A power amplifier linearization method based on KAN network and digital pre-distortion system

Abstract

The application discloses a kind of based on KAN network's power amplifier linearization method and digital pre-distortion system, belong to wireless communication technical field, this method in digital pre-distortion processing process, introduced the Kolmogorov-Arnold Networks (KAN), constructs real time delay KAN digital pre-distortion network and real time delay KAN digital pre-distortion network;For real time delay KAN digital pre-distortion network, the input process of this network considers current time and previous time input signal, can correspond to the memory of power amplifier compensation;For vector decomposition time delay KAN digital pre-distortion network, on the basis of real time delay KAN digital pre-distortion network, further introduces phase recovery layer and fully connected layer, in the case where similar performance with previous KAN model is maintained, network complexity can also be simplified again;KAN digital pre-distortion method used in the application compared with original neural network-based digital pre-distortion method, use less network parameter, realize higher linearization capacity.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication, and particularly relates to a power amplifier linearization method and a digital pre-distortion system based on a KAN network, which is applied to a radio frequency link of a transmitting end of a wireless communication system. BACKGROUND

[0002] In a transmitting system of wireless communication, the memory effect and nonlinearity of a power amplifier are main reasons for causing distortion of a transmitting signal. In order to make the amplified signal not distorted, the power amplifier can be limited to work in a linear region, but this will greatly reduce the energy efficiency of the power amplifier. At present, the most effective linearization technology is a digital pre-distortion technology.

[0003] The digital pre-distortion technology is to first perform pre-distortion processing on a digital signal, and then the pre-distorted digital signal enters a power amplifier after digital-to-analog conversion. After the non-linear distortion of the power amplifier, the output signal of the power amplifier only has a linear gain compared with the original input signal. That is, the entire system of the digital pre-distorter and the power amplifier in cascade is a linear system. Only the system function of the digital pre-distortion needs to be constructed as the inverse function of the system function of the power amplifier, so that the system after cascade of the two is a linear system, and the compensation for the non-linear distortion of the power amplifier is realized.

[0004] The traditional digital pre-distortion method needs to first perform mathematical modeling on the behavior characteristics of the power amplifier. Common modeling methods include a polynomial model, a Volterra series model, a memory polynomial (MP) model, a multi-box model, and a piecewise linear function model. Then, an inverse model is constructed according to the formula of the mathematical modeling as the system function of the digital pre-distortion. However, with the design of the power amplifier becoming more and more complex, its behavior characteristics are more and more difficult to be well represented by a mathematical model. With the development of deep learning, researchers have found that a deep neural network has strong fitting ability and can well represent various complex systems, so in recent years, many methods of modeling the power amplifier and realizing the digital pre-distortion using a deep neural network have appeared.

[0005] Although the neural network has stronger nonlinear fitting ability than the traditional mathematical modeling method, and has better linearization effect when applied to digital predistortion, there are still the following challenges in practical application: first, the scale of neural network coefficient is much higher than that of mathematical model, and the structure is complex, which will consume a lot of hardware resources in engineering implementation, so a low complexity digital predistortion neural network is needed. Secondly, the behavior characteristics of the power amplifier will change according to the signal waveform, bandwidth, frequency, power and temperature. In order to solve this problem, the existing methods are to store the digital predistortion coefficients corresponding to all nonlinear states, and load different coefficients in different states, and the second method is to recalculate the corresponding digital predistortion coefficients when the state of the power amplifier changes. However, the above two methods either occupy a large amount of storage space or consume a large amount of computing resources. SUMMARY

[0006] The purpose of the present application is to overcome the above-mentioned shortcomings of the prior art, and to provide a power amplifier linearization method and digital predistortion system based on KAN network, so as to solve the problem of large storage space or large computing resource consumption in the digital predistortion process of the prior art.

[0007] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0008] A power amplifier linearization method based on KAN network, comprising the following steps:

[0009] S1, obtaining the co-directional component and the quadrature component of the input signal, the input signal including the signal between the current time and the past time, the past time being the time of the current time minus the time delay;

[0010] S2, processing the input signal through a real-valued time delay KAN digital predistortion network, the real-valued time delay KAN digital predistortion network including a plurality of kanlayers, the input of the next layer being the output of the previous layer, and the output of each layer being the product of the input signal of the layer and the activation function of the layer; the kanlayer is used to compensate for the nonlinear distortion caused by the power amplifier;

[0011] S3, outputting the co-directional component and the quadrature component of the signal after predistortion processing.

[0012] Further improvement of the present application is:

[0013] Preferably, in S1, the length of the time delay is the memory depth of the power amplifier.

[0014] A power amplifier linearization method based on KAN network, comprising the following steps:

[0015] S1, obtaining the amplitude and phase of an input signal, the input signal including signals between a current time and a past time, the past time being the current time minus a time delay;

[0016] S2, processing the input signal by a vector-decomposed time-delay KAN digital predistortion network, the vector-decomposed time-delay KAN digital predistortion network including a kan layer, a phase recovery layer and a full connection layer, the phase recovery layer including a plurality of cos PRBs and a plurality of sin PRBs, the kan layer being used to compensate for nonlinear distortion caused by a power amplifier, the phase recovery layer being used to recover the amplitude and the phase into in-phase components and quadrature components, and the full connection layer being used to output the in-phase components and the quadrature components;

[0017] S3, outputting the in-phase components and the quadrature components of the signal after the predistortion processing.

[0018] Preferably, in S2, the operation formula in the cos PRB is:

[0019]

[0020] wherein M is a memory depth of the power amplifier, is an Lth node in an Lth layer, located in an Lth phase recovery group; is an Lth node in an Lth layer, located in an Lth phase recovery group.

[0021] the operation formula in the sin PRB is:

[0022]

[0023] wherein M is a memory depth of the power amplifier, is an Lth node in an Lth layer, located in an Lth phase recovery group; is an Lth node in an Lth layer, located in an Lth phase recovery group.

[0024] Preferably, in S1, the phase recovery layer calculation formula is:

[0025]

[0026] wherein M is a memory depth of the power amplifier, is a phase recovery vector.

[0027] Preferably, in S1, the size determination process of the real-valued time-delay KAN digital predistortion network or the vector-decomposed time-delay KAN digital predistortion network is: first, a dense network is established, and after the dense network is pruned, a corresponding predistortion network is obtained.

[0028] ​​Preferably, the real-valued time-delay KAN digital predistortion network or the vector-decomposed time-delay KAN digital predistortion network is trained by a training set and a validation set, and is verified by a test set; the input samples of the test set and the validation set are output signals of the power amplifier, and the target samples are input signals of the power amplifier; the input samples of the test set are input signals of the power amplifier, and the target samples are output signals of the power amplifier.

[0029] During the training process, the NMSE is used as the loss function, and the training is completed after the loss function converges.

[0030] Preferably, in S3, the co-directional component and the quadrature component processed by the predistortion are input to the power amplifier, and if a new state of the power amplifier appears, the coefficients of the real-valued time-delay KAN digital predistortion network or the vector-decomposed time-delay KAN digital predistortion network are updated, including the following steps:

[0031] S401, input signals and output signals of the power amplifier are collected, and a data set obtained by the power amplifier in the Nth time when a new state appears is recorded as .

[0032] S402, the data randomly sampled in the previous N-1 times is combined with the new state data to obtain a complete data set :

[0033] S403, the data randomly sampled in is used as , and the storage area of is overwritten;

[0034] S403, the real-valued time-delay KAN digital predistortion network or the vector-decomposed time-delay KAN digital predistortion network is trained using the complete data set , and the corresponding distortion network is updated after the training is completed.

[0035] A KAN-based digital predistortion device, comprising:

[0036] An input module configured to obtain co-directional components and quadrature components of an input signal, the input signal including signals between a current time and a past time, the past time being the current time minus a time delay;

[0037] A digital predistortion module configured to process the input signal by a real-valued time-delay KAN digital predistortion network, the real-valued time-delay KAN digital predistortion network including a plurality of kanlayers, an input of a next layer being an output of a previous layer, and an output of each layer being a product of an input signal of the layer and an activation function of the layer; the kanlayer is configured to compensate for nonlinear distortion caused by a power amplifier.​

[0038] An output module is configured to output the co-component and the quadrature component of the pre-distortion processed signal.

[0039] A KAN-based digital pre-distortion device comprises:

[0040] An input module is configured to acquire the amplitude and phase of an input signal, the input signal comprising signals between a current time and a past time, the past time being the current time minus a time delay;

[0041] A digital pre-distortion module is configured to process the input signal through a vector-decomposed time-delay KAN digital pre-distortion network, the vector-decomposed time-delay KAN digital pre-distortion network comprising a kanlayer, a phase recovery layer and a fully connected layer, the phase recovery layer comprising a plurality of cos PRBs and a plurality of sin PRBs, the kanlayer being configured to compensate for nonlinear distortion caused by a power amplifier, the phase recovery layer being configured to recover the amplitude and phase into the co-component and the quadrature component, and the fully connected layer being configured to output the co-component and the quadrature component.

[0042] An output module is configured to output the co-component and the quadrature component of the pre-distortion processed signal.

[0043] Compared with the prior art, the present application has the following beneficial effects:

[0044] The present application discloses a power amplifier linearization method based on a KAN network, which introduces a Kolmogorov-Arnold Network (KAN) in the digital pre-distortion processing process, and constructs a real-valued time-delay KAN digital pre-distortion network and a real-valued time-delay KAN digital pre-distortion network; for the real-valued time-delay KAN digital pre-distortion network, the input process of the network considers the input signals at the current time and the previous time, which can compensate for the memory of the power amplifier; for the vector-decomposed time-delay KAN digital pre-distortion network, on the basis of the real-valued time-delay KAN digital pre-distortion network, a phase recovery layer and a fully connected layer are further introduced, which can simplify the complexity of the network while maintaining similar performance to the previous KAN model; compared with the original digital pre-distortion method based on a neural network, the KAN digital pre-distortion method used in the present application uses fewer network parameters and achieves higher linearization capability. Meanwhile, in view of the problem that the behavior characteristics of the power amplifier will dynamically change with external conditions, a method for training and updating the coefficients of the digital pre-distorter is provided based on the memory of the KAN. Verification shows that, compared with a traditional fully connected neural network, the present application can achieve better fitting effect using a smaller network size, and has memory in addition to the catastrophic forgetting of the traditional neural network.

[0045] Further, based on the memory of KAN, the application provides a method for training and updating coefficients of a digital pre-distorter, which can train and update the coefficients of the digital pre-distorter when a new behavior characteristic of a power amplifier appears, and the updated digital pre-distorter can not only compensate the new nonlinear state, but also retain the memory of the previous state, so that the pre-distorter coefficients do not need to be updated and can be directly used for compensation when the nonlinear state of the power amplifier becomes the state that has appeared before. Therefore, the nonlinear state of the power amplifier can be compensated quickly, and the calculation resource or storage space can be saved. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 For the KAN-based digital pre-distortion architecture and training method;

[0047] Figure 2 For the real-valued time-delay KAN digital pre-distorter network structure;

[0048] Figure 3 For the vector decomposition time-delay KAN digital pre-distorter network structure;

[0049] Figure 4 For the structure block diagram of the performance evaluation method of the digital pre-distorter;

[0050] Figure 5 For the power spectrum comparison of the KAN-based digital pre-distorter and the traditional digital pre-distorter;

[0051] Figure 6 For the structure block diagram of the dynamic update of the KAN-based digital pre-distorter. DETAILED DESCRIPTION

[0052] Hereinafter, the terms "first", "second", "third", "fourth" are only used for description purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second", "third", "fourth" can explicitly or implicitly include one or more of the features.

[0053] The method for racking provided in the embodiments of the application can be applied to terminal devices such as mobile phones, tablet computers, wearable devices, vehicle-mounted devices, augmented reality (AR) / virtual reality (VR) devices, notebook computers, ultra-mobile personal computers (UMPCs), netbooks, personal digital assistants (PDAs), and the like. The embodiments of the application do not make any limitation on the specific type of the terminal device.

[0054] It is to be understood that the terms "first", "second", and the like, used in the description and the claims of this application are used to differentiate between similar objects, and are not necessarily used to describe a particular sequential or chronological order. It is to be understood that the use of the terms so construed can be interchanged, where appropriate, to refer to an embodiment of the application described herein in other than the order described. Furthermore, the terms "comprise" and "include", and variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, product, or apparatus that comprises a list of steps or units is not necessarily limited to those steps or units that are expressly listed, but can include other steps or units not expressly listed or inherent to such process, method, product, or apparatus.

[0055] Embodiment 1

[0056] The embodiment discloses a power amplifier linearization method based on KAN network, comprising the following steps:

[0057] S1, obtaining co-directional components and quadrature components of an input signal, the input signal comprising signals between a current time and a past time, the past time being the current time minus a time delay;

[0058] S2, processing the input signal through a real-valued time delay KAN digital predistortion network, the real-valued time delay KAN digital predistortion network comprising a plurality of kan layers, an input of a next layer being an output of a previous layer, and an output of each layer being a product of an input signal of the layer and an activation function of the layer; each kan layer being used to compensate for nonlinear distortion caused by a power amplifier;

[0059] S3, outputting co-directional components and quadrature components of the signal after predistortion processing.

[0060] In S2, in the real-valued time delay KAN (RVTDKAN for short) digital predistortion network, the input dimension of the network is determined by the memory depth of the power amplifier, and the output dimension is 2, representing two I and Q signals.

[0061] The network input is current I and Q data The I and Q data in the network respectively represent co-directional components and quadrature components, and past I and Q data The data delay length M is equal to the memory depth of the power amplifier, so the input dimension of the network is 2(M+1). The network output is I and Q data The relationship between the network input and the output can be expressed as:

[0062]

[0063] RVTDKAN is a multi-layer superimposed structure, each layer structure is the same. In the first layer, there are l input nodes, and output nodes, so the first layer has activation functions, l is the input scalar of the i-th node in the first layer is the input scalar of the i-th node in the first layer is the input scalar of the i-th node in the first layer l is the input scalar of the i-th node in the first layer is the input scalar of the i-th node in the first layer l is the input scalar of the i-th node in the first layer j is the input scalar of the i-th node in the first layer is the input scalar of the i-th node in the first layer l is the input scalar of the i-th node in the first layer i is the input scalar of the i-th node in the first layer is the input scalar of the i-th node in the first layer l is the input scalar of the i-th node in the first layer j is the input scalar of the i-th node in the first layer is the input scalar of the i-th node in the first layer

[0064]

[0065] is the input vector of the first layer l is the input vector of the first layer is the input vector of the first layer l is the input vector of the first layer is the input vector of the first layer

[0066]

[0067] The above formula is defined as the representation of a layer kanlayer, so the function expression of L-layer RVTDKAN is:

[0068]

[0069] wherein, the network activation function is a spline curve, which is expressed as:

[0070]

[0071] wherein, is the control point of the spline curve, which is also a trainable parameter of the network, and the number of control points is , the k order basis function of the spline curve, k the order basis function is calculated by the following iterative algorithm:

[0072]

[0073] wherein, is the i-th node in the spline curve, and the number of nodes is + k+1, initialized to uniform sampling in the interval [-1, 1].

[0074] Embodiment 2

[0075] S1, obtaining the amplitude and phase of the input signal, the input signal including the signal between the current time and the past time, the past time being the time of the current time minus the time delay;

[0076] S2, processing the input signal through a vector decomposition time delay KAN digital predistortion network, the vector decomposition time delay KAN digital predistortion network including a kanlayer, a phase recovery layer and a full connection layer, the phase recovery layer including a plurality of cosPRB and a plurality of sinPRB, the phase recovery layer being used for recovering the amplitude and the phase into the same direction component and the quadrature component;

[0077] S3, outputting the same direction component and the quadrature component of the signal after the predistortion processing.

[0078] In this embodiment, the specific structure of the vector decomposition time delay KAN (VDTDKAN for short) digital predistortion network in S2 is as follows:

[0079] 1) The network input is the amplitude and phase of the current time , and the amplitude and phase of the past time , the data delay length M being equal to the memory depth of the power amplifier. The output of the network is the IQ two-way data , and the relationship between the network input and the output can be expressed as:

[0080]

[0081] 2) The first layer input of the network is the amplitude and phase of the current and past time, assuming that the VDTDKAN has L layers of kanlayer, which is used to compensate the distortion caused by the nonlinearity of the power amplifier, then the first L layers of the VDTDKAN are expressed as:

[0082]

[0083] wherein .

[0084] 3) The L-layer kanlayer is connected to the phase recovery layer, which is used to recover the phase. The input to the phase recovery layer is the phase at the current and past times, as well as the output of the L-th layer of VDTDKAN. The phase recovery layer consists of multiple phase recovery blocks, each of which takes a phase value as input and corresponds to an output node value of the L-th layer. The phase recovery blocks (PRBs) are divided into two types: cos PRBs and sin PRBs, with an equal number of each type. M+1 cos PRBs and M+1 sin PRBs are defined as a phase recovery group, and the phase recovery layer has P phase recovery groups.

[0085] like The The node is located at the node. For each phase recovery group, the following operation is performed in the corresponding cos PRB, where For the output of cos PRB:

[0086]

[0087] like The The node is located at the node. For each phase recovery group, the following operation is performed in the corresponding sin PRB, where For the output of sin PRB:

[0088]

[0089] The entire phase retrieval layer can be expressed by the following formula:

[0090]

[0091] Where the phase recovery vector It is composed of P fundamental phase recovery vectors:

[0092]

[0093] The fundamental phase recovery vector is represented as:

[0094]

[0095] 4) Following the phase retrieval layer is a fully connected layer, used to separate the network output into I and Q forms. This is the last layer of VDTDKAN, represented as:

[0096]

[0097] in, The weights of the fully connected layer, Bias for the fully connected layer.

[0098] Embodiment 3

[0099] A KAN-based digital pre-distortion device comprises:

[0100] An input module is configured to acquire co-directional components and quadrature components of an input signal, the input signal comprising signals between a current time and a past time, the past time being the current time minus a time delay;

[0101] A digital pre-distortion module is configured to process the input signal through a real-valued time-delay KAN digital pre-distortion network, the real-valued time-delay KAN digital pre-distortion network comprising a plurality of kanlayers, an input of a next layer being an output of a previous layer, and an output of each layer being a product of an input signal of the layer and an activation function of the layer; the kanlayer is configured to compensate for nonlinear distortion caused by a power amplifier;

[0102] An output module is configured to output co-directional components and quadrature components of a signal after pre-distortion processing.

[0103] Embodiment 4

[0104] A KAN-based digital pre-distortion device comprises:

[0105] An input module is configured to acquire amplitudes and phases of an input signal, the input signal comprising signals between a current time and a past time, the past time being the current time minus a time delay;

[0106] A digital pre-distortion module is configured to process the input signal through a vector-decomposition time-delay KAN digital pre-distortion network, the vector-decomposition time-delay KAN digital pre-distortion network comprising a kanlayer, a phase recovery layer, and a fully connected layer, the phase recovery layer comprising a plurality of cos PRBs and a plurality of sin PRBs, the kanlayer being configured to compensate for nonlinear distortion caused by a power amplifier, the phase recovery layer being configured to recover the amplitudes and the phases into co-directional components and quadrature components, and the fully connected layer being configured to output the co-directional components and the quadrature components;

[0107] An output module is configured to output co-directional components and quadrature components of a signal after pre-distortion processing.

[0108] Embodiment 5

[0109] In this embodiment, a training acquisition process of the two RVTDKAN and VDTDKAN is disclosed.

[0110] S201, the input signal and the output signal of the power amplifier are collected as a set of data, the data is normalized and time-synchronized, and then the data is divided into a training set, a validation set and a test set according to a ratio of 8:1:1. The input sample in the training set and the validation set is the output signal of the power amplifier, and the target sample is the input signal of the power amplifier. The input sample in the test set is the input signal of the power amplifier, and the target sample is the output signal of the power amplifier.

[0111] S202, a real-valued time delay KAN (RVTDKAN) digital predistortion network or a vector decomposition time delay KAN (VDTDKAN) digital predistortion network is built, wherein the input dimension of the two networks is determined by the memory depth of the power amplifier, and the output dimension is 2, representing the output IQ two-way signal.

[0112] S203, the optimal size of the RVTDKAN and the VDTDKAN is determined. First, a dense network with a wide enough width of each hidden layer is established, and then a sparse network is automatically obtained through training and pruning, which is used as the final size of the digital predistorter.

[0113] S204, the training set in step 1 is used to train the network with the size determined in step 4. The NMSE is used as the loss function, and the training is completed when the loss function converges.

[0114] S205, the trained network is used as a digital predistorter to compensate for the nonlinearity of the power amplifier, and three predistortion effect indicators are measured, namely, the normalized mean square error (NMSE), the ACPR, and the error vector magnitude (EVM).

[0115] S206, the power amplifier will appear a new nonlinear state during use, so the coefficients in the digital predistorter need to be updated to compensate for the new nonlinear state. First, the power amplifier state detection is used to determine whether the power amplifier has a new state, if there is no new state, the digital predistorter coefficients are not updated, if there is a new state, the digital predistorter coefficients are updated. Since the KAN has memory, after updating the coefficients of the KAN, not only the new nonlinear state can be compensated, but also the previously appeared nonlinear state can be compensated, avoiding the need to update the digital predistorter coefficients when the power amplifier appears the previous nonlinear state. At the same time, in order to further improve the memory, the data backtracking method is used during training, that is, part of the data in the previous state data set is added to the current state data set.

[0116] In S206, the method for training and updating the digital predistorter coefficients when the power amplifier enters a new state is as follows:

[0117] 1) Acquire the input and output signals of the power amplifier in this state, process the data according to step 1, and obtain the dataset. Record the dataset obtained when the power amplifier enters a new state for the Nth time as [dataset name missing]. .

[0118] 2) Construct a complete dataset using data backtracking. That is, the data from the first N-1 random samples that were previously stored. With new state data Merging them yields a complete dataset. :

[0119]

[0120]

[0121] in Represents the random sampled dataset D The data.

[0122] 3) To Random sampling Data as and cover the storage area This serves as backtracking data when the power amplifier enters a new state for the (N+1)th time.

[0123] 4) Use the complete dataset Train a KAN-based digital predistortion network, and update the coefficients of the digital predistorter after training.

[0124] The following description, in conjunction with specific embodiments, provides further details.

[0125] Example 1, KAN-based digital predistortion architecture as follows Figure 1 As shown, the location of digital predistortion in the wireless communication transmission link is as follows: Figure 1 As shown, the signal, after baseband modulation and OFDM modulation, enters the digital predistorter. The predistorted signal, after passing through the power amplifier, compensates for the nonlinear characteristics of the power amplifier, ensuring that the output signal of the power amplifier does not exhibit significant distortion. The training method is also as follows... Figure 1 As shown, an indirect learning method is adopted, and the output of the power amplifier is collected as the input of the learned inverse model. During training, the loss function is the normalized mean square error between the output of the inverse model and the input of the power amplifier. When the loss function converges, it means that the training is complete. Then, the coefficients of the inverse model are copied into the digital predistorter.

[0126] In this embodiment, taking a transmission link with 16QAM modulation, 4096 subcarriers, a cyclic prefix length of 288, a signal bandwidth of 100MHz, an oversampling rate of 10, and a Doherty power amplifier as an example, the technical solution is clearly and completely described.

[0127] Step 1: Collect the input and output signals of the power amplifier into a dataset. After normalizing and synchronizing the data, divide it into training, validation, and test sets in an 8:1:1 ratio. In the training and validation sets, the input samples are the power amplifier's output signals, and the target samples are the power amplifier's input signals. In the test set, the input samples are the power amplifier's input signals, and the target samples are the power amplifier's output signals.

[0128] Step 2: Construct the Real-Valued Time Delay KAN (RVTDKAN) digital predistortion network and the Vector Decomposition Time Delay KAN (VDTDKAN) digital predistortion network.

[0129] The network structure of RVTDKAN is as follows: Figure 2 As shown, since the power amplifier has a memory depth of 4, the RVTDKAN input dimension is 10 and the output dimension is 2. The specific structural expression is as follows:

[0130] 1) The network input consists of I and Q data at the current time. The I and Q data represent the same-direction components and orthogonal components, respectively, as well as the I and Q data from past time points. The data delay length M is equal to the power amplifier's memory depth; therefore, the network's input dimension is 2(M+1). The network outputs two data streams, I and Q. The relationship between network input and output can be represented as:

[0131]

[0132] 2) RVTDKAN is a multi-layered structure, with each layer having the same structure. In the... l There are layers There are input nodes, with The nth output node, so the nth l There are a total of 100 floors One activation function, It is the first l The input scalar of the i-th node of the layer To the l +1st floor j Input scalar of each node The activation function, then the first l The first layer i Input scalar of each node To the l +1st floor j Input scalar of each node It can be represented as:

[0133]

[0134] Therefore, the first l Layer input vector To the l Layer output vector It can be represented as:

[0135]

[0136] Define the above expression as the representation of a single kanlayer, then the function expression of the L-layer RVTDKAN is:

[0137] 3)

[0139] The network activation function is a spline curve, expressed as:

[0140]

[0141] in, These are the control points of the spline curve, and also the trainable parameters of the network. The number of control points is... , spline curves k order basis functions, k The first-order basis functions are calculated using the following iterative algorithm:

[0142]

[0143] in, Let be the i-th node in the spline curve, and the number of nodes is . + k +1, initialized to uniform sampling in the interval [-1,1].

[0144] The network structure of VDTDKAN is as follows: Figure 3 As shown, since the power amplifier's memory depth is 4, the VDTDKAN input dimension is 5 and the output dimension is 2. The specific structural expression is as follows:

[0145] 1) The network input is the amplitude and phase at the current moment. And the amplitude and phase of past moments. The data delay length M is equal to the power amplifier's memory depth. The network output consists of two data streams, I and Q. The relationship between network input and output can be represented as:

[0146]

[0147] 2) The first layer input of the network is the amplitude at the current and past time points. Assuming VDTDKAN has L kanlayers to compensate for the distortion caused by the nonlinearity of the power amplifier, then the first L layers of VDTDKAN can be represented as follows:

[0148]

[0149] in .

[0150] 3) The L-layer kanlayer is connected to the phase recovery layer, which is used to recover the phase. The input to the phase recovery layer is the phase at the current and past times, as well as the output of the L-th layer of VDTDKAN. The phase recovery layer consists of multiple phase recovery blocks, each of which takes a phase value as input and corresponds to an output node value of the L-th layer. The phase recovery blocks (PRBs) are divided into two types: cos PRBs and sin PRBs, with an equal number of each type. M+1 cos PRBs and M+1 sin PRBs are defined as a phase recovery group, and the phase recovery layer has P phase recovery groups.

[0151] like The The node is located at the node For each phase recovery group, the following operation is performed in the corresponding cos PRB, where For the output of cos PRB:

[0152]

[0153] like The The node is located at the node For each phase recovery group, the following operation is performed in the corresponding sin PRB, where For the output of sin PRB:

[0154]

[0155] The entire phase retrieval layer can be represented by the following equation:

[0156]

[0157] Where the phase recovery vector The P basic phase recovery vectors are combined to form:

[0158]

[0159] The basic phase recovery vector is represented as:

[0160]

[0161] 3) The phase recovery layer is followed by a full connection layer, which is used to divide the output of the network into I and Q forms, and is the last layer of the VDTDKAN, and is represented as:

[0162]

[0163] wherein, is the weight of the full connection layer, is the bias of the full connection layer.

[0164] Step 3, determine the optimal size of the RVTDKAN and the VDTDKAN. First, a dense network with a wide enough width of each hidden layer is established, and then a sparse network is automatically obtained through training and pruning, and the sparse network is used as the final size of the digital pre-distorter. For the RVTDKAN, taking the initial network size set as (10, 10, 10, 2) as an example, after pruning, the RVTDKAN network size is (10, 6, 5, 2). For the VDTDKAN, the number of phase recovery groups p needs to be set first, taking p = 1 as an example, the initial network size is set as (5, 10, 10), (10, 2), and after pruning, the VDTDKAN network size is (5, 4, 10), (10, 2).

[0165] Step 4, use the training set in step 1 to train the network with the size determined in step 4. Take the normalized mean square error (NMSE) as the loss function, and the training is completed when the loss function converges. Taking the LBFGS optimizer as an example, the loss function has converged when the iteration reaches 100 steps, and the training is considered to be completed.

[0166] Step 5, use the trained network as a digital pre-distorter to compensate for the nonlinearity of the power amplifier, and calculate the normalized mean square error (NMSE), the absolute carrier power ratio (ACPR), and the error vector magnitude (EVM), respectively. The calculation method of each performance index is as follows: Figure 4The two KAN-based digital pre-distorters proposed by the application and three existing digital pre-distorters are compared in terms of parameter scale and performance index. As shown in Table 1, compared with the traditional neural network-based digital pre-distorters, the two KAN-based digital pre-distorters proposed by the application use fewer network parameters and achieve better linearization effect, and VDTDKAN uses fewer network scales and achieves the linearization effect close to that of RVTDKAN.

[0167] Table 1: Comparison of coefficient scale and performance of KAN-based digital pre-distorters and traditional digital pre-distorters

[0168]

[0169] Figure 5 The power spectrum of the power amplifier output signal is shown. Because the power amplifier nonlinear behavior causes the skirt of the signal power spectrum to appear on both sides of the bandwidth, the lower the skirt power value on both sides of the bandwidth of the digital pre-distorter, the better the performance. Figure 5 It can be seen intuitively that the two KAN-based digital pre-distorters proposed by the application have the lowest skirt power value on both sides of the bandwidth.

[0170] Step 6: The power amplifier will appear new nonlinear state in use, so the coefficients in the digital pre-distorter need to be updated to compensate for the new nonlinear state. The structure block diagram of the dynamic update of the KAN-based digital pre-distorter is shown in Figure 6 First, it is judged whether the power amplifier appears new state through power amplifier state detection. If no new state appears, the digital pre-distorter coefficients are not updated, and if a new state appears, the digital pre-distorter coefficients are updated. Because KAN has memory, after updating the coefficients of KAN, not only the new nonlinear state can be compensated, but also the previously appeared nonlinear state can be compensated, avoiding the need to update the digital pre-distorter coefficients when the power amplifier appears the previous nonlinear state. In order to further improve the memory, the data backtracking method is used during training, that is, part of the data of the previous state data set is added to the current state data set.

[0171] The method for training and updating the digital pre-distorter coefficients when the power amplifier appears a new state is as follows:

[0172] 1) Collect the input and output signals of the power amplifier in this state, process the data according to the method of step 1 and obtain the data set, and record the data set obtained by the Nth time that the power amplifier appears a new state as .

[0173] 2) Use the data backtracking method to construct a complete data set the data of the previous N-1 random sampling with the new state data merge to get a complete data set :

[0174]

[0175]

[0176] wherein, represent the data in the random sampling data set D , in practice, take .

[0177] 3) the data of the random sampling is taken as , and the storage area is overwritten as the backtracking data when the power amplifier appears a new state for the N+1 time. 4) use the complete data set

[0178] to train the KAN-based digital predistortion network, and update the coefficients of the digital predistorter after the training is completed. Table 2 is a comparison of the memory of the KAN-based digital predistorter and the original fully connected network-based digital predistorter. Since the power amplifier has different nonlinear characteristics under different signal bandwidths, the nonlinear characteristics of the power amplifier under signal bandwidths of 100MHz, 40MHz, and 15MHz are taken as states 1, 2, and 3. When the power amplifier sequentially experiences states 1, 2, and 3, the coefficients of the above two digital predistorters are trained and updated in the manner of step 6, respectively. After reaching state 3 and undergoing three times of coefficient updating, the performance indicators of the two digital predistorters with the latest updated coefficients under three states are calculated. As shown in Table 2, the enhanced real-time delay neural network digital predistorter, i.e., the fully connected network-based digital predistorter, only has good linearization ability under state 3, and has no linearization ability under states 1 and 2, i.e., the network has no memory. To compensate for the power amplifier under states 1 or 2, the network coefficients need to be updated again. Correspondingly, the KAN-based digital predistorter has good linearization ability under three states, verifying its memory.

[0179] Table 2 Comparison of memory of KAN-based digital predistorter and traditional digital predistorter.

[0180]

[0181]

[0182] ​The above merely provides the preferred embodiment of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for power amplifier linearization based on KAN network, characterized in that, Comprising the following steps: S1, obtaining the amplitude and phase of the input signal, the input signal comprising the signal between the current time and the past time, the past time being the time of the current time minus the time delay; S2, processing the input signal through the vector decomposition time delay KAN digital pre-distortion network, the vector decomposition time delay KAN digital pre-distortion network comprising a kanlayer layer, a phase recovery layer and a fully connected layer, the phase recovery layer comprising a plurality of cos PRBs and a plurality of sin PRBs, the kanlayer layer being used to compensate for the nonlinear distortion caused by the power amplifier, the phase recovery layer being used to recover the amplitude and phase into in-phase components and quadrature components, and the fully connected layer being used to output the in-phase components and the quadrature components; The specific structure of the vector decomposition time delay KAN (VDTDKAN) digital pre-distortion network in S2 is as follows: 1) Network input is the amplitude and phase at current time and the amplitude and phase at past time , data delay length M is equal to the memory depth of power amplifier, the network output is IQ two-way data The relationship between network input and output can be expressed as: 2) The first layer of the network inputs the amplitudes of the current and past times, assuming that the VDTDKAN has L layers of kanlayer, which are used to compensate for the distortion caused by the nonlinearity of the power amplifier, then the first L layers of the VDTDKAN are represented as: wherein ; 3) The L layers of kanlayer are connected to the phase recovery layer, which is used to recover the phase, the input of the phase recovery layer being the phases of the current and past times and the output of the Lth layer of the VDTDKAN, the phase recovery layer being composed of a plurality of phase recovery modules, each of which inputs a phase value corresponding to an output node value of the Lth layer, the phase recovery modules (PRBs) being divided into two types of cos PRBs and sin PRBs in equal number; defining M+1 cos PRBs and M+1 sin PRBs as a phase recovery group, the phase recovery layer having P phase recovery groups; If the first node is located in the first phase recovery group, then is the output of the cos PRB: Wherein, M is the memory depth of the power amplifier, is the Lth layer of the node, located in the phase recovery group; If the first node is located in the first phase recovery group, then is the output of the sin PRB: in, It is the Lth layer. The node is located at the node. One phase recovery group; The calculation formula of the phase recovery layer is: where the phase recovery vectors are combined from P base phase recovery vectors: The basic phase recovery vector is represented as: 4) The fully connected layer is after the phase recovery layer, which is used to divide the output of the network into I and Q forms, and is the last layer of the VDTDKAN, and is represented as: wherein, are weights of the fully connected layer, is a bias of the fully connected layer; S3, outputting the in-phase components and the quadrature components of the pre-distortion processed signal; further, inputting the in-phase components and the quadrature components processed by the pre-distortion into the power amplifier, and updating the coefficients of the vector decomposition time delay KAN digital pre-distortion network if a new state of the power amplifier appears.

2. The method of claim 1, wherein, In S1, the size determination process of the vector decomposition time delay KAN digital pre-distortion network is as follows: first, a dense network is established, and then a corresponding pre-distortion network is obtained after pruning the dense network.

3. The method of claim 1, wherein, The vector decomposition time delay KAN digital pre-distortion network is trained through the training set and the validation set, and verified through the test set; the input samples of the test set and the validation set are the output signals of the power amplifier, and the target samples are the input signals of the power amplifier; the input samples of the test set are the input signals of the power amplifier, and the target samples are the output signals of the power amplifier; During the training process, the NMSE is used as the loss function, and the training is completed after the loss function converges.

4. The method of claim 1, wherein, S3 comprises the following steps: S401, collect the input signal and the output signal of the power amplifier, and record the data set obtained by the power amplifier in the Nth new state as ; S402, combine the data of the previous N-1 random samplings with the new state data to obtain a complete data set : S403, to randomly sample data as , cover storage area of ; S403, using the complete data set Train the vector decomposition latency KAN digital predistortion network.

5. A KAN-based digital predistortion device for implementing the device of claim 1, characterized by Comprising: An input module is configured to acquire an amplitude and a phase of an input signal, the input signal including signals between a current time and a past time, the past time being the current time minus a time delay; A digital pre-distortion module is configured to process the input signal through a vector decomposition time-delay KAN digital pre-distortion network, the vector decomposition time-delay KAN digital pre-distortion network including a kan layer, a phase recovery layer and a full connection layer, the phase recovery layer including a plurality of cos PRBs and a plurality of sin PRBs, the kan layer being configured to compensate for nonlinear distortion caused by a power amplifier, the phase recovery layer being configured to recover the amplitude and the phase into in-phase components and quadrature components, and the full connection layer being configured to output the in-phase components and the quadrature components. An output module is configured to output the in-phase components and the quadrature components of the pre-distortion processed signal.

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