Precompensation method and precompensation circuit thereof

Abstract

To provide a pre-compensation method for a pre-compensation circuit coupled to a power amplifier so as to compensate non-linearity of the power amplifier.SOLUTION: A method includes the steps of: performing pre-distortion according to at least one parameter or at least one hyperparameter so as to convert a first input signal received by a pre-compensation circuit into a first pre-distorted output signal; updating the at least one parameter or at least one hyperparameter according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization; and performing predistortion according to the updated at least one parameter or the updated at least one hyperparameter so as to convert a second input signal received by the pre-compensation circuit into a second predistortion output signal.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a predistortion method and a predistortion circuit thereof, and more particularly to a predistortion method and a predistortion circuit thereof that reduces computational complexity or improves accuracy or efficiency. [Background technology]

[0002] Power amplifiers are inherently nonlinear. Nonlinearity reduces bit error rate (BER) and data throughput. To reduce nonlinearity, power amplifiers (PAs) are operated at lower power, resulting in lower efficiency.

[0003] On the other hand, digital predistortion (DPD) is one of the most cost-effective linearization techniques. A digital predistorter (or its algorithm) needs to accurately analyze or model the behavior of the PA for successful deployment of the digital predistorter. As the signal bandwidth becomes wider, PAs with more complex frequency, electrical, and thermal behavior tend to exhibit memory effects. Therefore, more advanced DPD algorithms are needed. The most common algorithms for DPD implementation are Volterra series and its derivatives. However, the large number of coefficients in Volterra series makes it unattractive for practical applications. This is because more coefficients increase the computational load and require more input / output data for statistical confidence of the unknown coefficients. Therefore, there is still room for improvement in DPD. Summary of the Invention [Problem to be solved by the invention]

[0004] The main object of the present invention is to provide a predistortion method and a predistortion circuit so as to reduce the computational complexity or to improve the accuracy or efficiency. [Means for solving the problem]

[0005] An embodiment of the present invention discloses a predistortion method for a predistortion circuit coupled to a power amplifier, comprising the steps of: performing predistortion according to at least one parameter or at least one hyperparameter to convert a first input signal received by the predistortion circuit into a first predistortion output signal; updating the at least one parameter or the at least one hyperparameter according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization; and performing predistortion according to the updated at least one parameter or the updated at least one hyperparameter to convert a second input signal received by the predistortion circuit into a second predistortion output signal.

[0006] An embodiment of the present invention discloses a pre-distortion circuit coupled to a power amplifier, the pre-distortion circuit comprising: a digital pre-distortion actuator configured to perform pre-distortion according to at least one parameter or at least one hyper-parameter to convert a first input signal received by the digital pre-distortion actuator into a first pre-distortion output signal; and a training module configured to update the at least one parameter or the at least one hyper-parameter according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization, wherein the digital pre-distortion actuator performs pre-distortion according to the updated at least one parameter or the updated at least one hyper-parameter to convert a second input signal received by the digital pre-distortion actuator into a second pre-distortion output signal.

[0007] These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings. [Brief description of the drawings]

[0008] [Figure 1] 1 is a schematic diagram of an amplifier circuit according to an embodiment of the present invention; [Diagram 2] FIG. 2 is a schematic diagram of an indirect learning architecture for an amplifier circuit 20 according to an embodiment of the present invention. [Diagram 3] FIG. 2 is a schematic diagram of a recursive indirect learning architecture for an amplifier circuit according to an embodiment of the present invention. [Figure 4] FIG. 1 is a schematic diagram of a regression-type DPD-PA cascade model according to an embodiment of the present invention. [Diagram 5] FIG. 2 is a schematic diagram of the relationship between loss functions, parameters, and hyperparameters according to an embodiment of the present invention. [Figure 6] FIG. 2 is a schematic diagram of Bayesian optimization for one-dimensional problems according to an embodiment of the present invention. [Figure 7] FIG. 2 is a schematic diagram of a portion of a causal graph according to an embodiment of the present invention; [Figure 8] FIG. 2 is a schematic diagram of a portion of grounding data and a causal graph according to an embodiment of the present invention; [Figure 9] FIG. 2 is a schematic diagram of causal variables and sub-data according to an embodiment of the present invention. [Figure 10] FIG. 1 is a schematic diagram of Bayesian optimization, causal Bayesian optimization, and dynamic causal Bayesian optimization. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] 1 is a schematic diagram of an amplifier circuit 10 according to an embodiment of the present invention. The predistortion circuit 120 of the amplifier circuit 10 can accommodate variations in nonlinearity of a power amplifier (PA) 150 of the amplifier circuit 10 that change over time, temperature, and different operating channels, and the predistortion circuit 120 can be considered or function as a digital predistorter.

[0010] Digital pre-distortion (DPD) may correct the nonlinearity of the PA 150 by modifying the complex waveform at the input before the signal enters the digital-to-analog converter (DAC). In another aspect, the nonlinearity of the PA 150 may correct the waveform of the predistortion output signal z(t) of the predistortion circuit 120, so that the cascade / combination of the predistortion circuit 120 and the PA 150 may achieve linearity. As a result, the output signal y(t) of the PA 150 after the predistortion circuit 120 appears to be derived from a highly linear component, and the input signal x(t) may be amplified with a certain gain. As shown by the dashed line in FIG. 1, the predistortion circuit 120 may be considered as the inverse of the PA 150. That is, the predistortion circuit 120 essentially inserts a nonlinear function (e.g., the inverse of the PA 150) between the input signal x(t) and the PA 150 to generate a (linear) output signal y(t). For example, the response function f PA is y(t)=f PA (z(t)), and the response function f DPD is z(t)=f DPD (x(t)), then fDPD=G×f PA -1 and G is essentially constant.

[0011] 2 is a schematic diagram of an indirect learning architecture for an amplifier circuit 20 according to an embodiment of the present invention. The amplifier circuit 20 may include a crest-factor reduction (CFR) 210 for reducing the peak-to-average power ratio (PAPR), a predistortion circuit 220, a DAC 230, an upconverter 240, a PA 250, a downconverter 260, and an analog-to-digital converter (ADC) 270.

[0012] The DPD (function) may be algorithmically defined by software. In an indirect learning architecture, the algorithm may use two identical memory polynomial models for predistortion and training. For example, the predistortion circuit 220 may include a DPD actuator 221 and a training module 222. The DPD actuator 221 is configured to perform predistortion of an input signal x(t) in real time. Since the DPD actuator 221 performs the same / similar calculations for each input signal x(t) at high speed, it is appropriate for the DPD actuator 221 to be implemented by a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or other circuit. The training module 222 updates the parameters or hyperparameters of the DPD actuator 221 based on the observation of the output signal y(t) of the PA 250 (shown by the dashed lines in FIG. 2). Since the training module 222 involves relatively complex calculations, it is appropriate for the training module 222 to be implemented by a digital signal processor (DSP) or other circuit.

[0013] Using an indirect learning architecture to train the predistortion circuit 220 allows the predistortion circuit 220 to be directly configured (i.e., to discover / determine the parameters or hyperparameters of the DPD actuator 221) according to the input signal x(t) and the output signal y(t) of the PA 250. The feedback path of the training module 222 may take y(t) / G as its input and ̂z(t) as its output, where G controls the gain of the PA 250 after linearization. The DPD actuator 221 may be considered as a copy of the feedback path (i.e., a copy of the training module 222), which may take the input signal x(t) as its input and the predistortion output signal z(t) as its output. The ideal is to make y(t)=G×x(t), which makes z(t)=̂z(t) and satisfies e(t)=0 for the error signal e(t) between the predistortion output signal z(t) and the output ̂z(t). The algorithm calculates an error signal e(t) equal to the difference between the predistortion output signal z(t) and the output ^z(t) or the square of the error signal e(t) (i.e., ||e(t)|| 2 ) is minimized.

[0014] Due to the memory effect, the PA 250 becomes a nonlinear system with memory. That is, the output signal y(t) input by the PA 250 (at present / instantaneous time) not only depends on the current input, but is also a function of the previous / past input value. For example, it is y(t)=f PA (z(τ)), where τ∈(-∞,t).

[0015] Regarding memory effect, Fig. 3 is a schematic diagram of a recurrent indirect learning architecture for an amplifier circuit 30 according to an embodiment of the present invention. The structure of the amplifier circuit 30 is basically similar to that of the amplifier circuit 20 (note that the CRF 210, the DAC 230, the up-converter 240, the down-converter 260, and the ADC 270 are not shown). The difference is mainly in the signal transmission.

[0016] Specifically, an input signal x(t) received by a DPD actuator 321 of a predistortion circuit 320 of the amplifier circuit 30 is predistorted by the DPD actuator 321 using parameters and hyperparameters of the DPD actuator 321, thereby outputting a predistorted output signal z(t). The predistorted output signal z(t) is amplified by a PA 350 of the amplifier circuit 30 to provide an output signal y(t) at an output of the PA 350. A training module 322 of the predistortion circuit 320 calculates / trains the parameters and hyperparameters such that the predistortion introduced by the DPD actuator 321 can compensate for the nonlinearity of the PA 350 (i.e., the predistortion is the inverse of the distortion resulting from the nonlinearity of the PA 350). The training module 322 can receive a (digital) signal S4 representing the output signal y(t) from the output of the PA 350. Depending on the difference between the signal S1 and the signal S2 output by the training module 322, the combiner 223 (which may be a subtraction unit / circuit) of the predistortion circuit 320 outputs an error signal S3. The training module 322 observes the error signal S3 and adaptively sets parameters and hyperparameters to minimize the loss function or the error signal S3 (e.g., to zero the error signal S3). The loss function may be a function of the model's output ^y(t) (e.g., the estimate) or a function of the label (e.g., the expectation) corresponding to the output ^y(t). For example, the loss function may be equal to the difference between the output ^y(t) and the label. The label may be a function of the input signal x(t).

[0017] In one embodiment, the signal S1 of the training module 322 may be split, for example, into an output ^z(t) (indicated by a dashed line in FIG. 3) corresponding to the output signal y(t) and an output ^y(t-1) (indicated by a dotted line in FIG. 3) corresponding to the output signal y(t-1). The signal S2 may be split, for example, into a predistortion output signal z(t) (indicated by another solid line in FIG. 3) and an output signal y(t-1) (indicated by another dotted line in FIG. 3). The combiner 223 may output an error signal e(t) (indicated by another solid line in FIG. 3 ) of the error signal S3 that satisfies e(t)=z(t)-^z(t) in response to the signals ^z(t) and z(t), and may output a signal e(t-1) (indicated by another dotted line in FIG. 3 ) of the error signal S3 that satisfies e(t-1)=y(t-1)-^y(t-1) in response to the signals ^y(t-1). In other words, as far as the memory effect is concerned, the recurrent indirect learning architecture in the embodiment of the present invention minimizes the loss function by considering two kinds of signals (or more kinds of error signals) of the error signal S3. Thus, embodiments of the present invention not only consider the predistortion output signal z(t) of the DPD actuator 321 for PA 350, but also consider at least one of the previous predistortion output signals z(t-1) to z(tk), where k is a positive integer, of the DPD actuator 321 for PA 350. PA 350 operates according to not only the predistortion output signal z(t), but also at least one of the previous output signals y(t-1) to y(tk) previously output from PA 350.

[0018] In other embodiments, the signal S1 of the training module 322 may be, for example, ^z(t)+^y(t-1) / G, ^z(t)+^z(t-1), or a0×^z(t)+a1×^z(t-1)+a2×^z(t-2)+a k ×^z(tk), where coefficients a0 to a kis a real number. In other words, the signal S1 is not only related to the current output signal y(t) of the PA 350, but also to the previous output signals y(t-1), y(t-2), ..., or y(tk) output from the PA 350 in the past. The signal S2 is, for example, z(t) + y(t-1) / G, z(t) + z(t-1), or a0 x z(t) + a1 x z(t-1) + a2 x z(t-2) ... + a k ×z(tk). In other words, the signal S2 is not only related to the current predistortion output signal z(t), but also to the previous predistortion output signals z(t-1), z(t-2), ..., or z(tk). The error signal S3 between the signals S1 and S2 can be, for example, e(t) + e(t-1) or b0 × e(t) + b1 × e(t-1) + b2 × e(t-2) ... + b k ×e(tk), where coefficients b0 to b k is a real number. In other words, the signal S3 is not only related to the error signal e(t), but also to the previous error signals e(t-1), e(t-2), ..., or e(tk). The response function PA of the DPD actuator 321 -1 The parameters or hyperparameters of may be determined / obtained by minimizing a loss function, so that a predistortion output signal z(t) that may reduce the final nonlinearity of the output signal y(t) may be determined / obtained.

[0019] As described above, the present invention may employ a recurrent DPD-PA cascade model instead of a Volterra series model. For example, FIG. 4 is a schematic diagram of a recurrent DPD-PA cascade model 40 according to an embodiment of the present invention. The recurrent DPD-PA cascade model 40 may be used in the amplifier circuit 30. As shown in FIG. 4, similar to a recurrent neural network (RNN), the recurrent DPD-PA cascade model 40 is configured such that the response function PA on the far right side of FIG. 4 (referred to as the first response function PA) multiplies the output signal y(t-1) of the left response function PA multiplied by a corresponding weight W, and the lower response function PA multiplied by a corresponding weight S. -1The predistortion output signal z(t) of the DPD actuator 321 may include weights V, W, S, and U to receive the predistortion output signal z(t) of the DPD actuator 321 (previous / first response function PA). Similar to an RNN, the cascade of the DPD actuator 321 and the PA 350 allows previous outputs to be used as inputs, so that decisions can be made based on the current input along with those learned from previous outputs. -1 may be a copy of the inverse of the response function PA of the PA 350. -1 may be updated in real time, as opposed to at intervals, by a copy of the inverse of the response function PA of PA350.

[0020] CFR 210 may be turned off before training of recursive DPD-PA cascade model 40 begins. Otherwise, CFR 210 may affect the training of recursive DPD-PA cascade model 40. That is, training of predistortion circuit 220 occurs when samples of PA 250 are collected with CFR 210 disabled so that all characteristics of PA 250 can be obtained for training predistortion circuit 220.

[0021] In the training (stage) of the regression type DPD-PA cascade model 40, first, the predistortion output signal z(t) and the output signal y(t) corresponding to samples of the input signal x(t) are trained by the training module 322 and the (initial) response function PA of the DPD actuator 321. -1 The predistortion output signal z(t) and the output signal y(t) may be used for incremental learning in the training module 322 to update the training module 322 (i.e., the response function PA -1 is the response function P A after incremental learning. -1 The present invention determines / estimates how the input signal x(t) is transformed into the output signal y(t) by the recurrent DPD-PA cascade model 40 of FIG. 4, and then calculates the response function PA -1 The response function of the DPD actuator 321 is -1After the iterations, the (final) response function PA -1 (That is, the response function PA in the lower right corner of Figure 4 -1 ) may be determined to optimally transform an input signal x(t) into an output signal y(t). In other words, as shown in FIG. 4, samples of signals x, z, y may be used to train a recurrent DPD-PA cascade model 40 so that the response function PA -1 (That is, the inverse function f PA -1 ) are calculated to update the predistortion circuit 320.

[0022] The predistortion circuit 320 calculates the trained response function PA for time instants t through tk. -1 After the parameters or hyperparameters of the model for are updated, the training (stage) is completed and the CFR 210 may be turned on to test the recurrent DPD-PA cascade model 40.

[0023] More specifically, in the training phase, in order to reduce computational complexity, the recurrent DPD-PA cascade model 40 may optimize parameters / hyperparameters of the recurrent DPD-PA cascade model 40 using Dynamic Causal Bayesian Optimization (or Bayesian optimization, causal Bayesian optimization) instead of training the recurrent DPD-PA cascade model 40 using backward propagation.

[0024] Take Bayesian optimization for example. Bayesian optimization is a black-box optimization algorithm for solving extremum problems of functions whose equations are unknown. For example, if L(P1, P2, , P m ,HP1,HP2,···,HP n )=uef(P1,P2,...,P m ,HP1,HP2,...HP n), where L() can represent the loss function of the model (which may serve as the objective function), uef() can represent a function whose equation is unknown, and m can represent the parameters of the model, HP1 to HP n may represent the hyperparameters of the model, where m and n are positive integers. In other words, the formula of the model's loss function L(), the relationship function uef() between the parameters and the hyperparameters, is unknown. The parameters and hyperparameters at any time that minimize / maximize the loss function L() may be calculated by using Bayesian optimization. In this way, the predistortion circuit 320 may be updated to combine the nonlinearities of the predistortion circuit 320 and the PA 350 into one linear result (i.e., to compensate for the nonlinearities).

[0025] For example, FIG. 5 illustrates a loss function L() and parameters P1 through P2 according to an embodiment of the present invention. m and hyperparameters HP1 to HP n However, Fig. 5 shows the relationship between the loss function L() and the parameters P1 to P m and hyperparameters HP1 to HP n This is merely an example to identify the relationship between the loss function L() and the parameters P1 to P m and hyperparameters HP1 to HP n The formula for the relationship function uef() between is unknown in most cases. The coordinates of one single point on the horizontal axis of Figure 5 are the parameters P1 to P m and hyperparameters HP1 to HP n may correspond to a point in a multidimensional space formed / constructed by

[0026] Since the equation of the relation function uef() is unknown, Bayesian optimization can roughly fit the relation function uef() using partial / finite sampling points to find extreme points, and use the information of the previous sampling points to determine the next sampling point. For example, Figure 6 is a schematic diagram of Bayesian optimization for a one-dimensional problem according to an embodiment of the present invention, in which the thick solid line represents the estimated function value of the loss function L(), the black points P1 to P5 respectively represent the found sampling points, the area surrounded by the two dotted lines represents the fluctuation range of the loss function L() at each point (centered on the mean value and proportional to the standard deviation), and the thin solid line represents the acquisition function. The idea of ​​Bayesian optimization is to first generate an initial candidate solution set (e.g., the loss function L(), parameters, and hyperparameters corresponding to the black point P1), then search for the next sampling point (e.g., the black point P2) that may have an extreme value based on the initial candidate solution set, and repeatedly search for the next sampling point (e.g., the black points P3 to P5) that may have an extreme value until the iteration is completed, and add all the searched sampling points (e.g., the black points P1 to P5) to the candidate solution set. Finally, a (global) extreme point is found as the solution to the problem from the sampling points of the candidate solution set (e.g., the loss function L(), parameters, and hyperparameters corresponding to the black point P5), thereby determining the parameters P1 to P5 used to update the precompensation circuit 320. m and hyperparameters HP1 to HP n Find.

[0027] The Bayesian optimization estimates the mean value and variance of the true loss function based on the function value of the found sampling point (e.g., the loss function corresponding to the black point P1) so as to determine the next sampling point (e.g., the black point P2) according to the already found sampling point (e.g., the black point P1). The estimated loss function (i.e., the mean value of the loss function at each point), represented by the thick solid line in FIG. 6, passes through the sampling points (e.g., the black points P1 to P4), and the variance is minimized. The variance increases as the estimated objective function moves away from the sampling points (e.g., the black points P1 to P4). The acquisition function, represented by the thin solid line in FIG. 6, may be constructed according to the mean value and the variance, i.e., the acquisition function may be a function of the mean value and the variance. The estimation of the likelihood that a point (e.g., one of the black points P1 to P5) is an extreme point of the loss function reflects the degree to which the point is worth searching. The relative extreme point of the acquisition function may correspond to the next sampling point of the loss function. For example, point P, which is represented by a rectangular box in Figure 6 * 5 is the maximum point of the acquisition function, (parameters P1 to P m and hyperparameters HP1 to HP n This may correspond to the next sampling point of the loss function (i.e., black point P5) according to

[0028] In one embodiment, a loss function L() corresponding to one of the black points P1 to P5, parameters P1 to P m , and hyperparameters HP1 to HP n may be obtained from, but is not limited to, the input signals x(t) to x(tk), the predistortion output signals z(t) to z(tk), the output signals y(t) to y(tk), the signals ̂z(t) to ̂z(tk), ̂y(t) to ̂y(tk), other signals, or other data stored internally. In one embodiment, the signals ̂y(t) to ̂y(tk) may be functions of the signals ̂z(t) to ̂z(tk).

[0029] The algorithm of the present invention may use Gaussian process regression to predict the probability distribution of the functional value of the loss function L() at any point based on the function of the loss function L() at the set of sampling points. Gaussian process regression may be extended to observations with independent normally distributed noise of known variance. Since the variance may be unknown, it may be assumed that the noise is common variance and the noise includes the variance as a hyper-parameter. The present invention uses the posterior mean of the noisy Gaussian process, which is the drift value rather than the noise of the Signal to Interference plus Noise Ratio (SINR). In one embodiment, environmental factors such as temperature and humidity or the PA350 itself may affect the gain of the PA350, causing the drift value of the loss function with respect to certain parameters and hyper-parameters. In other words, the selected sampling point (e.g., black point P5) may not select / correspond to the desired / expected extreme value of the functional relationship uef(), but may select / correspond to a relatively optimized extreme value close to the desired / expected extreme value of the functional relationship uef().

[0030] According to the results of the Gaussian process regression, an acquisition function (used to measure how much each point of the loss function is worth exploring) can be configured to solve the (relative) extrema of the acquisition function to determine the next sampling point of the loss function. The acquisition function can be, for example, a knowledge gradient (KG), an entropy search (ES), or a predictive entropy search (PES). Then, the extrema of the loss function of the set of sampling points (discovered since the start) is returned as the extrema of the loss function (e.g., the minimum loss function in response to the optimal parameters and optimal hyperparameters). The parameters P1 to P2 for updating the predistortion circuit 320 are calculated. m and hyperparameters HP1 to HP n can be discovered in this way.

[0031] In one embodiment, (parameters P1 to P m and hyperparameters HP1 to HP n There may be many independent variables considered by the algorithm of the present invention (in addition to ). As the spatial dimension increases, the performance of Bayesian optimization may degrade exponentially. Therefore, the algorithm of the present invention may be extended to Causal Bayesian Optimization (CBO). In other words, the present invention is based on the idea that the loss function L() is a function of the parameters P1 to P m , hyperparameters HP1 to HP n Causal Bayesian optimization may be used to calculate the optimal / minimal loss function when it is related to , and other independent variables.

[0032] Specifically, the present invention provides the loss function L(), parameters P1 to P m , hyperparameters HP1 to HP n , and / or causal relationships between other independent variables (e.g., loss function L(), parameters P1 to P m , hyperparameters HP1 to HP n , and / or other independent variables). Therefore, the loss function L(), parameters P1 to P m , hyperparameters HP1 to HP n , and other independent variables may be considered as causal variables. For example, FIG. 7 is a schematic diagram of a portion of a causal graph CG1 according to an embodiment of the present invention. The loss function L(), parameters P1 to P2, and the m , hyperparameters HP1 to HP nconstructs the causal graph CG1 used by the causal model, where q is a positive integer. As shown in FIG. 7, the causal dimensionality found by the causal Bayesian optimization may be m+n+q, so there are m+n+q independent variables that are fed into the loss function L() of the causal Bayesian optimization for optimization. Thus, the values ​​of m+n+q causal variables that can minimize the loss function L() are calculated. The causal graph CG1 can greatly improve the ability to reason about optimal decision-making strategies, thereby reducing optimization costs and avoiding suboptimal solutions.

[0033] In one embodiment, a causal model for optimization may be selected based on maximum a posterior (MAP) and point estimation to obtain / derive a causal graph of loss functions, parameters, hyperparameters, and other independent variables. Thus, the causal variables of the causal graph of the causal model (e.g., the number of causal variables, what attributes the causal variables have, or the number of attributes of the causal variables) and the causal structure of the causal graph (e.g., how the attributes are connected to each other) are determined / discovered / generated together (at once or all at once). Determining the causal variables and causal structure simultaneously / in parallel may avoid problems caused by first determining the causal variables and then the causal structure.

[0034] For example, FIG. 8 is a schematic diagram of a portion of a causal graph CG2 and grounding data 80g according to an embodiment of the present invention. In FIG. 8, (a) and (b) respectively represent two possibilities of the grounding data 80g and the causal graph CG2. The causal graph CG2 may function as the causal graph CG1. In one embodiment, the grounding data 80g may be obtained or derived from the space of all observable samples and may therefore be referred to as observed data. In one embodiment, the grounding data 80g may correspond to all deep learning models. In one embodiment, the grounding data 80g may be obtained or derived from all data being collected. In one embodiment, the grounding data 80g may be a part of all data (e.g., La The input signals x(t) to x(tk), the predistortion output signals z(t) to z(tk), and the model outputs ^y(t) to ^y(tk).

[0035] In Figure 8, the causal structure of the causal graph CG2 is the causal variables (e.g., causal variables cv (i-1) , cv i , cv (j-1) , and cv j ) can be used to show the relationship between the observation function f (i-1) , f i , f (j-1) , and f j is the sub-data of grounding data 80g (i-1) , w i , w (j-1) , and w j Let cv be the causal variable. (i-1) , cv i , cv (j-1) , and cv j and the causal variable cv (i-1) , cv i , cv (j-1) , cv j And sub data w (i-1) , w i , w (j-1) , w jHere, i and j are positive integers. The mapping here is not done on the grounding data 80g (whole), but on the corresponding sub-data (e.g., w (i-1) , w i , w (j-1) , w j ) (e.g., the area framed in Figure 8). For example, the causal variables cv (i-1) corresponds to parameter P1, then sub-data w (i-1) is the causal variable cv (i-1) Related to (attributes of) (e.g., subdata w (i-1) relates to all data relating to parameter P1.

[0036] In one embodiment, the sub-data w of the grounding data 80g i The observation function f i and the posterior probability P(f i ,C|w i ) is a sub-data of Grounding Data 80g i Based on the corresponding causal structure C and the corresponding causal variables cv i Thus, inference of a causal model can be achieved by applying a Bayesian network (e.g., for a causal structure) to an observation function (e.g., f (i-1) , f i , f (j-1) , and f j ) in the corresponding causal graph (e.g., CG). (i-1) , cv i , cv (j-1) , and cv j ) and the corresponding causal structure (e.g., C) are points that are obtained / determined together (i.e., the causal variables (e.g., cv (i-1) , cv i , cv (j-1) , and cv j ) are studied together with the causal structure (e.g., C). Thus, the causal variables (e.g., cv (i-1) , cv i , cv (j-1), and cv j ) and causal structures (e.g., C) may interact / influence / constrain each other.

[0037] In one embodiment, the posterior probability P(f i ,C|w i ,Int) is calculated by the Bayesian rule: P(f i ,C|w i ,Int) ∝ P(f i ,C)P(w i |f i ,C,Int) can be satisfied. Then, f i can represent the corresponding observation function, C can represent the corresponding causal structure, and w i may represent a portion (e.g., sub-data) of the grounding data 80g, and Int may represent an intervention. In one embodiment, the posterior probability P(f i ,C|w i ) is P(f i ,C)P(w i |f i ,C) or

number

number

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[0038] As mentioned above, Bayesian probability A mechanism is a mechanism that determines the causal variables (e.g., the causal variables cv (i-1) , cv i , cv (j-1) , and cv j ), the state of the causal variables, the causal structure of the causal variables, or the observation function for the causal variables (e.g., the observation function f (i-1) , f i , f (j-1) , and f j ) and draw relevant joint inferences to explain / interpret the grounded data 80g, thereby generating a causal graph CG2. (i-1) , cv i , cv (j-1) , and cv j ) (or the number of causal variables) and the causal structure (e.g., C) are determined simultaneously, thereby distinguishing (a) from (b) in FIG. 8, and vice versa.

[0039] As shown in Figure 8, each causal variable (e.g., cv i ) is the observation function (e.g., f i In one embodiment, the observation function (e.g., f i ) is a function of high-dimensional environmental variables (e.g., causal variables cv i The causal variables (e.g., cv (i-1) , cv i , cv (j-1) , and cv j ) are manually defined (e.g., causal variables are defined by a domain expert (non-automatically and individually) or automatically by using a program with rules written / provided by a domain expert). i ) maps the causal variables to the corresponding subdata (e.g., w i ) (e.g., the area framed in FIG. 8 ). This can be achieved by using a causal semantic generative observation function dedicated to grounding the sub-data (e.g., the sub-data w (i-1) , w i , w (j-1) , or w j ) is determined based on the definition of specific causal variables from domain experts. Furthermore, the causal semantic generative model can automatically determine the causal variables (e.g., cv i ) factors as sources of variation, and semantic factors can be treated as causal variables (e.g., cv i ) can be accurately determined. In one embodiment, the variation factors and semantic factors can constitute / belong to the observed data. In one embodiment, the causal semantic generative model is primarily based on the causal invariance principle and includes variational Bayes.

[0040] In one embodiment, the observation function f i s i,t =f i (w i,tIn one embodiment, the observation function f i may be implemented using a multivariate Gaussian distribution. For example, the observation function f i teeth,

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[0041] In one embodiment, the causal variables (e.g., cv i ) and subdata (e.g., w i ) may be unknown, but the causal variables can be predicted / inferred from the sub-data using a causal semantic generative model. For example, FIG. 9 illustrates a causal variable cv y And sub data w xIn this figure, (a), (b), (c), and (d) respectively represent the structural possibilities of the causal semantic generative model, where sc can represent semantic factors, v can represent variation factors, and the solid arrows represent the causal mechanisms p(w x |sc,v) and p(cv y |sc), and the dashed arrow represents the inference model q(sc,v|w x ) can be expressed as the domain-specific prior p(sc,v). In FIG. 9(a), the undirected solid line between the semantic factor sc and the variation factor v can represent the domain-specific prior p(sc,v). Compared with the undirected solid line between the semantic factor sc and the variation factor v in FIG. 9(a), FIG. 9(b) shows the independent prior p(sc,v) to reflect intervention to improve generalization performance out of the distribution. ⊥ We introduce the prior p(sc,v):=p(sc)p(v). Compared with the undirected solid line between the semantic factor sc and the variability factor v in Fig. 9(a), Fig. 9(c) introduces the prior p(sc,v):=p(sc)p(v) shown by the dashed line between the semantic factor sc and the variability factor v to reflect the intervention according to the causal invariance principle to utilize unsupervised data. ~ In one embodiment, the present invention calculates a causal semantic generative model p:=(sc,v) by maximizing the likelihood <p(sc,v)、p(w x |sc,v), p(cv y We can fit |sc)> to the sub-data, perform calculations using variational inference and the evidence lower bound (ELBO), and use Monte Carlo to estimate the expectation value after applying reparameterization tricks.

[0042] In one embodiment, causal Bayesian optimization involves selecting causal variables that are directly related to the loss function (e.g., parameters P1 to P2 in the causal graph CG1 that directly indicate or affect the loss function L()). m , hyperparameters HP1 to HP n , and / or the independent variables O1 to O q) . In other words, the causal intrinsic dimensionality of the causal Bayesian optimization is the sum of the parameters P1 to P m , hyperparameters HP1 to HP n , and / or the independent variables O1 to O q Rather than the number of causal variables that are factors of m , hyperparameters HP1 to HP n , and independent variables O1 through O q , thereby improving our ability to reason about optimal decision-making strategies.

[0043] In one embodiment, the causal variables (parameters P1 to P m , hyperparameters HP1 to HP n , independent variables O1 to O q , or the causal variable cv (i-1) , cv i , cv (j-1) , cv j ) are manually defined (e.g., by a domain expert). For example, the causal variables are defined (automatically and individually) by a domain expert, or alternatively, the causal variables are defined automatically using a program with rules written by a domain expert. In one embodiment, the sub-data (sub-data w corresponding to the framed area in FIG. 8) are (i-1) , w i , w (j-1) , or w j ) is defined / determined according to the definition of specific causal variables by the domain experts.

[0044] Causal Bayesian optimization is a method to find the output variables (e.g., the loss function L()) and the input causal variables (e.g., the parameters P1 to P m , hyperparameters HP1 to HP n , and / or the independent variables O1 to O q) as universal independent variables and ignores the existence of temporal evolution in both output and input causal variables (e.g., whether output and input causal variables change over time), thus breaking the time-dependent structure that exists between causal variables. While ignoring time significantly simplifies the problem, it does not identify optimal interventions at all time points and may lead to suboptimal solutions rather than providing the current optimal solution at any time point (especially in non-stationary scenarios). Thus, the present invention provides / explains causal relationships between causal variables and can be extended to dynamic causal Bayesian optimization where causal relationships may evolve / change over time, thus facilitating scenarios where all causal effects in the causal graph change over time.

[0045] For example, FIG. 10 is a schematic diagram of Bayesian optimization, causal Bayesian optimization, and dynamic causal Bayesian optimization. In FIG. 10, X1 to X3 represent causal variables at three different time points. Y1 to Y3 represent other causal variables at three different time points. Z1 to Z3 represent another causal variable at three different time points. However, the present invention is not so limited and can be extended to more time points and more causal variables. Dynamic causal Bayesian optimization combines Bayesian optimization and causal Bayesian optimization to explain the causal relationship between the causal variables, and the causal relationship may evolve over time. For example, in dynamic causal Bayesian optimization, as shown in FIG. 10, the causal variable Y1 at the first time point is a function of the causal variable Z1 at the first time point, so that the extreme value of the causal variable Y1 (which may represent or correspond to the loss function L()) is found by using only the causal variable Z1 that is directly related to the causal variable Y1, and the causal intrinsic dimension is 1. Similarly, because causal variable Y2 at the second time point is a function of causal variable Z2 at the second time point and causal variable Y1 at the first time point, extreme values ​​of causal variable Y2 (which may represent or correspond to the loss function L()) are found by using only causal variables Y1 and Z2 that are directly related to causal variable Y2, and the causal intrinsic dimension is 2. Similarly, causal variable Y3 at the third time point is a function of causal variable Z3 at the third time point and causal variable Y2 at the second time point, and the extreme values ​​of causal variable Y3 (which may represent or correspond to the loss function L()) are found by using only causal variables Y2 and Z3 that are directly related to causal variable Y3, and the causal intrinsic dimension is 2. In other words, since a causal variable acting as an independent variable at a given time point is a function of a causal variable at a previous time point (acting as either a dependent or independent variable), extreme values ​​of the former (i.e., the causal variable acting as a dependent variable at a particular time point) can be found by using only the latter (i.e., the causal variable acting as either a dependent or independent variable at a previous time point) that are directly related to the former.

[0046] The predistortion method in the embodiment of the present invention may be applied to the amplifier circuits 10 to 30 or the recurrent DPD-PA cascade model 40, and may be compiled into a code that can be executed by a processing circuit and stored in a storage circuit. The predistortion steps may include the following steps:

[0047] Step S10: Start.

[0048] Step S12: The DPD actuator 321 (or 221) performs predistortion according to at least one parameter or at least one hyperparameter to transform the input signal x(t) received by the DPD actuator 321 into a predistorted output signal z(t).

[0049] Step S14: The training module 322 (or 222) determines, calculates, or updates at least one parameter or at least one hyperparameter of the DPD actuator 321 according to Bayesian optimization, causal Bayesian optimization, or dynamic Bayesian optimization. The training module 322 may apply Bayesian optimization, causal Bayesian optimization, or dynamic Bayesian optimization to at least one data to determine the at least one parameter or at least one hyperparameter. The at least one data may be extracted / obtained from the predistortion output signal z(t) (output by the DPD actuator 321 in response to the input signal x(t)) or the output signal y(t) (output by the PA 350 (or 250) in response to the predistortion output signal z(t)). Alternatively, the at least one data may be extracted / obtained from the input signal x(t-1),..., or x(tk) (received by the DPD actuator 321 before the input signal x(t)), the predistortion output signal z(t-1),..., or z(tk) (output by the DPD actuator 321 before the predistortion output signal z(t) in response to the input signal x(t-1),..., or x(tk)), or the output signal y(t-1),..., or y(tk) (output by the PA 350 before the output signal y(t) in response to the predistortion output signal z(t-1),..., or z(tk). Alternatively, the at least one data may be extracted / obtained from a label corresponding to the input signal x(t) or the output signal y(t).

[0050] Step 16: The DPD actuator 321 performs predistortion according to the updated at least one parameter or the updated at least one hyperparameter to transform the input signal x(t+1) received by the DPD actuator 321 into a predistortion output signal z(t+1).

[0051] Step 18: Finish.

[0052] In one embodiment, the storage circuitry is configured to store image data or instructions. The storage circuitry may be, but is not limited to, a read-only memory (ROM), a flash memory, a random access memory (RAM), a hard disk, a non-volatile storage device, or a non-transitory computer readable medium. In one embodiment, the processing circuitry is configured to execute instructions (stored in the storage circuitry). The processing circuitry may be, but is not limited to, a microprocessor or an application specific integrated circuit (ASIC). The amplifier circuitry 10, 20, or 30 may be utilized in, but is not limited to, a radio unit (RU).

[0053] In an embodiment, the predistortion circuit is configured to compensate for the nonlinearity of the power amplifier. In an embodiment, a first ratio (G) of a first output signal (y(t-1)) to a first input signal (x(t-1)) is equal to a second ratio (G) of a second output signal (y(t)) to a second input signal (x(t)), where the first output signal is output by the power amplifier corresponding to a first predistortion output signal (z(t-1)), and the second output signal is output by the power amplifier corresponding to a second predistortion output signal (z(t)).

[0054] In an embodiment, the step of updating at least one parameter or at least one hyperparameter according to Bayesian optimization, causal Bayesian optimization, or dynamic Bayesian optimization includes applying Bayesian optimization, causal Bayesian optimization, or dynamic Bayesian optimization to determine at least one parameter or at least one hyperparameter of the predistortion circuit, wherein at least one data is extracted from the first predistortion output signal or a first output signal output by the power amplifier corresponding to the first predistortion output signal. At least one data is further extracted from at least one previous input signal (e.g., x(t-2), ..., or x(tk)) received by the predistortion circuit before the first input signal, at least one previous predistortion output signal (e.g., z(t-2), ..., or z(tk)) output by the predistortion circuit before the first predistortion output signal corresponding to the at least one previous input signal, or at least one previous output signal (e.g., y(t-2), ..., or y(tk)) output by the power amplifier corresponding to the at least one previous predistortion output signal, or a label corresponding to the first input signal or the first output signal.

[0055] In an embodiment, the step of updating at least one parameter or at least one hyperparameter according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization comprises jointly determining a plurality of independent variable optimal values ​​according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization, where the plurality of independent variable optimal values ​​comprises at least one parameter, at least one hyperparameter, and at least one first independent variable optimal value.

[0056] In an embodiment, the step of updating at least one parameter or at least one hyperparameter according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization comprises jointly searching for a plurality of independent variable optimal values ​​from a plurality of independent variables according to causal Bayesian optimization or dynamic Bayesian optimization, the plurality of independent variable optimal values ​​comprising at least one parameter or at least one hyperparameter, a causal structure of the causal graph and a plurality of causal variables of the causal graph having a loss function and at least one independent variable are determined jointly, the loss function being a function of the first output signal or a label corresponding to the first output signal. The causal graph is generated based on maximum a posterior (MAP) and point estimation. A plurality of sub-data in the grounding data are mapped to a plurality of causal variables of the causal graph by using a plurality of observation functions to generate a causal graph from the grounding data based on maximum a posterior and point estimation. The plurality of observation functions are obtained based on a causal semantic generative model. The step of updating at least one parameter or at least one hyperparameter according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization includes applying causal Bayesian optimization or dynamic causal Bayesian optimization to at least one data to determine at least one parameter or at least one hyperparameter of the predistortion circuit, wherein the grounding data includes the at least one data.

[0057] In an embodiment, a plurality of independent variable optimal values ​​are found from a plurality of independent variables jointly according to causal Bayesian optimization or dynamic causal Bayesian optimization, the plurality of independent variable optimal values ​​having at least one parameter or at least one hyperparameter, a causal structure of the causal graph and a plurality of causal variables of the causal graph having a loss function and at least one independent variable are determined jointly, the loss function is a function of the first output signal or a label corresponding to the first output signal, and a plurality of posterior probabilities of assigning a plurality of subsets of the grounding data to the plurality of observation functions and the causal structure of the causal graph are maximized to generate the causal graph. One of the plurality of posterior probabilities is:

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[0058] In summary, the present invention proposes a recurrent DPD-PA cascade model trained by dynamic causal Bayesian optimization (DPD is actually a “PA -1 In this way, computational complexity and calculations can be significantly reduced. DPD performs PA in real time as opposed to spaced. -1 This allows for efficient compensation of imperfections in the power amplifier, such as nonlinearities.

[0059] Those skilled in the art will readily recognize that numerous modifications and alterations of the devices and methods may be made while retaining the teachings of the present invention. Accordingly, the above disclosure should be construed as limited only by the scope and metrology of the appended claims. [Explanation of symbols]

[0060] 10,20,30 Amplification circuit 120,220,320 Precompensation circuit 150,250,350 PA 210 C.F.R. 221 DPD Actuator 222 Training Module 223 Combiner (Subtraction Unit) 230 DAC 240 Upconverter 260 Down Converter 270 ADC 40 Recurrent DPD-PA cascade model

Claims

1. 1. A predistortion method for a predistortion circuit, the predistortion circuit having a digital predistortion actuator and a training module, disposed in front of a power amplifier to compensate for nonlinearity of the power amplifier, comprising: the digital predistortion actuator performing predistortion according to at least one parameter to convert a first input signal received by the predistortion circuit into a first predistortion output signal; The training module comprises: receiving the first predistortion output signal and an output signal output by the power amplifier based on the first predistortion output signal; generating a training output signal according to a response function based on the output signal; optimizing at least one hyper-parameter for the response function of the training module according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization so as to approximate the training output signal to the first predistortion output signal; updating the at least one parameter such that the response function of the training module is copied to a response function of the digital predistortion actuator; performing predistortion according to the updated at least one parameter, such that the digital predistortion actuator converts a second input signal received by the predistortion circuit into a second predistortion output signal; A precompensation method comprising:

2. The step of the training module optimizing at least one hyperparameter of the training module according to the Bayesian optimization, the causal Bayesian optimization, or the dynamic causal Bayesian optimization and updating the at least one parameter comprises: applying the Bayesian optimization, the causal Bayesian optimization, or the dynamic causal Bayesian optimization to at least one data to determine the at least one parameter or the at least one hyperparameter of the predistortion circuit; The at least one data is derived from the first predistortion output signal or the output signal output by the power amplifier based on the first predistortion output signal. The precompensation method according to claim 1 .

3. The step of the training module optimizing at least one hyperparameter of the training module according to the Bayesian optimization, the causal Bayesian optimization, or the dynamic causal Bayesian optimization and updating the at least one parameter comprises: searching for a plurality of independent variable optimum values ​​collectively from a plurality of independent variables according to the causal Bayesian optimization or the dynamic causal Bayesian optimization; the plurality of independent variable optimum values ​​comprises the at least one parameter or the at least one hyperparameter; A causal structure of a causal graph constructed for the loss function and the plurality of independent variables and a plurality of causal variables of the causal graph are jointly determined; The loss function is a function of the output signal output by the power amplifier based on the first predistortion output signal, or a label corresponding to the output signal. The precompensation method according to claim 1 .

4. The step of the training module optimizing at least one hyperparameter of the training module according to the Bayesian optimization, the causal Bayesian optimization, or the dynamic causal Bayesian optimization and updating the at least one parameter comprises: searching for at least one independent variable optimum value from at least one independent variable according to the dynamic causal Bayesian optimization; the at least one independent variable optimum value comprises the at least one parameter or the at least one hyperparameter; the second loss function at a second time point is a function of the at least one independent variable at the second time point, the at least one independent variable at the first time point, or the first loss function at the first time point. The precompensation method according to claim 1 .

5. A predistortion circuit arranged in front of a power amplifier to compensate for nonlinearity of the power amplifier, A digital pre-distortion actuator and a training module; the digital predistortion actuator is configured to perform predistortion according to at least one parameter to convert a first input signal received by the digital predistortion actuator into a first predistortion output signal; The training module includes: receiving the first predistortion output signal and an output signal output by the power amplifier based on the first predistortion output signal; generating a training output signal according to a response function based on the output signal; optimizing at least one hyper-parameter for the response function of the training module according to Bayesian optimization, causal Bayesian optimization, or dynamic causal Bayesian optimization so as to approximate the training output signal to the first predistortion output signal; updating the at least one parameter such that the response function of the training module is copied to a response function of the digital predistortion actuator; It is configured as follows: the digital predistortion actuator is further configured to perform predistortion according to the updated at least one parameter to convert a second input signal received by the digital predistortion actuator into a second predistortion output signal. Pre-compensation circuit.

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