A parameter-efficient complex-valued convolutional neural network digital predistortion model

Abstract

The application discloses a digital predistortion model design of complex neural network, which can realize the linearization of a power amplifier with higher parameter efficiency. Neural networks have been widely used in digital predistortion (DPD) technology for compensating nonlinear distortion in power amplifiers (PAs). However, existing models mainly adopt real-valued neural networks (RVNN), which often process I / Q components separately, destroying the algebraic structure of complex signals, and have a large number of model parameters. This paper focuses on complex-valued neural networks (CVNN) and proposes a parameter-efficient complex-valued convolutional neural network (CVCNN) model. All parameters of the model are complex-valued, and the calculation is completed in the complex number domain. We designed an enhanced phase-preserving complex time (EPCT) input matrix for the model. In addition, this paper evaluates commonly used complex activation functions and proposes a complex envelope-dependent (CED) activation function more suitable for DPD tasks based on the physical interpretability of power amplifiers. Experiments show that the proposed model significantly reduces the number of parameters while achieving excellent linearization performance.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a design method and application of a parameter-efficient complex-valued convolutional neural network model for digital predistortion, and to an enhanced phase-preserving complex-valued delay matrix and a more suitable complex envelope-dependent activation function for DPD tasks. Background Technology

[0002] Modern communication systems constantly demand higher data transmission rates, pushing power amplifiers (PAs) to higher power states to accommodate expanded signal bandwidths, resulting in more pronounced nonlinear behavior. With the development of digital signal processing technology, digital predistortion technology has become a key technique widely used to counteract the nonlinear distortion of PAs.

[0003] Traditional digital predistortion models are primarily polynomial models based on Volterra series. Volterra series are often used to describe the behavior of nonlinear systems because they can capture the system's memory effect. Truncation models such as MP and GMP significantly reduce their complexity. Commonly used traditional models also include Dynamic Deviation Reduction (DDR) models, which are derived by separating static and dynamic nonlinearities and substituting the dynamic deviation into a truncated Volterra formula. However, the polynomial bases of these models often exhibit high correlations, making it difficult to improve their modeling performance. Furthermore, when these models are extended to accommodate wider bandwidths and higher frequencies, their complexity increases exponentially, posing challenges for practical deployment.

[0004] To address the aforementioned issues, inspired by artificial intelligence (AI) technologies in broadband communications, researchers have explored neural network-based DPD models. Neural network models possess powerful nonlinear fitting and adaptive learning capabilities, providing a more scalable and adaptable paradigm for representing nonlinear systems with memory effects. The most typical example is the deep neural network model that uses the real-valued time delay (RVTD) matrix and its augmented form as input. To further reduce computational complexity, research has proposed convolutional neural network models based on the RVTD matrix. Adding cross-memory terms composed of in-phase and orthogonal (I / Q) components to the RVTD matrix has led to the ARCTCNN model, which exhibits better performance and accuracy. However, these neural network models are all real-valued networks, often splitting the complex data of PA into I and Q channels for processing. This may disrupt phase correlation or cause phase distortion, leading to performance loss.

[0005] In recent years, research on complex neural networks (CVNNs) has become increasingly sophisticated, and more and more CVNN models are being applied to various complex signal domains. CVNNs directly process complex signals using complex weights, preserving the algebraic structure of complex signals. They can directly learn the amplitude and phase correlations of complex signals, making them theoretically the most compatible model for wave-related information processing. Information transmitted in communication systems is often in the form of complex-valued electromagnetic waves, and the output signal after power amplification remains complex-valued. Furthermore, the nonlinear distortion characteristics of power amplifiers (PAs) often manifest as gain compression and phase distortion, which naturally correspond to the phase rotation and amplitude scaling characteristics of complex multiplication. Moreover, compared to RVNNs, which use two independent real parameters to represent the real and imaginary parts, CVNNs only require one complex parameter to couple the real and imaginary parts, resulting in higher parameter efficiency. This allows CVNNs to capture the intrinsic correlation between amplitude and phase more effectively with fewer parameters. The reduction in model parameters often translates to lower computational complexity and memory costs, reducing power consumption in practical deployments, which is also an important consideration for digital phase detection (DPD) tasks. Therefore, we can expect complex neural networks to have advantages in modeling the behavior of power amplifiers and digital predistortion. However, only a few studies on complex neural networks in DPD tasks have been found so far, and most of them focus on network layer stacking or architecture optimization. Existing complex activation functions (such as split-tanh, cCardioid) are not fully adapted to the amplitude and phase distortion mechanism of PA.

[0006] Therefore, how to design a complex domain DPD model that can preserve the algebraic structure of complex signals, explicitly model the amplitude-phase coupling relationship, and has an efficient activation function is a problem that urgently needs to be solved in current technology. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention focuses on two-dimensional complex numerical convolutional neural networks (CVNNs), expanding the research of CVNNs in the field of power amplifier distortion (DPD) and solving the technical problems of phase information loss and inability to fully utilize the inherent advantages of the complex domain caused by the separation of I / Q processing in existing real-valued neural network DPD models. First, considering the difference between the real and complex domains, an enhanced phase-preserving complex-valued time-delay (EPCT) matrix is ​​introduced. This matrix preserves the algebraic structure and amplitude-phase coupling of the complex signal while explicitly embedding amplitude-phase nonlinearity into the network input. Second, a more suitable activation function for DPD, called the complex-valued envelope correlation (CED) activation function, is introduced, which effectively represents the amplitude-phase distortion mechanism of the power amplifier. Third, a parameter-efficient complex-valued CNN architecture is proposed, which uses the proposed EPCT matrix and CED activation function to improve nonlinear modeling performance. The proposed EPCTCNN model can fully utilize the advantages of CVNNs, achieving excellent pre-distortion performance with high parameter efficiency. To achieve the above objectives, the technical solution of this invention is as follows:

[0008] S1: Generate the power amplifier input signal on the PC, collect the output signal after power amplifier using the experimental platform, and use the experimental platform to execute the iterative learning control (ILC) algorithm to obtain the ideal predistortion signal;

[0009] S2: Obtain the input baseband signal of the power amplifier and construct a complex numerical input matrix based on the complex domain processing paradigm;

[0010] S3: Construct a two-dimensional complex convolutional neural network (CVCNN) model, which includes two-dimensional complex convolutional layers, complex activation function layers, and fully connected layers. All layer parameters and operations are performed in the complex domain.

[0011] S4: Input the proposed complex numerical input matrix and the ideal predistortion signal into the two-dimensional complex convolutional neural network model for offline training to obtain the weight parameters;

[0012] S5: Configure the weight parameters to the digital predistortion module and use the digital predistortion module to perform digital predistortion processing;

[0013] S6: Evaluate the difference between the PA output signal and the input signal after digital predistortion processing to obtain the real-time loss value;

[0014] S7: Calculate the weight gradient based on the real-time loss value and perform backpropagation to update the weight parameters of the digital predistortion module, thereby realizing the real-time adaptive adjustment of the digital predistorter and completing the linearization of the power amplifier.

[0015] Furthermore, in one embodiment of the present invention, the complex-valued input matrix is ​​an enhanced phase-preserving complex-valued time delay (EPCT) matrix, which aims to preserve the algebraic structure and amplitude-phase coupling relationship of the complex signal and explicitly embed the nonlinear characteristics of the PA into the network input.

[0016] Furthermore, in one embodiment of the present invention, the complex activation function layer adopts a complex envelope-dependent activation function (CED) specifically designed for DPD tasks to better fit the physical characteristics of PA (AM / AM and AM / PM distortion).

[0017] Furthermore, in one embodiment of the present invention, the CVCNN model operates entirely in the complex domain, directly processing complex signals using complex weights and utilizing the complex convolution formula. Perform calculations to more effectively capture the intrinsic correlation between amplitude and phase.

[0018] The beneficial effects of this invention include:

[0019] 1. The CVCNN model proposed in this invention processes signals directly in the complex domain, avoiding the phase correlation disruption caused by splitting complex data into I / Q dual-channel processing, and preserving the algebraic structure of complex signals.

[0020] 2. The CVTD and EPCT input matrices proposed in this invention reduce the difficulty for the network to implicitly learn the amplitude and phase structure from the original data by introducing amplitude and phase preservation terms, thereby enhancing the model's ability to express the nonlinear features of PA.

[0021] 3. The CED activation function proposed in this invention is designed based on the physical distortion mechanism of PA. Compared with the traditional complex activation function, it can more accurately fit the amplitude compression and phase rotation characteristics of PA, thus improving the linearization performance. Attached Figure Description

[0022] Figure 1 The diagram shows the proposed CVCNN model, which uses the proposed EPCT matrix as input and the proposed CED activation function for activation.

[0023] Figure 2 The experimental testing platform used in this embodiment.

[0024] Figure 3 The power spectrum comparison diagram of the linearization experiment of the model proposed in this invention and the existing model is provided as an example. Detailed Implementation

[0025] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0026] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] Example 1

[0029] This example provides a design method for a digital predistorter based on a complex convolutional neural network (CVCNN), the core of which lies in constructing a neural network architecture in the entire complex domain. The specific process is as follows: First, for the complex baseband signal of PA, instead of I / Q separation, an input matrix that preserves complex characteristics is constructed; second, a deep network containing complex convolutional layers is designed, where the weight parameters, inputs, outputs, and intermediate feature maps are all complex values; finally, nonlinearity is introduced through a specific complex activation function to output the predistorted signal. Compared to real-valued models such as RVTDCNN and ARCTCNN, the CVCNN described in this embodiment uses a complex parameter to couple the real and imaginary parts, resulting in higher parameter efficiency and the ability to directly learn the amplitude and phase correlation of complex signals, theoretically making it most compatible with wave-related information processing.

[0030] Example 2

[0031] This embodiment further defines the method described in Embodiment 1, focusing on the construction of the complex-valued input matrix. Although RVTD and ARCT inputs perform well in RVNNs, they are inherently designed for real-number processing. Directly applying them to the CVNN framework cannot fully utilize the inherent advantages of complex-domain learning. Particularly noteworthy is that the I / Q separation mechanism in RVTD and ARCT may disrupt the algebraic structure of complex signals, weakening the explicit modeling of amplitude-phase coupling—a fundamental characteristic of the nonlinearity of power amplifiers. Therefore, when migrating to CVNNs, the input representation must be redesigned to both conform to the characteristics of complex-domain operations and accurately reflect the physical behavior of the power amplifier. This embodiment proposes an enhanced phase-preserving complex-valued time delay (EPCT) input matrix, represented as follows:

[0032]

[0033] in express Units and The delayed term. It is the memory depth of the DPD model.

[0034] As can be seen, the proposed matrix consists of four characteristic terms, and the interpretation of each characteristic term is as follows:

[0035] First, in the complex domain processing, it is not necessary to decompose the complex signal into I / Q components. Therefore, the basis functions commonly used in traditional DPD models... These can be directly used as key features in constructing the input matrix. As the principal analytical component, it retains the original complex direction, forming the basis for linear gain modeling.

[0036] Secondly, conjugate terms frequently appear in the basis function construction of traditional models, such as in the DDR model. It captures phase asymmetry and mirror interference. A conjugate term is introduced. By introducing extensive linear representation capabilities, the network's ability to model mismatch effects and asymmetric distortions that may occur under real-world broadband operating conditions is enhanced.

[0037] Third, we choose To simulate higher-order intermodulation components in PA distortion, where It is a nonlinear order. These are also the main basis functions in the classic MP and GMP models, explicitly capturing amplitude-dependent modulation effects while maintaining phase consistency. Although odd-order terms, especially the third-order nonlinear components, constitute the main source of distortion in PA, models containing even-order terms exhibit excellent linearization performance. Therefore, we include them in the matrix. and .

[0038] Overall, the proposed EPCT matrix constitutes a set of minimal and non-redundant complex-valued features, ensuring that the phase does not deviate from the initial phase of the signal. This design allows subsequent complex-valued convolutional layers to focus more on learning memory effects and cross-channel interactions, without needing to implicitly reconstruct the amplitude-phase coupling structure from the I / Q separation representation. Therefore, this input matrix provides a structurally coherent and physically driven underlying representation for digital predistortion modeling based on complex-valued neural networks.

[0039] Example 3

[0040] This embodiment further defines the method described in Embodiment 1, with a focus on the design of the complex activation function.

[0041] Most existing activation functions are designed for specific problems and are not necessarily suitable for DPD tasks. In this invention, we mainly tested three existing activation functions: split-tanh (abbreviated as ctanh), complex cardioid (abbreviated as cCard), and phase-preserving tanh (abbreviated as pptanh), and their expressions are as follows:

[0042]

[0043]

[0044]

[0045] The split-tanh function is simple to implement, but it treats the real and imaginary parts of the complex signal as two independent real numbers for scaling, thus compromising the phase integrity of the signal. While the complex cardioid form is beneficial for signal expansion, its gain depends on the absolute phase of the input. This is inconsistent with the fact that the nonlinear characteristics of PA depend primarily on amplitude. While phase-preserving tanh best fits the nonlinear characteristics of PA, it forces the phase to remain unchanged, leaving phase changes entirely to be learned by linear layers, thus increasing the learning burden on the network. To address these limitations, we propose a novel complex activation function more suitable for DPD tasks, called the Complex Envelope Dependent Activation Function (CED):

[0046]

[0047] in and All of these are learnable parameters. Controlling the linear gain and reference phase offset, It determines the shape and direction of nonlinear distortion, and This modulates the sensitivity to changes in the envelope.

[0048] Example 4

[0049] This embodiment further defines the method described in Embodiment 1, focusing on two-dimensional complex convolution operations. The proposed CVCNN model consists of two-dimensional convolutional layers, hidden fully connected layers, and output fully connected layers. CVCNN contains only a single complex two-dimensional convolutional layer, with three... Macro-convolutional kernel; containing two fully connected layers: hidden layer ( Construct a high-dimensional nonlinear basis space, and output the layer ( This generates the final 1D complex signal. The complexity is mainly achieved through... Layer size is adjusted and measured by real-valued equivalent parameters and the number of floating-point operations. The formula for calculating complex convolution is defined as: This operation preserves the mathematical structure of complex-valued amplitude and phase. Compared to RVNN, which uses two independent real-part parameters, CVNN leverages the characteristics of complex number operations to capture the intrinsic correlation between amplitude and phase more effectively with fewer parameters, reducing computational complexity and memory costs.

[0050] Example 5

[0051] Based on the foregoing embodiments, this embodiment provides the following specific embodiments:

[0052] We built such as Figure 1 The experimental testing platform used in the digital predistortion system shown is as follows: Figure 2 As shown. The system's sampling rate is 491.52MHz. The excitation signal is a 100MHz OFDM signal conforming to the 3GPP 5G New Radio specification, with a peak-to-average power ratio adjusted to 7.8 dB. This signal contains 140,352 sampling points.

[0053] To compare performance differences between different input matrices, the RVTDCNN and ARCTCNN models were modified to match the proposed CVCNN while retaining the real-valued structure. ARVTDNN was also used as a comparison model, with its input matrix being RVTD. The memory depth of all models was set to a specific value.

[0054] The validation experiments consist of two parts: behavioral modeling and linearization experiments. Behavioral modeling uses the original input signal and an ideal predistortion signal obtained through an Iterative Learning Control (ILC) algorithm. The modeling performance of each model is evaluated by calculating the root mean square error (NMSE) between the ideal signal and the model's predicted output. Finally, the output generated by each model is fed into a power amplifier, and the linearization performance is measured by calculating the NMSE between the power amplifier output and the original input.

[0055] First, we conduct performance tests on behavior modeling. Half of the signal sample points are used for training to extract model coefficients, and the other half are used for testing to validate performance. Then, a linearization test is performed, where the pre-distorted signal output by the model is input through a power amplifier, and the linearization performance is observed. To fairly compare the behavior modeling performance of different models, we adjust the parameters of each model to ensure they operate at similar FLOP levels during experiments. Simultaneously, to systematically evaluate the effectiveness of the proposed CED activation function, comparative experiments are conducted by replacing it with three commonly used complex-valued activation functions within the EPCTCNN framework. Table 1 lists the comparative results of the behavior modeling experiments. In the table, EPCTCNN-ctanh refers to the EPCTCNN model using the ctanh activation function; other variants are defined similarly. It can be seen that although the EPCT matrix can perform effective modeling, its performance is still lower than existing models when using traditional activation functions. In contrast, the proposed CED activation function exhibits significantly superior FLOP efficiency compared to existing activation functions, achieving an improvement of approximately 1.8–2 dB. These results demonstrate that CED can fully capture the amplitude-dominated nonlinearity of PA, providing enhanced modeling flexibility while maintaining phase consistency. Compared to real-valued models, EPCTCNN-CED exhibits superior modeling performance compared to real-valued CNN models, requiring only 977 real-valued equivalent parameters, approximately 20% fewer than ARCTCNN and 50% fewer than RVTDCNN, demonstrating higher parameter efficiency than traditional real-valued convolutional neural networks. This indicates that the proposed model can achieve competitive accuracy while reducing parameter overhead.

[0056] In the linearization performance test, the same parameter settings as in the behavioral modeling experiment were used, which used approximately 5000 FLOPs. Figure 3 The linearized power spectral density (PSD) of different models around 5000 FLOPs is compared. Table 2 shows the linearization results of different models, with performance metrics measured by ACPR and NMSE. Compared to the case without DPD, all models significantly suppress spectral regeneration, demonstrating the effectiveness of nonlinear compensation. Clearly, EPCTCNN-CED consistently outperforms the traditional GMP model in linearization performance, and also outperforms traditional real-valued convolutional neural network models. Overall, the linearization results confirm that the proposed EPCTCNN-CED effectively suppresses spectral regeneration and improves NMSE performance. Compared to traditional real-valued models, it achieves competitive performance while reducing structural complexity, validating the advantages of complex domain feature representation and PA-oriented activation design.

[0057] Table 1: Behavioral modeling performance of different models.

[0058] Model Equivalent real parameters NMSE (dB) FLOPs GMP - 1356 -36.6545 5658 ARVTDNN 75 2102 -38.6612 5102 RVTDCNN 60 1832 -38.9284 5097 ARCTCNN 20 1208 -39.3221 5470 EPCT-ctanh 20 862 -37.7291 5324 EPCT-cCard 20 862 -37.5854 5058 EPCT-pptanh 20 862 -37.9315 5210 EPCT-CED 20 977 -39.7248 5248

[0059] Table 2: Linearization performance of different models.

[0060] Model NMSE (dB) ACPR (Lower / Upper) (dBc) w / o DPD -20.1164 -30.7993 / -27.0973 GMP -36.2065 -44.5922 / -44.1392 ARVTDNN -37.2960 -47.7353 / -45.8386 RVTDCNN -37.8198 -47.4090 / -45.6857 ARCTCNN -38.1409 -46.9797 / -45.7794 EPCT-ctanh -37.1459 -46.6690 / -45.1565 EPCT-cCard -36.5904 -46.0239 / -44.9981 EPCT-pptanh -36.3108 -46.9654 / -45.3053 EPCT-CED -38.3648 -47.5192 / -46.3293

[0061] The same or similar labels correspond to the same or similar parts;

[0062] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0063] Obviously, the above examples of the present invention are merely illustrative of the invention and are not intended to limit the implementation of the invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for designing a digital predistorter based on a complex convolutional neural network, characterized in that, The method includes the following steps: S1: Generate the power amplifier input signal on the PC, collect the output signal after power amplifier using the experimental platform, and use the experimental platform to execute the iterative learning control (ILC) algorithm to obtain the ideal predistortion signal; S2: Obtain the input baseband signal of the power amplifier and construct a complex numerical input matrix based on the complex domain processing paradigm; S3: Construct a two-dimensional complex convolutional neural network (CVCNN) model, which includes two-dimensional complex convolutional layers, complex activation function layers, and fully connected layers. All layer parameters and operations are performed in the complex domain. S4: Input the complex numerical input matrix and the ideal predistortion signal into the two-dimensional complex convolutional neural network model for offline training to obtain the weight parameters; S5: Configure the weight parameters to the digital predistortion module and use the digital predistortion module to perform digital predistortion processing; S6: Evaluate the difference between the PA output signal and the input signal after digital predistortion processing to obtain the real-time loss value; S7: Calculate the weight gradient based on the real-time loss value and perform backpropagation to update the weight parameters of the digital predistortion module, thereby realizing the real-time adaptive adjustment of the digital predistorter and completing the linearization of the power amplifier.

2. The digital predistorter design method based on complex convolutional neural networks according to claim 1, characterized in that, The construction of the complex-valued input matrix in S2 specifically involves constructing an enhanced phase-preserving complex-valued time delay (EPCT) matrix. The matrix is ​​constructed as follows: The four characteristics contained in the matrix are interpreted as follows: The proposed matrix consists of four characteristic terms, each of which is explained as follows: First, in the complex domain processing, it is not necessary to decompose the complex signal into I / Q components. Therefore, the basis functions commonly used in traditional DPD models... These can be directly used as key features in constructing the input matrix. As the principal analytical component, it retains the original complex direction, forming the basis for linear gain modeling. Secondly, conjugate terms frequently appear in the basis function construction of traditional models, such as in the DDR model. It captures phase asymmetry and mirror interference. A conjugate term is introduced. By introducing extensive linear representation capabilities, the network's ability to model mismatch effects and asymmetric distortions that may occur under real-world broadband operating conditions is enhanced. Third, we choose To simulate higher-order intermodulation components in PA distortion, where It is a nonlinear order. These are also the main basis functions in the classic MP and GMP models, explicitly capturing amplitude-dependent modulation effects while maintaining phase consistency. Although odd-order terms, especially the third-order nonlinear components, constitute the main source of distortion in PA, models containing even-order terms exhibit excellent linearization performance. Therefore, we include them in the matrix. and . Overall, the proposed EPCT matrix constitutes a set of minimal and non-redundant complex-valued features, ensuring that the phase does not deviate from the initial phase of the signal. This design allows subsequent complex-valued convolutional layers to focus more on learning memory effects and cross-channel interactions, without needing to implicitly reconstruct the amplitude-phase coupling structure from the I / Q separation representation. Therefore, this input matrix provides a structurally coherent and physically driven underlying representation for digital predistortion modeling based on complex-valued neural networks.

3. The digital predistorter design method based on complex convolutional neural networks according to claim 1, characterized in that, The complex activation function layer in S4 uses the complex envelope-dependent activation function (CED), whose expression is: in and All of these are learnable parameters. Controlling the linear gain and reference phase offset, It determines the shape and direction of nonlinear distortion, and This modulates the sensitivity to changes in the envelope.

4. The digital predistorter design method based on complex convolutional neural networks according to claim 1, characterized in that, In S3, the amplitude-phase coupling features of the signal are extracted using complex convolution operations. The formula for calculating the complex convolution is as follows: The proposed CVCNN model consists of a two-dimensional convolutional layer, hidden fully connected layers, and an output fully connected layer. CVCNN contains only a single complex two-dimensional convolutional layer and has three... Macro-convolutional kernel; containing two fully connected layers: hidden layer ( Construct a high-dimensional nonlinear basis space, and output the layer ( The final 1D complex signal is generated; the proposed CED activation function is used to activate each layer connection. The required CVCNN model uses the EPCT matrix as input.

5. A digital predistorter design system based on a complex convolutional neural network, the system being constructed based on the method described in claim 1, characterized in that, include: The input building module is used to receive baseband signals and construct a complex numerical input matrix EPCT that retains the complex algebraic structure. The complex inference module is equipped with a two-dimensional complex convolutional neural network (CVCNN) to perform convolutions and nonlinear mappings in the complex domain. The parameter update module is used to update the complex weight parameters in the network based on the error between the predistortion output and the target signal.

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