Power amplifier model and behavior modeling method based on compressed sensing

Abstract

The invention provides a power amplifier model and behavior modeling method based on compressed sensing. The method comprises the steps of setting of system parameters, establishment of a sparse memory polynomial model, construction of a measurement matrix, estimation of a nonlinear coefficient vector and sparseness and the like. According to the method, a sparse memory polynomial model is adopted to construct a relationship between input and output signals of the power amplifier, a corresponding measurement matrix is constructed based on the model, and then a compressed sensing technology and an iterative estimation algorithm are utilized to estimate a non-linear coefficient vector and sparseness with a small number of signals, so that the sparse degree of the power amplifier is estimated. Therefore, an accurate power amplifier behavior modeling result is obtained, and a basis is provided for a subsequent receiving end to detect a received nonlinear signal and restore an original signal.

Description

Technical Field

[0001] The present invention relates to a power amplifier model and a behavioral modeling method, and more particularly to a power amplifier model and a behavioral modeling method based on compressive sensing. Background Art

[0002] A power amplifier (PA) is one of the components in most wireless communication systems, which converts a low-power signal into a high-power signal. However, in an Orthogonal Frequency Division Multiplexing (OFDM) system, due to the high peak-to-average power ratio, the PA will introduce nonlinear distortion, resulting in a decline in signal quality. Behavioral modeling is an important method to describe the nonlinear characteristics of the PA. For the behavioral modeling of the PA, a variety of behavioral models have been proposed, including the Volterra series model based on dynamic bias reduction, the general memory polynomial model, etc. However, these models have problems such as too many parameters and a high complexity of the modeling method.

[0003] In order to reduce the number of parameters of the PA model, some simplified models based on the general memory polynomial have been proposed (see Xianzhe Gu's "Behavioral Modeling of Nonlinear RF Power Amplifiers Considering Memory Effects", "IEEE Transactions on Microwave Theory and Techniques", 2003, the twelfth issue; Jinting Liu's "An Improved Behavioral Modeling and Simulation of Nonlinear Memory Power Amplifiers", "Computer Simulation", 2019, the second issue). These simplified models only consider the nonlinear coefficients at specific delays, and on the basis of ensuring a certain accuracy, greatly reduce the number of parameters that need to be estimated in the model. For these simplified models, the authors of the above articles also proposed corresponding PA behavioral modeling methods, realizing the construction of the PA nonlinear characteristic model, and providing a basis for the subsequent detection and estimation of nonlinear signals.

[0004] Since these simplified models assume that the non - linear coefficients at specific delays are all non - zero, and the corresponding PA behavior modeling methods are only applicable to specific simplified models, this will lead to two deficiencies: First, the existing simplified models are prone to include some non - primary non - linear coefficients, ignoring the non - linear parameters that are more critical for PA model construction at other delays, thus resulting in a decrease in model accuracy and a decline in PA behavior modeling precision; Second, in actual modeling, the existing PA behavior modeling methods have limitations and are only applicable to specific simplified models. When the model is not accurate enough, it is impossible to obtain the accurate non - linear characteristics of the PA. Summary of the Invention

[0005] The object of the present invention is to overcome the above - mentioned deficiencies in the prior art and propose a power amplifier model and behavior modeling method based on compressive sensing.

[0006] The present invention provides a power amplifier model and behavior modeling method based on compressive sensing, including the following steps:

[0007] Step 1: Set the signal length as N, the non - linear order as D, the delay order as Q, the input signal x of the power amplifier, x = [x(0), x(1), …, x(N - 1)] T , and the output signal as y, y = [y(0), y(1), …, y(N - 1)] T , where, a T represents the transpose of vector a;

[0008] Step 2: Model the power amplifier using a sparse memory polynomial model, and construct an N×DQ measurement matrix G based on the input signal x and system parameters;

[0009] Step 3: Use the behavior modeling method based on compressive sensing to estimate the non - linear coefficient vector α and sparsity K of the model.

[0010] Furthermore, the expression of the sparse memory polynomial model in Step 2 is:

[0011]

[0012] where n = 0, 1, …, N - 1, K is the number of non - zero non - linear coefficients in the model, that is, the number of non - zero elements in the non - linear coefficient vector α, and K << D(Q + 1), k ∈ {1, …, K}, represents the coefficient at non - linear order 2d k -1 and delay q k , 1 ≤ d k ≤ D, 0 ≤ q k ≤ Q, y(n) is the nth element in the input signal y, and the expression of the function is:

[0013]

[0014] Among them, x(n - q k ) is the (n - q)-th element in the input signal x; k

[0015] The expression of matrix G is:

[0016]

[0017] Furthermore, the estimated value of the non - linear coefficient vector α in step 3 is calculated by the following formula:

[0018]

[0019] Among them, ‖y - Gα‖ 2 represents the 2 - norm of the vector y - Gα.

[0020] Furthermore, the behavior modeling method based on compressive sensing in step 3 specifically includes the following steps:

[0021] Input: signal length N, measurement matrix G, output signal y = [y(0), y(1), …, y(N - 1)] T , non - linear series number D, delay series number Q;

[0022] Output: final non - linear coefficient vector α and sparsity K estimation results;

[0023] Step 1) Initialization: iteration counter t = 0, maximum iteration number T = N, algorithm termination threshold η, α t = 0;

[0024] Step 2) t = t + 1;

[0025] Step 3) Based on the measurement matrix G and the output signal y, use the orthogonal matching pursuit algorithm to estimate the non - linear coefficient vector α with sparsity K = t t ;

[0026] Step 4) Calculate the non - linear sparse vector estimation error ρ = ‖α t - α t-1 ‖ 2 ;

[0027] Step 5) If t < T or ρ ≥ η, go to Step 2);

[0028] Step 6) Output the final estimation result α t

[0029] ​​Further, the preferred value of the algorithm termination threshold η in Step 1) of Step 3 is 0 - 0.1.

[0030] Further, the preferred value of the algorithm termination threshold η in Step 1) of Step 3 is 0 - 0.01.

[0031] Further, the preferred value of the algorithm termination threshold η in Step 1) of Step 3 is 0 - 0.001.

[0032] The beneficial effects of the present invention are as follows: Aiming at the limitations that the existing PA non - linear feature simplification model is not accurate enough and the existing behavior modeling method is only applicable to specific models, a power amplifier model and behavior modeling method based on compressive sensing are proposed. The proposed model no longer restricts that the non - linear coefficients at specific delays are all non - zero, incorporates the main non - linear coefficients into the model construction, and then, based on the constructed model, uses compressive sensing technology and iterative estimation algorithms to propose a behavior modeling method based on compressive sensing to accurately estimate the non - linear coefficient vector, providing a basis for subsequent detection and estimation of non - linear signals at the receiving end. Examples prove that this method is not only applicable to the proposed model but also to other existing simplified models. Therefore, the application scope of the proposed method is wider than that of the existing methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flowchart of the method of the present invention;

[0034] Figure 2 is a comparison diagram of the data bit error rate obtained by the proposed algorithm using different pilot frequencies. DETAILED DESCRIPTION OF THE INVENTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings and examples of the present invention.

[0037] The present invention is implemented through the following steps: As Figure 1 shown, first, system parameters are set according to actual requirements, including the signal length N, the input signal x = [x(0), x(1),..., x(N - 1)] of the power amplifier T , the output signal is y = [y(0), y(1),..., y(N - 1)] T , the non - linear order is D, the delay order is Q and other parameters. Then, the PA is modeled using a sparse memory polynomial model, and an N×DQ measurement matrix G is constructed based on the system parameters. Finally, compressive sensing technology and the proposed iterative algorithm are used to estimate the non - linear coefficient vector α and the sparsity K. The specific description is as follows:

[0038] The first step: The system parameter setting is specifically as follows:

[0039] The input signal of PA is x = [x(0), x(1), ..., x(N-1)] T , where a T Represents the transpose of vector a. After PA, the output signal is y=[y(0),y(1),…,y(N-1)] T , and assume that the nonlinear series of PA is D and the delay series is Q.

[0040] Step 2: Sparse memory polynomial model building and measurement matrix construction

[0041] The PA is modeled using a memory polynomial model, and the nth element in the PA output signal y is expressed as:

[0042]

[0043] Where n = 0, 1, ..., N-1, K is the number of non-zero nonlinear coefficients in the model, and K < < D(Q+1), k∈{1, ..., K}, Represented in the nonlinear series 2d k -1. Delay q k The coefficient on , 1≤d k ≤D,0≤q k ≤Q, function The expression is:

[0044]

[0045] Among them, x(nq k ) is the nqth k The output signal of PA is written in matrix form as:

[0046] y=Gα

[0047] Among them, the nonlinear coefficient vector α=[α 1,0 ,α 3,0 ,…,α 2D-1,0 ,…,α 1,1 ,α 3,1 ,…,α 2D-1,Q ], the measurement matrix G is constructed by the following formula:

[0048]

[0049] Different from the existing models, the proposed model no longer assumes that the coefficient of α at a specific delay q is not zero, that is, α 1,q ,α 3, q,…,α 2D-1,qIt is no longer mandatory that all are non - zero. Therefore, when actually modeling the behavior, the proposed model can more accurately find the positions of non - zero coefficients in α and accurately estimate the values of non - zero coefficients, thus improving the accuracy of PA behavior modeling.

[0050] Step 3: Use compressive sensing technology and the proposed iterative algorithm to estimate the non - linear coefficient vector α and the sparsity K specifically as follows:

[0051] The number of non - zero elements in the vector α is K, which is much smaller than the vector length D(Q + 1). Therefore, compressive sensing technology can be used to estimate α, and the specific estimation can be carried out through the following formula:

[0052]

[0053] where, ‖y - Gα‖ 2 represents the 2 - norm of the vector y - Gα. Although the estimated value of the non - linear vector α can be obtained by the method of compressive sensing, the sparsity K is unknown. In order to achieve accurate estimation of α, K also needs to be estimated. Therefore, in order to simultaneously achieve accurate estimation of α and K, a behavior modeling method based on compressive sensing is proposed, and the proposed method is as follows:

[0054] Input: Signal length N, measurement matrix G, output signal y = [y(0), y(1), …, y(N - 1)] T , non - linear order is D, delay order is Q;

[0055] Output: Final estimated results of the non - linear coefficient vector α and the sparsity K;

[0056] Step 1) Initialization: Iteration counter t = 0, maximum number of iterations T = N, algorithm termination threshold η, α t = 0;

[0057] Step 2) t = t + 1;

[0058] Step 3) Based on the measurement matrix G and the output signal y, use the orthogonal matching pursuit algorithm to estimate the non - linear coefficient vector α with sparsity K = t t ;

[0059] Step 4) Calculate the non - linear sparse vector estimation error ρ = ‖α t -α t-1 ‖ 2 ;

[0060] Step 5) If t < T or ρ ≥ η, go to Step 2);

[0061] Step 6) Output the final estimated results α t and sparsity K = t.

[0062] The proposed method fully considers the influence of non-zero coefficients and sparsity K in the non-linear coefficient vector α, no longer sets the restriction that the coefficients at specific delays are all non-zero, and while the estimated value of sparsity increases, it tries to preferentially obtain the non-zero coefficients in α that have a greater impact on the signal, thereby improving the accuracy of PA behavior modeling and providing a data basis for subsequent detection and estimation of non-linear signals at the receiving end.

[0063] Example: PA model and behavior modeling simulation experiment based on compressive sensing

[0064] Experiment: In the simulation experiment, an orthogonal frequency division multiplexing system with orthogonal phase shift coding is adopted. To avoid the contingency of test results, the present invention conducts a total of 500 random experiments. In each experiment, the present invention randomly generates a random signal x with a length N = 256. As shown in Table 1, the present invention conducts simulation experiments on two different PAs. For the first PA, the non-linear order D = 2, the delay order Q = 100, and the sparsity K = 8; for the second PA, the non-linear order D = 2, the delay order Q = 88, and the sparsity K = 8. To verify the effectiveness of the method, the present invention conducts the following simulation experiments.

[0065] Table 1: Non-linear parameters of two PAs

[0066]

[0067] Simulation 1: To verify the influence of different behavior models and behavior modeling methods on the PA behavior modeling results, the present invention conducts the following simulation experiments.

[0068] The present invention uses the proposed method to conduct behavior modeling on PA(1) and PA(2), and calculates the normalized mean squared error (NMSE) of the behavior modeling results. The calculation formula is as follows:

[0069]

[0070] Among them, This is the final estimated result of the non - linear coefficient vector α. The present invention compares the proposed method with the method of Gu Xianzhe (for the specific method, see Gu Xianzhe's "Behavioral Modeling of Nonlinear RF Power Amplifiers Considering Memory Effects", "IEEE Transactions on Microwave Theory and Techniques", 2003, the 12th issue). The specific results are shown in Table 2. As shown in Table 2, since PA(1) conforms to not only the proposed model but also the simplified model in the comparative literature, both the proposed method and the comparative method can achieve accurate modeling of PA(1). However, PA(2) does not conform to the simplified model in the comparative literature, so the comparative method cannot obtain accurate estimated results, resulting in an NMSE of 4.53×10 -4 , and the proposed model has a wider scope of application, making PA(2) conform to the proposed model. Therefore, the behavioral modeling method proposed based on the proposed model can accurately estimate the non - linear coefficient vector α of PA(2), and the result error is 0.

[0071] Table 2: Comparison of Behavioral Modeling Results

[0072]

[0073] Simulation 2: To verify the influence of the sparsity K on the performance of the proposed method, the following experiment is carried out.

[0074] For PA(2), the present invention assumes that the sparsity K ranges from 0 to 10, that is, the number of non - zero coefficients in the estimated result of is forced to range from 0 to 10. The compressed sensing technology is used for reconstruction, and the corresponding NMSE values are calculated. The specific results are as Figure 2 shown. It can be seen from Figure 2 that as the sparsity K increases, the NMSE decreases, indicating that the estimation of the non - linear coefficient vector α becomes more and more accurate. When K increases to 8, the NMSE is 0, indicating that the proposed behavioral modeling method has obtained accurate estimated values. At this time, the present invention increases the value of K to 10 again, and the NMSE still remains at 0. Therefore, the proposed method can accurately estimate the values of the non - linear coefficient vector α and the sparsity K.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: it is still possible to modify the specific implementation manners of the present invention or perform equivalent replacements on some technical features; without departing from the spirit of the technical solutions of the present invention, they should all be covered within the scope of the technical solutions claimed by the present invention.

Claims

1. A power amplifier model and behavior modeling method based on compressed sensing, characterized in that: It includes the following steps: Step 1: Set the signal length to N, the nonlinear series to D, the delay series to Q, and the input signal of the power amplifier to x, x = [x(0), x(1), ..., x(N-1)] T , the output signal is y, y=[y(0),y(1),…,y(N-1)] T , where a T represents the transpose of vector a; Step 2: Model the power amplifier using a sparse memory polynomial model, and construct an N×DQ measurement matrix G based on the input signal x and system parameters; Step 3: Use a behavior modeling method based on compressive sensing to estimate the nonlinear coefficient vector α and sparsity K of the model.

2. The power amplifier model and behavior modeling method based on compressed sensing according to claim 1, characterized in that: The specific content of Step 2 is as follows: The expression for modeling the power amplifier using a sparse memory polynomial model is: Where n = 0, 1, ..., N-1, K is the number of non-zero nonlinear coefficients in the model, that is, the number of non-zero coefficients in the nonlinear coefficient vector α, and K < < D(Q+1), k∈{1, ..., K}, Represented in the nonlinear series 2d k -1. Delay q k The coefficient on , 1≤d k ≤D,0≤q k ≤Q, y(n) is the nth element in the input signal y, function The expression is: Among them, x(nq k ) is the nqth k elements; The expression for the measurement matrix G is:

3. The power amplifier model and behavior modeling method based on compressed sensing according to claim 1, characterized in that: The estimated value of the nonlinear coefficient vector α in Step 3 is calculated by the following formula: where, ‖y - Gα‖2 represents the 2-norm of the vector y - Gα.

4. The power amplifier model and behavior modeling method based on compressed sensing according to claim 1, characterized in that: The specific steps of the behavior modeling method based on compressive sensing in Step 3 are as follows: Input: signal length N, measurement matrix G, output signal y = [y(0), y(1), ..., y(N-1)] T , the nonlinear series is D, and the delay series is Q; Output: The estimation results of the final nonlinear coefficient vector α and sparsity K; Step 1) Initialization: iteration counter t = 0, maximum number of iterations T = N, algorithm termination threshold η, α t =0; Step 2) t = t + 1; Step 3) Based on the measurement matrix G and the output signal y, the orthogonal matching pursuit algorithm is used to estimate the nonlinear coefficient vector α with sparsity K = t t ; Step 4) Calculate the nonlinear sparse vector estimation error ρ = ‖α t -α t-1 ‖2; Step 5) If t < T or ρ ≥ η, go to Step 2); Step 6) Output the final estimation result α t .

5. The power amplifier model and behavior modeling method based on compressed sensing according to claim 4, characterized in that: The preferred value of the algorithm termination threshold η in Step 1) of Step 3 is 0 - 0.

1.

6. The power amplifier model and behavior modeling method based on compressed sensing according to claim 5, characterized in that: The preferred value of the algorithm termination threshold η in Step 1) of Step 3 is 0 - 0.

01.

7. The power amplifier model and behavior modeling method based on compressed sensing according to claim 6, characterized in that: The preferred value of the algorithm termination threshold η in Step 1) of Step 3 is 0 - 0.001.

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