Methods, apparatuses, and computer program products for digitial pre-distortion modeling

Abstract

A method, apparatus and computer program product are provided for performing digital pre-distortion modeling of base station elements. In the context of a method, the method includes obtaining a neural network (NN) configured to model a base station element or an error signal thereof. The method further includes computing a forward path of the NN based on input data and an adaptation bandwidth associated with the element; generating an error metric of the NN based on a usable bandwidth associated with the at element of the base station, where the adaptation bandwidth exceeds the usable bandwidth; and applying the error metric to the hidden layers of the NN to adapt at least one coefficient toward reducing the error metric. The method includes increasing the adaptation bandwidth relative to the usable bandwidth and reprocessing the input data in response to the error of the NN failing to meet a threshold.

Description

METHODS, APPARATUSES, AND COMPUTER PROGRAM PRODUCTS FOR DIGITIAL PRE-DISTORTION MODEEINGTECHNICAE FIELD

[0001] An example embodiment relates generally to techniques for generating neural networks to model digital pre-distortion (DPD) in elements of a base station.BACKGROUND

[0002] Various types of base stations are subject to emission requirements based on the location in which the base station is deployed. Compliance with emissions requirements is typically achieved through use of DPD algorithms that model non-linear behavior of one or more elements of the base station. For example, traditional approaches may utilize a DPD algorithm to cancel intermodulation projects on adjacent channels caused by the non-linearity of a transmitting power amplifier (PA). Typical approaches to DPD use terms derived from Volterra Kernels in the form of generalized memory polynomials (GMP) that are representative of power shifts and time shifts (e.g., delays). However, such approaches require optimization of the GMP terms with respect to power and delay terms. The optimizations are dependent upon the signal configuration at the base station and require significant processing time due to the thousands of terms utilized in legacy DPD algorithms. For example, existing DPD algorithms typically require searching thousands of power and delay combinations and, thus, require an increased processing time of multiple days.

[0003] Due to the lengthy processing times, base stations are typically optimized offline prior to their installation at a target location. Traditionally, no further optimization is performed following installation. Further, the offline optimizations are commonly performed with worse case signal configurations. However, various installation sites may demonstrate diverse signal figurations and, thus, the existing approach of one offline optimization per-base station may result in sub-optimum performance.BRIEF SUMMARY

[0004] A method, apparatus and computer program product are provided in accordance with an example embodiment in order to generate and train neural network models to model characteristicsof one or more elements of a base station. In various embodiments, the present method, apparatus, and computer program product provide improved solutions for determining an optimal modeling result of nonlinear behavior of a base station element based at least in pail on a novel neural network architecture. In some embodiments, the model architecture defines new filtering domains that may be used in prediction and backpropagation. For example, the present disclosure provides a modified model architecture that avoids the complexities of model backpropagation (e.g., numerical gradient computation) and implementation by defining a filter bandwidth (also referred to herein as “adaptation bandwidth”) and a useable bandwidth for parametrizing the neural network. The modified neural network may perform forward path computation and back propagation based on the filter bandwidth and a plurality of non-filtered, non-linear activation functions. During training, the error of the modified neural network may be computed based on the useable bandwidth. The ratio of filter bandwidth to useable bandwidth may be configured to a value greater than 1.0. During optimization of the neural network (e.g., training iterations), the filter bandwidth may be further increased relative to the useable bandwidth until the neural network converges around an acceptable level of error.

[0005] In some embodiments, the filter bandwidth represents the bandwidth of a filter applied to the desired signal (e.g., output of the neural network), such as the output signal or error signal of a base station element. In some embodiments, the useable bandwidth represents a target bandwidth associated with the base station element. Traditional neural network architectures for modeling radio hardware are evaluated and optimized with an un-filtered desired function (e.g., power amplifier output), where input signals are band limited. However, in real-world implementations of radio hardware, both the input and output signals of the hardware are band-limited (e.g., no hardware is used that operates on an unfiltered basis). Accordingly, the desired signal of the neural network may be filtered to reflect the practical expectation of band-limited signals in real hardware. However, the introduction of filtering may contribute to a raise error power spectral density (PSD) beyond a threshold bandwidth. The root cause of the rise in error PSD may be the use of non-band limited activation functions in the hidden layers of the neural network. For example, the non-band limited activation functions, when produced with input, may produce a high order of intermodulation products that span beyond the bandwidth of the filter applied to the desired signal. When the activation function output has a mismatch bandwidth with the filtereddesired function, the adapted backpropagation coefficients may demonstrate increased levels of error, especially at higher frequency values.

[0006] In various embodiments, the present method, apparatus, and computer program product provide improved solutions to overcome the above-described challenges of neural network optimization and DPD modeling. In various embodiments, the modified neural network architecture overcomes these technical challenges by implementing the filter bandwidth and useable bandwidth as further described herein. In some embodiments, by increasing the filter bandwidth relative to the useable bandwidth, a significant improvement in model error is obtained within the useable bandwidth. Further, such improvement is achieved with a lower number of coefficients as compared to common neural networks and without requiring complex gradient computations in backpropagation. As a result, the modified neural network may be practically implemented at the base station to optimize base station operation in real time to comply with emission policies while fulfilling customer needs specific to the installation location. Additional examples arc described herein, and other embodiments will become apparent from the proceeding description without departing from the spirit and scope of the disclosure.

[0007] In at least one embodiment, a method is provided that includes obtaining a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; processing input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and a respective iteration of processing the input data comprises: computing, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; generating an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and applying the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; following the at least one iteration, determining that the error of the neural network fails to meet a predetermined threshold; and in response to the determining that the error of the neural network fails to meet a predetermined threshold: increasingthe adaptation bandwidth relative to the usable bandwidth; and reprocessing the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth.

[0008] In some embodiments, the method further includes predicting, via the at least one additional iteration, a plurality of adapted coefficients for the plurality of hidden layers of the neural network; and controlling operation of the base station based at least in part on the adapted coefficients of the neural network. In some embodiments, the method further includes training the neural network to generate a band-limited output signal based at least in part on the input data, the adaptation bandwidth, and the plurality of adapted coefficients, wherein the band-limited output signal comprises at least one of i) a pre-distortion signal of the at least one element of the base station, or ii) the at least one error signal of the at least one element of the base station; following convergence of the neural network, computing the forward path of the neural network to generate the band-limited output signal based at least in part on the input data and a portion of output bandwidth based at least in part on a ratio of the useable bandwidth to the adaptation bandwidth; and controlling operation of the base station based at least in part on the band-limited output signal.

[0009] In some embodiments, the method further includes predicting the plurality of adapted coefficients further based at least in part on at least one predefined emission policy. In some embodiments, the at least one element of the base station comprises at least one power amplifier (PA) of the base station such that, following the convergence, the neural network embodies an optimal model of an output signal of the at least one PA or the at least one error signal of the at least one PA in real time. In some embodiments, controlling operation of the base station comprises cancelling at least one intermodulation product of two or more adjacent channels of the base station based at least in part on at least one of the output signal or the at least one error signal.

[0010] In some embodiments, the plurality of hidden layers comprises a plurality of unfiltered, non-linear terms. In some embodiments, the plurality of unfiltered, non-linear terms are based at least in part on a set of values of signal power of the base station from memory. In some embodiments, the plurality of unfiltered, non-linear terms comprise at least one of a hyperbolic tangent (tanh) function, a Sigmoid function, or a rectified linear unit (ReLU) function.

[0011] In some embodiments, a respective hidden layer of the plurality of hidden layers comprises a plurality of neurons; and in a respective iteration of processing the input data, the computing of the forward path of the neural network is performed without band limiting the plurality of neurons.In some embodiments, a ratio of the increased adaptation bandwidth the usable bandwidth is greater than 1.0. In some embodiments, the base station embodies a gNodcB. In some embodiments, a respective iteration of processing the input data further comprises: performing phase normalization of the linear real input signals and imaginary input signals at the input layer of the neural network to generate phase-normalized input data; and computing the forward path of the neural network based at least in part on the phase-normalized input data and the adaptation bandwidth associated with the at least one element of the base station.

[0012] As further described below, in some embodiments, one or more operations of the abovedescribed methods are performed by an apparatus including at least one processor and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus to perform the one or more operations. For example, an apparatus may include at least one processor and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus to obtain a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; process input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and, in performance of a respective iteration of processing the input data, the instructions cause the apparatus at least to: compute, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; generate an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and apply the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; following the at least one iteration, determine that the error of the neural network fails to meet a predetermined threshold; and in response to a determination that the error of the neural network fails to meet a predetermined threshold: increase the adaptation bandwidth relative to the usable bandwidth; and reprocess the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth. Inthe same example, the apparatus may also perform other operations and / or embody additional aspects of the abovc-dcscribcd methods.

[0013] In various embodiments, as further described below, provided herein is a computer program product including at least one non-transitory computer-readable storage medium having computer-executable program code instructions stored therein, the computer-executable program code instructions including program code instructions configured for performing one or more operations and / or embody additional aspects of the above-described methods. For example, a computer program product may include at least one non-transitory computer-readable storage medium having computer-executable program code instructions stored therein, the computerexecutable program code instructions including program code instructions configured to obtain a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; process input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and, in performance of a respective iteration of processing the input data, the program code instructions are configured to: compute, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; generate an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and apply the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; following the at least one iteration, determine that the error of the neural network fails to meet a predetermined threshold; and in response to a determination that the error of the neural network fails to meet a predetermined threshold: increase the adaptation bandwidth relative to the usable bandwidth; and reprocess the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth. In the same example, the program code instructions may also be configured to perform additional operations and / or embody additional aspects of the above-described methods.

[0014] In various embodiments, as further described below, one or more operations of the abovedescribed methods arc performed by an apparatus having means for performing the one or more operations. For example, an apparatus may include means for obtaining a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; means for processing input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and means for performing a respective iteration of processing the input data comprises: means for computing, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; means for generating an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and means for applying the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; means for determining that the error of the neural network fails to meet a predetermined threshold following the at least one iteration; and, in response to the determining that the error of the neural network fails to meet a predetermined threshold: means for increasing the adaptation bandwidth relative to the usable bandwidth; and means for reprocessing the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth. In the same example, the apparatus may embody additional aspects and / or include additional means for performing additional operations of the above-described methods.BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Having thus described certain example embodiments of the present disclosure in general terms, reference will hereinafter be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

[0016] FIG. 1 illustrates an example of a communication network in which an example embodiment of the present disclosure may be implemented;

[0017] FIG. 2 illustrates a block diagram of an apparatus that may be configured in accordance with an example embodiment of the present disclosure;

[0018] FIG. 3 shows an example architecture of a modified neural network in accordance with some embodiments of the present disclosure;

[0019] FIG. 4 shows another example architecture of a modified neural network in accordance with some embodiments of the present disclosure;

[0020] FIG. 5 shows charts of example error power spectral density (PSD) achieved in an existing neural network and neural networks modified in accordance with some embodiments of the present disclosure;

[0021] FIG. 6 shows an example neural network optimization process that may be performed by a base station in accordance with some embodiments of the present disclosure;

[0022] FIG. 7 shows an example neural network optimization process that may be performed by a base station in accordance with some embodiments of the present disclosure;

[0023] FIG. 8 shows an example architecture of a common neural network according to existing machine learning techniques; and

[0024] FIG. 9 shows an example architecture of a common neural network augmented with phase rotation according to existing techniques for phase normalization.DETAILED DESCRIPTION

[0025] Some embodiments will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all, embodiments are shown. Indeed, various embodiments may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like reference numerals refer to like elements throughout.

[0026] As illustrated in FIG. 1 , a communication network 100 is provided in accordance with various embodiments of the present disclosure. In some embodiments, the communication network 100 includes a base station 101 configured to provide radio communication services to a plurality of user equipment (UEs) 110. By way of example, the network 100 may be deployed within a radio access architecture based on long term evolution advanced (LTE Advanced, LTE-A) and / or newradio (NR, 5G). However, the system may be deployed in other network architectures including within other communication networks including, for example, other communication networks developed in the future, e.g., sixth generation (6G) networks, as well as any of a number of existing networks including a universal mobile telecommunications system (UMTS) radio access network (UTRAN, E-UTRAN or NG-RAN), wireless local area network (WLAN or WiFi), worldwide interoperability for microwave access (WiMAX), Bluetooth®, personal communications services (PCS), ZigBee®, wideband code division multiple access (WCDMA), systems via ultra-wideband (UWB) technology, sensor networks, mobile ad-hoc networks (MANETs) and Internet Protocol multimedia subsystems (IMS) or any combination thereof. In some embodiments, the base station 101 embodies a gNodeB.

[0027] The UE 110 may be any type of user terminal, terminal device, etc. to which resources on the air interface are allocated and assigned. For example, the UE may be a portable computing device such as a wireless mobile communication device including, but not limited to, the following types of devices: a mobile station (mobile phone), smartphone, personal digital assistant (PDA), handset, device using a wireless modem (alarm or measurement device, etc.), laptop and / or touch screen computer, tablet, game console, notebook, and multimedia device. The user equipment may also be called a subscriber unit, mobile station, remote terminal, access terminal, user terminal or user equipment (UE) just to mention but a few names or apparatuses.

[0028] In some embodiments, the base station 101 is configured to obtain, train, and execute one or more neural networks to model the characteristics of one or more elements of the base station such that the operation of the base station may be optimized to meet emissions requirements and / or other performance criteria. In some embodiments, the base station 101 stores, trains, and executes a modified neural network 300 as diagrammed in FIG. 3 or FIG. 4 to model non-linear behavior of a power amplifier (or other base station element) to enable cancellation of intermodulation products on adjacent channels caused by non-linearity of the power amplifier output. In some embodiments, the architecture of the neural network 300 does not require optimization per each signal configuration as in legacy DPD techniques. In various embodiments, using the neural network 300, the base station 101 is able to identify the most optimum modeling result by adapting the weights (e.g., coefficients) of the model in real time. For example, the base station 101 may determine its own optimization automatically instead of relying upon pre-installation optimizationperformed in existing approaches. In doing so, the base station 101 may achieve more optimum performance at the installation location as compared to a base station optimized using legacy DPD.

[0029] In some embodiments, the base station 101 is configured to obtain a neural network configured to model one or elements of the base station (e.g., power amplifier, power supply, baseband unit, antennae, and / or the like). In some embodiments, the base station 101 is configured to train the neural network to generate a band-limited output signal of the modelled element based at least in part on input data including real and imaginary signals with memory. In some embodiments, the band-limited output signal embodies a pre-distortion signal of the element being modeled. Additionally, or alternatively, the band-limited output signal embodies one or more error signals of the element.

[0030] In some embodiments, the base station 101 is configured to process input data using the neural network for one or more iterations, the input data including linear real input signals and imaginary input signals with memory. In some embodiments, in an iteration of processing the input data, the base station 101 is configured to computing a forward path of the neural network based at least in part on the input data and an adaptation bandwidth of the element being modeled (also referred to herein as a “filter bandwidth”). In some embodiments, the base station 101 is further configured to generate an error metric of the neural network for the forward path based at least in part on a usable bandwidth associated with output signal of the element being modeled. The usable bandwidth may be configured to be less than the adaptation bandwidth. For example, a ratio of the adaptation bandwidth to the useable bandwidth may be greater than 1. In some embodiments, the base station 101 is further configured to apply the error metric to the neural network via backpropagation to adapt one or more coefficients of one or more network layers toward reducing the error metric. In some embodiments, the base station 101 is configured to perform additional iterations until the error metric converges around a final value.

[0031] In some embodiments, the base station 101 is configured to determine whether the error of the neural network meets a predetermined threshold following the one or more iterations. In some embodiments, in response to determining that the error of the neural network fails to meet the predetermined threshold, the base station 101 is configured to increase the adaptation bandwidth relative to the usable bandwidth. For example, the base station 101 may increase a ratio of the adaptation bandwidth to the usable bandwidth from 1.05 to 1.18 or another suitable value. It will be understood that the ratios described are provided by way of example and other values arecontemplated according to the ratio relationships described herein. In some embodiments, the base station 101 is configured to reprocess the input data using the neural network and based on the increased adaptation bandwidth for one or more additional iterations until the model converges and the error of the model meets the error threshold. The base station 101 may continue to increase the adaptation bandwidth and retraining the model until threshold-satisfying convergence is achieved. In the one or more additional iterations, the base station 101 may predict a plurality of adapted coefficients that optimize the neural network. The base station 101 may control one or more operations based at least in part on the adapted coefficients and trained neural network, such as cancellation of intermodulation products.

[0032] In some embodiments, the base station 101 is configured to predict the adapted coefficients further based on one or more predefined emission policies. In some embodiments, the base station 101 is configured to control base station operations based on the adapted coefficients, the bandlimited output signal obtained from the neural network, the error signal obtained from the neural network, and / or the like to achieve compliance with the one or more predefined emissions policies.

[0033] FIG. 2 shows an example apparatus 200 according to one embodiment. The apparatus 200 may be an embodiment of a base station 101. In some embodiments, the apparatus 200 may include a processor 202, memory 204, and network interface 206. The apparatus 200 may be configured to execute the operations described herein. For example, one or more of the apparatus 200 may be configured to perform the neural network optimization process 600 shown in FIG. 7 and described herein. As another example, one or more of the apparatus 200 may be configured to perform the neural network optimization process 700 shown in FIG. 7 and described herein. Although these components are described with respect to the performance of various functions, it should be understood that the particular implementations necessarily include the use of particular hardware. It should also be understood that certain of these components may include similar or common hardware. For example, two sets of circuitries may both leverage use of the same processor, network interface, storage medium, or the like to perform their associated functions, such that duplicate hardware is not required for each set of circuitries.

[0034] In some embodiments, the processor 202 (and / or co-processor or any other processing circuitry assisting or otherwise associated with the processor) may be in communication with the memory 204 via a bus for passing information among components of the apparatus. The memory 204 is non-transitory and may include, for example, one or more volatile and / or non-volatilememories. In other words, for example, the memory 204 may be an electronic storage device (e.g., a non-transitory computer-readable storage medium). The memory 204 may be configured to store information, data, content, applications, instructions, or the like for enabling the apparatus to carry out various functions in accordance with an example embodiment disclosed herein. For example, the memory 204 may store neural networks and related data such, as coefficients, weight values, error thresholds, adaptation bandwidths, useable bandwidths, band-limited output signals, and / lor the like. In another example, the memory 204 may store emissions policies. In still another example, the memory 204 may store error metrics associated with trained iterations of a neural network.

[0035] The processor 202 may be embodied in a number of different ways and may, for example, include one or more processing devices configured to perform independently. In some non-limiting embodiments, the processor 202 may include one or more processors configured in tandem via a bus to enable independent execution of instructions, pipelining, and / or multithreading. The use of the term “processor” may be understood to include a single core processor, a multi-core processor, multiple processors internal to the apparatus, and / or remote or “cloud” processors. In some embodiments, the processor 202 may be configured to execute instructions stored in the memory 204 and / or circuitry otherwise accessible to the processor 202. In some embodiments, the processor 202 may be configured to execute hard-coded functionalities. As such, whether configured by hardware or software methods, or by a combination thereof, the processor 202 may represent an entity (e.g., physically embodied in circuitry) capable of performing operations according to an embodiment disclosed herein while configured accordingly. Alternatively, as another example, when the processor 202 is embodied as an executor of software instructions, the instructions may specifically configure the processor 202 to perform the algorithms and / or operations described herein when the instructions are executed.

[0036] In some embodiments, the apparatus 200 may optionally include input / output circuitry that may, in turn, be in communication with processor 202 to provide output to a user and / or other entity and, in some embodiments, to receive an indication of an input. The input / output circuitry may comprise a user interface and may include a display, and may comprise a web user interface, a mobile application, a query-initiating computing device, a kiosk, or the like. In some embodiments, the input / output circuitry may also include a keyboard, a mouse, a joystick, a touch screen, touch areas, soft keys, a microphone, a speaker, or other input / output mechanisms. Theprocessor and / or user interface circuitry comprising the processor may be configured to control one or more functions of one or more user interface elements through computer program instructions (e.g., software and / or firmware) stored on a memory accessible to the processor (e.g., memory 204, and / or the like).

[0037] The network interface 206 may be any means such as a device or circuitry embodied in either hardware or a combination of hardware and software that is configured to receive and / or transmit data from / to a network and / or any other device, circuitry, or module in communication with the apparatus 200. In this regal’d, the network interface 206 may include, for example, a network interface for enabling communications with a user equipment, administrator console, control plane, and / or the like. For example, the network interface 206 may include one or more network interface cards, antennae, buses, switches, routers, modems, and supporting hardware and / or software, or any other device suitable for enabling communications via a network. Additionally, or alternatively, the network interface 206 may include the circuitry for interacting with the antenna / antennae to cause transmission of signals via the antenna / antennae or to handle receipt of signals received via the antenna / antennae.

[0038] FIG. 3 shows an example architecture of a modified neural network 300 in accordance with some embodiments of the present disclosure. The modified neural network 300 shown in FIG. 3 may be optimized (e.g., trained) to model DPD as shown in FIG. 6 and described herein. The modified neural network 300 may overcome rises in error PSD observed when common neural networks 800, 900 are used to perform DPD calculations (see FIG. 5). Additionally, the modified neural network 300 may achieve sufficient accuracy with substantially fewer coefficients and reduced processing time as compared to those required by common neural networks, thereby rendering the modified neural network practical for implementation at the base station. In some embodiments, the modified neural network 300 differs from common neural network networks shown in FIGS. 8, 9 by its implementation of two filtering domains referred to as filter bandwidth 320 (e.g., F0) and usable bandwidth 330 (e.g., Fl). In the present disclosure, the term “filter bandwidth” may be used interchangeably with “adaptation bandwidth.” In some embodiments, the filter bandwidth 320 refers to the bandwidth of the filter that may be applied on a desired signal of one or more elements of a base station. For example, the filter bandwidth 320 may refer to the filter applied to the output of a power amplifier. In some embodiments, the filter bandwidth 320 embodies a bandwidth where signals of the neural network are backpropagated. In variousembodiments, both the forward path (e.g., prediction path) and backward path (e.g., backpropagation path) of the modified neural network 300 arc configured to operate at the filter bandwidth 320.

[0039] In some embodiments, the usable bandwidth 330 refers to a bandwidth of interest for the one or more elements of the base station to be modeled by the modified neural network 300. Further, the usable bandwidth 330 may be the bandwidth within which the error of the neural network is calculated. In various embodiments, the usable bandwidth 330 differs in value from the filter bandwidth 320. The usable bandwidth 330 may be a value that is less than the filter bandwidth 320. For example, the filter bandwidth 320 may be 470 MHz and the useable bandwidth 320 may be 400 MHz. In various embodiments, the filtering techniques used in the architecture of FIG. 3 preserves normal backpropagation methods used with unfiltered neural network architecture, thereby avoiding a need to perform complex numerical gradient complication in backpropagation when training the model. As a result, the implementation of the modified neural network 300 may be further simplified without comprising model accuracy.

[0040] In some embodiments, the modified neural network 300 includes an input layer 301, a plurality of hidden layers 303, an output layer 305, a weight summation operator 307, and a filter operator 309. In some embodiments, the modified neural network 300 is configured to perform phase normalization performing phase normalization of the linear real input signals and imaginary input signals at the input layer of the neural network to generate phase-normalized input data. In some embodiments, the input layer 301 includes separated linear real xl(k) and imaginary xq(k) input signals with memory. In some embodiments, the hidden layers 303 include non-linear terms (NL). The non-linear terms may be formed from signal magnitude powers with memory. In some embodiments, the non-linear terms embody non-filtered activation functions. In some embodiments, the activation functions include hyperbolic tangent function, sigmoid function, rectified linear unit (ReLU) function, and / or the like. In some embodiments, the output layer 305 includes linear activation functions. In some embodiments, the filter operator 309 is configured to filter output from the summation operator 307 with the filter bandwidth 320. In other words, the desired output signal, such as power amplifier output, may be filtered to reflect the practical expectation of band-limited signals in real hardware. As shown in FIG. 5, the filter may cause a rise in error PSD beyond a threshold frequency. The modified neural network may flatten the risein error PSD by increasing the ratio of filter bandwidth to useable bandwidth beyond 1 .0. In doing so, a significant improvement in model error is obtained within the useable bandwidth.

[0041] As one example, when training the modified neural network 300, the band-limited output signal may be generated based on the filter bandwidth and the accuracy (e.g., error) of the neural network may be computed based on the useable bandwidth 330. In various embodiments, by increasing the sampling ratio of filter bandwidth to usable bandwidth (F0 / F1) to a value greater than 1.0 (e.g., 1.18 or another suitable value), the modified neural network 300 may be trained to achieve sufficient accuracy such that predefined emission policies may be met while avoiding substantial complexity in the model and lengthy processing times associated with legacy DPD. For example, the modified neural network 300 may achieve target performance with a reduced total quantity of coefficients (e.g., weights) as compared to existing approaches requiring several tens of thousands of coefficients, such as the common neural network 800 shown in FIG. 8. The modified neural network 300 may significantly reduce implementation costs of using a neural network to optimize the base station via DPD.

[0042] Additionally, in some embodiments, the modified neural network architectures of neural networks 400 and 900 (e.g., shown in FIGS. 4 and 9, respectively, and described herein) may also be used to produce efficient numbers of coefficients as compared to the common neural network 800.

[0043] FIG. 4 shows an alternative architecture of a modified neural network 400 in accordance with some embodiments of the present disclosure. In some embodiments, the modified neural network 400 includes an input layer 401, a plurality of hidden layers 403, an output layer 405, a weight summation operator 407, and a filter operator 409. In some embodiments, the input layer 401 includes separated linear real xl(k) and imaginary xq(k) input signals with memory. In some embodiments, the hidden layers 403 include non-linear terms (NL). The non-linear terms may be formed from signal magnitude powers with memory. In some embodiments, the non-linear terms embody filtered activation functions. A respective activation functions may include one or more neurons, where a respective neuron is filtered based at least in part on a filter bandwidth 420. In some embodiments, the activation functions include hyperbolic tangent function, sigmoid function, rectified linear unit (ReLU) function, and / or the like. In some embodiments, the output layer 405 includes linear activation functions. In some embodiments, the filter operator 409 is configured to filter output from the summation operator 407 with the filter bandwidth 420.

[0044] The modified neural network 400 shown in FIG. 4 may be optimized for modeling DPD as shown in FIG. 7 and described herein. In some embodiments, the alternative architecture embodies an additional approach to overcoming rises in error PSD observed in common neural networks tasked with modeling DPD at the base station. In some embodiments, the alternative architecture implements legacy DPD basis function filtering techniques in the neural network such that non-linearities (activation functions) are filtered to match the bandwidth of the desired signal (e.g., power amplifier output). In the alternative architecture, bandwidth limitation may be applied in all layers of the neural network, and filter bandwidth 420 and useable bandwidth 430 may be set to equal values. For example, the useable bandwidth 430 may be matched to the filter bandwidth 420. Further, the non-linear terms (e.g., neurons) of the hidden layers 403 may be filtered with the filter bandwidth 420. In doing so, the activation bandwidth of the neurons of the network may be matched to that of the desired signal bandwidth. In the alternative architecture, the forward path (e.g., prediction) and backward path (e.g., coefficient adaptation via backpropagation) may be performed with a band-limited neural network where all layers and neurons within layers operate within the defined bandwidth.

[0045] In some embodiments, Equation 1 shows the typical non-band-limited nature of a neuron, where NLtis the output of an z'hNeuron. xLis the z'11input and wtis the zthcoefficient. The bias coefficient is h(. f is the activation function.(Equation 1)

[0046] In some embodiments, Equation 2 shows the band-limited nature of the filtered neurons utilized in the alternative architecture shown in FIG. 4. In Equation 2, NLJ) is the filtered Neuron output. FIRBWis a filter that limits the bandwidth of Neuron output. A convolution operation is required between the activation output and the Filter taps of FIRBW.(Equation 2)

[0047] In various embodiments, with neuron outputs being filtered, the modified neural network 400 shown in FIG. 4 operates within the specified bandwidth. Hence, the adapted coefficients will be correct within that bandwidth (e.g., 400MHz in FIG. 5), and no rise in error spectrum is observed within the that bandwidth. The alternative architecture of FIG. 4 may demonstrate increased complexity as compared to the architecture shown in FIG. 3. For example, the filteredterms used in the alternative architecture may result in more complex backpropagation where gradients would have to be computed numerically. In contrast, the unfiltcrcd terms used in the architecture of FIG. 3 do not require numerical computation of gradients due to the gradients demonstrating well defined derivations, thus resulting in less complex backpropagation.

[0048] FIG. 5 shows charts 500A, 500B of example error power spectral density (PSD) 501 achieved in an existing neural network and neural networks modified in accordance with some embodiments of the present disclosure. In various embodiments, the charts 500A, 500B show error PSD 501 of the desired output signal (e.g., power amplifier output) as a function of output bandwidth 503. The trend 505 represents the power spectral density of output an example power amplifier. The trends 507A, 507B may represent rise in error PSD 501 of an example modified neural network 900 with architecture as shown in FIG. 9. The trends 509A, 509B may represent example performance of a neural network with modified architecture shown in FIG. 3, where the filter bandwidth is configured to 470 MHz (e.g., output is filtered using a 470 MHz filter) and the useable bandwidth is configured to 400 MHz (e.g., error computation is performed respective to a 400 MHz filter). Thus, the ratio of filter bandwidth to useable bandwidth in the trends 509A, 509B may be 470 / 400 (e.g., approximately 1.18). In some embodiments, the performance of a neural network 400 (e.g., with modified architecture as shown in FIG. 4) may also follow the trends 509A, 509B. For example, when considering the trends 509A, 509B in the context of the modified architecture of FIG. 4, the useable bandwidth may be matched to the filter bandwidth, and the output of each neuron at a respective hidden layer may be filtered using the filter bandwidth.

[0049] As shown by the trend 507 A, the common neural network 900 may demonstrate a rise in error PSD 501 after 260 MHz of bandwidth (e.g., + / - 130 MHz) and a further, more significant rise in error PSD around 400 MHz of bandwidth (e.g., + / - 200 MHz). As indicated by the trend 509A, the modified neural networks of FIGS. 3 and 4 may demonstrate superior performance (e.g., 2.5 decibel (dB) improvement) over the common neural network 900. In the trends 509A, 509B, the error PSD 501 is much flatter over the useable bandwidth 400 MHz as compared to the trends 507A, 507B. At the lower frequency edge (e.g., -200 MHz), the performance of the modified neural network of FIG. 3 shows a 10 dB improvement over the common neural network 900. The trends 509A, 509B demonstrate that the model architectures of FIGS. 3 and 4 may result in an improvement in error PSD 501 around the desired bandwidth (e.g., 400 MHz) as compared to the model architecture of FIG. 9.

[0050] Referring now to FIG. 6, shown is example neural network optimization process 600, which may be performed by an apparatus embodying a base station, such as the apparatus 200 of FIG. 2. In various embodiments, the apparatus 200 performs the process 600 to obtain and optimize a modified neural network 300 with architecture as shown in FIG. 3 and described herein. In some embodiments, a base station (e.g., including one or more apparatuses 200) performs the process 600 while installed at a customer location. In some embodiments, the base station embodies a gNodeB.

[0051] In some embodiments, at block 603, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for obtaining a neural network. In some embodiments, the apparatus 200 obtains a neural network configured to model one or more elements of a base station, one or more error signals of the element, and / or the like. For example, the apparatus 200 obtains a neural network 300 with architecture as shown in FIG. 3 and described herein. In some embodiments, the neural network includes an input layer, a plurality of hidden layers, and an output layer. The hidden layer may include one or more coefficients (e.g., weights) that may be adapted as described herein via backpropagation.

[0052] In some embodiments, the plurality of hidden layers comprise a plurality of unfiltered, nonlinear terms. In some embodiments, the non-linear terms are based at least in part on a set of values of signal power of a base station from memory. In some embodiments, the terms included one or more hyperbolic tangent (tanh) functions, Sigmoid functions, rectified linear unit (ReLU) functions, and / or the like. In some embodiments, a respective hidden layer comprises one or more neutrons. When computing the forward path of the neural network, the computation may be performed without band-limiting the neurons of the hidden layers.

[0053] In some embodiments, the output layer includes a plurality of linear terms. In some embodiments, the neural network includes a filter operator configured to filter output of the neural network based on an adaptation bandwidth (also referred to herein as a “filter bandwidth”).

[0054] In some embodiments, at block 606, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for processing input data using the neural network for at least one iteration. In some embodiments, the apparatus 200 processes the input data using the neural network according to blocks 609-615 and, optionally, block 608. In some embodiments, the input data includes linear real and imaginarysignals with memory. In some embodiments, in the one or more iterations, the apparatus 200 trains the neural network to generate a band- limited output signal based at least in part on the input data, an adaptation bandwidth of the modeled base station element, and coefficients adapted via backpropagation. In some embodiments, the band-limited output signal includes a pre-distortion signal of the modeled base station element, one or more error signals of the element, and / or the like. In some embodiments, the apparatus 200 repeats blocks 609-615 and 621 until an iteration of the neural network converges around a threshold-satisfying level of error.

[0055] In some embodiments, at block 608, the apparatus performing the process 600 optionally includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for performing phase normalization of the input data to generate phase-normalized input data. For example, the apparatus 200 may perform phase normalization of the linear real and imaginary input signals of the input layer to generate phase-normalized input data.

[0056] In some embodiments, at block 609, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for computing a forward path (e.g., prediction) of the neural network. For example, the apparatus 200 may computing, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data (or phase-normalized input data) and an adaptation bandwidth associated with the modeled base station element. In some embodiments, the forward path is computed without band limiting the neurons of the hidden layers of the neural network.

[0057] In some embodiments, at block 612, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for generating an error metric of the neural network based at least in part on a useable bandwidth, where the useable bandwidth is less than the adaptation bandwidth. For example, where the adaptation bandwidth is configured to 470 MHz, the apparatus 200 may generate an error metric of the neural metric based at least in part on a useable bandwidth of 400 MHz.

[0058] In some embodiments, at block 615, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for applying the error metric to the neural network to adapt one or more coefficients of one or more hidden layers toward reducing the error metric. For example, the apparatus 200 may perform backpropagation (e.g., compute a backward path of the neural network) based on the error metricto adapt the values of one or more coefficients toward reducing the error metric in a subsequent computation of the forward path.

[0059] In some embodiments, the process 600 repeats blocks 609-615 until the neural network reaches convergence. For example, the apparatus 200 may repeat blocks 609-615 until the error metric of the neural network converges around a final value.

[0060] In some embodiments, at block 618, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for determining whether the error of the model meets a predetermined error threshold. For example, following convergence in a respective set of training iterations, the apparatus 200 may compare the error metric of the convergent neural network to a predetermined error threshold. In some embodiments, the apparatus 200 determines that the error of the neural network meets the predetermined threshold and, in response, the process 600 proceeds to block 627. In some embodiments, the apparatus 200 determines that the error of the neural network fails to meet the predetermined threshold and, in response, the process 600 proceeds to block 621.

[0061] In some embodiments, at block 621, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for increasing the adaptation bandwidth relative to the usable bandwidth. For example, the apparatus 200 may increase the ratio of adaptation bandwidth to useable bandwidth such that model error computation remains based upon the original value of useable bandwidth while the forward path of the neural network is based on the increased adaptation bandwidth.

[0062] In some embodiments, at block 624, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for reprocessing the input data (or phase-normalized input data) for at least one additional iteration. For example, the apparatus 200 may repeat blocks 609-615 to retrain the neural network using the increased adaptation bandwidth until the neural network converges around a new error value. Following the one or more additional iterations, the process 600 may return to block 618, and the sequence may be repeated (e.g., including further increasing the adaptation bandwidth) until the error of the neural network meets the predetermined threshold. In some embodiments, following convergence around an acceptable error value, the neural network embodies an optimal model of the output signal or error signal of the base station element (e.g., power amplifier, power supply, baseband unit, and / or the like) in real time.

[0063] In some embodiments, at block 627, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for generating a plurality of adapted coefficients via the one or more additional iterations of reprocessing the input data. In some embodiments, the apparatus 200 predicts a plurality of adapted coefficients via the one or more additional iterations, which may be used to control operation of the base station at block 633. In some embodiments, the neural network is further configured to predict the plurality of adapted coefficients based on one or more predefined emissions policies.

[0064] In some embodiments, at block 630, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for predicting a band-limited signal respective to the base station element being modeled. For example, following convergence of the neural network, the apparatus 200 may compute the forward path of the neural network to generate the band-limited output signal based at least in part on the input data and a portion of output bandwidth based at least in part on a ratio of the adaptation bandwidth to the useable bandwidth. The ratio may be greater than 1.0 as described herein. In some embodiments, the band-limited output signal includes a pre-distortion output signal of the base station element, an error signal of the element, and / or the like.

[0065] In some embodiments, at block 633, the apparatus performing the process 600 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for controlling operation of the base station based at least in part on the band-limited signal of block 630. For example, the apparatus 200 may control one or more aspects of the base station based at least in part on a pre-distortion output signal, error signal, and / or the like, that is predicted via the forward path of the optimized neural network. In some embodiments, controlling operation of the base station includes cancelling one or more intermodulation products of two or more adjacent channels of the base station based at least in part on the band-limited signal. For example, the modeled base station element may be a power amplifier and, following training and convergence, the neural network may embody an optimal model of the power amplifier in real-time for emissions policy compliance. The apparatus 200 may predict an output signal of the power amplifier using the neural network and cancel one or more intermodulation products of adjacent channels of the base station based on the output signal.

[0066] Referring now to FIG. 7, shown is example neural network optimization process 700, which may be performed by an apparatus embodying a base station, such as the apparatus 200 ofFIG. 2. In various embodiments, the apparatus 200 performs the process 700 to obtain and optimize a modified neural network 400 with architecture as shown in FIG. 4 and described herein. In some embodiments, a base station (e.g., including one or more apparatuses 200) performs the process 600 while installed at a customer location. Alternatively, in some embodiments, the optimization process 600 is performed at the base station prior to its installation at a customer location.

[0067] In some embodiments, at block 703, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for obtaining a neural network. In some embodiments, the apparatus 200 obtains a neural network configured to model one or more elements of a base station, one or more error signals of the element, and / or the like. For example, the apparatus 200 obtains a neural network 400 with architecture as shown in FIG. 4 and described herein. In some embodiments, the neural network includes an input layer, a plurality of hidden layers, and an output layer. The hidden layer may include one or more coefficients (e.g., weights) that may be adapted as described herein via backpropagation.

[0068] In some embodiments, the plurality of hidden layers comprise a plurality of filtered, nonlinear terms. The non-linear terms may be filtered based on an adaptation bandwidth associated with the base station element being modeled. For example, each neuron at a respective hidden layer may be filtered based on the adaptation bandwidth. In some embodiments, the non-linear terms are based at least in part on a set of values of signal power of a base station from memory. In some embodiments, the terms included one or more hyperbolic tangent (tanh) functions, Sigmoid functions, rectified linear unit (ReLU) functions, and / or the like. In some embodiments, a respective hidden layer comprises one or more neutrons. In some embodiments, the output layer includes a plurality of unfiltered linear terms. In some embodiments, the neural network includes a filter operator configured to filter output of the neural network based on the adaptation bandwidth.

[0069] In some embodiments, at block 704, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for matching the adaptation bandwidth of the neural network to a useable bandwidth. For example, the apparatus 200 may match the adaptation value to the desired signal bandwidth of the base station element being modeled.

[0070] In some embodiments, at block 706, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for processing input data using the neural network. In some embodiments, the apparatus 200 performs block 706 is performed similar to block 606 of the process 600 shown in FIG. 6 and described herein. In some embodiments, for a respective iteration, the process 700 includes performing blocks 709-715 and, optionally block 708. In some embodiments, blocks 708 and 715 are performed similar to blocks 608 and 615, respectively.

[0071] In some embodiments, at block 709, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for computing a forward path of the neural network, where computing the forward path of the neural network includes filtering the output of each neuron of the one or more hidden layers of the neural network based on an activation bandwidth. The apparatus 200 may apply the filter according to Equation 2 to band limit each neuron. The apparatus 200 may compute a forward path of the neural network based on input data (or phase-normalized input data) and the activation bandwidth. For example, at block 709 the forward path of the neural network may utilize non-linear activation functions that are filtered based on the adaptation bandwidth (e.g., the value thereof being equal to the usable bandwidth). The blocks 709-715 may be repeated until the neural network reaches convergence.

[0072] In some embodiments, at block 718, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for determining whether the error of the model meets a predetermined error threshold. For example, following convergence in a respective set of training iterations, the apparatus 200 may compare the error metric of the convergent neural network to a predetermined error threshold. In some embodiments, the apparatus 200 determines that the error of the neural network meets the predetermined threshold and, in response, the process 700 proceeds to block 721. In some embodiments, the apparatus 200 determines that the error of the neural network fails to meet the predetermined threshold and, in response, the process 600 proceeds to block 709 and one or more additional iterations are performed until the neural network converges around a thresholdsatisfying error level.

[0073] In some embodiments, at block 718, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, forpredicting a plurality of adapted coefficients for the hidden layers of the neural network. In some embodiments, the apparatus performs block 718 similar to block 627 of the process 600. As described herein the total quantity of coefficients of neural network obtained via the process 700 may exceed a target threshold set by product development goals, whereas the total quantity of coefficients of the neural network obtained via the process 600 may be meet or fall below the target threshold.

[0074] In some embodiments, at block 724, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for predicting a band-limited output signal of the base station element using the trained neural network. In some embodiments, the apparatus 200 performs block 724 similar to block 630.

[0075] In some embodiments, at block 718, the apparatus performing the process 700 includes means, such as the processor 202, the memory 204, the network interface 206, or the like, for controlling operation of the base station based at least in part on the band-limited signal, the plurality of adapted coefficients, and / or the like to enable the base station to comply with one or more predefined emissions policies. In some embodiments, the apparatus 200 performs block 727 similar to block 633.

[0076] FIG. 8 shows an example architecture of a common neural network 800 according to existing machine learning techniques. In current techniques, the neural network 800 may be modified with inputs 801 such that the neural network 800 models a power amplifier. For example, the inputs 801 may include separated linear real xl(k) and imaginary xq(k) input signals (e.g., nonlinear inputs) with memory. Further, the hidden layers of the neural network 800 includes nonlinear terms 803. The non-linear terms may be formed from signal magnitude powers with memory. The non-linear terms 803 may improve the non-linear modeling accuracy of the neural network 800 when modeling the power amplifier and, thus, the neural network may be theoretically used to control operation of a base station. However, the neural network 800 requires an impractically large number of coefficients to achieve modeling accuracy that meets emissions policies stipulated by regulatory authorities. For example, the neural network 800 may require several tens of thousands of coefficients to achieve modeling accuracy levels required to meet emissions policies. The large number of coefficients may be caused by increased memory depth of the input terms, increased quantities of network layers, and increased quantities of neurons in each layer. As a result, the neural network 800 becomes impractically complex and costly suchthat the model cannot be afforded for product development where base stations are optimized for performance with a minimum cost structure. In various embodiments, the modified neural network 300 shown in FIG. 3 and described herein overcomes these technical challenges by defining and augmenting the neural network using two filtering domains (e.g., filter bandwidth and usable bandwidth) to increase model accuracy while avoiding increasing the model complexity. For example, the modified neural network 300 may be substantially smaller than the neural network 800 such that the modified neural network 300 meets or falls below a target threshold for total coefficients.

[0077] FIG. 9 shows an example architecture of a common neural network 900 augmented with phase rotation according to existing techniques for phase normalization. The neural network 900 may perform a phase rotation operation 902 on the input signals of the input layer 901. The phase rotation may cause the neural network 900 to model the relative signal phases instead of the absolute phase that contributed by the modulation technique. The modulation phase may be removed by incorporating the modulation phase into the in-phase and quadrature portions of the complex signal. The phase rotated neural network architecture may improve the modeling accuracy of the neural network 900 as compared to the neural network 800. However, as shown by the error PSD trend 507A, 507B in FIG. 5, the performance of the neural network model 900 with phase rotation fails to meet performance expectations beyond + / - 130 MHz when the total number of coefficients is constrained to meet a target threshold set by product development goals. In various embodiments, the modified neural network 300 shown in FIG. 3 and described herein resolves the rise in error PSD beyond + / - 130 MHz (see error PSD trends 509A, 509B in FIG. 5). In doing so, the model neural network 300 provides the accuracy needed to meet emissions policies at the base station while demonstrating a total quantity of coefficients at or below a target threshold such that the modified neural network 300 may be afforded for product development of and deployment on a base station.

[0078] As used herein, the terms “data,” “content,” “information,” and similar terms may be used interchangeably to refer to data capable of being transmitted, received and / or stored in accordance with the described embodiments. Thus, use of any such terms should not be taken to limit the spirit and scope of the embodiments.

[0079] Additionally, as used herein, the term ‘circuitry’ refers to (a) hardware-only circuit implementations (e.g., implementations in analog circuitry and / or digital circuitry); (b)combinations of circuits and computer program product(s) comprising software and / or firmware instructions stored on one or more computer readable memories that work together to cause an apparatus to perform one or more functions described herein; and (c) circuits, such as, for example, a microprocessor(s) or a portion of a microprocessor(s), that require software or firmware for operation even if the software or firmware is not physically present. This definition of ‘circuitry’ applies to all uses of this term herein, including in any claims. As a further example, as used herein, the term ‘circuitry’ also includes an implementation comprising one or more processors and / or portion(s) thereof and accompanying software and / or firmware. As another example, the term ‘circuitry’ as used herein also includes, for example, a baseband integrated circuit or applications processor integrated circuit for a mobile phone or a similar integrated circuit in a server, a cellular network device, other network device (such as a core network apparatus), field programmable gate array, and / or other computing device.

[0080] The term “comprising” means including but not limited to and should be interpreted in the manner it is typically used in the patent context. Use of broader terms such as comprises, includes, and having should be understood to provide support for narrower terms such as consisting of, consisting essentially of, and comprised substantially of. Furthermore, to the extent that the terms “includes” and “including,” and variants thereof are used in either the detailed description or the claims, these terms are intended to be inclusive in a manner similar to the term “comprising.”

[0081] The phrases “in one embodiment,” “according to one embodiment,” “in some embodiments,” “in various embodiments”, and the like generally refer to the fact that the particular feature, structure, or characteristic following the phrase may be included in at least one embodiment of the present disclosure, but not necessarily all embodiments of the present disclosure. Thus, the particular feature, structure, or characteristic may be included in more than one embodiment of the present disclosure such that these phrases do not necessarily refer to the same embodiment.

[0082] As used herein, the terms “example,” “exemplary,” and the like are used to mean “serving as an example, instance, or illustration.” Any implementation, aspect, or design described herein as “example” or “exemplary” is not necessarily to be construed as preferred or advantageous over other implementations, aspects, or designs. Rather, use of the terms “example,” “exemplary,” and the like are intended to present concepts in a concrete fashion.

[0083] If the specification states a component or feature “may,” “can,” “could,” “should,” “would,” “preferably,” “possibly,” “typically,” “optionally,” “for example,” “often,” or “might” (or other such language) be included or have a characteristic, that particular component or feature is not required to be included or to have the characteristic. Such component or feature may be optionally included in some embodiments, or it may be excluded.

[0084] As used herein, the term “computer-readable medium” refers to signal, non-transitory computer-readable medium and the like. The term ‘non-transitory computer-readable medium’ refers to non-transitory storage hardware, non-transitory storage device or non-transitory computer system memory that may be accessed by a controller, a microcontroller, a computational system or a module of a computational system to encode thereon computer-executable instructions or software programs. A non-transitory “computer-readable medium” may be accessed by a computational system or a module of a computational system to retrieve and / or execute the computer-executable instructions or software programs encoded on the medium. Examples of non- transitory computer-readable media may include, but are not limited to, one or more types of hardware memory, non-transitory tangible media (for example, one or more magnetic storage disks, one or more optical disks, one or more USB flash drives), computer system memory or random-access memory (such as, DRAM, SRAM, EDO RAM), and the like.

[0085] It will be understood that each block of the flowcharts and combination of blocks in the flowcharts show in the figures and described herein may be implemented by various means, such as hardware, firmware, processor, circuitry, and / or communication devices associated with execution of software including one or more program instructions. For example, one or more of the procedures or operations described above may be embodied by computer program instructions. In this regard, the computer program instructions which embody the procedures or operations described above may be stored by a memory 204 of an apparatus (e.g., base station) employing a disclosed embodiment and executed by a processor 202. As will be appreciated, any such computer program instructions may be loaded onto a computer or other programmable apparatus (for example, hardware) to produce a machine, such that the resulting computer or other programmable apparatus implements the functions specified in the flowchart blocks. These computer program instructions may also be stored in a computer-readable memory that may direct a computer or other programmable apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture the execution of which implementsthe function specified the flowchart blocks. The computer program instructions may also be loaded onto a computer or other programmable apparatus to cause a scries of operations to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide operations for implementing the functions specified in the flowchart blocks.

[0086] Many modifications and other embodiments of the present disclosure set forth herein will come to mind to one skilled in the art to which these embodiments pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the disclosure is not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Moreover, although the foregoing descriptions and the associated drawings describe example embodiments in the context of certain example combinations of elements and / or functions, it should be appreciated that different combinations of elements and / or functions can be provided by alternative embodiments without departing from the scope of the appended claims. In this regard, for example, different combinations of elements and / or functions than those explicitly described above are also contemplated as can be set forth in some of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

CLAIMSWHAT IS CLAIMED IS:

1. A method for optimizing a neural network, comprising: obtaining a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; processing input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and a respective iteration of processing the input data comprises: computing, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; generating an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and applying the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; following the at least one iteration, determining that the error of the neural network fails to meet a predetermined threshold; and in response to the determining that the error of the neural network fails to meet a predetermined threshold: increasing the adaptation bandwidth relative to the usable bandwidth; and reprocessing the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth.

2. The method of claim 1 , further comprising:predicting, via the at least one additional iteration, a plurality of adapted coefficients for the plurality of hidden layers of the neural network; and controlling operation of the base station based at least in part on the adapted coefficients of the neural network.

3. The method of claim 2, further comprising: training the neural network to generate a band-limited output signal based at least in part on the input data, the adaptation bandwidth, and the plurality of adapted coefficients, wherein the band-limited output signal comprises at least one of i) a pre-distortion signal of the at least one element of the base station, or ii) the at least one error signal of the at least one element of the base station; following convergence of the neural network, computing the forward path of the neural network to generate the band-limited output signal based at least in part on the input data and a portion of output bandwidth based at least in pail on a ratio of the useable bandwidth to the adaptation bandwidth; and controlling operation of the base station based at least in part on the band-limited output signal.

4. The method of claim 3, further comprising: predicting the plurality of adapted coefficients further based at least in part on at least one predefined emission policy.

5. The method of claim 3, wherein: the at least one element of the base station comprises at least one power amplifier (PA) of the base station such that, following the convergence, the neural network embodies an optimal model of an output signal of the at least one PA or the at least one error signal of the at least one PA in real time; and controlling operation of the base station comprises cancelling at least one intermodulation product of two or more adjacent channels of the base station based at least in part on at least one of the output signal or the at least one error signal.

6. The method of claim 1 , wherein: the plurality of hidden layers comprises: a plurality of unfiltered, non-linear terms.

7. The method of claim 6, wherein: the plurality of unfiltered, non-linear terms are based at least in part on a set of values of signal power of the base station from memory.

8. The method of claim 6, wherein: the plurality of unfiltered, non-linear terms comprise at least one of a hyperbolic tangent (tanh) function, a Sigmoid function, or a rectified linear unit (ReLU) function.

9. The method of claim 1, wherein: a respective hidden layer of the plurality of hidden layers comprises a plurality of neurons; and in a respective iteration of processing the input data, the computing of the forward path of the neural network is performed without band limiting the plurality of neurons.

10. The method of claim 1, wherein: a ratio of the increased adaptation bandwidth the usable bandwidth is greater than 1.0.

11. The method of claim 1 , wherein: the base station embodies a gNodeB.

12. The method of claim 1, wherein: a respective iteration of processing the input data further comprises: performing phase normalization of the lineal’ real input signals and imaginary input signals at the input layer of the neural network to generate phase-normalized input data; andcomputing the forward path of the neural network based at least in part on the phase- normalized input data and the adaptation bandwidth associated with the at least one element of the base station.

13. An apparatus, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to: obtain a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; process input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and, in performance of a respective iteration of processing the input data, the instructions cause the apparatus at least to: compute, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; generate an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and apply the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; following the at least one iteration, determine that the error of the neural network fails to meet a predetermined threshold; and in response to a determination that the error of the neural network fails to meet a predetermined threshold:increase the adaptation bandwidth relative to the usable bandwidth; and reprocess the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth.

14. The apparatus of claim 13, wherein: the instructions, in execution with the at least one processor, cause the apparatus to: predict, via the at least one additional iteration, a plurality of adapted coefficients for the plurality of hidden layers of the neural network; and control operation of the base station based at least in part on the adapted coefficients of the neural network.

15. The apparatus of claim 14, wherein: the instructions, in execution with the at least one processor, further cause the apparatus to: train the neural network to generate a band-limited output signal based at least in part on the input data, the adaptation bandwidth, and the plurality of adapted coefficients, wherein the band-limited output signal comprises at least one of i) a pre-distortion signal of the at least one element of the base station, or ii) the at least one error signal of the at least one element of the base station; following convergence of the neural network, compute the forward path of the neural network to generate the band-limited output signal based at least in part on the input data and a portion of output bandwidth based at least in part on a ratio of the useable bandwidth to the adaptation bandwidth; and control operation of the base station based at least in part on the band-limited output signal.

16. The apparatus of claim 15, wherein: the instructions, in execution with the at least one processor, further cause the apparatus to predict the plurality of adapted coefficients further based at least in part on at least one predefined emission policy.

17. The apparatus of claim 15, wherein: the at least one clement of the base station comprises at least one power amplifier (PA) of the base station such that, following the convergence, the neural network embodies an optimal model of an output signal of the at least one PA or the at least one error signal of the at least one PA in real time; and the instructions, in execution with the at least one processor, further cause the apparatus to cancel at least one intermodulation product of two or more adjacent channels of the base station based at least in pail on at least one of the output signal or the at least one error signal.

18. The apparatus of claim 15, wherein: a respective hidden layer of the plurality of hidden layers comprises a plurality of neurons; and in a respective iteration of processing the input data, the instructions, in execution with the at least one processor, cause the apparatus to compute the forward path of the neural network without band limiting the plurality of neurons.

19. The apparatus of claim 13, wherein: a ratio of the increased adaptation bandwidth the usable bandwidth is greater than 1.0.

20. A computer program product comprising at least one non-transitory computer-readable storage medium having computer-executable program code instructions stored therein, the computer-executable program code instructions comprising program code instructions configured to: obtain a neural network configured to model at least one of i) at least one element of a base station, or ii) at least one error signal of the at least one element of the base station, wherein: the neural network comprises an input layer, a plurality of hidden layers, and an output layer; and a respective hidden layer comprises at least one coefficient; process input data using the neural network for at least one iteration, wherein the input data comprises linear real input signals and imaginary input signals and, in performance of a respective iteration of processing the input data, the program code instructions are configured to:compute, using the plurality of hidden layers and the output layer, a forward path of the neural network based at least in part on the input data and an adaptation bandwidth associated with the at least one element of the base station; generate an error metric of the neural network at the output layer based at least in part on a usable bandwidth associated with the at least one element of the base station, wherein the adaptation bandwidth exceeds the usable bandwidth; and apply the error metric of the neural network to the plurality of hidden layers to adapt at least one coefficient of a respective hidden layer toward reducing the error metric; following the at least one iteration, determine that the error of the neural network fails to meet a predetermined threshold; and in response to a determination that the error of the neural network fails to meet a predetermined threshold: increase the adaptation bandwidth relative to the usable bandwidth; and reprocess the input data using the neural network for at least one additional iteration based at least in part on the increased adaptation bandwidth.

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