Neural network based power amplifier linearization system

Abstract

The invention provides a method and system for linearizing a nonlinear power amplifier (PA) in a radio frequency (RF) transmitter. The method begins with splitting the input RF signal into magnitude and phase components. The phase component is then processed using zero-phase digital filtering (ZPDF) in both forward and reverse directions to remove phase distortion. Following this, the phase-processed signal and its magnitude are transformed into in-phase (I) and quadrature (Q) components. These I and Q components are fed into a Time-Delay Feed- Forward Neural Network (TDFFNN), which models the nonlinear behavior of the PA. The trained TDFFNN generates a linearized output signal that compensates for the PA's nonlinear distortions, ensuring improved signal fidelity and transmission quality. The method includes performance evaluation to verify the linearization's effectiveness, including key metrics such as Adjacent Channel Leakage Ratio (ACLR), Normalized Mean Square Error (NMSE), and Error Vector Magnitude (EVM). This approach optimizes RF signal transmission in modern communication systems.

Description

[0001] NEURAL NETWORK BASED POWER AMPLIFIER LINEARIZATION SYSTEM

[0002] Field of the Invention

[0003] The present invention relates to power amplifier linearization techniques, and more particularly to a neural network-based method for linearizing power amplifiers using phase-processed input signals.

[0004] Background of the Invention

[0005] Power amplifiers are essential components in wireless communication systems, responsible for boosting the power of radio frequency (RF) signals before transmission. However, power amplifiers inherently exhibit nonlinear behaviour, especially when operated near their saturation region to maximize power efficiency. This nonlinearity introduces distortion in the amplified signal, leading to spectral regrowth and adjacent channel interference.

[0006] As wireless communication standards evolve and demand higher data rates, more complex modulation schemes with high peak-to-average power ratios (PAPR) are employed. These high PAPR signals are particularly susceptible to nonlinear distortion when passed through power amplifiers. Consequently, there is an ongoing need for effective linearization techniques to mitigate the nonlinear effects of power amplifiers while maintaining high power efficiency.Digital predistortion (DPD) has emerged as a widely adopted technique for power amplifier linearization. DPD involves applying a nonlinear function to the input signal that is inverse to the power amplifier's nonlinearity, thereby compensating for the distortion introduced by the amplifier. Traditional DPD approaches often rely on polynomial-based models, such as memory polynomials or generalized memory polynomials, to capture the nonlinear behaviour of power amplifiers.

[0007] However, as wireless systems become more complex and operate across wider bandwidths, conventional DPD techniques may struggle to accurately model and compensate for the increasingly intricate nonlinear characteristics of power amplifiers. This has led to growing interest in applying machine learning and neural network-based approaches to power amplifier linearization.

[0008] Neural networks offer the potential for more flexible and adaptive modelling of power amplifier behaviour compared to traditional polynomialbased methods. However, challenges remain in designing neural network architectures that can effectively capture both the static nonlinearity and memory effects exhibited by power amplifiers while maintaining computational efficiency for real-time operation.

[0009] Furthermore, the specific nature of RF signal processing introduces unique considerations for neural network-based linearization approaches. The complex-valued nature of baseband signals and the role of signalphase in RF nonlinearity present challenges that must be addressed to fully leverage the potential of neural networks for power amplifier linearization.

[0010] As wireless communication continues to advance, there is an ongoing need for improved linearization techniques that can enhance the performance and efficiency of power amplifiers across a wide range of operating conditions and signal characteristics.

[0011] Objective of the Invention

[0012] The principal objective of the present invention is to develop and implement Zero-Phase Digital Filtering (ZPDF) for preprocessing phase signals, thereby reducing phase discontinuities and enhancing neural network performance.

[0013] Another objective of the present invention is to utilize the h-swish activation function in neural networks to mitigate gradient vanishing issues and improve the modelling accuracy of power amplifiers.

[0014] Another objective of the present invention is to integrate these advancements into a Time-Delay Feed-Forward Neural Network (TDFFNN) for precise modelling and linearization of nonlinear power amplifiers (PAs).

[0015] Another objective of the present invention is to optimize the neural network architecture with tailored hidden layers and activation functions to support efficient real-time linearization of power amplifiers.

[0016] Another objective of the present invention is to enable neural networks to model complex nonlinearities and memory effects in poweramplifiers by transforming phase and magnitude components into in-phase (I) and quadrature (Q) representations.

[0017] A further objective of the present invention is to leverage machine learning methodologies for efficient training and adaptation of TDFFNNs in high-bandwidth communication systems, ensuring robust performance across diverse operating conditions.

[0018] Summary of the Invention

[0019] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0020] An aspect of the present invention introduces an approach to enhancing the linearization of nonlinear power amplifiers (PAs) in wireless communication systems. This invention addresses the challenges of signal distortion, spectral spreading, and reduced efficiency caused by nonlinearities and memory effects in PAs, especially in wideband scenarios characteristic of 5G and 6G networks.

[0021] The disclosed method incorporates Zero-Phase Digital Filtering (ZPDF) to preprocess the input signal by removing phase discontinuities. This ensures smoother phase transitions and enhances the accuracy of the subsequent modeling process. The system employs a Time-Delay Feed-Forward Neural Network (TDFFNN) equipped with advanced h-swish activation functions, which mitigate gradient vanishing issues and improve learning efficiency. The TDFFNN is designed to model the nonlinear behaviour of the PA with high precision, supporting wideband and high-throughput applications.

[0022] The architecture of the system facilitates the separation and processing of in-phase (I) and quadrature (Q) components of the signal, enabling accurate compensation for nonlinear distortions. By leveraging the flexibility and adaptability of neural network-based modeling, the system delivers superior linearization performance compared to traditional approaches.

[0023] This invention is fully compatible with existing RF transmitter systems, allowing seamless integration into current infrastructure. It provides a scalable, efficient, and adaptive solution to the challenges of PA linearization, significantly improving signal fidelity, adjacent channel leakage ratio (ACLR), and overall communication system performance. The innovation is particularly suited for high-bandwidth, next-generation wireless communication systems where precision and efficiency are paramount.

[0024] Brief description of the drawings

[0025] The figures described below depict various aspects of the system and methods disclosed herein. It should be understood that each figure depicts an embodiment of a particular aspect of the disclosed system andmethods, and that each of the figures is intended to accord with a possible embodiment thereof. Further, wherever possible, the following description refers to the reference numerals included in the following figures, in which features depicted in multiple figures are designated with consistent reference numerals.

[0026] Figure 1 depicts a block diagram of a transmitter line-up chain incorporating Digital Pre-Distortion (DPD) (100), according to one embodiment of the present invention.

[0027] Figure 2 illustrates the architecture of a Time-Delay Feed-Forward Neural Network (TDFFNN) (200) with integrated phase processing, designed for Digital Pre-Distortion (DPD) modeling and linearization, featuring two hidden layers, according to one embodiment of the present invention.

[0028] Figure 3 illustrates the flowchart for linearizing a nonlinear power amplifier (PA) (300), according to one embodiment of the present invention.

[0029] Figure 4 illustrates the input signal characteristics before and after applying Zero-Phase Digital Filtering (ZPDF) (400), in accordance with one embodiment of the present invention.

[0030] Figure 4(A) represents the phase characteristics of the input signal, comparing the signal before filtering, with conventional filtering and after ZPDF application.Figure 4(B) depicts the spectrum of the input signal, demonstrating the effects of ZPDF filtering on spectral characteristics compared to conventional filtering.

[0031] Figure 5 depicts a comparison of different activation functions, emphasizing their unique characteristics and behaviours (500), according to one embodiment of the present invention.

[0032] Fig. 6 illustrates the measured responses of the power amplifier (PA) with and without Digital Pre-Distortion (DPD) (600), according to one embodiment of the present invention.

[0033] Fig. 6(A) shows the measured AM-AM (Amplitude Modulation to Amplitude Modulation) response of the PA, comparing performance with and without the application of DPD.

[0034] Fig. 6(B) shows the measured AM-PM (Amplitude Modulation to Phase Modulation) response of the PA, comparing performance with and without DPD.

[0035] Fig. 7 illustrates the spectrum of the signal (700), comparing the performance of the linearized signal with that of the non-linearized signal.

[0036] Persons skilled in the art will appreciate that elements in the figures are illustrated for simplicity and clarity and may have not been drawn to scale. For example, the dimensions of some of the elements in the figure may be exaggerated relative to other elements to help to improve understanding of various exemplary embodiments of the present disclosure.Throughout the drawings, it should be noted that like reference numbers are used to depict the same or similar elements, features, and structures.

[0037] Detailed Description of the Invention

[0038] The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of exemplary embodiments of the invention as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary.

[0039] Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the invention. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness.

[0040] The terms and words used in the following description and claims are not limited to the bibliographical meanings but are merely used by the inventor to enable a clear and consistent understanding of the invention. Accordingly, it should be apparent to those skilled in the art that the following description of exemplary embodiments of the present invention are provided for illustration purpose only and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a component surface” includes reference to one or more of such surfaces.

[0041] By the term “substantially” it is meant that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations and other factors known to those of skill in the art, may occur in amounts that do not preclude the effect the characteristic is intended to provide.

[0042] Figures discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way that would limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged system. The terms used to describe various embodiments are exemplary. It should be understood that these are provided to merely aid the understanding of the description, and that their use and definitions, in no way limit the scope of the invention. Terms first, second, and the like are used to differentiate between objects having the same terminology and are in no way intended to represent a chronological order, unless where explicitly stated otherwise. A set is defined as a non-empty set including at least one element.FIG. 1 is a block diagram illustrating a transmitter line-up chain system incorporating Digital Predistortion (DPD) (100) for enhancing signal quality and linearity during transmission, in accordance with one embodiment. The transmitter system is configured to process and transmit a signal while mitigating the effects of non-linear distortions introduced by a Power Amplifier (PA). The system is designed to ensure that the transmitted signal maintains its integrity by employing a sophisticated feedback mechanism to counteract distortion caused by the PA.

[0043] In one embodiment, the system begins with a Predistorter (105), which is responsible for processing the input digital signal prior to transmission. The predistorter applies a predistortion algorithm that compensates for the inherent non-linearities of the PA. This algorithm alters the characteristics of the input signal in such a way that, when the signal passes through the PA, the output is rendered linear, effectively counteracting any distortions that would otherwise degrade the signal quality.

[0044] The modified digital signal is then passed to a Digital-to-Analog Converter (DAC) (110). The DAC is configured to convert the processed digital signal into an analog form suitable for further analog processing. In some cases, the DAC operates at a high resolution and a high sampling rate to ensure that the analog signal is a precise representation of the digital signal, thereby preserving the integrity of the transmitted data.Next, the analog signal is supplied to a Modulator (115) which is responsible for modulating the analog signal onto a carrier frequency. The modulation process enables the signal to be transmitted over radio frequencies, facilitating wireless communication. The modulated signal is then amplified by a series of amplification stages (120), which include a Predriver, a Driver, and a Main Power Amplifier (PA).

[0045] The Pre-driver amplifies the signal to an intermediate power level, preparing it for further amplification by the Driver. The Driver amplifies the signal to a higher power level, which is then transmitted to the Main PA for final amplification. The Main PA amplifies the signal to the necessary output power, ensuring that the signal reaches the required transmission power level for effective transmission over long distances.

[0046] In accordance with one embodiment, the transmitter system includes a Coupled Port (125) that enables monitoring of the output signal. The coupled port allows a portion of the amplified signal to be feedback into the system for analysis. This feedback mechanism facilitates continuous monitoring of the output signal, enabling the system to make real-time adjustments to ensure optimal performance. The inclusion of the coupled port ensures that any deviations from the desired output are detected and corrected promptly.

[0047] To further enhance the signal strength, a Voltage Gain Amplifier (VGA) (130) is included in the system. The VGA is configured to amplify the signal once more before transmission, ensuring that the final transmittedsignal meets the required power levels for reliable communication. The VGA ensures that the signal maintains a sufficiently high strength, even after undergoing multiple stages of amplification and signal processing.

[0048] Upon transmission, the signal is received and undergoes a Demodulator (135), which is responsible for extracting the original data from the modulated carrier signal. The demodulated signal is then converted back into a digital format by an Analog-to-Digital Converter (ADC) (140). The ADC operates at a high resolution to accurately capture the analog signal's characteristics and convert it into a digital signal for subsequent processing.

[0049] The digital signal is then processed by a Digital Down Converter (DDC) (145), which reduces the sampling rate and shifts the signal’s frequency down to baseband. This down conversion simplifies the signal, making it more suitable for further digital processing. In one embodiment, the DDC ensures that the signal is at the appropriate frequency and sampling rate for the next stages of signal processing.

[0050] Finally, a Predistorter is incorporated into the system as part of a feedback mechanism that continuously monitors the transmitted signal and makes real-time adjustments to maintain linearity. The predistorter operates by applying a complementary predistortion algorithm to the received signal, compensating for any distortions introduced during transmission, such as those caused by the PA or the environmental factors affecting signal propagation. The use of a predistorter in the feedback loop allows thesystem to ensure that the transmitted signal remains linear and distortion-free throughout the transmission process.

[0051] The transmitter system described herein leverages Digital Predistortion (DPD) techniques to enhance the quality and linearity of the transmitted signal. By incorporating predistortion algorithms both at the input and output stages of the transmission process, the system compensates for non-linearities introduced by the PA and other components, ensuring that the transmitted signal remains accurate and reliable. Additionally, the feedback mechanism provided by the coupled port and the predistorter enables real-time adjustments to maintain optimal performance, further enhancing the signal quality. This system is particularly beneficial in modem communication systems that require high fidelity and low distortion for effective data transmission.

[0052] Figure 2 introduces a Time-Delay Feed-Forward Neural Network (TDFFNN) architecture optimized for linearizing nonlinear power amplifiers (PAs) within radio frequency (RF) transmitters (200). This architecture employs advanced preprocessing and neural network modelling techniques to address nonlinearities and memory effects inherent in PAs, ensuring high signal fidelity and improved performance metrics.

[0053] In one embodiment, the method begins with the splitting the input RF signal into its magnitude and phase components. The phase component undergoes Zero-Phase Digital Filtering (ZPDF), which is a preprocessing step designed to eliminate phase distortion. ZPDF processes the inputsignal in both forward and reverse temporal directions, resulting in a bidirectional filtering process. Initially, the forward-filtered output is expressed as:

[0054] T

[0055]

[0056] (e7C0) = X(e>)H(e>)

[0057] where x

[0058]

[0059] (ejw) and H (ejw)are the Fourier transforms of the input signal and the filter, respectively.

[0060] Subsequently, the forward-filtered output undergoes a time-reversal process to produce a reverse-filtered signal. This reverse filtering operation ensures that any phase distortions introduced during the forward pass are negated. Mathematically, the reverse-filtered signal is represented as A

[0061]

[0062] '(e-7W) / f(e_7W), where X(e_7W) corresponds to the time-reversed representation of the input signal, and

[0063]

[0064] H(e-7lv), denotes the reversed frequency response of the filter. This bidirectional filtering approach ensures that the resulting signal is symmetric, free from phase distortions, and accurately preserves the original signal's properties. The combination of forward and reverse filtering effectively eliminates phase distortions, resulting in a signal that is well-suited for subsequent processing in the TDFFNN architecture.

[0065] The combination of the forward-filtered and reverse-filtered outputs ensures the elimination of any phase distortion in the signal. This process results in a zero-phase distortion output that preserves the integrity of the original signal. To further refine the signal, a second pass through the filter is performed, where the forward-filtered output is multiplied by the filter'sfrequency response ff(ejw). The resulting final output in the frequency domain is mathematically expressed as

[0066] 2

[0067] T

[0068]

[0069] (e>) = X(e7<0)|H(e>)|

[0070] 2

[0071] where |

[0072]

[0073] / / (ejw)| is the squared magnitude of the filter's frequency response. This result ensures a real-valued, distortion-free signal with smooth phase transitions and preserved spectral properties.

[0074] After preprocessing, the system transforms the phase-processed signal and its magnitude into in-phase (I) and quadrature (Q) components. This transformation enables the TDFFNN to model the temporal dependencies and memory effects of the PA. The signal fed into the TDFFNN is represented as:

[0075] X(n) = [I(n),... / (n - p), Q(r),... Q(n - p)]

[0076] where n is the current sample, and p is the memory order capturing past signal states.

[0077] The TDFFNN architecture consists of an input layer, two hidden layers, and an output layer. The first hidden layer contains 10 neurons, and the second hidden layer comprises 12 neurons. Each neuron computes its net input as:

[0078] net J} = / / ,. w} tjj Of t + b J}

[0079]

[0080] 7 = 1where wj represents the weight connecting the ithinput to the jthneuron, 0° is the output of the previous layer, and b is the bias term for the jthneuron.

[0081] The TDFFNN utilizes the h-Swish activation function in its hidden layers to enhance training performance and mitigate issues such as the vanishing gradient problem. The h-Swish activation function is mathematically defined as:

[0082] ( 0 if x < —3 '

[0083] f(x) = < x if x > +3 ■

[0084]

[0085] ^x (x + 3\6) otherwise

[0086] This activation function is designed to be smooth and unbounded, offering significant advantages over traditional activation functions like sigmoid or ReLU. The function helps the network learn more effectively by avoiding saturation issues and maintaining a steady gradient flow, which improves training efficiency and the overall performance of the TDFFNN model. This function enhances training efficiency, mitigates the vanishing gradient problem, and ensures robust modelling of nonlinear PA characteristics.

[0087] The output layer of the Time-Delay Feed-Forward Neural Network (TDFFNN) generates the linearized signal, which compensates for the nonlinearities introduced by the power amplifier (PA). The linearized output signal is represented as a combination of in-phase (I) and quadrature (Q) components, which are the modelled results of the PA behaviour. Mathematically, the output signal can be expressed as:Y( ) ~ VOUTW’ QOUTW}

[0088] Where IQUTW and Qour n) represent the in-phase and quadrature components of the linearized output signal at time step n, respectively. This output signal is the final step in the TDFFNN's operation, ensuring that the transmitted RF signal is linearized, thereby mitigating distortions caused by the PA and maintaining the quality of the transmitted signal.

[0089] The TDFFNN architecture effectively maps the nonlinear behaviour of the PA to produce a complex-valued output. This approach avoids simulating distortions for every possible input phase, thus reducing computational complexity and improving accuracy. The linearized output enhances key performance metrics such as adjacent channel leakage ratio (ACLR), normalized mean square error (NMSE), and error vector magnitude (EVM).

[0090] Figure 3 illustrates the method for linearizing a nonlinear power amplifier (PA), which follows several key steps to address PA nonlinearity and enhance overall signal fidelity and transmission quality. The method integrates signal splitting, phase preprocessing, neural network-based modelling, and performance evaluation to achieve effective linearization and improved signal integrity. Each step is specifically designed to address different aspects of the PAs behaviour, ensuring optimal performance throughout the process.

[0091] In one embodiment, the method begins at Step 305 by splitting the input radio frequency (RF) signal into its magnitude and phase components.This splitting is essential as it isolates these components, which are critical for precise processing in subsequent stages. By separating the magnitude and phase, the method ensures that the different aspects of the signal are handled independently. The magnitude component provides information on the amplitude of the signal, while the phase component contains critical timing and phase-related details that are required for phase preprocessing in later steps. This splitting ensures that the signal is properly prepared for further transformation and refinement, which is vital for accurate modelling and linearization of the nonlinear power amplifier.

[0092] At Step 310, a Zero-Phase Digital Filtering (ZPDF) technique is applied to the phase component of the signal. This technique employs bidirectional filtering, processing the phase data in both the forward and reverse temporal directions. The purpose of this step is to eliminate phase distortion, ensuring that the phase component remains free of artifacts that could degrade the accuracy of subsequent modelling. By maintaining the integrity of the phase, the method ensures that no distortion is introduced that could negatively impact the overall signal quality and subsequent linearization process.

[0093] At Step 315, the magnitude and phase-processed components of the signal are transformed into in-phase (I) and quadrature (Q) components. This transformation is critical because the l / Q components provide a complete and accurate representation of the signal in terms that can be effectively modelled. The l / Q components serve as the foundation forsubsequent steps in the method, ensuring that the signal is accurately captured and ready for the input into the neural network in later stages of the process.

[0094] At Step 320, input vectors are created for the Time-Delay Feed-Forward Neural Network (TDFFNN). These vectors include present and past values of the l / Q components, allowing the neural network to account for the temporal dependencies of the signal and its nonlinear behavior. This step is essential for capturing the dynamic and time-varying nature of the power amplifier’s (PA) nonlinearity, enabling the TDFFNN to accurately model the PAs behaviour over time and generate a linearized output signal.

[0095] Step 325 involves training the TDFFNN using the prepared l / Q components as input. The neural network utilizes an h-Swish activation function, designed to optimize training efficiency, mitigate gradient vanishing problems, and improve model accuracy. The TDFFNN consists of input, hidden, and output layers, each specifically tailored to address the nonlinearities inherent in the PA. During training, the network learns to model the PAs nonlinear behaviour, preparing it to generate an output signal that compensates for the PAs distortion.

[0096] At Step 330, the trained TDFFNN generates the linearized output signal. The trained network compensates for the nonlinearities introduced by the PA, ensuring that the output signal preserves its spectral characteristics and maintains high fidelity. This step is critical in the linearization process, as it effectively mitigates the distortion caused by thePA, allowing the signal to be suitable for transmission without compromising quality.

[0097] Step 335 involves evaluating the linearized output signal using key performance metrics. Metrics such as Adjacent Channel Leakage Ratio (ACLR), Normalized Mean Square Error (NMSE), and Error Vector Magnitude (EVM) are assessed to validate the effectiveness of the linearization process. These metrics are crucial for ensuring that the linearized signal meets the necessary transmission quality standards by reducing distortion, minimizing error, and improving overall signal integrity.

[0098] At Step 340, additional refinements are applied to the phase preprocessing step. These refinements include phase unwrapping to ensure smooth transitions and continuity in the phase signal. The aim of this step is to eliminate any residual inconsistencies from the phase processing, thereby enhancing the overall linearization process. The improved phase component contributes to further reducing distortion and improving the signal quality.

[0099] Finally, Step 345 concludes the method by emphasizing the overall improvements achieved in the PAs linearization, spectral efficiency, and signal quality. The method compensates for the nonlinearities of the PA, ensuring that the signal retains its integrity and is suitable for deployment in modern RF transmitter systems. This approach significantly improves signal fidelity and transmission quality, making it a robust solution for addressing PA nonlinearity in real-world communication systems.Figure 4 provides a comprehensive analysis of the input signal characteristics before and after the application of Zero-Phase Digital Filtering (ZPDF) (400), with a focus on both the time and frequency domains. ZPDF is a digital filtering technique with a frequency response, denoted as |

[0100]

[0101] / / (ejw)|.that is purely real-valued, ensuring the absence of phase distortions. In one embodiment, this feature is particularly significant for applications such as Digital Predistortion (DPD) and Power Amplifier (PA) linearization in 5G New Radio (NR) systems, where the accuracy of the signal directly influences the overall system performance. A 100 MHz TM 1.1 signal was utilized in one embodiment to validate the ZPDF method, demonstrating its capability to smooth phase transitions while preserving the spectral integrity of the signal, which is essential for efficient and reliable wireless communication.

[0102] In one embodiment, Figure 4(a) illustrates the time domain behaviour of the input signal, the ZPDF-filtered signal, and a conventionally filtered signal. The ZPDF-filtered signal exhibits significantly smoother phase transitions compared to the conventional filtered signal, which demonstrates abrupt phase changes. Such discontinuities in phase transitions, as observed with conventional filtering methods, may negatively impact the accuracy of DPD modelling and hinder effective PA linearization. In one embodiment, the smoother phase transitions achieved through ZPDF filtering improve the linearity of the transmitter system, ensuring superiorsignal integrity during transmission and thereby improving the overall system performance.

[0103] In some cases, Figure 4(a) also highlights the normalized mean square error (NMSE) between the input signal and the ZPDF-filtered signal, which is recorded at an impressive -47.24 dB. This low NMSE value indicates that the ZPDF technique preserves the original signal quality while simultaneously eliminating phase distortions. This optimization ensures that the signal is well-suited for DPD and PA linearization, leading to improved transmission accuracy and efficiency. In one embodiment, ZPDF’s ability to deliver smoother phase characteristics without compromising signal quality represents a significant advantage over conventional filtering techniques, which frequently degrade signal performance during preprocessing.

[0104] In one embodiment, Figure 4(b) presents the power spectral density (PSD) of the original input signal alongside that of the ZPDF-filtered signal. The near-perfect correlation between the two spectra demonstrates that ZPDF preserves the signal's frequency distribution and power levels. In contrast, conventional filtering methods often introduce spectral irregularities that may result in adjacent channel interference and diminished spectral efficiency. In one embodiment, the preservation of spectral characteristics is essential for maintaining compliance with regulatory emission standards and optimizing the utilization of frequency spectrum resources.In some cases, Figure 4(b) depicts the ZPDF-filtered signal retains a consistent power distribution, confirming the absence of spectral distortions. This feature is particularly advantageous in advanced wireless communication systems, such as 5G, where spectral efficiency and regulatory compliance are paramount. By mitigating adjacent channel leakage and ensuring spectral fidelity, ZPDF contributes to the reliability and efficiency of signal transmission. In one embodiment, these benefits make ZPDF an indispensable tool for systems requiring high signal fidelity and optimal spectrum utilization, particularly in dense network environments.

[0105] Figure 5 presents a comprehensive comparison of several commonly used activation functions in neural networks (500), emphasizing their distinct output behaviours and operating ranges. Each activation function has unique characteristics that influence how a neural network learns and processes data. The figure provides valuable insight into the properties of these functions, allowing practitioners to make informed decisions about which activation function is most suitable for a given task.

[0106] In one embodiment, the Sigmoid function is widely used for binary classification tasks due to its output range between 0 and 1, which is ideal for generating probabilistic outputs. The sigmoid function has an S-shaped curve, but one limitation is its susceptibility to the vanishing gradient problem. This occurs when gradients become exceedingly small for extreme input values, slowing or halting learning, particularly in deep networks.In some cases, the h-Swish (Hard Swish) function is depicted, with an output range from -1 to 1. This function is a computationally efficient approximation of the Swish function. By combining the benefits of Swish with the efficiency of ReLU, h-Swish is particularly suited for resource-constrained environments, such as mobile and edge devices, where computational resources are limited but efficiency is critical.

[0107] The ReLU (Rectified Linear Unit) function is also featured in the figure, with an output range of 0 to infinity. ReLU is one of the most commonly used activation functions due to its simplicity and effectiveness. It outputs the input value directly if positive and zero otherwise. While ReLU helps mitigate the vanishing gradient problem, it suffers from the "dying neuron" issue, where neurons can become inactive and contribute nothing to further learning.

[0108] Additionally, the Tansig function is shown, which operates in the range of 0 to infinity. The Tansig function is essentially a variation of the tanh function, emphasizing its zero-centered output. It can help with faster convergence, but like tanh, it is susceptible to the vanishing gradient problem when input values are extreme, limiting its effectiveness in deep networks.

[0109] Lastly, the Swish function, with an output range of 0 to infinity, is depicted in the figure. Swish is a smooth, non-monotonic activation function. It has been shown to outperform ReLU in certain deep learning tasks dueto its ability to maintain a non-zero gradient for all input values, facilitating more stable learning and improved performance.

[0110] Figure 6 provides a detailed analysis of the performance of a Power Amplifier (PA) under varying conditions, comparing its behaviour with and without the application of Digital Pre-Distortion (DPD) (600). The figure highlights the effectiveness of DPD in addressing the inherent nonlinearities of the PA, ensuring improved signal linearity and fidelity.

[0111] Figure 6(a) demonstrates the Amplitude Modulation to Amplitude Modulation (AM-AM) response of the PA. Without DPD, the PA exhibits a pronounced non-linear relationship between the input and output amplitudes, particularly at higher input power levels. This non-linearity introduces distortion into the transmitted signal, degrading communication system performance. In contrast, with the application of DPD, the AM-AM response is significantly linearized. This enhanced linearity ensures that the output power of the PA closely matches the input signal amplitude, thereby minimizing distortion and improving overall system reliability and efficiency.

[0112] The effectiveness of various activation functions in modeling the PAs non-linear characteristics is supported by the data presented in Table I. Among the tested activation functions, the h-Swish function achieves the highest accuracy, with an inverse modelling NMSE of -39.27 dB and a forward modelling NMSE of -39.13 dB when combined with Zero-Padding Digital Filtering (ZPDF). This highlights the importance of selecting anappropriate activation function to optimize the performance of the DPD model.

[0113] TABLE I :INVERSE MODELLING PERFROMANCE COMPARISON

[0114] Signal Activation Inverse Modelling NMSE Forward Modeling Function (dB) NMSE (dB) Without With ZPDF Without With ZPDF ZPDF ZPDF TM Sigmoid -36.57 -37.58 -36.39 -37.36 1.1 ReLU -37.18 -38.19 -37.24 -38.15 5G- Swish -37.74 -38.81 -37.71 -38.83 NR h-Swish -37.91 -39.27 -38.02 -39.13 100

[0115] MHz

[0116]

[0117] Table I presents the performance comparison of various activation functions used for inverse modelling and forward modelling of the power amplifier (PA) non-linearities, evaluated with and without Zero-Padding Digital Filtering (ZPDF) for TM1.1 5G-NR signals with a bandwidth of 100 MHz. The results highlight that the inclusion of ZPDF consistently improves both inverse and forward modelling normalized mean square error (NMSE). Among the activation functions tested, h-Swish demonstrates the best performance, achieving an inverse modelling NMSE of -39.27 dB and a forward modelling NMSE of -39.13 dB with ZPDF. This underscores thesuperior capability of h-Swish in capturing the PA's non-linear characteristics and enhancing the accuracy of the DPD model, compared to other activation functions such as Sigmoid, ReLU, and Swish

[0118] Further insights into the impact of DPD on PA linearization can be drawn from Table II, which compares the performance of various DPD techniques using TM1.1 5G-NR signals. The proposed PNN-DPD method outperforms conventional methods, such as MP-DPD and GMP-DPD, by achieving an NMSE of -38.13 dB, an EVM of 2.49%, and an ACPR of -53.21 dB.

[0119] TABLE II: DPD PERFROMANCE COMPARSION WITH TM1.1

[0120] Method Parameters

[0121] NMSE (dB) EVM (%) ACPR (dB) Without DPD -6.48 7.64 -33.28 MP - DPD -33.92 3.82 -47.64 GMP - DPD -36.51 3.04 -49.37 NN - DPD -37.85 2.81 -51.69 This work -38.13 2.49 -53.21 (PNN - DPD)

[0122]

[0123] Table II compares the performance of various Digital Pre-Distortion (DPD) methods applied to the TM1.1 5G-NR signal, evaluating the parameters of Normalized Mean Square Error (NMSE), Error Vector Magnitude (EVM), and Adjacent Channel Power Ratio (ACPR). The resultsdemonstrate significant improvements in performance with the application of DPD. The proposed PNN-DPD method outperforms all other techniques, achieving an NMSE of -38.13 dB, an EVM of 2.49%, and an ACPR of -53.21 dBc. These values represent a notable enhancement in signal linearity and integrity, compared to the baseline performance without DPD, which has an NMSE of -6.48 dB, an EVM of 7.64%, and an ACPR of -33.28 dBc. The PNN-DPD method also surpasses other DPD methods, including MP-DPD, GMP-DPD, and NN-DPD, in all three-performance metrics, highlighting its superior effectiveness in reducing distortion and improving the overall PA output.

[0124] Figure 6(b) illustrates the Amplitude Modulation to Phase Modulation (AM-PM) response of the power amplifier (PA), focusing on the phase distortion introduced by the PA as a function of the input signal's amplitude. Without Digital Pre-Distortion (DPD), the PA exhibits substantial phase distortion at higher input amplitudes, which leads to degradation in the transmitted signal's quality. This non-linear relationship between the input amplitude and output phase can impair the performance of advanced communication systems, where signal integrity is essential.

[0125] The application of DPD, however, effectively mitigates these phase distortions, leading to a more linear AM-PM response. This improvement in phase linearity is critical for maintaining the accuracy and reliability of modulated signals, especially in sophisticated communication systems where phase distortion can significantly impact performance. Thelinearization achieved by DPD ensures that the phase of the output signal closely tracks the input signal, reducing errors and enhancing signal fidelity.

[0126] Table III supports the findings in Figure 6(b) by presenting a performance comparison of various Digital Pre-Distortion (DPD) methods applied to TM3.1A signals. The proposed PNN-DPD method outperforms other methods, achieving a Normalized Mean Square Error (NMSE) of - 37.78 dB and an Error Vector Magnitude (EVM) of 2.68%, indicating a substantial improvement in phase linearity.

[0127] TABLE III: DPD PERFROMANCE COMPARSION WITH TM3.1A

[0128] Method Parameters

[0129] NMSE (dB) EVM (%) ACPR (dB) Without DPD -6.43 7.62 -33.19 MP - DPD -33.52 4.02 -47.03 GMP - DPD -36.09 3.25 -48.78 NN - DPD -37.46 3.1 -51.12 This work -37.78 2.68 -52.61 (PNN - DPD)

[0130]

[0131] Table III compares the performance of different Digital Pre-Distortion (DPD) methods applied to the TM3.1 A signal in terms of Normalized Mean Square Error (NMSE), Error Vector Magnitude (EVM), and Adjacent Channel Power Ratio (ACPR). Without any DPD, the PA shows significantdistortion with an NMSE of -6.43 dB, EVM of 7.62%, and ACPR of -33.19 dB, indicating poor signal quality. The application of various DPD techniques improves these metrics. Memory Polynomial DPD (MP-DPD) achieves an NMSE of -33.52 dB and an EVM of 4.02%, while Generalized Memory Polynomial DPD (GMP-DPD) further reduces distortion with an NMSE of -36.09 dB and an EVM of 3.25%. Neural Network DPD (NN-DPD) shows continued improvement, achieving an NMSE of -37.46 dB, an EVM of 3.1%, and an ACPR of -51.12 dB, signaling a noticeable enhancement in linearity and spectral performance.

[0132] The proposed PNN-DPD method surpasses all previous techniques, demonstrating the highest performance across all parameters. It achieves an NMSE of -37.78 dB, an EVM of 2.68%, and an ACPR of -52.61 dB, reflecting a significant reduction in signal distortion and adjacent channel interference. This outperforms MP-DPD, GMP-DPD, and NN-DPD, offering the best linearization of the power amplifier (PA) and improving overall signal quality and spectral efficiency. The results underscore the effectiveness of the proposed PNN-DPD method for achieving superior linearization in communication systems, ensuring enhanced system performance with minimal distortion.

[0133] Furthermore, Table IV provides information about the computational complexity of the various DPD methods, demonstrating that the proposed PNN-DPD requires 720 floating-point operations (FLOPs), which is relatively efficient considering the improvements in performance.Additionally, the PNN-DPD method delivers a superior Adjacent Channel Power Ratio (ACPR) of -53.21 dBc, which highlights its effectiveness in reducing spectral regrowth and adjacent channel interference. This result further underscores the efficiency and effectiveness of the proposed method in enhancing both the linearity and overall performance of the PA.

[0134] TABLE IV: COMPUTATION COMPLEXITY

[0135] Method Num. of floatingACPR (dB)

[0136] point operations

[0137] MP - DPD 624 -47.64 GMP - DPD 695 -49.37

[0138] NN - DPD 735 -51.69

[0139] This work 720 -53.21

[0140] (PNN - DPD)

[0141]

[0142] Table IV presents the computational complexity of different Digital Pre-Distortion (DPD) methods in terms of the number of floating-point operations (FLOPs) required and the resulting Adjacent Channel Power Ratio (ACPR). The table compares four DPD methods: MP-DPD, GMP-DPD, NN-DPD, and the proposed PNN-DPD method.

[0143] In some cases, MP-DPD requires 624 FLOPs and achieves an ACPR of -47.64 dB, indicating a relatively lower computational burden and good performance in terms of adjacent channel power. GMP-DPD increases thecomputational load to 695 FLOPs but delivers a better ACPR of -49.37 dB, showing improved performance at the cost of increased complexity. NN-DPD further increases the number of FLOPs to 735, providing an even better ACPR of -51.69 dB, indicating that more computation leads to improved performance. In comparison, the proposed PNN-DPD method strikes a balance between computational complexity and performance, requiring 720 FLOPs and achieving the best ACPR of -53.21 dB. This demonstrates that PNN-DPD achieves superior linearization and spectral efficiency while maintaining a reasonable computational complexity compared to the other methods.

[0144] Figure 7 provides a detailed comparison of the spectrum of signals processed through Digital Pre-Distortion (DPD) versus those without linearization (700). This illustration underscores the transformative impact of DPD on signal quality and spectral efficiency, which is critical in modern communication systems. The key focus of the figure lies in the differences between linearized and non-linearized signals, specifically highlighting improvements in spectral regrowth, power distribution, and adherence to allocated frequency bands.

[0145] The linearized signal, processed with DPD, demonstrates a spectrum that is sharply confined within its intended frequency band. This outcome reflects the effectiveness of DPD in mitigating the non-linear distortions introduced by the power amplifier (PA). Non-linearities in PAs are a primary cause of spectral regrowth, where signal power leaks into adjacentfrequency bands, creating interference and violating regulatory requirements. With DPD, the spectrum is clean and free of excessive spurious emissions, ensuring better compliance with spectral masks and reduced adjacent channel interference. This translates into enhanced spectral efficiency, allowing for better utilization of available bandwidth.

[0146] In contrast, the non-linearized signal exhibits substantial spectral distortion due to the absence of DPD correction. The non-linear behaviour of the PA leads to significant spectral regrowth, as seen in the broadened signal power into adjacent frequency channels. This spectral leakage not only reduces the efficiency of the communication system but also risks interference with nearby signals, degrading overall network performance. Additionally, the non-linearized signal may display lower power efficiency, with energy being wasted in the out-of-band emissions rather than being concentrated within the desired signal band.

[0147] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.

Claims

We Claim:

1. A method for linearizing a power amplifier (PA) in a radio frequency (RF) transmitter, comprising:receiving an input signal;splitting the input signal into magnitude and phase components; processing the phase component using zero-phase digital filtering (ZPDF) in forward and reverse directions to eliminate phase distortion; transforming the phase-processed signal and associated magnitude into in-phase (I) and quadrature (Q) components;supplying the I and Q components to a Time-Delay Feed-Forward Neural Network (TDFFNN); andgenerating a linearized output signal to compensate for nonlinear distortions of the PA.

2. The method as claimed in claim 1, wherein ZPDF comprises convolving the input signal with a filter's impulse response in the forward direction, resulting in a frequency-domain representation as:y(e^) = %(e>)H(e>),where x(ejw) and ff(ejw)are the Fourier transforms of the input signal and the filter, respectively.

3. The method as claimed in claim 2, further comprising reversing the forward-filtered signal in time and combining forward and reverse outputs to achieve zero-phase distortion.

4. The method as claimed in claim 3, wherein the combined forward and reverse outputs produce a frequency-domain representation that ensures the output is real-valued and free from phase distortion, expressed as:T(e>) = X(e^)| / f(e>)|5. The method as claimed in claim 1, wherein the TDFFNN is configured to model the nonlinear behaviour of the PA and generates a complex-valued output that accurately represents the linearized signal.

6. The method as claimed in claim 5, wherein the TDFFNN separates I and Q components into past and present data vectors and incorporates at least two hidden layers for processing.

7. The method as claimed in claim 6, wherein the TDFFNN utilizes an h-swish activation function, designed to enhance training efficiency and address vanishing gradient challenges, defined as:( 0 if x < —3 'f(x) = < x if x > +3 ■^x (x + 3\6) otherwise8. The method as claimed in claim 1, wherein the linearized output signal improves PA performance metrics, including adjacent channel leakage ratio (ACLR), normalized mean square error (NMSE), and error vector magnitude (EVM).

9. The method as claimed in claim 1, wherein the phase processing stage smooths the phase signals, removing the need for additional unwrapping and seamlessly integrating them into the Zero-Phase Digital Filtering (ZPDF) process.

10. A system for linearizing a nonlinear power amplifier (PA) within a radio frequency (RF) transmitter, the system comprising:a preprocessing module configured to split an input signal into magnitude and phase components and perform phase processing using zero-phase digital filtering (ZPDF);a signal transformation module configured to convert the phase-processed signal into in-phase (I) and quadrature (Q) components;a Time-Delay Feed-Forward Neural Network (TDFFNN) with at least two hidden layers;a training subsystem to model the nonlinear behaviour of the PA; and an output module to generate a linearized output signal.

11. The system as claimed in claim 10, wherein the preprocessing module includes a phase normalization mechanism to ensure consistency during phase signal processing.

12. The system as claimed in claim 10, wherein the TDFFNN comprises a first hidden layer and a second hidden layer, each with a specific number of neurons, and utilizes linear activation in the output layer.

13. The system as claimed in claim 10, further comprising a feedback loop to monitor real-time performance metrics and adjust TDFFNN parameters dynamically for optimal performance.

14. The system as claimed in claim 10, wherein the PA is selected from the group consisting of laterally diffused metal-oxide-semiconductor (LDMOS) amplifiers, gallium nitride (GaN) amplifiers, and silicon-based amplifiers.

15. The system as claimed in claim 10, wherein the TDFFNN is trained using datasets that encompass a diverse range of modulation schemes, including but not limited to Quadrature Phase Shift Keying (QPSK), Orthogonal Frequency Division Multiplexing (OFDM), and 16- Quadrature amplitude modulation (QAM), 64 QAM, 256 QAM.

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