, the next step is entered.
Step 3.4.4, treating
And
the update values of the thresholds calculated by substituting equations (11) to (14) are recorded
Setting the number of iterations
Then step 3.4.2 is entered to start the next iteration process.
Through the iteration process, the corresponding optimized threshold value and the corresponding model coefficient can be solved, the obtained optimized threshold value and the model coefficient are updated for the predistorter, and the whole predistortion process is completed.
The baseband signal is an I/Q double-tone complex signal, a 5G-NR signal with a bandwidth of 100MHz is used in the test, the peak-to-average ratio is 9.3dB, and the sampling rate is 500 MHz. The predistortion processing capability of the predistortion device for the broadband signal can be well embodied. The specific parameters are set as follows:
1. the first and third terms in the simplified second order DDR predistortion model based on the CPWL function are used.
2. The memory depth M of the model is 4, and the threshold number K is 4 and 10 respectively.
The results of the corresponding Adjacent Channel Leakage Ratio (ACLR) are summarized in table 1, comparing the pre-distortion without pre-distortion using 4 un-optimized thresholds, 4 optimized thresholds and 10 un-optimized thresholds. And the power amplifier output power spectrum under each condition is plotted and compared, as shown in fig. 3. It can be seen through comparison that when 4 thresholds are also used, the predistortion performance is greatly improved when the optimized threshold provided by the invention is used, and even slightly better than the performance when 10 unoptimized thresholds are used. Compared with the method using 10 non-optimized thresholds, the number of thresholds and the number of coefficients of the method are reduced by 60%, and the calculation amount and the power consumption of the predistorter are greatly reduced.
TABLE 1
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein 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 (2)
1. A threshold value optimization method suitable for a power amplifier model based on a CPWL function is characterized by comprising the following steps:
step 1, establishing a simplified second-order DDR power amplifier model expression based on a CPWL function:
n is belonged to [0, N-1] in formula (1)]Indicating the index positions of the sampling points, and having N sampling points; i is the memory depth and i belongs to [0, M ]]M is the maximum memory depth;
is an input complex signal of the power amplifier,
for the output complex signal of the power amplifier, | | is defined as taking the module value of the complex number and taking the absolute value of the real number to operate ")*Defining as conjugate operation for complex number; k is the number of segments for the nonlinear fit interval, K ∈ [1, K]Denoted as the k-th segment thereof; beta is akIs the k-th section threshold value;
is the model coefficient corresponding to the first term,
is the model coefficient corresponding to the second term,
is the model coefficient corresponding to the third term,
is the model coefficient corresponding to the fourth term; the subscript ki represents the model coefficient corresponding to the kth section and the memory depth i; when the model is used, one item or a plurality of items are used in combination according to the power amplifier used and the requirement on linearization of the power amplifier; all the following derivations are based on a scenario where only model 1 order terms are used, and the addition of the corresponding terms and coefficients in equation (1) to equations (3) to (6) can be extended to use multiple terms;
step 2, deriving model coefficients
Is solved forMethod of expressing a model in matrix form as
Y＝Hc (2)
Wherein Y represents a vector of the output signal, H is a model matrix, and c is a model coefficient vector, each defined as
H＝[h10,…，hkm]，
(·)TA transpose operation representing a vector; wherein h iskiDefined as the kth segment, and the memory depth is the model item corresponding to i, expressed as
Solving the coefficients using a least squares method, the corresponding solution being expressed as
In the formula (4)
Representing the solved coefficient vector (·)HConjugate transpose of complex matrix representation, (.)-1Representing the inverse of the matrix;
step 3, deriving a threshold optimization method:
step 3.1, mixing
Expressed in the form of the addition of real and imaginary parts
Wherein [. ]]rRepresenting the real part of a complex number [ ·]iRepresents the imaginary part of the complex number; j is the unit imaginary number;
step 3.2, define Φki(n) is
Then
Is represented by the real part of
Wherein sgn (. cndot.) is a sign function defined as
Step 3.3, if coefficient
Is an optimal solution, and the optimal threshold is expressed as
The desired output corresponding to the optimized threshold is
Its real part is expressed as
Order to
Definition of
Current output
And desired output
The real part of the error is obtained by subtraction and is defined as
Expression of formula (11) in matrix form
Er＝-ΨΔβ (12)
E in formula (12)rAs an error vector, Ψ is a threshold matrix, and Δ β is a threshold update vector, each defined as Ψ [ [ ψ [ ]10(0)，…,ψ10(N-1)]T，…，[ψKM(0)，…，ψKM(N-1)]T]，
(·)TA transpose operation representing a vector; Δ β ═ Δ β1，…，Δβk]T(ii) a Solving for a least squares solution of Δ β, defined as
Step 3.4, solving the difference between the current threshold value and the optimized threshold value through multiple iterative approximation to the optimized threshold value, thereby indirectly obtaining the optimized value of the threshold, wherein the multiple iterative approximation to the optimized threshold value is expressed as
Wherein l represents the number of iterations;
and 4, updating the obtained optimization threshold and model coefficients to the predistorter to complete the whole predistortion process.
2. The threshold optimization method for the CPWL function-based power amplifier model according to claim 1, wherein the specific iteration process in step 3.4 is as follows:
step 3.4.1, searching to obtain ideal output of the predistorter by using an iterative learning control method
Selecting the initial threshold as uniformly distributed, beta1＝[1/K，2/K，…，1]TSetting a variable l which represents the iteration number to be 1;
3.4.2 outputting the ideal output
Threshold betalAnd input
Substituting the model coefficient into formula (4) to solve the model coefficient corresponding to the iteration, and recording the model coefficient as
Step 3.4.3, treating
βlAnd input
Substituting formula (2) to calculate the current coefficient and the corresponding model output under the threshold, and recording the current coefficient and the corresponding model output as
Computing
And ideal output
If the error meets the requirement, the modeling is finished, and the iteration is ended; otherwise, entering the next step;
step 3.4.4, treating
βl，
And
the update values for the thresholds calculated by substituting equations (11) to (14) are denoted as βl+1Setting the iteration number l as l + 1; then step 3.4.2 is entered to start the next iteration process.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114629756A (en) * | 2022-05-16 | 2022-06-14 | 成都凯腾四方数字广播电视设备有限公司 | Adaptive predistortion method and system for multimode 5G broadcast transmitter |
| CN115603673A (en) * | 2022-11-23 | 2023-01-13 | 成都芯通软件有限公司（Cn） | Method and system for realizing digital predistortion based on reconstructed DVR model |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114629756A (en) * | 2022-05-16 | 2022-06-14 | 成都凯腾四方数字广播电视设备有限公司 | Adaptive predistortion method and system for multimode 5G broadcast transmitter |
| CN114629756B (en) * | 2022-05-16 | 2022-08-16 | 成都凯腾四方数字广播电视设备有限公司 | Self-adaptive predistortion method and system for multimode 5G broadcast transmitter |
| CN115603673A (en) * | 2022-11-23 | 2023-01-13 | 成都芯通软件有限公司（Cn） | Method and system for realizing digital predistortion based on reconstructed DVR model |
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