Systems and methods for cross band channel prediction

Abstract

An example method includes: receiving an uplink channel by an RF front end module; partitioning the uplink channel into a plurality of sub-channels by a neural network channel divider, wherein the plurality of sub-channels correspond to a plurality of non-overlapping distance ranges; generating, a plurality of coarse distance estimates by a neural network distance estimator, wherein the plurality of coarse distance estimates comprise a distance estimate for each of the plurality of sub-channels; generating a plurality of fine-tuned distance estimates by optimizing the plurality of coarse distance estimates; and determining, from the plurality of fine-tuned distance estimates, a downlink channel prediction, wherein the downlink channel prediction predicts a downlink channel based on the uplink channel.

Description

SYSTEMS AND METHODS FOR CROSS BAND CHANNEL PREDICTION CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. provisional patent application No. 63 / 644,821, filed on May 9, 2024, and titled “METHOD FOR ACCURATE CROSS BAND CHANNEL PREDICTION,” the disclosure of which is expressly incorporated herein by reference in its entirety. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under 2007581, 2112471, and 2128567 awarded by National Science Foundation. The government has certain rights in the invention. BACKGROUND

[0003] Advancements in wireless technologies have enabled high-throughput communication systems with the help of MIMO (Multiple Input Multiple Output). An approach to increase the wireless system capacity is through the use of Multi-User MIMO (MU-MIMO) and Mega-MIMO. These technologies allow multiple users to be served simultaneously by a single base station using multiple antennas. In applications like cellular networks, FDD (Frequency Division Duplexing) methods are used in conjunction with MIMO to simultaneously receive and transmit on different frequency bands. However, due to the lack of channel reciprocity across frequency bands, base stations require channel feedback from the clients to perform signal processing and modulation. This technique of channel feedback introduces expensive overhead and is unsustainable for MIMO systems.

[0004] Improvements to the prediction of the downlink channel based on the uplink channel can improve base station systems. SUMMARY

[0005] In some aspects, implementations of the present disclosure include a method including: receiving an uplink channel; partitioning the uplink channel into a plurality of sub- channels by a neural network channel divider, wherein the plurality of sub-channelscorrespond to a plurality of non-overlapping distance ranges; generating a plurality of coarse distance estimates by a neural network distance estimator, wherein the plurality of coarse distance estimates include a distance estimate for each of the plurality of sub-channels; generating a plurality of fine-tuned distance estimates by optimizing the plurality of coarse distance estimates; and determining from the plurality of fine-tuned distance estimates, a downlink channel prediction, wherein the downlink channel prediction predicts a downlink channel based on the uplink channel.

[0006] In some aspects, implementations of the present disclosure include a method, further including transmitting a downlink signal based on the downlink channel prediction.

[0007] In some aspects, implementations of the present disclosure include a method, wherein the downlink signal includes a beamformed signal.

[0008] In some aspects, implementations of the present disclosure include a method, wherein the neural network distance estimator includes a plurality of neural network distance estimator networks each configured for a different range of distances.

[0009] In some aspects, implementations of the present disclosure include a method, wherein the neural network distance estimator includes a neural network trained only on synthetic data.

[0010] In some aspects, implementations of the present disclosure include a method, wherein the neural network channel divider includes two hidden layers.

[0011] In some aspects, implementations of the present disclosure include a method, wherein the neural network channel divider is configured with a exponential linear unit activation function.

[0012] In some aspects, implementations of the present disclosure include a method, wherein the neural network distance estimator includes five hidden layers.

[0013] In some aspects, implementations of the present disclosure include a system including a radio transceiver including a receiver front end and a transmitter front end; a controller operably coupled to the radio transceiver, the controller including a processor and a memory storing a neural network channel divider and a neural network distance estimator, wherein the memory further stores computer-executable instructions that, when executed by the processor, cause the processor to: receive an uplink channel by the receiver front end; partition the uplink channel into a plurality of sub-channels by a neural network channel divider, wherein the plurality of sub-channels correspond to a plurality of non-overlapping distance ranges; generating, a plurality of coarse distance estimates by a neural network distance estimator, wherein the plurality of coarse distance estimates include a distanceestimate for each of the plurality of sub-channels; generating a plurality of fine-tuned distance estimates by optimizing the plurality of coarse distance estimates; and determining, from the plurality of fine-tuned distance estimates, a downlink channel prediction, wherein the downlink channel prediction predicts a downlink channel based on the uplink channel.

[0014] In some aspects, implementations of the present disclosure include a system, further including transmitting a downlink signal based on the downlink channel prediction.

[0015] In some aspects, implementations of the present disclosure include a system, wherein the downlink signal includes a beamformed signal.

[0016] In some aspects, implementations of the present disclosure include a system, wherein the neural network distance estimator includes a plurality of neural network distance estimator networks each configured for a different range of distances.

[0017] In some aspects, implementations of the present disclosure include a system, wherein the neural network distance estimator includes a neural network trained only on synthetic data.

[0018] In some aspects, implementations of the present disclosure include a system, wherein the neural network channel divider includes two hidden layers.

[0019] In some aspects, implementations of the present disclosure include a system, wherein the neural network channel divider is configured with a exponential linear unit activation function.

[0020] In some aspects, implementations of the present disclosure include a system, wherein the neural network distance estimator includes five hidden layers.

[0021] In some aspects, implementations of the present disclosure include a method of training a neural network channel divider, the method including: (a) generating a synthetic dataset including a plurality of simulated uplink channels; (b) selecting a set of sub channels from the synthetic dataset, wherein the sub channels include paths within a zone; and (c) training a neural network to extract a sub-channels from an uplink signal based on the set of sub-channels and the synthetic dataset.

[0022] In some aspects, implementations of the present disclosure include a method, further including: repeating steps (a), (b), and (c) to train a plurality of neural networks, wherein each of the plurality of neural networks are configured to extract different sub-channels for different zones.

[0023] In some aspects, implementations of the present disclosure include a method wherein generating the synthetic dataset includes performing a multipath physics simulation.

[0024] In some aspects, implementations of the present disclosure include a method, wherein the synthetic dataset includes at least one of: center frequency, bandwidth, component distances, attenuation, and phase.

[0025] Other systems, methods, features and / or advantages will be or may become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features and / or advantages be included within this description and be protected by the accompanying claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The components in the drawings are not necessarily to scale relative to each other. Like reference numerals designate corresponding parts throughout the several views.

[0027] FIG. 1 illustrates an example system for cross-band communication, according to implementations of the present disclosure.

[0028] FIG. 2 illustrates an example method of downlink channel prediction, according to implementations of the present disclosure.

[0029] FIG. 3 illustrates an example method of training a neural network channel divider (NNCD), is shown, according to implementations of the present disclosure.

[0030] FIG. 4 illustrates an example computing device.

[0031] FIG. 5 illustrates an example of cross band channel prediction according to implementations of the present disclosure.

[0032] FIG. 6 illustrates the relationship of path loss correlation with the underlying physical environment, according to a study of an example implementation of the present disclosure.

[0033] FIG. 7 illustrates the performance gain of an example implementation as compared to conventional techniques, according to a study of an example implementation of the present disclosure.

[0034] FIG. 8 illustrates comparative results demonstrating that an example implementation of the present disclosure outperforms conventional techniques, according to a study of an example implementation of the present disclosure.

[0035] FIG. 9 illustrates a study of a conventional method of estimating components, showing that the conventional method fails to estimate components correct.

[0036] FIG. 10 illustrates the performance of an example NNCD block, according to a study of an example implementation of the present disclosure.

[0037] FIG. 11 illustrates the prediction accuracy of blocks, according to a study of an example implementation of the present disclosure.

[0038] FIG. 12 illustrates a cumulative distribution function (CDF) plot for a with and without a path, according to a study of an example implementation of the present disclosure.

[0039] FIG. 13 shows the values for different SNRs, according to a study of an example implementation of the present disclosure.

[0040] FIG. 14 illustrates the performance of example mNNDE (mini neural network distance estimator) blocks, according to a study of an example implementation of the present disclosure.

[0041] FIG. 15 illustrates the accuracy of an example implementation of the present disclosure.

[0042] FIG. 16 illustrates the prediction performance of an example implementation of the present disclosure. disclosure.

[0043] FIG. 17 illustrates the prediction performance of an example implementation of the present disclosure. disclosure.

[0044] FIG. 18 illustrates the CDF plot of channel prediction accuracy gain in dB of HORCRUX compared to conventional systems, according to a study of an example implementation of the present disclosure.

[0045] FIG. 19 illustrates the CDF plot of channel prediction accuracy gain in dB of HORCRUX compared to conventional systems, according to a study of an example implementation of the present disclosure.

[0046] FIG. 20 illustrates the performance of an example implementation using a 4-antenna base station, according to a study of an example implementation of the present disclosure.

[0047] FIG. 21 illustrates SNR and channel prediction accuracy, according to a study of an example implementation of the present disclosure.

[0048] FIG. 22 illustrates SNR and channel accuracy predictions, according to a study of an example implementation of the present disclosure.

[0049] FIG. 23 illustrates, according to a study of an example implementation of the present disclosure.

[0050] FIG. 24 illustrates the performance of an example implementation in a two-antenna setup, according to a study of an example implementation of the present disclosure.

[0051] FIG. 25 illustrates the performance of an example implementation in a four-antenna setup, according to a study of an example implementation of the present disclosure.

[0052] FIG. 26 illustrates the performance of an example implementation in a two-antenna setup for the clients, according to a study of an example implementation of the present disclosure.

[0053] FIG. 27 illustrates the performance of an example implementation in a four-antenna setup, as compared to conventional techniques according to a study of an example implementation of the present disclosure.

[0054] FIG. 28 illustrates the performance of the example implementation in larger antennas systems, according to a study of an example implementation of the present disclosure.

[0055] FIG. 29 illustrates path loss correlation values in different environments, according to a study of an example implementation of the present disclosure.

[0056]

[0057] FIG. 30 illustrates the performance of a conventional system, according to a study of an example implementation of the present disclosure.

[0058] FIG. 31 illustrates the performance of the conventional system of FIG. 30 across different environments, according to a study of an example implementation of the present disclosure.

[0059] FIG. 32 illustrates the performance of the example implementation across different downlink frequency bands, according to a study of an example implementation of the present disclosure.

[0060] FIG. 33 illustrates channel prediction accuracy of the example implementation compared to conventional techniques, according to a study of an example implementation of the present disclosure.

[0061] FIG. 34 illustrates channel prediction accuracy of the example implementation compared to conventional techniques, according to a study of an example implementation of the present disclosure.

[0062] FIG. 35 illustrates processing time of conventional techniques as compared to an example implementation of the present disclosure.DETAILED DESCRIPTION

[0063] Implementations of the present disclosure include improvements to systems and methods for performing cross-band transmission, including improvements to downlink channel prediction. Downlink channel prediction refers to the process of determining the downlink channel based on the uplink channel. The downlink channel is the set of distortions that are applied to the signal that is transmitted by a transmitter by the environment between the transmitter (e.g., a base station) and a receiver (e.g., a client device). By predicting the downlink channel, the transmitter can configure the signal that is transmitted to compensate for the distortions and improve the signal that is received by the client device.

[0064] In a conventional system where the uplink channel and downlink channel operate at the same frequencies, the uplink channel can be used to predict the downlink channel. However, in cross-band systems, the transmit and receive frequencies can be different, so the downlink channel cannot be predicted easily based on the uplink signal. Conventional computational methods of downlink channel prediction can be computationally expensive or prohibitive for base stations with large numbers of antennas and / or devices.

[0065] Implementations of the present disclosure include improved systems and methods for downlink channel prediction that overcome the limitations of existing systems and methods. An example implementation of the present disclosure includes two trained neural networks: a neural network channel divider and a neural network distance estimator, that can be used to overcome limitations of conventional downlink channel prediction. One neural network, a neural network channel divider, extracts sub channels from the uplink channel, and a second neural network is configured as a neural network distance estimator and configured to estimate the distance for the sub-channels of the uplink channel. By using these two specialist neural networks, the computational complexity of downlink channel prediction is reduced and / or the accuracy of downlink channel prediction is increased (e.g., an ~8 dB improvement in accuracy in the Example described herein). Thus, implementations of the present disclosure improve cross-band base stations and other systems that rely on cross-band channels for communication.

[0066] The present disclosure further includes a study of an example implementation of the present disclosure (referred to herein as “HORCRUX”) that first subdivides the uplink channel into smaller sub-divisions based on underlying physical parameters of the channel and then utilizes a neural network model to estimate distances on each subdivision. A fast and efficient optimization is applied to each sub-division to estimate the downlink channel. The example implementation can be trained using simulated data that is grounded by theunderlying physical laws of the wireless channel. Unlike conventional techniques, this implicit form of grounding

[0010] enables HORCRUX to generalize beyond the simulated environment it was trained on. The study described herein implemented HORCRUX on WARP radios and compare its performance with FIRE

[0035] , OptML

[0011] , and R2F2

[0054] in different indoor and outdoor test beds and simulations. FIG. 8 shows comparative results demonstrating HORCRUX outperforms the state-of-the-art. Applications: Apart from widespread application in a multiantenna base station for wireless systems, the zero feedback-based FDD system that HORCRUX subscribes to can have a significant impact in systems with a single antenna (e.g., smart home devices) or devices with antennas arranged in a random fashion (e.g., laptop or access points) that want to use different bands for uplink and downlink based on data-traffic and SNR (signal to noise ratio). Contemporary efforts, such as the FIRE architecture, will fail to support such variability in number of multipath components and their distances. Channel is highly uncorrelated when there are more than 2 multipaths. Everyday indoor and outdoor environments have uncorrelated channels.

[0067] With reference to FIG. 1, an example system is shown according to implementations of the present disclosure. The example system can optionally be a base station. As used herein, a base station refers to a fixed transceiver that is configured to send and / or receive data from one or more client devices. For example, a base station can be a Wi- Fi or cellular base station for networking personal computers, cell phones, and / or any other client devices.

[0068] The system can include a radio transceiver with a receiver front end 102 and a transmitter front end 114. The transmitter front end 114 can optionally include antennas configured for beam-forming. The transmitter front end 114 can further include circuitry configured to apply a channel prediction 112 to a signal that will be transmitted by the transmitter. As used herein, “applying” a channel prediction 112 can include configuring a signal that will be transmitted to compensate for the distortions of the channel prediction 112. The receiver front end 102 receives an uplink channel input, which can be input into the neural network channel divider 104.

[0069] The system can further include a controller 101 that is operably coupled to the receiver front end 102 and transmitter front end 114. The controller 101 can include one or more computing devices (e.g., the computing device 400 of FIG. 4). The controller 101 can further include a neural network channel divider 104 and / or a neural network distance estimator 108 stored in memory.

[0070] Neural Network Channel Divider. As described with reference to FIG. 3, the neural network channel divider 104 includes one or more neural networks configured to partition the uplink channel into a set of sub-channels from different distance “zones.” Non-limiting examples of zones that can used include 0-25 meters; 25-50 meters; 50-75 meters, etc. Optionally, the neural network channel divider 104 can be a neural network with two hidden layers and / or a neural network using a exponential linear unit activation function. The neural network channel divider 104 can be configured a set of small neural networks (referred to herein as “mini” neural network channel dividers, mNNCDs) that can be lightweight to run, fast, efficient, and / or easy to train.

[0071] Distance Estimate Initiator. The system further includes a distance estimate initiator 106. The distance estimate initiator can determine whether to initiate distance estimation for each of the sub channels based on detecting whether the channel is active (e.g., by comparing the energy of the channel to a threshold value). The distance estimate initiator 106 can increase the efficiency of the system by avoiding performing distance estimates for channels that do not include a signal.

[0072] Neural Network Distance Estimator. The neural network distance estimator 108 can generate a coarse distance estimate for each of the sub-channels partitioned by the neural network channel divider 104. Optionally, the neural network distance estimator can include any number of individual neural network distance estimators that are each configured for different ranges of distance. For example, each of the neural network distance estimators can include a neural network with five hidden layers. Thus, the neural network channel divider 104 and neural network distance estimator 108 can provide a more efficient solution to estimating distances by first dividing the uplink signal into zones, and then estimating ranges for the zones separately, which can be more efficient than trying to estimate distances of the entire signal. Additionally, the neural network distance estimator can optionally be trained using only synthetic data, which can make the neural network distance estimator faster and more efficient to deploy by eliminating the step of collecting training data using a deployed system.

[0073] The system can further include an optimizer 110 that can be used to optimize the coarse distance estimates into fine-tuned distance estimates. The fine-tuned distance estimates can be used in creating a channel prediction 112 that quantifies the distortions that will impact the downlink signal that will be transmitted.

[0074] With reference to FIG. 2, an example method is shown according to implementations of the present disclosure. The methods described with reference to FIG. 2can optionally be implemented using the system shown in FIG. 1. For example, the method can be configured as a computer-implemented method performed by a computing device configured to control a base station of a communications network.

[0075] At step 210, the method includes receiving an uplink channel.

[0076] At step 220, the method includes partitioning the uplink channel into a plurality of sub-channels by a neural network channel divider, wherein the plurality of sub-channels correspond to a plurality of non-overlapping distance ranges.

[0077] At step 230, the method includes generating, a plurality of coarse distance estimates by a neural network distance estimator, wherein the plurality of coarse distance estimates comprise a distance estimate for each of the plurality of sub-channels. As described in greater detail with reference to FIG. 1, the neural network distance estimator can optionally include a set of neural network distance estimator networks each configured for a different range of distances, referred to herein as “zones.”

[0078] At step 240, the method includes generating a plurality of fine-tuned distance estimates by optimizing the plurality of coarse distance estimates.

[0079] At step 250, the method includes determining, from the plurality of fine-tuned distance estimates, a downlink channel prediction, wherein the downlink channel prediction predicts a downlink channel based on the uplink channel. Optionally, the method can further include transmitting a downlink signal (e.g., a beamformed signal) based on the downlink channel prediction.

[0080] With reference to FIG. 3, an example method of training a neural network distance estimator, is shown, according to implementations of the present disclosure.

[0081] At step 310, the method includes generating a synthetic dataset comprising a plurality of simulated uplink channels. The synthetic dataset can include a multipath physics simulation of uplink and / or downlink channels. As non-limiting examples, that synthetic dataset can include any or all of center frequency, bandwidth, component distances, attenuation, and / or phase.

[0082] At step 320 the method includes selecting a set of sub channels from the synthetic dataset, where the sub channels comprise paths within a zone.

[0083] At step 330 the method includes training a neural network to extract a sub-channels from an uplink signal based on the set of sub-channels and the synthetic dataset.

[0084] Optionally, the steps of FIG. 3 can be repeated iteratively to train any number of neural network distance estimators that are each configured to estimate distances for different zones of distances (e.g., the zones from 0-25 meters, 25-50 meters, and 50-75 metersdescribed above). It should be understood that the zones described herein are non-limiting examples, and that any number of neural network distance estimators can be configured for any number of zones, and that the zones can span different ranges of distances.

[0085] The construction and arrangement of the systems and methods as shown in the various implementations are illustrative only. Although only a few implementations have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes, and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative implementations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the implementations without departing from the scope of the present disclosure.

[0086] It should be appreciated that the logical operations described herein with respect to the various figures may be implemented (1) as a sequence of computer implemented acts or program modules (i.e., software) running on a computing device (e.g., the computing device described in FIG. 4), (2) as interconnected machine logic circuits or circuit modules (i.e., hardware) within the computing device and / or (3) a combination of software and hardware of the computing device. Thus, the logical operations discussed herein are not limited to any specific combination of hardware and software. The implementation is a matter of choice dependent on the performance and other requirements of the computing device. Accordingly, the logical operations described herein are referred to variously as operations, structural devices, acts, or modules. These operations, structural devices, acts and modules may be implemented in software, in firmware, in special purpose digital logic, and any combination thereof. It should also be appreciated that more or fewer operations may be performed than shown in the figures and described herein. These operations may also be performed in a different order than those described herein.

[0087] Referring to FIG. 4, an example computing device 400 upon which the methods described herein may be implemented is illustrated. It should be understood that the example computing device 400 is only one example of a suitable computing environment upon which the methods described herein may be implemented. Optionally, the computing device 400 can be a well-known computing system including, but not limited to, personal computers, servers,handheld or laptop devices, multiprocessor systems, microprocessor-based systems, network personal computers (PCs), minicomputers, mainframe computers, embedded systems, and / or distributed computing environments including a plurality of any of the above systems or devices. Distributed computing environments enable remote computing devices, which are connected to a communication network or other data transmission medium, to perform various tasks. In the distributed computing environment, the program modules, applications, and other data may be stored on local and / or remote computer storage media.

[0088] In its most basic configuration, computing device 400 typically includes at least one processing unit 406 and system memory 404. Depending on the exact configuration and type of computing device, system memory 404 may be volatile (such as random access memory (RAM)), non-volatile (such as read-only memory (ROM), flash memory, etc.), or some combination of the two. This most basic configuration is illustrated in FIG. 4 by box 402. The processing unit 406 may be a standard programmable processor that performs arithmetic and logic operations necessary for operation of the computing device 400. The computing device 400 may also include a bus or other communication mechanism for communicating information among various components of the computing device 400.

[0089] Computing device 400 may have additional features / functionality. For example, computing device 400 may include additional storage such as removable storage 408 and non-removable storage 410 including, but not limited to, magnetic or optical disks or tapes. Computing device 400 may also contain network connection(s) 416 that allow the device to communicate with other devices. Computing device 400 may also have input device(s) 414 such as a keyboard, mouse, touch screen, etc. Output device(s) 412 such as a display, speakers, printer, etc. may also be included. The additional devices may be connected to the bus in order to facilitate communication of data among the components of the computing device 400. All these devices are well known in the art and need not be discussed at length here.

[0090] The processing unit 406 may be configured to execute program code encoded in tangible, computer-readable media. Tangible, computer-readable media refers to any media that is capable of providing data that causes the computing device 400 (i.e., a machine) to operate in a particular fashion. Various computer-readable media may be utilized to provide instructions to the processing unit 406 for execution. Example tangible, computer-readable media may include, but is not limited to, volatile media, non-volatile media, removable media and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules orother data. System memory 404, removable storage 408, and non-removable storage 410 are all examples of tangible, computer storage media. Example tangible, computer-readable recording media include, but are not limited to, an integrated circuit (e.g., field- programmable gate array or application-specific IC), a hard disk, an optical disk, a magneto- optical disk, a floppy disk, a magnetic tape, a holographic storage medium, a solid-state device, RAM, ROM, electrically erasable program read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices.

[0091] In an example implementation, the processing unit 406 may execute program code stored in the system memory 404. For example, the bus may carry data to the system memory 404, from which the processing unit 406 receives and executes instructions. The data received by the system memory 404 may optionally be stored on the removable storage 408 or the non-removable storage 410 before or after execution by the processing unit 406.

[0092] It should be understood that the various techniques described herein may be implemented in connection with hardware or software or, where appropriate, with a combination thereof. Thus, the methods and apparatuses of the presently disclosed subject matter, or certain aspects or portions thereof, may take the form of program code (i.e., instructions) em1bodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium wherein, when the program code is loaded into and executed by a machine, such as a computing device, the machine becomes an apparatus for practicing the presently disclosed subject matter. In the case of program code execution on programmable computers, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device. One or more programs may implement or utilize the processes described in connection with the presently disclosed subject matter, e.g., through the use of an application programming interface (API), reusable controls, or the like. Such programs may be implemented in a high level procedural or object-oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language and it may be combined with hardware implementations.

[0093] Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also, two or more steps may be performed concurrently orwith partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.

[0094] It is to be understood that the methods and systems are not limited to specific synthetic methods, specific components, or to particular compositions. It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only and is not intended to be limiting.

[0095] As used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another implementation includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another implementation. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0096] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0097] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of” and is not intended to convey an indication of a preferred or ideal implementation. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0098] Disclosed are components that can be used to perform the disclosed methods and systems. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed that while specific reference of each various individual and collective combinations and permutation of these may not be explicitly disclosed, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application including, but not limited to, steps in disclosed methods. Thus, if there are a variety of additional steps that canbe performed it is understood that each of these additional steps can be performed with any specific implementation or combination of implementations of the disclosed methods.

[0099] Examples

[0100] The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how the compounds, compositions, articles, devices and / or methods claimed herein are made and evaluated, and are intended to be purely exemplary and are not intended to limit the disclosure. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.), but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in degrees C or is at ambient temperature, and pressure is at or near atmospheric.

[0101] Described herein are systems and methods for accurate cross band channel prediction (herein, “HORCRUX”), which achieves high channel estimation accuracy with zero feedback across any wireless environment and can be utilized across a single-antenna to a multi-antenna system, as shown in FIG. 5. The example implementation includes a physics- guided hierarchical model to divide uplink channels into sub-channels based on multipath distances. HORCRUX further utilizes a neural network model to estimate channel parameters in each sub-division. The data used to train the neural networks is simulated and grounded by the underlying physical laws of the wireless channel. The implementations overcome limitations of conventional systems and enable cross band channel prediction that can be generalized and scaled easily to any wireless environment without prior knowledge.

[0102] MIMO systems take advantage of the multipath-rich environment to improve performance and capacity. Multipaths arriving at a separation of ( is the speed of light and is bandwidth) can be resolved accurately. Previous efforts [11,54] are inspired by this physics-guided intuition, and the resulting systems are trained based on understanding and resolving the underlying physical environment variables. For example, assume wireless channel of 20 MHz bandwidth 12 multipaths can be resolved within the delay spread of 1- 200 meters

[0011] . In a particular environment, we measure the relationship between the observed wireless channels at different positions by a metric called path loss correlation. We used Pearson correlation

[0016] of the absolute values of the channel to calculate the path loss correlation. A realistic everyday environment should have uncorrelated path loss because of different combinations of multipaths (number of multipaths and their distances). FIG. 6 shows the relationship of path loss correlation with the underlying physical environment.Path loss of the channels observed is highly correlated ( 0.7 ) when there is less variation in multipath and distance. However, with more environmental variation, the channels observedare uncorrelated ( 0.2 0 ). Most channels in a realistic environment have uncorrelatedpath loss. Herein, the path loss correlation is used as a metric to estimate the diversity of wireless channels in experimented environments and clarify the performance gain of HORCRUX over the state-of-the-art systems.

[0103] State-of-the-art systems either use signal processing techniques (R2F2

[0054] ) or use physics-guided neural models to estimate these underlying multipaths (OptML

[0011] ). However, our experiments show that such systems fail to perform accurately under uncorrelated path loss environments as they can only resolve up to 2-3 combinations of multipaths and do not perform well in unseen environments. FIRE

[0035] leverages a generative process with a VAE architecture for this purpose. However, it has been shown that such ideas do not work well if there is variability in the training data

[0061] . Specifically, the study herein shows that if the wireless environment is complex, i.e., if the channel path losses are uncorrelated, FIRE fails to train accurately, resulting in erroneous estimations. Again, like OptML and R2F2, FIRE does not generalize to unseen environments. FIG. 7 shows a the performance gain of HORCRUX against OptML, FIRE, and R2F2 under varying wireless environments. We observe that these contemporary systems perform poorly in environments with uncorrelated channels. However, HORCRUX continues to perform accurately under different wireless environments and outperforms state-of-the-art by 8 dB gain in channel prediction accuracy when wireless channels are uncorrelated.

[0104] Channels

[0105] In wireless communication, the receiver receives the composite signal from thetransmitter after it has traveled across paths with different distances ( ), attenuations ( ),and reflections ( ). This composite effect of the environment that the signal undergoes isdenoted as the wireless channel ( ). Thus, for a signal transmitted at frequency (wavelength ), the multipath channel ( ) can be represented as follows [11, 52]:

[0107] where is the number of multipaths, and is the subcarrier. Thus, for a singleantenna, a multipath channel can be described by a set of 3-tuples, {( , , )}

[0011] .

[0108] MIMO systems exploit the multipath environment to simultaneously send and receive multiple data streams. For massive MIMO, the base station composes multipleantennas ( ) which talk with multiple clients ( < ) at the same time

[0037] . The datastream transmitted by the base station needs to be precoded to eliminate interference from other clients. Thus, the received signal can be expressed as

[0109] y = H + (2)

[0110] where is noise, is the × 1 vector of the transmitted signal, and is the ×channel matrix (each antenna of the base station to each client). Each client is assumed tohave a single antenna for simplicity. is the × precoding matrix. The study usedzeroforcing precoding technique [35, 57]. Zero-forcing is a standard precoding techniquewhere = , where is the right pseudo-inverse of the channel matrix . Thus, it isessential to estimate the channel accurately. Otherwise, the clients will suffer from interference and can decrease the data rate and SINR (signal-to-interference-plus-noise ratio). The study used SINR as one of the metrics to evaluate HORCRUX on the MU-MIMO setup.

[0111] Implementations of the present disclosure improve on the limitations of the existing OptML

[0011] methodology.

[0112] OptML

[0011] is one of the state-of-the-art methods that enable a device having single or randomly arranged antenna elements to predict the channel to a client in frequency band based on the uplink channel observed from the client in frequency band . To achieve that goal, authors develop a method for producing rough estimates of the distances of multiple paths by comparing the characteristics of the detected channel with those created by signals that have traveled different distances.

[0114] For a channel measured over I sub-carriers, let represent the channel at wavelength . Then, the likelihood of containing a path from a distance can be computed by Eq. 3

[0011] . The distances with large values give the coarse estimate of the multipaths.

[0115] OptML uses a fully connected neural network to estimate the initial distance guesses. The input to the network is the uplink channel, and the output is a sparse vector containing the likelihood of the multipath components from different distances (ranging from 0 to 200 m) being a part of the channel. The neural net is trained on simulated data governed by the channel model as mentioned in Eq. 1. However, such a simplified network can, at most, estimate 2-3 multipaths using a single antenna and often underestimates the number of paths affecting the channel. FIG. 9 shows OptML cannot estimate all the components correctly.

[0116] OptML leverages an optimization framework to fine-tune the coarse estimates before predicting the cross band channel. They propose that the optimization can be framedin terms of { } (distance estimates) as the other variables can be estimated based on the leastsquares approach.

[0118] where represents the channel observed on a single antenna, represents a matrixof size × , , = , where is the number of subcarriers in the signal and isthe number of multipath components estimated by the NNDE. is the pseudo-inverse, and=(the complex attenuation associated with each multipath component). Authors use adifferential evolution algorithm and limit the search space within bounds 20 m around the coarse estimates. However, the optimization becomes expensive with an increase in the number of multipath components. Using multiple antennas, OptML can resolve more paths but at the cost of computation time.

[0119] Example Implementation

[0120] FIG. 1 illustrates the example implementation of HORCRUX used in the study, which takes the uplink channel as input and feeds into the Neural Network Channel Divider (NNCD) block. This block includes of parallel neural networks that divide the input channel into sub-channels based on the distances of the multipath components. The output from the NNCD blocks is then passed into the Distance Estimate Initiator block, which decides whether to initiate distance estimation for that predicted sub-channel.

[0121] As further shown in FIG. 1, the example implementation includes a neural network distance estimator 108, which in the example implementation is configured as a mini-Neural Network Distance Estimator block (mNNDE), with parallel mNNDEs that are simpler and lightweight, and can be trained on smaller datasets.

[0011] Each of the mNNDEs focuses on a specific distance range and gives coarse estimates of distances of multipath components from that range. Then, HORCRUX uses the optimization framework similar to OptML to fine-tune distance estimates so that the channel based on the forecasted estimates closely fits the observed channel. However, HORCRUX converges faster as the bounds for each of the components are minimal ( 4 m ). Once converged, the estimates predict the cross band channel using Eq. 4. The neural nets are trained using simulated channel data on a single antenna system. For multi-antenna, HORCRUX will run simultaneously on each antenna.

[0122] Neural Network Channel Divider. Instead of using the input channel to estimate coarse distances, the example implementation divides the input channel into smaller subsections. This divide-and-conquer approach significantly improves the performance of HORCRUX as each divided channel has at most 1-2 multipath components (correlated channels) and can therefore be easily estimated by the mN NDE. Say, for example, for a wireless channel that has four multipath components, Eq. 1 can be:

[0124] As shown in Eq. 5, the purpose of the NNCD block is to divide the input channel h into separate zones. Each zone has a different neural network (NNCDi ) as shown in FIG. 1. The input to these NNCDs is the observed channel h, and the output is the channel (hi) for that particular zone.

[0125] Physics-Guided Zone Division. The example implementation designs the division of zones based on the physics of a wireless environment. i) The channels with multipath components of similar distances have a high probability of similar responses. ii) The multipath components affecting the channel can be resolved based on the channel'sbandwidth ( / ).

[0126] Thus, for example, for a channel with 20 MHz bandwidth, the study can resolvemultipath components with distances ( > 15 ) apart. Therefore, for simplicity, the studycan introduce eight zones for a 20 MHz channel and a maximum delay spread of 200 m. Eachzone has a distance range of 25 m(> / ), i.e., divides the channel into sub-channel formed by multipath components of distances [ 0 m, 25 m ),: [25 m, 50 m)and similarly : [175 m, 200 m ). The study assumes that eachzone has at most 1-2 multipath components. This assumption makes it easier to train each of the blocks accurately, or it will try to fit noise without any multipath.

[0127] FIG. 10 shows the performance of the NNCD block for a typically observed channel. The observed channel consists of 8 multipath components (1 from each Zone), as shown as in the figure. The blocks take this observed channel as an input and divide the channel into the corresponding sub-division. As shown, predicts the sub-channel formed by the multipath component from Zone 1 (0 25 m), i.e., 13.79 m.Similarly, the rest of blocks perform their channel division. In FIG. 10, forsimplicity, the study shows the prediction of , , , only. As youcan see, the example channel prediction is near identical to the actual subdivided channel.

[0128] The NNCD blocks are separately trained on simulated channel data. FIG. 11 shows the prediction accuracy of each of the blocks. The study defined channel prediction accuracy

[0035] , as

[0129] Accuracy

[0130] where is the predicted sub-channel and is the ground truth sub-channel. As seen in FIG. 11, all the NNCD blocks predict the sub-divided channel with a mean accuracy > 15 dB . However, as you can see the edge blocks and perform better (> 20 dB ). The performance degrades towards the middle blocks due to error propagation in dividing the channels. Adjacent zones since having multipath components with similardistances ( < 25 m ) can be erroneous in estimation. Edge blocks (e.g., ) have errorpropagating from only one adjacent block , thus can be trained accurately compared to middle blocks (e.g., ) where error propagates from both adjacent zones. However,this error propagation is nominal ( < 3 dB ) and does not hurt downlink channel predictionaccuracy.

[0131] Distance Estimate Initiator. One of the assumptions made in training for the NNCD is that there is always at least one multipath from each section. This assumption helps to train the neural network models without fitting noise in case there is no multipath in a particular section. However, in actual experiments, such an assumption is not guaranteed to hold. Thus, even in the absence of a multipath component from a zone, the NNCD of that zone will still try to divide the channel into a corresponding sub-channel. If this sub-channel is further used for distance estimation, it will generate false distance estimates. Thus, if not taken care of, it will result in erroneous channel prediction in the downlink band. To overcome this, the example implementation uses a Distance Estimate Initiator block. The corresponding NNCD predicts the sub-channel with a very low mean absolute power (noise) if there is no multipath component from a particular zone. FIG. 12 shows the cumulative distribution function (CDF) plot for a with and without a path. The mean absolute power of the predicted sub- channel in the presence of a component is around 1 mW (mean CDF), similar to the ground truth sub-channel. However, in the absence of a multipath component, the predicted sub- channel of the is 0.4 mW. Thus, the example implementation defines a threshold that decides whether to initiate the distance estimation for that particular sub-channel.

[0132] = 1, if0, otherwise (7)

[0133] where decides whether to initiate the (Sec. 3.3). Note that will change with different signal SNR. FIG. 13 shows the values for different SNRs. Also note that the is chosen as the minimum of all the blocks, as the middle blocks may suffer minor erroneous estimations as described herein.

[0134] mini-Neural Network Distance Estimator. Each of the blocks is accompanied by a mini-Neural Network Distance Estimator ( ) as shown in FIG. 1. HORCRUX leverages a fully connected neural network. However, the model size is much smaller than OptML since each only estimates 1-2 multipath components, focuses on a smaller distance range of 25 m , and can be trained on a smaller dataset. These blocks are separately and independently trained on physically governed simulated data based on Eq. 1 and are not dependent on the training of .

[0135] FIG. 14 shows the performance of mNNDE blocks. The study used the example discussed in FIG. 10. After being subdivided by the blocks, the observed inputchannel is fed into . in FIG. 14 shows the Distance Estimator Initiator for eachflow. Each takes the predicted sub-channel of as input and gives the coarse estimates of the distance of the multipath components. FIG. 14 shows that the mNNDE blocks accurately estimate the multipath components. Thus, using this technique, the example implementation can resolve 8-10 components for a 20 MHz channel, while OptML can only support two to three multipath estimations using a single antenna.

[0136] Optimization Framework. HORCRUX can fine-tune the coarse estimates of the distance estimator blocks before predicting the channel in different frequencies. A differential evolution algorithm is used for the optimization. However, the example implementation canconstrict the bounds for each coarse distance estimate ( ) to about 4 m, 4x faster thanOptML. In other words, HORCRUX can converge more quickly even if the number of multipath components is eight. FIG. 15 shows the result for the optimization framework.HORCRUX fits the observed channel accurately by estimating the channel variables{ , }. These variables are used to estimate the cross band channel. HORCRUX predictsthe downlink channel with high accuracy as shown in FIG. 15.

[0137] Channel Prediction Algorithm. Algorithm 1 shows the overall algorithm for HORCRUX channel prediction. It takes as the number of zones as input and thecorresponding and blocks. It runs for all antenna elements ( ) in parallel.For each antenna ( ), blocks run parallel to subdivide the uplink channelinto. Distance Estimate Initiator calculates . If true, each of the blocks gives thecoarse distance estimates. { } = { , … } estimated by the . The initial estimatesare then replaced with bounded variables { }bounded = { 1 ± , 2 ± … } (getBounded inAlgo. 1) to reduce the search space and are then used in the optimization algorithm. The finetuned estimates { }final are then used to compute . Finally, HORCRUX computes thedownlink channel .

[0138] Algorithm 1 Input:Output:for all do in parallel for all do in parallel{ } =Calculate based on Eq. 7 if == 1 then{ } = ( )end if end for{ }bounded = getBounded ( { }, b){ }final , error = Optimize { }bounded ,= getMatrix ({ }final , )= D{ } final ,

[0139] 3.5 Training data

[0140] Each of the and is trained separately on physically grounded simulated data (Eq. 1 is used to generate the wireless channels). Example Parameters - RF parameters: center frequency and bandwidth; Component distances [ dmin, max];Attenuation, (0,1]; Phase, [ , ].

[0141] The center frequency is chosen based on the uplink of the WiFi channel, and thebandwidth is 20 MHz . Each multipath is represented by a set of 3-tuples, {( , , )}.varies between 0 to 200 m . Note that the wireless channels generated are highly diverse and uncorrelated with a path loss correlation value 0, which resembles a dynamic wireless environment.

[0142] NNCD: The example implementation can separately simulate a sub-channel for each zone based on the above variables. The sub-channel is simulated based on the{( , , )} of the multipaths of that particular zone. Each zone has at least one multipathcomponent. The input channel to the NNCD is calculated by summation (normalized) of all the sub-channels for that particular data point. The output is the generated sub-channels. FIG. 10 shows the input and output of the NNCD blocks. mNNDE: The simulated sub-channels for NNCD are used as input to mNNDE. The output is the sparse vector of true distances for that sub-channel. The number of zones for HORCRUX depends on the channel's bandwidth. The study used 20 MHz bandwidth and eight zones.

[0143] Digital Twin Advantage: A benefit of the example implementation is leveraging a physically grounded digital twin environment to train the neural models. Such ideas have been recently explored in various contexts such as manufacturing [6, 69], intelligent transportation

[0025] , and aeronautical designs

[0038] . This simulated environment, guided by accurate real-world physical models, has significant advantages over training on data within a specific environment

[0035] . First, unlike models trained on specific environmental conditions that required specialized detection and resolution strategies for out-of-distribution observations, the example digital twin-based training framework can sidestep this issue, allowing it to generalize to arbitrary environments. Second, since these signals are being generated with ground truth labels, the example implementation does not require manual ground truth labeling by experts, which can be both expensive and prone to error. Third, the process facilitates an implicit form of grounding for the models described herein

[0010] . Finally, the experimental results of the study demonstrate that such a strategy can be enhanced and cross-validated with real-world information.

[0144] Implementation

[0145] To evaluate the performance of HORCRUX in the real world, the study built a prototype with the WARP v3 software-defined radio platform [1]. The study tested the system on a 2 -antenna and a 4antenna base station, talking with two clients. Experiments were conducted in different wireless environments (a sizeable indoor office space, smaller indoor household) in i) LOS (line-of-sight) ii) NLOS (non-line-of-sight) and iii) moving client conditions. The wireless environments had varied path loss correlations. The details of the path loss correlation of each environment are shown in FIG. 29. The study used path loss correlation as a metric to show the diversity of channels in the wireless environments. Clients talk with the base station using Wi-Fi 802.11n protocol. The base station uses the Long Training Symbols (LTS) to do channel estimation after Carrier Frequency Offset (CFO) and Sampling Frequency Offset (SFO) correction. The base stations have the antennas separated by around half wavelength ( 6 cm ) for the 2.4 GHz band. 20 MHz bandwidth and 64OFDM subcarriers were used. The example implementation splits the channel measurements into two halves (26 subcarriers after removing guard bands). The study used the first half as uplink and estimated the other half using HORCRUX. FDD: The study also evaluated the example system in the FDD hardware setup using WARP nodes, where the uplink and downlink happen on different frequencies and across other devices.

[0146] NNCD architecture. The study implemented the NNCD models within Keras

[0019] . Each NNCD comprises two hidden layers, each with 128 neurons with an Exponential Linear Unit (ELU) activation function. The models are trained separately on 100 K data points with the same input channel and target sub-channels. The input and output to the neural net is alinear array of 2 × (real and imaginary part of the complex channel withsubcarriers). The study generated various training channels with different SNRs, and each NNCD zone had at least one multipath component. mNNDE architecture: Similar to NNCD, each of the mNNDE models is trained separately on 100 K data points, each of which represents input channels generated by multipath components of that particular zone and target vector of distance estimates (range of 25m). Each of the models is composed of 5 hidden layers, with 200 neurons on each layer.

[0147] Optimization: For optimization, based on path resolution, the study limited themaximum multipath component to 12 for 20 MHz . The trained models (8 × NNCD and8 × mNNDE ) take less than 7 MB of disk space (similar to OptML).

[0148] RESULTS

[0149] The study included an empirical evaluation of HORCRUX. We compared performance of HORCRUX with state-of-the-art works FIRE

[0035] , OptML

[0011] , and R2F2

[0054] . The study also evaluated performance in multiple environments. The study implemented these baselines from scratch.

[0150] The study included microbenchmarks to evaluate the performance of HORCRUX and other state-of-the-art systems. Specifically, the study trained HORCRUX, FIRE, and OptML using simulated channel measurements. The simulated channels during training are uncorrelated (using a path loss correlation value of 0.01 ). The study used 2 -antenna and 4 -antenna base stations to implement the system for testing. The study moved the client across more than 500 different LOS and NLOS positions with varying SNR in both household and office environments. FIG. 16 and FIG. 17 show the prediction performance of HORCRUX. The study shows that HORCRUX predictions are very similar to the actual channel measurements (absolute and phase values).

[0151] Channel Prediction Accuracy. The study defined channel prediction accuracy by Eq. 6. This is an important metric in the MU-MIMO setup, as errors in predicting the downlink channel can result in interference across clients, affecting SINR performance. FIG. 18 and FIG. 19 show the CDF plot of channel prediction accuracy gain in dB of HORCRUX compared to state-of-the-art systems. Experiments are done in LOS and NLOS conditions for a 2-antenna base station and a single client in a small room. The mean CDF channel prediction accuracy for HORCRUX for LOS condition is 10.34 dB and for NLOS is 11.02 dB. The study shows that HORCRUX achieves 8 dB gain compared to the state-of-the-art systems. The main reason is that FIRE, OptML, and R2F2 perform poorly in multipath-rich environments and need accurate knowledge to train in such environments. Such low prediction accuracy affects MU-MIMO for such systems. However, HORCRUX, because of its unique architecture, can perform accurately in such environments, even though HORCRUX is trained on simulation data only and has no prior knowledge of the environment.

[0152] FIG. 20 shows the performance of HORCRUX using a 4-antenna base station. The experiments are performed on a single client across 200 positions in an office environment. HORCRUX continues to outperform the baselines by a margin of 6 dB. The channel prediction accuracy is dependent on the signal SNR. The dashed line in FIG.21 shows the signal SNR across the experimental measurements. The SNR varies between 10-20 dB. The dotted line in FIG. 21 shows the HORCRUX channel prediction accuracy for different SNRs. HORCRUX continues to perform quite accurately even under low SNR conditions. The study also performed channel prediction for a moving client. The study moved a client around the office for 2.5 minutes and predicted the downlink channel. The study shows in FIG. 22 that HORCRUX performs accurately under varied SNR conditions.

[0153] To understand this relationship between accuracy and SNR in detail, the study performed controlled experiments where the client was placed in locations with SNR varying from 25 dB to 10 dB . FIG. 23 shows the performance of HORCRUX across different SNR values - showing that HORCRUX achieves around 15 dB mean channel prediction accuracy for high SNR environments ( 25 dB ). Accuracy decreases with a decrease in SNR values. Such variation is also observed in state-of-the-art systems. However, even in a low SNR environment ( 10 dB ), HORCRUX performs quite accurately.

[0154] Beamforming Performance. One of the applications of MIMO systems is beamforming, where the base station uses multiple antennas to steer a beam to a specific client. Such techniques can improve SNR and data rates at the client. The study evaluates theperformance by utilizing the predicted channels in the downlink to beamform to the client. The experimental results were compared to the ground truth channel (Grd Truth) that will achieve optimal beamforming and a random downlink channel as the baseline where there is no beamforming (No beam).

[0155] FIG. 24 and FIG. 25 show the performance of HORCRUX for 2 -antenna and 4 - antenna setups, respectively. HORCRUX can beamform near optimally to the ground truthchannel beam. The beam gain difference from optimal is < 0.1 dB. FIRE, OptML, and R2F2follow closely with a beam gain difference of 2 dB from HORCRUX. We note that the channel accuracy requirement for beam gain performance is low

[0035] . Thus, state-of-the-art works can perform well in beamforming even with low channel accuracy.

[0156] Multi-User MIMO Performance. Multi-antenna base stations enable multi-user MIMO technique where it can simultaneously talk with multiple clients. However, the onerous requirement to perform MU-MIMO is to predict accurate downlink channels. Errors in channel prediction can result in signal leakage into different non-intended clients and cause interference. SINR was used as the metric to evaluate the performance of MU-MIMO. The study experimented on 2-antenna and 4 -antenna base stations, talking to two clients using the zero-forcing technique described herein. The experiments are repeated across more than 20 different locations of the clients for office environments with well-conditioned channels. HORCRUX achieves 9.2 dB median SINR for the 2-antenna 2 -client setup and 11.12 dB for the 4 -antenna 2 client setup. FIG. 26 shows the performance of HORCRUX for 2 -antenna and 4 -antenna setups for each of the clients. FIG. 27 shows the SINR gain of HORCRUX over state-of-the-art systems for the 4 -antenna setup where HORCRUX outperforms the baselines by a mean of 8-10 dB. FIG. 28 shows the performance of HORCRUX across larger antenna systems. The study used simulation data to evaluate the performance. The uplink channels were generated using Eq. 1 and four multipaths ranging from 1 to 200 meters were used. For an increase in antenna elements, HORCRUX outperforms the baselines with a higher margin. For 16-antenna elements, HORCRUX has around 15 dB improvement over the state-of-the-art. The main reason is that FIRE, OptML, and R2F2 estimate channels with low accuracy in multipath-rich environments (i.e., uncorrelated observed channel path loss).

[0157] Robustness Across Environment

[0158] To evaluate the performance across different conditions, the study experimented in 6 different environments: i) Small room, ii) Large Office, iii) Argos indoor, iv) Argos outdoor, v) Simulated environment with four multipaths ranging from 1-100m , vi) Simulated environment with two multipaths ranging from 1-50 m.

[0159] FIG. 29 shows the path loss correlation values in different environments. It measures the relationship of the observed channels in that particular environment. We observe that Small room, Argos indoor, and Argos outdoor experience high mean pathcorrelation ( > 0.5 ) among the channels observed, while Office and the simulatedenvironments show uncorrelated channel observations (<0.5). A realistic experimental setup should have uncorrelated observations because of the varying multipath combinations. We find that path loss correlation is a key metric that helps explain the comparitive performance of HORCRUX with baselines.

[0160] The Argos2channel measurements were collected in the RENEW testbed

[0047] with 64-antenna base stations across eight clients. The study used a subset of the data (four antennae across four clients) to evaluate the performance. 2-antenna base stations were used in the small room setup, and the client was moved around at 20 different locations a few feet apart. In the office environment, a 4-antenna base station was used, and the client was moved around 20 different locations around 10 feet apart.

[0161] The study trained FIRE on the Argos indoor dataset and tested it for all the environments. For HORCRUX, the study used simulated data described herein for training. FIG. 32 illustrates that HORCRUX accurately estimates channel across different frequency bands. The observed channel is shown in FIG. 32 with the actual and predicted channels. FIRE requires to be trained for a particular uplink and downlink frequency pair and does not generalize well across another frequency band.

[0162] FIG. 30 shows that FIRE performs well in the trained environment (Argos indoor), but it fails to estimate the channel accurately across other environments. FIRE, being an end- to-end architecture, fails to capture the underlying physical environment and cannot be generalized across other environments having different combinations of multipaths.

[0163] The study also trained and tested FIRE on each of the environments separately. FIG. 31 shows the performance across multiple environments. Even with enough knowledge about the wireless environment, FIRE can only perform well in an environment (Small room, Argos indoor and Argos outdoor) with correlated channels, as shown in FIG. 29. In an environment with uncorrelated channels, FIRE fails to perform well.

[0164] On the other hand, as seen in FIG. 30 and FIG. 31, HORCRUX enjoys accurate estimations across different environments. It can be trained only on simulated data and does not require training across environments. Unlike systems trained on specific environmental conditions, the digital twin-based training framework within HORCRUX, with the help of NNCD and mNNDE architectures, as described herein, captures a broad range of possiblephysical environments and thus can give good channel prediction allowing it to generalize to arbitrary environments. However, for the Argos dataset, there is a decrease in channel prediction accuracy because of inaccurate offset correction.

[0165] FDD Hardware Implementation

[0166] The study implemented an FDD setup using a 2-antenna base station. Uplink and downlink are in different frequency channels, and separate radio-frequency (RF) chains are used. Experiments are carried out in multiple LOS and NLOS positions with varying SNR.We measured uplink on channel 1 (2.412GHz) and predicted downlink on channel6(2.437GHz, 25 MHz separation) and channel 11 ( 2.462GHz 50MHz separation),respectively, in a separate set of experiments. FIG. 33 and FIG. 34 show the channel prediction accuracy gain of HORCRUX compared to state-of-the-art where uplinkdownlinkare separated by 25 MHz and 50 MHz , respectively. HORCRUX enjoys a mean gain of6 dB. To summarize, HORCRUX outperforms the state-of-the-art on the FDD hardwareimplementation.

[0167] Across Frequency Bands. To show the performance of HORCRUX across the different frequency bands, the study performed a simulation observing the uplink band on a particular frequency and tried to predict channel measurements across different frequency bands. FIG. 32 shows the performance of HORCRUX across different downlink frequency bands. The green line shows the observed channel measurements in a particular band. HORCRUX accurately predicted the downlink channel across different bands (see dotted line). However, for state-of-the-art FIRE, one must extensively train the system (100K channel measurements) for separate downlink bands to predict in that particular band, which is time-consuming and / or inefficient, and therefore may not be feasible.

[0168] Processing Time. Given the observed uplink channel, an essential performance aspect is the processing time to estimate the downlink channel. FIG. 35 shows the processing time required for state-of-the-art systems. FIRE does not require estimating the underlying physical parameters and thus can estimate the downlink channel within a mean of 1 ms across any number of multipath components. For HORCRUX, OptML, and R2F2, the processing time includes the estimation of initial guesses and the optimization framework to estimate the channel. HORCRUX observes a run time of 30 ms for both 2 and 8 multipath components. The increased processing time is mostly because of the optimization framework. However, due to NNCD and mNNDE, HORCRUX can rapidly converge with a small search window. Thus, even with an increase in the number of components, HORCRUX performs almostsimilarly. OptML performs faster if the number of components is less ( 2 ), however as shown in FIG. 35, with the increase in the number of multipath components, the optimization framework takes a reasonable amount of time to converge. HORCRUX outperforms OptML by 4x. R2F2 performs worst because of its signal processing technique to estimate the initial guesses. HORCRUX is more than 50x faster than R2F2 in 8 multipath case. The coherencetime for the outdoor environment for the 2.4 GHz band is 1 50 ms

[0035] , which means theunderlying channel parameters do not change much within this time frame. HORCRUX thus can accurately estimate the downlink channel. Even though FIRE performs the fastest, it cannot be generalized and extended to other environments and frequency bands as it is unable to estimate the underlying physical parameters.

[0169] Discussion

[0170] The example implementation “HORCRUX,” includes a physics-based machine learning system that can predict wireless channels across different frequency bands and can be used by various wireless devices ranging from single-antenna IoT devices to massive MIMO base stations. The study herein evaluated and compared the example system with state-of-the-art techniques across different wireless testbeds and simulations. The evaluationsshow that HORCRUX can predict crossband channels with high accuracy and achieves8 dB SINR gain over the state-of-the-art. HORCRUX can continue to provide accurateestimations across multiple wireless environments with low correlation without any prior knowledge of that particular environment, improving on conventional systems and methods. Integration of the example system can enable the success of next-generation wireless networks, such as 5 G and 6G, and these tools will help to improve the overall performance and efficiency of wireless communication systems.

[0171] The example implementation of the present disclosure presents advantages when compared to conventional methods of downlink channel prediction. Approaches such as R2F2, OptML, and FIRE address this challenge by removing the requirement of channel feedback and estimating the downlink channel based on the measured uplink channel. R2F2 and OptML are motivated by the fact that the underlying frequency-independent channel variables (multipath distance, attenuation, etc.) remain the same for both uplink and downlink channels. R2F2 proposes a signal processing technique to estimate the uplink’s underlying parameters and thereby estimate the downlink channel. However, such a technique can be computationally expensive if the number of multipaths and antenna components is large. OptML, on the other hand, proposes a fast neural-network-based approach to estimate thechannel variables and predict the downlink channel. FIRE uses an end-to-end variational autoencoder (VAE) to estimate the downlink channel from the uplink channel. However, both OptML and FIRE estimate channels with low accuracy in multipath-rich environments if the training set differs from the testing environment. Such low accuracy in channel estimates hurts MIMO gains for multi-user settings. Embodiments of the present disclosure address these and other problems with the conventional methods of downlink channel prediction.

[0172] Additionally, the example implementation includes improvements over existing machine learning architectures that predict the downlink channel directly from the uplink channel, because those existing methods require training on particular environments and / or frequency bands and therefore fail to generalize to other environments and frequency bands. Additionally, implementations of the present disclosure improve over methods of using mixture of experts techniques by not requiring a gating model and allowing for the separate training of each neural network of the neural network distance estimator.

[0173] Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

[0174] References

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Claims

WHAT IS CLAIMED IS:

1. A method comprising: receiving an uplink channel; partitioning the uplink channel into a plurality of sub-channels by a neural network channel divider, wherein the plurality of sub-channels correspond to a plurality of non- overlapping distance ranges; generating, a plurality of coarse distance estimates by a neural network distance estimator, wherein the plurality of coarse distance estimates comprise a distance estimate for each of the plurality of sub-channels; generating a plurality of fine-tuned distance estimates by optimizing the plurality of coarse distance estimates; and determining, from the plurality of fine-tuned distance estimates, a downlink channel prediction, wherein the downlink channel prediction predicts a downlink channel based on the uplink channel.

2. The method of claim 1, further comprising transmitting a downlink signal based on the downlink channel prediction.

3. The method of claim 2, wherein the downlink signal comprises a beamformed signal.

4. The method of any one of claims 1-3, wherein the neural network distance estimator comprises a plurality of neural network distance estimator networks each configured for a different range of distances.

5. The method of any one of claims 1-4, wherein the neural network distance estimator comprises a neural network trained only on synthetic data.

6. The method of any one of claims 1-5, wherein the neural network channel divider comprises two hidden layers.

7. The method of any one of claims 1-6, wherein the neural network channel divider is configured with a exponential linear unit activation function.

8. The method of any one of claims 1-7, wherein the neural network distance estimator comprises five hidden layers.

9. A system comprising a radio transceiver comprising a receiver front end and a transmitter front end; a controller operably coupled to the radio transceiver, the controller comprising a processor and a memory storing a neural network channel divider and a neural network distance estimator, wherein the memory further stores computer-executable instructions that, when executed by the processor, cause the processor to: receive an uplink channel by the receiver front end; partition the uplink channel into a plurality of sub-channels by a neural network channel divider, wherein the plurality of sub-channels correspond to a plurality of non- overlapping distance ranges; generate, a plurality of coarse distance estimates by a neural network distance estimator, wherein the plurality of coarse distance estimates comprise a distance estimate for each of the plurality of sub-channels; generate a plurality of fine-tuned distance estimates by optimizing the plurality of coarse distance estimates; and determine, from the plurality of fine-tuned distance estimates, a downlink channel prediction, wherein the downlink channel prediction predicts a downlink channel based on the uplink channel.

10. The system of claim 9, further comprising transmitting a downlink signal based on the downlink channel prediction.

11. The system of claim 10, wherein the downlink signal comprises a beamformed signal.

12. The system of any one of claims 9-11, wherein the neural network distance estimator comprises a plurality of neural network distance estimator networks each configured for a different range of distances.

13. The system of any one of claims 9-12, wherein the neural network distance estimator comprises a neural network trained only on synthetic data.

14. The system of any one of claims 9-13, wherein the neural network channel divider comprises two hidden layers.

15. The system of any one of claims 9-14, wherein the neural network channel divider is configured with a exponential linear unit activation function.

16. The system of any one of claims 9-15, wherein the neural network distance estimator comprises five hidden layers.

17. A method of training a neural network channel divider, the method comprising: (a) generating a synthetic dataset comprising a plurality of simulated uplink channels; (b) selecting a set of sub channels from the synthetic dataset, wherein the sub channels comprise paths within a zone; and (c) training a neural network to extract a sub-channels from an uplink signal based on the set of sub-channels and the synthetic dataset.

18. The method of claim 17, further comprising: repeating steps (a), (b), and (c) to train a plurality of neural networks, wherein each of the plurality of neural networks are configured to extract different sub-channels for different zones.

19. The method of claim 17 or claim 18, further wherein generating the synthetic dataset comprises performing a multipath physics simulation.

20. The method of any one of claims 17-19, wherein the synthetic dataset comprises at least one of: center frequency, bandwidth, component distances, attenuation, and phase.

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