Signal generator digital pre-distortion method based on conjugate gradient

Abstract

The invention discloses a signal generator digital pre-distortion method based on conjugate gradient, and belongs to the technical field of electronic testing. The regularization parameter mu is introduced when the model coefficient matrix W is solved, the model coefficient matrix solving method based on the conjugate gradient is provided on the basis, and compared with the prior art, the calculated amount is reduced; two rapid and effective regularization parameter mu calculation methods, namely a power method-based regularization parameter calculation method and a Guerre circle-based regularization parameter calculation method, are provided. According to the regularization parameter calculation method, the regularization parameters can be set in a reasonable range, and in the process of solving the model coefficient matrix W, the model precision can be guaranteed, and calculation errors caused by too large condition numbers are avoided.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic testing, and in particular relates to a digital predistortion method of a signal generator based on conjugate gradient. Background Art

[0002] The RF power amplifier in the signal generator is a nonlinear system, which has AM-AM (amplitude-amplitude) and AM-PM (amplitude-phase) nonlinear distortions, and the RF power amplifier also has memory effects. The invention relates to digital compensation of RF power amplifiers and other nonlinear circuits or systems. The invention is particularly suitable for efficient and fast parameterization of digital predistorters (DPDs) in signal generators.

[0003] At present, the traditional digital predistorter used in power amplifiers and other nonlinear systems needs to solve the inverse matrix in the process of determining the model system parameters. Affected by noise, model characteristics, and model complexity, the inverse matrix to be solved will have problems such as high condition number, complex solution, and even singular inverse matrix to be solved, which cannot meet the accuracy and speed requirements of the digital predistorter for solving the model system parameters.

[0004] The main disadvantages of existing technologies include:

[0005] 1. Traditional pre-distortion correction algorithms require matrix inversion when solving the model coefficient matrix. Affected by factors such as noise, the inverse matrix to be solved may have high condition numbers or even singular inverse matrices, which will lead to inaccurate inversion or even non-existence of the matrix inverse.

[0006] 2. Traditional pre-distortion correction algorithms require matrix inversion when solving the model coefficient matrix. As the complexity of the power amplifier model increases, the dimension of the inverse matrix to be solved increases, and the computational complexity of matrix inversion is high, resulting in slow algorithm operation. Summary of the invention

[0007] In view of the above technical problems existing in the prior art, the present invention proposes a signal generator digital predistortion method based on conjugate gradient, which has a reasonable design, overcomes the shortcomings of the prior art and has good effects.

[0008] In order to achieve the above object, the present invention adopts the following technical solution:

[0009] A signal generator digital predistortion method based on conjugate gradient includes the following steps:

[0010] Step 1: Select PA model;

[0011] Step 2: Solve the system matrix S according to the selected PA inverse model;

[0012] Step 3: Solve the matrix S based on the power method T The maximum eigenvalue λ of S max ; Estimate the matrix S based on the Gail circle method T Upper bound of the maximum eigenvalue of S

[0013] Step 4: Determine the regularization parameter μ according to the maximum eigenvalue;

[0014] Step 5: Use the regularization parameter and use the conjugate gradient method to solve the PA inverse model coefficient matrix.

[0015] Preferably, in step 1, the PA model includes an MP model, a GMP model, and a Volterra model; the output of the MP model is expressed as shown in formula (1):

[0016]

[0017] in,

[0018] x(n): amplifier input data;

[0019] y(n): power amplifier output data;

[0020] P: Maximum nonlinear order of the model;

[0021] M: model memory depth;

[0022] W mp :MP model parameters;

[0023] p: model nonlinear order index variable;

[0024] m: Model memory depth index variable.

[0025] Preferably, in step 2, the MP model is used to obtain the PA inverse model, as shown in formula (2):

[0026]

[0027] in,

[0028] S: inverse model sensitivity matrix after power amplification;

[0029] W: inverse model coefficient matrix after power amplification;

[0030] W 00 ,W 01 ,W 02 …: elements in matrix W;

[0031] Y: observation data matrix;

[0032] Elements in the observation data matrix;

[0033] and All are the output data of the inverse model after power amplifier;

[0034] Inverse model input data after power amplifier;

[0035] z0(n): inverse model input data after power amplification,

[0036] G: gain of the power amplifier;

[0037] z(n): power amplifier (PA) output;

[0038] use Approximate the objective function y(n), as shown in formula (3):

[0039]

[0040] in,

[0041] e(n): residual;

[0042] y(n): objective function. In formula (3), the objective function y(n) is the power amplifier input data x(n);

[0043] Solve the optimization problem in (3) and obtain the PA inverse model coefficient matrix.

[0044] Preferably, in step 3, the power method is used to solve the matrix S T The maximum eigenvalue of S is shown in formula (4):

[0045] (4); among them,

[0046] u0: Iteration start vector, belongs to space R n ;

[0047] u k : K-th step iteration intermediate vector;

[0048] η k-1 : The k-1th step iterates the intermediate vector to calculate y k-1 ;

[0049] y k-1 : The k-1th step iterates the intermediate vector, used to calculate u k ;

[0050] β k : is the calculation result of the kth step of the power method;

[0051] λ max : Matrix S TThe largest eigenvalue of S, when the power method converges: λ max =β k ;

[0052] S T S: Matrix S T Multiply by matrix S, matrix S T is the transpose of the matrix S;

[0053] After the iteration of formula (4) converges, β k For S T The largest eigenvalue of S, i.e., λ max =β k ;

[0054] Use the Gail circle method to estimate the matrix S T The upper bound of the maximum eigenvalue of S is shown in formula (5):

[0055]

[0056] in,

[0057] a ii : Matrix S T S diagonal elements, row i, column i;

[0058] a ij : Matrix S T S element, i row, j column;

[0059] λ i : Matrix S T The i-th eigenvalue of S;

[0060] Matrix S T The upper bound of the maximum eigenvalue of S is shown in formula (6):

[0061]

[0062] Among them, the symbol max(·) is the maximum value operation; Matrix S T S is the upper bound of the largest eigenvalue.

[0063] Preferably, in step 4, the specific contents are as follows:

[0064] The regularization parameter based on the power method is shown in formula (7):

[0065]

[0066] in,

[0067] μ: regularization parameter;

[0068] r: adjustment parameter;

[0069] The regularization parameter based on the Gale circle is shown in formula (8):

[0070]

[0071] Preferably, in step 5, the specific contents are as follows:

[0072] Formula (3) is approximately equal to formula (9):

[0073]

[0074] in, Objective function matrix, the elements in the matrix are y(n) in formula (3);

[0075] S T S+μI satisfies the positive definite symmetry condition. Using the conjugate gradient method, we solve formula (9) and obtain the coefficient matrix of the PA inverse model;

[0076]

[0077] in,

[0078] x (0) : Conjugate gradient method to initialize variables, belonging to space R N ;

[0079] r (0) : Conjugate gradient method initialization variables, r (0) = b-Ax (0) ;

[0080] p (0) :Conjugate gradient method initialization variables, r (0) =p (0) ;

[0081] A: intermediate variable of conjugate gradient method;

[0082] b: intermediate variable of conjugate gradient method;

[0083] I: unit variable;

[0084] α k : Conjugate gradient method k-th iteration intermediate variable;

[0085] r (k) : Conjugate gradient method k-th iteration intermediate variable;

[0086] β k : Conjugate gradient method k-th iteration intermediate variable;

[0087] p (k) : Conjugate gradient method k-th iteration intermediate variable;

[0088] W (k) : The inverse model coefficient matrix of the power amplifier (PA) obtained by iterative calculation in the kth step;

[0089] The backward inverse model calculated in formula (10) is used to replace the forward inverse model to achieve digital predistortion of the power amplifier.

[0090] Beneficial technical effects brought by the present invention:

[0091] 1. The present invention introduces a regularization parameter μ when solving the model coefficient matrix W, and on this basis proposes a method for solving the model coefficient matrix based on conjugate gradient, which reduces the amount of calculation compared with the existing technology.

[0092] 2. The present invention proposes two fast and effective methods for calculating the regularization parameter μ, a regularization parameter calculation method based on the power method and a regularization parameter calculation method based on the Gale circle. The above regularization parameter calculation method can set the regularization parameter in a reasonable range, and in the process of solving the model coefficient matrix W, the model accuracy can be guaranteed while avoiding the calculation error caused by an excessively large condition number. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 Indirect learning structure diagram for power amplifier predistortion;

[0094] Figure 2 is a flow chart of a digital predistortion method based on conjugate gradient;

[0095] Figure 3 This is a measured effect diagram of the present invention;

[0096] Figure 3 (a) is the output spectrum of the power amplifier without using DPD. In this case, the parameters M=2 and P=4 in the MP model. Figure 3 (b) is the output spectrum after using the Gale circle for maximum upper bound estimation and conjugate gradient correction;

[0097] 4 is a diagram showing the actual measurement effect of the present invention;

[0098] Figure 4 (a) is the output spectrum of the power amplifier without using DPD. In this case, the parameters M=17 and P=4 in the MP model. Figure 4 (b) in the figure is the output spectrum after using the Gay circle for maximum upper bound estimation and conjugate gradient correction. DETAILED DESCRIPTION

[0099] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0100] A digital predistortion method for a signal generator based on conjugate gradient, the process is as follows Figure 2As shown, the following steps are included:

[0101] Step 1: Select a PA model; currently common PA models include but are not limited to the MP model, GMP model, Volterra model, etc. Taking the MP model as an example, the MP model output is expressed as shown in formula (1):

[0102]

[0103] in,

[0104] x(n): amplifier input data;

[0105] y(n): power amplifier output data;

[0106] P: Maximum nonlinear order of the model;

[0107] M: model memory depth;

[0108] W mp :MP model parameters;

[0109] p: model nonlinear order index variable;

[0110] m: Model memory depth index variable.

[0111] Step 2: Solve the system matrix S according to the selected PA inverse model;

[0112] Using the MP model, find the PA inverse model (post-inverse), as shown in formula (2):

[0113]

[0114] in,

[0115] S: inverse model sensitivity matrix after power amplification;

[0116] W: inverse model coefficient matrix after power amplification;

[0117] W 00 ,W 01 ,W 02 …: elements in matrix W;

[0118] Y: observation data matrix;

[0119] Elements in the observation data matrix;

[0120] and All are the output data of the inverse model after power amplifier;

[0121] Input data of the inverse model after power amplifier

[0122] z0(n): inverse model input data after power amplification,

[0123] G: gain of the power amplifier;

[0124] z(n): power amplifier (PA) output;

[0125] use Approximate the objective function y(n), as shown in formula (3):

[0126]

[0127] in,

[0128] e(n): residual;

[0129] y(n): objective function. In formula (3), the objective function y(n) is the power amplifier input data x(n);

[0130] Solve the optimization problem in (3) and obtain the PA inverse model coefficient matrix.

[0131] Step 3: Solve the matrix S based on the power method T The maximum eigenvalue of S; Estimate the matrix S based on the Gail circle method T The upper bound of the maximum eigenvalue of S;

[0132] Solving the matrix S T The largest eigenvalue of S. Matrix S T S has a semi-positive symmetric property. The second step is to solve or estimate the matrix S. T The maximum eigenvalue of S. Common methods for solving the maximum eigenvalue of a matrix include but are not limited to the power method, Rayleigh quotient iteration method, etc. In this patent, the power method is used to solve the matrix S T The maximum eigenvalue of S. In addition, the Gale circle can be used to estimate the matrix S T The upper bound of the largest eigenvalue of S. Using the power method, the matrix S T The maximum eigenvalue of S is shown in formula (4):

[0133]

[0134] in,

[0135] u0: Iteration start vector, belongs to space R n ;

[0136] u k : The k-th step iteration intermediate vector;

[0137] η k-1 : The k-1th step iterates the intermediate vector to calculate y k-1 ;

[0138] y k-1 : The k-1th step iterates the intermediate vector, used to calculate u k ;

[0139] β k : is the calculation result of the kth step of the power method;

[0140] λ max : Matrix S T The largest eigenvalue of S, when the power method converges: λ max =β k ;

[0141] S T S: Matrix S T Multiply by matrix S, matrix S T is the transpose of the matrix S;

[0142] After the iteration of formula (4) converges, β k For S T The largest eigenvalue of S, i.e., λ max =β k ;

[0143] Use the Gail circle method to estimate the matrix S T The upper bound of the maximum eigenvalue of S is shown in formula (5):

[0144]

[0145] in,

[0146] a ii : Matrix S T S diagonal elements, row i, column i;

[0147] a ij : Matrix S T S element, i row, j column;

[0148] λ i : Matrix S T The i-th eigenvalue of S;

[0149] Matrix S T The upper bound of the maximum eigenvalue of S is shown in formula (6):

[0150]

[0151] Among them, the symbol max(·) is the maximum value operation; Matrix S T S is the upper bound of the maximum eigenvalue. Step 4: Determine the regularization parameter μ based on the power method and the Gale circle method;

[0152] The specific contents are as follows:

[0153] The regularization parameter based on the power method is shown in formula (7):

[0154]

[0155] The regularization parameter based on the Gale circle is shown in formula (8):

[0156]

[0157] Step 5: Use the regularization parameter and use the conjugate gradient method to solve the PA inverse model coefficient matrix.

[0158] The specific contents are as follows:

[0159] Formula (3) is approximately equal to formula (9):

[0160]

[0161] in,

[0162] Objective function matrix, the elements in the matrix are y(n) in formula (3);

[0163] S T S+μI satisfies the positive definite symmetry condition. Using the conjugate gradient method, we solve formula (9) and obtain the coefficient matrix of the PA inverse model;

[0164]

[0165] in,

[0166] x (0) : Conjugate gradient method to initialize variables, belonging to space R N ;

[0167] r (0) : Conjugate gradient method initialization variables, r (0) = b-Ax (0) ;

[0168] p (0) :Conjugate gradient method initialization variables, r (0) =p (0) ;

[0169] A: intermediate variable of conjugate gradient method;

[0170] b: intermediate variable of conjugate gradient method;

[0171] I: unit variable;

[0172] α k : Conjugate gradient method k-th iteration intermediate variable;

[0173] r (k) : Conjugate gradient method k-th iteration intermediate variable;

[0174] β k : Conjugate gradient method k-th iteration intermediate variable;

[0175] p (k) : Conjugate gradient method k-th iteration intermediate variable;

[0176] W (k) : The inverse model coefficient matrix of the power amplifier (PA) obtained by iterative calculation in the kth step;

[0177] The backward inverse model calculated in formula (10) is used to replace the forward inverse model to achieve digital predistortion of the power amplifier.

[0178] Figure 1 This is an indirect learning structure diagram of the power amplifier pre-distortion. The actual measured effect of the patent of this invention is as follows Figure 3 , Figure 4 shown.

[0179] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A signal generator digital predistortion method based on conjugate gradient, characterized in that: The steps include: Step 1: Select PA model; Step 2: Solve the system matrix S according to the selected PA inverse model; Step 3: Solve the matrix S based on the power method T The maximum eigenvalue λ of S max ; Estimate the matrix S based on the Gail circle method T Upper bound of the maximum eigenvalue of S Step 4: Determine the regularization parameter μ according to the maximum eigenvalue; Step 5: Solve the PA inverse model coefficient matrix based on the regularization parameter and using the conjugate gradient method.

2. The signal generator digital predistortion method based on conjugate gradient according to claim 1, characterized in that: In step 1, the PA model includes the MP model, the GMP model, and the Volterra model; the output of the MP model is expressed as shown in formula (1): (1)； in, x(n): amplifier input data; y(n): power amplifier output data; P: Maximum nonlinear order of the model; M: model memory depth; W mp :MP model parameters; p: model nonlinear order index variable; m: Model memory depth index variable.

3. The signal generator digital predistortion method based on conjugate gradient according to claim 1, characterized in that: In step 2, the MP model is used to find the PA inverse model, as shown in formula (2): in, S: inverse model sensitivity matrix after power amplification; W: inverse model coefficient matrix after power amplification; W 00 ,W 01 ,W 02 …: elements in matrix W; Y: observation data matrix; Elements in the observation data matrix; and All are the output data of the inverse model after power amplifier; Inverse model input data after power amplifier; z0(n): inverse model input data after power amplification, G: gain of the power amplifier; z(n): amplifier output; use Approximate the objective function y(n), as shown in formula (3): in, e(n): residual; y(n): objective function. In formula (3), the objective function y(n) is the power amplifier input data x(n); Solve the optimization problem in (3) and obtain the PA inverse model coefficient matrix.

4. The signal generator digital predistortion method based on conjugate gradient according to claim 3, characterized in that: In step 3, the power method is used to solve the matrix S T The maximum eigenvalue of S is shown in formula (4): in, u0: Iteration start vector, belongs to space R n ; u k : The k-th step iteration intermediate vector; η k-1 : The k-1th step iterates the intermediate vector to calculate y k-1 ; y k-1 : The k-1th step iterates the intermediate vector to calculate u k ; β k : is the calculation result of the kth step of the power method; λ max : Matrix S T The largest eigenvalue of S, when the power method converges: λ max =β k ; S T S: Matrix S T Multiply by matrix S, matrix S T is the transpose of the matrix S; After the iteration of formula (4) converges, β k For S T The largest eigenvalue of S, i.e., λ max =β k ; Use the Gail circle method to estimate the matrix S T The upper bound of the maximum eigenvalue of S is shown in formula (5): in, a ii : Matrix S T S diagonal elements, row i, column i; a ij : Matrix S T S element, i row, j column; λ i : Matrix S T The i-th eigenvalue of S; Matrix S T The upper bound of the maximum eigenvalue of S is shown in formula (6): Among them, the symbol max(·) is the maximum value operation; Matrix S T S is the upper bound of the largest eigenvalue.

5. The signal generator digital predistortion method based on conjugate gradient according to claim 3, characterized in that: In step 4, the specific contents are as follows: The regularization parameter based on the power method is shown in formula (7): in, μ: regularization parameter; r: adjustment parameter; The regularization parameter based on the Gale circle is shown in formula (8):

6. The signal generator digital predistortion method based on conjugate gradient according to claim 3, characterized in that: In step 5, the specific contents are as follows: Formula (3) is approximately equal to formula (9): in, Objective function matrix, the elements in the matrix are y(n) in formula (3); S T S+μI satisfies the positive definite symmetry condition. Using the conjugate gradient method, we solve formula (9) and obtain the coefficient matrix of the PA inverse model; in, x (0) : Conjugate gradient method to initialize variables, belonging to space R N ; r (0) : Conjugate gradient method initialization variables, r (0) = b-Ax (0) ; p (0) :Conjugate gradient method initialization variables, r (0) =p (0) ; A: intermediate variable of conjugate gradient method; b: intermediate variable of conjugate gradient method; I: unit variable; α k : Conjugate gradient method k-th iteration intermediate variable; r (k) : Conjugate gradient method k-th iteration intermediate variable; β k : Conjugate gradient method k-th iteration intermediate variable; p (k) : Conjugate gradient method k-th iteration intermediate variable; W (k) : The inverse model coefficient matrix of the power amplifier (PA) obtained by iterative calculation in the kth step; The backward inverse model calculated in formula (10) is used to replace the forward inverse model to achieve digital predistortion of the power amplifier.

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