Equal variant generation priori for inverse problems with unknown rotation

Abstract

A processor-implemented method for estimating a channel through a depth generative model includes receiving, at a device, an observation of the channel; and mapping, at the device, the observation to a mean value associated with the channel and a covariance matrix associated with the channel. The processor-implemented method also includes reconstructing, at the device, the channel based on the mean value and the covariance matrix.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. patent application No. 18 / 100,263, filed on January 23, 2023, and entitled “EQUIVARIANT GENERATIVE PRIOR FOR INVERSE PROBLEMS WITH UNKNOWNROTATION,” and claims the benefit of U.S. Provisional Patent Application No. 63 / 303,938, filed on January 27, 2022, and entitled “EQUIVARIANT GENERATIVE PRIOR FOR INVERSE PROBLEMS WITH UNKNOWN ROTATION,” the disclosures of which are expressly incorporated by reference in their entirety. Technical Field

[0003] Aspects of the present disclosure relate generally to wireless communications, and more particularly to estimating wireless channels using equivariant generative priors. Background Art

[0004] Wireless communication systems are widely deployed to provide various telecommunication services such as telephone, video, data, messaging, and broadcasting. Typical wireless communication systems may employ multiple access technologies that can support communication with multiple users by sharing available system resources (e.g., bandwidth, transmit power, etc.). Examples of such multiple access technologies include code division multiple access (CDMA) systems, time division multiple access (TDMA) systems, frequency division multiple access (FDMA) systems, orthogonal frequency division multiple access (OFDMA) systems, single carrier frequency division multiple access (SC-FDMA) systems, time division synchronous code division multiple access (TD-SCDMA) systems, and long term evolution (LTE). LTE / LTE Advanced is an enhancement set of the Universal Mobile Telecommunications System (UMTS) mobile standard released by the Third Generation Partnership Project (3GPP). Narrowband (NB) Internet of Things (IoT) and enhanced machine type communication (eMTC) are enhancement sets of LTE for machine type communication.

[0005] A wireless communication network may include multiple base stations (BSs) that may support communication of multiple user equipments (UEs). User equipments (UEs) may communicate with base stations (BSs) via downlinks and uplinks. Downlinks (or forward links) refer to the communication link from a BS to a UE, while uplinks (or reverse links) refer to the communication link from a UE to a BS. As will be described in more detail, a BS may be referred to as a Node B, an evolved Node B (eNB), a gNB, an access point (AP), a radio head, a transmit receive point (TRP), a new radio (NR) BS, a 5G Node B, and the like.

[0006] The above multiple access technologies have been adopted in various telecommunication standards to provide a common protocol that enables different user equipment to communicate at the city, country, region, and even global level. New Radio (NR) (also known as 5G) is a set of enhancements to the LTE mobile standard released by the Third Generation Partnership Project (3GPP). NR is designed to better integrate with other open standards by improving spectrum efficiency, reducing costs, improving services, utilizing new spectrum, and using orthogonal frequency division multiplexing (OFDM) (CP-OFDM) with cyclic prefix (CP) on the downlink (DL), using CP-OFDM and / or SC-FDM (e.g., also known as discrete Fourier transform spread OFDM (DFT-s-OFDM)) on the uplink (UL), and supporting beamforming, multiple input multiple output (MIMO) antenna technology and carrier aggregation, so as to better support mobile broadband Internet access.

[0007] An artificial neural network may include an interconnected group of artificial neurons (e.g., a neuron model). An artificial neural network may be a computing device or represented as a method performed by a computing device. A convolutional neural network, such as a deep convolutional neural network (DCN), is a feed-forward artificial neural network. A convolutional neural network may include layers of neurons that may be configured in a tiled receptive field. It would be desirable to apply neural network processing to wireless communications to achieve higher efficiency. Summary of the invention

[0008] In one aspect of the present disclosure, a method for estimating a channel by a deep generative model includes: receiving an observation of the channel. The method also includes: mapping the observation to a mean value associated with the channel and a covariance matrix associated with the channel. The method still includes: reconstructing the channel based on the mean value and the covariance matrix.

[0009] Another aspect of the present disclosure relates to an apparatus comprising: means for receiving an observation of the channel. The apparatus further comprises: means for mapping the observation to a mean value associated with the channel and a covariance matrix associated with the channel. The apparatus still further comprises: means for reconstructing the channel based on the mean value and the covariance matrix.

[0010] In another aspect of the present disclosure, a non-transitory computer-readable medium having non-transitory program code recorded thereon is disclosed. The program code is executed by a processor and includes: program code for receiving an observation of a channel. The program code also includes: program code for mapping the observation to a mean value associated with the channel and a covariance matrix associated with the channel. The program code still includes: program code for reconstructing the channel based on the mean value and the covariance matrix.

[0011] Another aspect of the present disclosure relates to an apparatus having: a processor; and a memory coupled to the processor and storing instructions that, when executed by the processor, are operable to cause the apparatus to: receive an observation of the channel. Execution of the instructions further causes the apparatus to: map the observation to a mean value associated with the channel and a covariance matrix associated with the channel. Execution of the instructions further causes the apparatus to: reconstruct the channel based on the mean value and the covariance matrix.

[0012] Aspects generally include methods, apparatus, systems, computer program products, non-transitory computer readable media, user equipment, base stations, wireless communication devices, and processing systems as substantially described with reference to and as illustrated in the accompanying drawings and description.

[0013] The features and technical advantages of examples according to the present disclosure have been outlined quite extensively above so that the following specific embodiments may be better understood. Additional features and advantages will be described below. The disclosed concepts and specific examples may be easily used as a basis for modifying or designing other structures for achieving the same purpose of the present disclosure. Such equivalent constructions do not depart from the scope of the appended claims. The characteristics of the disclosed concepts in terms of their organization and method of operation and the associated advantages will be better understood by considering the following description in conjunction with the accompanying drawings. Each of the accompanying drawings is provided for the purpose of illustration and description, and not as a definition of the limitations of the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to understand the features of the present disclosure in detail, a more specific description may be made with reference to various aspects, some of which are illustrated in the accompanying drawings. It should be noted, however, that the accompanying drawings illustrate only certain aspects of the present disclosure and should not be considered as limiting the scope thereof, as the description may allow for other equivalent aspects. The same reference numerals in different drawings may identify the same or similar elements.

[0015] Figure 1 is a block diagram conceptually illustrating an example of a wireless communication network in accordance with various aspects of the present disclosure.

[0016] Figure 2 is a block diagram conceptually illustrating an example of a base station communicating with a user equipment (UE) in a wireless communication network according to various aspects of the present disclosure.

[0017] Figure 3 An example implementation of designing a neural network using a system on a chip (SOC) including a general-purpose processor in accordance with certain aspects of the present disclosure is illustrated.

[0018] Figure 4A , Figure 4B and Figure 4C is a diagram illustrating a neural network according to aspects of the present disclosure.

[0019] Figure 4D is a diagram illustrating an exemplary deep convolutional network (DCN) according to aspects of the present disclosure.

[0020] Figure 5 is a block diagram illustrating an exemplary deep convolutional network (DCN) according to aspects of the present disclosure.

[0021] Figure 6 A diagram illustrating an example decomposed base station architecture is shown.

[0022] Figure 7 is a block diagram illustrating an example of a wireless communication system according to various aspects of the present disclosure.

[0023] Figure 8 is a block diagram illustrating an example of a variational autoencoder (VAE) according to various aspects of the present disclosure.

[0024] Fig. 9 is a flow chart illustrating an example process performed, for example, by a deep generative model in accordance with various aspects of the present disclosure. DETAILED DESCRIPTION

[0025] The various aspects of the present disclosure are described more fully below with reference to the accompanying drawings. The present disclosure may be embodied by one or more elements of the claims, but may be embodied in many different forms, and should not be construed as being limited to any specific structure or function presented throughout the present disclosure. On the contrary, these aspects are provided so that the present disclosure will be thorough and complete, and the protection scope of the present disclosure will be fully conveyed to those skilled in the art. Based on the teachings, those skilled in the art should recognize that the scope of the present disclosure is intended to cover any aspect of the present disclosure, whether the aspect is implemented independently of any other aspect of the present disclosure or implemented in combination with any other aspect. For example, an apparatus or a method may be implemented using any number of aspects described. In addition, the scope of the present disclosure is intended to cover such apparatus or methods that are practiced using other structures, functionality, or structures and functionality as supplements to the various aspects of the present disclosure described or in addition. It should be understood that any aspect of the present disclosure disclosed may be embodied by one or more elements of the claims.

[0026] Several aspects of telecommunication systems will now be presented with reference to various devices and techniques. These devices and techniques will be described in the following detailed description and illustrated in the accompanying drawings by various blocks, modules, components, circuits, steps, processes, algorithms, etc. (collectively referred to as "elements"). These elements may be implemented using hardware, software, or a combination thereof. Whether these elements are implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system.

[0027] It should be noted that while various aspects may be described using terminology typically associated with 5G and later wireless technologies, various aspects of the present disclosure may be applied in communication systems based on other generations, such as and including 3G, 4G and / or 6G technologies.

[0028] Artificial neural networks such as deep generative models can be used to estimate channels such as wireless channels. Variational autoencoders (VAEs) are examples of deep generative models. During training, the encoding distribution of the VAE can be regularized so that the latent space of the VAE can generate new data. In some examples, the VAE can estimate the channel or properties associated with the channel based on one or more observations of the channel. In one such example, for medical imaging, the VAE can generate an entire image of the organ based on one or more observations of the received organ. As another example, upon receiving one or more observations of the channel (such as pilot symbols associated with the channel), the VAE can generate the channel or properties associated with the channel by finding latent variables that generate the channel.

[0029] In some examples, compressed sensing can reconstruct a signal from an underdetermined system of linear measurements. The compressed sensing solution can use a priori knowledge of the signal to reconstruct the signal. In some examples, the signal or object has an unknown orientation before measurement. As an example, the orientation or beam direction of the user equipment (UE) relative to the base station may be unknown. As another example, the posture of an organ may be unknown. Therefore, conventional compressed sensing solutions may not be able to reconstruct a signal with an unknown orientation.

[0030] Various aspects of the present disclosure relate to using equivariant priors to solve inverse problems with unknown orientations. In some examples, an equivariant generative model encapsulates orientation information in a latent space of the equivariant generative model. The equivariant generative model may include an equivariant variational autoencoder (VAE). The VAE may include an equivariant encoder and an equivariant decoder. The encoder of the VAE may include two sub-parts. The first part may model an equivariant mean μ(x). The second part may model the covariance by learning a full rank equivariant matrix V(x). The covariance may be based on the equivariant matrix V(x) and the transpose V(x) of the equivariant matrix T In such aspects, a signal with unknown orientation may be recovered using iterative gradient descent on the latent space of an equivariant generative model.

[0031] Various aspects of the present disclosure may be applied to estimate one or more communication properties, such as estimating channels, delays, and / or Doppler shifts. Various aspects of the present disclosure may be applied to mmWave and / or massive multiple-input multiple-output (MIMO) channel estimation. In some examples, orientation may be estimated, and additional sensors may be used to estimate other communication properties based on the estimated orientation.

[0032] Certain aspects of the subject matter described in this disclosure can be implemented to achieve one or more of the following potential advantages. In some examples, by estimating the channel via an equivariant VAE of a deep generative model, aspects of the disclosure reduce convergence time by reducing the time associated with estimating the channel and also reduce network latency.

[0033] Figure 11 is a diagram illustrating a network 100 in which various aspects of the present disclosure may be practiced. The network 100 may be a 5G or NR network, or some other wireless network such as (but not limited to) an LTE network. The wireless network 100 may include a plurality of base stations (BSs) 110 (shown as BSs 110a, BSs 110b, BSs 110c, and BSs 110d) and other network entities. A BS is an entity that communicates with a user equipment (UE), and may also be referred to as a base station, NR BS, Node B, gNB, 5G Node B, access point, transmit and receive point (TRP), network node, network entity, etc. The BS may be implemented as an aggregated base station, a decomposed base station, an integrated access and backhaul (IAB) node, a relay node, a side link node, etc. The BS may be implemented in an aggregated or monolithic base station architecture, or alternatively in a decomposed base station architecture, and may include one or more of a central unit (CU), a distributed unit (DU), a radio unit (RU), a near real-time (near RT) RAN intelligent controller (RIC), or a non-real-time (non-RT) RIC. Each BS may provide communication coverage for a particular geographic area. In 3GPP, the term "cell" may refer to a coverage area of ​​a BS and / or a BS subsystem serving the coverage area, depending on the context in which the term is used.

[0034] A BS may provide communication coverage for a macro cell, a pico cell, a femto cell, and / or another type of cell. A macro cell may cover a relatively large geographic area (e.g., a radius of several kilometers) and may allow unrestricted access by UEs with service subscriptions. A pico cell may cover a relatively small geographic area and may allow unrestricted access by UEs with service subscriptions. A femto cell may cover a relatively small geographic area (e.g., a home) and may allow restricted access by UEs associated with the femto cell (e.g., UEs in a closed subscriber group (CSG)). A BS for a macro cell may be referred to as a macro BS. A BS for a pico cell may be referred to as a pico BS. A BS for a femto cell may be referred to as a femto BS or a home BS. In Figure 1 In the example shown in , BS 110a may be a macro BS for macro cell 102a, BS 110b may be a pico BS for pico cell 102b, and BS 110c may be a femto BS for femto cell 102c. A BS may support one or more (e.g., three) cells. The terms "eNB", "base station", "NR BS", "gNB", "AP", "Node B", "5G NB", "TRP", and "cell" may be used interchangeably.

[0035] In some aspects, the cell need not be stationary, and the geographic area of ​​the cell may move depending on the location of the mobile BS. In some aspects, the BSs may be interconnected with each other and / or to one or more other BSs or network nodes (not shown) in the wireless network 100 through various types of backhaul interfaces (such as direct physical connections, virtual networks, etc.) using any suitable transport network.

[0036] The wireless network 100 may also include a relay station. A relay station is an entity that can receive transmissions of data from an upstream station (e.g., a BS or a UE) and transmit the transmissions of the data to a downstream station (e.g., a UE or a BS). A relay station may also be a UE that can relay transmissions for other UEs. Figure 1 In the example shown, a relay station 110d may communicate with the macro BS 110a and the UE 120d to facilitate communication between the BS 110a and the UE 120d. A relay station may also be referred to as a relay BS, a relay base station, a relay, or the like.

[0037] The wireless network 100 may be a heterogeneous network including different types of BSs (e.g., macro BSs, pico BSs, femto BSs, relay BSs, etc.). These different types of BSs may have different transmit power levels, different coverage areas, and different effects on interference in the wireless network 100. For example, a macro BS may have a high transmit power level (e.g., 5 watts to 40 watts), while a pico BS, a femto BS, and a relay BS may have a lower transmit power level (e.g., 0.1 watt to 2 watts).

[0038] The network controller 130 may be coupled to a group of BSs and may provide coordination and control for these BSs. The network controller 130 may communicate with the BSs via a backhaul (not shown). The BSs may also communicate with each other directly or indirectly, for example, via a wireless or wired backhaul (not shown).

[0039] UE 120 (e.g., 120a, 120b, 120c) may be dispersed throughout the wireless network 100, and each UE may be stationary or mobile. UE may also be referred to as an access terminal, terminal, mobile station, subscriber unit, station, etc. UE may be, but is not limited to, a cellular phone (e.g., a smart phone), a personal digital assistant (PDA), a wireless modem, a wireless communication device, a handheld device, a laptop computer, a cordless phone, a wireless local loop (WLL) station, a tablet device, a camera, a gaming device, a netbook, a smartbook, an ultrabook, a medical device or equipment, a biosensor / device, a wearable device (smart watch, smart clothing, smart glasses, smart wristband, smart jewelry (e.g., smart ring, smart bracelet)), an entertainment device (e.g., a music or video device or a satellite radio), a vehicle-mounted component or sensor, a smart meter / sensor, an industrial manufacturing device, a global positioning system device, or any other suitable device configured to communicate via a wireless or wired medium.

[0040] Some UEs may be considered as machine type communication (MTC) or evolved or enhanced machine type communication (eMTC) UEs. For example, MTC and eMTC UEs include robots, drones, remote devices, sensors, meters, monitors, location tags, etc. that can communicate with a base station, another device (e.g., a remote device), or some other entity. A wireless node may provide connectivity to or to a network (e.g., a wide area network (such as the Internet) or a cellular network), for example, via a wired or wireless communication link. Some UEs may be considered as Internet of Things (IoT) devices and / or may be implemented as NB-IoT (narrowband Internet of Things) devices. Some UEs may be considered as customer premises equipment (CPE). UE 120 may be included in a housing that houses components of UE 120 (e.g., processor components, memory components, etc.).

[0041] In general, any number of wireless networks may be deployed in a given geographic area. Each wireless network may support a specific radio access technology (RAT) and may operate on one or more frequencies. RAT may also be referred to as radio technology, air interface, etc. Frequency may also be referred to as carrier, frequency channel, etc. Each frequency may support a single RAT in a given geographic area to avoid interference between wireless networks of different RATs. In some cases, NR or 5G RAT networks may be deployed.

[0042] In some aspects, two or more UEs 120 (e.g., shown as UE 120a and UE 120e) may communicate directly (e.g., without using base station 110 as an intermediary to communicate with each other) using one or more sidelink channels. For example, UE 120 may communicate using peer-to-peer (P2P) communication, device-to-device (D2D) communication, vehicle-to-everything (V2X) protocols (e.g., which may include vehicle-to-vehicle (V2V) protocols, vehicle-to-infrastructure (V2I) protocols, etc.), mesh networks, etc. In this case, UE 120 may perform scheduling operations, resource selection operations, and / or other operations described elsewhere herein performed by base station 110. For example, base station 110 may configure UE 120 via downlink control information (DCI), radio resource control (RRC) signaling, medium access control-control element (MAC-CE), or via system information (e.g., system information block (SIB)).

[0043] The UE 120 may include a machine learning (ML) module 140. For simplicity, only one UE 120d is shown as including a machine learning (ML) module 140. The ML module 140 may receive observations of a channel; map the observations to a mean value associated with the channel and a covariance matrix associated with the channel; and reconstruct the channel based on the mean value and the covariance matrix.

[0044] The base stations 110 may include a machine learning (ML) module 138. For simplicity, only one base station 110a is shown as including a machine learning (ML) module 138. In various aspects, the ML module 138 may receive observations of a channel; map the observations to a mean value associated with the channel and a covariance matrix associated with the channel; and reconstruct the channel based on the mean value and the covariance matrix.

[0045] As indicated above, Figure 1 This is provided as an example only. Other examples can be found in Figure 1 The examples described are different.

[0046] Figure 2 A block diagram of a design 200 of a base station 110 and a UE 120 is shown, where the base station and the UE may be Figure 1 One of the base stations in Figure 1 Base station 110 may be equipped with T antennas 234a through 234t, and UE 120 may be equipped with R antennas 252a through 252r, where in general T≧1 and R≧1.

[0047] At the base station 110, the transmit processor 220 may receive data for one or more UEs from the data source 212, select one or more modulation and coding schemes (MCS) for each UE based at least in part on a channel quality indicator (CQI) received from the UE, process (e.g., encode and modulate) the data for the UE based at least in part on the MCS selected for each UE, and provide data symbols for all UEs. Reducing the MCS reduces throughput but increases the reliability of transmission. The transmit processor 220 may also process system information (e.g., for semi-static resource allocation information (SRPI), etc.) and control information (e.g., CQI requests, grants, upper layer signaling, etc.), and provide overhead symbols and control symbols. The transmit processor 220 may also generate reference symbols for reference signals (e.g., cell-specific reference signals (CRS)) and synchronization signals (e.g., primary synchronization signals (PSS) and secondary synchronization signals (SSS)). The transmit (TX) multiple-input multiple-output (MIMO) processor 230 may perform spatial processing (e.g., pre-coding) on ​​data symbols, control symbols, overhead symbols, and reference symbols where applicable, and may provide T output symbol streams to T modulators (MOD) 232a to 232t. Each modulator 232 may process a corresponding output symbol stream (e.g., for OFDM, etc.) to obtain an output sample stream. Each modulator 232 may further process (e.g., convert to analog, amplify, filter, and up-convert) the output sample stream to obtain a downlink signal. The T downlink signals from modulators 232a to 232t may be transmitted via T antennas 234a to 234t, respectively. According to various aspects described in more detail below, position coding may be used to generate synchronization signals to convey additional information.

[0048] At UE 120, antennas 252a to 252r may receive downlink signals from base station 110 and / or other base stations, and may provide received signals to demodulators (DEMODs) 254a to 254r, respectively. Each demodulator 254 may condition (e.g., filter, amplify, downconvert, and digitize) received signals to obtain input samples. Each demodulator 254 may further process these input samples (e.g., for OFDM, etc.) to obtain received symbols. MIMO detector 256 may obtain received symbols from all R demodulators 254a to 254r, perform MIMO detection on the received symbols (if applicable), and provide detected symbols. Receive processor 258 may process (e.g., demodulate and decode) the detected symbols, provide decoded data for UE 120 to data sink 260, and provide decoded control information and system information to controller / processor 280. The channel processor may determine a reference signal received power (RSRP), a received signal strength indicator (RSSI), a reference signal received quality (RSRQ), a channel quality indicator (CQI), and / or the like. In some aspects, one or more components of UE 120 may be included in a housing.

[0049] On the uplink, at the UE 120, the transmit processor 264 may receive data from the data source 262 and control information (e.g., for reports including RSRP, RSSI, RSRQ, CQI, etc.) from the controller / processor 280 and process the data and control information. The transmit processor 264 may also generate reference symbols for one or more reference signals. The symbols from the transmit processor 264 may be pre-decoded by the TX MIMO processor 266, if applicable, further processed by the modulators 254a to 254r (e.g., for discrete Fourier transform spread OFDM (DFT-s-OFDM), CP-OFDM, etc.), and transmitted to the base station 110. At the base station 110, uplink signals from the UE 120 and other UEs may be received by the antenna 234, processed by the demodulator 254, detected by the MIMO detector 236 (if applicable), and further processed by the receive processor 238 to obtain decoded data and control information transmitted by the UE 120. The receive processor 238 may provide the decoded data to the data sink 239 and the decoded control information to the controller / processor 240. The base station 110 may include a communication unit 244 and communicate with the network controller 130 via the communication unit 244. The network controller 130 may include a communication unit 294, a controller / processor 290, and a memory 292.

[0050] The controller / processor 240 of the base station 110, the controller / processor 280 of the UE 120, and / or Figure 2Any other component(s) of the controller / processor 240 of the base station 110, the controller / processor 280 of the UE 120, and / or Figure 2 Any other component of the Fig. 9 The operations of the processing and / or other processing as described herein. Memories 242 and 282 may store data and program codes for base station 110 and UE 120, respectively. Scheduler 246 may schedule UEs for data transmission on the downlink and / or uplink.

[0051] In some aspects, UE 120 and / or base station 110 may include means for receiving observations of a channel; means for mapping the observations to a mean value associated with the channel and a covariance matrix associated with the channel; and means for reconstructing the channel based on the mean value and the covariance matrix. Such means may include combining Figure 2 One or more components of a UE 120 or base station 110 are described.

[0052] As indicated above, Figure 2 This is provided as an example only. Other examples can be found in Figure 2 The examples described are different.

[0053] In some cases, different types of devices supporting different types of applications and / or services may coexist in a cell. Examples of different types of devices include UE handsets, customer premises equipment (CPE), vehicles, Internet of Things (IoT) devices, etc. Examples of different types of applications include ultra-reliable low-latency communications (URLLC) applications, massive machine type communications (mMTC) applications, enhanced mobile broadband (eMBB) applications, vehicle-to-everything (V2X) applications, etc. In addition, in some cases, a single device may support different applications or services simultaneously.

[0054] Figure 3An example implementation of a system on chip (SOC) 300 according to certain aspects of the present disclosure is illustrated, which may include a central processing unit (CPU) 302 or a multi-core CPU configured to generate gradients for neural network training. The SOC 300 may be included in a base station 110 or a UE 120. Variables (e.g., neural signals and synaptic weights), system parameters associated with a computing device (e.g., a neural network with weights), delays, frequency bin information, and task information may be stored in a memory block associated with a neural processing unit (NPU) 308, a memory block associated with the CPU 302, a memory block associated with a graphics processing unit (GPU) 304, a memory block associated with a digital signal processor (DSP) 306, a memory block 318, or may be distributed across multiple blocks. Instructions executed at the CPU 302 may be loaded from a program memory associated with the CPU 302, or may be loaded from a memory block 318.

[0055] The SOC 300 may also include additional processing blocks tailored for specific functions, such as a GPU 304, a DSP 306, a connectivity block 310 (which may include fifth generation (5G) connectivity, fourth generation long term evolution (4G LTE) connectivity, Wi-Fi connectivity, USB connectivity, Bluetooth connectivity, etc.), and a multimedia processor 312 that may, for example, detect and recognize gestures. In one specific implementation, the NPU is implemented in the CPU, DSP, and / or GPU. The SOC 300 may also include a sensor processor 314, an image signal processor (ISP) 316, and / or a navigation module 320, which may include a global positioning system.

[0056] SOC 300 may be based on the ARM instruction set. In one aspect of the present disclosure, the instructions loaded into the general purpose processor 302 may include code for receiving observations of a channel; code for mapping the observations to a mean value associated with the channel and a covariance matrix associated with the channel; and code for reconstructing the channel based on the mean value and the covariance matrix.

[0057] Deep learning architectures can perform object recognition tasks by learning to represent inputs at successively higher levels of abstraction in each layer, thereby building useful feature representations of the input data. In this way, deep learning solves the main bottleneck of traditional machine learning. Before the advent of deep learning, machine learning methods for object recognition problems may rely heavily on human-engineered features, possibly combined with shallow classifiers. A shallow classifier can be a two-class linear classifier, for example, in which the weighted sum of feature vector components can be compared to a threshold to predict which class the input belongs to. Human-engineered features can be templates or kernels customized for a specific problem domain by engineers with domain expertise. In contrast, although deep learning architectures can learn to represent features similar to those that human engineers may design, they require training. In addition, deep networks can learn to represent and recognize new types of features that humans may not have considered.

[0058] Deep learning architectures can learn hierarchies of features. For example, if presented with visual data, the first layer can learn to recognize relatively simple features in the input stream, such as edges. In another example, if presented with auditory data, the first layer can learn to recognize spectral power in specific frequencies. The second layer, taking the output of the first layer as input, can learn to recognize combinations of features, such as simple shapes for visual data or combinations of sounds for auditory data. For example, higher layers can learn to represent complex shapes in visual data or words in auditory data. Even higher layers can learn to recognize common visual objects or spoken phrases.

[0059] Deep learning architectures perform particularly well when applied to problems that have a natural hierarchical structure. For example, the classification of motorized vehicles can benefit from first learning to recognize wheels, windshields, and other features. These features can be combined in different ways at higher levels to recognize cars, trucks, and airplanes.

[0060] Neural networks can be designed to have a variety of connectivity patterns. In a feedforward network, information is passed from a lower layer to a higher layer, where each neuron in a given layer communicates with a neuron in a higher layer. As described above, hierarchical representations can be constructed in successive layers of a feedforward network. Neural networks can also have loops or feedback (also known as top-down) connections. In a loop connection, the output from a neuron in a given layer can be communicated to another neuron in the same layer. The loop architecture can help identify patterns that span more than one input data block in the input data blocks that are sequentially passed to the neural network. The connection from a neuron in a given layer to a neuron in a lower layer is called a feedback (or top-down) connection. When the recognition of a high-level concept can assist in discerning specific low-level features of the input, a network with many feedback connections may be helpful.

[0061] The connections between neural network layers can be fully connected or partially connected. Figure 4A An example of a fully connected neural network 402 is illustrated. In a fully connected neural network 402, a neuron in a first layer may communicate its output to every neuron in a second layer, such that every neuron in the second layer will receive input from every neuron in the first layer. Figure 4B An example of a locally connected neural network 404 is illustrated. In the locally connected neural network 404, neurons in a first layer may be connected to a limited number of neurons in a second layer. More generally, the locally connected layers of the locally connected neural network 404 may be configured such that each neuron in the layer will have the same or similar connection pattern, but the connection strengths may have different values ​​(e.g., 410, 412, 414, and 416). The connection patterns of the local connections may produce spatially different receptive fields in higher layers because higher layer neurons in a given region may receive inputs that are tuned through training to the characteristics of a limited portion of the total input to the network.

[0062] An example of a locally connected neural network is a convolutional neural network. Figure 4C An example of a convolutional neural network 406 is illustrated. The convolutional neural network 406 can be configured such that the connection strengths associated with the inputs of each neuron in the second layer are shared (e.g., 408). Convolutional neural networks may be well suited for problems where the spatial location of the inputs is meaningful.

[0063] One type of convolutional neural network is a deep convolutional network (DCN). Figure 4D A detailed example of a DCN 400 designed to recognize visual features from an image 426 input from an image capture device 430 (such as a vehicle-mounted camera) is illustrated. The DCN 400 of the current example can be trained to identify traffic signs and numbers provided on traffic signs. Of course, the DCN 400 can be trained for other tasks, such as identifying lane markings or identifying traffic lights.

[0064] The DCN 400 may be trained by supervised learning. During training, an image (such as an image 426 of a speed limit sign) may be presented to the DCN 400, and a forward pass may then be calculated to produce an output 422. The DCN 400 may include a feature extraction portion and a classification portion. Upon receiving the image 426, a convolutional layer 432 may apply a convolutional kernel (not shown) to the image 426 to generate a first set of feature maps 418. As an example, the convolutional kernel of the convolutional layer 432 may be a 5x5 kernel that generates a 28x28 feature map. In this example, because four different feature maps are generated in the first set of feature maps 418, four different convolutional kernels are applied to the image 426 at the convolutional layer 432. A convolutional kernel may also be referred to as a filter or a convolution filter.

[0065] The first set of feature maps 418 may be subsampled by a max pooling layer (not shown) to generate a second set of feature maps 420. The max pooling layer reduces the size of the first set of feature maps 418. That is, the size of the second set of feature maps 420 (such as 14x14) is smaller than the size of the first set of feature maps 418 (such as 28x28). The reduced size provides similar information to subsequent layers while reducing memory consumption. The second set of feature maps 420 may be further convolved by one or more subsequent convolutional layers (not shown) to generate one or more sets of subsequent feature maps (not shown).

[0066] exist Figure 4D In the example of , the second set of feature maps 420 are convolved to generate a first feature vector 424. In addition, the first feature vector 424 is further convolved to generate a second feature vector 428. Each feature of the second feature vector 428 may include a number corresponding to a possible feature of the image 426, such as "sign", "60", and "100". A softmax function (not shown) may convert the numbers in the second feature vector 428 into probabilities. Therefore, the output 422 of the DCN 400 may be the probability that the image 426 includes one or more features.

[0067] In this example, the probability of "logo" and "60" in output 422 is higher than the probability of other numbers (such as "30", "40", "50", "70", "80", "90", and "100") in output 422. Before training, the output 422 generated by DCN 400 may be incorrect. Therefore, the error between the output 422 and the target output can be calculated. The target output is the ground truth value of image 426 (e.g., "logo" and "60"). The weights of DCN 400 can then be adjusted so that the output 422 of DCN 400 is closer to the target output.

[0068] To adjust the weights, the learning algorithm may calculate a gradient vector for the weights. The gradient may indicate the amount by which the error will increase or decrease when the weights are adjusted. At the top layer, the gradient may correspond directly to the value of the weights connecting the activated neurons in the penultimate layer and the neurons in the output layer. In lower layers, the gradient may depend on the value of the weights and the calculated error gradients of the higher layers. The weights may then be adjusted to reduce the error. This way of adjusting weights may be called "back propagation" because it involves a "backward pass" through the neural network.

[0069] In practice, the error gradient of the weights may be calculated over a small number of examples so that the calculated gradient is close to the true error gradient. This approximation method may be referred to as stochastic gradient descent. Stochastic gradient descent may be repeated until the achievable error rate of the entire system stops decreasing or until the error rate reaches a target level. After learning, a new image (e.g., a speed limit sign of image 426) may be presented to DCN 400, and a forward pass through DCN 400 may produce output 422, which may be considered an inference or prediction of DCN 400.

[0070] Deep belief network (DBN) is a probabilistic model including multiple layers of hidden nodes. DBN can be used to extract hierarchical representations of training data sets. DBN can be obtained by stacking the layers of restricted Boltzmann machine (RBM). RBM is a type of artificial neural network that can learn probability distributions through a set of inputs. Because RBM can learn probability distributions without information about the categories to which each input should be classified, RBM is generally used for unsupervised learning. Using an unsupervised and supervised hybrid paradigm, the bottom RBM of DBN can be trained in an unsupervised manner and can be used as a feature extractor, while the top RBM can be trained in a supervised manner (on the joint distribution of the input and target class from the previous layer) and can be used as a classifier.

[0071] A deep convolutional network (DCN) is a network that is a convolutional network configured with additional pooling and normalization layers. DCNs have achieved state-of-the-art performance on many tasks. DCNs can be trained using supervised learning, where both the input and output targets are known for many examples and are used to modify the weights of the network by using a gradient descent method.

[0072] The DCN may be a feed-forward network. In addition, as described above, the connections from a neuron in the first layer of the DCN to a set of neurons in the next higher layer are shared across the neurons in the first layer. The feed-forward and shared connections of the DCN can be used for fast processing. For example, the computational burden of the DCN may be much smaller than that of a similarly sized neural network that includes loops or feedback connections.

[0073] The processing of each layer of the convolutional network can be considered as a spatially invariant template or basis projection. If the input is first decomposed into multiple channels, such as the red, green and blue channels of a color image, the convolutional network trained on the input can be considered to be three-dimensional, where two spatial dimensions are along the axis of the image and the third dimension captures color information. The output of the convolutional connection can be considered to form a feature map in a subsequent layer, each element in which receives input from a certain range of neurons in the previous layer (e.g., feature map 218) and from each channel in the multiple channels. The values ​​in the feature map can be further processed with nonlinearity (such as correction, max(0,x)). The values ​​from adjacent neurons can be further pooled, which corresponds to downsampling and can provide additional local invariance and dimensionality reduction. Normalization corresponding to whitening can also be applied by lateral inhibition between neurons in the feature map.

[0074] The performance of deep learning architectures can increase as more labeled data points become available or as computing power increases. Modern deep neural networks are often trained with computing resources that are thousands of times greater than what was available to a typical researcher just fifteen years ago. New architectures and training paradigms can further improve the performance of deep learning. Rectified linear units can reduce the training problem known as vanishing gradients. New training techniques can reduce overfitting, allowing larger models to achieve better generalization. Encapsulation techniques can extract data within a given receptive field and further improve overall performance.

[0075] Figure 5 is a block diagram illustrating a DCN 550. The DCN 550 may include multiple different types of layers based on connection and weight sharing. Figure 5 As shown, DCN 550 includes convolution blocks 554A, 554B. Each of the convolution blocks 554A, 554B may be configured with a convolution layer (CONV) 556, a normalization layer (LNorm) 558, and a maximum pooling layer (MAX POOL) 560. Although only two of the convolution blocks 554A, 554B are shown, the present disclosure is not limited thereto, and any number of convolution blocks 554A, 554B may be included in DCN 550 according to design preferences.

[0076] The convolution layer 556 may include one or more convolution filters that may be applied to the input data to generate a feature map. The normalization layer 558 may normalize the output of the convolution filter. For example, the normalization layer 558 may provide whitening or lateral suppression. The maximum pooling layer 560 may provide spatial downsampling aggregation to achieve local invariance and dimensionality reduction.

[0077] For example, a parallel filter bank of a deep convolutional network may be loaded on the SOC 300 (e.g., Figure 3) on the CPU 302 or GPU 304 of the SOC 300 to achieve high performance and low power consumption. In an alternative embodiment, the parallel filter bank can be loaded on the DSP 306 or ISP 316 of the SOC 300. In addition, the DCN 550 can access other processing blocks that may exist on the SOC 300 (such as the sensor processor 314 and the navigation module 320 dedicated to sensors and navigation, respectively).

[0078] The DCN 550 may also include one or more fully connected layers 562 (FC1 and FC2). The DCN 550 may also include a logistic regression (LR) layer 564. Between each layer 556, 558, 560, 562, 564 of the DCN 550 are weights (not shown) to be updated. The output of each layer in the layer (e.g., 556, 558, 560, 562, 564) can be used as an input to a subsequent layer in the layer (e.g., 556, 558, 560, 562, 564) in the DCN 550 to learn a hierarchical feature representation from the input data 552 (e.g., image, audio, video, sensor data, and / or other input data) supplied at the first convolution block in the convolution block 554A. The output of the DCN 550 is a classification score 566 for the input data 552. The classification score 566 can be a set of probabilities, where each probability is a probability of the input data, including features from the feature set.

[0079] Figure 6 A diagram illustrating an example decomposed base station 600 architecture is shown. The decomposed base station 600 architecture may include one or more central units (CUs) 610 that may communicate directly with a core network 620 via a backhaul link, or indirectly with the core network 620 through one or more decomposed base station units, such as a near real-time (near-RT) RAN intelligent controller (RIC) 625 via an E2 link, or a non-real-time (non-RT) RIC 615 associated with a service management and orchestration (SMO) framework 605, or both. The CU 610 may communicate with one or more distributed units (DUs) 660 via respective mid-haul links, such as an F1 interface. The DU 660 may communicate with one or more radio units (RUs) 640 via respective forward links. The RU 640 may communicate with respective UEs 120 via one or more radio frequency (RF) access links. In some implementations, a UE 120 may be served simultaneously by multiple RUs 640.

[0080] Each of these units (e.g., CU 610, DU 660, RU 640, and near-RT RIC 625, non-RTRIC 615, and SMO framework 605) may include one or more interfaces, or may be coupled to one or more interfaces configured to receive or send signals, data, or information (collectively referred to as signals) via a wired or wireless transmission medium. Each of the units or an associated processor or controller that provides instructions to the communication interface of these units may be configured to communicate with one or more of the other units via a transmission medium. For example, these units may include a wired interface that is configured to receive or send signals to one or more of the other units on a wired transmission medium. Additionally, these units may include a wireless interface that may include a receiver, a transmitter, or a transceiver (such as a radio frequency (RF) transceiver) that is configured to receive or send signals, or both, to one or more of the other units on a wireless transmission medium.

[0081] In some aspects, CU 610 may be responsible for one or more high-level control functions. Such control functions may include radio resource control (RRC), packet data convergence protocol (PDCP), service data adaptation protocol (SDAP), etc. Each control function may be implemented as having an interface configured to communicate signals with other control functions managed by CU 610. CU 610 may be configured to handle user plane functionality (e.g., central unit-user plane (CU-UP)), control plane functionality (e.g., central unit-control plane (CU-CP)), or a combination thereof. In some specific implementations, CU 610 may be logically split into one or more CU-UP units and one or more CU-CP units. When implemented in an O-RAN configuration, the CU-UP unit may communicate bidirectionally with the CU-CP unit via an interface (such as an E1 interface). As needed, CU 610 may be implemented to communicate with DU 660 for network control and signaling.

[0082] DU 660 may correspond to a logical unit that includes one or more base station functions for controlling the operation of one or more RU 640. In some aspects, DU 660 may host one or more of a radio link control (RLC) layer, a medium access control (MAC) layer, and one or more high physical (PHY) layers (such as modules for forward error correction (FEC) encoding and decoding, scrambling, modulation and demodulation, etc.) depending at least in part on a functional partitioning such as that defined by the 3rd Generation Partnership Project (6GPP). In some aspects, DU 660 may also host one or more low PHY layers. Each layer (or module) may be implemented with an interface that is configured to communicate signals with other layers (and modules) hosted by DU 660 or with control functions hosted by CU 610.

[0083] The low-level functionality may be implemented by one or more RUs 640. In some deployments, a RU 640 controlled by a DU 660 may correspond to a logical node that hosts RF processing functions or low PHY layer functions (such as performing Fast Fourier Transform (FFT), Inverse FFT (iFFT), digital beamforming, physical random access channel (PRACH) extraction and filtering, etc.), or both, based at least in part on a functional split (such as a lower-level functional split). In such an architecture, the RU 640 may be implemented to handle over-the-air (OTA) communications with one or more UEs 120. In some implementations, real-time and non-real-time aspects of control plane and user plane communications with the RU 640 may be controlled by the corresponding DU 660. In some scenarios, this configuration may enable the implementation of the DU 660 and the CU 610 in a cloud-based RAN architecture (such as a vRAN architecture).

[0084] The SMO framework 605 may be configured to support RAN deployment and provisioning of non-virtualized network elements and virtualized network elements. For non-virtualized network elements, the SMO framework 605 may be configured to support the deployment of dedicated physical resources for RAN coverage requirements, which may be managed via an operation and maintenance interface (such as an O1 interface). For virtualized network elements, the SMO framework 605 may be configured to interact with a cloud computing platform (such as an open cloud (O-cloud) 690) to perform network element lifecycle management (such as instantiating virtualized network elements) via a cloud computing platform interface (such as an O2 interface). Such virtualized network elements may include, but are not limited to, CU 610, DU 660, RU 640, and near-RT RIC 625. In some specific implementations, the SMO framework 605 may communicate with hardware aspects of the 4G RAN such as an open eNB (O-eNB) 611 via the O1 interface. Additionally, in some specific implementations, the SMO framework 605 may communicate directly with one or more RUs 640 via the O1 interface. The SMO framework 605 may also include a non-RT RIC 615 configured to support the functionality of the SMO framework 605 .

[0085] The non-RT RIC 615 may be configured to include logic functions that enable non-real-time control and optimization of RAN elements and resources, artificial intelligence / machine learning (AI / ML) workflows including model training and updating, or policy-based guidance of applications / features in the near-RT RIC 625. The non-RT RIC 615 may be coupled to or communicate with the near-RT RIC 625 (such as via an A1 interface). The near-RT RIC 625 may be configured to include logic functions that enable near-real-time control and optimization of RAN elements and resources via data collection and actions on an interface (such as via an E2 interface) that connects one or more CUs 610, one or more DUs 660, or both, and the O-eNB 611 with the near-RT RIC 625.

[0086] In some implementations, in order to generate an AI / ML model to be deployed in the near-RT RIC 625, the non-RT RIC 615 may receive parameters or external enrichment information from an external server. Such information may be utilized by the near-RT RIC 625 and may be received from a non-network data source or from a network function at the SMO framework 605 or the non-RT RIC 615. In some examples, the non-RT RIC 615 or the near-RT RIC 625 may be configured to tune RAN behavior or performance. For example, the non-RT RIC 615 may monitor long-term trends and patterns of performance and employ AI / ML models to perform corrective actions through the SMO framework 605 (such as via reconfiguration of O1) or via the creation of RAN management policies (such as A1 policies).

[0087] Artificial neural networks such as deep generative models can be used to estimate channels such as wireless channels. Variational autoencoders (VAEs) are examples of deep generative models. During training, the encoding distribution of the VAE is regularized so that the latent space of the VAE can generate new data. In some examples, the VAE can estimate the channel or properties associated with the channel based on one or more observations of the channel. In one such example, for medical imaging, the VAE can generate an entire image of the organ based on one or more observations of the received organ. As another example, upon receiving one or more observations of the channel (such as pilot symbols associated with the channel), the VAE can generate the channel or properties associated with the channel by finding latent variables that generate the channel. In some examples, compressed sensing can reconstruct signals from underdetermined systems of linear measurements. Compressed sensing solutions can use prior knowledge of the signal to reconstruct the signal.

[0088] Figure 7 is a block diagram illustrating an example of a wireless communication system 700 according to various aspects of the present disclosure. Figure 7 In the example of , UE 120 may communicate with network node 702 via channel H, such as a digital channel. As an example, wireless communication system 700 may be a millimeter wave (mmWave) communication system or another type of digital communication system. Network node 702 may be a reference Figure 1 and Figure 2 The base station 110 described or referenced Figure 6 UE 120 may include multiple receiver antennas (1 to N). r ), which is connected to multiple receiver sub-arrays (1 to N rx ) is associated with the parameter N r represents the total number of receiver antennas, and the parameter N rx represents the total number of receiver subarrays at UE 120. The total number of receiver subarrays N rxCan be greater than or equal to the total number of receiver antennas N r The network node 702 may include multiple antennas (1 to N t ), which is related to multiple sub-arrays (1 to N tx ) is associated with the parameter N t represents the total number of antennas, and the parameter N tx represents the total number of sub-arrays at the network node 702. The total number of transmitter sub-arrays N tx Can be greater than or equal to the total number of transmitter antennas N t .

[0089] exist Figure 7 In the example of ) may be transmitted from the network node 702 via analog beamforming channel B and received at the UE 120 via analog beamforming channel A. The transmitted analog beamforming channel B may be beamformed on a first beam direction 704, and the received analog beamforming channel A may be received on a second beam direction 706. Channel H may be composed of a channel having dimensions (N rx ×N tx ), the transmitted analog beamforming channel B can be represented by a matrix with dimension (N tx ×N t ), and the received analog beamforming channel A can be represented by a matrix with dimension (N r ×N rx ) is a matrix representation of the channel H. The channel H can be estimated at UE 120 based on the observation Y, where Y = AHB and Observation Y can be reformulated as the inverse problem, It is an example of an underdetermined problem.

[0090] exist Figure 7 In the example of , the channel H may be sparse in the angular domain. The structure of the channel H may be used for channel estimation. For example, the channel estimation problem may be an example of a sparse channel (e.g., sparse signal) recovery problem. In such an example, the angular spaces at the UE 120 and the network node 702 may be discretized into G, respectively. R and G T The parameter G R represents the UE element response matrix and the parameter G T Represents the network node element response matrix. Sparse channel H d It can be recovered based on the following formula:

[0091]

[0092] In formula 1, can be an example of a sparse dictionary Ψ. The channel estimation problem can be reformulated as follows:

[0093]

[0094] In Equation 2, the parameter Φ represents a function of the beamforming matrix used for channel measurement, and the parameter z d represents the sparse representation of the channel vector.

[0095] As discussed, compressed sensing can be used to reconstruct the unobserved channel (eg, signal) x∈R from the m linear measurements generated as the observation y=Ax+ε m , where the parameter A∈R m×n represents the task-specific measurement matrix and parameter ε represents the additive noise. That is, the unobserved channel x can be recovered based on the observed y. Recovering the unobserved channel x based on the observed y is an example of an underdetermined problem

[0096] Some conventional compressed sensing solutions assume that the channel x is sparse in a given dictionary. For example, x = Dz, where the latent space variable z is sparse and D is the dictionary. Such conventional compressed sensing solutions solve the inverse problem by solving an optimization problem, such as min||z||1s.ty=ADz, where ||z||1=∑ i |z i |. In some examples, a sparse basis may not be available. Additionally or alternatively, the dimension of the dictionary matrix may be larger. Therefore, such conventional compressed sensing solutions may increase latency and / or increase convergence time of a compressed sensing solution (e.g., a compressed sensing model).

[0097] Some other conventional compressed sensing solutions may train a generative model G(z) on channel x, where parameter z is a latent variable. Such conventional compressed sensing solutions may solve the inverse problem by gradient descent on the latent variable of G, such as min||y-AG(z)||2. As an example, the generative model G(z) may be a generative adversarial network (GAN), a variational autoencoder (VAE), or a flow-based generative model. Such conventional compressed sensing solutions may additionally increase latency and / or increase convergence time of a compressed sensing solution (e.g., a compressed sensing model).

[0098] In some examples, the rotation r of channel x θ may be unknown, where the parameter θ represents the angle of rotation. As an example, the orientation or beam direction of the user equipment (UE) relative to the base station may be unknown. As another example, the pose of an organ may be unknown. Given the observation y=Ar θx , restore the rotation r θ and channel x(r θx or θ ,x) may be desirable. Rotation rθ The recovery of the rotation r and the channel x is another example of an underdetermined problem. Some conventional solutions may perform an exhaustive search to recover the rotation r θ , and also for the rotation r θ Such solutions can also increase latency and / or increase the convergence time of the model.

[0099] In some examples, observe y = Ar θ x can be expressed as y = AT g x+ε, where T g :G×X→X is the effect of the group element g in the group G on the channel x (e.g., channel space). Group transformation T g unknown.

[0100] Various aspects of the present disclosure relate to using equivariant priors to solve inverse problems with unknown orientations. In some examples, an equivariant generative model encapsulates orientation information in a latent space of the equivariant generative model. The equivariant generative model may include an equivariant variational autoencoder (VAE), and the decoder of the VAE may be used as a generative prior for compressed sensing. In such aspects, channels with unknown orientations may be recovered using iterative gradient descent on the latent space of the equivariant generative model. For ease of explanation, the equivariant generative model may be referred to as a generative model G(·), where the generator function G(·) maps latent variables z to the space of channels x.

[0101] In the generative model, for each rotation r on channel x θ action, there is an equivariant rotation r′ θ , so that G(r′ θ z)=r θ x, and vice versa, where the parameter z is a latent variable. Thus, if channel x is rotated to r by an unknown angle θ θx , then Ar θ x=AG(r′ θ z). Therefore, if the input r′ of the generative model θ z rotates, then output r θx On the other hand, the rotation output r θx (e.g., channel x) corresponds to the potential r′ θ A rotated version of z. In some examples, the unknown transform may be decoded in latent space, and the channel may be estimated by estimating the transformed (eg, rotated) latent code. According to aspects of the present disclosure, the solution may directly determine r′ θ z, so that it is not necessary to determine the rotation angles θ and r′ separately θ The generative model G(z) can be trained on inputs without data augmentation. Gradient descent can solve the following questions about the latent variables: In some examples, an equivariant VAE can be trained to generate an equivariant prior.

[0102] VAE is a method that transforms the observed random variable x∈X (for example, x∈R D ) and latent variables z∈R d The joint distribution of φ (x,z)=p φ Example of a deep generative model for (x|z)p(z). For a given set of points x1,...x n , the deep generative model can be trained to maximize the marginal likelihood p φ (x). Figure 8 800 is a block diagram illustrating an example of a VAE 800 according to various aspects of the present disclosure. In some examples, the VAE 800 may be included in a deep generative model. The VAE 800 is an example of a probabilistic unsupervised model. Figure 8 As shown in the example of , VAE 800 includes an encoder 802 and a decoder 804. Encoder 802 can be an example of an approximate posterior network, and decoder 804 can be an example of a generator.

[0103] In some examples, encoder 802 may be configured by a function q φ (z|x) indicates that the function maps the input (e.g., channel x) to the latent space z obtained from the prior p(z) (e.g., z ≈ p(z)). That is, during the forward pass through VAE 800, encoder 802 returns the parameters q of the variational posterior φ (z|x). Then, the distribution can be sampled so that Reparameterization can obtain samples such that The parameter n represents a zero-mean unit-variance random vector. The decoder 804 can be represented by the function p θ (x|z) denotes that the function maps the latent space z to the output (e.g., the reconstruction of channel x). In some examples, the sample May be received at decoder 804 to return the parameters of the generated distribution In such examples, the distribution can be generated based on (e.g., ) to reconstruct the channel.

[0104] The latent space z may be a random variable. Thus, the VAE 800 may be trained to learn a distribution (e.g., a Gaussian distribution) over the latent space z. Thus, the output of the encoder 802 may be a mean expected value (e.g., a mean associated with channel x) and a variance associated with the distribution. The mean expected value may be the mean of the distribution.

[0105] Conventional VAEs may not be equivariant. Therefore, various aspects of the present disclosure are directed to learning a symmetry-aware latent space during training so that the VAE 800 is equivariant. That is, both the encoder 802 and the decoder 804 are trained to be equivariant.

[0106] For the decoder 804, the reconstructed channel x output from the decoder 804 should be rotated based on the rotation of the latent variable z input to the decoder 804. That is, the decoder 804 may generate the distribution (p θ (x|g′z)(e.g., x g′ ~p θ (p|g′z)) receives the rotation latent variable g′z and outputs the rotation channel x g′ , where the parameter g′ represents the rotation operation. Therefore, when the decoder 804 is equivariant, the equality of the distribution of the rotated channel gx can be equal to the reconstructed rotated channel x g′ The equality of the distribution of d z g , where = d For encoder 802, the rotation channel r received as input θx The rotated distribution of the latent variable z should be generated as output. That is, the encoder 802 uses the rotated channel gx received as input to vary the posterior q φ Sampling is performed to rotate the distribution z g Sampling (e.g., z g ~q φ (z|gx)), where the parameter g represents the rotation operation. Therefore, when the encoder 802 is equivariant, the distribution of the latent variable z is z g The equality of can be equal to the equality of the distribution of the rotated latent variable g′z (e.g., g′z= d z g ). In other words, in order for the encoder 802 to be equivariant, sampling the latent code of the variational posterior conditioned on the transformed input gx should be the same as transforming the latent code sampled from the variational distribution conditioned on the non-transformed input x.

[0107] In some examples, the equivariant encoder 802 can be parameterized as a Gaussian distribution determined by the following two sub-networks: the mean network μ(·) and the variance network Σ(·). In some examples, the mean network μ(·) can be equivariant. That is, the mean network μ(·) should be adjusted to satisfy the following formula:

[0108] E(z g )=g′E(z)→μ(gx)=g′μ(x) (3)

[0109] In Formula 3, when the rotation distribution z gis equivalent to a rotation of the latent variable z (e.g., E(z g )=g′E(z)), then the expected value (e.g., mean value) μ(gx) of the rotated channel should be equivalent to the rotation g′μ(x) of the expected value of the channel (e.g., μ(gx)=g′μ(x)). The mean value network μ(·) satisfies the property of Formula 3 when an equivariant neural network is used to model the mean value function μ(·). Additionally, E() is a function for the expected value.

[0110] Additionally, the variance network ∑(·) should satisfy the following formula:

[0111]

[0112] In Formula 4, when the rotation distribution z g Transpose of the rotation distribution The product of is equal to the latent variable z, the transpose of the latent variable z T and the rotation transpose g′ T The rotation (for example, ), the variance of the rotated channel Σ(gx) should be equal to the variance of the product of the channel variance and the transpose of the rotation g′Σ(x)g′ T (For example, Σ(gx)=g′Σ(x)g′ T ). Therefore, the variance network Σ(·) can be bi-equivariant so that the latent variable z can be sampled. The Gaussian distribution of the latent variable z can be reparameterized so that z = μ + Lε, ε ~ N(0, I), where L is a matrix. Additionally, when the variance network Σ(·) is bi-equivariant, the Kulbak-Leibler (KL) divergence can be calculated. The KL divergence can be expressed as:

[0113]

[0114] Conventional autoencoders such as diagonal autoencoders use a diagonal covariance matrix such that Σ(x) = diagσ(x). Figure 8 In the example of , the covariance Σ(gx) of the rotated channel can maintain the diagonal. However, the rotation of the covariance of the channel g′Σ(x)g′ T The diagonal may not be maintained. Therefore, aspects of the present disclosure use a non-diagonal covariance matrix. Additionally, when using a non-diagonal covariance matrix, the encoder 802 is specified to maintain its ability to sample the latent variable z, calculate the logarithmic determinant on the forward pass and maintain a positive definite matrix. Therefore, the full rank covariance matrix V(x) can be used in the variance network Σ(·).

[0115] In some examples, the covariance matrix can be parameterized as V(x)V(x) T , where V(x) is any equivariant d×d matrix such that Σ(x)=V(x)V(x)T In this example, the Kollersky decomposition: ∑ = LL T Can be used for sampling. For example, sampling can be as follows:

[0116] log|∑|=log|LL T |=log|L| 2 =logΠ i L ii 2 =2∑ i log L ii (6)

[0117] In some other examples, a spectral decomposition of the covariance matrix is ​​used, so that Σ(x)=V(x)D(x)V(x) T , where V(x) is an equivariant orthogonal d×d matrix and D(x) is an invariant diagonal d×d matrix.

[0118] exist Figure 8 In the example of , decoder 804 is also equivariant. In some examples, decoder 804 can be adjusted to satisfy the following formula:

[0119] E(x g′ )=gE(x)→μ(g′z)=gμ(z) (7)

[0120] In Formula 7, when the rotation channel x g′ is equivalent to the rotation of channel x (e.g., E(x g′ )=gE(x)), then the expected value (e.g., mean value) μ(g′z) of the rotated latent variable should be equivalent to the rotation gμ(z) of the latent variable (e.g., μ(g′z)=gμ(z)).

[0121] Additionally, during training, VAE 800 can maximize the evidence lower bound (ELBO) To learn the low-dimensional latent space. ELBO can be maximized as follows:

[0122]

[0123] In formula 8, represents the reconstruction loss, and (q φ (z|x)||p(z)) represents the variational posterior q φ The divergence between (z|x) and the prior p(z).

[0124] During training, the VAE 800 may receive an input such as a channel x to optimize a reconstruction loss at the output of the VAE 800. Because the VAE 800 is probabilistic, the VAE 800 learns a reconstruction that follows a specific distribution associated with the prior p(z). Therefore, the latent space z follows a Gaussian distribution. Additionally, the Gaussian distribution can be parameterized by a mean μ(x) and a variance ∑(x). Therefore, as discussed, the encoder 802 includes a mean network and a variance network. The variance network may also be referred to as a covariance network or an expected value network. The distribution of the input (e.g., channel x) may be determined based on the mean μ(x) and variance ∑(x) of the input. The encoder 802 may sample from the distribution. Therefore, the encoder 802 may be represented as:

[0125] q φ (z|x)=N(z|μ(x), Σ(x)), p(z)=N(0,1), (9)

[0126] Where N(0,1) represents a normal distribution.

[0127] As discussed, during training, the VAE 800 receives an input, such as a channel x. During the forward pass, the encoder 802 determines the mean μ(x) of the input and the expected value of the input based on the covariance ∑(x). As discussed, the covariance matrix can be parameterized as V(x)V(x) T . Additionally, the Kollersky decomposition: ∑ = LL T (For example, L = Chol (∑)) can be used for sampling. The encoder 802 can then obtain samples from the latent space z based on the mean μ(x) and the expected value of the input based on the covariance ∑(x) (e.g., z=μ+Lε,ε~N(0,I)). VAE 800 can then determine the Kulbak-Leibler (KL) divergence (e.g., KL(q φ (z|x)||p(z))), which provides the variational posterior q φ The divergence between (z|x) and the prior p(z). Sample Then the decoder Processing to obtain a reconstruction of the input (For example, ). The reconstruction loss can be based on the reconstruction of the input The reconstruction loss can be defined as (For example, Re = -logp θ (x|z)). VAE 800 may then determine ELBOL(θ, φ) based on the reconstruction loss and KL divergence (e.g., ).

[0128] Fig. 9900 is a flowchart illustrating an example process 900 performed, for example, by a deep generative model according to various aspects of the present disclosure. In some examples, the deep generative model includes a VAE (e.g., an equivariant VAE), such as reference Figure 8 The VAE 800 described herein. A deep generative model may be a component of a wireless device, such as a reference Figure 1 , Figure 2 , Figure 6 and Figure 7 UE 120 or base station 110 described, or reference Figure 7 Depicted network node 702. Process 900 is an example of reconstructing a channel where the rotation of the channel is unknown.

[0129] like Fig. 9 As shown in the example of , at block 902, process 900 begins with a device (eg, UE, BS, network node, etc.) receiving an observation of a channel. The channel may be an example of a wireless communication channel.

[0130] At block 904, the device maps the observations to a mean associated with the channel and a covariance matrix associated with the channel. Specifically, in some examples, the observations are mapped to the mean and the covariance matrix at an equivariant encoder of the equivariant VAE. In some examples, the device may generate a latent space representation based on the mean and the covariance matrix.

[0131] At block 906, the device reconstructs the channel based on the mean and the covariance matrix. In some examples, the channel may be reconstructed based on the latent space representation. Additionally, the channel may be reconstructed at an equivariant decoder of an equivariant VAE.

[0132] Specific implementation examples are described in the following numbered clauses.

[0133] Clause 1. A method for estimating a channel through a deep generative model, the method comprising: receiving observations of the channel; mapping the observations to a mean value associated with the channel and a covariance matrix associated with the channel; and reconstructing the channel based on the mean value and the covariance matrix.

[0134] Clause 2. The method of clause 1, wherein the deep generative model comprises an equivariant variational autoencoder (VAE).

[0135] Clause 3. A method according to clause 2, wherein the observations are mapped to the mean and the covariance matrix at an equivariant encoder of an equivariant VAE.

[0136] Clause 4. The method of clause 2, wherein the channel is reconstructed at an equivariant decoder of the equivariant VAE.

[0137] Clause 5. The method of any one of clauses 1 to 5, further comprising: generating a latent space representation based on the mean and the covariance matrix.

[0138] Clause 6. The method of clause 5, wherein reconstructing the channel comprises reconstructing the channel based on the latent space representation.

[0139] Clause 7. The method of any one of clauses 1 to 7, wherein the channel is a wireless communication channel.

[0140] Clause 8. An apparatus for estimating a channel, the apparatus comprising: means for causing a deep generative network to perform any of clauses 1 to 7.

[0141] Clause 9. An apparatus for estimating a channel, the apparatus comprising: a processor; and a memory coupled to the processor and storing instructions that, when executed by the processor, are operable to cause a deep generative network to perform any one of clauses 1 to 7.

[0142] Clause 10. A non-transitory computer-readable medium having program code recorded thereon for estimating a channel, the program code being executed by a processor and comprising program code causing a deep generative network to perform any one of clauses 1 to 7.

[0143] The foregoing disclosure provides illustration and description, but is not intended to be exhaustive or to limit the aspects to the precise forms disclosed. Modifications and variations are possible in light of the above disclosure or may be acquired from practice of these aspects.

[0144] As used, the term "component" is intended to be broadly interpreted as hardware, firmware, and / or a combination of hardware and software. As used herein, a processor is implemented using hardware, firmware, and / or a combination of hardware and software.

[0145] Some aspects are described in conjunction with thresholds. As used herein, satisfying a threshold may refer to a value being greater than a threshold, greater than or equal to a threshold, less than a threshold, less than or equal to a threshold, equal to a threshold, not equal to a threshold, etc., depending on the context.

[0146] It will be apparent that the described systems and / or methods can be implemented in various forms of hardware, firmware, and / or a combination of hardware and software. The actual dedicated control hardware or software code used to implement these systems and / or methods does not limit the aspects. Therefore, the operation and performance of these systems and / or methods are described without reference to specific software code, and it should be understood that software and hardware used to implement these systems and / or methods can be designed based at least in part on the description herein.

[0147] Although the specific combination of features is set forth in the claims and / or disclosed in the specification, these combinations are not intended to limit the disclosure of various aspects. In fact, many of these features can be combined in a manner that is not specifically set forth in the claims and / or not disclosed in the specification. Although each dependent claim listed below may directly rely only on one claim, the disclosure of various aspects includes each dependent claim combined with each other claim in the claim set. The phrase "at least one" mentioned in the list of items refers to any combination of those items, including a single member. For example, "at least one of a, b or c" is intended to cover a, b, c, ab, ac, bc and abc, and any combination with multiple identical elements (e.g., aa, aaa, aab, aac, abb, acc, bb, bbb, bbc, cc and ccc, or any other ordering of a, b and c).

[0148] The elements, actions or instructions used should not be interpreted as critical or essential unless explicitly described as such. In addition, as used herein, the articles "one" and "an" are intended to include one or more items, which can be used interchangeably with "one or more". In addition, as used herein, the terms "set" and "group" are intended to include one or more items (e.g., related items, unrelated items, combinations of related items and unrelated items, etc.), and can be used interchangeably with "one or more". If only one item is intended to be referred to, the phrase "only one" or similar terms will be used. In addition, as used herein, the terms "having" and the like are intended to be open terms. In addition, the phrase "based on" is intended to mean "based at least in part on", unless otherwise explicitly stated.

Claims

1. A processor-implemented method for estimating a channel via a deep generative model, the method comprising: receiving, at a device, observations of the channel; mapping, at the device, the observations to a mean associated with the channel and a covariance matrix associated with the channel; as well as The channel is reconstructed at the device based on the mean and the covariance matrix.

2. The processor-implemented method of claim 1 , wherein the deep generative model comprises an equivariant variational autoencoder (VAE).

3. A processor-implemented method according to claim 2, wherein the observations are mapped to the mean and the covariance matrix at an equivariant encoder of the equivariant VAE.

4. The processor-implemented method of claim 2, wherein the channel is reconstructed at an equivariant decoder of the equivariant VAE.

5. The processor-implemented method of claim 1 , further comprising: A latent space representation is generated based on the mean and the covariance matrix.

6. The processor-implemented method of claim 5, wherein the channels are reconstructed based on the latent space representation.

7. The processor-implemented method of claim 1, wherein the channel is a wireless communication channel.

8. The processor-implemented method of claim 1 , further comprising: The deep generative model is trained by mapping the observations to latent codes associated with the channels based on gradient descent on a latent space.

9. An apparatus for estimating a channel, the apparatus comprising: means for receiving, at a device, observations of said channel; means for mapping, at the device, the observations to a mean value associated with the channel and a covariance matrix associated with the channel; and means for reconstructing, at the device, the channel based on the mean and the covariance matrix.

10. The apparatus according to claim 9, wherein the apparatus comprises: Device for equivariant variational autoencoding.

11. The apparatus of claim 10, wherein the means for equivariant variational autoencoding comprises means for equivariant encoding.

12. The apparatus of claim 10, wherein the means for equivariant variational autoencoding comprises means for equivariant decoding.

13. The apparatus according to claim 9, further comprising: Means for generating a latent space representation based on the mean and the covariance matrix.

14. The apparatus of claim 13, wherein means for reconstructing the channel comprises means for reconstructing the channel based on the latent space representation.

15. The apparatus of claim 9, wherein the channel is a wireless communication channel.

16. The apparatus according to claim 9, further comprising: Means for training a deep generative network associated with the apparatus, the means for training comprising means for mapping the observations to latent codes associated with the channels based on gradient descent on a latent space.

17. An apparatus for estimating a channel via a deep generative model, the apparatus comprising: processor; and a memory coupled to the processor and storing instructions that, when executed by the processor, are operable to cause the apparatus to: receiving observations for the channel; mapping the observations to a mean associated with the channel and a covariance matrix associated with the channel; and The channel is reconstructed based on the mean and the covariance matrix.

18. The apparatus of claim 17, wherein the deep generative model comprises an equivariant variational autoencoder (VAE).

19. An apparatus according to claim 18, wherein the observations are mapped to the mean and the covariance matrix at an equivariant encoder of the equivariant VAE.

20. The apparatus of claim 18, wherein the channel is reconstructed at an equivariant decoder of the equivariant VAE.

21. The apparatus of claim 17, wherein execution of the instructions further causes the apparatus to: generate a latent space representation based on the mean and the covariance matrix.

22. The apparatus of claim 21, wherein execution of the instructions further causes the apparatus to: reconstruct the channel based on the latent space representation.

23. The apparatus of claim 17, wherein the channel is a wireless communication channel.

24. The apparatus of claim 17, wherein execution of the instructions further causes the apparatus to: train the deep generative model by mapping the observations to latent codes associated with the channels based on gradient descent on a latent space.

25. A non-transitory computer readable medium having recorded thereon program code for estimating a channel via a deep generative model, the program code being executed by a processor and comprising: program code for receiving observations of said channel; program code for mapping the observations to means associated with the channels and to covariance matrices associated with the channels; and Program code for reconstructing the channel based on the mean and the covariance matrix.

26. The non-transitory computer-readable medium of claim 25, wherein the deep generative model comprises an equivariant variational autoencoder (VAE).

27. The non-transitory computer-readable medium of claim 26, wherein the observations are mapped to the mean and the covariance matrix at an equivariant encoder of the equivariant VAE.

28. The non-transitory computer readable medium of claim 26, wherein the channel is reconstructed at an equivariant decoder of the equivariant VAE.

29. The non-transitory computer readable medium of claim 25, wherein the program code further comprises: Program code for generating a latent space representation based on the mean and the covariance matrix.

30. The non-transitory computer readable medium of claim 29, wherein the program code further comprises: Program code for reconstructing the channel based on the latent space representation.

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