A neural network digital predistortion method and system considering low complexity and high linearity

Abstract

The application discloses a neural network digital pre-distortion method and system with low complexity and high linearity, and relates to the technical field of computers, and is committed to greatly reducing the calculation complexity and hardware resource consumption of a neural network DPD model while guaranteeing high linearization performance. The method comprises the following steps: generating an initial population, dividing individuals in the population into multiple species based on the calculation complexity of each individual; performing customized training on each individual, determining the breeding quota of each species according to the performance score of each species, selecting parent individuals in each species and performing at least one mutation operation to generate offspring individuals, and forming a next-generation population from all offspring individuals; repeating the division, customized training and breeding steps for iterative evolution until a preset termination condition is met, and outputting an individual with optimal performance as a final neural network digital pre-distortion model.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a neural network digital predistortion method and system that balances low complexity and high linearity. Background Technology

[0002] With the rapid development of fifth-generation (5G) and future sixth-generation (6G) mobile communication technologies, wireless communication systems are evolving towards larger bandwidths, higher frequency bands, higher spectral efficiency, and ultra-dense networking. To improve power efficiency, power amplifiers in transmitters typically operate in a near-saturation nonlinear state, introducing in-band distortion and out-of-band spectral spread. This leads to deterioration of the error vector amplitude, increased adjacent channel leakage power ratio, and interference with neighboring channels. Therefore, digital predistortion technology is widely used for linearization compensation in power amplifiers.

[0003] In recent years, wireless communication system architecture has been evolving from traditional high-power centralized devices towards miniaturization, distribution, and terminalization. Numerous micro base stations and small base stations have been widely deployed, and the consumer electronics sector's demand for high-order modulation and low-power transmission continues to increase. These application scenarios place demands on digital predistortion systems to achieve high-performance linearization under limited chip area, power budget, and heat dissipation capabilities. While existing digital predistortion schemes based on neural networks possess strong nonlinear function approximation capabilities, they typically employ fixed and complex network topologies containing numerous redundant connections and parameters. This results in high computational complexity and hardware resource consumption, limiting the efficiency of the models in practical deployments.

[0004] Therefore, how to effectively reduce the computational complexity of neural network digital predistortion models while ensuring high linearization performance is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] This application provides a neural network digital predistortion method and system that balances low complexity and high linearity, aiming to significantly reduce the computational complexity and hardware resource consumption of neural network DPD models while ensuring high linearization performance.

[0006] Firstly, to address the aforementioned technical problems, this invention provides a neural network digital predistortion method that balances low complexity and high linearity. The method includes: generating an initial population containing multiple individuals, each corresponding to a neural network with an initial simple topology, the neural network being used for digital predistortion of a power amplifier; dividing the individuals in the population into multiple species based on the computational complexity of each individual, with individuals within each species having similar computational complexity; performing customized training on each individual, the customized training constructing a training matrix by merging existing and potential connections and performing gradient backpropagation, pruning and updating the connection genes of the individuals based on the weight magnitudes after training; determining the breeding quota of each species based on its performance score, selecting parent individuals within each species and performing at least one mutation operation to generate offspring individuals, all offspring individuals forming the next generation population; repeating the division, customized training, and breeding steps for iterative evolution until a preset termination condition is met, at which point the individual with the best performance is output as the final neural network digital predistortion model.

[0007] In one possible implementation, generating the initial population includes: setting the initial simple topology of each individual to include a finite number of finite-length unit impulse response filter nodes, a finite number of learnable edge localization activation nodes, and a preset number of connection genes, and randomly initializing the weight parameters of the connection genes.

[0008] In one possible implementation, individuals in the population are divided into multiple species based on the computational complexity of each individual. This includes: using the computational complexity of the first individual assigned to a species as the representative complexity of that species; calculating the difference between the current individual and the representative complexity of each species; and taking the smallest difference as the similarity distance; when the similarity distance is less than a dynamic threshold, the current individual is assigned to the corresponding species; otherwise, a new species is created with the current individual as the initial member; the dynamic threshold increases with the current generation.

[0009] In one possible implementation, constructing the training matrix includes: constructing a first parameter matrix to represent the weights of existing connections, a second parameter matrix to represent the weights of unconnected potential connections, and a binary mask matrix with the same dimension as the first parameter matrix. In the binary mask matrix, the position corresponding to the non-zero element in the first parameter matrix is ​​assigned a first value, and the position corresponding to the zero element is assigned a second value. The first parameter matrix and the binary mask matrix are multiplied element-wise, and the second parameter matrix and the logical inverse of the binary mask matrix are multiplied element-wise. The two product matrices are then added together to obtain the training matrix.

[0010] One possible implementation involves customized training, including: using a composite loss function for gradient backpropagation, the composite loss function comprising a main loss term, a first regularization term, and a second regularization term; the main loss term being the mean square error between the neural network output and the target predistortion signal; the first regularization term acting on the elements in the first parameter matrix corresponding to the binary mask matrix with a first value, used to drive the weight magnitude of that element towards zero; and the second regularization term acting on the elements in the second parameter matrix corresponding to the binary mask matrix with a second value, used to drive the weight magnitude of that element to increase.

[0011] In one possible implementation, pruning and activating the individual's connectivity genes based on the weight magnitudes after training specifically includes: after completing gradient backpropagation, setting the corresponding connectivity genes to an inactive state based on elements in the first parameter matrix whose weight magnitudes are less than a first preset threshold; and activating or creating new connectivity genes based on elements in the second parameter matrix whose weight magnitudes are greater than a second preset threshold.

[0012] In one possible implementation, the performance score for each species is calculated as follows: the average normalized mean squared error of all individuals within the species, the worst normalized mean squared error of all individuals in the current population, the difference between the best and worst normalized mean squared errors in the current population, the number of generations in which the best normalized mean squared error within the species has not improved, and the total number of individuals within the species are obtained; the performance score is obtained by multiplying the quotient obtained by dividing the difference between the average and the worst normalized mean squared error by the difference itself by an activity decay factor determined based on the number of generations in which improvement has not been achieved, and then multiplying by the square root of the total number of individuals, where the activity decay factor decreases exponentially with the number of generations in which improvement has not been achieved.

[0013] In one possible implementation, the reproductive quota of each species is determined based on its performance score. Parent individuals are selected within each species, and at least one mutation operation is performed. This includes: dividing the performance score of each species by the sum of the performance scores of all species, and then multiplying by a preset population size to obtain the number of offspring allocated to that species; within each species, a preset number of individuals are retained in ascending order of normalized mean square error (NMSE) to form candidate sub-species; two individuals are randomly selected from the candidate sub-species, and the individual with the smaller NMSE is chosen as the parent individual; a preset probability is used to determine whether to perform a mutation operation on the parent individual, and offspring individuals are generated after the mutation operation; the mutation operation includes a first type of mutation, a second type of mutation, and a third type of mutation, wherein the first type of mutation is used to add two real-valued finite-length unit impulse response filters in the finite-length unit impulse response layer of the neural network, the second type of mutation is used to add a node and establish a connection gene in any layer of the learnable edge localization activation module of the neural network, and the third type of mutation is used to add connection genes between existing nodes or increase the activation function order of existing connection genes.

[0014] In one possible implementation, the preset termination condition is: the current evolutionary generation reaches the preset total evolutionary generation, or the normalized mean square error of the best individual in the current population is less than or equal to a preset performance threshold; after terminating the evolution, the individual that meets the preset normalized mean square error requirement and has the lowest computational complexity is selected from all the generated individuals as the final neural network digital predistortion model.

[0015] Secondly, this application provides a neural network digital predistortion system that balances low complexity and high linearity. The system includes: an initial population construction module for generating an initial population containing multiple individuals, each corresponding to a neural network with an initial simple topology, used for digital predistortion of a power amplifier; a species division module for dividing individuals in the population into multiple species based on the computational complexity of each individual, with individuals within each species having similar computational complexity; a customized training module for performing customized training on each individual, where customized training constructs a training matrix by merging existing and potential connections and performing gradient backpropagation, pruning and updating the connection genes of the individuals based on the weight magnitudes after training; a reproduction and iterative evolution module for determining the reproduction quota of each species based on its performance score, selecting parent individuals within each species and performing at least one mutation operation to generate offspring individuals, with all offspring individuals forming the next generation population; and the reproduction and iterative evolution module further for iterative evolution by repeating the division, customized training, and reproduction steps until a preset termination condition is met, at which point the individual with the best performance is output as the final neural network digital predistortion model.

[0016] This application has at least the following beneficial effects: By adopting the digital predistortion method of topological evolutionary neural network described in this solution, starting from a simple initial structure, classifying species based on computational complexity, merging existing and potential connections in customized training, and iterative evolution based on performance scores for reproduction and mutation, it can adaptively generate a simplified network topology that matches the nonlinear characteristics of a specific power amplifier. This effectively removes redundant connections and parameters in traditional fixed-structure neural networks. While maintaining or even improving linearization performance (such as reducing normalized mean square error and improving adjacent channel leakage power ratio), it significantly reduces the computational complexity and hardware resource consumption of the model, thereby meeting the deployment requirements of miniaturized, low-power communication devices. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the structure of a neural network digital predistortion system that balances low complexity and high linearity, as provided in this application. Figure 2 This is a flowchart illustrating a neural network digital predistortion method that balances low complexity and high linearity, as provided in this application. Figure 3 This is another flowchart illustrating a neural network digital predistortion method that balances low complexity and high linearity, as provided in this application. Figure 4 This is a framework diagram of training DPD using ILC provided in this application; Figure 5 This is the amplitude and phase diagram of the PA output provided in this application. Detailed Implementation

[0018] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments. The components of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0019] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this application, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0020] With the rapid development of fifth-generation (5G) and future sixth-generation (6G) mobile communication technologies, wireless communication systems are evolving towards larger bandwidths, higher frequency bands, higher spectral efficiency, and ultra-dense networking. Simultaneously, to improve power efficiency, power amplifiers (PAs) in transmitters typically operate in a near-saturation nonlinear state, introducing significant in-band distortion and out-of-band spectral spread. This leads to deterioration of the error vector magnitude (EVM), an increase in the adjacent channel power ratio (ACPR), and interference with neighboring channels. Therefore, digital predistortion (DPD) technology is widely used for power amplifier linearization to compensate for the nonlinear characteristics of power amplifiers.

[0021] On the other hand, in recent years, wireless communication system architecture has been gradually evolving from traditional high-power centralized equipment towards miniaturization, distribution, and terminalization. For example, in 5G mobile communication systems, a large number of micro base stations and small base stations have been widely deployed; in indoor coverage scenarios, Fiber to the Room (FTTR) technology has driven a continuous increase in the number of wireless access nodes; and in the consumer electronics field, the demand for high-order modulation and low-power transmission from sixth-generation and seventh-generation wireless LAN technologies and mobile terminal devices is constantly increasing. All of these application scenarios have placed new demands on DPD systems, namely, achieving high-performance power amplifier linearization under limited chip area, limited power budget, and limited heat dissipation capabilities.

[0022] Early DPD models were primarily based on linear parameter structures, with the Generalized Memory Polynomial (GMP) model being widely adopted due to its ability to effectively characterize nonlinear properties with memory effects. To further balance linearization performance and hardware complexity, the Decomposed Vector Combination Search (DVCS) model was subsequently proposed. This model improves modeling efficiency by introducing an evolutionary optimization strategy during basis function selection, enabling adaptive construction of basis functions.

[0023] To further enhance the nonlinear modeling capabilities of DPD systems, neural network (NN)-based DPD models have attracted increasing attention due to their strong ability to approximate nonlinear functions. In early neural network DPD architectures, the Real-Valued Time-Delay Neural Network (RVTDNN) was widely used for power amplifier behavior modeling. Subsequently, inspired by block-oriented nonlinear system structures, the Block-Oriented Time-Delay Neural Network (BOTDNN) was proposed to further improve linearization capabilities. Furthermore, to meet the requirements of low-complexity DPD implementation, the Learnable Edge-Located Activation Neural Network (LEANN) was proposed to achieve a good trade-off between linearization performance and computational complexity.

[0024] Traditional neural network DPD models typically employ fixed and complex network topologies, often containing numerous redundant connections and parameters. While these models possess strong nonlinear modeling capabilities, their computational complexity and hardware resource consumption remain high, thus limiting their implementation efficiency and practical deployment capabilities.

[0025] To further improve the linearization efficiency of neural network-based digital predistortion, this application introduces evolutionary algorithms into neural network architecture design, proposing a Topology-Evolving Neural Network (TENN) model. This method improves the linearization performance of the model while maintaining low computational complexity by dynamically optimizing the network topology.

[0026] The following is an introduction to the architecture of the neural network digital predistortion system (hereinafter referred to as System 10) described in this solution. Figure 1 As shown, the system 10 includes: an initial population construction module 11, a species division module 12, a customized training module 13, and a reproduction and iterative evolution module 14. Each module is described in turn below.

[0027] (1) Initial population construction module 11.

[0028] The initial population construction module 11 is responsible for generating the initial population for subsequent evolutionary searches. This module can be implemented using a random number generator and data structure initialization program on a computer's central processing unit or graphics processing unit, providing the entire system with a starting set of individuals with structural diversity.

[0029] Optionally, the initial population construction module 11 is used to generate an initial population containing multiple individuals, each corresponding to a neural network with an initial simple topology, which is used to perform digital predistortion on the power amplifier.

[0030] In its implementation, the initial population construction module 11 first sets the population size parameter, and then, for each individual, constructs its initial neural network topology: containing a finite number of finite-length unit impulse response filter nodes, a finite number of learnable edge localization activation nodes, and a preset number of connection genes. Afterward, this module randomly initializes the weight parameters of the connection genes for each individual, for example, using small random numbers from a normal distribution. All individuals together constitute the initial population, which is then output to the species classification module 12.

[0031] (2) Species classification module 12.

[0032] The species classification module 12 is responsible for receiving the initial population generated by the initial population construction module 11, as well as the new population generated by the subsequent reproduction and iterative evolution module 14, and classifying them into different species based on the computational complexity of each individual. This module can be implemented using complexity calculation algorithms and dynamic clustering algorithms running on embedded processors or digital signal processors to ensure that the diversity of network structure is preserved during the evolution process.

[0033] Optionally, the species division module 12 is used to divide individuals in the population into multiple species based on the computational complexity of each individual, with individuals within each species having similar computational complexity.

[0034] Specifically, the species classification module 12 first calculates the computational complexity of each individual (e.g., by counting the total number of multipliers and adders in the neural network), and uses the computational complexity of the first individual in each species to be classified as the representative complexity of that species. For the individual to be classified, the module calculates the difference between the individual and the representative complexity of each species, and takes the smallest difference as the similarity distance. Then, the species classification module 12 obtains a dynamic threshold, which increases with the current generation. When the similarity distance is less than the dynamic threshold, the module classifies the current individual into the corresponding species; otherwise, the module creates a new species with the current individual as the initial member. After classification, the species classification module 12 outputs the population with species labels to the customized training module 13.

[0035] (3) Customized training module 13.

[0036] The customized training module 13 is responsible for performing customized training on each individual in the population output by the species division module 12. It constructs a training matrix by merging existing and potential connections and performs gradient backpropagation. Based on the weight magnitudes after training, it prunes and updates the connection genes of each individual. This module can be implemented on a neural network training accelerator or a general-purpose graphics processor and is the core module for achieving coordinated network structure optimization and parameter learning.

[0037] Optionally, a customized training module 13 is used to perform customized training on each individual. This customized training constructs a training matrix by merging existing connections and potential connections and performs gradient backpropagation. Based on the weight magnitudes after training, the individual's connection genes are pruned and activated and updated.

[0038] In its specific implementation, the customized training module 13 performs the following operations for each individual: First, it constructs a first parameter matrix to represent the weights of existing connections, a second parameter matrix to represent the weights of unconnected potential connections, and a binary mask matrix with the same dimension as the first parameter matrix. In the binary mask matrix, the position corresponding to a non-zero element in the first parameter matrix is ​​assigned a first value (e.g., 1), and the position corresponding to a zero element is assigned a second value (e.g., 0). Then, the module performs element-wise multiplication of the first parameter matrix and the binary mask matrix, and element-wise multiplication of the second parameter matrix and the logical inversion of the binary mask matrix. Finally, it adds the two product matrices to obtain the training matrix. Subsequently, the customized training module 13 performs gradient backpropagation using a composite loss function, which includes a main loss term, a first regularization term, and a second regularization term: the main loss term is the mean square error between the neural network output and the target pre-distortion signal; the first regularization term acts on the elements in the first parameter matrix whose corresponding binary mask matrix values ​​are the first value, driving the weight magnitude of these elements towards zero; the second regularization term acts on the elements in the second parameter matrix whose corresponding binary mask matrix values ​​are the second value, driving the weight magnitude of these elements to increase. After gradient backpropagation is completed, the module sets the corresponding connection genes to an inactive state based on the elements in the first parameter matrix whose weight magnitude is less than a first preset threshold; based on the elements in the second parameter matrix whose weight magnitude is greater than the second preset threshold, it activates the corresponding potential connection genes or creates new connection genes. The customized training module 13 outputs the updated population to the reproduction and iterative evolution module 14.

[0039] (4) Reproduction and Iterative Evolution Module 14.

[0040] The reproduction and iterative evolution module 14 is responsible for receiving the updated population from the customized training module 13, determining the reproduction quota for each species based on its performance score, selecting parent individuals within each species and performing at least one mutation operation to generate offspring individuals, and forming the next generation population from all offspring individuals. Simultaneously, this module is responsible for repeatedly triggering the species division module 12 and the customized training module 13 for iterative evolution until a preset termination condition is met, at which point the individual with the best performance is output as the final neural network digital predistortion model. This module can perform loop control and algorithm scheduling using a finite state machine implemented by the main control microprocessor and a hardware description language.

[0041] Optionally, the reproduction and iterative evolution module 14 is used to determine the reproduction quota of each species based on the performance score of each species, select parent individuals within each species and perform at least one mutation operation to produce offspring individuals, and form the next generation population from all offspring individuals; and to repeatedly trigger the reproduction operations of the species division module 12, the customized training module 13 and the reproduction and iterative evolution module 14 itself to perform iterative evolution until the preset termination condition is met, and output the individual with the best performance as the final neural network digital predistortion model.

[0042] In determining reproductive quotas, this module first calculates the performance score for each species: it obtains the average normalized mean square error (MSE) of all individuals within the species, the worst MSE of all individuals in the current population, the difference between the best and worst MSE in the current population, the number of generations in which the best MSE has not improved, and the total number of individuals in the species. Then, it multiplies the quotient of the difference between the average and worst MSE by the difference itself, multiplies it by an activity decay factor determined based on the number of generations with no improvement, and then multiplies this by the square root of the total number of individuals to obtain the performance score. The activity decay factor decreases exponentially with the number of generations with no improvement. Finally, the module divides the performance score of each species by the sum of the performance scores of all species and multiplies this by a preset population size to obtain the number of offspring allocated to that species.

[0043] In terms of parent selection and mutation operations, the reproduction and iterative evolution module 14 retains a preset number of individuals within each species in ascending order of normalized mean square error (MSE) to form candidate subspecies. Two individuals are randomly selected from these candidate subspecies, and the one with the smaller MSE is chosen as the parent individual. A preset probability is used to determine whether to perform a mutation operation on the parent individual. The mutation operation includes three types: The first type of mutation adds two real-valued finite-length unit impulse response (FIR) filters to the finite-length unit impulse response layer of the neural network. Each filter is preset to be second-order, and the input node to be connected is selected based on the importance score of the input node. The second type of mutation adds a node to any layer of the learnable edge localization activation module of the neural network. An input node is randomly selected from the output nodes of the previous layer, and two connection genes are established between the selected input node and the newly added node. Each connection gene corresponds to an activation function. The third type of mutation adds a connection gene between two existing unconnected nodes, or adds another connection gene between two already connected nodes to increase the order of the activation function corresponding to the connection gene. After performing the mutation operation, this module generates offspring individuals. All offspring individuals together constitute the next generation population, which is then output to the species division module 12 to begin a new round of evolution.

[0044] In terms of iterative evolution control, the reproduction and iterative evolution module 14 incorporates an iteration counter and performance monitoring logic. The preset termination condition is: the current evolutionary generation reaches the preset total evolutionary generation, or the normalized mean square error of the best individual in the current population is less than or equal to a preset performance threshold. After terminating evolution, this module selects the individual from all generated individuals that meets the preset normalized mean square error requirement and has the lowest computational complexity, as the final output of the neural network digital predistortion model.

[0045] For example, such as Figure 2 The diagram shown is a flowchart illustrating a neural network digital predistortion method that balances low complexity and high linearity according to an embodiment of the present invention, comprising the following steps: S201, Generate the initial population.

[0046] The initial population consists of multiple individuals, each corresponding to a neural network with an initial simple topology. The neural network is used to perform digital predistortion on the power amplifier.

[0047] For example, this step can be performed by the initial population construction module 11 in the neural network digital predistortion system 10 described above, and specifically includes the following steps: (1) Set population size parameters. The initial population construction module 11 determines the total number of individuals to be generated based on the preset initial population size value.

[0048] (2) Create the initial neural network topology for each individual. For each individual, the initial population construction module 11 constructs a neural network containing a finite number of finite-length unit impulse response filter nodes, a finite number of learnable edge-localization activation nodes, and a preset number of connection genes. Among them, the finite-length unit impulse response filter nodes are used to characterize the memory effect of the power amplifier, and the learnable edge-localization activation nodes are used to characterize the static nonlinear characteristics of the power amplifier.

[0049] (3) Initialize the weight parameters of the connecting genes. The initial population construction module 11 randomly initializes the weight parameters of all connecting genes in each individual, for example, by assigning values ​​using tiny random numbers that follow a normal distribution. After initialization, all individuals together constitute the initial population, which is then output to the subsequent species division module 12.

[0050] In some embodiments, the initial simple topology of each individual can be set to include a finite number of finite-length unit impulse response filter nodes, a finite number of learnable edge localization activation nodes, and a preset number of connection genes, and the weight parameters of the connection genes can be randomly initialized.

[0051] This application proposes three mutation mechanisms to design the framework for TENN models: 1) Sudden Change in the Number of Finite-Length Unit Impulse Response (FIR) Filters (Type I): A Type I change allows the introduction of two additional real-valued FIR filters into the FIR layer. The newly introduced filters are denoted as... and The order of each newly added FIR filter is set to 2. Therefore, the two filters can be represented as follows:

[0052] This indicates that the first newly added FIR filter (i.e. The output I-channel (in-phase component) signal. This filter selects two input nodes from the input vector. and The weighted summation is performed, and the output is used for nonlinear modeling of subsequent network layers (such as the LEA layer). This indicates that the second newly added FIR filter (i.e. The output Q-channel (quadrature component) signal of the filter is also applied to the input node. and A weighted sum is performed, and the output is used in subsequent network layers. , , and They represent and The filter coefficients. Variables and According to the established rules, the following input vector is selected:

[0053] M represents the memory depth, which is the total number of sampling points from the current and historical moments included in the input vector. This parameter characterizes the memory effect of the power amplifier, and its value determines how many past input moments the model considers. In this scheme, it is used to construct the candidate set of input nodes for the FIR filter. n represents the index of the current sampling moment. Elements in the input vector x and Let I and Q represent the I-channel and Q-channel input signals at the current time n, respectively. and This represents the I-path and Q-path signals looking back M-1 time steps. Q represents the quadrature component. In communication systems, baseband signals are typically decomposed into in-phase (I) and quadrature (Q) components for separate processing to fully characterize the signal's amplitude and phase information. The superscripts I and Q in the formula are used to identify the in-phase and quadrature components in the input vector, respectively. T represents the transpose of a matrix or vector. [In the formula...] ] T This indicates that the sequence within the square brackets is arranged as a column vector, meaning that the input vector x is a column vector. This is a common way of representing vectors in mathematics.

[0054] The established rule is as follows: First, the importance of an input node is evaluated based on the average absolute value of all connection weights derived from it. The importance score of each input node can be represented as:

[0055] in Indicates connection to the first The total number of FIR filter taps at each input node Indicates the relationship with the first The first FIR filter connected to the first The coefficients corresponding to each input node. Then, the two largest input nodes are selected and used as... and Furthermore, k nodes are randomly selected from the first Learnable Edge-Located Activation (LEA) layer as output nodes, and connection genes are established between these nodes and the outputs corresponding to the FIR filters.

[0056] 2) Type II Mutation of LEA Layer Nodes: Type II mutation allows adding a new node to any LEA layer in the TENN model. The mutation process can be described as follows: First, a LEA layer is randomly selected from the LEA modules. Then, a new node is added to this layer. Next, an input node is randomly selected from the set of nodes input to this layer. For LEA1, its candidate input node corresponds to the output node of the FIR layer; for the remaining LEA layers, its candidate input node corresponds to the output node of the previous LEA layer. Two connection genes are then established between the selected input and output nodes. The activation function represented by each connection gene can be described by the following formula:

[0057] This represents the index number of the previous level node. During connection establishment, this node serves as the input source for signals, and its output value... It is processed by the current activation function. This indicates the index number of the node in the next layer. This node is the target node for signal transmission, connecting genes from the previous layer node. Point to the next level node . Indicates the first The output value of each node (i.e., the activation value of that node) is used as the input argument of the current activation function. This represents the weight parameter corresponding to the nth connection gene, which acts on the slave node. To the node On the connection, this parameter is updated during training via gradient backpropagation. This represents the bias parameter corresponding to the nth linker gene, which also applies to the slave node. To the node On the connection, this parameter is updated during training via gradient backpropagation. This indicates that the input value is processed first. Take the absolute value and then subtract the bias parameter. Finally, the absolute value of the difference is taken. This two-layer absolute value structure is a unique form of this activation function, and its function is to introduce nonlinear characteristics into the network. (The symbols mentioned above...) The superscript indicates that the parameter belongs to the nth linker gene; the subscript indicates that the parameter belongs to the nth linker gene. , This identifies the source and target nodes connected to the connection gene. The entire formula expresses the mathematical form of a connection gene in the LEA layer performing a nonlinear transformation on the input signal. The weight parameter controls the magnitude of the transformation, and the bias parameter controls the translation position of the transformation. Together, they determine the nonlinear response characteristics of the activation function.

[0058] The weight and bias parameters in the formula are randomly initialized according to a normal distribution and a uniform distribution over the interval [0,1], respectively. To avoid perturbing the nonlinear modeling characteristics already established by other nodes, newly added nodes do not establish connections with subsequent LEA layers; their outputs are directly connected to the output layer. If the output of this node needs to participate in higher-order nonlinear modeling in a later layer, the corresponding connection can be introduced during subsequent mutation processes or constructed using the training strategies mentioned later.

[0059] Activation function number mutation (Type III): Type III mutation introduces a connection gene, i.e., a first-order activation function, between two currently unconnected nodes. Furthermore, if a connection already exists between the two nodes, a new connection can be added, effectively increasing the piecewise order of the corresponding activation function.

[0060] Through the three mutation types mentioned above, the TENN model can progressively construct its backbone network structure. Specifically, Type I mutation is responsible for constructing the FIR layer, where the number and configuration of FIR filters can be selected based on the memory effect of PA. Type II and Type III mutations jointly construct the LEA module. Through these two mutation operations, activation functions of different orders can be introduced at different locations in the network based on the static nonlinear characteristics of PA. Specifically, Type II mutation mainly expands the nonlinear representation space of the model by introducing additional activation functions; in contrast, Type III mutation enhances its nonlinear expressive power by increasing the order of the activation function, thereby improving model performance without introducing additional multipliers. In TENN, mutation probabilities are pre-set to determine whether to perform mutation and which mutation type to choose, thereby controlling the model evolution speed.

[0061] Continuous type I and type II mutations can continuously increase the number of nodes in the FIR layer and LEA module while introducing only a small number of connections. However, as the number of nodes increases, a large number of potential input-output node pairings are generated. If all feasible connections are traversed solely through mutation, it will incur extremely high computational overhead, resulting in low evolutionary efficiency. To address this issue, this paper designs a dedicated training strategy that evaluates various potential input-output node pairings during training to determine whether to introduce entirely new connection genes.

[0062] To achieve efficient gradient-based training, the network topology needs to be transformed into matrix form, allowing both forward and backward propagation to be performed in a vectorized manner. The parameter matrix of a certain layer is recorded as follows: In this matrix, non-zero elements indicate the presence of a connection at the corresponding position, and their values ​​represent the parameter values ​​of the corresponding connection genes; zero elements indicate the absence of a connection gene at the corresponding position. Subsequently, a new parameter matrix is ​​constructed. To replace the original parameter matrix Training is defined as follows:

[0063] in, Let be a binary mask matrix whose elements take values ​​of {0,1} and are consistent with . They have the same dimensions. Specifically, when When the corresponding element is non-zero, The corresponding element is defined as 1; otherwise, it is defined as 0. (Matrix) Similarly Having the same dimension, it contains parameters corresponding to potential connections that are absent or inactive in the TENN. Its elements are initialized with small random values ​​following a normal distribution. (Symbol) This represents the logical negation operation. Assume it exists:

[0064] but It can be written as:

[0065] in, This is a pre-set, small constant. After the training process is complete, based on the training results... Further adjustments were made to the connectivity genes. For connections already existing in the TENN model, from... Elements with smaller amplitudes are selected, and their corresponding connecting genes are set to an inactive state, thereby removing unimportant connections and reducing model complexity. Meanwhile, for connections formed by... The potential connections are represented, and several elements with relatively large amplitudes are selected to activate or create corresponding connection genes, thereby enhancing the nonlinear modeling capability of TENN. Therefore, the TENN model can continuously optimize its network topology during evolution, allowing previously unimportant connections to be re-evaluated and gradually evolve into important connections, while suppressing connections that contribute little to modeling performance.

[0066] To further guide the model in identifying redundant connections and uncovering high-quality potential connections, a composite loss function is used during training, defined as follows:

[0067] in, This represents the mean square error (MSE) between the model output and the target label. and These are two regularization terms designed for existing connections and potential connections, respectively. Hyperparameters and Used to control the penalty strength of the two regularization terms. and The expression is as follows:

[0068] in and Representing sets respectively and The number of elements in The small positive constant is introduced to avoid numerical instability when the independent variable approaches zero.

[0069] S202. Based on the computational complexity of each individual, individuals in the population are divided into multiple species.

[0070] Individuals within each species have similar computational complexity.

[0071] For example, this step can be performed by the species classification module 12 in the neural network digital predistortion system 10 described above, specifically including the following steps: (1) Calculate the computational complexity of each individual. The species division module 12 counts the total number of operations of all multipliers and adders in the neural network corresponding to each individual, and uses the total number of operations as the computational complexity of that individual.

[0072] (2) Determine the representative complexity of each species. For each existing species, the species division module 12 uses the computational complexity of the first individual in the species to be assigned to the species as the representative complexity of the species.

[0073] (3) Calculate the similarity distance between the current individual and each species. For the current individual to be classified, the species classification module 12 calculates the difference between the computational complexity of the individual and the representative complexity of each species, and takes the smallest difference as the similarity distance between the individual and the species.

[0074] (4) Obtain a dynamic threshold and perform species classification. The species classification module 12 obtains a dynamic threshold based on the current evolutionary generation, which increases with the number of evolutionary generations. When the similarity distance is less than the dynamic threshold, the species classification module 12 classifies the current individual into the corresponding species; otherwise, the species classification module 12 creates a new species with the current individual as the initial member. After the classification is completed, the population with species labels is output to the customized training module 13.

[0075] In some embodiments, this application uses the computational complexity of the first individual in each species to be assigned to that species as the representative complexity of that species, calculates the difference between the current individual and the representative complexity of each species, and takes the smallest difference as the similarity distance; when the similarity distance is less than the dynamic threshold, the current individual is assigned to the corresponding species, otherwise a new species is created with the current individual as the initial member; the dynamic threshold increases with the increase of the current evolutionary generation.

[0076] Next, we will introduce the entire execution process of the designed evolutionary algorithm. First, we define three concepts: a TENN is called an individual; individuals with similar structural features are grouped into the same species; and all species together constitute a population. During the selection phase, competition occurs at the species level, rather than directly between populations. This helps preserve the diversity of TENN structures throughout the evolutionary process. The specific definition of the species division rule is as follows: In a TENN, the computational complexity of a single individual is used as a similarity metric for species division. The computational complexity of each species is defined as the computational complexity of the first individual assigned to that species. Accordingly, the similarity difference between an individual and each species is defined as the difference in their computational complexity, denoted as . Then, the species with the smallest similarity distance to the individual and its corresponding similarity distance are determined, specifically defined as follows:

[0077] Furthermore, the dynamic threshold for species grouping is defined as follows:

[0078] in, This represents the pre-set basic threshold for species classification. This represents the annealing intensity parameter used to control the rate of change of the threshold. Wherein, Indicates the current generation number. This represents the set total number of generations. When the minimum similarity distance satisfies... At that time, the individual Classified to the corresponding species In the middle; otherwise, with Create new species as initial members.

[0079] S203. Perform customized training for each individual.

[0080] Customized training involves merging existing and potential connections to construct a training matrix and performing gradient backpropagation. Based on the weight magnitudes after training, the connection genes of individuals are pruned and activated and updated.

[0081] For example, this step can be performed by the customized training module 13 in the neural network digital predistortion system 10 described above, specifically including the following steps: (1) Construct a first parameter matrix to represent the existing connection weights. The customized training module 13 extracts the weight values ​​of the currently active connection genes in each individual and arranges them according to the correspondence between input nodes and output nodes to form a first parameter matrix. The position corresponding to the inactive connection genes in this matrix is ​​zero.

[0082] (2) Construct a second parameter matrix to characterize the potential connection weights. Customized training module 13 constructs a second parameter matrix with the same dimension as the first parameter matrix. Each element in this matrix corresponds to the weight parameter of a potential connection gene that does not currently exist. All elements are initialized with small random values ​​that follow a normal distribution.

[0083] (3) Construct a binary mask matrix. The customized training module 13 constructs a binary mask matrix with the same dimension as the first parameter matrix, wherein the mask position corresponding to the non-zero element in the first parameter matrix takes the first value (e.g., 1), and the mask position corresponding to the zero element in the first parameter matrix takes the second value (e.g., 0).

[0084] (4) Merge to obtain the training matrix. The customized training module 13 multiplies the first parameter matrix and the binary mask matrix element by element, multiplies the second parameter matrix and the logical inversion result of the binary mask matrix element by element, and then adds the two product matrices to obtain the training matrix used for gradient backpropagation.

[0085] (5) Gradient backpropagation is performed using a composite loss function. The customized training module 13 uses the Adam backpropagation algorithm to update the parameters in the training matrix with the composite loss function as the target. The composite loss function includes a main loss term, a first regularization term, and a second regularization term: the main loss term is the mean square error between the output of the neural network and the target predistortion signal; the first regularization term acts on the element in the first parameter matrix whose corresponding binary mask matrix value is the first value, to drive the weight magnitude of the element to tend to zero; the second regularization term acts on the element in the second parameter matrix whose corresponding binary mask matrix value is the second value, to drive the weight magnitude of the element to increase. It should be noted that the specific expression of the composite loss function in this step is shown in step S503 below, and will not be repeated here.

[0086] (6) Pruning and activation updates are performed based on the weight magnitudes after training. After gradient backpropagation is completed, the customized training module 13 sets the corresponding connection genes to an inactive state based on the elements in the first parameter matrix whose weight magnitudes are less than the first preset threshold; and activates or creates new connection genes based on the elements in the second parameter matrix whose weight magnitudes are greater than the second preset threshold. The first and second preset thresholds can be preset according to the actual application scenario. For example, the first preset threshold is 0.001 and the second preset threshold is 0.005. The value rules are as follows: the first preset threshold is used to filter redundant connections that contribute very little to the model output, and the second preset threshold is used to screen new connections with significant modeling potential. After the update is completed, the customized training module 13 outputs the updated population to the reproduction and iterative evolution module 14.

[0087] S204. Determine the reproductive quota of each species based on its performance score, select parent individuals within each species and perform at least one mutation operation to produce offspring individuals, and form the next generation population from all offspring individuals.

[0088] For example, this step can be performed by the breeding and iterative evolution module 14 in the neural network digital predistortion system 10 described above, specifically including the following steps: (1) Calculate the performance score for each species. The reproduction and iterative evolution module 14 obtains the average normalized mean square error of all individuals within each species, the worst normalized mean square error of all individuals in the current population, the difference between the best and worst normalized mean square errors in the current population, the number of generations in which the best normalized mean square error within the species has not improved, and the total number of individuals within the species. Then, the reproduction and iterative evolution module 14 calculates the performance score for each species based on the above parameters. It should be noted that the specific calculation formula for the performance score is described in step S504 below, and will not be repeated here.

[0089] (2) Determine the reproductive quota for each species. The Reproduction and Iterative Evolution module 14 divides the performance score of each species by the sum of the performance scores of all species, and then multiplies it by the preset population size (e.g., 260) to obtain the number of offspring allocated to that species.

[0090] (3) Select parent individuals within each species. For each species, the reproduction and iterative evolution module 14 retains a preset number of individuals (e.g., the first 8) in order of increasing normalized mean square error to form candidate subspecies. Then, two individuals are randomly selected from the candidate subspecies, and the individual with the smaller normalized mean square error is selected as the parent individual.

[0091] (4) Perform mutation operations to generate offspring individuals. The reproduction and iterative evolution module 14 determines whether to perform mutation operations on the selected parent individuals based on a preset probability. Mutation operations include first-type mutation, second-type mutation, and third-type mutation: the first-type mutation is used to add two real-valued finite-length unit impulse response filters in the finite-length unit impulse response layer of the neural network; the second-type mutation is used to add a node and establish a connection gene in any layer of the learnable edge localization activation module of the neural network; the third-type mutation is used to add connection genes between existing nodes or increase the activation function order of existing connection genes. Offspring individuals are generated after performing mutation operations. The above parent selection and mutation operations are repeated for all species, and all generated offspring individuals together constitute the next generation population. It should be noted that the specific implementation methods of the three mutation operations are described in steps S505-S507 below, and will not be repeated here.

[0092] After individuals are assigned to different species, their performance is evaluated. Subsequently, some of the best-performing individuals are selected from each species and used to reproduce and generate the next generation. During the reproductive phase, the score for each species is evaluated to determine its contribution to the next generation population. The species score is defined as:

[0093] in, Indicates species The average of the normalized mean squared error (NMSE) of all individuals in the dataset. This represents the worst NMSE for all individuals in the current generation. This represents the range of NMSE in the population, defined as the difference between the best NMSE and the worst NMSE. Used to characterize the activity level of a species, among which, This represents the number of generations in which the best NMSE in a species has not been improved. This is a pre-set time decay constant used to control the rate at which activity decays. This represents the population size of a species, i.e., the total number of individuals in that species. Based on the scores of each species, the number of offspring allocated to each species is defined as:

[0094] in, This represents the pre-defined total population size for the next generation. Therefore, species with better average NMSE, higher activity, and larger population size will be allocated more offspring, thus enabling them to make a greater contribution to evolution.

[0095] A complete summary of the evolutionary process is as follows: Figure 3 As shown. The algorithm first initializes... Individuals constitute the initial population. These initial individuals contain only a few nodes and connecting genes, thus possessing a relatively simple initial structure. Subsequently, these individuals are classified into different species. Next, the proposed training strategy is used to train all individuals. After training, the performance of each individual is evaluated based on NMSE. Then, based on the obtained... and The connection genes of each individual are updated. The updated population is then input into the breeding phase. In the breeding phase, individuals within each species are first sorted according to their NMSE (Neural Mean Squared Equation), and only the top k individuals are retained to form candidate subspecies. Subsequently, two individuals are randomly selected from the candidate subspecies, with the individual with the better NMSE chosen as the parent to participate in evolution. After parent selection, whether the parent performs mutation and what type of mutation is used is determined probabilistically. The resulting offspring are called offspring. This process is repeated until all offspring constitute a new population. Then, according to a predefined species classification criterion, the new population is reclassified into different species. Next, the proposed training strategy is used to train all individuals, and the connection gene information of each individual is updated. The updated population is then input into the next breeding cycle. The evolutionary process terminates when the predefined performance indicators are met or the maximum number of generations is reached. Finally, individuals from all generations are comprehensively evaluated, and those that meet the predefined performance and complexity requirements are selected as the final TENN model.

[0096] To ensure the model is searched and evaluated under stable PA conditions, an iterative learning control (ILC) algorithm is used to obtain a reference predistortion signal for model performance evaluation. The iterative process of the ILC algorithm is as follows: Figure 4 As shown, it should be noted that the training of the TENN model still employs an indirect learning architecture. Specifically, the ILC algorithm is first applied to PA to obtain the target predistortion signal corresponding to the input signal x. Then, the acquired dataset was divided into training and test sets in a 3:2 ratio. Afterwards, using x as input... As a label, utilize Figure 3 The described TENN evolutionary method searches for the optimal TENN model. During model training, the Adam backpropagation algorithm is used to update the coefficients. The parameters in the evolutionary algorithm are set as follows: the initial population size is set to... Population size set to The base threshold is set to annealing factor set to The time decay factor is set to Select quantity set to The penalty factor is and Furthermore, when the weight corresponding to a potential connector gene is greater than or equal to 0.005, the corresponding potential connector gene will be activated or created. In the obtained TENN model, the FIR layer contains 69 connector genes, and the LEA module contains 43 activation functions. Finally, by deploying the TENN model to preprocess the input signal, the output characteristics of PA are as follows: Figure 5 The amplitude-amplitude / amplitude-phase diagram is shown below. It can be seen that after preprocessing with the TENN model, the output of PA exhibits good linearity.

[0097] S205, repeated division, customized training and reproduction steps are carried out iteratively until the preset termination condition is met, and the individual with the best performance is output as the final neural network digital predistortion model.

[0098] For example, this step can be performed by the breeding and iterative evolution module 14 in the neural network digital predistortion system 10 described above, specifically including the following steps: (1) Iterative evolution control. The reproduction and iterative evolution module 14 has a built-in iteration counter. After each completion of S204, the next generation population is used as the current population, and the steps from S202 to S204 are triggered again to form an iterative cycle.

[0099] (2) Termination condition judgment. After each iteration cycle, the reproduction and iterative evolution module 14 judges whether the current evolution generation has reached the preset total evolution generation (e.g., the preset total evolution generation is 200), or whether the normalized mean square error of the best individual in the current population is less than or equal to the preset performance threshold (e.g., the preset performance threshold is 0.001). When any of the above conditions are met, the iterative evolution is terminated.

[0100] (3) Output the final model. After the evolution is terminated, the reproduction and iterative evolution module 14 selects the individual that meets the preset normalized mean square error requirement (e.g., less than or equal to 0.001) and has the lowest computational complexity from all the generated individuals (including individuals in the population of previous generations), and outputs the neural network corresponding to the individual as the final neural network digital predistortion model.

[0101] Based on the above technical solution, the embodiments of the present invention can adaptively generate a simplified network topology that matches the nonlinear characteristics of a specific power amplifier by starting from a simple initial structure, classifying species based on computational complexity, merging existing and potential connections in customized training, and iterative evolution of reproduction and mutation based on performance scores. This effectively removes redundant connections and parameters in traditional fixed-structure neural networks, and significantly reduces the computational complexity of the model while maintaining linearization performance.

[0102] The above are merely embodiments of this application and are not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A neural network digital predistortion method that balances low complexity and high linearity, characterized in that, include: An initial population is generated, which contains multiple individuals, each corresponding to a neural network with an initial simple topology. The neural network is used to perform digital predistortion on the power amplifier. Based on the computational complexity of each individual, individuals in the population are divided into multiple species, and individuals within each species have similar computational complexity. Customized training is performed on each individual, which involves constructing a training matrix by merging existing and potential connections and performing gradient backpropagation, and pruning and updating the individual's connection genes based on the weight magnitudes after training. Each species’ reproductive quota is determined based on its performance score. Parent individuals are selected within each species and at least one mutation operation is performed to produce offspring individuals. All offspring individuals form the next generation population. The process of iteratively evolving by repeatedly performing species division, customized training, and generation of the next generation population based on computational complexity, until a preset termination condition is met, outputting the individual that meets the preset performance requirements and has the lowest computational complexity as the final neural network digital predistortion model. The generation of the initial population includes: setting the initial simple topology of each individual to include a preset number of finite-length unit impulse response filter nodes, a preset number of learnable edge localization activation nodes, and a preset number of connection genes, and randomly initializing the weight parameters of the connection genes. Each species' reproductive quota is determined based on its performance score. Within each species, parent individuals are selected and at least one mutation operation is performed, including: Divide the performance score of each species by the sum of the performance scores of all species, and then multiply by the preset population size to obtain the number of offspring allocated to that species. Within each species, a predetermined number of individuals are retained in order of increasing normalized mean square error to form candidate subspecies; Two individuals are randomly selected from the candidate subspecies, and the individual with the smaller normalized mean square error is selected as the parent individual. Whether to perform a mutation operation on the parent individual is determined by a preset probability. After performing the mutation operation, a child individual is generated. The mutation operation includes a first type of mutation, a second type of mutation, and a third type of mutation. The first type of mutation is used to add two real-valued finite-length unit impulse response filters in the finite-length unit impulse response layer of the neural network. The second type of mutation is used to add a node and establish a connection gene in any layer of the learnable edge localization activation module of the neural network. The third type of mutation is used to add a connection gene between existing nodes or increase the activation function order of existing connection genes.

2. The method according to claim 1, characterized in that, The method of classifying individuals in the population into multiple species based on the computational complexity of each individual includes: The computational complexity of the first individual in each species to be assigned to that species is used as the representative complexity of that species. The difference between the current individual and the representative complexity of each species is calculated, and the smallest difference is used as the similarity distance. When the similarity distance is less than the dynamic threshold, the current individual is assigned to the corresponding species; otherwise, a new species is created with the current individual as the initial member. The dynamic threshold increases with the current generation.

3. The method according to claim 1, characterized in that, Constructing the training matrix includes: Construct a first parameter matrix to characterize the weights of existing connections, a second parameter matrix to characterize the weights of unconnected potential connections, and a binary mask matrix with the same dimension as the first parameter matrix. In the binary mask matrix, the position corresponding to the non-zero element in the first parameter matrix is ​​given a first value, and the position corresponding to the zero element is given a second value. The training matrix is ​​obtained by multiplying the first parameter matrix element-wise with the binary mask matrix, multiplying the second parameter matrix element-wise with the logical inverse of the binary mask matrix, and then adding the matrix obtained by multiplying the first parameter matrix with the binary mask matrix element-wise with the logical inverse of the second parameter matrix with the binary mask matrix.

4. The method according to claim 3, characterized in that, Customized training includes: gradient backpropagation using a composite loss function, wherein the composite loss function includes a main loss term, a first regularization term, and a second regularization term; the main loss term is the mean square error between the output of the neural network and the target pre-distortion signal; the first regularization term acts on the elements in the first parameter matrix that correspond to the binary mask matrix with a first value, to drive the weight magnitude of the element to tend to zero; the second regularization term acts on the elements in the second parameter matrix that correspond to the binary mask matrix with a second value, to drive the weight magnitude of the element to increase.

5. The method according to claim 3, characterized in that, The specific steps of pruning and activating the individual's connective genes based on the trained weight magnitudes include: after gradient backpropagation, setting the corresponding connective genes to an inactive state based on elements in the first parameter matrix whose weight magnitudes are less than a first preset threshold; and activating or creating new connective genes based on elements in the second parameter matrix whose weight magnitudes are greater than a second preset threshold.

6. The method according to claim 1, characterized in that, The performance score of each species is calculated as follows: the average normalized mean square error of all individuals in the species, the worst normalized mean square error of all individuals in the current population, the difference between the best and worst normalized mean square errors in the current population, the number of generations in which the best normalized mean square error in the species has not improved, and the total number of individuals in the species. The normalized difference is obtained by dividing the difference between the average value and the worst normalized mean square error by the difference between the best normalized mean square error and the worst normalized mean square error. The performance score is obtained by multiplying the normalized difference by the activity decay factor determined based on the number of consecutive unimproved algebras, and then multiplying it by the square root of the total number, wherein the activity decay factor decreases exponentially with the number of consecutive unimproved algebras.

7. The method according to claim 1, characterized in that, The preset termination conditions are: the current evolutionary generation reaches the preset total evolutionary generation, or the normalized mean square error of the best individual in the current population is less than or equal to a preset performance threshold; if there is an individual that meets the preset performance threshold at the time of termination, then the individual with the lowest normalized mean square error and the lowest computational complexity is selected from all the generated individuals as the final neural network digital predistortion model; if there is no individual that meets the preset performance threshold at the time of termination, then the individual with the smallest normalized mean square error is selected from all the generated individuals as the final neural network digital predistortion model.

8. A neural network digital predistortion system that balances low complexity and high linearity, characterized in that, The system applied to the neural network digital predistortion method according to any one of claims 1 to 7, which balances low complexity and high linearity, comprises: An initial population construction module is used to generate an initial population, which contains multiple individuals, each individual corresponding to a neural network with an initial simple topology, and the neural network is used to perform digital predistortion on the power amplifier. The species division module is used to divide individuals in the population into multiple species based on the computational complexity of each individual, with individuals within each species having similar computational complexity. A customized training module is used to perform customized training on each individual. The customized training constructs a training matrix by merging existing connections and potential connections and performs gradient backpropagation. Based on the weight magnitude after training, the connection genes of the individual are pruned and activated and updated. The Reproduction and Iterative Evolution module is used to determine the reproduction quota of each species based on its performance score, select parent individuals within each species and perform at least one mutation operation to produce offspring individuals, and form the next generation population from all offspring individuals. The reproduction and iterative evolution module is also used to repeatedly perform the process of species division, customized training and generation of the next generation population based on computational complexity for iterative evolution until the preset termination condition is met, and output the individual that meets the preset performance requirements and has the lowest computational complexity as the final neural network digital predistortion model.

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