Determining a precoder for transmission via a wireless channel

Abstract

Embodiments include methods for determining a precoder. Such methods include determining (930) a plurality of scalar products based on a plurality of complex channel vectors that represent a wireless channel at a first time. The scalar products are based on respective different combinations of one of the complex channel vectors and a complex conjugate of the same or a different complex channel vector. Such methods include determining (940) one or more predicted feature vectors to represent the wireless channel at a second time after the first time, based on: one or more feature vectors derived from the plurality of scalar products, and for each of at least one third time before the first time, one or more previous feature vectors that represent the wireless channel at the third time. Such methods include, based on the predicted feature vectors, determining (960) a precoder for a transmission via the wireless channel at the second time.

Description

[0001] P106755W001

[0002] DETERMINING A PRECODER FOR TRANSMISSION VIA A WIRELESS CHANNEL

[0003] TECHNICAL FIELD

[0004] The present disclosure relates generally to wireless networks, and more specifically to techniques for determining appropriate precoders for multiple-input multiple-output (MIMO) transmissions via a wireless channel during a future time interval.

[0005] BACKGROUND

[0006] Currently the fifth generation (“5G”) of cellular systems, also referred to as New Radio (NR), is being standardized within the Third-Generation Partnership Project (3GPP). NR is developed for maximum flexibility to support multiple and substantially different use cases. These include enhanced mobile broadband (eMBB), machine type communications (MTC), ultra-reliable low latency communications (URLLC), side-link device-to-device (D2D), and several other use cases. NR was initially specified in Release 15 (Rel-15) and continues to evolve through subsequent releases.

[0007] In addition to providing coverage via cells as in earlier generations, NR networks also provide coverage via “beams.” In general, a downlink (DL, i.e., network to UE) “beam” is a coverage area of a network-transmitted reference signal (RS) that may be measured or monitored by a UE. In NR, for example, RS can include any of the following: synchronization signal / PBCH block (SSB), channel state information RS (CSI-RS), tracking reference signals (or any other sync signal), positioning RS (PRS), demodulation RS (DMRS), phase-tracking reference signals (PTRS), etc.

[0008] 5G / NR networks are expected to operate at higher frequencies such as 25-60 GHz, which are typically referred to as “millimeter wave” or “mmW” for short. Such systems are also expected to utilize multi-antenna technology at the transmitter, the receiver, or both. In general, multiantenna technology can include a plurality of antenna elements (“antenna array”) combined with advanced signal processing techniques. Multi-antenna technology can be used to improve various aspects of a communication system, including system capacity (e.g, more users per unit bandwidth per unit area), coverage (e.g, larger area for given bandwidth and number of users), and increased per-user data rate (e.g, in a given bandwidth and area).

[0009] Availability of multiple antennas at the transmitter and / or the receiver can be utilized in different ways to achieve different goals. For example, multiple antennas at the transmitter and / or the receiver can be used to shape or “form” the overall antenna beam (e.g., transmit and / or receive beam, respectively) in a certain way, with the general goal being to improve the received signal-to-interference-plus-noise ratio (SINR) and, ultimately, system capacity and / or coverage. This can be done, for example, by maximizing the overall antenna gain in the direction of the target receiver P106755W001

[0010] or transmitter or by suppressing specific dominant interfering signals. More specifically, the transmitter and / or receiver can determine an appropriate weight for each antenna element in an antenna array so as to produce one or more beams, with each beam covering a particular range of azimuth and elevation relative to the antenna array.

[0011] In relatively good channel conditions, the capacity of the channel becomes saturated such that further SINR improvement provides limited capacity improvements. In such cases, using multiple antennas at both the transmitter and the receiver can be used to create multiple parallel communication "channels" over the radio interface. This can facilitate a highly efficient utilization of both the available transmit power and the available bandwidth resulting in, e.g., very high data rates within a limited bandwidth without a disproportionate degradation in coverage. These techniques are commonly referred to as “spatial multiplexing” or multiple-input, multiple-output (MIMO) antenna processing.

[0012] Accordingly, spatial multiplexing is a key feature to increase the spectral efficiency and / or capacity of wireless systems, including 5G / NR. Transmitting multiple layers on the same time-frequency resource can increase the data-rate for a single user (referred to as “SU-MIMO”). Alternatively, transmitting multiple layers on the same time-frequency resource to multiple users (referred to as “MU-MIMO”) can increase the system capacity in number of users. In general, the number of antennas required for a MIMO system can be readily determined based on a desired throughput, spectral efficiency, and / or traffic load.

[0013] In general, a base station transmitter must employ some type of MIMO precoding to be able to utilize its antenna arrays to achieve these performance gains. The base station can derive the precoding based on knowledge of the channel from each transmit antenna to each UE receive antenna. For example, a UE can measure amplitude and phase of received downlink (DL) RS (e.g., CSI-RS, DM-RS) and send information derived from these measurements to the RS transmitter (e.g., base station) as “channel state information” (CSI). For example, CSI can include transmission parameters recommended for the channel based on the channel measurements.

[0014] Alternately or additionally, the base station receiver can measure amplitude and phase of uplink (UL) RS (e.g., SRS) transmitted by the UE via the channel, from which it infers CSI for the DL channel based on an assumption of UL-DL channel reciprocity. This approach is particularly beneficial for time division duplexing (TDD) arrangements in which UL and DL are on the same frequency.

[0015] Based on CSI received from the UE and / or measured on the UL, the base station derives a precoder to be applied to a next DL MIMO transmission to the UE.

[0016] Even so, there are several causes of performance degradation in actual MIMO systems, such as in 5G networks. One major cause of performance degradation is that the channel may P106755W001

[0017] change faster than the frequency of UE CSI feedback or base station UL measurements. In other words, the CSI is out-of-date and inaccurate when it is used to determine precoding for the next DL transmission. The time variance of the channel is due to mobility the UE introducing Doppler spread and changes to channel impulse response as the UE location changes.

[0018] Another cause of performance degradation in actual MIMO systems is hardware impairments in the transmitter and / or receiver, such as phase noise, active and passive intermodulation distortion, in-phase and quadrature imbalance, manufacturing imperfections, etc. In general, these impairments may make the UL-DL channel reciprocity assumption invalid by introducing an effect that is only present in one direction (e.g., UL), or by introducing different effects in each direction.

[0019] As a more specific example, when a UE switches from DL reception to UL transmission (or vice versa) in TDD, a random phase change will be generated by the UE radio components. If the UE then transmits UL RS over the wireless channel, the base station’s channel measurements - and any MIMO precoder derived therefrom - will include this random phase change.

[0020] SUMMARY

[0021] However, this can cause various problems, issues, and / or difficulties when the base station relies on multiple channel estimates to track evolution of the wireless channel. Tracking evolution of the channel is important for predicting future CSI, which can be used to combat the problem of using out-of-date CSI to determine MIMO precoders.

[0022] For example, adjacent (e.g., in time) channel estimates may be based on different random phase changes by the UE, caused by respective DL-UL or UL-DL switches in TDD. In such case, the phase coherency between adjacent channel measurements are corrupted, making these measurements non-coherent. As such, when applied to non-coherent rather than expected coherent channel measurements, the channel prediction algorithms used by the base station may fail to predict accurate CSI for the DL channel due to inaccurate modeling of how the DL channel evolves over time. Existing techniques for addressing this situation have been found to be inadequate.

[0023] An object of embodiments of the present disclosure is to improve determination of precoders based on predicted CSI or other channel-related information, such as by providing, enabling, and / or facilitating solutions to overcome exemplary problems summarized above and described in more detail below.

[0024] Embodiments include methods e.g., procedures) for determining a precoder for a transmission by a second node to a first node via a wireless channel. For example, these exemplary methods may be performed by a network node. P106755W001

[0025] These exemplary methods include determining a plurality of scalar products based on a plurality of complex channel vectors that represent the wireless channel at a first time. The plurality of scalar products are based on respective different combinations of the following: one of the complex channel vectors, and a complex conjugate of the same or a different one of the complex channel vectors. These exemplary methods also include determining one or more predicted feature vectors to represent the wireless channel at a second time after the first time, based on the following: one or more feature vectors derived from the plurality of scalar products, and for each of at least one third time before the first time, one or more previous feature vectors that represent the wireless channel at the third time. These exemplary methods also include, based on the one or more predicted feature vectors, determining a precoder for a transmission by the second node via the wireless channel at the second time.

[0026] In some embodiments, the plurality of scalar products include the following:

[0027] • a plurality of first scalar products corresponding to the plurality of complex channel vectors, wherein each first scalar product is determined based on a corresponding complex channel vector and its complex conjugate; and

[0028] • a plurality of second scalar products corresponding to different pairs of the plurality of complex channel vectors, wherein each second scalar product is determined based on one complex channel vector of the corresponding pair and a complex conjugate of the other complex channel vector of the corresponding pair.

[0029] In some embodiments, the transmission by the first node at the second time is non-phase-coherent with one or more previous transmissions by the first node, on which the plurality of complex channel vectors are based. In such case, the determined plurality of scalar products represent the wireless channel independent of the non-phase-coherence. Put differently, the forming of the scalar products may eliminate the non-phase coherence between the transmission at the first time and the one or more previous transmissions by the first node.

[0030] In some embodiments, the plurality of complex channel vectors correspond respectively to a plurality of second antenna ports of the second node (i.e., one complex channel vector per second antenna port). Each complex channel vector includes channel estimates of the wireless channel from a plurality of first antenna ports of the first node to the corresponding second antenna port (i.e., each element of a complex channel vector is a channel estimate of the wireless channel from a particular first antenna port to a corresponding second antenna port).

[0031] In some embodiments, these exemplary methods also include, using the determined precoder, encoding data to be included in the transmission by the second node via the wireless channel at the second time.

[0032] Other embodiments include network nodes (e.g., RAN nodes) configured to perform P106755W001

[0033] operations corresponding to any of the exemplary methods described herein. Other embodiments include non-transitory, computer-readable media storing program instructions that, when executed by processing circuitry, configure such network nodes to perform operations corresponding to any of the exemplary methods described herein.

[0034] These and other embodiments described herein can provide various benefits and / or advantages. For example, embodiments may address phase discontinuity problems that may occur in TDD systems due to a UE switching from DL reception to UL transmission in different timeslots. In other words, embodiments may facilitate accurate precoder determination even when measured CSI is based on or includes such random phase changes. Moreover, embodiments may be realized by low complexity implementations, such that they can be deployed in the RAN (e.g., in base stations), in UEs, or in both.

[0035] These and other objects, features, and advantages of embodiments of the present disclosure will become apparent upon reading the following Detailed Description in view of the Drawings briefly described below.

[0036] BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 shows a high-level views of an exemplary 5G / NR network architecture.

[0038] Figures 2A-C show various arrangements for transmit beamforming.

[0039] Figure 3 show a high level block diagram of exemplary transmission beamforming based on Kalman prediction of future channel state.

[0040] Figure 4 shows a model of random phase change that occurs when a UE switches from DL reception to UL transmission in TDD.

[0041] Figure 5 shows exemplary distributions of phase changes observed from channel logs of different UEs in a 5G network.

[0042] Figure 6 shows a block diagram of algorithm modules arranged in accordance with some embodiments of the present disclosure.

[0043] Figure 7 shows results of an experiment based on measurements of an actual 100-MHz bandwidth wireless channel, illustrating efficacy of some embodiments of the present disclosure.

[0044] Figure 8 shows exemplary simulation results that illustrate efficacy of some embodiments of the present disclosure.

[0045] Figure 9 shows a flow diagram of an exemplary method (e.g., procedure), according to various embodiments of the present disclosure.

[0046] Figure 10 shows a communication system according to some embodiments of the present disclosure.

[0047] Figure 11 shows a network node according to some embodiments of the present disclosure. P106755W001

[0048] Figure 12 shows a virtualization environment in which some embodiments of the present disclosure may be virtualized.

[0049] DETAILED DESCRIPTION

[0050] Some of the embodiments contemplated herein will now be described more fully with reference to the accompanying drawings. Other embodiments, however, are contained within the scope of the subject matter disclosed herein, the disclosed subject matter should not be construed as limited to only the embodiments set forth herein; rather, these embodiments are provided as examples to convey the scope of the subject matter to those skilled in the art.

[0051] In general, all terms used herein should be interpreted according to their ordinary meaning to a person of ordinary skill in the relevant technical field, unless a different meaning is expressly defined and / or implied from the context of use. All references to a / an / the element, apparatus, component, means, step, etc. are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise or clearly implied from the context of use. The operations of any methods and / or procedures disclosed herein do not have to be performed in the exact order disclosed, unless an operation is explicitly described as following or preceding another operation and / or where it is implicit that an operation must follow or precede another operation. Any feature of any embodiment disclosed herein can apply to any other disclosed embodiment, as appropriate. Likewise, any advantage of any embodiment described herein can apply to any other disclosed embodiment, as appropriate.

[0052] Furthermore, the following terms are used throughout the description given below:

[0053] • Radio Access Node: As used herein, a “radio access node” (or equivalently “radio network node,” “radio access network node,” or “RAN node”) can be any node in a radio access network (RAN) that operates to wirelessly transmit and / or receive signals. Some examples of a radio access node include, but are not limited to, a base station (e.g., gNB in a 3GPP 5G / NR network or an enhanced or eNB in a 3 GPP LTE network), base station distributed components (e.g, CU and DU), a high-power or macro base station, a low-power base station (e.g., micro, pico, femto, or home base station, or the like), an integrated access backhaul (IAB) node, a transmission point (TP), a transmission reception point (TRP), a remote radio unit (RRU or RRH), and a relay node.

[0054] • Core Network Node: As used herein, a “core network node” is any type of node in a core network. Some examples of a core network node include, e.g., a Mobility Management Entity (MME), a serving gateway (SGW), a PDN Gateway (P-GW), a Policy and Charging Rules Function (PCRF), an access and mobility management function (AMF), a session management function (SMF), a user plane function (UPF), a Charging Function (CHF), a P106755W001

[0055] Policy Control Function (PCF), an Authentication Server Function (AUSF), a location management function (LMF), or the like.

[0056] • Wireless Device: As used herein, a “wireless device” (or “WD” for short) is any type of device that is capable, configured, arranged and / or operable to communicate wirelessly with network nodes and / or other wireless devices. Communicating wirelessly can involve transmitting and / or receiving wireless signals using electromagnetic waves, radio waves, infrared waves, and / or other types of signals suitable for conveying information through air. Unless otherwise noted, the term “wireless device” is used interchangeably herein with the term “user equipment” (or “UE” for short), with both of these terms having a different meaning than the term “network node”.

[0057] • Network Node: As used herein, a “network node” is any node that is either part of the radio access network (e.g., a radio access node or equivalent term) or of the core network (e.g., a core network node discussed above) of a cellular communications network. Functionally, a network node is equipment capable, configured, arranged, and / or operable to communicate directly or indirectly with a wireless device and / or with other network nodes or equipment in the cellular communications network, to enable and / or provide wireless access to the wireless device, and / or to perform other functions (e.g, administration) in the cellular communications network.

[0058] • Node: As used herein, the term “node” (without prefix) can be any type of node that can communicate in or with a wireless network (including RAN and / or core network), including a radio access node (or equivalent term), core network node, or wireless device. However, the term “node” may be limited to a particular type (e.g., radio access node, IAB node) based on its specific characteristics in any given context.

[0059] The above definitions are not meant to be exclusive. In other words, various ones of the above terms may be explained and / or described elsewhere in the present disclosure using the same or similar terminology. Nevertheless, to the extent that such other explanations and / or descriptions conflict with the above definitions, the above definitions should control.

[0060] Note that the description given herein focuses on a 3GPP cellular communications system and, as such, 3GPP terminology or terminology similar to 3GPP terminology is oftentimes used. However, the concepts disclosed herein are not limited to a 3 GPP system and can be applied to any communication system that may benefit from them.

[0061] Figure 1 shows a high-level view of an exemplary 5G network architecture, including a next-generation RAN (NG-RAN) 199 and a 5G core network (5GC) 198. As shown in the figure, the NG-RAN can include gNBs 110a,b and ng-eNBs 120a,b that are interconnected with each other via respective Xn interfaces. The gNBs and ng-eNBs are also connected via the NG P106755W001

[0062] interfaces to the 5GC, more specifically to access and mobility management functions (AMFs) 130a,b via respective NG-C interfaces (not shown) and to user plane functions (UPFs) 140a, b via respective NG-U interfaces (not shown). Moreover, AMFs can communicate with one or more policy control functions (PCFs) 150a, b and network exposure functions (NEFs) 160a, b.

[0063] Each of the gNBs can support the NR radio interface including frequency division duplexing (FDD), TDD, or a combination thereof. Each of ng-eNBs can support the fourth generation (4G) Long-Term Evolution (LTE) radio interface but unlike conventional LTE eNBs, ng-eNBs connect to the 5GC via the NG interface. Each of the gNBs and ng-eNBs can serve a geographic coverage area including one or more cells llla,b and 121a, b shown in Figure 1. Depending on the cell in which it is located, a UE 105 can communicate with the gNB or ng-eNB serving that cell via the NR or LTE radio interface, respectively. Although Figure 1 shows gNBs and ng-eNBs separately, it is also possible that a single NG-RAN node provides both types of functionality.

[0064] Although not shown explicitly, each gNB in Figure 1 may include a Central Unit (CU or gNB-CU) and one or more Distributed Units (DUs or gNB-DUs). CUs are logical nodes that host higher-layer protocols and perform various gNB functions such as controlling operation of DUs. In contrast, DUs are decentralized logical nodes that host lower layer protocols and can include, depending on the functional split option, various subsets of the gNB functions. Each CU and DU can include various circuitry needed to perform their respective functions, including processing circuitry, communication interface circuitry (e.g., transceivers), and power supply circuitry.

[0065] As discussed above, beamforming can be used to create multiple parallel communication "channels" in a single wireless channel, such as from a base station (e.g., gNB) transmitter to a UE receiver. This is also referred to as spatial multiplexing an involves transmitting multiple layers on the same time-frequency resources, either to a single user ( “SU-MIMO”) or to multiple users (“MU-MIMO”). In general, the number of antennas required for a MIMO system can be readily determined based on a desired throughput, spectral efficiency, and / or traffic load.

[0066] There are three main beamforming techniques: analog, digital, and hybrid (a combination of analog and digital). Analog beamforming can compensate for high mmW pathloss, while digital precoding can provide additional performance gains necessary to achieve a reasonable coverage. The implementation complexity of analog beamforming is significantly less than digital since it can utilize simple phase shifters, but it is limited in terms of multi-direction flexibility (i.e., a single beam can be formed at a time and the beams are then switched in time domain), transmission bandwidth (i.e., not possible to transmit over a sub-band), inaccuracies in the analog domain, etc.

[0067] Digital beamforming requires more complex converters between the digital domain (i.e., OFDM FFT / IFFT) and the intermediate frequency (IF) radio domain. However, digital P106755W001

[0068] beamforming, which is often used today in LTE networks, provides the best performance in terms of data rate and multiplexing capabilities. For example, multiple beams over multiple sub-bands can be formed simultaneously. Even so, digital beamforming presents challenges in terms of power consumption, integration, and cost. Furthermore, while cost generally scales linearly with the number of transmit / receive units, the gains of digital beamforming increase more slowly.

[0069] Figure 2A shows an exemplary hybrid transmit beamforming arrangement, which includes baseband processing circuitry 220 coupled to an analog beamformer (BF) 240 via intermediate conversion circuitry 230. For example, the arrangement shown in Figure 2A can be part of or operably coupled to a RAN node, such as any of the gNBs and ng-eNBs shown in Figure 1.

[0070] The baseband processing circuitry includes a MIMO-related functionality such as layer mapping and precoding. The conversion circuitry can include one or more conversion chains, with multiple conversion chains shown in the figure. Each conversion chain can include an inverse FFT, a parallel-to-serial (P / S) converter, and a digital-to-analog converter (DAC). The analog beamformer includes a transmitter 242, also referred to as transmit circuitry, and an antenna array 244. Additionally, the arrangement shown in Figure 2A includes processing / control circuitry 210 that manages and / or controls the baseband processing circuitry, the conversion circuitry, and the transmitter.

[0071] Figure 2B shows an exemplary arrangement of analog beamformer 240. In this arrangement, antenna panel 244 includes two panels (or sub-panels), with each panel including eight (8) two-element sub-arrays. Each antenna element provides vertical and horizontal polarization, as indicated by crosses in the respective circles. Transmitter 242 includes an independent beamforming circuit for each panel, with each beamforming circuit include an upconverter (e.g., mixer) from intermediate frequency (IF) to radio frequency (RF), as well as independent phase shifters and power amplifiers (PAs, also referred to as VGAs) for each two-element sub-array.

[0072] Figure 2C shows another exemplary arrangement of analog beamformer 240. In this arrangement, antenna panel 244 includes one antenna panel with 16 two-element sub-arrays. Each antenna element provides vertical and horizontal polarization, as indicated by crosses in the respective circles. Transmitter 242 includes one beamforming circuit arranged in a similar manner as shown in Figure 2B. In this exemplary arrangement, only a single conversion chain is needed in conversion circuitry 230 shown in Figure 2A.

[0073] Note that the exemplary transmitters 242 shown in Figures 2B-C feed a single polarization on the antenna panel 244. Duplicate transmitters 242 can be used to feed the respective horizontal and vertical polarizations on the antenna panel 244. Although the antenna arrays shown in Figures P106755W001

[0074] 2B-C are two-dimensional grids of elements, this is only exemplary. Other exemplary antenna arrays can have linear and / or one-dimensional arrangements of elements.

[0075] A beamformer steers the analog beam of each antenna panel toward a single orientation or direction for each polarization on each OFDM symbol. For example, the processing / control circuitry can configure the phase shifters and the PAs associated with each subarray to generate a beam having a desired orientation. The number of subarrays in a panel determines the array gain for the panel. The arrangement shown in Figure 2B supports one beam per panel per polarization (four total for two panels and two polarizations), while the arrangement shown in Figure 2C supports only one beam per polarization (two total).

[0076] For systems deployed at mmW frequencies, it is common to perform beamforming on the time-domain (TD) signal after OFDM transformation. The beamforming operation can be performed by analog circuitry or by a digital implementation before DAC (e.g., in the digital precoding section of Figure 2A). Since implementing multiple analog beamforming networks (e.g., phase shifters and PAs) behind one antenna element may be difficult, multi-layer transmission is often implemented with several panels, with each panel transmitting a single layer per polarization.

[0077] To achieve highest MIMO throughput, it is necessary to transmit using beams that are optimal for the propagation channel(s) between the transmitter (e.g., base station) and the receiver (e.g., UE(s)). MIMO beamforming relies heavily on correct estimation of the propagation channel, which is generally unknown. For example, a base station transmitter must employ some type of precoding to be able to utilize its antenna arrays to achieve desired DL MIMO performance gains. The base station can derive the precoding based on knowledge of the channel from each transmit antenna to each UE receive antenna.

[0078] In some cases, a UE can measure amplitude and phase of received DL RS (e.g., CSI-RS, DM-RS) and send information derived from these measurements to the RS transmitter (e.g., base station) as CSI. For example, CSI can include transmission parameters recommended for the channel based on the channel measurements.

[0079] Alternately or additionally, the base station can measure amplitude and phase of UL RS (e.g., SRS) transmitted by the UE via the channel, from which the base station infers CSI for the DL channel based on an assumption of UL-DL channel reciprocity. This approach is particularly beneficial for time division duplexing (TDD) arrangements in which UL and DL are on the same frequency. Based on CSI received from the UE and / or measured on the UL, the base station derives a precoder to be applied to a next DL MIMO transmission to the UE.

[0080] 3GPP specifications for MIMO precoding generally do not refer to physical antenna branches (or elements) such as shown in Figures 2B-2C. Instead, these specifications refer to P106755W001

[0081] logical abstractions of antenna elements called “antenna ports”, which are defined with respect to the RS of a corresponding transmission. For example, an antenna port is defined such that the channel over which a symbol on the antenna port is conveyed can be inferred from the channel over which another symbol (e.g., RS) on the same antenna port is conveyed. These RS include DM-RS, CSI-RS, and phase tracking reference signal (PT-RS), among others.

[0082] In general, DM-RS is used by the UE to estimate the channels of data resource elements (REs, corresponding to the DM-RS antenna ports) for coherent demodulation of downlink data. According to 3GPP specifications, DM-RS are linearly precoded by a matrix W in the same way as physical DL shared channel (PDSCH). A UE observes a noisy version of a DM-RS at the channel output. The UE’s channel estimation algorithm tries to estimate the corresponding channel seen by DM-RS, which includes propagation channel H, multi-antenna precoding W, and the reference signal port to physical antenna mapping F. In other words:

[0083] HDMRS ■■= HFW.

[0084] The UE’s estimate of HDMRS, i.e., HDMRS, can be used to coherently demodulate data because DM-RS and PDSCH are associated by transmission over the same antenna ports and, therefore, include the same linear precoding, antenna mapping, and propagation channel.

[0085] CSI-RS mapping is slightly different than DM-RS in terms of the precoders used before reception. Since a primary purpose of CSI-RS is to obtain channel state information and noise / interference estimates for link adaptation and precoder suggestions to the base station, a baseline for CSI-RS mapping is that it at least goes through the physical antenna mapping F before experiencing the channel H. In other word, the multi-antenna precoding matrix U for CSI-RS can be different from the multi-antenna precoding matrix W used for DM-RS.

[0086] Nevertheless, there are several causes of performance degradation in actual MIMO systems, such as in 5G networks. One major cause of performance degradation is that the channel may change faster than the frequency of UE CSI feedback or base station UL measurements. In other words, the CSI is out-of-date and inaccurate when it is used to determine precoding for the next DL transmission. The time variance of the channel is due to mobility of the UE introducing Doppler spread and changes to channel impulse response as the UE location changes.

[0087] Channel tracking and prediction algorithms may be used to combat channel aging and enhance DL precoding performance. The goal of these algorithms is to accurately predict CSI for the channel at a future time, based on which a precoder can be determined so it is ready for use at that future time. For example, Kalman filter based channel prediction may be used due to its robustness. By modelling evolution of the channel overtime using an auto-regressive (AR) model, the Kalman filter may be formulated based on a state-space model that projects historical measurements into future channel states. Figure 3 show a high level block diagram of exemplary P106755W001

[0088] transmission beamforming based on Kalman prediction of future channel state. Alternately, artificial intelligence / machine learning (AI / ML) models may be used for channel prediction.

[0089] Another cause of performance degradation in actual MIMO systems is hardware impairments in the transmitter and / or receiver, such as phase noise, active and passive intermodulation distortion, in-phase and quadrature imbalance, manufacturing imperfections, etc. In general, these impairments may make the UL-DL channel reciprocity assumption invalid by introducing an effect that is only present in one direction (e.g., UL), or by introducing effects that differ in the two directions (e.g., UL vs. DL).

[0090] As a more specific example, when a UE switches from DL reception to UL transmission in TDD, some random phase change will be generated by the UE radio components. Figure 4 shows a model of this scenario, in which S(t) represents an UL RS transmitted by a UE (e.g., SRS) and H represents actual CSI for the channel. The random phase change at time t for a UE antenna can be modelled as e / 6(. with 6tbeing a time varying random variable with a distribution that may be unknown.

[0091] A common assumption is that these random phase changes may differ depending on the UE transmission ports. A worst-case scenario is that the random phase changes introduced by UE DL-UL (or vice versa) switching are uniformly distributed between — n and n radians (i.e., -180 to +180 degrees), and have little or no time dependence (e.g., between successive phase changes). Figure 5 shows exemplary distributions of phase changes observed from channel logs of different UEs in a 5G network.

[0092] At the receiver (e.g., base station), an estimate of the channel is obtained after the matched filter is applied to S(t). The effective channel observed by the receiver is H = e^H, including the phase change, based on which the receiver determines a channel estimate H. Thus, any MIMO precoder derived from this channel estimate will include the random phase change 6t.

[0093] However, this can cause various problems, issues, and / or difficulties when the base station relies on multiple channel estimates to track evolution of the wireless channel. As discussed above, tracking evolution of the channel is important for predicting future CSI, which can be used to combat the problem of using out-of-date CSI to determine MIMO precoders.

[0094] For example, adjacent (e.g., in time) channel estimates may be based on different random phase changes by the UE, caused by respective DL-UL or UL-DL switches in TDD. In such case, the phase coherency between adjacent channel measurements are corrupted, making these measurements non-coherent. As such, when applied to non-coherent rather than expected coherent channel measurements, the channel prediction algorithms used by the base station may fail to predict accurate CSI for the DL channel due to inaccurate modeling of DL channel evolution over time. Existing techniques for addressing this situation have been found to be inadequate. P106755W001

[0095] Embodiments of the present disclosure address these and other problems, issues, and / or difficulties by techniques for determining a precoder for a transmission, via a wireless channel, by a second node having a plurality of transmit antenna ports to a first node having a plurality of receive antenna ports. Such techniques may provide improved precoding even based on CSI derived from non-coherently transmitted RS, such as due to random phase changes during first node (e.g., UE) switching between DL reception and UL transmission (or vice versa) in a TDD arrangement.

[0096] Embodiments are based on Applicant’s recognition that predicted channel estimates are unnecessary for determining a precoder to be used at a future time, and that other channel metrics may be used instead. More specifically, embodiments are based on Applicant’s recognition that the random phase change is a scalar variable represented by a diagonal matrix that “disappears” during the determination of a sample “covariance” matrix of the channel estimates. When transformed into a particular form in which this occurs, the precoder may be determined based only on the sample covariance matrix of the channel, without influence by the random phase change.

[0097] Some embodiments may be realized as multiple components or modules, each of which performs certain portions of the novel techniques. Figure 6 shows an example realization based on the following modules:

[0098] • a dimension reduction module 610 that maps the channel estimate Htf) (e.g., based on RS) into another space with reduced dimensionality, i.e.,

[0099]

[0100] • a feature projection module 620 that receives the reduced dimension channel estimate Ht(f) and outputs a feature vector

[0101]

[0102] based on a sample covariance matrix calculation. During this calculation, any random phase change in the first node (e.g., UE) transmission is “consumed” without impacting the features of the actual channel needed for accurate transmit precoder determination.

[0103] • (optional) a correction module 625 configured to adjust or correct the feature vectorsothat a predicted covariance matrix is positive semi-definite (i.e., valid) and corresponds to the actual transmission condition.

[0104] • a covariance forecast (or prediction) module 630 that uses the feature vector

[0105]

[0106] (together with past feature vectors) to predict a feature vector (^t+at f hi the reduced- dimension feature vector space and an estimate of the channel covariance matrix Xt+at f hi the full-dimension (original) space, for a future time t + 8t. P106755W001

[0107] • a precoder determination module 640 that calculates a precoder Wt(f) for the future time based on the estimate of the channel covariance matrix Xt+at f inthe full-dimension space.

[0108] In the notation used above and in Figure 6, the quantity “f ’ represents a frequency unit of the channel and may take on any of the values f= 1... N. The frequency units f = 1... N may represent different (i.e., non-overlapping) contiguous subset of frequencies, such that Htf ) represents the channel estimate for the respective frequency units. For example, each frequency unit may represent a different physical resource block (PRB), bandwidth part (BWP), sub-band, etc.

[0109] Note that each of the modules summarized above may be implemented by any combination of hardware and software. Moreover, the modules may be implemented in a single network node (e.g., base station, gNB, etc.), may be spread across multiple network nodes, or may be virtualized in a cloud computing environment (e.g., cloud RAN).

[0110] Embodiments can provide various benefits and / or advantages. At a high level, embodiments may address the phase discontinuity problem that may occur in TDD systems due to a UE switching from DL reception to UL transmission (or vice versa) for different timeslots. In other words, embodiments may facilitate accurate precoder determination even when measured CSI is based on or includes such random phase changes. Moreover, embodiments may be realized by low complexity implementations, such that they can be deployed in the RAN (e.g., in base stations), in UEs, or in both.

[0111] Embodiments include methods for determining a precoder for a transmission from a second node to a first node via a wireless channel, and network node configured to perform such methods. Embodiments will now be described in more detail based on an example in which the second node determines the precoder, particularly the case where the second node is a RAN node that determines a precoder for DL transmission to a UE. However, it should be understood that a network node other than the second node may also perform the exemplary methods in some embodiments.

[0112] The RAN node determines an estimate of the channel at time t, based on a RS (e.g., SRS) transmitted by the UE and measured by the RAN node (or measurements received from another node). These channel estimates can be denoted as Ht, which is a tensor of dimension [rxports, txports, freq_units]. Alternately, the channel estimates can be denoted as

[0113]

[0114] where frequency units f = 1... freq_units represent different (i.e., non-overlapping) contiguous subset of frequencies. In other words, each Ht(f) is a matrix where an entry in row i and column) represents an estimate of the channel from the / -th UE transmit port ( / = 1... txports) to the z-th RAN node receive port (z = 1... rxports). Note that each Ht(f) may be referred to as a “channel matrix.” P106755W001

[0115] Subsequently, a feature mapping matrix B with the dimension of [rxports, rxports] can be used to project the channel matrices Htf) onto a beam space of the RAN node’s receive antenna array (or panel). For example, the feature mapping matrix B can be a two-dimensional Discrete Fourier Transform (DFT) matrix that corresponds to the structure of the receive antenna array. In other words, this 2D DFT matrix represents the “beam space” of the RAN node’s receive antenna array. However, the feature mapping matrix B may also be non-square, such as when the number of beams is less than the number of antennas. In any case, the projected channel matrices are given by:

[0116] W) = BHt(f).

[0117] Next, a power vector P is computed from the projected channel matrices. The entries of the power vector correspond to the respective receive antenna ports, with each entry calculated based on a sum of powers on the frequency power for all frequency units f = 1... freq_units, namely:

[0118] P

[0119]

[0120] \P1> P2> ■■■ > Prxports]- Pi / ) |, where ht(i,j,f) is the (i, j)-th entry of the matrix

[0121]

[0122] In other words, ptrepresents the total power of the channel projected to beam index i over the entire frequency band of interest.

[0123] Subsequently, embodiments select the largest K entries in power vector P, when K is a design parameter determined based on a fraction (a) of the total power to be used in the reduced dimensionality feature vectors. This operation can be represented mathematically as selecting an set of indices 3 c {1, 2,3,..., rxports, with cardinality |7| = K, where K E [1, rxports] is a design parameter, such that:

[0124] Pi >= Pj, V i E 3,j g J, and

[0125] Pi < a pj, Vi E 3,j E {1,2,3,..., rxports], 0 < a < 1

[0126]

[0127] i j

[0128] The selected set 7 indicates the row-indices of the entries of the beam space-projected channel matrix Ht(f) to be used in the representation with reduced dimensionality. In other words, each row of a reduced-dimension channel matrix Ht(f) correspond to a row in Ht(f) having a row index in the set 3. Thus, Ht(f) has dimensions [K, txports].

[0129] Equivalently, the reduced-dimension channel matrix Ht(f) can be determined by the projection Ht(f) = BjHtf ). where Bj is a matrix containing the rows from B having row indices in set 3. Thus, Bj has dimensions [K, txports]. In some variants, the feature selection may be time varying, such that the reduced dimension beam space matrix at time t is denoted as Z?7(t).

[0130] Subsequently, embodiments calculate a “covariance matrix” S£( ) based on the reduced-dimension channel matrix as follows: P106755W001

[0131] W) =

[0132] where the superscript “H” denotes Hermitian, i.e., the transpose of the complex conjugate. The resulting matrix St( ) is therefore a Hermitian matrix with dimension [ / <, K, Note that the term “covariance matrix” is used loosely in this context and does not necessarily follow a strict mathematical definition of this term. Instead, it is used as a shorthand way to refer to the reduced-dimension channel matrix multiplied by its Hermitian.

[0133] In some embodiments, the main diagonal and the lower triangular entries of St( ) are

[0134]

[0135] collected into a feature vector cf)t f), which is complex valued with dimension [ — - — 1], This feature vector

[0136]

[0137] will be used in subsequent operations, as explained below.

[0138] In other embodiments, the complex values of the main diagonal and the lower triangular entries of St( ) are separated into real and imaginary parts, which are then concatenated to form feature vector

[0139]

[0140] In these embodiments, the feature vector

[0141]

[0142] is real-valued with dimension [K2, 1], which is due to the main diagonal entries of St( ) being real-valued with no imaginary parts.

[0143] To summarize these embodiments, the values cr =

[0144]

[0145] are computed and used as a feature vector, where ht is an entry in the i-th row and j -th column of

[0146]

[0147] The benefit of this calculation is that the unknown UE transmitted phase is then “consumed” without removing the essence of the channel for the purpose of transmit precoder computation.

[0148] Although embodiments are described above in terms of calculating the covariance matrices St( ), f= 1... freq_units, skilled persons will readily comprehend that only the entries collected into the feature vector

[0149]

[0150] need to be computed, such that the computation of other entries may be omitted as needed or desired in any given implementation. Moreover, various scaling may be applied uniformly to the computed entries as needed or desired in any given implementation.

[0151] In other embodiments, the Ht(f) matrices, f = 1... freq units, can be stacked in the transmit port dimension, resulting in matrix Hthaving dimension [K, txports*freq_units]. Based on this matrix, a single [K, K] matrix Stis calculated as

[0152]

[0153] .

[0154] In other embodiments, the channel matrix can be indexed by a parameter other than frequency units f. For example, the channel estimate Htf) in the frequency domain (e.g., OFDM sub-carriers) can be transformed to Ht(r) by applying a Discrete Cosine Transform (DCT) or a DFT. Once transformed in this manner, similar operations can be applied to

[0155]

[0156] where T represents the DCT / DFT domain tap index.

[0157] Once the feature vector is calculated according to any of the embodiments described above, it can be added to a storage area that may be referred to as a “feature bank.” More P106755W001

[0158] specifically, the feature bank stores the historical record for the feature vector for f <= t. In other words, the feature bank stores one or more feature vectors determined for past times prior to t. The collection of feature vectors in the feature bank at a given time t can be represented by matrix <ht, whose columns represent the stored feature vectors <>t( ).

[0159] The number of past feature vectors stored may be fixed or variable, and may be subject to the memory capacity of the node where the feature bank is stored. In some embodiments, the feature bank may be updated at each time t based on timing and quality considerations. For example, feature vectors that are not older than a time (or age) threshold and meet a quality constraint can be maintained, with other feature vectors being discarded.

[0160] In some embodiments, a stochastic function that models evolution of the features over time may be estimated based on the feature vectors stored in the feature bank. In mathematical terms, at time t, gt+at\t is a stochastic function that maps the feature vectors to a feature vector space for future time t + 8t (i.e., 8t > 0), such that:

[0161]

[0162] 9t+6t\t- < Pt+at(D> f= 1...freq units.

[0163] In different embodiments, the stochastic function gt+at\tcanbeestimated based on various training model assumptions for the feature vectors <>t( ).

[0164] In some embodiments, gt+8t\t can be estimated based on the following AR model:

[0165] 0

[0166]

[0167] t( / ) = +^2< Z’t-2( / ) + - + et, where Atis the i-th AR model coefficient matrix with dimension consistent with feature vectors (f)t f), and etrepresent the modelling noise vector. The AR model coefficients and modelling noise estimation can be derived based on <ht. Additionally, a state-space model may be derived from this AR model using well-understood techniques, with the state space model producing the actual form of gt+St\t.

[0168] In other embodiments, gt+st\t can be estimated based on a Gaussian process modelling. For example, the marginal distribution P ^t+at f)' d’t) is a multi-dimension Gaussian distribution with a certain mean and covariance, while the conditional distribution P(<>t+<5t( / )| ‘I’t) is a multi-dimension Gaussian distribution with a conditional mean and covariance. In these embodiments, these means and covariances can be obtained via kernel function training based on feature vectors

[0169]

[0170] in <ht. Various known kernel functions may be used in these embodiments.

[0171] In other embodiments, gt+at\t can be estimated based on a deep neural network (DNN) that has been trained based on feature vectors

[0172]

[0173] in <ht. For example, gradient descent (or similar) algorithm may be used to optimize the DNN parameters based on a given training data set and a loss function (e.g., mean square error, mean absolute error, Huber, log-cosh, etc.). P106755W001

[0174] Subsequently, the predicted (or forecasted) feature vector (^t+at f can be determined from the estimated function gt+gt\t based on a design or optimization criterion, such as maximum a posteriori, maximum likelihood, etc. In other embodiments, if the conditional distribution F(^t+at( / )| ^t) is estimated, the predicted (or forecasted) feature vector (f^t+st f) can be determined by taking random samples from this estimated distribution.

[0175] Based on the predicted feature vector t+at f, the estimate of the covariance matrix St+5t( ) for future time interval t + 8t can be determined by copying the entries of (^t+at f) to corresponding positions in main diagonal and sub-diagonal parts of the covariance matrix. For example, the entries of (f^t+at f that correspond to the lower-triangular entries of St( ) collected in feature vector

[0176]

[0177] are copied to respective places in the lower triangular part of the covariance matrix S£+at( '). with the upper triangular part of this matrix being filled out by the complex conjugates of the lower triangular entries.

[0178] This predicted covariance matrix St+at( / ) is in the reduced dimension beam space represented by B3(t). It can projected back to the full-dimension antenna space based on the following transformation:

[0179] &( / ) = F7(t)+&( / )(F; / (t)H)+.

[0180] where B3(t)+represents the Moore-Penrose inverse (also referred to as “pseudoinverse”) of matrix B3(t) (or corresponding Hermitian form). This or similar back projection to the fulldimension antenna space may also be referred to in a shorthand manner as “inverse projection”. The resulting predicted covariance matrix St+at( / ) has dimension [reports, reports].

[0181] In some embodiments, the predicted covariance matrix St+<5t( ) can be adjusted based on CSI feedback from the UE. The goal of this adjustment is to force the covariance matrix to be a positive (semi-)definite matrix with at least rank R, as indicated by the CSI feedback. For example, this adjustment may be performed by adding a scaled identity matrix to the St+5t( ). In some embodiments, this adjustment or correction step can be applied as part of the prediction algorithm, e.g., in each iteration.

[0182] Given this full dimension predicted covariance matrix, the precoder for future time interval t + 8t can be determined in various ways. In some embodiments, the precoder can be determined based on a singular value decomposition (SVD) of the predicted covariance matrix

[0183]

[0184] (including any adjustments). In other embodiments, the precoder can be determined based on regularized zero-forcing of the predicted covariance matrix St+at( / ) (including any adjustments). In general, the precoder may be determined in any known manner that is appropriate and / or preferred, given the size and structure of the predicted covariance matrix St+<5t( ) (including any adjustments). P106755W001

[0185] Measurements of actual propagation channels in a wireless network illustrate the efficacy of the dimension reduction used in embodiments of the present disclosure. Figure 7 shows results of an experiment based on channel matrices derived from measurements on a 100-MHz bandwidth wireless channel between a gNB with 64 antenna elements and a UE with four antenna elements. The UE is moving with speed of 10 km / h. The dimension reduction algorithm discussed above is applied to project the full-dimension channel into a reduced-dimension beam space.

[0186] Figure 7 shows beam index 0-63 on the vertical axis and time on the horizontal axis. The vertical width of the horizontal lines represents the distribution of energy received from the channel in the respective beam directions (i.e., width is proportional to energy). In particular, Figure 7 shows that energy distribution of the channel is concentrated in a few strong beam directions and is consistent over time. Thus, the reduced-dimension beam space may capture a large portion of the energy and may produce consistent feature vectors that may result in improved prediction of future feature vectors, channel matrices, and resulting precoders.

[0187] Simulated propagation channels also illustrate the efficacy of the dimension reduction used in embodiments of the present disclosure. Figure 8 shows simulation results for a UE moving at 20 km / h in a channel based on the clustered delay line model B (CDL-B), as defined in 3GPP TR 38.901 (vl6.1.0), with SNR = 25 dB and the following spread parameters:

[0188] • azimuth angle of departure (AoD) spread = 15 degrees,

[0189] • azimuth angle of arrival (AoA) spread = 45 degrees,

[0190] • zenith angle of arrival (ZoA) spread = 10 degrees, and

[0191] • zenith angle of departure (ZoD) spread = 2 degrees, and SNR 25 dB.

[0192] The horizontal axis of Figure 8 shows time while the vertical axis shows beamforming gain, which is defined as:

[0193] VHHHHV,

[0194] where V is a unitary precoding vector (i.e., precoder) for the first transmission layer and H represents the DL MIMO channel. In mathematical terms, the beamforming gain is maximized by the leading eigenvector of the matrix product HHH. The beamforming gain is also referred to as the Rayleigh quotient.

[0195] Figure 8 compares exemplary beamforming gain over a four-second segment based on using an ideal (or “genie”) precoder, a predicted precoder according to embodiments of the present disclosure, and a precoder that was ideal 5 ms earlier (i.e., t-5ms). The curves show that beamforming gain of the predicted precoder based on embodiments of the present disclosure tracks beamforming gain of the ideal precoder very well, and provides improvement relative to simply using an out-of-date ideal precoder.

[0196] Various features of the embodiments described above correspond to various operations P106755W001

[0197] illustrated in Figure 9, which shows an exemplary method (e.g., procedure) for determining a precoder for a transmission by a second node to a first node via a wireless channel. The method can be performed by a network node (e.g., RAN node, base station, eNB, gNB, etc.), as described elsewhere herein. Although Figure 9 shows specific blocks in a particular order, the operations of the exemplary method can be performed in different orders than shown and can be combined and / or divided into blocks having different functionality than shown. Optional blocks or operations are indicated by dashed lines.

[0198] The exemplary method includes the operations of block 930, where the network node determines a plurality of scalar products based on a plurality of complex channel vectors that represent the wireless channel at a first time. The plurality of scalar products are based on respective different combinations of the following: one of the complex channel vectors, and a complex conjugate of the same or a different one of the complex channel vectors. The exemplary method also includes the operations of block 940, where the network node determines one or more predicted feature vectors to represent the wireless channel at a second time after the first time, based on the following: one or more feature vectors derived from the plurality of scalar products, and for each of at least one third time before the first time, one or more previous feature vectors that represent the wireless channel at the third time. The exemplary method also includes the operations of block 960, where based on the one or more predicted feature vectors, the network node determines a precoder for a transmission by the second node via the wireless channel at the second time.

[0199] In some embodiments, the plurality of scalar products include the following:

[0200] • a plurality of first scalar products corresponding to the plurality of complex channel vectors, wherein each first scalar product is determined based on a corresponding complex channel vector and its complex conjugate; and

[0201] • a plurality of second scalar products corresponding to different pairs of the plurality of complex channel vectors, wherein each second scalar product is determined based on one complex channel vector of the corresponding pair and a complex conjugate of the other complex channel vector of the corresponding pair.

[0202] For example, the first scalar products may correspond to main-diagonal terms of the covariance matrix St( ) mentioned above, while the second scalar products may correspond to off-main-diagonal terms of the covariance matrix St( ).

[0203] In some embodiments, the transmission by the first node at the second time is non-phase-coherent with one or more previous transmissions by the first node, on which the plurality of complex channel vectors are based. In such case, the determined plurality of scalar products represent the wireless channel independent of the non-phase-coherence. Put differently, the P106755W001

[0204] forming of the scalar products may eliminate the non-phase coherence between the transmission at the first time and the one or more previous transmissions by the first node.

[0205] In some embodiments, the plurality of complex channel vectors correspond respectively to a plurality of second antenna ports of the second node (i.e., one complex channel vector per second antenna port). Each complex channel vector includes channel estimates of the wireless channel from a plurality of first antenna ports of the first node to the corresponding second antenna port (i.e., each element of a complex channel vector is a channel estimate of the wireless from a particular first antenna port to a corresponding second antenna port).

[0206] In some embodiments, each complex channel vector includes respective channel estimates for a plurality of frequency units within a bandwidth of the wireless channel (i.e., a three-dimensional tensor representation as discussed above). In such case, the one or more feature vectors include a single feature vector that represents the bandwidth of the wireless channel.

[0207] In other embodiments, each complex channel vector includes channel estimates for one of a plurality of frequency units within the bandwidth of the wireless channel. In such case, the one or more feature vectors include a plurality of feature vectors that represent respectively the plurality of frequency units within the bandwidth of the wireless channel (i.e., one feature vector per frequency unit).

[0208] In some embodiments, each of the one or more feature vectors includes a plurality of entries, with each entry being one of the following: one of the determined scalar products, or a real value derived from one of the determined scalar products (e.g., when the scalar product is a complex value).

[0209] In some embodiments, the exemplary method also includes the operations of block 970, where using the determined precoder (e.g., from block 960), the network node encodes data to be included in the transmission by the second node via the wireless channel at the second time.

[0210] In some embodiments, the exemplary method also includes the following operations, labelled with corresponding block numbers:

[0211] • (910) obtaining measurements of reference signals that are transmitted by the first node via a plurality of first antenna ports and received by the second node via a plurality of second antenna ports; and

[0212] • (920) determining the plurality of complex channel vectors based on the measurements of the reference signals.

[0213] In some of these embodiments, determining the plurality of complex channel vectors based on the measurements of the reference signals in block 920 includes the following operations, labelled with corresponding sub-block numbers: P106755W001

[0214] • (921) determining a second plurality of complex channel vectors based on the measurements of the reference signals; and

[0215] • (922) determining the plurality of complex channel vectors based on a projection of the second plurality of complex channel vectors onto a subset of a complete beam space for an antenna array arranged to provide the plurality of second antenna ports.

[0216] In some variants of these embodiments, determining the plurality of complex channel vectors based on a projection of the second plurality of complex channel vectors onto a subset of a complete beam space in sub-block 922 includes the following operations:

[0217] • determining a first projection of the second plurality of complex channel vectors onto the complete beam space over a bandwidth of the wireless channel; and

[0218] • selecting, as the subset, a predetermined number of beams of the complete beam space according to a criterion of maximizing power of the first projection over the bandwidth of the wireless channel.

[0219] In some embodiments, the first node is a user equipment (UE) and the second node is a radio access network (RAN) node. In some of these embodiments, the method is performed by the RAN node (i.e., the second node). In other embodiments, the method is performed by a network node coupled to the RAN node.

[0220] In some embodiments, determining the one or more predicted feature vectors to represent the wireless channel at a second time in block 940 includes the following operations, labelled with corresponding sub-block numbers:

[0221] • (941 ) determining a function that maps the one or more feature vectors and the one or more previous feature vectors, for each of the at least one third time, to a feature vector space at the second time; and

[0222] • (942) determining the one or more predicted feature vectors based on the function.

[0223] For example, the function may be a stochastic function, such as discussed above.

[0224] In some of these embodiments, the function is a state-space model based on an autoregressive (AR) random process, and determining the one or more predicted feature vectors in sub-block 942 is based on applying a maximization criterion to the state-space model (e.g., to identify a set of parameters that maximizes a performance criterion over a given training dataset). For example, the state-space model may represent a Kalman filter, as discussed above.

[0225] In other of these embodiments, the function is a multi-dimensional Gaussian distribution and determining the one or more predicted feature vectors in sub-block 942 is based on random selection (i.e., of feature vectors) from the multi-dimensional Gaussian distribution.

[0226] In some embodiments, the exemplary method also includes the operations of block 950, where the network node determines a projection of the one or more predicted feature vectors onto P106755W001

[0227] a complete beam space for an antenna array of the second node. This projection was referred to as an “inverse projection” in the above description of various embodiments. The precoder is determined in block 960 based on the projection of the one or more predicted feature vectors.

[0228] In some of these embodiments, for each of the one or more predicted feature vectors, determining the projection onto the complete beam space in block 950 includes the following operations, labelled with corresponding sub-block numbers:

[0229] • (951) determining a predicted feature matrix based on entries of the predicted feature vector; and

[0230] • (952) using a matrix representation Bj of a subset of the complete beam space, determining a projection of the predicted feature matrix from the subset of the complete beam space to the complete beam space.

[0231] In some of these embodiments, determining the predicted feature matrix in sub-block 951 includes the following operations:

[0232] • using first entries from the predicted feature vector to form entries on a main diagonal of the predicted feature matrix; and

[0233] • using second entries from the predicted feature vector to form entries above and below the main diagonal of the predicted feature matrix.

[0234] In some further variants, the projection of the predicted feature matrix is determined using pseudoinverses of the matrix representation Bj and of a complex conjugate transpose of the matrix representation Bj. An example of these operations was described above.

[0235] In some of these embodiments, determining the precoder for a transmission by the second node via the wireless channel at the second time in block 960 is based on the operations of subblock 961, wherein the network node performs a singular value decomposition (SVD) of each projection of the predicted feature matrix, or of a matrix derived therefrom.

[0236] As mentioned above, the exemplary method shown in Figure 9 can be implemented by a network node (e.g., RAN node), such as the second node. The network node may include processing circuitry configured to perform operations of the exemplary method. For example, the processing circuitry may be configured to execute computer program code that facilitates such operations. As another example, the processing circuitry may include circuitry similar to processing / control circuitry 210 and baseband processing circuitry 220 shown in Figure 2A.

[0237] In some embodiments, if the network node is the second node, the network node may also include an antenna array arranged as a plurality of second antenna ports and communication interface circuitry operably coupled to the processing circuitry and configured to transmit and receive via the antenna array. For example, the communication interface circuitry may include P106755W001

[0238] circuitry similar to conversion circuitry 230 and transmitter circuitry 242 shown in Figures 2A-2C. Likewise, the antenna array may be similar to antenna array 244 shown in Figures 2A-2C.

[0239] Additionally, the exemplary method shown in Figure 9 can be realized as a non-transitory, computer-readable medium storing computer-executable instructions. When executed by processing circuitry of a network node configured to determine a precoder for a transmission from a second node to a first node via a wireless channel, the instructions configure the network node to perform operations corresponding to any of those described above with reference to Figure 9.

[0240] Additionally, the exemplary method shown in Figure 9 can be realized as a computer program (or computer program product) comprising computer-executable instructions. When executed by processing circuitry of a network node configured to determine a precoder for a transmission from a second node to a first node via a wireless channel, the instructions configure the network node to perform operations corresponding to any of those described above with reference to Figure 9.

[0241] Figure 10 shows an example of a communication system 1000 in accordance with some embodiments. In this example, communication system 1000 includes a telecommunication network 1002 that includes an access network 1004 (e.g., RAN) and a core network 1006, which includes one or more core network nodes 1008. Access network 1004 includes one or more access network nodes, such as network nodes 1010A-B (one or more of which may be generally referred to as network node 1010), or any other similar 3 GPP access nodes or non-3GPP access points. Moreover, as will be appreciated by those of skill in the art, a network node is not necessarily limited to an implementation in which a radio portion and a baseband portion are supplied and integrated by a single vendor. Thus, it will be understood that network nodes include disaggregated implementations or portions thereof. For example, in some embodiments, telecommunication network 1002 includes one or more Open-RAN (ORAN) network nodes. An ORAN network node is a node in telecommunication network 1002 that supports an ORAN specification (e.g., a specification published by the O-RAN Alliance, or any similar organization) and may operate alone or together with other nodes to implement one or more functionalities of any node in telecommunication network 1002, including one or more network nodes 1010 and / or core network nodes 1008.

[0242] Examples of an ORAN network node include an open radio unit (O-RU), an open distributed unit (O-DU), an open central unit (O-CU), including an O-CU control plane (O-CU-CP) or an O-CU user plane (O-CU-UP), a RAN intelligent controller (near-real time or non-real time) hosting software or software plug-ins, such as a near-real time control application (e.g., xApp) or a non-real time control application (e.g., rApp), or any combination thereof (the adjective “open” designating support of an ORAN specification). The network node may support a P106755W001

[0243] specification by, for example, supporting an interface defined by the ORAN specification, such as an Al, Fl, Wl, El, E2, X2, Xn interface, an open fronthaul user plane interface, or an open fronthaul management plane interface. Moreover, an ORAN access node may be a logical node in a physical node. Furthermore, an ORAN network node may be implemented in a virtualization environment (described further below) in which one or more network functions are virtualized. For example, the virtualization environment may include an O-Cloud computing platform orchestrated by a Service Management and Orchestration Framework via an 0-2 interface defined by the 0-RAN Alliance or comparable technologies. Network nodes 1010 facilitate direct or indirect connection of UEs, such as by connecting UEs 1012A-D (one or more of which may be generally referred to as UEs 1012) to core network 1006 over one or more wireless connections.

[0244] Example wireless communications over a wireless connection include transmitting and / or receiving wireless signals using electromagnetic waves, radio waves, infrared waves, and / or other types of signals suitable for conveying information without the use of wires, cables, or other material conductors. Moreover, in different embodiments, communication system 1000 may include any number of wired or wireless networks, network nodes, UEs, and / or any other components or systems that may facilitate or participate in the communication of data and / or signals whether via wired or wireless connections. Communication system 1000 may include and / or interface with any type of communication, telecommunication, data, cellular, radio network, and / or other similar type of system.

[0245] UEs 1012 may be any of a wide variety of communication devices, including wireless devices arranged, configured, and / or operable to communicate wirelessly with network nodes 1010 and other communication devices. Similarly, network nodes 1010 are arranged, capable, configured, and / or operable to communicate directly or indirectly with UEs 1012 and / or with other network nodes or equipment in telecommunication network 1002 to enable and / or provide network access, such as wireless network access, and / or to perform other functions, such as administration in telecommunication network 1002.

[0246] In the context of communication system 1000 shown in Figure 10, various embodiments of the exemplary method shown in Figure 9 can be implemented by any of network nodes 1010 or core network node 1008.

[0247] In the depicted example, core network 1006 connects network nodes 1010 to one or more hosts, such as host 1016. These connections may be direct or indirect via one or more intermediary networks or devices. In other examples, network nodes may be directly coupled to hosts. Core network 1006 includes one or more core network nodes (e.g., 1008) that are structured with hardware and software components. Features of these components may be substantially similar to those described with respect to the UEs, network nodes, and / or hosts, such that the descriptions P106755W001

[0248] thereof are generally applicable to the corresponding components of core network node 1008. Example core network nodes include functions of one or more of a Mobile Switching Center (MSC), Mobility Management Entity (MME), Home Subscriber Server (HSS), Access and Mobility Management Function (AMF), Session Management Function (SMF), Authentication Server Function (AUSF), Subscription Identifier De-concealing function (SIDF), Unified Data Management (UDM), Security Edge Protection Proxy (SEPP), Network Exposure Function (NEF), and / or a User Plane Function (UPF).

[0249] Host 1016 may be under the ownership or control of a service provider other than an operator or provider of access network 1004 and / or telecommunication network 1002, and may be operated by the service provider or on behalf of the service provider. Host 1016 may host a variety of applications to provide one or more service. Examples of such applications include live and pre-recorded audio / video content, data collection services such as retrieving and compiling data on various ambient conditions detected by a plurality of UEs, analytics functionality, social media, functions for controlling or otherwise interacting with remote devices, functions for an alarm and surveillance center, or any other such function performed by a server.

[0250] As a whole, communication system 1000 of Figure 10 enables connectivity between the UEs, network nodes, and hosts. In that sense, the communication system may be configured to operate according to predefined rules or procedures, such as specific standards that include, but are not limited to: Global System for Mobile Communications (GSM); Universal Mobile Telecommunications System (UMTS); Long Term Evolution (LTE), and / or other suitable 2G, 3G, 4G, 5G standards, or any applicable future generation standard (e.g., 6G); wireless local area network (WLAN) standards, such as the Institute of Electrical and Electronics Engineers (IEEE) 802.11 standards (WiFi); and / or any other appropriate wireless communication standard, such as the Worldwide Interoperability for Microwave Access (WiMax), Bluetooth, Z-Wave, Near Field Communication (NFC) ZigBee, LiFi, and / or any low-power wide-area network (LPWAN) standards such as LoRa and Sigfox.

[0251] In some examples, telecommunication network 1002 is a cellular network that implements 3GPP standardized features. Accordingly, telecommunication network 1002 may support network slicing to provide different logical networks to different devices that are connected to telecommunication network 1002. For example, telecommunication network 1002 may provide Ultra Reliable Low Latency Communication (URLLC) services to some UEs, while providing Enhanced Mobile Broadband (eMBB) services to other UEs, and / or Massive Machine Type Communication (mMTC) / Massive loT services to yet further UEs.

[0252] In some examples, UEs 1012 are configured to transmit and / or receive information without direct human interaction. For instance, a UE may be designed to transmit information to access P106755W001

[0253] network 1004 on a predetermined schedule, when triggered by an internal or external event, or in response to requests from access network 1004. Additionally, a UE may be configured for operating in single- or multi -RAT or multi-standard mode. For example, a UE may operate with any one or combination of Wi-Fi, NR (New Radio) and LTE, i.e. being configured for multi-radio dual connectivity (MR-DC), such as E-UTRAN (Evolved-UMTS Terrestrial Radio Access Network) New Radio - Dual Connectivity (EN-DC).

[0254] In the example, hub 1014 communicates with access network 1004 to facilitate indirect communication between one or more UEs, (e.g., 1012C and / or 1012D) and network nodes, (e.g., 1010B). In some examples, hub 1014 may be a controller, router, content source and analytics, or any of the other communication devices described herein regarding UEs. For example, hub 1014 may be a broadband router enabling access to core network 1006 for the UEs. As another example, hub 1014 may be a controller that sends commands or instructions to one or more actuators in the UEs. Commands or instructions may be received from the UEs, network nodes 1010, or by executable code, script, process, or other instructions in hub 1014. As another example, hub 1014 may be a data collector that acts as temporary storage for UE data and, in some embodiments, may perform analysis or other processing of the data. As another example, hub 1014 may be a content source. For example, for a UE that is a VR headset, display, loudspeaker or other media delivery device, hub 1014 may retrieve VR assets, video, audio, or other media or data related to sensory information via a network node, which hub 1014 then provides to the UE either directly, after performing local processing, and / or after adding additional local content. In still another example, hub 1014 acts as a proxy server or orchestrator for the UEs, in particular if one or more of the UEs are low energy loT devices.

[0255] Hub 1014 may have a constant / persistent or intermittent connection to network node 1010B. Hub 1014 may also allow for a different communication scheme and / or schedule between hub 1014 and UEs, (e.g., 1012C and / or 1012D), and between hub 1014 and core network 1006. In other examples, hub 1014 is connected to core network 1006 and / or one or more UEs via a wired connection. Moreover, hub 1014 may be configured to connect to a machine-to-machine (M2M) service provider over access network 1004 and / or to another UE over a direct connection. In some scenarios, UEs may establish a wireless connection with network nodes 1010 while still connected via hub 1014 via a wired or wireless connection. In some embodiments, hub 1014 may be a dedicated hub - that is, a hub whose primary function is to route communications to / from the UEs from / to network node 1010B. In other embodiments, hub 1014 may be a non-dedicated hub - that is, a device which is capable of operating to route communications between the UEs and network node 1010B, but which is additionally capable of operating as a communication start and / or end point for certain data channels. P106755W001

[0256] Figure 11 shows a network node 1100 in accordance with some embodiments. Examples of network nodes include, but are not limited to, access points (APs, e.g., radio access points), base stations (e.g., radio base stations, Node Bs, eNBs, gNBs), and O-RAN nodes or components of an O-RAN node (e.g., O-RU, O-DU, O-CU).

[0257] Base stations may be categorized based on the amount of coverage they provide (or, stated differently, their transmit power level) and so, depending on the provided amount of coverage, may be referred to as femto base stations, pico base stations, micro base stations, or macro base stations. A base station may be a relay node or a relay donor node controlling a relay. A network node may also include one or more (or all) parts of a distributed radio base station such as centralized digital units, distributed units (e.g., in an O-RAN access node) and / or remote radio units (RRUs), sometimes referred to as Remote Radio Heads (RRHs). Such remote radio units may or may not be integrated with an antenna as an antenna integrated radio. Parts of a distributed radio base station may also be referred to as nodes in a distributed antenna system (DAS).

[0258] Other examples of network nodes include multiple transmission point (multi-TRP) 5G access nodes, multi-standard radio (MSR) equipment such as MSR BSs, network controllers such as radio network controllers (RNCs) or base station controllers (BSCs), base transceiver stations (BTSs), transmission points, transmission nodes, multi-cell / multicast coordination entities (MCEs), Operation and Maintenance (O& M) nodes, Operations Support System (OSS) nodes, Self-Organizing Network (SON) nodes, positioning nodes (e.g., Evolved Serving Mobile Location Centers (E-SMLCs)), and / or Minimization of Drive Tests (MDTs).

[0259] Network node 1100 includes processing circuitry 1102, memory 1104, communication interface 1106, and power source 1108. Network node 1100 may be composed of multiple physically separate components (e.g., a NodeB component and a RNC component, or a BTS component and a BSC component, etc.), which may each have their own respective components. In certain scenarios in which network node 1100 comprises multiple separate components (e.g., BTS and BSC components), one or more of the separate components may be shared among several network nodes. For example, a single RNC may control multiple NodeBs. In such a scenario, each unique NodeB and RNC pair, may in some instances be considered a single separate network node. In some embodiments, network node 1100 may be configured to support multiple radio access technologies (RATs). In such embodiments, some components may be duplicated (e.g., separate memory 1104 for different RATs) and some components may be reused (e.g., a same antenna 1110 may be shared by different RATs). Network node 1100 may also include multiple sets of the various illustrated components for different wireless technologies integrated into network node 1100, for example GSM, WCDMA, LTE, NR, WiFi, Zigbee, Z-wave, LoRaWAN, Radio Frequency Identification (RFID) or Bluetooth wireless technologies. These wireless P106755W001

[0260] technologies may be integrated into the same or different chip or set of chips and other components within network node 1100.

[0261] Processing circuitry 1102 may comprise a combination of one or more of a microprocessor, controller, microcontroller, central processing unit, digital signal processor, application-specific integrated circuit, field programmable gate array, or any other suitable computing device, resource, or combination of hardware, software and / or encoded logic operable to provide network node 1100 functionality, either alone or in conjunction with other network node 1100 components, such as memory 1104.

[0262] In some embodiments, processing circuitry 1102 includes a system on a chip (SOC). In some embodiments, processing circuitry 1102 includes one or more of radio frequency (RF) transceiver circuitry 1112 and baseband processing circuitry 1114. In some embodiments, RF transceiver circuitry 1112 and baseband processing circuitry 1114 may be on separate chips (or sets of chips), boards, or units, such as radio units and digital units. In alternative embodiments, part or all of RF transceiver circuitry 1112 and baseband processing circuitry 1114 may be on the same chip or set of chips, boards, or units.

[0263] Memory 1104 may comprise any form of volatile or non-volatile computer-readable memory including, without limitation, persistent storage, solid-state memory, remotely mounted memory, magnetic media, optical media, random access memory (RAM), read-only memory (ROM), mass storage media (for example, a hard disk), removable storage media (for example, a flash drive, a Compact Disk (CD) or a Digital Video Disk (DVD)), and / or any other volatile or non-volatile, non-transitory device-readable and / or computer-executable memory devices that store information, data, and / or instructions that may be used by processing circuitry 1102. Memory 1104 may store any suitable instructions, data, or information, including a computer program, software, an application including one or more of logic, rules, code, tables, and / or other instructions (collectively denoted computer program 1104a, which may be in the form of a computer program product) capable of being executed by processing circuitry 1102 and utilized by network node 1100. Memory 1104 may be used to store any calculations made by processing circuitry 1102 and / or any data received via communication interface 1106. In some embodiments, processing circuitry 1102 and memory 1104 is integrated.

[0264] Communication interface 1106 is used in wired or wireless communication of signaling and / or data between a network node, access network, and / or UE. As illustrated, communication interface 1106 comprises port(s) / terminal(s) 1116 to send and receive data, for example to and from a network over a wired connection. Communication interface 1106 also includes radio frontend circuitry 1118 that may be coupled to, or in certain embodiments a part of, antenna 1110. Radio front-end circuitry 1118 comprises filters 1120 and amplifiers 1122. Radio front-end P106755W001

[0265] circuitry 1118 may be connected to an antenna 1110 and processing circuitry 1102. The radio front-end circuitry may be configured to condition signals communicated between antenna 1110 and processing circuitry 1102. Radio front-end circuitry 1118 may receive digital data that is to be sent out to other network nodes or UEs via a wireless connection. Radio front-end circuitry 1118 may convert the digital data into a radio signal having the appropriate channel and bandwidth parameters using a combination of filters 1120 and / or amplifiers 1122. The radio signal may then be transmitted via antenna 1110. Similarly, when receiving data, antenna 1110 may collect radio signals which are then converted into digital data by radio front-end circuitry 1118. The digital data may be passed to processing circuitry 1102. In other embodiments, communication interface 1106 may comprise different components and / or different combinations of components.

[0266] In certain alternative embodiments, network node 1100 does not include separate radio front-end circuitry 1118, instead, processing circuitry 1102 includes radio front-end circuitry and is connected to antenna 1110. Similarly, in some embodiments, all or some of RF transceiver circuitry 1112 is part of communication interface 1106. In still other embodiments, communication interface 1106 includes one or more ports or terminals 1116, radio front-end circuitry 1118, and RF transceiver circuitry 1112, as part of a radio unit (not shown), and communication interface 1106 communicates with baseband processing circuitry 1114, which is part of a digital unit (not shown).

[0267] Antenna 1110 may include one or more antennas, or antenna arrays, configured to send and / or receive wireless signals. Antenna 1110 may be coupled to radio front-end circuitry 1118 and may be any type of antenna capable of transmitting and receiving data and / or signals wirelessly. In certain embodiments, antenna 1110 is separate from network node 1100 and connectable to network node 1100 through an interface or port.

[0268] Antenna 1110, communication interface 1106, and / or processing circuitry 1102 may be configured to perform any receiving operations and / or certain obtaining operations described herein as being performed by the network node. Any information, data and / or signals may be received from a UE, another network node and / or any other network equipment. Similarly, antenna 1110, communication interface 1106, and / or processing circuitry 1102 may be configured to perform any transmitting operations described herein as being performed by the network node. Any information, data and / or signals may be transmitted to a UE, another network node and / or any other network equipment.

[0269] Power source 1108 provides power to the various components of network node 1100 in a form suitable for the respective components (e.g., at a voltage and current level needed for each respective component). Power source 1108 may further comprise, or be coupled to, power management circuitry to supply the components of network node 1100 with power for performing P106755W001

[0270] the functionality described herein. For example, network node 1100 may be connectable to an external power source (e.g., the power grid, an electricity outlet) via an input circuitry or interface such as an electrical cable, whereby the external power source supplies power to power circuitry of power source 1108. As a further example, power source 1108 may comprise a source of power in the form of a battery or battery pack which is connected to, or integrated in, power circuitry. The battery may provide backup power should the external power source fail.

[0271] Embodiments of network node 1100 may include additional components beyond those shown in Figure 11 for providing certain aspects of the network node’s functionality, including any of the functionality described herein and / or any functionality necessary to support the subject matter described herein. For example, network node 1100 may include user interface equipment to allow input of information into network node 1100 and to allow output of information from network node 1100. This may allow a user to perform diagnostic, maintenance, repair, and other administrative functions for network node 1100.

[0272] Additionally, various embodiments of the exemplary method illustrated in Figure 9 can be implemented by network node 1100, including processing circuitry 1102 and communication interface 1106.

[0273] Figure 12 is a block diagram illustrating a virtualization environment 1200 in which functions implemented by some embodiments may be virtualized. In the present context, virtualizing means creating virtual versions of apparatuses or devices which may include virtualizing hardware platforms, storage devices and networking resources. As used herein, virtualization can be applied to any device described herein, or components thereof, and relates to an implementation in which at least a portion of the functionality is implemented as one or more virtual components. Some or all of the functions described herein may be implemented as virtual components executed by one or more virtual machines (VMs) implemented in one or more virtual environments 1200 hosted by one or more of hardware nodes, such as a hardware computing device that operates as a network node, UE, core network node, or host. Further, in embodiments in which the virtual node does not require radio connectivity (e.g., a core network node or host), then the node may be entirely virtualized. In some embodiments, the virtualization environment 1200 includes components defined by the O-RAN Alliance, such as an O-Cloud environment orchestrated by a Service Management and Orchestration Framework via an O-2 interface.

[0274] Applications 1202 (which may alternatively be called software instances, virtual appliances, network functions, virtual nodes, virtual network functions, etc.) are run in the virtualization environment 1200 to implement some of the features, functions, and / or benefits of some of the embodiments disclosed herein. As a more specific example, the exemplary method P106755W001

[0275] illustrated in Figure 9 can be implemented as an application 1202 or as part of a virtual node 1202, in virtualization environment 1200.

[0276] Hardware 1204 includes processing circuitry, memory that stores software and / or instructions (collectively denoted computer program 1204a, which may be in the form of a computer program product) executable by hardware processing circuitry, and / or other hardware devices as described herein, such as a network interface, input / output interface, and so forth. Software may be executed by the processing circuitry to instantiate one or more virtualization layers 1206 (also referred to as hypervisors or virtual machine monitors (VMMs)), provide VMs 1208A-B (one or more of which may be generally referred to as VMs 1208), and / or perform any of the functions, features and / or benefits described in relation with some embodiments described herein. Virtualization layer 1206 may present a virtual operating platform that appears like networking hardware to the VMs 1208.

[0277] VMs 1208 comprise virtual processing, virtual memory, virtual networking or interface and virtual storage, and may be run by a corresponding virtualization layer 1206. Different embodiments of the instance of a virtual appliance 1202 may be implemented on one or more of VMs 1208, and the implementations may be made in different ways. Virtualization of the hardware is in some contexts referred to as network function virtualization (NFV). NFV may be used to consolidate many network equipment types onto industry standard high volume server hardware, physical switches, and physical storage, which can be located in data centers, and customer premise equipment.

[0278] In the context of NFV, each VM 1208 may be a software implementation of a physical machine that runs programs as if they were executing on a physical, non-virtualized machine. Each VM 1208, and that part of hardware 1204 that executes that VM, be it hardware dedicated to that VM and / or hardware shared by that VM with others of the VMs, forms separate virtual network elements. Still in the context of NFV, a virtual network function is responsible for handling specific network functions that run in one or more VMs 1208 on top of the hardware 1204 and corresponds to the application 1202.

[0279] Hardware 1204 may be implemented in a standalone network node with generic or specific components. Hardware 1204 may implement some functions via virtualization. Alternatively, hardware 1204 may be part of a larger cluster of hardware (e.g. such as in a data center or customer premises equipment) where many hardware nodes work together and are managed via management and orchestration function 1210, which, among others, oversees lifecycle management of applications 1202. In some embodiments, hardware 1204 is coupled to one or more radio units that each include one or more transmitters and one or more receivers that may be coupled to one or more antennas. Radio units may communicate directly with other hardware P106755W001

[0280] nodes via one or more appropriate network interfaces and may be used in combination with the virtual components to provide a virtual node with radio capabilities, such as a radio access node or a base station. In some embodiments, some signaling can be provided with the use of a control system 1212 which may alternatively be used for communication between hardware nodes and radio units.

[0281] The foregoing merely illustrates the principles of the disclosure. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. It will thus be appreciated that those skilled in the art will be able to devise numerous systems, arrangements, and procedures that, although not explicitly shown or described herein, embody the principles of the disclosure and are within the spirit and scope of the disclosure. Various exemplary embodiments can be used together with one another, as well as interchangeably therewith, as should be understood by those having ordinary skill in the art.

[0282] The term unit, as used herein, can have conventional meaning in the field of electronics, electrical devices and / or electronic devices and can include, for example, electrical and / or electronic circuitry, devices, modules, processors, memories, logic solid state and / or discrete devices, computer programs or instructions for carrying out respective tasks, procedures, computations, outputs, and / or displaying functions, and so on, such as those that are described herein.

[0283] Any appropriate steps, methods, features, functions, or benefits disclosed herein may be performed through one or more functional units or modules of one or more virtual apparatuses. Each virtual apparatus may comprise a number of these functional units. These functional units may be implemented via processing circuitry, which may include one or more microprocessor or microcontrollers, as well as other digital hardware, which may include Digital Signal Processors (DSPs), special-purpose digital logic, and the like. The processing circuitry may be configured to execute program code stored in memory, which may include one or several types of memory such as Read Only Memory (ROM), Random Access Memory (RAM), cache memory, flash memory devices, optical storage devices, etc. Program code stored in memory includes program instructions for executing one or more telecommunications and / or data communications protocols as well as instructions for carrying out one or more of the techniques described herein. In some implementations, the processing circuitry may be used to cause the respective functional unit to perform corresponding functions according one or more embodiments of the present disclosure.

[0284] As described herein, device and / or apparatus can be represented by a semiconductor chip, a chipset, or a (hardware) module comprising such chip or chipset; this, however, does not exclude the possibility that a functionality of a device or apparatus, instead of being hardware implemented, be implemented as a software module such as a computer program or a computer P106755W001

[0285] program product comprising executable software code portions for execution or being run on a processor. Furthermore, functionality of a device or apparatus can be implemented by any combination of hardware and software. A device or apparatus can also be regarded as an assembly of multiple devices and / or apparatuses, whether functionally in cooperation with or independently of each other. Moreover, devices and apparatuses can be implemented in a distributed fashion throughout a system, so long as the functionality of the device or apparatus is preserved. Such and similar principles are considered known to a skilled person.

[0286] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

Claims

P106755W001CLAIMS1. A method for determining a precoder for a transmission by a second node to a first node via a wireless channel, the method performed by a network node and comprising:determining (930) a plurality of scalar products based on a plurality of complex channel vectors that represent the wireless channel at a first time, wherein the plurality of scalar products are based on respective different combinations of the following: one of the complex channel vectors, anda complex conjugate of the same or a different one of the complex channel vectors;determining (940) one or more predicted feature vectors to represent the wireless channel at a second time after the first time, based on the following:one or more feature vectors derived from the plurality of scalar products, and for each of at least one third time before the first time, one or more previous feature vectors that represent the wireless channel at the third time; and based on the one or more predicted feature vectors, determining (960) a precoder for a transmission by the second node via the wireless channel at the second time.

2. The method of claim 1, wherein the plurality of scalar products include the following: a plurality of first scalar products corresponding to the plurality of complex channel vectors, wherein each first scalar product is determined based on a corresponding complex channel vector and its complex conjugate; anda plurality of second scalar products corresponding to different pairs of the plurality of complex channel vectors, wherein each second scalar product is determined based on one complex channel vector of the corresponding pair and a complex conjugate of the other complex channel vector of the corresponding pair.

3. The method of any one of claims 1-2, wherein:the transmission by the first node at the second time is non-phase-coherent with one or more previous transmissions by the first node, on which the plurality of complex channel vectors are based; andthe plurality of scalar products represent the wireless channel independent of the nonphase-coherence.P106755W0014. The method of any one of claims 1-3, wherein the plurality of complex channel vectors correspond respectively to a plurality of second antenna ports of the second node, and each complex channel vector includes channel estimates of the wireless channel from a plurality of first antenna ports of the first node to the corresponding second antenna port.

5. The method of any one of claims 1-4, wherein:each complex channel vector includes respective channel estimates for a plurality of frequency units within a bandwidth of the wireless channel; and the one or more feature vectors include a single feature vector that represents the bandwidth of the wireless channel.

6. The method of any one of claims 1-4, wherein:each complex channel vector includes channel estimates for one of a plurality of frequency units within a bandwidth of the wireless channel; and the one or more feature vectors include a plurality of feature vectors that represent respectively the plurality of frequency units within the bandwidth of the wireless channel.

7. The method of any one of claims 1-6, wherein each of the one or more feature vectors includes a plurality of entries, with each entry being one of the following: one of the determined scalar products, or a real value derived from one of the determined scalar products.

8. The method of any one of claims 1-7, wherein the method further comprises, using the determined precoder, encoding (970) data to be included in the transmission by the second node via the wireless channel at the second time.

9. The method of any one of claims 1-8, further comprising:obtaining (910) measurements of reference signals that are transmitted by the first node via a plurality of first antenna ports and received by the second node via a plurality of second antenna ports; anddetermining (920) the plurality of complex channel vectors based on the measurements of the reference signals.

10. The method of claim 9, wherein determining (920) the plurality of complex channel vectors based on the reference signal measurements comprises:P106755W001determining (921) a second plurality of complex channel vectors based on the measurements of the reference signals; anddetermining (922) the plurality of complex channel vectors based on a projection of the second plurality of complex channel vectors onto a subset of a complete beam space for an antenna array arranged to provide the plurality of second antenna ports.

11. The method of claim 10, wherein determining (922) the plurality of complex channel vectors based on a projection of the second plurality of complex channel vectors onto a subset of a complete beam space comprises:determining a first projection of the second plurality of complex channel vectors onto the complete beam space over a bandwidth of the wireless channel; and selecting, as the subset, a predetermined number of beams of the complete beam space according to a criterion of maximizing power of the first projection over the bandwidth of the wireless channel.

12. The method of any one of claims 1-11, wherein the first node is a user equipment, UE, and the second node is a radio access network, RAN, node.

13. The method of claim 1-12, wherein the network node that performs the method is one of the following: the second node, or a network node coupled to the second node14. The method of any one of claims 1-13, wherein determining (940) the one or more predicted feature vectors to represent the wireless channel at the second time comprises:determining (941) a function that maps the one or more feature vectors and the one or more previous feature vectors, for each of the at least one third time, to a feature vector space at the second time; anddetermining (942) the one or more predicted feature vectors based on the function.

15. The method of claim 14, wherein the function is a state-space model based on an autoregressive, AR, random process, and determining the one or more predicted feature vectors is based on applying a maximization criterion to the state-space model.P106755W00116. The method of claim 14, wherein the function is a multi-dimensional Gaussian distribution, and determining the one or more predicted feature vectors is based on random selection from the multi-dimensional Gaussian distribution.

17. The method of any one of claims 1-16, further comprising determining (950) a projection of the one or more predicted feature vectors onto a complete beam space for an antenna array of the second node, wherein the precoder is determined based on the projection of the one or more predicted feature vectors.

18. The method of claim 17, wherein for each of the one or more predicted feature vectors, determining (950) the projection onto the complete beam space comprises:determining (951) a predicted feature matrix based on entries of the predicted feature vector; andusing a matrix representation Bj of a subset of the complete beam space, determining (952) a projection of the predicted feature matrix from the subset of the complete beam space to the complete beam space.

19. The method of claim 18, wherein determining (951) the predicted feature matrix comprises:using first entries from the predicted feature vector to form entries on a main diagonal of the predicted feature matrix; andusing second entries from the predicted feature vector to form entries above and below the main diagonal of the predicted feature matrix.

20. The method of any one of claims 18-19, wherein determining (960) the precoder for a transmission by the second node via the wireless channel at the second time is based on performing (961) a singular value decomposition, SVD, of each projection of the predicted feature matrix, or of a matrix derived therefrom.

21. A network node (110, 120, 1008, 1010, 1100, 1202) configured to determine a precoder for a transmission from a second node (110, 120, 1010, 1100) to a first node (105, 1012) via a wireless channel, the network node comprising processing circuitry (210, 220, 1102, 1204) configured to:determine a plurality of scalar products based on a plurality of complex channel vectors that represent the wireless channel at a first time, wherein the plurality of scalarP106755W001products are based on respective different combinations of the following: one of the complex channel vectors, and a complex conjugate of the same or a different one of the complex channel vectors;determine one or more predicted feature vectors to represent the wireless channel at a second time after the first time, based on the following:one or more feature vectors derived from the plurality of scalar products, and for each of at least one third time before the first time, one or more previous feature vectors that represent the wireless channel at the third time; and based on the one or more predicted feature vectors, determine a precoder for a transmission by the second node via the wireless channel at the second time.

22. The network node of claim 21, wherein the network node is the second node and further comprises:an antenna array (244, 1110) arranged as a plurality of second antenna ports; communication interface circuitry (230, 242, 1106, 1204) operably coupled to the processing circuitry and configured to transmit and receive via the antenna array.

23. The network node of any one of claims 21-22, wherein the processing circuity is further configured to perform operations corresponding to any one of the methods of claims 2-20.

24. A network node (110, 120, 1008, 1010, 1100, 1202) configured to determine a precoder for a transmission from a second node (110, 120, 1010, 1100) to a first node (105, 1012) via a wireless channel, the network node being further configured to:determine a plurality of scalar products based on a plurality of complex channel vectors that represent the wireless channel at a first time, wherein the plurality of scalar products are based on respective different combinations of the following: one of the complex channel vectors, and a complex conjugate of the same or a different one of the complex channel vectors;determine one or more predicted feature vectors to represent the wireless channel at a second time after the first time, based on the following:one or more feature vectors derived from the plurality of scalar products, and for each of at least one third time before the first time, one or more previous feature vectors that represent the wireless channel at the third time; and based on the one or more predicted feature vectors, determine a precoder for a transmission by the second node via the wireless channel at the second time.P106755W00125. The network node of claim 24, wherein the network node is further configured to perform operations corresponding to any one of the methods of claims 2-20.

26. A non-transitory, computer-readable medium (1104, 1204) storing computer-executable instructions that, when executed by processing circuitry (210, 220, 1102, 1204) of a network node (110, 120, 1008, 1010, 1100, 1202) configured to determine a precoder for a transmission from a second node (110, 120, 1010, 1100) to a first node (105, 1012) via a wireless channel, configure the network node to perform operations corresponding to any one of the methods of claims 1-20.

27. A computer program product (1104a, 1204a) comprising computer-executable instructions that, when executed by processing circuitry (210, 220, 1102, 1204) of a network node (110, 120, 1008, 1010, 1100, 1202) configured to determine a precoder for a transmission from a second node (110, 120, 1010, 1100) to a first node (105, 1012) via a wireless channel, configure the network node to perform operations corresponding to any one of the methods of claims 1-20.

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