Nonlinear behavior modeling method and system for Class D power amplifier based on RRU network

Abstract

The present invention discloses a method and system for modeling the nonlinear behavior of a Class D power amplifier based on an RRU network, which belongs to the field of wireless communication technology and solves the problem that traditional models in the prior art are difficult to accurately characterize the nonlinear characteristics of Class D power amplifiers. The present invention first uses a filter with adjustable weights to extract dynamic features of the input complex signal, then integrates the dynamic features with the current input, and uses an internal reference normalization factor for processing, and then inputs the normalized features into an improved RRU network. The network deeply learns the nonlinear time series dynamics of the signal through cyclic state alignment and residual update mechanism; finally, through the output layer and reference restoration step, the output behavior of the Class D power amplifier is accurately predicted. The present invention combines the advantages of adaptive filtering, internal reference normalization and RRU network, significantly improving the accuracy and robustness of the nonlinear model of the Class D power amplifier, and laying the foundation for applications such as efficient digital pre-distortion.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and more particularly, relates to a method and system for modeling nonlinear behavior of a Class D power amplifier based on an RRU network. Background Art

[0002] Class-D power amplifiers (Class-D PAs), with their outstanding energy conversion efficiency, offer significant advantages and broad application prospects in modern sonar transmission systems, which have stringent power consumption and heat dissipation requirements. Sonar systems, particularly active sonar, require high-power transmit signals for long-range detection and high signal-to-noise ratio reception. The high efficiency of Class-D PAs makes them an ideal choice, helping to extend the life of underwater equipment while reducing system size and weight.

[0003] However, the high efficiency of Class D amplifiers stems from their unique switching principle: the power transistors operate in either a "fully on" or "fully off" state, modulating the input signal into a high-frequency pulse sequence through high-speed switching, which is then restored to the amplified signal through low-pass filtering. This operating mechanism inevitably introduces complex nonlinear distortion and strong memory effects. For example, the PWM modulation process itself generates harmonic distortion. In actual circuits, factors such as dead time, power supply ripple coupling, and the dynamic characteristics of the output filter all cause distortion in the transmitted signal waveform, making the current output dependent on historical input and operating conditions. These nonlinear and memory effects can severely affect the integrity and spectral purity of the sonar transmission signal, potentially reducing detection range, degrading target recognition accuracy, or causing unnecessary interference to the underwater environment.

[0004] Therefore, accurate modeling of the nonlinear behavior of Class D amplifiers is crucial for subsequent distortion correction techniques to improve signal quality. However, existing mainstream PA modeling methods often face challenges when applied to Class D amplifiers. Traditional models struggle to accurately characterize the nonlinear characteristics of Class D amplifiers. Traditional white-box models, such as memory polynomials (MPs) and Volterra series models, are based on the assumption that system nonlinearities can be described by analytical power series. However, the discontinuous switching characteristics and strong nonlinearities of Class D amplifiers make these models difficult to directly apply. They typically require extremely high order and long memory depth to achieve a reasonable fitting accuracy, which in turn leads to problems such as an explosion in the number of parameters, difficulty in model identification, poor convergence, and numerical instability. Furthermore, while deep learning-based black-box models, such as long short-term memory networks (LSTMs), possess powerful nonlinear fitting capabilities and the potential to process sequential data, direct application to Class D amplifier modeling often suffers from poor results without targeted structural design and parameter optimization due to difficulties in characterizing high-frequency switching waveforms, the required network size and sequence length, and unstable training convergence. Summary of the Invention

[0005] The present invention aims to solve the technical problems existing in the prior art and provides a method and system for modeling the nonlinear behavior of a Class D power amplifier based on an RRU network.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] A method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network includes the following steps:

[0008] S1. Divide the data set and initialize the algorithm; divide the input and output data of the power amplifier into training set, verification set and test set, and initialize the state information of the RRU layer in the network;

[0009] S2, the generated length is M Memory Window X M ( k );The current time step sample x ( k ) and before M The historical sample information forms a memory window, which is used to characterize the short-term dynamic change characteristics of the input signal;

[0010] S3, frequency domain feature extraction; use filters to process the input signal X M ( k ), extract the characteristics of the signal in different frequency bands;

[0011] S4. Calculate the phase normalization factor r ( k ); Calculate the complex conjugate and amplitude of the current time step sample to calculate the phase normalization factor r ( k );

[0012] S5. Construct composite input signal X F (k); the sample of the current time step x ( k ) is integrated with the information output by the filter to provide a composite input signal X for the RRU unit F ( k );

[0013] S6, X F ( k ) Apply phase normalization; X F ( k ) is rotated to the phase of x ( k ) phase alignment to achieve phase normalization of features;

[0014] S7, update RRU network status; F( k ) input, calculate the output and hidden state of multiple RRU layers;

[0015] S8, based on the updated I / Q hidden state of the last layer of recursive units, predict the phase normalized complex value output y ′( k );

[0016] S9. Using phase normalization factor r ( k ) for phase normalized complex output y ′( k ) to perform inverse phase normalization to obtain the output of network prediction y ( k );

[0017] S10, use mean square error as the loss function of RRU network; according to the output y ( k ) and actual amplifier output y 0( k ), update the weight information of the RRU layer;

[0018] S11, train the RRU network on the training set. When the loss function in the training set is continuously less than the threshold, the RRU network stops training. If it is not reached, repeat S2-S10 until the training times are completed;

[0019] S12, RRU network testing: Apply the trained RRU network to the test set.

[0020] Preferably, in S2, before the entire sequence processing cycle begins, the original input sequence x Create a memory window of all time steps, each time step k Memory Window X M ( k )Include x ( k ), x ( k -1),..., x ( k - M ) A total of M+1 samples, M+1 complex-valued samples are used as the input of the filter to extract time domain features.

[0021] Preferably, in S3, the filter-based frequency domain feature extraction includes:

[0022] Use L filters to filter X M ( k) to filter and extract the characteristics of the signal in different frequency bands. The coefficient information of the filter is set as a learnable network parameter, and the filtering output is realized through two fully connected layers;

[0023] Real filter output calculation: Through a first linear transformation layer, X M ( k )'s real part X MI ( k ) is input into L filters to obtain Y FIR,I ( k ), the calculation formula is:

[0024]

[0025] in, is the learnable weight matrix, is the learnable bias vector;

[0026] Imaginary filter output calculation: Through a second linear transformation layer, X M ( k )'s imaginary part X MQ ( k ) is input into L filters to obtain Y FIR,Q ( k ), the calculation formula is:

[0027]

[0028] in, is the learnable weight matrix, is the learnable bias vector.

[0029] Preferably, in S4, the current time sample is calculated x ( k )’s phase normalization factor r( k ), which is calculated as follows:

[0030]

[0031] in, yes x ( k ), yes x ( k ) amplitude information.

[0032] Preferably, in S5, the current time sample and the filter output Y FIR,I ( k ) and Y FIR,Q ( k ) combination to obtain the composite input vector X F (k ), whose value is:

[0033] ;

[0034] In S6, Applying a phase normalization factor r ( k ),Will The phase is rotated to x ( k ) phase alignment to achieve composite input eigenvector The phase normalization processing is calculated as follows:

[0035] .

[0036] Preferably, in S7, the output and hidden state of the RRU layer are calculated, and the following cyclic state update operation is performed for each RRU unit in the network, including:

[0037] S701, I / Q hidden state renormalization:

[0038] Calculate the relative rotation factor; if the time step k >1, calculate a relative rotation factor Δ r ( k ), the factor represents the current time step input x ( k ) phase and the previous time step input x ( k −1) The relative change in phase is calculated as:

[0039] Δ r ( k ) = r ( k )·r * ( k −1)

[0040] in, is the phase normalization factor of the previous time step r ( k -1), if the time step k =1, then Δ r ( k ) = 1+ j 0;

[0041] Apply rotation; the historical value of the I / Q hidden state of the current layer RRU unit Perform complex multiplication with the relative rotation factor Δr(k) to obtain the renormalized I / Q hidden state ,Right now:

[0042] ;

[0043] S702, RRU unit core update:

[0044] Construct a joint input vector; concatenate the current input of the RRU unit and the renormalized I / Q hidden state and envelope hidden state , forming a joint input vector ;

[0045] The update vector is calculated using a two-layer activation function; the update vector is obtained from the joint input vector Calculate an update vector v( k ), realize deep nonlinear mapping, update v( k ) is calculated as follows:

[0046] The output of the first layer activation function:

[0047]

[0048] The output of the second layer activation function:

[0049]

[0050] in, and is the learnable weight matrix, and is the learnable bias vector;

[0051] S703, Joint Status Update:

[0052] Based on the update vector v( k ) and the complete hidden state of history , update the complete hidden state h(k) of the current layer, and the update follows the following core formula:

[0053]

[0054] in, is the complete hidden state of the previous step, is the tanh() activation function, C is the learnable parameter, Z is the learnable parameter, and ⊙ is the element-wise multiplication;

[0055] S704, State Decomposition and Storage:

[0056] The updated complete hidden state h( k ) is split into the I / Q hidden state h of the current layer iq ( k ) and the envelope hidden state henv ( k ), and stored as the input of the next time step, and at the same time as the input of the next layer of RRU units or the input of the output layer.

[0057] Preferably, in S8, the final prediction result is extracted from the internal representation of the network, and the result is still phase normalized when output. The process uses the output layer of the RRU network to update the I / Q hidden state of the last layer of RRU units. As input, it is mapped into a phase-normalized complex-valued output through two independent linear layers. y ′( k ), which is calculated as follows:

[0058]

[0059]

[0060] in, and is the learnable weight matrix, and is the learnable bias vector.

[0061] Preferably, in S9, the phase normalization factor calculated in S4 is used in the inverse phase normalization process. r ( k )'s complex conjugate r ∗ ( k ), the phase normalized complex value output y ′( k ) is rotated in the opposite direction to obtain

[0062] y ( k ) = y ′( k )· r * ( k )

[0063] in, yes r ( k ) is used to convert y ′( k ) Rotate from the normalized phase reference frame back to the phase reference frame of the original signal;

[0064] In S10, the mean square error is used as the loss function of the RRU network, which is defined as:

[0065]

[0066] in,y ( n ) represents the actual signal value obtained by actual sampling, y pre ( n ) is the signal value predicted by the model, and the square and mean of the difference between the true and predicted values ​​are used as the loss function of the neural network.

[0067] Preferably, in S12, NMSE is used as the evaluation index of RRU network performance, and its calculation formula is:

[0068]

[0069] in, is the actual measured signal data, y pre ( n ) is the model output signal data, N is the total number of samples.

[0070] Furthermore, the present invention also provides a nonlinear behavior modeling system for a Class D power amplifier based on an RRU network. The system has a program module corresponding to any of the above steps, and when the program module is running, it executes the steps in the nonlinear behavior modeling method for a Class D power amplifier based on an RRU network.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] The present invention first uses a filter with adjustable weights to extract block-based dynamic features from the input complex signal. The dynamic features are then integrated with the current input and processed using an internal reference normalization factor. The normalized features are then fed into an improved RRU network, which deeply learns the signal's nonlinear temporal dynamics through cyclic state alignment and a residual update mechanism. Finally, through the output layer and reference restoration steps, the output behavior of the Class D amplifier is accurately predicted. Combining the advantages of adaptive filtering, internal reference normalization, and the RRU network, the present invention significantly improves the accuracy and robustness of the Class D amplifier's nonlinear model, laying the foundation for applications such as efficient digital predistortion. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0074] Figure 1 Schematic diagram of the internal structure of an RRU unit in an embodiment of the present invention;

[0075] Figure 2 This is a schematic diagram of the network algorithm provided by the present invention. DETAILED DESCRIPTION

[0076] To make the technical problems, technical solutions, and beneficial effects to be solved by this application more clearly understood, the following, in conjunction with the accompanying drawings and embodiments, further describes in detail a method and system for modeling the nonlinear behavior of a Class D power amplifier based on an RRU network provided by this application. It should be understood that the specific embodiments described herein are merely intended to explain this application and are not intended to limit this application.

[0077] Example 1

[0078] An embodiment of the present invention provides a method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network, comprising the following steps:

[0079] S1. Divide the data set and initialize the algorithm; divide the input and output data of the power amplifier into training set, verification set and test set, and initialize the state information of the RRU layer in the network;

[0080] S2, the generated length is M Memory Window X M ( k );The current time step sample x ( k ) and before M The historical sample information forms a memory window, which is used to characterize the short-term dynamic change characteristics of the input signal;

[0081] S3, frequency domain feature extraction; use filters to process the input signal X M ( k ), extract the characteristics of the signal in different frequency bands;

[0082] S4. Calculate the phase normalization factor r ( k ); Calculate the complex conjugate and amplitude of the current time step sample to calculate the phase normalization factor r ( k );

[0083] S5. Construct composite input signal X F ( k ); the sample of the current time step x ( k ) is integrated with the information output by the filter to provide a composite input signal X for the RRU unit F ( k );

[0084] S6, X F (k ) Apply phase normalization; X F ( k ) is rotated to the phase of x ( k ) phase alignment to achieve phase normalization of features;

[0085] S7, update RRU network status; F ( k ) input, calculate the output and hidden state of multiple RRU layers;

[0086] S8, based on the updated I / Q hidden state of the last layer of recursive units, predict the phase normalized complex value output y ′( k );

[0087] S9. Using phase normalization factor r ( k ) for phase normalized complex output y ′( k ) to perform inverse phase normalization to obtain the output of network prediction y ( k );

[0088] S10, use mean square error as the loss function of RRU network; according to the output y ( k ) and actual amplifier output y 0( k ), update the weight information of the RRU layer;

[0089] S11, train the RRU network on the training set. When the loss function in the training set is continuously less than the threshold, the RRU network stops training. If it is not reached, repeat S2-S10 until the training times are completed;

[0090] S12, RRU network testing: Apply the trained RRU network to the test set.

[0091] The present invention first uses a filter with adjustable weights to extract block-based dynamic features from the input complex signal. The dynamic features are then integrated with the current input and processed using an internal reference normalization factor. The normalized features are then fed into an improved RRU network, which deeply learns the signal's nonlinear temporal dynamics through cyclic state alignment and a residual update mechanism. Finally, through the output layer and reference restoration steps, the output behavior of the Class D amplifier is accurately predicted. Combining the advantages of adaptive filtering, internal reference normalization, and the RRU network, the present invention significantly improves the accuracy and robustness of the Class D amplifier's nonlinear model, laying the foundation for applications such as efficient digital predistortion.

[0092] Example 2

[0093] An embodiment of the present invention provides a method for modeling the nonlinear behavior of a Class-D power amplifier (Class-D PA) based on a residual recurrent unit (RRU) network. This embodiment uses the Texas Instruments TPA3116D2D Class-D PA as the modeling object, aiming to accurately capture its nonlinear memory effect under OFDM signal excitation. A finite impulse response filter (FIR filter) is used as the filter.

[0094] Experimental environment and data collection:

[0095] This example uses an Orthogonal Frequency Division Multiplexing (OFDM) signal source with a center carrier frequency of 10 kHz. This signal is generated using an arbitrary waveform generator and input to a TPA3116D2D power amplifier. Signal data is collected synchronously at the amplifier's input and output for a total of 10 seconds, with a sampling rate of 112 kHz.

[0096] Thus, a total of 1,120,000 complex sample points were collected, and the collected amplifier input signal sequence is recorded as x ( n ), the actual output signal sequence is recorded as y 0( n ).

[0097] Specifically, such as Figure 1 、 Figure 2 As shown, the steps of the embodiment of the present invention are as follows:

[0098] S1. Divide the data set and initialize the algorithm

[0099] First, the 1,120,000 sets of input / output data pairs collected ( x ( n ), y 0( n )) is divided into training set, validation set and test set in the ratio of 8:1:1.

[0100] When the network is constructed, the hidden state (I / Q hidden state) of the RRU layer included in the model is initialized. h iq and envelope hidden state h env ) status information, initialized to a zero vector.

[0101] S2, generate a length of M Memory Window X M ( k )

[0102] The current time step sample x ( k ) and before M The historical sample information forms a memory window, which is used to characterize the short-term dynamic change characteristics of the input signal. In order to capture the memory effect of the power amplifier, it is necessary to use the historical input information. Before the entire sequence processing cycle begins, the original input sequence is pre-processed. x Create a memory window of all time steps, each time step k Memory Window X M ( k )Include x ( k ), x ( k -1),..., x ( k - M )common M +1 sample, M +1 complex-valued sample is used as input to the FIR filter to extract time domain features.

[0103] Specifically, this embodiment sets the memory depth M =15, in the processing time step k Input sample x ( k ), the current sample is combined with the previous 10 historical samples into a memory window X M ( k ):

[0104]

[0105] The memory window X M ( k ) is a M +1=16 complex sample vectors that represent the input signal at time step k To improve computational efficiency, corresponding memory windows can be generated for all time steps before the entire sequence processing begins.

[0106] S3. Frequency domain feature extraction based on FIR filter

[0107] Process the input signal X using an FIR filter with adjustable weights M ( k ),get L The complex FIR filter output is used to extract the characteristics of the signal in different frequency bands.

[0108] Specifically, in order to get the memory window X from the time domainM ( k ) to extract richer dynamic and frequency-related features. This embodiment uses a set of learnable parallel FIR filters for processing, and the coefficient information of the FIR filters is set as learnable network parameters. Set the number of parallel filters L =5, L A complex-valued FIR filter is implemented by two independent fully connected layers (linear layers), one for the real part and one for the imaginary part, without nonlinear activation. M ( k ) is decomposed into the real part X MI ( k ) and the imaginary part X MQ ( k ), are real number vectors with dimension 16 respectively.

[0109] Real filter output calculation: Through a first linear transformation layer, X M ( k )'s real part X MI ( k ) input to L FIR filter to get Y FIR,I ( k ), which is calculated as follows:

[0110]

[0111] in, is the learnable weight matrix, is the learnable bias vector.

[0112] Imaginary filter output calculation: Through a second linear transformation layer, X M ( k )'s imaginary part X MQ ( k ) input to L FIR filter to get Y FIR,Q ( k ), which is calculated as follows:

[0113]

[0114] in, is the learnable weight matrix, is the learnable bias vector.

[0115] This embodiment uses the back propagation algorithm to learn weights and , which enables these five filters to adaptively extract the most useful signal dynamic features for nonlinear modeling. and The weight matrix is ​​learned to effectively model the complex coefficients of each parallel FIR filter, so that each FIR filter can produce a unique dynamic effect on the different frequency components of the input signal without the need to preset fixed filter characteristics, thereby providing X M ( k) dynamic response characteristics.

[0116] S4. Calculate the phase normalization factor r ( k )

[0117] In order to make the model focus on learning the amplitude and relative phase distortion rather than the absolute phase, the features need to be phase normalized. Therefore, the complex conjugate of the current time step sample and its amplitude are calculated to calculate the phase normalization factor r ( k ).

[0118] Specifically, calculate the input sample of the current time step x ( k ) is the phase normalization factor r ( k ), which is calculated as follows:

[0119]

[0120] in, yes x ( k ), yes x ( k ) amplitude information.

[0121] Furthermore, when When it approaches zero, a small constant can be set to avoid calculation instability. ϵ (e.g. 10 −8 ) as the lower limit of the denominator. This factor r ( k )'s physical meaning is to carry x ( k )’s negative phase information.

[0122] S5. Construct composite input signal X F ( k )

[0123] The sample of the current time step x ( k ) is integrated with the information output by L complex FIR filters to provide the RRU unit with a rich input signal X containing the current instantaneous signal and historical frequency domain features. F ( k), thereby providing the RRU network with more information about the input signal, enabling it to learn more data feature information.

[0124] Specifically, the current instantaneous sample x ( k ) (decomposed into real and imaginary parts) and obtained in S3 L = 5 FIR filter outputs (Y FIR,I ( k ) and Y FIR,Q ( k )) to combine and splice to form a richer composite input vector , the formula is:

[0125]

[0126] The vector The dimension is 2+5+5=12.

[0127] S6, X F ( k ) Apply phase normalization

[0128] X F ( k ) is rotated to the phase of x ( k ) to achieve phase normalization of features.

[0129] Specifically, the phase normalization factor calculated in S4 is r ( k ) applied to the composite input vector .because is a real vector and must be converted to complex form before rotation.

[0130] In this embodiment, The phase is rotated to x (k) phase alignment to achieve composite input eigenvector The phase normalization process of the composite input vector is performed by [real( x ( k )), Y FIR,I ( k )], the imaginary part consists of [imag( x ( k )),Y FIR,Q ( k )], and this complex vector is combined with r ( k ) to obtain the phase-normalized eigenvector The calculation formula is:

[0131]

[0132] The above operation makes the phase of all features consistent with the current input x ( k ) phase alignment, which simplifies the subsequent RRU network learning task.

[0133] In this embodiment, X F ( k ) Apply the phase normalization factor r ( k ), ensuring that the features entering the RRU unit are phase-normalized, so that the RRU focuses on learning the relative relationship between amplitude information and phase changes rather than the absolute phase, thereby improving the accuracy of the RRU network's nonlinear fitting of the power amplifier.

[0134] S7, RRU network status update

[0135] In X F ( k ) input, calculate the output and hidden state of multiple RRU layers, and normalize the phase feature vector Input into the RRU network.

[0136] Specifically, this embodiment adopts a stack structure including multiple RRU layers, and each RRU unit contains an I / Q hidden state h iq and an envelope hidden state h env , the dimensions are all set to 32. For each RRU unit in the network, the output and hidden state of the RRU layer are calculated. j RRU layers, at time step k The status update process includes the following:

[0137] S701, I / Q hidden state renormalization:

[0138] Renormalize the historical values ​​of the I / Q hidden state of the corresponding layer of the RRU unit to ensure that its phase is consistent with the complex value sample of the current time step x ( k ) to maintain synchronization, thereby achieving the robustness of the entire network to absolute phase.

[0139] a1. Calculate the relative rotation factor; if the time step k >1, calculate a relative rotation factor Δ r ( k ), the factor represents the current time step input x ( k ) phase and the previous time step input x (k −1)Relative change of phase.

[0140] For the j RRU layer, the hidden state of the previous moment Perform phase compensation to synchronize it with the current input phase. Calculate the relative rotation factor, which is calculated as follows:

[0141] Δ r ( k ) = r ( k )·r * ( k −1)

[0142] in, is the phase normalization factor of the previous time step r ( k -1), if the time step k =1, then Δ r ( k ) = 1+ j ·0.

[0143] a2. Apply rotation; the historical value of the I / Q hidden state of the current layer RRU unit and the relative rotation factor Δ r ( k ) to perform complex multiplication to obtain the renormalized I / Q hidden state , for the j RRU layers, Apply the rotation, that is:

[0144] .

[0145] S702, RRU unit core update:

[0146] The RRU core unit adopts a residual connection mechanism to update its combined hidden state, which utilizes two key learnable parameter vectors: a contribution control parameter Z (usually initialized to a zero vector at the beginning of training), and a scaling control parameter vector C.

[0147] The renormalized I / Q hidden state and envelope hidden state , combined with the input of the current layer RRU unit (for the first layer RRU unit, its input is the normalized feature vector The real and imaginary parts of the vector are concatenated; for the RRU units in the subsequent layers, the input is the updated I / Q hidden state of the RRU units in the previous layer) for joint update.

[0148] The joint update process includes:

[0149] b1. Construct a joint input vector; concatenate the current input of the RRU unit and the renormalized I / Q hidden state and envelope hidden state , forming a joint input vector .

[0150] b2. Use a double-layer activation function to calculate the update vector; use a double-layer activation function to update the vector from the joint input vector Calculate an update vector v( k ), realize deep nonlinear mapping, update v( k ) is calculated as follows:

[0151] The output of the first layer activation function:

[0152]

[0153] The output of the second layer activation function:

[0154]

[0155] in, and is the learnable weight matrix, and is the learnable bias vector.

[0156] S703, Joint Status Update:

[0157] Based on the update vector v( k ) and the complete hidden state of history , update the complete hidden state h(k) of the current layer, and the update follows the following core formula:

[0158]

[0159] in, is the complete hidden state of the previous step, composed of the I / Q hidden state and envelope hidden state Spliced ​​together; is the tanh() activation function; C is a learnable parameter, and its initial value can be set to σ (C) Uniformly distributed in [0,1], Z is a learnable parameter whose initial value is all zero; ⊙ is element-wise multiplication.

[0160] S704, State Decomposition and Storage:

[0161] The updated complete hidden state h( k ) is split into the I / Q hidden state h of the current layer iq (k ) and the envelope hidden state h env ( k ), and stored as the input of the next time step, and at the same time as the input of the next layer of RRU units or the input of the output layer.

[0162] S8, predicted phase normalized output y '( k )

[0163] Based on the updated I / Q hidden state of the last recurrent unit, a phase-normalized complex-valued output is predicted y ′( k ).

[0164] Specifically, the final prediction result is extracted from the internal representation of the network, and the result is still phase normalized when output. The process uses the output layer of the RRU network to update the I / Q hidden state of the last layer of RRU units. As input, it is mapped into a phase-normalized complex-valued output through two independent linear layers. y ′(k), which is calculated as follows:

[0165]

[0166]

[0167] in, and is the learnable weight matrix, and is the learnable bias vector.

[0168] S9, inverse phase normalization

[0169] Using the phase normalization factor r ( k ) for phase normalized complex output y ′( k ) to perform inverse phase normalization to obtain the output of network prediction y ( k ).

[0170] Specifically, the prediction result after phase normalization is y ′( k ) is restored to the original phase space to obtain the final output with the correct phase y ( k ).

[0171] The phase normalization factor calculated in S4 during the inverse phase normalization process r ( k )'s complex conjugate r∗ ( k ), the phase normalized complex value output y ′( k ) is rotated in the opposite direction to obtain

[0172] y ( k ) = y ′( k )· r * ( k )

[0173] in, yes r ( k ) is used to convert y ′( k ) is rotated from the normalized phase reference frame back to the phase reference frame of the original signal.

[0174] S10, loss function and weight update

[0175] According to the output y ( k ) and actual amplifier output y 0( k ), and use the back propagation algorithm to update the weight information of the RRU layer.

[0176] Specifically, the mean square error (MSE) is used as the loss function of the RRU network to measure the prediction output y pre ( n ) and the actual output of the amplifier y 0( n ), which is defined as:

[0177]

[0178] in, y ( n ) represents the actual signal value obtained by actual sampling, y pre ( n ) is the signal value predicted by the model, and the square and mean of the difference between the true and predicted values ​​are used as the loss function of the neural network.

[0179]

[0180] in, Nbatchis the size of a mini-batch during training and is set to 512 in this embodiment. The Adam optimizer is used with a learning rate of 0.001. The backpropagation algorithm is used to calculate the gradient of the loss function with respect to all learnable parameters in the network (such as FIR filter weights, RRU internal weights, and output layer weights) and update these parameters.

[0181] Furthermore, to determine the weight vector that minimizes the error, the gradient descent method starts with an initial weight vector and gradually reduces the error by continuously adjusting the weight vector along the direction of steepest descent on the error surface. Each adjustment step finds the direction of steepest descent by calculating the partial derivatives of the error function with respect to each weight and threshold. These partial derivatives form the gradient of the error function with respect to the weights. Using this gradient information, the network weights are gradually adjusted until the error between the network output and the target output is minimized.

[0182] S11. Network training and stopping conditions

[0183] The RRU network is trained on the training set. When the loss function in the training set is continuously less than the threshold, the RRU network stops training. If it is not reached, S2-S10 are repeated until the training times are completed.

[0184] Specifically, in this embodiment, the entire network model is iteratively trained on the training set, and after each training cycle (epoch), the NMSE of the model is calculated on the validation set to monitor performance.

[0185] The judgment basis for stopping RRU training on the training set is set as:

[0186] When the loss on the validation set does not decrease for five consecutive epochs, the early stopping mechanism is triggered and training stops. Alternatively, training stops when the number of training epochs reaches a preset maximum (e.g., 200 epochs).

[0187] Furthermore, in this embodiment, when the MSE loss on the validation set is less than 10 −6 When , the model is considered to have fully converged, and training can be stopped to save the model parameters with the best performance on the validation set.

[0188] When the mean square error of the RRU network reaches 10 -6 Or if this performance standard is not achieved within the prescribed number of training sessions, training will be stopped to prevent overtraining.

[0189] S12. Network testing and performance evaluation

[0190] The trained RRU network is applied to the test set, and the normalized mean square error is used as the evaluation metric of the model.

[0191] Specifically, the best model saved during the training process is used to evaluate performance on a test set that has never been used in training. The normalized mean square error (NMSE) is used as the final evaluation indicator for RRU network performance, and its calculation formula is:

[0192] Using NMSE, the calculation formula is:

[0193]

[0194] in, y 0( n ) is the actual measured signal data, y pre ( n ) is the model output signal data, N test is the total number of samples in the test set (112,000).

[0195] Low NMSE values ​​(e.g., below -30dB) demonstrate that the proposed modeling method can accurately replicate the nonlinear behavior of the TPA3116D2D amplifier. Low NMSE values ​​indicate that the amplifier nonlinear model accurately fits the amplifier's nonlinear behavior. The error between the actual output signal and the model-predicted signal is small, indicating that the amplifier's nonlinear characteristics are well modeled and the model can accurately predict the amplifier's actual output.

[0196] Furthermore, the present invention also provides a nonlinear behavior modeling system for a Class D power amplifier based on an RRU network. The system has a program module corresponding to any of the above steps, and when the program module is running, it executes the steps in the nonlinear behavior modeling method for a Class D power amplifier based on an RRU network.

[0197] Specifically, the modeling method is implemented through software programming. The modeling system includes a data preprocessing module, a memory window generation module, an FIR feature extraction module, a phase normalization module, an RRU network module, an inverse phase normalization module, a training control module and a performance evaluation module. Each module works together and executes the above-mentioned RRU network-based Class D power amplifier nonlinear behavior modeling method when running on a computer or dedicated hardware (such as FPGA, DSP).

[0198] This invention discloses a method and system for modeling the nonlinear behavior of Class D power amplifiers based on an RRU network. This method addresses modeling challenges unique to Class D amplifiers, such as switching modulation distortion, strong memory effects, and complex harmonics. The method first uses a complex finite impulse response (FIR) filter with adjustable weights to extract block-based dynamic features from the input complex signal. The dynamic features are then integrated with the current input and processed using an internal reference normalization factor. The normalized features are then fed into an improved RRU network, which deeply learns the signal's nonlinear temporal dynamics through cyclic state alignment and a residual-based update mechanism. Finally, through the output layer and reference restoration steps, the Class D amplifier's output behavior is accurately predicted. By combining the advantages of adaptive FIR filtering, internal reference normalization, and the RRU network, the method significantly improves the accuracy and robustness of the Class D amplifier's nonlinear model, laying the foundation for applications such as efficient digital predistortion. It also accurately describes and predicts the complex nonlinear behavior of Class D amplifiers, providing a solid foundation for improving their performance and reliability in demanding applications such as sonar.

[0199] In describing the present invention, it should be understood that the embodiments of the present invention describe in detail the specific implementation process of the present invention method, but the present invention is not limited to the above embodiments. Within the scope of the present invention, those skilled in the art may adjust hyperparameters such as the memory depth M, the number of FIR filters L, the number of RRU layers, and the number of hidden units, or apply the present invention to other types or models of power amplifiers. Such variations are intended to be within the scope of the present invention.

[0200] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. Throughout the description of this application, "plurality" means two or more, unless otherwise specifically defined.

[0201] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A nonlinear behavior modeling method for a Class D power amplifier based on an RRU network, characterized in that: The following steps are involved: S1. Divide the data set and initialize the algorithm; divide the input and output data of the power amplifier into training set, verification set and test set, and initialize the state information of the RRU layer in the network; S2, the generated length is M Memory Window X M ( k );The current time step sample x ( k ) and before M The historical sample information forms a memory window, which is used to characterize the short-term dynamic change characteristics of the input signal; S3, frequency domain feature extraction; Use the filter to process the input signal X M ( k ), extract the characteristics of the signal in different frequency bands; S4. Calculate the phase normalization factor r ( k ); Calculate the complex conjugate and amplitude of the current time step sample to calculate the phase normalization factor r ( k ); S5. Construct composite input signal X F ( k ); the sample of the current time step x ( k ) is integrated with the information output by the filter to provide a composite input signal X for the RRU unit F ( k ); S6, against X F ( k ) Apply phase normalization; X F ( k ) is rotated to the phase of x ( k ) phase alignment to achieve phase normalization of features; S7, update RRU network status; F ( k ) input, calculate the output and hidden state of multiple RRU layers; S8, based on the updated I / Q hidden state of the last layer of recursive units, predict the phase normalized complex value output y ′( k ); S9. Using phase normalization factor r ( k ) for phase normalized complex output y ′( k ) to perform inverse phase normalization to obtain the output of network prediction y ( k ); S10, use mean square error as the loss function of RRU network; according to the output y ( k ) and actual amplifier output y 0( k ), update the weight information of the RRU layer; S11, train the RRU network on the training set. When the loss function in the training set is continuously less than the threshold, the RRU network stops training. If it is not reached, repeat S2-S10 until the training times are completed; S12, RRU network testing: Apply the trained RRU network to the test set.

2. The nonlinear behavior modeling method of a Class D power amplifier based on an RRU network according to claim 1, characterized in that: In S2, before the entire sequence processing cycle begins, the original input sequence is pre-processed. x Create a memory window of all time steps, each time step k Memory Window X M ( k )Include x ( k ), x ( k -1),..., x ( k - M )common M +1 sample, M +1 complex-valued sample is used as the input of the filter to extract time domain features.

3. The nonlinear behavior modeling method of a Class D power amplifier based on an RRU network according to claim 1, characterized in that: In S3, the filter-based frequency domain feature extraction includes: use L filter pair X M ( k ) to perform filtering to extract the characteristics of the signal in different frequency bands, wherein the coefficient information of the filter is set as a learnable network parameter, and the filtering output is realized through two fully connected layers; Real filter output calculation: Through a first linear transformation layer, X M ( k )'s real part X MI ( k ) input to L The filter gets Y FIR,I ( k ), the calculation formula is: in, is the learnable weight matrix, is the learnable bias vector; Imaginary filter output calculation: Through a second linear transformation layer, X M ( k )'s imaginary part X MQ ( k ) is input into L filters to obtain Y FIR,Q ( k ), the calculation formula is: in, is the learnable weight matrix, is the learnable bias vector.

4. The method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network according to claim 1, wherein: In S4, the current time sample is calculated x ( k ) is the phase normalization factor r ( k ), which is calculated as follows: in, yes x ( k ), yes x ( k ) amplitude information.

5. The method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network according to claim 1, wherein: In S5, the current time sample and the filter output Y FIR,I ( k ) and Y FIR,Q ( k ) combination to obtain the composite input vector X F ( k ), whose value is: ； In the above S6, Applying a phase normalization factor r ( k ),Will The phase is rotated to x ( k ) phase alignment to achieve composite input eigenvector The phase normalization processing is calculated as follows: 。 6. The method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network according to claim 1, wherein: In S7, the output and hidden state of the RRU layer are calculated, and the following cyclic state update operations are performed for each RRU unit in the network, including: S701, I / Q hidden state renormalization: Calculate the relative rotation factor; if the time step k >1, calculate a relative rotation factor Δ r ( k ), the factor represents the current time step input x ( k ) phase and the previous time step input x ( k −1) The relative change in phase is calculated as: D r ( k ) = r ( k )·r * ( k −1) in, is the phase normalization factor of the previous time step r ( k -1), if the time step k =1, then Δ r ( k )= 1+ j 0; Apply rotation; the historical value of the I / Q hidden state of the current layer RRU unit With the relative rotation factor Δ r ( k ) to perform complex multiplication to obtain the renormalized I / Q hidden state ,Right now: ； S702, RRU unit core update: Construct a joint input vector; concatenate the current input of the RRU unit and the renormalized I / Q hidden state and envelope hidden state , forming a joint input vector ; The update vector is calculated by using a double-layer activation function; the update vector is obtained from the joint input vector by the double-layer activation function. Calculate an update vector v( k ), realizing deep nonlinear mapping, the update to v( k ) is calculated as follows: The output of the first layer activation function: The output of the second layer activation function: in, and is the learnable weight matrix, and is the learnable bias vector; S703, Joint Status Update: Based on the update vector v( k ) and the complete hidden state of history , update the complete hidden state h(k) of the current layer, and the update follows the following core formula: in, is the complete hidden state of the previous step, is the tanh() activation function, C is the learnable parameter, Z is the learnable parameter, and ⊙ is the element-wise multiplication; S704, State Decomposition and Storage: The updated complete hidden state h( k ) is split into the I / Q hidden state h of the current layer iq ( k ) and the envelope hidden state h env ( k ), and stored as the input of the next time step, and at the same time as the input of the next layer of RRU units or the input of the output layer.

7. The method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network according to claim 1, wherein: In S8, the final prediction result is extracted from the internal representation of the network, and the result is still phase normalized when output. The process uses the output layer of the RRU network to update the I / Q hidden state of the last layer of RRU units. As input, it is mapped into a phase-normalized complex-valued output through two independent linear layers. y ′( k ), which is calculated as follows: in, and is the learnable weight matrix, and is the learnable bias vector.

8. The method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network according to claim 1, wherein: In the S9, the phase normalization factor calculated in S4 is used in the inverse phase normalization process. r ( k )'s complex conjugate r ∗ ( k ), the phase normalized complex value output y ′( k ) is rotated in the opposite direction to obtain y ( k ) = y ′( k )· r * ( k ) in, yes r ( k ) is used to convert y ′( k ) Rotate from the normalized phase reference frame back to the phase reference frame of the original signal; In S10, the mean square error is used as the loss function of the RRU network, which is defined as: in, y ( n ) represents the real signal value obtained by actual sampling, y pre ( n ) is the signal value predicted by the model, and the square and mean of the difference between the true and predicted values ​​are used as the loss function of the neural network.

9. The method for modeling nonlinear behavior of a Class D power amplifier based on an RRU network according to claim 1, wherein: In S12, NMSE is used as the evaluation index of RRU network performance, and its calculation formula is: in, is the actual measured signal data, y pre ( n ) is the model output signal data, N is the total number of samples.

10. A nonlinear behavior modeling system for a Class D power amplifier based on an RRU network, characterized in that: When the system is running, the steps in the RRU network-based class D power amplifier nonlinear behavior modeling method according to any one of claims 1 to 9 are executed.

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