RLS algorithm-based power amplifier DPD coefficient estimation method

Abstract

The application discloses a power amplifier DPD coefficient estimation method based on an RLS algorithm, obtains an input signal of an input power amplifier (PA) and a feedback output signal after gain adjustment; performs time delay alignment processing on the input signal and the feedback signal; based on a memory polynomial model and a memory polynomial model of cross terms, constructs a nonlinear input matrix and a coefficient matrix of the PA; the recursive least square (RLS) algorithm based on Givens rotation of complex QR decomposition is adopted, a CORDIC algorithm is used to solve a rotation angle and a modulus value, the nonlinear input matrix and the coefficient matrix are iteratively calculated, and DPD coefficients are estimated. The memory polynomial model or the memory polynomial model of cross terms is adopted, so that the PA model is clearer, and data processing is facilitated; the RLS algorithm adopts the RLS expression based on Givens rotation of complex QR decomposition, direct solution of a matrix inverse is not needed, a large number of division operations are avoided, and the problem that the original RLS algorithm is not conducive to engineering implementation in DPD coefficient estimation is solved.

Description

Technical Field

[0001] This invention relates to the field of wireless communication, and more specifically, to a method for estimating the DPD coefficients of a power amplifier based on the RLS algorithm. Background Technology

[0002] In the transmit link of a power amplifier (PA), when the input signal power approaches the PA's saturation region, its nonlinear characteristics cause distortions such as intermodulation distortion, gain compression, and phase shift. These distortions not only reduce transmit efficiency but also induce adjacent channel interference (ACLR degradation) and increase the bit error rate (BER), severely restricting the linearity and reliability of the communication system. Digital pre-distortion (DPD) effectively counteracts the PA's nonlinear effects by introducing distortion compensation opposite to the PA's nonlinear characteristics before the signal input, resulting in a linear amplification characteristic throughout the transmit link. However, the effectiveness of DPD is highly dependent on accurate modeling and coefficient estimation of the PA's nonlinear characteristics. Since the PA's nonlinear response typically exhibits high-order, memory effects, and frequency dependence, its dynamic characteristics drift with temperature, aging, and load changes. Therefore, it is necessary to acquire the PA's output signal through a real-time feedback link, combine it with the transmit link signal to construct an adaptive algorithm, and dynamically update the DPD coefficients to achieve real-time compensation. The accuracy and convergence speed of the DPD coefficient estimation directly determine the system's linearization effect.

[0003] Current DPD coefficient estimation mainly relies on algorithms such as LS (Least Squares), LMS (Least Mean Squares), and RLS (Recursive Least Squares). The LS algorithm solves for the coefficients by constructing a normal equation for the input-output signals, but it requires calculating the pseudo-inverse of the matrix and is sensitive to noise, making it difficult to meet real-time requirements in engineering implementation. The LMS algorithm uses gradient descent to iteratively update the coefficients, avoiding matrix inversion, but its convergence speed is significantly affected by the step size parameter: too large a step size leads to steady-state errors, while too small a step size results in slow convergence; furthermore, its fixed step size strategy is prone to coefficient oscillations or even divergence when signal power changes abruptly. Although the RLS algorithm improves the convergence speed by introducing a forgetting factor, thus improving the convergence speed compared to LMS, its iterative formula involves a large number of division operations and high-dimensional matrix operations. Furthermore, the coefficients of different powers in the higher-order nonlinear model of PA can vary by tens to hundreds of times or even more. When RLS is applied directly, small-scale coefficients are easily overwhelmed by large values, resulting in a loss of accuracy. Therefore, the original RLS algorithm is not conducive to the engineering implementation of DPD coefficient estimation, and few people use the original RLS algorithm to calculate DPD coefficients. Summary of the Invention

[0004] The present invention aims to overcome at least one defect in the prior art and provide a power amplifier DPD coefficient estimation method based on the RLS algorithm to solve the problem that the original RLS algorithm is not conducive to engineering implementation in DPD coefficient estimation.

[0005] The technical solution adopted in this invention is a method for estimating the DPD coefficients of a power amplifier based on the RLS algorithm. S1. Obtain the input signal of the input power amplifier PA and the feedback output signal after gain adjustment; S2. Perform time delay alignment processing on the input signal and the feedback signal; S3. Based on the memory polynomial model or the memory polynomial model of the cross term, construct the nonlinear input matrix and coefficient matrix of PA; S4. The recursive least squares (RLS) algorithm based on Givens rotation and complex QR decomposition is adopted. The CORDIC algorithm is used to solve for the rotation angle and magnitude. The nonlinear input matrix and coefficient matrix are iteratively calculated to estimate the DPD coefficients.

[0006] The input signal first introduces distortion opposite to the nonlinear characteristics of the PA, then passes through the power amplifier PA to obtain the amplified input signal, i.e., the output signal. This distortion is then introduced by the PA... The distortion with opposite nonlinear characteristics makes the final gain linear. Time delay alignment of the input and feedback signals results in a synchronized sequence of input and output signals, which serves as the input to the memory model. If the input and output signals are not aligned, the input and output signals used to construct the matrix will not be causally related at the same time, leading to errors in the constructed memory model and failing to accurately characterize the nonlinear characteristics of the power amplifier (PA). The digital predistortion memory model is calculated using the same method as the PA model, consisting of a memory polynomial model and a cross-term memory polynomial model, differing only in input and output. Therefore, the nonlinear input matrix and coefficient matrix of the PA are constructed based on the memory model. The RLS expression based on Givens rotation of complex QR decomposition yields the same result as the original RLS expression. The reason for using the RLS expression based on Givens rotation of complex QR decomposition instead of the original RLS is to avoid directly solving for the matrix inverse, reduce the large number of divisions in the calculation, improve computational efficiency, and make it more suitable for engineering applications.

[0007] To improve the accuracy of the results, the memory polynomial model or cross-term memory polynomial model in step S3 is specifically as follows:

[0008] For output signal, For gain, The number of elements in the column vector of the input matrix. ; The column vectors of the input matrix. is the column vector of the coefficient matrix.

[0009] The higher the power of an element in the input matrix, the smaller the corresponding coefficient value in the coefficient matrix. Multiplying elements of different powers with their corresponding coefficients results in a final order of magnitude that remains essentially unchanged. The cross-term memory polynomial model differs from the memory polynomial model only in its input and output. Compared to the memory polynomial model, the cross-term memory polynomial considers cross terms, resulting in higher accuracy, although its expression is more complex.

[0010] To avoid directly solving for the matrix inverse, the iterative formula of the RLS algorithm based on Givens rotation and complex QR decomposition is as follows:

[0011] , , , , , , , , , It can be a vector or a matrix; The initial value of i is 1, the step size is 1, and the final value is m; The initial value of i is m, the step value is -1, and the final value is 1; This is the output of the j-th RLS iteration, and it contains only one value. The nonlinear model data for the j-th iteration of the feedback signal after adjusting the gain through PA consists of m×1 values. Indicates transpose. The coefficients obtained in the (j-1)th iteration There are m×1 values; This represents the error between the expected result and the output of RLS, and is a single value. The transmitted signal before the PA is used to adjust the gain; the desired result is represented by one value. Let be the square root covariance matrix obtained in the j-th iteration, which is an m×m matrix, and its initial value is set to the identity matrix; The forgetting factor ranges from 0 to 1; Let be the square root covariance matrix obtained in the (j-1)th iteration, which is an m×m matrix; Given an iterative vector of m×1 values, initially set to all zeros, the final result is... Given an m×m upper triangular matrix, back substitution yields the m×1 values ​​of the DPD coefficients. ; Let J be the iteration vector for the (j-1)th iteration. The j-th nonlinear model data for the feedback signal after adjusting the gain through PA. The conjugate value, To obtain the conjugate operation, To adjust the gain of the transmitted signal before the PA The conjugate value, Let i be a vector that starts at i, increments by 1, and ends at m. The square root covariance matrix obtained in the j-th iteration. The real part of the value in the i-th row and i-th column, where real is the real part. The square root covariance matrix obtained in the j-th iteration. The value in the i-th row and i-th column, This is a conjugate value derived from the data input of a nonlinear model. It is the reciprocal of the modulus related to ri and xi. For angle cosine value, For angle The sine value and angle The product of complex values, The square root covariance matrix obtained in the j-th iteration. The values ​​from the i-th row and i-th column to the m-th column, , for Iteration vector The i-th value, , for The iterative vector, To adjust the gain of the transmitted signal before the PA The conjugate value, , The j-th nonlinear model data for the feedback signal after adjusting the gain through PA. The values ​​of the conjugate values ​​are the i-th to m-th numbers. , The square root covariance matrix obtained in the j-th iteration. The value in the i-th row and k-th column, Let k be the kth coefficient with k as the variable.

[0012] Through a relatively complex mathematical derivation, an RLS expression based on complex QR decomposition and Givens rotation was obtained, which is consistent with the original RLS expression. This algorithm does not require directly solving for the matrix inverse, but the mathematical expression is much more complex than the original RLS expression.

[0013] To further improve computational efficiency, the rotation parameters in the Givens rotation are calculated using the CORDIC algorithm, specifically as follows: Solving angles using the vector pattern of the CORDIC algorithm:

[0014] and For angle, To find the angle function, find the arctangent in each of the four quadrants; It is a conjugate value derived from the input data of a nonlinear model. Indicates modulo, The square root covariance matrix obtained in the j-th iteration. The real part of the value in the i-th row and i-th column. The imaginary unit is equal to , For angle cosine value, For angle The sine value and angle The product of complex values; Solve using the rotation mode of the CORDIC algorithm or by looking up cosine and sine tables. and .

[0015] By using the above method, a large number of division operations can be avoided, making it more suitable for engineering applications.

[0016] An engineering application method for power amplifier DPD coefficient estimation based on the RLS algorithm is provided. This method applies the aforementioned RLS-based power amplifier DPD coefficient estimation method to the engineering field, including a three-point function part and a complex QR decomposition part. The three-point function part includes: solving for angles... Solving for the modulus of the nonlinear input value Solution angle and solve and The complex QR decomposition part includes an initialization part and an iteration part.

[0017] This solves the problem that the original RLS algorithm is not suitable for engineering implementation in DPD coefficient estimation.

[0018] The solution angle Specifically: Set the sign-limited bit width of the trigonometric function amplitude to [value]. The signed phase-limited bit width is ,by Bit width scaling quantization is to... Quantize to a number not exceeding the specified signed bit width to obtain a new value. The calculation method is as follows: S1, find Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by this maximum value. ; S2. Calculate the signed bit width occupied by the maximum value. With signed limited bit width bit width difference ; S3, if This indicates that the input data value does not exceed the specified signed bit width. ;like This indicates that the input data value exceeds the specified signed bit width, so the scaled value is adjusted accordingly. for ; S4, to Using the Cordic algorithm to calculate the angle, the signed bit width can be obtained as follows: of Fixed-point phase value .

[0019] The modulus of the input value being solved for nonlinearity Specifically: First solve Then perform the square root operation, setting the signed bit width limit of the square root input used in the project to [value missing]. The signed, limited bit width of the output is ,by bit width Scaling quantization is performed, and the calculation method is as follows: T1. Calculate the nonlinear input value. Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by the maximum value. ; T2. Calculate the signed bit width occupied by the maximum value. With signed limited bit width bit width difference ; T3, if This indicates that the number of input data does not exceed the signed bit width limit. ;like This indicates that the number of input data exceeds the signed bit width limit, so the scaled data is... for ; T4, Yes The modulus is calculated using the Cordic algorithm, resulting in a signed bit width of... of Fixed-point modulus .

[0020] The solution angle Specifically: right Scaling , ,by bit width Perform scaling and quantization to obtain new values. The calculation method is as follows: K1, find Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by this maximum value. ; K2, find and bit width difference ; K3, if This indicates that the input data value does not exceed the specified signed bit width. ;like This indicates that the input data value exceeds the specified signed bit width, so the scaled value is adjusted accordingly. for ; K4, to Using the Cordic algorithm to calculate the angle, the signed bit width can be obtained as follows: of Fixed-point phase value .

[0021] The solution and Specifically: Will and Fixed-point value and Substitute respectively and In the text, the Cordic algorithm is used to obtain the signed bit width as... locating and Solve First, multiply the sine term by the exponent term, then shift the value. Rounding to the nearest integer, keeping the result consistent with the original value. Same bit width, .

[0022] The initialization part specifically includes: set up initial value It is an m×m square matrix with all 1s on its diagonal. initial value A row vector consisting of all zeros and whose length is the number of coefficients. Fixed-point conversion to signed bit width is of ,in , Maximum signed bit width value , ; The iterative part specifically includes: Will The maximum signed bit width in the data is set to , Fixed-point conversion to signed bit width is of ,in , Fixed-point conversion to signed bit width is Bit ,in ; Solve and At that time, shift the summation result. Bit; Solving First, solve Then shift again; solve. At that time, first displacement Bit, For signed Bits; solve for and Then, the DPD coefficients with m×1 values ​​are obtained. .

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows: This paper presents matrix and non-matrix expressions for common memory polynomial and cross-term memory polynomial models for power amplifiers (PAs), making PA models clearer and facilitating data processing. It also addresses the practical limitations of the original RLS algorithm in DPD coefficient estimation by using a Givens rotation-based RLS expression with complex QR decomposition, consistent with the original RLS expression. This eliminates the need for direct matrix inverse calculations and avoids numerous division operations. A specific implementation method for corresponding fixed-point transformation in engineering is also provided, further facilitating practical applications. Attached Figure Description

[0024] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the invention. To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0025] Figure 1 This is a mind map illustrating the time delay estimation and compensation of a power amplifier DPD coefficient estimation method based on the RLS algorithm according to the present invention.

[0026] Figure 2 This is an architecture diagram of the digital predistortion data relationship of a power amplifier DPD coefficient estimation method based on the RLS algorithm according to the present invention.

[0027] Figure 3 This is a comparison diagram of the feedback signal of the transmitted power amplifier (PA) and the reverse-derived PA signal of the power amplifier DPD coefficient estimation method based on the RLS algorithm of the present invention.

[0028] Figure 4 This is a comparison result of the original transmitted signal (yellow) without PA and the feedback signal (blue) after PA in a power amplifier DPD coefficient estimation method based on RLS algorithm of the present invention.

[0029] Figure 5 This is a comparison diagram of the original transmitted signal (yellow) without PA and the signal (blue) after DPD and PA processing, based on the RLS algorithm for estimating the power amplifier DPD coefficients according to the present invention.

[0030] Figure 6 This is an ACPR result diagram of the original transmitted signal without PA, based on the power amplifier DPD coefficient estimation method of the RLS algorithm of the present invention.

[0031] Figure 7 This is an ACPR result diagram of the feedback signal after PA in a power amplifier DPD coefficient estimation method based on RLS algorithm according to the present invention.

[0032] Figure 8 This is an ACPR result diagram of the PA signal after DPD, based on the power amplifier DPD coefficient estimation method of the RLS algorithm of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0035] Example 1 Generally, a power amplifier (PA) model is based on the input signal, gain, and coefficient matrix of the PA, yielding the output signal. Digital predistortion, on the other hand, is based on the input, output signal, and gain of the PA, yielding the predistortion coefficient matrix. Using the PA's input and the output signal (after gain and time delay alignment), the predistortion coefficient matrix is ​​calculated. The PA input is then predistorted by passing it through a predistorted amplifier ("power amplifier"), and finally through the actual PA to recover the distortion-free signal.

[0036] like Figure 1-2 As shown, the input signal x first passes through a DPD (Digital Predistortion) amplifier, then through a power amplifier PA, resulting in an output signal y via the PA link. The DPD coefficients are estimated on the output signal y after removing the gain G0, and then input to the DPD amplifier to obtain the increased input signal x·G0. The DPD amplifier and PA are inverse nonlinear modules; their combination ensures that the final output of the input x only shows a change in gain G0 without other nonlinear components. The signal power after passing through the DPD amplifier and PA changes linearly.

[0037] The memory model of digital predistortion is calculated in the same way as the PA model. It is divided into the memory polynomial model and the cross-term memory polynomial model. The only difference between the two models is the input and output. The coefficient estimation algorithm is a variation of the original expression of RLS - the RLS expression based on the Givens rotation of complex QR decomposition.

[0038] Memory model of power amplifier The most common model for power amplifiers is the memory model, which generally includes the memory polynomial model and the cross-term memory polynomial model. Let the memory depth be... The polynomial series is Based on the non-linear correspondence, each input... The signal at each point is The corresponding output signal for one point is The power gain is Then the amplitude scaling factor is .

[0039] The input matrix of the memory polynomial is:

[0040] The coefficient matrix of the memorized polynomial is:

[0041] Input matrix sum coefficient matrix Multiply the elements at corresponding positions, sum them over all elements, and then multiply by the gain. , get output . The matrices are respectively and Extract the data column by column, multiply the corresponding elements, and sum them to obtain:

[0042] in for A column vector of elements. Also for A column vector of n elements. In the input Only after receiving this signal can we obtain it. The result corresponding to each input. If the index is updated by +1, then The index is also updated by +1. The higher the power of the element in the input matrix, the smaller the corresponding coefficient value in the coefficient matrix. After multiplying the elements of different powers with their corresponding coefficients, the final order of magnitude remains basically unchanged.

[0043] The cross-term memory polynomial model, compared to the memory model, considers cross terms and has higher accuracy, but its expression is more complex. The input matrix is:

[0044] The coefficient matrix of the cross-memory polynomial is:

[0045] Input matrix sum coefficient matrix Multiply the elements at corresponding positions, sum them over all elements, and then multiply by the gain. , get output .

[0046] Each matrix and Extract the data column by column, multiply the corresponding elements, and sum them to obtain:

[0047] in for A column vector of elements. Also for A column vector of n elements. In the input Only after receiving this signal can we obtain it. The result corresponding to each input. If the index is updated by +1, then The index is also updated by +1. The higher the power of the element in the input matrix, the smaller the corresponding coefficient value in the coefficient matrix. After multiplying the elements of different powers with their corresponding coefficients, the final order of magnitude remains basically unchanged.

[0048] The DPD coefficient estimation algorithm is the RLS algorithm: RLS primitive expression Let the DPD coefficients to be estimated be... There are m non-linear data. Given an n x m matrix, where n is the total signal length and also the number of iterations, and each row contains... For a nonlinear model with 1×m values ​​corresponding to the index of the row, the expression for the original RLS algorithm is as follows:

[0049] in, , , , , , , For vectors, The gain vector obtained in the j-th iteration has m×1 values; Let be the inverse matrix of the autocorrelation matrix obtained in the (j-1)th iteration; To perform the conjugate operation; The forgetting factor, ranging from 0 to 1, has a significant impact on the algorithm, and its effective memory length is... , The larger the value, the greater the effective memory length, which allows for full utilization of all available data. Generally, a value close to 1 is chosen. The nonlinear model data for the j-th iteration of the feedback signal after over-PA adjustment is used to adjust the gain. There are m×1 values. Gain adjustment aims to make the transmitted and feedback signals consistent with the reference power, eliminating signal amplitude scaling. Impact on the RLS algorithm; Indicates transpose; This is the output of the j-th RLS iteration, and it contains only one value. The coefficients obtained in the (j-1)th iteration There are m×1 values; This represents the error between the expected result and the output of RLS, and is a single value. The transmitted signal before the PA is used to adjust the gain, which is the desired result and has one value. The coefficient obtained in the j-th iteration There are m×1 values, and the initial values ​​can be set to all 0; Let be the inverse matrix of the autocorrelation matrix obtained in the j-th iteration, and its initial value can be set as an m×m identity matrix.

[0050] RLS Expression Based on Givens Rotation of Complex QR Decomposition Through complex mathematical derivation, an RLS expression based on complex QR decomposition and Givens rotation was obtained, which is consistent with the original RLS expression. It does not require directly solving for the matrix inverse, but the mathematical expression is more complex than the original RLS expression. The RLS expression based on complex QR decomposition and Givens rotation is as follows:

[0051] in, , , , , , , , , , It can be a vector or a matrix; The initial value of i is 1, the step size is 1, and the final value is m; The initial value of i is m, the step value is -1, and the final value is 1; This is the output of the j-th RLS iteration, containing only one value. The nonlinear model data for the j-th iteration of the feedback signal after adjusting the gain through PA consists of m×1 values. Indicates transpose. The coefficients obtained in the (j-1)th iteration There are m×1 values; This represents the error between the expected result and the output of RLS, and is a single value. The transmitted signal before the PA is used to adjust the gain; the desired result is represented by one value. Let be the square root covariance matrix obtained in the j-th iteration, which is an m×m matrix, and its initial value is set to the identity matrix; The forgetting factor ranges from 0 to 1; Let be the square root covariance matrix obtained in the (j-1)th iteration, which is an m×m matrix; Given an iterative vector of m×1 values, initially set to all zeros, the final result is... Given an m×m upper triangular matrix, back substitution yields the m×1 values ​​of the DPD coefficients. ; Let J be the iteration vector obtained in the (j-1)th iteration. The j-th nonlinear model data for the feedback signal after adjusting the gain through PA. The conjugate value, To obtain the conjugate operation, To adjust the gain of the transmitted signal before the PA The conjugate value, Let i be a vector that starts at i, increments by 1, and ends at m. The square root covariance matrix obtained in the j-th iteration. The real part of the value in the i-th row and i-th column, where real is the real part. The square root covariance matrix obtained in the j-th iteration. The value in the i-th row and i-th column, This is a conjugate value derived from the data input of a nonlinear model. It is the reciprocal of the modulus related to ri and xi. For angle cosine value, For angle The sine value and angle The product of complex values, The square root covariance matrix obtained in the j-th iteration. The values ​​from the i-th row and i-th column to the m-th column, , for Iteration vector The i-th value, , for The iterative vector, To adjust the gain of the transmitted signal before the PA The conjugate value, , The j-th nonlinear model data for the feedback signal after adjusting the gain through PA. The values ​​of the conjugate values ​​are the i-th to m-th numbers. , The square root covariance matrix obtained in the j-th iteration. The value in the i-th row and k-th column, Let k be the value of the kth coefficient with k as the variable.

[0052]

[0053] in, The imaginary unit is equal to , To find the angle function, i.e., to find the arctangent in each of the four quadrants, the angle... , And modulus The cosine and sine can be obtained using the vector mode of the Cordic algorithm. Alternatively, they can be obtained using the rotation mode of the Cordic algorithm, or by looking up the cosine and sine tables based on the angle values, thus avoiding division operations.

[0054] Example 2 This embodiment provides an engineering application method for a power amplifier DPD coefficient estimation method based on the RLS algorithm. It applies the power amplifier DPD coefficient estimation method based on the RLS algorithm from Embodiment 1 to engineering applications, including: a three-point function part and a complex QR decomposition part. The three-point function part includes: solving for the angle... Solving for the modulus of the nonlinear input value Solution angle and solve and The complex QR decomposition part includes the initialization part and the iteration part.

[0055] Solution angle

[0056] For a value derived from a nonlinear input, its amplitude and phase bit width may exceed the sign-limited bit width of trigonometric functions typically used in engineering. And signed phase-limited bit width , to be Bit width is scaled and quantized, that is, the bit width is scaled and quantized. Quantize to a number no greater than the specified signed bit width, reducing larger values ​​while keeping smaller values ​​unchanged, to obtain a new value. The calculation method is as follows: S1, first find The larger of the absolute values ​​of the real and imaginary parts is determined, and the signed bit width occupied by this larger value is determined. ; S2. Calculate the signed bit width occupied by the maximum value. With signed limited bit width bit width difference ; S3, if This indicates that the input data value does not exceed the specified signed bit width and no scaling is required. ;like This indicates that the input data value exceeds the specified signed bit width, so the scaled value is adjusted accordingly. for , shift Bit, To round to the nearest integer; S4, to Using the Cordic algorithm to calculate the angle, the signed bit width can be obtained as follows: of Fixed-point phase value .

[0057] Solving for the modulus of the nonlinear input value

[0058] beg Need to seek first When performing the square root operation, the signed bit width limit for square root input may exceed the limit typically used in engineering. and the signed limited bit width of the output ,generally , to be bit width Scaling and quantization are performed to make the output value after square root... No more than the limit bit width The calculation method is as follows: T1, first find The larger of the absolute values ​​of the real and imaginary parts is determined, and the signed bit width occupied by this larger value is determined. ; T2. Calculate the signed bit width occupied by the maximum value. With signed limited bit width bit width difference ; T3, if This indicates that the input data value does not exceed the signed bit width limit and no scaling processing is required. ;like This indicates that the number of input data exceeds the signed bit width limit, so the scaled data is... for This is for rounding to the nearest integer.

[0059] T4, Yes Using the Cordic algorithm to calculate the modulus, the signed bit width can be obtained as follows: of Fixed-point modulus .

[0060] Solution angle

[0061] Due to the solution Time It has been scaled, so it also needs to be scaled. If you scale it, then you will have , ,by bit width Scaling and quantization are performed, along with solving the problem. The method is the same, and a new value is obtained. ,right By finding the angle, the signed bit width can be calculated. of Fixed-point phase value The calculation method is as follows: K1, find Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by this maximum value. ; K2, find and bit width difference ; K3, if This indicates that the input data value does not exceed the specified signed bit width. ;like This indicates that the input data value exceeds the specified signed bit width, so the scaled value is adjusted accordingly. for ; K4, to Using the Cordic algorithm to calculate the angle, the signed bit width can be obtained as follows: of Fixed-point phase value .

[0062] beg and

[0063] Directly obtain and Fixed-point value and Substitute respectively and In this case, the Cordic algorithm can be used to obtain the signed bit width. locating and The solution It is necessary to first multiply the sine term by the exponent term and then shift the value. Rounding to the nearest integer, keeping the result consistent with the original value. The same bit width, i.e. .

[0064] Complex QR decomposition Initialization section initial value It can be set as an m×m square matrix with all 1s on the diagonal. initial value It can be set as a row vector with all zeros equal to the length of the number of coefficients. Fixed-point conversion to signed bit width is of ,in , To not exceed the maximum signed bit width value of division used in general engineering. , .

[0065] Iterative Part Iteration and At that time, the accuracy of its value has a decisive impact on the entire fixed-point calculation, and for The data in the file is assumed to have a maximum signed bit width of 1. . Fixed-point conversion to signed bit width is of ,in , Fixed-point conversion to signed bit width is Bit ,in .

[0066] Solve and hour, , , and Solve each solution individually, then sum them up, and finally shift the summation result. Bit. (Pair) The solution needs to consider iteration and subsequent steps. Solve this problem first. Then shift Bits. But for The solution requires shifting. Bit, For signed Bit.

[0067] Seeking and Then, the DPD coefficients of m×1 values ​​can be obtained. .

[0068] Example 3 This embodiment provides a practical application of a power amplifier DPD coefficient estimation method based on the RLS algorithm, which is used to demonstrate the application results of the power amplifier DPD coefficient estimation method based on the RLS algorithm in Embodiment 1.

[0069] The signal was transmitted using actual equipment, digital predistortion was performed, and then compared with the signal before and after power amplification. The selected PA model was a cross-term memory polynomial model with a memory depth of 3, a polynomial series of 5, and the coefficient estimation algorithm was the RLS algorithm with a forgetting factor of 0.999999.

[0070] 1. Estimation effect of measured coefficients The DPD coefficients of the 3 × 5 = 15 memory polynomials are shown in the table below:

[0071] The PA coefficients of the 3 × 13 = 39 cross-term memory polynomials are shown in the table below:

[0072] like Figure 3 As shown, the feedback signal of the transmitted PA and the PA signal with inverse coefficients are compared. The sampling rate is 122.88MHz, and the time interval of one sample point is 1 / 122.88 = 8.138ns. Under the conditions of phase alignment, delay, and gain, the estimation effect of PA coefficients is verified. The overlap is high in the frequency band within a range of about ±6MHz, and the overlap in the time domain is also high. The normalized MSE (Mean Square Error) of the time domain IQ is found to be about 0.26% and 0.27%, respectively.

[0073] Comparison of measured power spectra: like Figure 4-5 As shown, comparing the power spectrum of the original transmitted signal without PA and the signal fed back by PA, and comparing the power spectrum of the original transmitted signal without PA and the PA signal after DPD, the 99% power bandwidth is about 4.5M. However, the ACPR (Adjacent Channel Power Ratio) of the feedback signal after PA is worse than that of the signal after PA after DPD.

[0074] 3. Actual ACPR comparison results: like Figure 6-8 As shown, the measured ACPR results of the original emission signal without PA, the measured ACPR results of the feedback signal after PA, and the measured ACPR results of the signal after DPD and PA were obtained. It can be seen that the ACPR of the original emission signal without PA is -50.92 dBc and -53.14 dBc, respectively; the ACPR of the feedback signal after PA is -25.69 dBc and -29.31 dBc, respectively; and the ACPR of the signal after DPD and PA is -46.77 dBc and -47.39 dBc, respectively. The ACPR of the feedback signal after PA deteriorated by 25.23 dB and 23.83 dB, while the ACPR of the signal after DPD and PA recovered by 21.08 dB and 18.08 dB, respectively. These ACPRs are only 4.15 dB and 5.75 dB different from the original emission signal, and can accurately approximate the original signal.

[0075] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to specific implementation methods. Clearly, many modifications and variations can be made based on the content of this specification. The selection and detailed description of these embodiments are intended to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize it. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for estimating the DPD coefficients of a power amplifier based on the RLS algorithm, characterized in that, S1. Obtain the input signal of the input power amplifier PA and the feedback output signal after gain adjustment; S2. Perform time delay alignment processing on the input signal and the feedback signal; S3. Based on the memory polynomial model or the memory polynomial model of the cross term, construct the nonlinear input matrix and coefficient matrix of PA; S4. The recursive least squares (RLS) algorithm based on Givens rotation and complex QR decomposition is adopted. The CORDIC algorithm is used to solve for the rotation angle and magnitude. The nonlinear input matrix and coefficient matrix are iteratively calculated to estimate the DPD coefficients.

2. The power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 1, characterized in that, The memory polynomial model or cross-term memory polynomial model in step S3 is specifically as follows: For output signal, For gain, The number of elements in the column vector of the input matrix. ; The column vectors of the input matrix. is the column vector of the coefficient matrix.

3. The power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 1, characterized in that, The iterative formula for the Givens rotation-based RLS algorithm based on complex QR decomposition is as follows: , , , , , , , , , It can be a vector or a matrix; The initial value of i is 1, the step size is 1, and the final value is m; The initial value of i is m, the step value is -1, and the final value is 1; This is the output of the j-th RLS iteration, and it contains only one value. The nonlinear model data for the j-th iteration of the feedback signal after adjusting the gain through PA consists of m×1 values. Indicates transpose. The coefficients obtained in the (j-1)th iteration There are m×1 values; This represents the error between the expected result and the output of RLS, and is a single value. The transmitted signal before the PA is used to adjust the gain; the desired result is represented by one value. Let be the square root covariance matrix obtained in the j-th iteration, which is an m×m matrix, and its initial value is set to the identity matrix; The forgetting factor ranges from 0 to 1; Let be the square root covariance matrix obtained in the (j-1)th iteration, which is an m×m matrix; Given an iterative vector of m×1 values, initially set to all zeros, the final result is... Given an m×m upper triangular matrix, back substitution yields the m×1 values ​​of the DPD coefficients. ; Let J be the iteration vector for the (j-1)th iteration. The j-th nonlinear model data for the feedback signal after adjusting the gain through PA. The conjugate value, To obtain the conjugate operation, To adjust the gain of the transmitted signal before the PA The conjugate value, Let i be a vector that starts at i, increments by 1, and ends at m. The square root covariance matrix obtained in the j-th iteration. The real part of the value in the i-th row and i-th column, where real is the real part. The square root covariance matrix obtained in the j-th iteration. The value in the i-th row and i-th column, This is a conjugate value derived from the data input of a nonlinear model. It is the reciprocal of the modulus related to ri and xi. For angle cosine value, For angle The sine value and angle The product of complex values, The square root covariance matrix obtained in the j-th iteration. The values ​​from the i-th row and i-th column to the m-th column, , for Iteration vector The i-th value, , for The iterative vector, To adjust the gain of the transmitted signal before the PA The conjugate value, , The j-th nonlinear model data for the feedback signal after adjusting the gain through PA. The values ​​of the conjugate values ​​are the i-th to m-th numbers. , The square root covariance matrix obtained in the j-th iteration. The value in the i-th row and k-th column, Let k be the value of the kth coefficient with k as the variable.

4. The power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 3, characterized in that, The rotation parameters in the Givens rotation are calculated using the CORDIC algorithm, specifically: Solving for angles and magnitudes using the vector pattern of the CORDIC algorithm: and For angle, To find the angle function, find the arctangent in each of the four quadrants; It is a conjugate value derived from the input data of a nonlinear model. Indicates modulo, The square root covariance matrix obtained in the j-th iteration. The real part of the value in the i-th row and i-th column. The imaginary unit is equal to , For angle cosine value, For angle The sine value and angle The product of complex values; Solve using the rotation mode of the CORDIC algorithm or by looking up cosine and sine tables. and .

5. An engineering application method for estimating the DPD coefficients of a power amplifier based on the RLS algorithm, characterized in that, This method, used to apply the RLS algorithm-based power amplifier DPD coefficient estimation method of claim 4 to the engineering field, includes a three-point function part and a complex QR decomposition part. The three-point function part includes: solving for angles. Solving for the modulus of the nonlinear input value Solution angle and solve and The complex QR decomposition part includes an initialization part and an iteration part.

6. The engineering application method of the power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 5, characterized in that, The solution angle Specifically: Set the sign-limited bit width of the trigonometric function amplitude to [value]. The signed phase-limited bit width is ,by Bit width scaling quantization is to... Quantize to a number not exceeding the specified signed bit width to obtain a new value. The calculation method is as follows: S1, find Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by this maximum value. ; S2. Calculate the signed bit width occupied by the maximum value. With signed limited bit width bit width difference ; S3, if This indicates that the input data value does not exceed the specified signed bit width. ;like This indicates that the input data value exceeds the specified signed bit width, so the scaled value is adjusted accordingly. for ; S4, to Using the Cordic algorithm to calculate the angle, the signed bit width can be obtained as follows: of Fixed-point phase value .

7. The engineering application method of the power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 6, characterized in that, The modulus of the input value being solved for nonlinearity Specifically: First solve Then perform the square root operation, setting the signed bit width limit of the square root input used in the project to [value missing]. The signed, limited bit width of the output is ,by bit width Scaling quantization is performed, and the calculation method is as follows: T1. Calculate the nonlinear input value. Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by the maximum value. ; T2. Calculate the signed bit width occupied by the maximum value. With signed limited bit width bit width difference ; T3, if This indicates that the number of input data does not exceed the signed bit width limit. ;like This indicates that the number of input data exceeds the signed bit width limit, so the scaled data is... for ; T4, Yes The modulus is calculated using the Cordic algorithm, resulting in a signed bit width of... of Fixed-point modulus .

8. The engineering application method of the power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 7, characterized in that, The solution angle Specifically: right Scaling , ,by bit width Perform scaling and quantization to obtain new values. The calculation method is as follows: K1, find Find the maximum absolute value of the real and imaginary parts, and determine the signed bit width occupied by this maximum value. ; K2, find and bit width difference ; K3, if This indicates that the input data value does not exceed the specified signed bit width. ;like This indicates that the input data value exceeds the specified signed bit width, so the scaled value is adjusted accordingly. for ; K4, to Using the Cordic algorithm to calculate the angle, the signed bit width can be obtained as follows: of Fixed-point phase value .

9. An engineering application method for a power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 8, characterized in that, The solution and Specifically: Will and Fixed-point value and Substitute respectively and In the text, the Cordic algorithm is used to obtain the signed bit width as... locating and Solve First, multiply the sine term by the exponent term, then shift the value. Rounding to the nearest integer, keeping the result consistent with the original value. Same bit width, .

10. An engineering application method for a power amplifier DPD coefficient estimation method based on the RLS algorithm according to claim 5, characterized in that, The initialization part specifically includes: set up initial value It is an m×m square matrix with all 1s on its diagonal. initial value A row vector consisting of all zeros and whose length is the number of coefficients. Fixed-point conversion to signed bit width is of ,in , Maximum signed bit width value , ; The iterative part specifically includes: Will The maximum signed bit width in the data is set to , Fixed-point conversion to signed bit width is of ,in , Fixed-point conversion to signed bit width is Bit ,in ; Solve and At that time, shift the summation result. Bit; Solving First, solve Then shift again; solve. At that time, first displacement Bit, For signed Bits; solve for and Then, the DPD coefficients with m×1 values ​​are obtained. .

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