Channel Mapping in Wireless Systems

Abstract

A processing platform in an illustrative embodiment includes one or more processing devices, each processing device including at least one processor coupled to a memory. The processing platform is configured to extract channel features of a wireless channel of a wireless system from channel state information characterizing a radio geometry of the wireless channel, generate a forward mapping function that maps the extracted channel features to a channel map characterizing a representative spatial geometry of the wireless channel, and use the channel map to estimate at least one position-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel. Generating the forward mapping function illustratively includes performing an unsupervised learning process to learn the forward mapping function from the extracted channel features. The channel map is illustratively configured to preserve local geometries of multiple spatial locations associated with the extracted features in the actual spatial geometry of the wireless channel.

Description

[0001] priority

[0002] This application claims priority to U.S. Provisional Patent Application Serial No. 62 / 625,431, filed on February 2, 2018, entitled “Channel Charting in Wireless Systems,” the entire contents of which are incorporated herein by reference. Technical Field

[0003] The field relates generally to wireless systems and, more particularly, to techniques for processing radio channel measurements and other types of channel data generated in wireless systems. Background Art

[0004] Fifth generation (5G) networks will need to support a significant increase in traffic, number of terminals, and reliability / latency requirements. To address these challenges, researchers have proposed a range of new technologies that improve spectral efficiency through massive multiple-input multiple-output (mMIMO), increase bandwidth by leveraging millimeter wave (mmWave) bands for mobile communications, and rely on extreme densification of network elements. Although the advantages of these emerging technologies are obvious, they also bring severe practical challenges. In particular, mobility poses problems for dense small cell networks and mMIMO and mmWave networks that provide extremely fine-grained angular spacing. In mmWave networks, coverage is often patchy and the handover areas between cells are sharp. Therefore, smooth handover, multipoint operation, and / or cell search require multipoint channel state information (CSI). However, potential solutions to some of these problems (such as integrated multi-band operation and mobile relaying) will require a large amount of multipoint CSI. Summary of the invention

[0005] Exemplary embodiments of the present invention provide techniques for mapping or otherwise characterizing radio channels in a wireless system in a manner that addresses many of the above-described challenges.

[0006] The processing platform in the exemplary embodiment includes one or more processing devices, each of which includes at least one processor coupled to a memory. The processing platform is configured to extract channel characteristics of a wireless channel of a wireless system from CSI characterizing a radio geometry of the wireless channel, generate a forward mapping function that maps the extracted channel characteristics to a channel map characterizing a representative spatial geometry of the wireless channel, and use the channel map to estimate at least one position-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel.

[0007] Generating the forward mapping function illustratively includes performing an unsupervised learning process to learn the forward mapping function from the extracted channel features. The channel map is illustratively configured to preserve local geometry of a plurality of spatial locations associated with the extracted features in the actual spatial geometry of the wireless channel.

[0008] In some embodiments, a processing platform of the type described above includes at least a portion of at least one of a base station of the wireless system and a baseband unit of a cloud radio access network of the wireless system. Additional or alternative system components such as a wireless access point of the wireless system and / or a given one of the one or more wireless devices of the wireless system may be used to implement at least a portion of the processing platform. The processing platform may also be implemented at least in part within an information processing system coupled to or otherwise associated with the wireless system. Therefore, the term "processing platform" as used herein is intended to be broadly interpreted, and in other embodiments, various alternative implementations of the processing platform are possible.

[0009] These and other embodiments of the present invention include, but are not limited to, wireless systems, information processing systems, methods, apparatuses, processing devices, integrated circuits, and computer program products including processor-readable storage media having software program code embodied therein. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a block diagram of a wireless system with channel mapping capabilities in an exemplary embodiment.

[0011] Figure 2A and Figure 2B More detailed views of portions of a wireless system with channel mapping capabilities in other illustrative embodiments are shown.

[0012] Figure 3 is a diagram illustrating the relationship between geometric shapes in channel mapping in an illustrative embodiment.

[0013] Figure 4 is a diagram illustrating the importance of CSI scaling during feature extraction in an exemplary embodiment.

[0014] Figure 5 is a block diagram of an encoder-decoder arrangement for implementing channel mapping in an exemplary embodiment.

[0015] Figure 6 Three example uses of channel mapping in various embodiments are shown.

[0016] Figure 7 is a flow chart of a process for channel mapping in an illustrative embodiment. DETAILED DESCRIPTION

[0017] Embodiments of the present invention may be implemented, for example, in the form of a wireless system and / or an associated information processing system, each of which is included in at least a portion of what is generally referred to herein as a "processing platform". In some embodiments, the wireless system includes an information processing system or is otherwise associated with the information processing system, which performs data analysis on channel data or otherwise processes radio channel measurements or other types of channel data generated in the wireless system. Exemplary embodiments of such wireless systems and / or associated information processing systems will be described in detail herein. However, it should be understood that embodiments of the present invention are more generally applicable to various other types of wireless systems and / or information processing systems. Therefore, terms such as "wireless system" and "information processing system" as used herein are intended to be broadly interpreted.

[0018] The illustrative embodiments described in detail below are configured to provide a novel architecture referred to herein as "channel mapping" or CC for short, in which a multi-antenna network element learns a map of the radio geometry in the area around it. The channel map captures the local spatial geometry of the area so that points that are close in space will also be close in the channel map, and vice versa. CC illustratively works in a completely unsupervised manner, for example, learning is based only on radio channel measurements that are passively collected at a single point in space, but collected from multiple transmit locations in the area over time. CC then extracts channel features that characterize large-scale fading effects. Finally, the channel map is generated using tools such as dimensionality reduction, manifold learning, metric learning, and artificial neural networks.

[0019] A given network element performing CC may comprise, for example, a multi-antenna base station in a cellular system, or a baseband unit (BBU) in a cloud radio access network, and the mapped area may be a serving cell, or a multi-cell area covered by a BBU. Logical relationships related to the location of transmitters (e.g., user equipment) in the cell may then be derived directly by comparing the measured radio channel characteristics with the channel map. The unsupervised nature of CC enables many new applications for network planning, user scheduling, multipoint connectivity, handover, cell search, and other cognitive tasks that rely on CSI and user movement relative to the base station.

[0020] Figure 1A wireless system 100 with channel mapping functionality in an illustrative embodiment is shown. The wireless system 100 includes a wireless network 102 that is configured to communicate with a plurality of wireless devices 106-1, 106-2, ... 106-N. The wireless devices 106 may include mobile phones, portable computers, or other types of user equipment in any combination. The wireless network 102 illustratively includes a plurality of base stations of a radio access network (RAN) of the wireless system 100, as well as other system components, such as core network components of the type typically associated with a 5G wireless system or other types of wireless systems. For example, the wireless network 102 may additionally or alternatively include a plurality of remote radio heads (RRHs) and BBUs in a cloud-based RAN ("Cloud-RAN"). Many other arrangements are possible and may involve various types of baseband processors in addition to the BBU.

[0021] The wireless system 100 further includes a processing platform 104 that is associated with the wireless network 102 and configured to process CSI or other types of channel data generated in the wireless system 100 .

[0022] The illustrative embodiments are configured to exploit multi-dimensional characteristics of a radio channel in the wireless system 100. These characteristics include, for example, radio channel measurements (e.g., channel snapshots) at multiple antennas (e.g., measurements from all antennas that provide information about the spatial domain), radio channel measurements at multiple frequencies (e.g., measurements over a wide frequency band), and / or radio channel measurements at multiple delays (e.g., measuring delays caused by scatterers). In contrast to many existing approaches that use scalar information, such as received signal strength indication (RSSI) or angle of arrival (AoA), the illustrative embodiments exploit the availability of multi-dimensional CSI.

[0023] Furthermore, in some embodiments, channel mapping is completely unsupervised and can be configured to collect only radio channel measurements to build a channel map without relying in any way on a physical channel model. These embodiments can be further configured so as not to rely in any way on positioning information from a global navigation satellite system (GNSS) such as a global positioning system (GPS) or other.

[0024] Processing platform 104 includes multiple components for implementing channel mapping functionality in wireless system 100, including feature processing module 110, forward mapping function 112, reverse mapping function 114, machine learning algorithm 116, and channel mapping application 118. In other embodiments, additional or alternative channel mapping components may be used.

[0025] Although shown as being separate from the wireless network 102, in some embodiments, at least a portion of the processing platform 104 may be implemented within the wireless network 102. For example, at least a portion of the channel mapping functionality of the processing platform 104 may be implemented at least in part in one or more of a base station or a BBU of a RAN of the wireless network 102. One or more of the wireless devices 106 and / or one or more wireless access points may additionally or alternatively be used to implement at least a portion of the channel mapping functionality of the processing platform 104. Thus, a given "processing platform," as the term is used broadly, may include at least one of a base station, a BBU, a wireless access point, and a wireless device.

[0026] The processing platform 104 may also be implemented at least in part in an information processing system separate from the wireless system 100. For example, the processing platform 104 may include a big data analytics platform that processes CSI or other types of channel data from the wireless network 102. In other embodiments, many alternative processing platform arrangements are possible.

[0027] The processing platform 104 is an example of what is more generally referred to herein as a "mapping entity" that is implemented within or otherwise associated with the wireless system 100. Such an entity generates a channel map or other related output of a channel mapping process as disclosed herein. In some embodiments, the channel map takes the form of one or more data structures that store vector data.

[0028] In some embodiments, the wireless system 100 generates proximity information of a plurality of wireless devices at a mapping entity. Illustratively, this involves collecting a plurality of signal snapshots of wireless devices, wherein a given signal snapshot describes multi-dimensional characteristics of a radio frequency channel between a corresponding wireless device and a single communication entity controlled by the mapping entity. A proximity map of the wireless devices is generated based on the collected signal snapshots, wherein wireless devices that are close in physical space are close in the proximity map. The physical size of the communication entity controlled by the mapping entity is typically small compared to the average distance between the wireless devices.

[0029] Such proximity graphs are considered examples of what is more generally referred to herein as "channel graphs." The term "channel graph" and related terms such as "channel mapping" as used herein are intended to be interpreted broadly so as to encompass data mapping and / or associated visualizations, as well as other arrangements of information that characterize channel data in a low-dimensional representation. For example, in some embodiments, the channel graphs are each implemented at least in part in the form of one or more data structures generated and processed by the processing platform 104. Therefore, in conjunction with performing various automated operations or implementing other types of wireless system functions (such as controlling switching, beam selection, and other aspects of wireless communications), references to "channel graphs" herein should not be construed as requiring any particular visualization, but rather may more generally include data structures that are processed by computers or other network elements or more generally by processing devices within a given wireless system and / or associated information processing system.

[0030] The communication entities in an arrangement of the above type illustratively include access points of base stations of the wireless network 102 .

[0031] The mapping entity need not include the intended receiver for communications. For example, the mapping entity may include a standalone "box" or other type of processing platform that passively listens to communications to build a channel map. Such an arrangement may be particularly useful, for example, in defense or law enforcement applications, because tracking and positioning may be performed without the mapping entity being necessarily part of the wireless network 102.

[0032] It should be noted that in addition to proximity information, relative speed information may also be extracted from the measured signal snapshots. Thus, some embodiments may utilize, for example, proximity maps and speed maps. In other embodiments, other types of channel maps may be used.

[0033] Proximity and velocity information may be utilized in the wireless system 100 to perform a variety of different tasks related to managing the wireless network 102 and other aspects of the wireless system 100. These different tasks may be considered part of the application 118 and illustratively include the following:

[0034] 1. Positioning: The generated proximity graph can be used to extract relative position information between a wireless device and a mapping entity or between wireless devices. This can be used to extract information, for example, when device-to-device communication may be more advantageous than communication via a base station. By associating certain points in the proximity graph with semantic position information, one can use this technique for positioning services. Advantageously, these and other positioning tasks can be achieved without relying in any way on positioning information from GNSS.

[0035] 2. Event marking: The proximity graph is marked with events in the network, such as handover, radio link failure, and presence of small cells.

[0036] 3. Rate Adaptation: The generated proximity map indicates whether multiple wireless devices are in a common location, which can be used to guide communication rate adaptation for each such user. If a wireless device moves towards a cell boundary (as extracted from the proximity and velocity information), the rate can be preventively reduced even before the device will be in an area of ​​poor reception. This mitigates transmission failures and improves communication reliability.

[0037] 4. Network planning: The generated proximity map can be used to identify locations where the channel conditions are poor or difficult to separate from other channels or locations. Additional antennas can then be deployed in such poor reception areas to improve coverage and spacing of users or to mitigate interference between users.

[0038] 5. Turning base stations on and off: For energy efficiency, small cell base stations can be turned off during low traffic times to save energy. Network management has no a priori way to estimate when turning small cells back on would be beneficial. A labeled proximity graph can be used for this.

[0039] 6. User Scheduling: Proximity and velocity information can be used to determine which user the mapping entity should communicate with, versus, for example, communicating with the user with the best channel. This approach can be used to proactively schedule traffic to a user before the user enters an area with poor reception, or defer scheduling when the user is about to enter a hotspot served by a high-capacity small cell or WiFi access point.

[0040] 7. Handover: Proximity and speed information can be used to determine if the user is moving into proximity with another cell or another service (e.g., WiFi or pico cell). One can then perform a handover to another cell or another service before conventional algorithms would detect that a handover would be needed. This improves reliability for cell edge users or reduces data rates to and from the base station since other services can be used. Also, the user needs to perform fewer or no measurements to determine the possibility / need for a handover.

[0041] 8. Beam selection and cell search: The generated proximity map can be used to determine the beam between the wireless device and the base station, or to determine the training required when a new user enters the cell or turns on mobile service. In addition, the method enables one to transmit the beam that the user wants to use, so that the direction to the future base station can be found faster or more reliably.

[0042] 9. User Tracking: The generated proximity and speed maps can be used to track and predict the movement of wireless devices, and can be used to identify traffic conditions (e.g., traffic conditions of vehicles, trains, or other modes of transportation), the location of large moving crowds, or detect or predict other activities related to user movement.

[0043] 10. Cognitive Tasks: The generated proximity and velocity graphs can be used to anticipate events in the network, which include the intention of users to move, which may be related to their location, movement, velocity, relative positions between users, relative positions to static objects, etc.

[0044] As is apparent from the foregoing examples, proximity maps, speed maps, and other types of channel maps or associated channel mapping information, as disclosed herein, can be used to anticipate a variety of different types of events within a wireless system, thereby enabling the wireless system to take appropriate responsive measures to address such anticipated events. This provides improved wireless system performance and other advantageous results relative to conventional practice.

[0045] The following will be combined Figure 2A and Figure 2B A more detailed view of possible implementations of wireless system components such as components of the processing platform 104: feature processing module 110, forward mapping function 112, reverse mapping function 114, machine learning algorithm 116, and channel mapping application 118 in an illustrative embodiment is described.

[0046] If not implemented within the wireless network 102, the processing platform 104 may communicate with other wireless system components via one or more other networks including, for example, a global computer network such as the Internet, a wide area network (WAN), a local area network (LAN), a satellite network, or various portions or combinations of these and other types of communication networks.

[0047] The processing platform 104 in this embodiment further includes a processor 120, a memory 122, and a network interface 124. It is assumed that the processor 120 is operatively coupled to the memory 122 and the network interface 124, although such interconnections are not explicitly shown in the figure.

[0048] The processor 120 may include, in any combination, for example, a microprocessor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a central processing unit (CPU), a graphics processing unit (GPU), an arithmetic logic unit (ALU), a digital signal processor (DSP), or other similar processing device components, as well as other types and arrangements of processing circuit systems.

[0049] The memory 122 stores software program codes for execution by the processor 120 when implementing a portion of the functionality of the processing platform 104. For example, the program codes stored in the memory 122 may be used to implement at least a portion of the functionality of one or more of the components of the processing platform 104 related to channel mapping, i.e., the feature processing module 110, the forward mapping function 112, the reverse mapping function 114, the machine learning algorithm 116, and the channel mapping application 118.

[0050] A given such memory storing such program code for execution by a corresponding processor is an example of what is more generally referred to herein as a processor-readable storage medium (having program code contained therein), and may include, for example, electronic memory (such as SRAM, DRAM or other types of random access memory), read-only memory (ROM), magnetic storage, optical storage, non-volatile memory, or other types of storage devices, in any combination.

[0051] Articles of manufacture that include such processor-readable storage media are considered embodiments of the present invention.The term "article of manufacture" as used herein should be understood to exclude transitory, propagating signals.

[0052] In other embodiments, other types of computer program products including processor-readable storage media may be implemented.

[0053] Additionally, embodiments of the present invention may be implemented in the form of an integrated circuit including a processing circuit system configured to implement processing operations associated with components of processing platform 104, namely, feature processing module 110, forward mapping function 112, reverse mapping function 114, machine learning algorithm 116, and channel mapping application 118, as well as other channel mapping related functions.

[0054] Network interface 124 is configured to allow processing platform 104 to communicate with other system elements over one or more networks, and may include one or more conventional transceivers.

[0055] In operation, the processing platform 104 in the exemplary embodiment is configured to extract channel characteristics of a wireless channel of the wireless system 100 from CSI characterizing the radio geometry of the wireless channel, generate a forward mapping function that maps the extracted channel characteristics to a channel map characterizing a representative spatial geometry of the wireless channel, and utilize the channel map to estimate at least one location-dependent characteristic of one or more of the wireless devices 106 of the wireless system 100 in the actual spatial geometry of the wireless channel. The term "wireless channel" as used herein is intended to be broadly interpreted and should not be considered limited to any particular example channel type referenced herein.

[0056] The extraction of channel features is illustratively performed by a feature extractor implemented in feature processing module 110. The generated forward mapping function comprises one of forward mapping functions 112 in processing platform 104.

[0057] The CSI is illustratively generated by one or more multi-antenna receivers of wireless system 100 utilizing communications received from one or more of wireless devices 106 over a wireless channel.

[0058] For example, in some embodiments, the CSI may include channel measurements collected over time by a given one of the multi-antenna receivers from multiple wireless device transmit locations in a designated area of ​​the wireless system 100. The designated area may include, for example, a serving cell of a base station including the given multi-antenna receiver, or a multi-cell area covered by a BBU of the Cloud-RAN, although other types of designated areas may also be used.

[0059] Generating the forward mapping function illustratively includes performing an unsupervised learning process to learn the forward mapping function from the extracted channel features. For example, in some embodiments, the unsupervised learning process is configured to implement a specified dimensionality reduction technique to map a relatively high-dimensional point set of the extracted channel features to a relatively low-dimensional point set of the channel map.

[0060] Several specific examples of the above-described dimensionality reduction techniques for providing unsupervised learning of a forward mapping function are described in detail elsewhere herein, including principal component analysis (PCA) performed on a centered version of the extracted channel features, a Sammon mapping process configured to map a relatively high-dimensional set of points of the extracted channel features to a relatively low-dimensional set of points of a channel map, and an autoencoder process that implements an artificial neural network for unsupervised dimensionality reduction.

[0061] However, it should be appreciated that, although described in detail herein, PCA, Sammon mapping, and autoencoders are merely examples. Various other types of dimensionality reduction techniques may be utilized in illustrative embodiments to map the high-dimensional point set of extracted channel features to a low-dimensional point set of the channel map, again by way of example only, including multidimensional scaling (MDS), Laplace eigenmaps (LE), diffusion mapping, stochastic neighbor embedding (SNE) or t-type Student SNE, and Siamese neural networks that implement a pair of equivalent artificial neural networks for unsupervised dimensionality reduction.

[0062] In some embodiments, the unsupervised learning process is configured to utilize information, referred to herein as “side information,” illustratively obtained from a baseband unit of wireless system 100. For example, such side information may include information indicating that a particular subset of extracted channel features is associated with a particular one of wireless devices 106. Other types of side information obtained from other components of wireless system 100 may additionally or alternatively be used.

[0063] In some embodiments, at least a portion of the extracted channel features characterize at least one of large-scale fading effects, directional information, and time-of-flight (ToF) information of the wireless channel. In other embodiments, other types of channel features may be extracted from the CSI.

[0064] As described above, in the exemplary embodiment, the representative spatial geometry characterized by the channel graph has a much lower dimensionality than the radio geometry of the wireless channel.

[0065] Furthermore, a given channel map generated by the processing platform 104 is advantageously configured to preserve the local geometry of the plurality of spatial locations associated with the extracted features in the actual spatial geometry of the wireless channel. Thus, a first point and a second point that are located close to each other in the actual spatial geometry of the wireless channel are also close to each other in the channel map, and vice versa.

[0066] The processing platform 104 is further configured to generate an inverse mapping function that relates a spatial position in a representative spatial geometry of a wireless channel to a channel characteristic of the wireless channel. The generated inverse mapping function comprises one of the inverse mapping functions 114 of the processing platform 104. Generating the inverse mapping function illustratively comprises performing an unsupervised learning process to learn the inverse mapping function from the representative spatial geometry. For example, fully unsupervised learning may be performed to generate both a forward mapping function and a reverse mapping function.

[0067] In some embodiments, the channel mapping application 118 is configured to estimate at least one location-related characteristic of one or more of the wireless devices 106 in the actual spatial geometry of the wireless channel. Such estimation may more particularly involve, for example, estimating location information of a given one of the wireless devices 106, predicting intra-cell events involving the given wireless device, estimating CSI between the given wireless device and one or more base stations in one or more cells other than the current cell of the given wireless device in the wireless system 100, and estimating CSI between the given wireless device and at least one other wireless device. Figure 6 An example of such an estimation arrangement is described.

[0068] In some estimation applications, using a channel map to estimate at least one location-related characteristic of one or more of the wireless devices 106 in the actual spatial geometry of a wireless channel includes: extracting additional channel features from additional CSI characterizing the radio geometry of the wireless channel, comparing the additional channel features to the channel map, and estimating the location-related characteristic based at least in part on a result of the comparison.

[0069] Various other types of channel mapping applications 118 may be configured to utilize channel maps generated in the manner disclosed herein.

[0070] Now refer to Figure 2A and Figure 2B Additional exemplary embodiments implementing channel mapping functionality are described.

[0071] Figure 2AA portion 200 of one possible implementation of a wireless system with channel mapping functionality is shown. Portion 200 may represent a portion of wireless system 100. Portion 200 includes a set of receivers 202-1, ... 202-M coupled to a feature extractor 210, and includes a forward mapping function 212 and a reverse mapping function 214, as well as associated side information and memory instances 204-1 and 204-2, and multiple sets of applications 218-1, 218-2, and 218-3, all arranged as shown. In this embodiment, each of receivers 202 includes a set of multiple antennas. Figure 2A The feature extractor 210, the forward mapping function 212, the reverse mapping function 214, and the application 218 of the embodiment can be viewed as Figure 1 1 , and a channel mapping application 118. The wireless system 100 of FIG. 1 is an example of a specific instance of each corresponding component of the wireless system 100, namely, the feature processing module 110, the forward mapping function 112, the reverse mapping function 114, and the channel mapping application 118.

[0072] In this embodiment, feature extractor 210 receives a received signal (S) from receiver 202 to generate high-dimensional channel features (F). Forward mapping function 212 receives F from feature extractor 210 and uses F in combination with side information and memory (M) from component 204-1 to learn a low-dimensional representation (L). Reverse mapping function 214 receives L from forward mapping function 212 and uses L in combination with M from component 204-2 to learn F. Such learning functions illustratively use Figure 1 The wireless system 100 may be implemented by one or more of the machine learning algorithms 116 in the embodiments. By way of example, techniques such as manifold learning, metric learning, and / or artificial neural networks may be applied in a given embodiment. Other types of artificial intelligence (AI) functions may be incorporated into the wireless system 100 to support unsupervised learning in conjunction with the generation of channel maps. Moreover, various sets of applications 118-1, 118-2, and 118-3 may use F and L.

[0073] Figure 2B A portion 200' of another possible implementation of a wireless system with channel mapping functionality is shown. Again, portion 200' may represent a portion of wireless system 100. Portion 200' includes a single multi-antenna receiver 202 that communicates with a specific wireless device 201 over a wireless channel. Mapping entity 205 includes a feature extractor 210 and a forward mapping function 212, as well as one or more associated side information and memory instances 204. Portion 200' further includes a reverse mapping function 214.

[0074] Figure 2A and Figure 2BReceivers 202 in the exemplary embodiment of may comprise, for example, receivers associated with one or more base stations or BBUs of wireless system 100, where each such base station has a potentially large number of antennas. Other arrangements are possible. For example, a given one of the receivers may be associated with a single mobile device, or may comprise a static receiver having only one antenna.

[0075] It should be recognized that Figure 1 , Figure 2A and Figure 2B The specific arrangements of components and other system elements shown in the drawings are presented by way of illustrative examples only, and many alternative embodiments are possible.

[0076] For example, the following combination Figures 3 to 7 Other embodiments of wireless systems and / or information processing systems configured to provide channel mapping functionality are described. One or more of these embodiments may be considered Figure 1 The wireless system 100 and / or Figure 2A and Figure 2B A more detailed example of a possible implementation of parts 200 and 200' of a wireless system is shown.

[0077] Likewise, it should be appreciated that these and other embodiments disclosed herein are presented by way of illustrative examples only and should not be construed as limiting in any way.In other embodiments, many alternative arrangements for implementing the channel mapping functionality may be utilized.

[0078] For example, although the illustrative embodiments are described in the context of 5G wireless systems and are well suited for use in channel mapping within such systems, the disclosed techniques are applicable to various other types of wireless systems, including other systems that provide multi-dimensional CSI, channel snapshots, or other types of channel data.

[0079] Other types of wireless systems that may be configured to incorporate channel mapping functionality of the type disclosed herein include systems configured in accordance with standards such as, for example, 3GPP Long Term Evolution (LTE), 5G / NR, WiFi (IEEE 802.11), WiMax (IEEE 802.16e), TD-SCDMA, HSDPA / EDGE / GSM, Bluetooth, Zigbee, LoRa, SigFox, NB-IoT, and CDMA-2000. Thus, the wireless system 100 may more particularly include a wireless system configured in accordance with one of these standards.

[0080] Therefore, the embodiments described herein are considered to be illustrative only and should not be considered to be limited to any particular arrangement of features. For example, those skilled in the art will recognize that alternative processing operations and associated system component configurations may be used in other embodiments. Therefore, other embodiments may include additional or alternative system components relative to the components of the illustrative embodiments. Moreover, in other embodiments, the specific channel mapping process and the associated channel data format and channel map format may be changed.

[0081] It should also be noted that the above-described wireless system and / or information processing system arrangements are merely exemplary and that alternative system arrangements may be used in other embodiments.

[0082] Now refer to Figures 3 to 7 Additional details are described regarding the operation of an example implementation of a wireless system having channel mapping functionality as disclosed herein.

[0083] The following notation will be used to describe these exemplary embodiments. Lowercase and uppercase bold letters represent column vectors and matrices, respectively. For a matrix A, the Hermitian is A H , and the entry in row k and column l is A k,l or [A] k,l . For a vector a, the kth term is a k The Euclidean norm of a and the Frobenius norm of A are respectively given by ‖a‖2 and ‖A‖ F Represents. M×N all-zero and all-one matrices are 0 M×N and 1 M×N , the M×M identity matrix is ​​I M . K vectors a k ,k=1,...,the set of K is The real and imaginary parts of vector a are represented by and express.

[0084] The principles of an illustrative embodiment of channel mapping ("CC") will now be described. As previously described, the CC is illustratively configured to learn a low-dimensional embedding, a so-called channel graph, from a large amount of high-dimensional CSI of transmitters at different spatial locations (e.g., mobile or fixed UEs) over time. The channel graph locally preserves the original spatial geometry, i.e., transmitters that are nearby in real space will be placed nearby in the low-dimensional channel graph, and vice versa. The CC will understand whether two transmitters are close to each other by forming a dissimilarity measure between the CSI features of the two transmitters. Based on this, the CC generates a low-dimensional channel graph from the CSI only in an unsupervised manner, and no assumptions are made about the physical channel, i.e., without the help of information from GNSS, such as GPS, triangulation / trilateration techniques, or fingerprinting-based positioning methods. This important property enables the CC to extract geometric information about the transmitter in a completely passive manner, opening up a variety of novel applications.

[0085] Example 1. In some embodiments, the wireless system includes a massive MIMO BS with a uniform linear array (ULA) of B=32 antennas that receive data from N=2048 UE locations. We simulate a narrowband line-of-sight (LoS) channel with a signal-to-noise ratio (SNR) of 0 dB. As will be described in more detail below, the example channel graphs generated in such a system use pairs of transmitters, where each pair of transmitters is associated with a pair of spatial distances and a pair of characteristic dissimilarity. The channel characteristics are designed to ensure that the pair-wise characteristic dissimilarity is approximately lower-bounded by the pair-wise spatial distance (when divided by a suitable reference distance). Therefore, UEs that are far apart in space will have dissimilar channel characteristics. In the resulting channel graph, the local geometry characteristics of the original spatial geometry are well preserved.

[0086] In the previously described Figure 2B In the embodiment of FIG. 1 , for the sake of simplicity of illustration, a single antenna transmitter (Tx) 201 is shown, which is static or moving in real space. (in represents its spatial position at discrete time n=1,...,N, where D is the dimension of the spatial geometry (e.g., the three dimensions representing the x, y, and z coordinates of the UE in real space). At each time n, Tx sends data s n (e.g., pilot or information symbols), which is received at a multi-antenna receiver (Rx) with B antennas; this could be an mMIMO BS. The received data is modeled as y n =H(s n )+n n , where the function H(·) represents the wireless channel between the transmitter and the receiver, and the vector n nSimulate noise.

[0087] In the following, we are not interested in the transmitted data, but in the associated CSI. Specifically, Rx uses the received data y n To extract the vector denoted by M, where M represents the dimensionality of the CSI obtained from all antennas, frequencies and / or delays. The generated CSI typically describes the AoA, power delay profile, Doppler shift, RSS, signal phase, or simply the first and second moments (e.g., mean and covariance) of the received data; typically, we make M>>D. We use the following channel function to represent the CSI from spatial position x n To CSI n The mapping:

[0088]

[0089] in refers to the radio geometry. Obviously, h n The CSI represented depends mainly on the spatial position x of Tx n , and also depends on the mobile objects in the cell as well as the noise and interference. For the following description of the exemplary embodiment, we make the following assumptions:

[0090] Assumption 1. We assume that the statistical properties of the multi-antenna channel vary relatively slowly throughout space, on length scales related to the macroscopic distances between scatterers in the channel, rather than on the small fading length scale of the wavelength. We further assume that the channel function is static, although it will be appreciated that other embodiments may be extended to time varying channels.

[0091] It should be noted that this and other assumptions cited herein when describing exemplary embodiments do not necessarily apply to other embodiments.

[0092] Large-scale effects of the channel are believed to arise from reflections, diffractions, and scattering of the physical environment, while small-scale effects are caused by multipath propagation and the correlated destructive / constructive addition of signal components. To motivate Assumption 1, we consider the following example, which illustrates that certain statistical moments of interest of the illustrative embodiments do capture large-scale effects of wireless channels.

[0093] Example 2. The channel between a single Tx and B-antenna Rx is modeled by a set of rays, and we assume that N s scatterers. We consider a non-LoS (NLoS) scenario where all rays are in the far field, so that they can be modeled with plane waves. The distance from Tx t to the scatterer s is d ts , the distance from the scatterer s to the Rx antenna r is dsr The attenuation between two points x and y is modeled as a function of distance, a xy =a(d xy ), which incorporates relevant scatterer cross sections, antenna gains, etc. The distance dependence is generally a power law, and the variation of a(d) occurs over length scales much larger than the wavelength λ; for conventional ray tracing, a(d) ≈ ​​d -2 , which corresponds to the free space path loss. In addition, each scatterer s is affected by a phase shift φ that is related to the dielectric properties of the scatterer s To model; assign these independent and identically distributed (iid) random variables to each scatterer. The channel between t and r can be modeled as

[0094]

[0095] When the number of scatterers N s →∞, the channel will become Rayleigh fading. This is a property of the distribution of the absolute values ​​of the channel coefficients when viewed as random variables, where the randomness is based on the location of the transmitter within a small-scale neighborhood of a few wavelengths. The long-term channel characteristics are averaged over this neighborhood. For the average value of the MIMO channel, the relevant characteristics are thus the average absolute value of the channel at each antenna r and the average relative phase difference between the antennas as large-scale channel characteristics that describe the small-scale fading statistics. For this method, by averaging over a small-scale neighborhood of a few wavelengths, it is found that the wavelength (λ) dependence disappears. For the angular differences, similar arguments lead to the observation that they are large-scale effects of the channel.

[0096] Specifically, evaluating the raw second-order moment of the channel from Tx t to Rx antenna r,r′ yields

[0097]

[0098] where for clarity, the distance is assumed to be fixed and we consider only the expectation of the random phase φ. In the limit, this expression is simply obtained by the decay function a ts With the distance d ts Now consider the (original) covariance matrix estimated for two transmitters t and t′. If for all scatterers s, a ts ≈a t′s , then the covariance matrix R t and R t′ and are approximately the same. The covariance matrix differs only on length scales where the distance between the transmitter and the scatterers varies significantly - the change in channel covariance is an effect of large-scale fading, which is driven by the quenching stochastic process that forms scatterers in the environment.

[0099] Relying on Assumption 1, we will describe the CC process in detail in the exemplary embodiments. In these embodiments, CC begins with converting CSI h n Distill it into suitable channel features that capture the large-scale properties of the wireless channel Here, M′ denotes the feature dimension, and we typically let M′>>D. Additional details on the design of channel-specific features are provided elsewhere in this paper. We represent the feature extraction stage as

[0100]

[0101] Feature extraction is mainly used for three purposes: (i) extracting large-scale fading properties from CSI, (ii) refining CSI into useful information for the subsequent CC pipeline, and (iii) reducing the large amount of channel data. CC then uses a set of N collected features We proceed to learn what is referred to in this paper as the forward mapping function (possibly exploiting side information) in an unsupervised manner. We denote the forward mapping function to be learned as

[0102]

[0103] It converts each channel feature f n Mapped to points in the low-dimensional channel map Typically, we make D′≈D. The goal of learning C is as follows.

[0104] The forward mapping function C should preserve the local geometry between adjacent data points, i.e., it should satisfy the following conditions:

[0105] d z (z,z′)≈d x (x,x′).

[0106] Here, are two points in real space in some neighborhood, and is the corresponding vector in the learned channel graph. Function d x (x,x′) and d z (z,z′) is a suitably defined measure of distance (or more generally, dissimilarity), and the neighborhood size depends on the physical channel.

[0107] The goal of CC is to generate a channel graph that satisfies the above distance property for x and x′ as much as possible in the neighborhood We wish to learn from a set of N channel features in an unsupervised manner The channel map is learned without using the real spatial position of the UE

[0108] Obtain channel characteristics from a single transmitter (e.g., UE) The assumption of is not important. In fact, we are only interested in collecting N channel features from as many locations as possible in the spatial geometry. The fact that some subset of channel features originates from a single UE can be used as potential side information, which can improve the geometric relationships in the learned channel graph.

[0109] Figure 3 A diagram 300 is shown, which shows an example geometry involved in a CC in an exemplary embodiment. The transmitter Tx is located at The spatial geometry 302 is represented, and the receiver (Rx) extracts The CSI in the represented radio geometry 304. The mapping entity 305 processes The feature geometry 306 represented and obtained by feature extraction. The mapping entity 305 uses the extracted features of the feature geometry 306 to learn a forward mapping function, which maps the extracted features to a low-dimensional channel map 308, which represents the preserved spatial geometry. The representative spatial geometry of the local geometry of the original spatial position in

[0110] exist Figure 3 In an embodiment, the transmitter is located by (e.g., indicating its coordinates) in the spatial geometry 302. The physical wireless channel Mapping data (e.g., pilot and information) to The CSI in the radio geometry 304 represented by . This nonlinear mapping to the radio geometry obscures the spatial relationships between the transmitters. The goal of feature extraction is to find a representation that can easily recover the spatial geometry. CC then - in an unsupervised manner - learns a forward mapping function C that maps the channel features to 308, so that neighboring transmitters (in real-world coordinates) will also be neighboring points in the channel graph, i.e., CC preserves local geometry. Note that in some application scenarios, one may be interested in the inverse mapping function C that maps channel graph information to characteristic geometry. -1 For example, by using C -1 , which can reduce the number of multi-point CSIs required for multi-point transmission and interference alignment.

[0111] Example 3. An example of how the above CC embodiments may be used in practice is as follows. A mobile UE is served by a cellular network and is connected to a specific BS. Conventionally, cell switching is performed based on RSS measurements performed at the UE. The UE continuously monitors the synchronization signals transmitted by all BSs in the network and sends the measurements to the BS. Then, based on these measurements, the switching is performed reactively. In a location-based mobility management scenario, in order to reduce signaling and UE measurements, the network proactively performs switching based on the spatial positioning of the UE. The user is first located by fusing the ToF and AoA measurements of multiple BSs. Based on the location of the UE, environment-specific information is used to calculate the best cell. In a CC-based cell switching approach, the BS will have a graph of the radio characteristics in the cells served by it, marked by the locations where switching events occur. Through the uplink pilot transmitted by the UE, it can locate the UE in the radio geometry and perform the switching when the CC indicates the point where the switching occurs. Note that in some embodiments of the CC, the decision to perform the switching is based on measurements at a single BS; no network-wide fusion is required, thus reducing complexity relative to conventional approaches. Furthermore, by tracking and predicting the movement of UEs in the channel graph, one can anticipate cell switching events even before they occur.

[0112] In order to extract accurate channel maps in an unsupervised manner in the exemplary embodiment, we utilize high-dimensional CSI, which comes from as many different transmission locations as possible and is acquired on multiple BS antennas with large bandwidth and fast rate. Fortunately, almost all modern wireless systems already generate high-dimensional CSI data at extremely fast rates.

[0113] Example 4. A BS for a 3GPP LTE wireless system can measure up to 100 MIMO channels per millisecond, resulting in more than 10 MIMO channels per day for a 2×4 MIMO channel. 10 A similar amount of data is collected by active user equipment instances (UEs), signaling up to 226 bits of CSI to the BS every 2 ms. Currently, most of this data is discarded immediately after use (e.g., for data detection or precoding), and a limited amount is retained in order to track the average received signal strength (RSS) of the UE.

[0114] An exemplary embodiment of the CC is configured to collect and process the acquired CSI to learn a channel map. The total dimension M of each CSI vector is determined by the number of receiver antennas B multiplied by the number of subcarriers (or delays) W. As will be described in more detail below, in some embodiments, we intentionally "lift" the CSI vectors into a higher dimensional space, effectively squaring the total feature dimension. We collect channel features from N different transmitter locations, which further amplifies the amount of data available for channel mapping. Therefore, the total number of channel features for a CC can easily reach billions.

[0115] Example 5. Consider a wideband massive MIMO receiver with B = 32 BS antennas and W = 128 subcarriers, which yields M = BW = 2 12 dimensional CSI vector. If each CSI vector is upgraded to M′=M 2 dimensional space, we will have M′=2 24 By collecting channel features from n = 2,048 different spatial locations, we obtain 2 35 The total dimension of , which is a data set containing more than 34 billion complex-valued channel feature coefficients.

[0116] Note that these numbers are conservative. 5G wireless networks are likely to have many more BS antennas and subcarriers, and receive data from a large number of UEs. This flood of channel features is both a blessing and a curse. Obviously, the CC embodiments disclosed herein will have enough data to support unsupervised learning. However, the large amount of CSI poses severe challenges to storage and processing. Therefore, the channel feature extraction is illustratively configured to reduce the size of such data, and the mapping algorithm is illustratively configured to scale appropriately. Additional details about these aspects of the illustrative embodiments are described below.

[0117] A number of quality metrics for channel characteristics and channel graphs will now be described.

[0118] To characterize the usefulness of channel features and the quality of the generated channel map, we need to measure how well the channel features or points in the channel map preserve the spatial geometry of the true transmitter location - a suitable feature will preserve the local geometry as much as possible for the neighborhood. To evaluate the channel mapping quality in the exemplary embodiment, we utilize two metrics commonly used to measure the quality of dimensionality reduction methods, namely continuity (CT) and confidence (TW).

[0119] Next, we explain these two quality measures simultaneously in the context of two sets of abstract data points with cardinality N, i.e., and the representation from the original space It is called the use point v n Indicates un In the CC context, the original space will be the spatial geometry, while the representation space can be the feature geometry or the channel map (see Figure 3 ), it depends on whether we want to measure the quality of the channel features or the quality of the learned channel map.

[0120] In the following, we choose the distance (or dissimilarity) function d u (u,u′) defines the K-neighborhood of point u as the set of its K nearest neighbors. Similarly, using d v (v,v′) is used to define the neighborhood of v.

[0121] Regarding continuity, neighboring elements in the original space may be far away (distinct) in the representation space. In such cases, we say that the representation space does not preserve the continuity of the original point set. To measure such cases, we first define a data point u i The point-by-point continuity of the K neighbors of . Let is the point u in the original space i The K-neighborhood of (but not necessarily the point in the representation space). Moreover, let For point v i The points between the neighboring elements of v j The ranking is based on its relationship with v i . For example, Indicator point v i is the kth i The most similar point. Then, point u i The representation of v i The pointwise continuity of is defined as

[0122]

[0123] Point Set Rather than expressing The (global) continuity between is just the average of all point-wise continuity values, i.e. Both point-wise and global continuity measures range between zero and one. If continuity is low (e.g., 0.5 or less), points that are similar in the original space are dissimilar in the representation space. When continuity is large (close to 1), the representation mapping preserves neighboring elements.

[0124] Continuity measures whether neighbors in the original space are preserved in the representation space. However, the representation mapping may introduce new neighbor relationships that do not exist in the original space.

[0125] The confidence measures how well the feature map avoids introducing these false relationships. Similar to point-wise continuity, we first define a point v i The point-by-point credibility of the K-neighborhood of . Let is a set of "false neighbor elements" in v i in the K neighborhood of ; but not in the original space u i . Moreover, let r(i,j) be the point u j A point u in the neighborhood of i The ranking is based on its relationship with u i The similarity is arranged. Then point u i The pointwise credibility of the representation of is then

[0126]

[0127] Point Set Rather than expressing The (global) credibility between is just the average of all point-wise credibility values, i.e. Both point-wise and global confidences range between zero and one. Low confidence values ​​indicate a situation where most data points that appear similar in the representation space are actually dissimilar in the original space. If the confidence is close to one, then data points that are close in the representation space are also similar (close) in the original space.

[0128] Since we are interested in preserving local geometry, we set K to 5% of the total number of points N, i.e., K = 0.05N. Note that this is a common choice in conventional dimensionality reduction methods.

[0129] We use the above CT and TW metrics for two purposes. First, we will use both metrics to evaluate the channel characteristics To this end, we measure the CT and TW between the spatial geometry and the feature geometry (see Figure 3 ). The following provides additional details on how the specific channel features of CT and TW are preserved and are therefore well suited for use in CC. Next, we will use these metrics to evaluate the learned channel graphs. To this end, we measure the CT and TW between the spatial geometry and the channel map.

[0130] We now focus on the feature extraction stage. Specifically, we show that computing the raw 2nd-order moments of the CSI, performing feature scaling, and transforming the results in the angular domain yields channel features that accurately represent the large-scale fading properties of the wireless channel.

[0131] To restrict the search for suitable channel features, we focus on the Frobenius (or Euclidean) distance as the dissimilarity measure for feature pairs, i.e., we use d f (F,F′)=||FF′|| F, where (by using the notation) the feature is allowed to be a matrix. To generate appropriate channel features, we focus on the second-order statistical moments of the received CSI. Let is a vector containing the CSI acquired at time t (e.g., during the training phase). We compute the dimension M 2 The raw second moment (R2M) of is as follows: Here, the expectation is that noise, interference, and potential variations in CSI due to small-scale motion are present over short time periods (i.e., well below the coherence time of the channel). It is important to note that computing the outer product results in a representation of the CSI that is incoherent with any global phase rotation that may originate from small-scale fading. In practice, we only compute θ for a small number of time instants T (e.g., ten or less). We can then use The necessary channel features are extracted by following two steps: (i) CSI scaling and (ii) feature transformation. These two steps are described in detail below.

[0132] Step 1: CSI Scaling

[0133] One of the most critical aspects in good feature design of CC is to realize that CSI in radio geometry is not a good representation of spatial geometry.

[0134] Figure 4 A diagram 400 is shown illustrating the importance of CSI scaling during feature extraction. Diagram 400 illustrates the relationship between spatial geometry 402, radio geometry 404, and feature geometry 406. The solid lines illustrate the dissimilarity between UEs A and B, and between C and D in the various geometries 402, 404, and 406. The dashed lines represent UEs located on the same incident ray, i.e., A and C, and D and B. In radio geometry 404, the acquired CSI incorrectly represents the true Tx distance due to path loss. Specifically, UEs that are farther away in spatial geometry appear similar in radio geometry, and vice versa. To compensate for this distortion effect, we perform CSI scaling, which unfolds the radio geometry into a feature geometry that can better represent the Euclidean space.

[0135] refer to Figure 4 , assuming that two TxA and B are close to Rx, while TxC and D are far away. Due to path loss, the CSI measurement value H of TxC and D C and H D It looks better than the measured value H near Tx. A and H Bis weaker (i.e., the Frobenius norm is smaller). If we now directly compare the Frobenius distance between C and D, even though they are farther apart, their distance will appear to be smaller than the distance between A and B (because their norm is smaller). To compensate for this, we “unfold” the CSI to make it more compatible with the geometry of the space, such as Figure 4 shown.

[0136] This approach is referred to herein as CSI scaling and will now be explained in further detail.

[0137] Consider a transmitter separated by d meters from a ULA with B antennas. Assume a narrowband LoS channel with no scatterers and a 2D plane wave model (PWM). For this scenario, the normed (h phase of the vector is rotated so that h1 is real and positive) CSI vector Each term b of is given by

[0138]

[0139] For b=1,...,B, where ρ>0 is the path loss exponent, Δr is the antenna spacing, and φ is the incident angle from Tx to Rx. Let is the associated R2M. Figure 4 As shown, assume that two TxA and C have the same incident angle φ, but the distance from the receiver is d A and d C Now our goal is to scale the CSI matrix so that and Frobenius distance is exactly their real distance. For the above LoS scenario, we get the following results.

[0140] Consider the LoS channel model in (1) above. Assume that two UEs A and C have the same incident angle and are at a distance d from the BS. A and d C It can be shown that by scaling the R2M of the two UEs to

[0141]

[0142] Scaling Moment and Distance This is exactly their real distance

[0143]

[0144] If the parameter σ∈(0,ref) matches the path loss exponent ρ.

[0145] Since β ≥ , the CSI from distant transmitters is amplified, and the CSI from nearby transmitters is attenuated. In other words, feature scaling as shown in (2) can expand the radio geometry, such as Figure 4 shown.

[0146] Since the path loss exponent ρ is usually unknown in practice, we can use the parameter σ in (2) as a tuning parameter. For example, simulations show that 1 as a tuning parameter yields excellent CC quality (in terms of TW and CT) for a variety of scenarios. Moreover, it can be seen from (2) that the extreme case of σ→∞ completely ignores the magnitude of the CSI; this is useful, for example, in multi-user systems deploying transmit power control or in scenarios where shadowing effects dominate.

[0147] Step 2: Feature Transformation

[0148] Now, we are ready to convert the scaled CSI matrix Since we focus on the Frobenius distance as the dissimilarity, a straightforward choice for channel features is to set the features directly to the scaled CSI moment We use represents such a feature. However, as described below, applying certain nonlinear transformations to the scaled CSI moments can significantly improve the feature quality. In particular, we also consider taking the term-wise real part of the scaled CSI moment (given by ), the imaginary part (represented by denoted by “∠(·)”), angle (denoted by “∠(·)”), or absolute value (denoted by “|·|”). Furthermore, we say that all these channel features are taken from the antenna domain (denoted by “Ant”). We also consider the case where we take the scaled CSI vector and transform it into the angular domain (denoted by “Ang.”), followed by one of the above nonlinearities. Denoting the scaled R2M, we calculate Where D is the value that satisfies D H D=I M The M×M discrete Fourier transform matrix of . This approach transforms the scaled CSI moments from the antenna domain to the angular domain (or beam space), which represents the angle of incidence of the Tx and potential scatterers to the array in a compact way. We then either use this feature directly or apply one of the nonlinearities mentioned above.

[0149] We now evaluate the validity of the channel characteristics discussed above. We first specify the simulation parameters and then evaluate the measured correlation CT and TW between the spatial geometry and the radio geometry.

[0150] We consider a scenario involving a narrowband NLoS channel generated from the Quadriga channel model. The key parameters are summarized in Table 1 below. We record the CSI for N = 2048 randomly selected (except for a limited number of points placed to form a continuous curve for visual comparison purposes) spatial locations within a square area of ​​1000m × 500m; the median distance between nearest neighbors is about 7.86 meters, i.e., we sample the CSI at roughly 53 wavelengths in space. We take the CSI with an SNR of 0dB and average it over T = 10 times, then set σ = 16.

[0151] It should be noted that the specific channel types, parameters, and other features of this scenario, as well as the channel types, parameters, and features of other illustrative embodiments disclosed herein, are merely examples and should not be considered limiting in any way.

[0152] parameter set up Scenario BERLIN_UMa_NLOS Carrier frequency <![CDATA[f c =2.0GHz]]> Channel bandwidth BW=312.5KHz Number of BS antennas B＝32 Antenna Array ULA, where Δr = λ / 2

[0153] Table 1: Key parameters of Quadriga NLoS channel The global TW and CT of the channel characteristics for a range of neighborhoods with K = 0.05N are summarized in Table 2 below.

[0154]

[0155] Table 2: Comparison of channel features extracted from R2M in terms of TW and CT

[0156] The numbers in brackets in Table 2 represent the standard deviation of the point-wise TW and CT metrics. We see that the absolute value of R2M in the angular domain produces higher TW and CT values. Other features, such as the absolute value of R2M in the antenna domain, perform worse.

[0157] The above simulation results show that, given appropriate channel characteristics, even challenging NLoS channel scenarios at low SNR exhibit surprisingly high TW and CT. This observation supports the effectiveness of Hypothesis 1 and the example CC algorithm described in detail below. It should be noted that similar simulations were performed for the "vanilla" LoS (V-LoS) channel in (1) and the Quadriga-based LoS (Q-LoS) channel, and we reached the same conclusions. We emphasize that in these specific illustrative embodiments, for all considered channel models and scenarios, the absolute value of R2M in the angular domain proves to be the most robust channel characteristic. However, other types of channel characteristics may be utilized in other embodiments.

[0158] We now introduce three different CC unsupervised learning algorithms with varying complexity, flexibility, and accuracy. As mentioned earlier, the three exemplary algorithms to be described include PCA, Sammon Mapping, and Autoencoders. For each method, we will briefly discuss its pros and cons. The corresponding channel graph results will also be described.

[0159] Principal component analysis

[0160] As a baseline mapping algorithm, we perform PCA on the centered version of the channel features. PCA is one of the most popular linear and parametric methods for dimensionality reduction, and is used in the exemplary embodiments disclosed herein to map a high-dimensional set of points (channel features) to a low-dimensional set of points (channel graph) in an unsupervised manner. The specific method we use for channel mapping will be described in detail below.

[0161] We collect all N channel features, vectorize them, and then concatenate them into an M′×N matrix F =[f1,...,f N ] in the . Then, we will F Each row of is normalized to have zero empirical mean; we call the resulting matrix We then compute the eigenvalue decomposition on the empirical covariance matrix of the central channel features, such that U H Here, the N×N matrix U is a unitary matrix, that is, U H U=I N , Σ is a diagonal matrix where the N eigenvalues ​​on the main diagonal are arranged in descending order of their values ​​(assuming all eigenvalues ​​are real values), that is, the Σ eigenvalues ​​are arranged in descending order of their values ​​(σ1,...,σ N ), so that for 1≤k <l≤N,σ k ≥σ l Finally, we calculate the channel graph Z = [z1, ..., z N ] contains a D-dimensional matrix of low-dimensional points. Let u d represents the dth column of U. Then, the channel map obtained by PCA is given by

[0162]

[0163] PCA is easy to implement and can be performed in a computationally efficient manner using power iteration. However, compared to the nonlinear CC methods described below, PCA performs poorly in terms of TW and CT.

[0164] Salmon Map

[0165] Sammon Map (SM) is a classic nonlinear method that maps a high-dimensional point set to a low-dimensional point set with the goal of keeping a small pairwise distance between the two point sets, and is therefore very suitable for use in CC. Next, we describe SM for CC in detail, explain an efficient algorithm for computing the channel graph, and propose a modified version (hereafter referred to as SM+) that takes side information into account.

[0166] Initially the basic aspects of SM will be described.

[0167] First, we calculate the pairwise distance matrix D of all channel features

[0168] D n,l =d f (F n ,F l ),n=1,...,N,l=1,...,N,

[0169] where we use the Frobenius distance described elsewhere in this paper. SM attempts to find a low-dimensional channel graph, i.e., the set of points obtained by the following optimization problem

[0170]

[0171] We omitted D n,l = 0. The objective function of Sm improves the channel graph. For these channel graphs, The Euclidean distance of adjacent point pairs in is consistent with the feature distance. Ignore Smaller points (i.e., points that are dissimilar in feature geometry); this ensures that the SM maintains small pairwise distances between the two point sets. Since the objective function is invariant to global transformations, we use constraints to enforce the channel graph to be The center of each of the coordinates in .

[0172] The problem (SM) is non-convex and is typically solved using a quasi-Newton method. Next, we detail an efficient first-order method that allows us to include side information that can be used for CC. We use an accelerated forward-backward splitting (FBS) procedure that solves a convex optimization problem of the following general form:

[0173] Minimize f(Z)+g(Z)

[0174]

[0175] The function should be convex and smooth, and g should be convex but not smooth or bounded. FBS consists mainly of the following simple iterations

[0176]

[0177] t=1,...,T max , or until convergence. Here, is the gradient of the smooth function f, and the neighboring operator of the non-smooth function g is defined as

[0178]

[0179] sequence Contains a carefully chosen step size parameter to ensure FBS convergence.

[0180] For CC, the matrix Z = [z1,...,z N ] contains all the points in the channel graph. The function f is chosen as

[0181]

[0182] And the nth column of the gradient of f is

[0183]

[0184] The center constraint in (SM) is enforced by choosing

[0185]

[0186] The "characteristic function" χ is its independent variable It is zero when is zero and infinite otherwise. The proximity operator for this characteristic function is simply a reprojection of the center constraint given by

[0187]

[0188] Since the function f is non-convex, FBS is not guaranteed to find a global minimum solution. However, we found that FBS with appropriate initialization and step size criteria produces excellent CC results in a computationally efficient manner. Specifically, we use the PCA PCA Z detailed above (1) =Z PCA The solution initializes FBS and adopts the adaptive step size procedure described by T. Goldstein, C. Studer, and RGBaraniuk, "A field guide to forwardbackwardsplitting with a FASTA implementation", arXiv preprint: 1411.3406, November 2014, which is incorporated herein by reference.

[0189] We now provide examples of how CC can be improved through side information. Note that the methods described here remain unsupervised in that they do not require information about the spatial location of the transmitter.

[0190] In practice, one often collects many CSI vectors from a single transmitter (e.g., UE). In this case, the channel characteristics for a given transmitter u form a time series in contains the time-ordered channel characteristic indices associated with UE u. Since the transmitter moves at a finite speed, we know that temporally adjacent CSI vectors from the same UE should be close in the channel graph. To exploit this information, we include a squared e2-norm penalty in the objective function, which reduces In particular, for each transmitter u, we write

[0191]

[0192] Added to the objective of (SM), where the parameter α u > 0 determines the spatial smoothness of the channel graph for transmitter u. The nth row of the gradient of this penalty can be computed efficiently and is given by

[0193]

[0194] in In the following, we refer to the resulting CC algorithm as Sammon Map Plus (SM+).

[0195] The main advantages of SM / SM+ are that (i) they directly implement the requirements of CC outlined previously, resulting in excellent TW and CT, and (ii) temporal side information can be easily included. Disadvantages are that (i) they are non-parametric, requiring an out-of-sample extension procedure if new points need to be mapped without relearning the channel map, and (ii) the complexity is significantly higher than PCA.

[0196] Autoencoder

[0197] Autoencoders (AEs) are single-layer or multi-layer (deep) artificial neural networks that are commonly used for unsupervised dimensionality reduction tasks and have shown excellent performance on many real-world datasets. We now explain in detail how to use AEs for CC.

[0198] The basic idea of ​​AE is to learn two functions, namely encoder and decoder where M is the device that is learned so that the average approximation error

[0199]

[0200] For a set of vectors is the minimum. Since the dimension of the codomain (output) of the encoder C is usually smaller than the domain (input), we get f n ≈C -1 (C(f n )); but this is not a perfect equation. Hopefully AE can capture the input f n The low-dimensional representation of the principal components of n =C(f n ).

[0201] Now we describe how to use AE with CC. First, it is important to realize that in f n The encoder C directly corresponds to the forward mapping function when the input is -1 Corresponding to the inverse mapping function. Second, we will use a multi-layer (or deep) AE to learn these two functions C and C in an unsupervised manner -1 .

[0202] Example 6. Consider a simple (shallow) AE whose encoder and decoder consist of a single layer, the input is the channel features, and the output of the decoder corresponds to the point in the channel map. Each layer first multiplies the input with a matrix (containing weights) and then adds a bias term; then applies a (non-linear) activation function (also called a neuron) element by element to generate the output.

[0203] Mathematically, such a shallow AE is described as follows:

[0204] C: z = f enc (w enc f+b enc ) (7)

[0205]

[0206] Here, the forward mapping function C(encoder) first calculates the weight matrix The matrix-vector product between the vectorized channel features f(input) and then the bias vector is added The result of this operation is then passed through a nonlinear activation function f enc Passed, the function operates element-by-element on the terms of the independent variable. Reverse plotting function C -1 (Decoder) uses another weight matrix Deviation Vector And the activation function f dec Enter Map to The characteristic geometry of the channel in .

[0207] In practice, one often relies on multi-layer (or so-called deep) AEs rather than the shallow networks discussed in Example 6, as they often yield superior performance for many dimensionality reduction tasks. For such deep AEs, one can simply cascade the inputs and outputs of multiple single-layer networks, as shown in (7) and (8). The key design parameters for such deep AEs are the number of layers L (per encoder and decoder), the dimensions of the weight matrix and bias vector at each layer, and the type of activation function at each layer, all of which can be fixed at design time. In the CC process, only a set of channel features are extracted from the kernel. We learn the weight matrix together and the deviation vector , where l = 1, ..., L denotes the layer index, such that the approximation error in (6) is minimized. Learning is usually done via a process called back-propagation, which is computationally efficient and scales well to large datasets.

[0208] Figure 5 The structure of a deep autoencoder 500 for CC in an exemplary embodiment is shown. The deep autoencoder 500 includes an encoder 502 and a decoder 504 arranged as shown. The entire artificial neural network consists of 10 layers; the circles correspond to activation functions, and the trapezoids correspond to weights and biases; the bottom text indicates the activation function type, and the top text indicates the output size of each layer. As will be described in more detail below, the deep autoencoder 500 utilizes a specific number of layers, activation functions, number of neurons, and other parameters, which are carefully selected in the exemplary embodiment to provide the desired performance level, but it should be recognized that alternative parameters may also be used in other embodiments.

[0209] The encoder 502 and the decoder 504, also denoted as C and C in the drawings, -1 , each containing L=5 layers. The input of encoder 502 implementing forward mapping function C is M′-dimensional channel feature And the output of encoder 502 corresponds to the D′-dimensional channel graph For each layer l, using the weight and deviation The linear operation is given by Figure 5 For layers l = {1, 2, 4}, we set the activation to the hyperbolic tangent function For the third layer, we use the softplus function For the fifth layer, we use the identity The number of neurons in each layer is as follows: R (1) =500, R (2) =100, R (3) =50, R (4)=20, and R (5) =D′.

[0210] Implement reverse mapping function C -1 The input of the decoder 504 is a channel graph of dimension D′ The output of decoder 504 corresponds to the M′-dimensional channel feature Estimation of Figure 5 As shown, decoder 504 is essentially a mirrored version of encoder 502, with the same number of neurons per layer (but in reverse order). The only difference is the activation function on the sixth layer, where we use the definition The rectified linear unit (ReLU) replaces the hyperbolic tangent.

[0211] Likewise, alternative numbers of layers, activation functions, numbers of neurons, and other parameters may be used in other embodiments.

[0212] In order to reduce the approximation error of the above deep autoencoder and obtain better TW and CT values, the weights in layer l=5 have been regularized. By using the following average approximation error, we (also called weight decay) includes a squared Frobenius norm regularization term:

[0213]

[0214] The parameter β>0 is adjusted to obtain the best performance. To learn AE, we use Tensorflow.

[0215] The main advantages of AE-based CC over PCA, SM, and SM+ are as follows: (i) AE directly produces parameter maps for the forward and back-channel mapping functions, and (ii) it can be trained efficiently even for very large datasets. The main disadvantage lies in the fact that identifying good network topology, activation function, and learning rate parameters for AE is very difficult and usually involves tedious and time-consuming trial and error by the user.

[0216]

[0066] Simulation results for illustrative embodiments of CC for the various channel models and algorithms described above will now be summarized.

[0217] As described above, simulations were performed in which we recorded the CSI for N = 2048 randomly (in addition to 234 points representing continuous curves for visualization purposes) placed spatial locations within a square area of ​​1000m × 500m; the median sampling distance measured in the spatial domain and between nearest neighbors is approximately 53 wavelengths. We acquired the CSI at an SNR of 0dB, averaged the noise over T = 10 samples, and set ρ = 16. We compare the results for the “vanilla” LoS channel (V-LoS) in (1) with an antenna spacing of λ / 2 at a carrier frequency of 2GHz with those for the Quadriga LoS (Q-LoS) and Quadriga NLoS (Q-NLoS) channels (see Table 1 for model parameters). Since the analysis described in this article shows that the feature configuration {R2M,Ant.,|·|} in the illustrative embodiment produces the most robust results in terms of CT and TW for all the above channel models, we only generate channel plots for this channel feature. For each channel map, we determined the global CT and TW values ​​measured between the spatial geometry and the channel map for the K = 0.05N nearest neighbors.

[0218] We compared the simulation results for V-LoS, Q-LoS, and Q-NLoS channel models using PCA, SM, SM+, and AE CC algorithms. We found that AE, SM, and SM achieved the highest CT and TW, while SM+ provided the most visually pleasing results.

[0219] For the channel graphs learned for PCA, SM, SM+, and AE, and the three channel models, we obtain CT values ​​between 0.91 and 0.94. This means that the neighborhood of a point in the spatial geometry is strongly preserved in the channel graph, i.e., most points that are neighboring in the spatial geometry are neighboring in the channel graph. The TW values ​​are also high, ranging between 0.84 and 0.89; this indicates that most of the neighbors of a point in the channel graph are also neighbors in the spatial geometry.

[0220] Additional findings from the simulation results are as follows:

[0221] 1. PCA produces higher CT and TW values ​​for all channel models and can also provide visually accurate spatial geometry embeddings. This behavior is due to the fact that we use channel features that represent spatial geometry well.

[0222] 2. Relative to PCA, SM produces superior CT and TW values ​​and provides excellent color gradient preservation, especially for the two LoS ​​scenarios.

[0223] 3. SM+ provides almost the same CT and TW values ​​as SM, but provides extremely well-preserved channel geometry embedding even in extremely challenging Q-NLoS scenarios.

[0224] 4.AE produces higher CT and TW values, comparable to SM / SM+, but slightly lower CT for Q-NLoS. In addition, the visual effect of the channel map is not as satisfactory as that of SM+, but it shows excellent preservation of local spatial geometry.

[0225] To further understand the quality of the learned channel graphs, we performed additional simulations where we measured the CT and TW values ​​for different neighborhood sizes (i.e., K ranging from 1 to 100). We found that for simple V-LoS channels, AE provides the best performance in terms of both CT and TW; SM and SM+ perform slightly worse, as does PCA. For more realistic QLoS scenarios, which take multipath propagation into account, the performance of AE drops significantly, while even PCA performs better. SM and SM+ again have similar performance, but perform better than the other two methods. For the most challenging scenarios, Q-NLoS, SM, and SM+ perform the best, followed by PCA. Clearly, AE still struggles to achieve high CT. This is attributed to the fact that we only trained AE on N = 2048 points. Additional adjustments to the neural network architecture and learning rate may improve AE performance.

[0226] To summarize the above simulations, AE outperforms the other algorithms in terms of TW, while SM and SM+ perform only slightly worse. However, in terms of CT, AE only works for simple LoS channels, while SM and SM+ perform better for channels generated by the Quadriga model. PCA produces surprisingly good results across the board, and for more challenging channel scenarios (Q-LoS and Q-NLoS), its performance in terms of CT is close to SM and SM+.

[0227] The above-described CC embodiments provide a novel unsupervised framework to learn the mapping between CSI acquired at a single BS and the relative transmitter (e.g., UE) location. Some embodiments extract appropriate features from a large amount of high-dimensional CSI acquired at a massive MIMO BS, followed by a CC algorithm that utilizes dimensionality reduction and / or manifold learning. Exemplary embodiments include four different CC algorithms (PCA, SM, SM+, and AE) with varying complexity, flexibility, and accuracy, which produce channel maps that preserve the local geometry of the transmitter location for a range of actual channel models. Since the channel mapping in these embodiments is unsupervised, i.e., no knowledge of the actual user location is required, such embodiments can be used in numerous applications related to 5G networks, including but not limited to rate adaptation, network planning, user scheduling, switching, cell search, user tracking, user grouping for device-to-device (D2D) communication, beam prediction for mmWave or terahertz systems, and other cognitive tasks that rely on CSI and UE movement relative to the BS.

[0228] As previously stated, these and other embodiments disclosed herein are presented by way of illustrative examples, and many alternative embodiments are possible.

[0229] For example, additional illustrative embodiments to be described below provide representations of constrained autoencoders, and associated applications in wireless positioning and other related functions in wireless systems. Although these additional embodiments are described below primarily in the context of autoencoders, it will be apparent to those skilled in the art that the disclosed arrangements can be modified in a straightforward manner for use with other dimensionality reduction techniques of the type disclosed herein.

[0230] Some of these additional embodiments are configured to utilize partial location information, i.e., for some of the channel features, we know the associated location. This information helps determine the items in the channel map, which improves localization performance. With this adjustment, the method will be semi-supervised (because some data points are now labeled).

[0231] Additionally or alternatively, we can include some side information from the CSI measurement process. For example, if the system is tracking a user that is moving in space, the CSI obtained from that user can be grouped. When learning the channel graph, we know that the associated points in the low-dimensional channel graph must be nearby because the user can only move at a limited speed. In some embodiments, this method is illustratively configured to utilize information from the measurement process, but not directly utilize location information from the UE.

[0232] These and other techniques may be used in illustrative embodiments to generate channel graphs of the type disclosed herein, which in some cases exhibit various performance improvements over one or more of the previously described arrangements.

[0233] As described above, certain applications provide additional constraints or side information that can be imposed on the low-dimensional representation. Such side information may originate from the dataset itself or from the application (e.g., from the way the data was collected). An example is acquiring data over time. In such a scenario, it is natural to enforce constraints between representations by exploiting the fact that for time-related data points, the associated low-dimensional representations should exhibit a certain degree of similarity. Another embodiment occurs in the case where a subset of the representations is known a priori, for example, when a subset of the training data is annotated. The obtained annotation information can then be converted into representation constraints, which leads to an embodiment with semi-supervised training of the AE.

[0234] An example application where representation constraints are important involves locating users in a wireless system in conjunction with CC embodiments of the type described elsewhere herein. As previously described, in some embodiments, the CC measures high-dimensional CSI of users transmitting data to a wireless access point or cell tower. By collecting CSI over time, one can train a low-dimensional representation of the AE that reflects the relative user location. Such techniques can achieve logical (or relative) positioning without access to GNSS and without expensive measurement activities.

[0235] These and other embodiments are illustratively configured to exploit various types of side information that may be available. For example, a user may only be able to move at a limited speed. This information can be included when training the AE to ensure that time-related data points are nearby in the representation space. Additionally, certain points in the space with known locations (e.g., coffee shops) can be associated with measured CSI; this helps determine a small portion of the spatial location in the representation space, allowing absolute positioning in the space. Thus, by enforcing constraints between representations, one can improve the efficiency of the AE and make the learned low-dimensional representations interpretable.

[0236] In the embodiments to be described, four different example representation constraints for AE are provided, as well as a framework for including such representation constraints during training. We propose constraints on pairwise representations where absolute or relative distances between (subsets of) representations are enforced. We formulate these constraints as non-convex regularization terms that can be easily included in existing deep learning frameworks. Our simulations show that only a small number of representation constraints are required to (often significantly) improve the representation quality of AE. As a byproduct of our framework, we demonstrate that one of the proposed constraint types enables one to learn a parametric version of the Salmon mapping that avoids the need for expensive out-of-sample expansion. The representation constraints as disclosed herein are highly effective for the above-mentioned applications of CC-based positioning in wireless systems, and can provide similar advantages in many other applications involving CC. Therefore, combining partially annotated data points with temporal constraints caused by the acquisition process can significantly improve the positioning performance of certain CC embodiments.

[0237] Certain embodiments to be described extend AE with representation constraints that further improve performance in certain applications. For example, wireless positioning provides a unique set of representation constraints derived from the acquisition process, at least a subset of which can be incorporated into AE to significantly improve CC performance and facilitate accurate positioning via CC.

[0238] Before describing example representation constraints for AE, we describe some additional aspects of AE in an exemplary embodiment to introduce further description. It should be understood that the notation used in the following description is different from that used elsewhere in this document. For example, in the following description of representation constraints for AE, certain variables referenced in the context of other embodiments described above are used in a different manner.

[0239] Assume that such an AE in the exemplary embodiment to be described takes N data points (vectors) of dimension D n=1,...,N high-dimensional data set, and learn two functions: encoder and decoder The encoder maps the data points to a low-dimensional representation n=1,...,N, where D′<<D is the dimensionality of the representation, and the decoder maps the representation back to data points, i.e. we get

[0240] y n =f e (x n ) and x n =f d (y n ),n=1,...,N.

[0241] The encoder and decoder functions of the AE are implemented as multi-layer (shallow or deep) feed-forward neural networks, which are trained to minimize the mean squared error (MSE) between the network input and output. Specifically, one seeks to minimize the following loss function:

[0242]

[0243] Here, we need to The parameters learned in is the set and The weight terms and bias terms contained in define the neural networks that form the encoder and decoder, respectively. All norms used in this article are l2 norms. Although it is well known that AE is very difficult to train, many strategies known to those skilled in the art can be used to improve the quality of training and reduce the possibility of falling into local minima.

[0244] Encoder f e The D′-dimensional output is usually smaller than the input x i is embedded in a D-dimensional manifold. Therefore, we get x n ≈f d (f e (x n )),n=1,...,N, unless the data set is D′-dimensional, and we are able to learn the underlying structure. Nevertheless, AEs usually find lower-dimensional representations with less loss They capture the inherent dimensionality of the input data vectors.

[0245] We now describe four different example representation constraints, which are summarized in Table 3 below. In the following, underlined quantities represent constant scalars or vectors that are known a priori and used during AE training. Ununderlined quantities are optimization variables.

[0246] name constraint Regularization term Fixed Absolute Distance (FAD) <![CDATA[||y i - y j ||= d i,j ]]> <![CDATA[(||y i - y j ||- d i,j ) 2 ]]> Fixed relative distance (FRD) <![CDATA[||y i -and j ||= d i,j ]]> <![CDATA[(||y i -and j ||- d i,j ) 2 ]]> Maximum Absolute Distance (MAD) <![CDATA[||y i - y j ||≤ d i,j ]]> <![CDATA[max{||y i - y j ||- d i,j ,0} 2 ]]> Maximum relative distance (MRD) <![CDATA[||y i -and j ||≤ d i,j ]]> <![CDATA[max{||y i -and j ||- d i,j ,0} 2 ]]>

[0247] Table 3: Example representation constraint summary for Ae

[0248] The fixed absolute distance (FAD) and fixed relative distance (FRD) constraints are based on ||y i -y j ||= d i,j Enforce a known distance on a pair of representations d I,J The difference between FAD and FRD constraints is that for FAD, one of the two representations, e.g. y jis a constant known before AE learning (i.e., not to be confused with the representation in the dataset); for FRD, the two representations y i and j are all optimization variables. To facilitate including these constraints in a deep learning framework, we propose to use a regularization term with generalized gradients (see Table 3). Specifically, the FAD and FRD constraints are relative to the representation y i The generalized gradient of

[0249]

[0250] It indicates y j The FAD is known. If d i,j = 0, then the FRD regularization term will benefit these two representations y i and j is equivalent to, while the FAD regularization term will try to learn a vector close to the constant y j The representation of y i Intuitively, d i,j The FAD constraint with y = 0 plays the role of a semi-supervised extension in which one knows part of the prior representation.

[0251] It should be noted that the FRD regularization term is similar to the regularization term for the Salmon map described elsewhere in this paper. In fact, it can be shown that by including the FRD regularization term on all data vectors, if we write By multiplying each FRD regularization term by a factor of , we can train a parametric AE version of the Sammon map.

[0252] The maximum absolute distance (MAD) and maximum relative distance (MRD) constraints are based on ||y i -y j ||≤d i,j Enforce a maximum a priori known distance between a pair of representations d i,j For MAD, one of the two vectors in the constraint (e.g., y j ) is a constant known a priori; for MRD, both representations are learned. We include these constraints as regularization terms with the following generalized gradients (see Table 3)

[0253]

[0254] in y jIt is known that MAD. It is obvious that maximum distance regularization terms usually produce better results than their fixed distance counterparts because they allow the AE more "degrees of freedom" when learning representations. Note that when d i,j When =0, FAD, MAD, FRD and MRD are all equal.

[0255] We implemented a stochastic optimizer using the Keras machine learning framework to minimize the sum of the AE fidelity term (1') and the regularization constraint penalty. Because the penalty term can represent a pairwise constraint involving two data points, a stochastic approximation to the regularization term is formed by randomly sampling constraints instead of data points.

[0256] To improve the numerical robustness of the generalized gradient in (2') and (3'), we use the approximation Here ρ≥0 is set to a small constant.

[0257] In addition to measuring the local neighborhood preservation properties via TW and CT, we also consider the Kruskal stress (KS), which measures the How well does the global structure in the map to the low-dimensional embedding KS is in the range of [0, 1], and smaller values ​​indicate that the global structure is better preserved. If KS = 0, the structure will be fully preserved.

[0258] The same AE topology was used for simulations for all datasets and constraints. The AE consists of three hidden layers of encoder and decoder (9, 7 and 3 neurons each with rectified linear units). The encoder output of the extracted representation consists of 2 neurons with linear activation function. The datasets were generated using well-known conventional techniques. For each dataset, we generated N = 5000 points and added a variable σ 2 = 0.05 iid zero-mean Gaussian noise.

[0259] Results show that for most datasets considered, the improvements of TW, CT, and KS only increase the representation constraints by 1%. Relative constraints often outperform absolute constraints; we attribute this to the fact that relative constraints give the AE more "degrees of freedom" to learn representations. Furthermore, we find that fixed constraints often outperform maximal constraints.

[0260] In other embodiments, alternative methods of imposing representation constraints may be used. We note that the dataset itself provides tentative distances in the representation set, and incorporate these distances as Samon map constraints on the AE. To this end, we use the FRD regularization term and as described above d i,j -1The AE augmented with the Sammon mapping is scaled by the corresponding factor of . Such Sammon augmented AEs trained on the same dataset used previously are simulated and the TW and CT values ​​are determined for K = 250 (5% of the dataset). It is found that the AE augmented with the Sammon mapping function can almost perfectly represent the manifold underlying each dataset, with some exceptions for specific datasets. It is important to note that the proposed representation constraints are obtained directly from the dataset itself and enable the design of a parametric version of the Sammon mapping that advantageously avoids out-of-sample expansion.

[0261] We now describe an example of the application of representation constraints in wireless positioning. In particular, we exploit representation constraints that naturally arise from the data and the application itself to expand the illustrative embodiment of the CC's unsupervised user positioning. As described elsewhere in this document, in some embodiments, the CC measures CSI from users at different spatial locations and learns a low-dimensional channel graph that locally preserves the geometry of the original space. More specifically, users that are nearby in physical space will also be placed nearby in the channel graph, and vice versa - without preserving the global geometry. In this framework, high-dimensional features are extracted from the CSI and then processed with a dimensionality reduction method to obtain a low-dimensional channel graph. The illustrative embodiment of the CC operates in an unsupervised manner, for example, learning is based only on CSI passively collected at the infrastructure BS (and is necessary for data detection and precoding anyway), but over time from multiple user locations in the service area. CC advantageously facilitates a variety of location-based applications in wireless systems because it provides BS providers with relative user location information without having to access GPS or fingerprinting methods that require expensive measurement activities.

[0262] In some CC embodiments described previously, SM and AE are used to learn channel graphs. While SM shows good performance, AE scales well to large problems and provides a parameterized mapping that allows one to map new, unseen CSI features to relative position information. In addition to these advantages of AE, valuable side information generated from the application itself can also be used as representation constraints for AE. Compared to SM, conventional AE does not enforce any geometric structure on its representation. However, by tracking a user's CSI over time, the corresponding low-dimensional representation reflecting the user's location should be similar due to the speed constraint.

[0263] Therefore, some exemplary embodiments impose MAD constraints on pairs of representations from users over time to ensure that nearby spatial locations are used for nearby representations. We can estimate an upper bound on the maximum distance in the representation space based on measuring CSI acquisition times. Note that this information comes from the CSI measurement process and the fact that we know how to collect data in real systems. This approach of utilizing MAD constraints is still passive because no supervision or measurement activities are necessary.

[0264] Furthermore, to enable true positioning capabilities using CC, we unroll the channel graph using so-called anchor vectors, i.e. points in space for which we know both the CSI and the true position. One can imagine measuring the CSI at a small number of locations when setting up a new BS. With this information, we can use d i,j = 0 imposes a FAD representation constraint on AE to enforce accurate anchor locations. We note that including such constraints results in a semi-supervised version of CC (and AE, in general) and requires minimal measurement activity. However, we emphasize that compared to conventional fingerprinting methods that are fully supervised and need to be trained in space at wavelength resolution, we only require a small number of anchor vectors and use the rest of the (unlabeled) data to improve the localization accuracy of the channel map.

[0265] Simulations were performed for illustrative embodiments of CC with representation constraints and compared to corresponding simulations of those CC embodiments without representation constraints as described elsewhere in this document. We found that utilizing only a small portion of the representation constraints can produce significant improvements in TW, CT, and KS. We also found that there is a trade-off in preserving the properties of the neighborhood. More specifically, an increase in TW means that we introduce fewer "false values" near neighboring elements, and a decrease in CT means that the original neighborhood in the original space is not preserved as much in the channel graph as before. Regarding global geometry, we found that for all AEs with representation constraints, KS is significantly improved; this means that including constraints enables us to recover global geometry. This is especially true in the simulation results for AEs that include both FAD constraints (anchor vectors) and MAD constraints (to enforce continuity of the user's motion over time). Finally, we found that propagation conditions do not substantially affect the performance of CC.

[0266] As is apparent from the foregoing, some exemplary embodiments use side information about user motion and anchor vectors to improve the localization performance of the CC. Numerical results of example localization applications show that easy-to-use representation constraints can produce significant improvements in the recovered global geometry in wireless localization scenarios.

[0267] In other embodiments, additional aggregation constraints may be included, such as when CSI is acquired from multiple cell towers or access points.

[0268] Likewise, although representation constraints are primarily described in the context of AE, similar techniques may be applied using other types of dimensionality reduction, including those described elsewhere herein.

[0269] Reference now Figure 6, showing a number of example uses of channel mapping in an illustrative embodiment. These are considered to be illustrative examples of arrangements in which a channel map generated in the manner described above is used to estimate at least one location-dependent characteristic of one or more wireless devices in the actual spatial geometry of a wireless channel.

[0270] In the upper portion of the accompanying drawings, an example of a prediction of an event in a cell of a wireless system is shown, such as predicting when a particular wireless device will leave the cell. In the present example, this more particularly includes estimating location information of a given wireless device. At times t1 and t2, the wireless device (e.g., UE) is at a specific location within the spatial geometry of a given cell. These correspond to corresponding points in a low-dimensional representation provided by a channel graph. In this example, the prediction of an event within the cell illustratively involves using a low-dimensional representation provided by a channel graph to predict the location where the wireless device will be at a future time t3. As shown, this illustratively involves a prediction based on a channel graph that the wireless device will have left a given cell at time t3.

[0271] In the middle part of the figure, an example of estimating CSI between a given wireless device and one or more base stations in one or more cells in a wireless system other than the current cell of the given wireless device is shown. This is an example referred to as estimation of other cell CSI in the figure, and includes supplementing CSI 1 from a first cell currently including the given wireless device with another estimated cell CSI 2 from a second cell other than the current cell of the given wireless device. The estimated another cell CSI 2 is determined by using a channel map.

[0272] In the lower part of the figure, an example of estimating CSI between a given wireless device and at least one other wireless device (illustratively in the same cell of the wireless system) is shown. This is an example referred to as estimation of inter-UE CSI in the figure, and includes supplementing CSI 1 and CSI 2 of the corresponding first and second wireless devices in a given cell with inter-UE CSI 12 of the second wireless device due to the first wireless device. The estimated inter-UE CSI 12 is determined by using a channel map.

[0273] In such Figure 6 In some estimation scenarios such as those depicted in , using a channel map to estimate at least one location-related characteristic of one or more wireless devices in an actual spatial geometry of a wireless channel illustratively includes: extracting additional channel features from additional CSI characterizing the radio geometry of the wireless channel, comparing the additional channel features to the channel map, and estimating the location-related characteristic based at least in part on a result of the comparison.

[0274]

[0066] Channel maps generated in the manner disclosed herein may be used to implement various other use cases within a wireless system.

[0275] For example, in some embodiments, a channel map generated in the manner disclosed herein is used for RAN optimization or for facilitating other types of RAN management functions.

[0276] In some embodiments, network event anticipation mapping can be used to anticipate events in the network. Once the BS has a channel map, it can roughly locate the user in the map. By marking the map based on previous events in the cell (such as switching to a given neighboring cell), the BS can identify upcoming events, for example, the user is moving towards another cell. Therefore, when the user is observed to be moving towards a point in the map marked with a switching event to the neighboring cell, the network can proactively prepare for events such as switching. This would be a particularly good solution for ultra-reliable communications, where communication interruptions can be anticipated and reliability can be ensured by taking proactive actions.

[0277] When the network expects the user to be moving towards a location with poor coverage based on the channel map, it can also proactively schedule traffic to the user. Alternatively, scheduling can be postponed when the network expects the user to be moving towards a location with high data rate coverage (such as a small cell or WiFi hotspot) based on the channel map. In these and other applications, in addition to feature extraction at the serving BS and related processing of the channel map, the mapping function can be used to anticipate events without any other measurements. By using multi-point mapping, the exact quality of the channels of other cells can also be predicted.

[0278] In mmWave networks, mobile users must not only find neighboring cells, but also neighboring beams. In a BS with a large number of antennas, a large number of narrow beams must be transmitted so that mobile users can find cells and beams. The conventional solution is to select a set of beams and use them to transmit at the same time at once, hoping that the user approaching the cell will find one of these beams. Through channel mapping, the donor BS observes that the user is moving towards the cell boundary and towards the point in the map where the user earlier switched to a specific target cell. In a beam-based cell search method, the BS can additionally mark the map with the beam in the target cell to which the user has switched. Now, the donor knows both the target cell and the beam in the target cell without any neighboring cell measurements. The network can use this to activate only certain beams for transmission in the target cell-the target cell knows the beam that the user is entering from the donor cell. Here, since no transmission is required to obtain the beam identification in the target cell, channel mapping is used to provide CSI that is not available in other ways.

[0279] Channel mapping can also be used to accurately identify the location of small cells or WiFi access points. Such arrangements can be directly used for integrated multi-band operation. An umbrella macro cell providing coverage can determine when a second smaller cell connection is available through the marked channel map without the need to make excessive measurements on the high frequency carrier of the small cell. Similarly, in CP / UP separation, the control plane connection will remain to the umbrella macro cell, which will use marked mapping to determine which cell will provide service to the user plane. Given the separated uplink and downlink, the required multi-point CSI can also be anticipated through the multi-point channel mapping function without the need for excessive measurements.

[0280] Channel mapping can be similarly used to manage BS activity. For example, if a BS has been turned off to save energy, there is no information available on the network to accurately estimate whether turning on the BS would be beneficial. Consider a situation where cell A covers a wide area, and a small cell B is turned off within the coverage area of ​​A. Through channel mapping, BS A can know that certain users are in the area of ​​this cell and would be served by B if B were turned on. Through multi-point channel mapping, BS A can even know the channel quality between such users and BS B, effectively estimating the CSI that would otherwise be unavailable. Based on this information, the network can estimate whether turning on BS B, which has been turned off, would be beneficial to network energy efficiency.

[0281] In other embodiments, channel mapping as disclosed herein is used to implement inter-cell interference alignment and cancellation (ICIAC). ICIAC is a network-wide physical layer optimization that has not yet been supported by the industry due to the considerable cost of obtaining CSI. However, channel mapping as disclosed herein can be used to provide the required information. It should be noted in this regard that interference alignment and interference cancellation have opposite goals. In interference alignment, interference to certain subspaces of the receiver is minimized, leaving the user with interference-free portions of the channel. For interference cancellation, it is important that the interference victim receives the dominant interfering signal on a channel that is stronger than the desired signal to achieve cancellation. Channel mapping makes the combined view of these methods feasible in practice.

[0282] Massive MIMO technology brings both challenges and opportunities to interference considerations. On the one hand, the processing / implementation complexity increases due to the need for large data management. On the other hand, very high-dimensional antenna arrays ensure highly directional channel vectors, which can be modeled with Gaussian vectors with a small number of principal eigenvectors (e.g., principal eigenvectors of the corresponding Wishart matrix). Therefore, massive MIMO ensures directional beamforming that achieves simultaneous spatial multiplexing of intended users and mitigates interference to unintended users. This can be accomplished by zeroing certain spatial directions. By using channel mapping information as disclosed herein, zeroing can be performed more efficiently based on knowledge of the mean and covariance information of the interfering channel.

[0283] Depending on the available CSI, users can be assigned to a set of base stations where ICIAC is performed. Resources are allocated to logical entities that control these sets. Based on the metrics derived from the channel mapping function, a column generation method can be used to find a set of valid logical entities.

[0284] ICIAC technology can be viewed as a control algorithm for a complex dynamic system. Reliable and efficient operation of such a system has controllability (i.e., the ability to bring the wireless network into a target state via appropriate control actions) and stability (i.e., robustness to interference). In the case of imperfect input data, the network may become uncontrollable and / or unstable. Therefore, analyzing the controllability and stability of the ICIAC algorithm with imperfect and / or incomplete CSI represented by the channel mapping function is important for network management.

[0285] Channel mapping in the illustrative embodiments can also be used to facilitate multi-connectivity in mmWave networks. Multi-connectivity is beneficial in mmWave networks due to spotty coverage and obstruction by, for example, human bodies. In NLoS channels, the path loss in mmWave frequencies is estimated to be 20 dB higher than the path loss in LoS channels. For this reason, multi-connectivity is critical for reliable mmWave connections in areas where users are in cell boundary areas, where blocking events may disrupt service. Consider, by way of example, a continuous coverage ultra-dense network (UDN) mMIMO mmWave layer, where multi-connectivity is applied to ensure continuity of service. Multi-connectivity in mmWave networks is further complicated by the extreme angular selectivity of mMIMO mmWave devices. If a UE close to a cell boundary is blocked by a human body or other obstacle from cell i, the channel toward cell j may be quite good, but the channel toward cell i may be so weak that handover preparation is not possible. If the blocking configuration changes suddenly, the situation may be reversed.

[0286] In the exemplary embodiment, this problem is solved by using a multi-point mapping function. The mapping function achieves reconnectivity, i.e., the CSI towards both i and j is known, regardless of the blocking conditions. Note that in this case, the blocking probability is part of the feature space considered by the mapping function.

[0287] Some embodiments are configured such that the network is managed as a collection of user-centric intersection graphs provided by channel mapping. For each user, there is a set of active BSs, and beams within those BSs. Each active set is managed by a logical controller that controls how the user is served.

[0288] The foregoing are merely examples of RAN optimization and other network management functions facilitated by using channel maps as disclosed herein, and many other use cases are possible.

[0289] Figure 7 An exemplary process is shown, which illustratively utilizes at least in part such as Figure 2B The mapping entity 205 or Figure 3 The mapping entity 305 of FIG. 304 may be implemented as a mapping entity such as Figure 1 At least a portion of a processing platform such as processing platform 104 of an embodiment. It should be understood that this particular process is merely an example, and in other embodiments, additional or alternative processes may be performed at least in part by a channel mapping entity including wireless system components or other types of processing platforms.

[0290] In this embodiment, the process illustratively includes steps 700 to 706. As noted above, it is assumed that at least a portion of these steps are performed at least in part by a channel mapping entity of the type described elsewhere herein.

[0291] In step 700, channel features are extracted from CSI that characterizes the radio geometry of a wireless channel.

[0292] In step 702, a forward mapping function is generated that maps the extracted channel characteristics to a channel map in a representative spatial geometry of a wireless channel.

[0293] In step 704, the channel map is utilized to estimate at least one location-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel.

[0294] In step 706, it is determined whether there are one or more additional location-dependent characteristics to be estimated in the current processing interval. If there is at least one such location-dependent characteristic to be estimated in the current processing interval, the process returns to step 704 to estimate the one or more location-dependent characteristics to be estimated using the channel map. Otherwise, the process returns to step 700 to extract channel features from the additional CSI, and then updates the forward mapping function used to obtain the channel map in step 702. Therefore, Figure 7 The process is illustratively configured to collect CSI over a plurality of processing intervals and to update a forward mapping function in one or more of the plurality of processing intervals.

[0295] In an exemplary embodiment, many other techniques may be used in association with the generation and processing of a channel map.For example, an alternative process may utilize predictions or other types of estimates generated using a channel map to initiate various types of automated actions in a wireless system.

[0296] Therefore, combined with Figure 7 The specific processing operations and other functions described in the flowcharts are presented only by way of illustrative examples and should not be interpreted in any way as limiting the scope of the invention. Alternative embodiments may use other types of processing operations involving channel graphs. For example, in other embodiments, the order of the process steps may be changed, or certain steps may be performed concurrently with each other rather than in series. Moreover, multiple instances of the process may be performed in correspondingly different base stations or other wireless system components and / or for correspondingly different sets of one or more wireless devices.

[0297] It should be recognized that the above combination Figures 3 to 7 The specific CC algorithms, parameters, and other arrangements described are presented by way of illustrative examples only, and various alternative channel mapping implementations may be used in other embodiments.

[0298] For example, other embodiments may utilize additional or alternative channel features that are particularly resilient to masking, as well as more advanced CC algorithms, such as methods that rely on metric learning or convolutional neural networks that take into account side information. Other possible extensions include the use of semi-supervised methods. Relative to the illustrative embodiments, other embodiments may also be specifically configured to address time-varying channels, multi-user scenarios, and other variations.

[0299] A given processing platform or other system component implementing one or more channel mapping operations is illustratively configured by utilizing a corresponding processing device comprising a processor coupled to a memory. The processor executes software program code stored in the memory to control the performance of the processing operations and other functions. The processing device also includes a network interface that supports communication over one or more networks.

[0300] The processor may include, for example, a microprocessor, an ASIC, an FPGA, a CPU, a GPU, an ALU, a DSP, or other similar processing device components, as well as other types and arrangements of processing circuitry in any combination. For example, such circuitry may be used to implement a given module or set of modules configured to perform one or more channel mapping operations in a processing device as disclosed herein.

[0301] The memory stores software program code for execution by the processor in implementing part of the functionality of the processing device. A given such memory storing such program code for execution by the corresponding processor is an example of what is more generally referred to herein as a processor-readable storage medium (with program code contained therein), and may include, for example, electronic memory (such as SRAM, DRAM or other types of random access memory), ROM, magnetic storage, optical storage, non-volatile memory or other types of storage devices in any combination.

[0302] Articles of manufacture that include such processor-readable storage media are considered embodiments of the present invention.The term "article of manufacture" as used herein should be understood to exclude transitory, propagating signals.

[0303] In other embodiments, other types of computer program products including processor-readable storage media may be implemented.

[0304] Additionally, embodiments of the present invention may be implemented in the form of an integrated circuit including processing circuitry configured to perform processing operations associated with channel mapping and other related functions.

[0305] The processing device in a given embodiment may include, for example, a computer or other type of processing hardware and associated software and firmware implemented in a base station, RRH, BBU, or other component of a wireless system.

[0306] One or more processing platforms, or portions thereof, may be used to implement a wireless system and / or an information processing system as disclosed herein.

[0307] For example, an illustrative embodiment of a processing platform that can be used to implement at least a portion of a wireless system and / or information processing system includes a cloud infrastructure that includes virtual machines implemented using a hypervisor running on a physical infrastructure. Such virtual machines can include corresponding processing devices that communicate with each other through one or more networks. As a more particular example of this type of arrangement, a virtual machine can be used to implement wireless system components, such as RRHs and BBUs of Cloud-RAN. Many other wireless system components can be implemented at least in part using virtual machines or other types of virtualized infrastructure.

[0308] The cloud infrastructure in such an embodiment may further include one or more groups of applications running on corresponding ones of the virtual machines under the control of the hypervisor. Multiple hypervisors may also be used, each hypervisor providing a group of virtual machines using at least one underlying physical machine. Different groups of virtual machines provided by one or more hypervisors may be used to configure multiple instances of various components of the wireless system and / or the information processing system.

[0309] Additionally or alternatively, operating system-level virtualization technology based on Linux control groups can be used. Such arrangements illustratively include Docker containers or other types of Linux containers. Similarly, such containers can be used to implement wireless system components, such as RRHs and BBUs of Cloud-RAN.

[0310] Another exemplary embodiment of a processing platform that can be used to implement at least a portion of a wireless system and / or information processing system as disclosed herein includes multiple processing devices that communicate with each other through at least one network. It is assumed that each processing device of the processing platform includes a processor coupled to a memory.

[0311] Again, these specific processing platforms are presented by way of example only, and the wireless system and / or the information handling system may include additional or alternative processing platforms, as well as many different processing platforms in any combination, with each such platform including one or more computers, servers, storage devices or other processing devices.

[0312] For example, instead of or in addition to a virtualization infrastructure including a virtual machine, other processing platforms for implementing embodiments of the present invention may include a different type of virtualization infrastructure. Thus, in some embodiments, system components may run at least partially in a cloud infrastructure or other type of virtualization infrastructure.

[0313] It should therefore be understood that in other embodiments, different arrangements of additional or alternative elements may be used.At least a subset of these elements may be implemented together on a common processing platform, or each such element may be implemented on a separate processing platform.

[0314] Moreover, many other arrangements of computers, servers, storage devices or other components are possible in a wireless system and / or associated information processing system. Such components may communicate with other components via any type of network or other communication medium.

[0315] As previously mentioned, the components of a given system as disclosed herein may be implemented at least in part in the form of one or more software programs stored in a memory and executed by a processor of a processing device. For example, certain functions associated with a channel mapping component of a wireless system and / or an associated information processing system may be implemented at least in part in the form of software.

[0316] The specific configurations of the wireless systems and / or information handling systems described herein are exemplary only, and a given such system in other embodiments may include other elements in addition to or in place of those specifically shown, including one or more elements of the type that are common in conventional implementations of such systems.

[0317] For example, in some embodiments, wireless systems and / or information handling systems may be configured to utilize the disclosed techniques in other contexts to provide additional or alternative functionality.

[0318] Thus, the techniques illustrated in some embodiments herein in the context of providing a channel mapping function in a 5G wireless system may be modified in a straightforward manner for use in other contexts involving different types of wireless systems.

[0319] Thus, the exemplary embodiments of the present invention should not be construed as limited to use with 5G wireless systems or any other particular type of wireless system or its associated processing context.

[0320] It should also be appreciated that the specific processing steps used in the embodiments described herein are exemplary only, and other embodiments may utilize different types and arrangements of processing operations. For example, certain processing steps described as being performed serially in the illustrative embodiments may be performed at least partially in parallel with each other in other embodiments.

[0321] It should be emphasized again that the embodiments of the present invention as described herein are intended to be illustrative only. Other embodiments of the present invention may be implemented using wireless systems, information processing systems and / or processing devices of various types and arrangements compared to those utilized in the specific illustrative embodiments described herein, and may be implemented in many alternative processing contexts. In addition, the specific assumptions made herein in the context of describing certain embodiments need not apply to other embodiments. These and many other alternative embodiments will be apparent to those skilled in the art.

Claims

1. A device comprising: a processing platform comprising one or more processing devices, each processing device including at least one processor coupled to a memory; The processing platform is configured to: extracting channel characteristics of a wireless channel of the wireless system from channel state information characterizing a radio geometry of the wireless channel; In an unsupervised learning process, a learned forward mapping function is generated, wherein the learned forward mapping function performs a dimensionality reduction technique to map the extracted channel features to a channel graph of a lower dimensional representative spatial geometry characterizing the wireless channel, wherein The dimensionality reduction technique performed by the learned forward mapping function is applied to the extracted channel features as part of the unsupervised learning process, the dimensionality reduction technique being configured to map a relatively high-dimensional set of points of the extracted channel features to a relatively low-dimensional set of points of the channel map; as well as The channel graph generated using the learned forward mapping function is utilized to estimate at least one position-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel.

2. The apparatus of claim 1, wherein the channel state information is generated by one or more multi-antenna receivers of the wireless system using communications received from the one or more wireless devices over the wireless channel.

3. The apparatus of claim 2, wherein the channel state information comprises channel measurements collected over time by a given one of the multiple antenna receivers from a plurality of wireless device transmission locations in a specified area of ​​the wireless system.

4. The device of claim 3, wherein the designated area comprises one of: a serving cell of a base station, the base station including the given multi-antenna receiver; and A multi-cell area is covered by a baseband unit of a cloud radio access network.

5. The apparatus of claim 1, wherein generating the forward mapping function comprises performing the unsupervised learning process to learn the forward mapping function from the extracted channel features.

6. The apparatus of claim 5, wherein the unsupervised learning process utilizes side information obtained from a baseband unit of the wireless system.

7. The apparatus of claim 6, wherein the side information obtained from the baseband unit comprises information indicating that a particular subset of the extracted channel characteristics is associated with a particular one of the one or more wireless devices.

8. The apparatus of claim 1, wherein at least a portion of the extracted channel features characterizes at least one of large-scale fading effects, directional information, and time-of-flight information of the wireless channel.

9. The apparatus of claim 1, wherein the representative spatial geometry characterized by the channel map has a substantially lower dimensionality than the radio geometry of the wireless channel.

10. The apparatus according to claim 1, wherein the channel map is configured to preserve the local geometry of multiple spatial positions associated with the extracted features in the actual spatial geometry of the wireless channel, so that a first point and a second point that are close to each other in the actual spatial geometry of the wireless channel are also close to each other in the channel map, or so that a first point and a second point that are far from each other in the actual spatial geometry of the wireless channel are also far from each other in the channel map.

11. The apparatus of claim 1, wherein the processing platform is further configured to generate an inverse mapping function that relates spatial locations in the representative spatial geometry of the wireless channel to channel characteristics of the wireless channel.

12. The apparatus of claim 11, wherein generating the inverse mapping function comprises performing an unsupervised learning process to learn the inverse mapping function from the representative spatial geometry.

13. The apparatus of claim 12, wherein fully unsupervised learning is performed to generate both the forward mapping function and the reverse mapping function.

14. The apparatus of claim 1 , wherein utilizing the channel map to estimate at least one location-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel comprises at least one of: estimating location information of a given wireless device; predicting an intra-cell event involving the given wireless device; estimating channel state information between the given wireless device and one or more base stations in one or more cells of the wireless system other than a current cell of the given wireless device; as well as Channel state information between the given wireless device and at least one other wireless device is estimated.

15. The apparatus of claim 1 , wherein utilizing the channel map to estimate at least one location-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel comprises: extracting additional channel features from additional channel state information characterizing the radio geometry of the wireless channel; comparing the additional channel characteristics to the channel map; as well as The position-dependent characteristic is estimated based at least in part on a result of the comparing.

16. The device of claim 1, wherein the processing platform comprises at least one of: A base station of the wireless system; a baseband unit of a cloud radio access network of the wireless system; A wireless access point of the wireless system; and A given one of the one or more wireless devices of the wireless system.

17. A method comprising: extracting channel characteristics of a wireless channel of the wireless system from channel state information characterizing a radio geometry of the wireless channel; generating, in an unsupervised learning process, a learned forward mapping function that performs a dimensionality reduction technique to map the extracted channel features to a channel graph of a lower dimensional representative spatial geometry characterizing the wireless channel, wherein the dimensionality reduction technique performed by the learned forward mapping function is applied to the extracted channel features as part of the unsupervised learning process, the dimensionality reduction technique being configured to map a relatively high dimensional set of points of the extracted channel features to a relatively low dimensional set of points of the channel graph; and estimating at least one position-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel using the channel map generated using the learned forward mapping function; Wherein the method is performed by a processing platform comprising at least one processing device, the at least one processing device comprising a processor coupled to a memory.

18. The method of claim 17, wherein generating the forward mapping function comprises performing the unsupervised learning process to learn the forward mapping function from the extracted channel features.

19. The method of claim 17, wherein the channel map is configured to retain local geometries of a plurality of spatial positions associated with the extracted features in the actual spatial geometry of the wireless channel, such that a first point and a second point that are close to each other in the actual spatial geometry of the wireless channel are also close to each other in the channel map, or such that a first point and a second point that are far from each other in the actual spatial geometry of the wireless channel are also far from each other in the channel map.

20. A computer program product comprising a non-transitory processor-readable storage medium having program code of one or more software programs stored therein, wherein when executed by at least one processing device of a processing platform, the program code causes the processing platform to: extracting channel characteristics of a wireless channel of the wireless system from channel state information characterizing a radio geometry of the wireless channel; In an unsupervised learning process, a learned forward mapping function is generated, wherein the learned forward mapping function performs a dimensionality reduction technique to map the extracted channel features to a channel graph of a lower dimensional representative spatial geometry characterizing the wireless channel, wherein The dimensionality reduction technique performed by the learned forward mapping function is applied to the extracted channel features as part of the unsupervised learning process, the dimensionality reduction technique being configured to map a relatively high-dimensional set of points of the extracted channel features to a relatively low-dimensional set of points of the channel map; as well as The channel graph generated using the learned forward mapping function is utilized to estimate at least one position-dependent characteristic of one or more wireless devices in an actual spatial geometry of the wireless channel.

21. The computer program product of claim 20, wherein generating the forward mapping function comprises performing the unsupervised learning process to learn the forward mapping function from the extracted channel features.

22. The computer program product of claim 20, wherein the channel map is configured to preserve local geometries of a plurality of spatial positions associated with the extracted features in the actual spatial geometry of the wireless channel, such that a first point and a second point that are close to each other in the actual spatial geometry of the wireless channel are also close to each other in the channel map, or such that a first point and a second point that are far from each other in the actual spatial geometry of the wireless channel are also far from each other in the channel map.

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