A Bandwidth-Limited Digital Predistortion Solving Method with High Numerical Stability

Abstract

The present invention belongs to the field of communication technologies, specifically: a method for solving band-limited digital predistortion with high numerical stability. The technical problem to be solved by the present invention is that the existing band-limited predistortion has a numerical instability problem when solving the model. The coefficient solving method based on truncated singular value decomposition proposed by the present invention improves the numerical stability, enables the band-limited predistortion to have a better linearization effect, and at the same time has a lower complexity.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and specifically relates to a method for improving the numerical stability of band-limited digital predistortion. Background Art

[0002] In the next-generation wireless communication system 5G, a wider bandwidth is required in higher frequency bands to meet the need for high-rate data transmission. As an essential core component in a wireless communication system, a radio frequency power amplifier (RF Power Amplifier PA) has certain non-linearity. To make the output meet the transmission requirements, the power amplifier needs to operate in the saturation region, and at this time, serious non-linear characteristic distortions will occur. This distortion includes two parts: one is in-band distortion, which affects the quality of the transmitted signal; the other is out-of-band spectrum regeneration of the signal, and the regenerated spectrum will affect adjacent channels. Due to its advantages such as high model accuracy, low cost, and good stability, digital predistortion (DPD) is the most promising linearization method in current communication systems. The principle of digital predistortion technology is: place a predistorter with characteristics opposite to those of the power amplifier at the front end of the power amplifier. The signal first passes through the predistorter and then through the power amplifier. Because the characteristics of the predistorter are opposite to those of the power amplifier, the predistorter can compensate for the non-linear characteristics of the power amplifier, so that the output signal of the final power amplifier has a linear relationship with the original input signal, as Figure 1 shown.

[0003] To achieve full-band linearization of the PA output, it is often necessary to obtain full-band information of the output. Due to the expansion of the output spectrum of the PA, the spectrum bandwidth of the output signal is often 3 to 5 times that of the input signal bandwidth. In the case of a narrowband input signal, existing ADCs can meet the requirements of the feedback loop sampling rate, and traditional digital predistortion can work properly. As the input signal bandwidth increases, for example, for a 500 MHz input signal, the bandwidth of the output signal can expand to between 1.5 GHz and 2.5 GHz. It is too costly for existing ADCs to support such a high sampling rate to capture the full-band information of the PA output.

[0004] To reduce the requirement for the feedback loop ADC sampling rate in digital predistortion, by adding a band-pass filter before feedback channel sampling to limit the feedback signal sampling bandwidth, Liu et al. utilized the limited feedback bandwidth to achieve full-band linearization of the power amplifier output, and its structure is as Figure 2As shown. By restricting the sampling bandwidth of the output signal, the requirement for the ADC sampling rate is reduced. However, since a digital filter needs to be inserted into the model, the condition number of the matrix increases significantly, causing numerical instability problems, especially when the non-linear order and memory depth are large. This leads to the PA model coefficients obtained by solving deviating from the accurate values, thereby affecting the linearization performance. To improve numerical stability, Su uses an adaptive iterative method to solve the PA model, alleviating the ill-conditioning problem during the model solving process. However, this method requires multiple iterations to solve the model coefficients, resulting in a high complexity.

[0005] The present invention proposes a new method for solving the band-limited predistortion model, which overcomes the numerical instability problem of the band-limited digital predistortion method caused by the introduction of the filter, and at the same time reduces the complexity during the model solving process. Summary of the Invention

[0006] In order to solve the numerical instability problem that occurs during the process of solving the band-limited model coefficients, the present invention proposes a method for solving the band-limited predistortion model based on truncated singular value decomposition (TSVD).

[0007] The specific steps are as follows:

[0008] Step 1: Obtain the input signal x(n) of the power amplifier and the output signal y BF (n) of the power amplifier after band-pass filtering.

[0009] Take the baseband signal before digital-to-analog conversion as the input signal of the power amplifier;

[0010] After the input signal of the power amplifier undergoes digital-to-analog conversion, it is processed through the transmit channel and then input into the power amplifier as the input signal. For the signal amplified by the power amplifier, a part of it passes through analog band-pass filtering, down-conversion, and sampling in the predistortion feedback channel, and then passes through a digital low-pass filter (this step is an optional step) to obtain the output signal of the power amplifier.

[0011] Step 2: Perform synchronization processing and normalization processing on the input signal of the power amplifier and the output signal of the power amplifier after band-pass filtering.

[0012] Use the cross-correlation method to perform synchronization processing on the input signal of the power amplifier and the output signal of the power amplifier after band-pass filtering, and obtain the input signal of the power amplifier and the output signal of the power amplifier after band-pass filtering after synchronization processing;

[0013] The power amplifier input signal after synchronization processing and the power amplifier output signal after band - pass filtering are respectively normalized using the maximum amplitude value of each signal, obtaining the normalized power amplifier input signal and the power amplifier output signal after band - pass filtering.

[0014] Step 3: Model the power amplifier using the power amplifier input signal and the power amplifier output signal after band - pass filtering. The specific steps are as follows:

[0015] (1) Express the function of the band - pass filter or the cascaded system of the band - pass filter and the low - pass digital filter using the equivalent matrix F, where F = [f(0); f(1); f(2);...; f(N - 1)];

[0016]

[0017] where, [h0, h1, h2,...h L-1 is the frequency response after the band - pass filter or the cascaded system of the band - pass filter and the low - pass digital filter.

[0018] Model the power amplifier using the input signal x(n) and the power amplifier output y BF (n) after passing through the band - pass filter by using a polynomial - like model. The matrix form of the model expression can be represented as

[0019] FY BF =(FX)W (2)

[0020] where the matrix X is a matrix composed of polynomial - like basis functions of the power amplifier input signal x(n);

[0021] (2) Solve the above matrix equation using the truncated singular value decomposition method to obtain the power amplifier model parameter W. The truncation parameter p value is determined by the L - curve method. The specific steps include:

[0022] 1) Let Z=(FX) H (FX), and perform singular value decomposition on the matrix;

[0023] Decompose the matrix Z into Z = UΣV H , where (·) H represents the conjugate transpose. The matrices U and V are unitary orthogonal matrices, satisfying UU H =I, VV H =I, and Σ m×m is the singular value matrix, in the form as follows:

[0024]

[0025] where the diagonal elements are all real numbers and satisfy σ0 > σ1 >... > σm-1 . In general, the more ill-conditioned the matrix Z is, the larger the value of i is, and the smaller σ is. i The closer it is to 0, the closer it is to 0.

[0026] 2) Determine the cutoff parameter p value by L curve method;

[0027] In the method based on truncated singular value decomposition, the truncation parameter determines the accuracy and stability of the model. The larger the value, the higher the accuracy of the model but the worse the numerical stability. The smaller the value, the higher the stability of the model but the loss of accuracy. In the matrix ∑, t singular values ​​are truncated, t∈[1,m], W t is the solution of the model when the corresponding singular values ​​are different, expressed as lg||W t || 2 is the vertical axis, lg||FXW t -FY BF || 2 As the horizontal axis, draw the corresponding curve, such as Figure 3 The t value corresponding to the point where the curvature of the curve is maximum is the truncation parameter p selected in the truncated singular value decomposition method.

[0028] Let η = 2lg||W t ||,ρ=2lg||FXW t -FY BF ||, the curvature k of the L curve is calculated by formula (4):

[0029]

[0030] Among them, ρ' and η' are first-order derivatives, and ρ", η" are second-order derivatives.

[0031] 3) Discard the smaller singular values ​​in the ill-conditioned matrix and solve the power amplifier model parameter W;

[0032] Cut off the first p large singular values ​​in the singular value matrix Σ, set the remaining smaller singular values ​​to 0, and cut off the first p columns in the corresponding matrix U, and the matrix V H Intercept the first p rows to form a new matrix Z new :

[0033]

[0034] Calculate the amplifier model coefficients:

[0035]

[0036] Step 4: Use the power amplifier model coefficients obtained in step 3 to estimate the full-band output signal y of the power amplifier. esti (n);

[0037] Substitute the power amplifier input signal after normalization into the power amplifier model solved by the above method to obtain an estimated value y of the full-band output signal of the power amplifier without band-pass filtering processing. esti (n):

[0038] Y esti = XW (7)

[0039] Step Five: Calculate the pre-distorter coefficients using the power amplifier input signal and the estimated value of the full-band output signal of the power amplifier.

[0040] Based on the estimated value y esti (n) of the full-band power amplifier output signal, construct a pre-distortion model based on polynomial classes, and then calculate the pre-distorter coefficients W using the least squares method. pd :

[0041]

[0042] where Y * esti is a matrix composed of polynomial class basis functions of y esti (n), and the matrix X * is the matrix composed of the power amplifier input signals:

[0043] X * = [x(0), …, x(N - 1)] T (9)

[0044] The advantages of the present invention are as follows:

[0045] 1) Compared with traditional methods, it can improve numerical stability and reduce the complexity of model solution.

[0046] 2) The optimal value of the truncation parameter of the TSVD method is obtained by the L-curve method, which can better balance the relationship between the accuracy and stability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The present invention will be further described below in conjunction with the drawings and embodiments.

[0048] Figure 1 is the schematic diagram of pre-distortion implementation.

[0049] Figure 2 is the block diagram of the improved band-limited digital pre-distortion method proposed by Liu.

[0050] Figure 3 is the L-curve method diagram of the present invention for solving the optimal truncation parameter.

[0051] Figure 4This is the algorithm implementation flowchart for improving the numerical stability in the method of band-limited digital predistortion of the present invention. Detailed implementation manners

[0052] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0053] The present invention is a method for improving the numerical stability of band-limited digital predistortion. Compared with the traditional band-limited method, it improves the linearization performance and has a lower complexity.

[0054] As Figure 4 shown, the specific steps are as follows:

[0055] Step 1: Obtain the input signal x(n) of the power amplifier and the output signal y BF (n) of the power amplifier after band-pass filtering.

[0056] Take the baseband signal before digital-to-analog conversion as the input signal of the power amplifier;

[0057] After the input signal of the power amplifier undergoes digital-to-analog conversion, it is processed through the transmitting channel and then input into the power amplifier as the input signal. For the signal amplified by the power amplifier, a part of it passes through analog band-pass filtering, down-conversion and sampling in the predistortion feedback channel, and then passes through a digital low-pass filter (this step is an optional step) to obtain the output signal of the power amplifier.

[0058] Step 2: Perform synchronization processing and normalization processing on the input signal of the power amplifier and the output signal of the power amplifier after band-pass filtering.

[0059] Use the cross-correlation method to perform synchronization processing on the input signal of the power amplifier and the output signal of the power amplifier after band-pass filtering to obtain the input signal of the power amplifier after synchronization processing and the output signal of the power amplifier after band-pass filtering;

[0060] Perform normalization processing on the input signal of the power amplifier after synchronization processing and the output signal of the power amplifier after band-pass filtering respectively with the maximum amplitude value of each signal to obtain the input signal of the power amplifier after normalization processing and the output signal of the power amplifier after band-pass filtering.

[0061] Step 3: Model the power amplifier through the input signal of the power amplifier and the output signal of the power amplifier after band-pass filtering. Take the memory polynomial model as an example, but it is not limited to the scope of the patent. The specific steps are as follows:

[0062] (1) Based on the normalized input signal of the power amplifier and the band-pass filtered output signal of the power amplifier, use the memory polynomial model to model the power amplifier, and obtain the relationship expression between the normalized input signal x(n) of the power amplifier after normalization and the normalized band-pass filtered output signal y BF (n):

[0063]

[0064] where K and Q are the non-linear order and memory depth of the model respectively. Replace the filtering operation L{} with the equivalent matrix F:

[0065] F = [f(0); f(1); f(2); …; f(N - 1)];

[0066]

[0067] where, [h0, h1, h2, … h L-1 is the frequency response of the band-pass filter or the cascaded system of the band-pass filter and the low-pass digital filter.

[0068] The matrix X is the matrix composed of the basis functions of the power amplifier model:

[0069]

[0070] The matrix form of expression (1) can be expressed as:

[0071] FY BF = (FX)W (4)

[0072] (2) Solve the above matrix equation by the truncated singular value decomposition method to obtain the power amplifier model parameter W, and the truncation parameter p value is determined by the L-curve method. The specific steps include:

[0073] 1) Let Z = (FX) H (FX), and perform singular value decomposition on the matrix;

[0074] Decompose the matrix Z into Z = UΣV H , where (·) H denotes the conjugate transpose, the matrices U and V are unitary orthogonal matrices, satisfying UU H = I, VV H = I, Σ m×m is the singular value matrix, and its form is as follows:

[0075]

[0076] where the diagonal elements are all real numbers and satisfy σ0 > σ1 > … > σ m-1. In general, the more ill-conditioned the matrix Z is, the larger the value of i is, and the smaller σ is. i The closer it is to 0, the closer it is to 0.

[0077] 2) Determine the cutoff parameter p value by L curve method;

[0078] In the method based on truncated singular value decomposition, the truncation parameter determines the accuracy and stability of the model. The larger the value, the higher the accuracy of the model but the worse the numerical stability. The smaller the value, the higher the stability of the model but the loss of accuracy. In the matrix ∑, t singular values ​​are truncated, t∈[1,m], W t is the solution of the model when the corresponding singular values ​​are different, expressed as lg||W t || 2 is the vertical axis, lg||FXW t -FY BF || 2 As the horizontal axis, draw the corresponding curve, such as Figure 3 The t value corresponding to the point where the curvature of the curve is maximum is the truncation parameter p selected in the truncated singular value decomposition method.

[0079] Let η = 2lg||W t ||,ρ=2lg||FXW t -FY BF ||, the curvature k of the L curve is calculated by formula (6):

[0080]

[0081] Among them, ρ' and η' are first-order derivatives, and ρ", η" are second-order derivatives.

[0082] 3) Discard the smaller singular values ​​in the ill-conditioned matrix and solve the power amplifier model parameter W;

[0083] Cut off the first p large singular values ​​in the singular value matrix Σ, set the remaining smaller singular values ​​to 0, and cut off the first p columns in the corresponding matrix U, and the matrix V H Intercept the first p rows to form a new matrix Z new :

[0084]

[0085] Calculate the amplifier model coefficients:

[0086]

[0087] Step 4: Use the power amplifier model coefficients obtained in step 3 to estimate the full-band output signal y of the power amplifier. esti (n):

[0088] Substitute the power amplifier input signal after normalization into the power amplifier model solved by the above method to obtain the estimated value y of the full-band power amplifier output signal without band-pass filtering processing esti (n):

[0089] Y esti = XW (9)

[0090] Step Five: Calculate the pre-distorter coefficients by using the power amplifier input signal and the estimated value of the power amplifier full-band output signal

[0091] Based on the estimated value y esti (n) construct a pre-distortion model based on the memory polynomial, and then use the least squares method to calculate the pre-distorter coefficients W pd :

[0092]

[0093] where Y * esti is a matrix composed of the memory polynomial basis functions of y esti (n), and the matrix X * is the matrix composed of the power amplifier input signals:

[0094]

[0095] The present invention is verified by the following tests. The test environment includes: R&S signal source SMW200A, class AB power amplifier of model "ZHL-16W-43-S+", R&S FSW43 spectrum analyzer, and N9030A PXA signal analyzer. A 100M band-pass filter is placed at the power amplifier output to limit the output signal bandwidth, and at the same time, a 100M narrow-band digital filter further processes the collected low-speed digital signals. It can be seen from Table 1 that when the structure proposed by Liu uses the least squares method to solve the model, as the memory depth increases, the linearization performance gradually deteriorates and the numerical stability is poor. In Table 2, when the non-linear order K of the memory polynomial model is 6 and the memory depth M is 4, both the adaptive method and the truncated singular value decomposition method can improve the numerical stability of the band-limited pre-distortion to a certain extent, and thus improve the linearization effect. Compared with the adaptive method, the truncated singular value decomposition method proposed by the present invention has better numerical stability, thus obtaining better linearization performance and lower complexity at the same time.

[0096] The present invention discloses a method for improving the numerical stability of band-limited digital predistortion. The present invention has conducted multiple experiments, and the tests on most current power amplifiers are successful. Compared with traditional band-limited digital predistortion, the method of the present invention can achieve better linearization effects and has lower complexity.

[0097] Table 1 Linearization performance at different memory depths when using the least squares method

[0098]

[0099] Table 2 Linearization performance and complexity of different methods for improving numerical stability

[0100]

Claims

1. A method for solving a band-limited digital pre-distortion, which can be used to improve the numerical stability of the band-limited digital pre-distortion method, is characterized by: Obtain the input signal x(n) of the power amplifier and the output signal y of the power amplifier after band-pass filtering. BF (n), where the input signal of the power amplifier is a baseband signal, and the output signal of the power amplifier after band-pass filtering is obtained by amplifying the input signal of the power amplifier by a radio frequency power amplifier, and then through analog band-pass filtering, down-conversion operation, digital sampling, and digital low-pass filtering. The digital low-pass filtering can be optionally applied according to the situation. Performing synchronization and normalization processing on the power amplifier input signal and the power amplifier output signal after bandpass filtering to obtain a normalized power amplifier input signal and a bandpass filtered power amplifier output signal; Based on the power amplifier input signal after synchronous processing and the power amplifier output signal after band-pass filtering, a power amplifier model based on polynomial class is used to model the power amplifier, obtaining the matrix form of the relationship expression between the power amplifier input signal x(n) after synchronous processing and the power amplifier output signal y BF (n) after synchronous processing and passing through band-pass filtering, and the matrix equation is solved by the truncated singular value decomposition method to obtain the power amplifier model parameter W, where the truncation parameter p value is determined by the L-curve method; Substituting the normalized power amplifier input signal into the power amplifier model calculated by the above method, an estimated value of the full-band power amplifier output signal without bandpass filtering can be obtained; The normalized power amplifier input signal and the estimated value of the full-band power amplifier output signal are used as known information to calculate the parameters of the digital predistorter.

2. The method for solving band-limited digital predistortion according to claim 1, characterized in that, The step of obtaining the input signal and the output signal of the power amplifier comprises: Using the baseband signal before digital-to-analog conversion as the input signal of the power amplifier; After the digital-to-analog conversion, the input signal of the power amplifier is processed by the transmitting channel and input into the power amplifier as the input signal. A part of the signal amplified by the power amplifier is coupled into the pre-distortion feedback channel through coupling, and then the output signal of the power amplifier is obtained after analog bandpass filtering, down-conversion, sampling and digital filtering. The digital filtering processing can be applied according to the situation.

3. The method for solving band-limited digital pre-distortion according to claim 1, characterized in that The step of performing synchronization processing and normalization processing on the power amplifier input signal and the power amplifier output signal after bandpass filtering to obtain the normalized power amplifier input signal and the power amplifier output signal after bandpass filtering comprises: The power amplifier input signal and the power amplifier output signal after bandpass filtering are respectively normalized by using the maximum amplitude value of each signal to obtain the normalized power amplifier input signal and the power amplifier output signal after bandpass filtering; The normalized power amplifier input signal and the normalized power amplifier output signal after bandpass filtering are synchronously processed by using a cross-correlation method to obtain a synchronously processed power amplifier input signal and a bandpass filtered power amplifier output signal.

4. The method for solving band-limited digital pre-distortion according to claim 1, characterized in that, Based on the synchronized power amplifier input signal and the band-pass filtered power amplifier output signal, a power amplifier model based on a polynomial class is used to model the power amplifier, obtaining the matrix form of the relationship expression between the synchronized power amplifier input signal x(n) and the synchronized and band-pass filtered power amplifier output signal y BF (n), and the matrix equation is solved by the truncated singular value decomposition method to obtain the power amplifier model parameter W, where the truncation parameter p value is determined by the L-curve method. The specific steps are as follows: (1) The effect of the bandpass filter or the cascade system of the bandpass filter and the low-pass digital filter is expressed by the equivalent matrix F: Among them, [h0, h1, h2, … h L-1 is the frequency response of a band-pass filter or a cascaded system of a band-pass filter and a low-pass digital filter; Model the power amplifier using the input signal x(n) and the power amplifier output y BF (n) passing through the band - pass filter, and the matrix form of the model expression can be represented as FY BF = (FX)W (2) Wherein, the matrix X is a matrix composed of polynomial-like basis functions of the power amplifier input signal x(n); (2) Solving the above matrix equation by truncated singular value decomposition method to obtain the power amplifier model parameter W, wherein the truncated parameter p value is determined by L curve method. The specific steps include: Step 1. Let \(Z=(FX)\) H (FX), and perform singular value decomposition on the matrix; Decompose matrix Z into Z = UΣV H , where (·) H denotes conjugate transpose, matrices U and V are unitary orthogonal matrices, satisfying UU H = I, VV H = I, and Σ m×m is a singular value matrix, in the form as follows: where the diagonal elements are all real numbers and satisfy σ0 > σ1 > … > σ m-1； Step 2: Determine the cutoff parameter p value by L curve method; Intercept t singular values in the matrix ∑, where t ∈ (1, m), and W t is the solution of the model when the corresponding singular values are different. Using lg||W t || 2 as the vertical axis and lg||FXW t -FY BF || 2 as the horizontal axis, draw the corresponding curve; the t value corresponding to the point with the maximum curvature of the curve is the truncation parameter p selected in the truncated singular value decomposition method; If we let η = 2lg||W t ||, ρ = 2lg||FXW t -FY BF ||, the curvature k of the L-curve can be calculated by formula (4): Among them, ρ' and η' are first-order derivatives, ρ", η" are second-order derivatives; Step 3: discard the smaller singular values ​​in the ill-conditioned matrix and solve the power amplifier model parameter W; Extract the top p largest singular values from the singular value matrix Σ, set the remaining smaller singular values to 0, extract the first p columns from the corresponding matrix U, and for matrix V H Extract the first p rows to form a new matrix Z new : The power amplifier model coefficient W can be calculated by the following formula: 。 5. The method for solving the band-limited digital pre-distortion according to claim 1, characterized in that, Substitute the input signal of the power amplifier after synchronous processing into the power amplifier model solved by the above method to obtain the estimated value Y of the full-band output signal of the power amplifier esti : Y esti = XW (7).

6. The method for solving the band-limited digital pre-distortion according to claim 1, wherein Using the normalized power amplifier input signal and the estimated value of the full-band power amplifier output signal as known information, the digital predistorter parameters are calculated: Based on the estimated value Y of the output signal of the full-band power amplifier esti Construct a model based on the polynomial class and calculate the pre-distortion coefficient using the least squares method.

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