Handling coefficients of co-variability of antenna elements

Abstract

A first node (101) determines (405), within each subset of one or more subsets of coefficients of co-variability between pairs of antenna elements in an antenna array (150), an indication of similarity between pairs of coefficients within a same subset. Each of the subsets corresponds to antenna elements sharing a geometrical relationship in the array. Each of the subsets comprises at least two coefficients selected to represent a respective subset. The determining (405) is based on measurements of reference signals transmitted from, or received by, the antenna elements. The first node (101) determines (406) subgroups of coefficients for each of the subsets comprising at least one coefficient having the first indication below a threshold, so that within the determined subgroups, the coefficients have a respective indication within a respective range. The first node (101) then provides (407) a second indication indicating the subgroups.

Description

[0001] HANDLING COEFFICIENTS OF CO-VARIABILITY OF ANTENNA ELEMENTS

[0002] TECHNICAL FIELD

[0003] The present disclosure relates generally to a first node and methods performed thereby for handling coefficients of co-vari ability of antenna elements. The present disclosure further relates generally to a second network node and methods performed thereby, for handling the coefficients of co-variability of the antenna elements. The present disclosure also relates generally to a computer programs and a computer-readable storage mediums, having stored thereon the computer programs to carry out these methods.

[0004] BACKGROUND

[0005] Wireless devices within a wireless communications network may be e.g., User Equipments (UE), stations (STAs), mobile terminals, wireless terminals, terminals, and / or Mobile Stations (MS). Wireless devices are enabled to communicate wirelessly in a cellular communications network or wireless communication network, sometimes also referred to as a cellular radio system, cellular system, or cellular network. The communication may be performed e.g., between two wireless devices, between a wireless device and a regular telephone and / or between a wireless device and a server via a Radio Access Network (RAN) and possibly one or more core networks, comprised within the wireless communications network. Wireless devices may further be referred to as mobile telephones, cellular telephones, laptops, or tablets with wireless capability, just to mention some further examples. The wireless devices in the present context may be, for example, portable, pocket-storable, hand-held, computer-comprised, or vehicle-mounted mobile devices, enabled to communicate voice and / or data, via the RAN, with another entity, such as another terminal or a server.

[0006] The wireless communications network covers a geographical area which may be divided into cell areas, each cell area being served by a network node, which may be an access node such as a radio network node, radio node or a base station, e.g., a Radio Base Station (RBS), which sometimes may be referred to as e.g., gNB, evolved Node B (“eNB”), “eNodeB”, “NodeB”, “B node”, Transmission Point (TP), or Base Transceiver Station (BTS), depending on the technology and terminology used. The base stations may be of different classes such as e.g., Wide Area Base Stations, Medium Range Base Stations, Local Area Base Stations, Home Base Stations, pico base stations, etc... , based on transmission power and thereby also cell size. A cell is the geographical area where radio coverage is provided by the base station or radio node at a base station site, or radio node site, respectively. One base station, situated on the base station site, may serve one or several cells. Further, each base station may support one or several communication technologies. The base stations communicate over the air interface operating on radio frequencies with the terminals within range of the base stations. The wireless communications network may also be a non-cellular system, comprising network nodes which may serve receiving nodes, such as wireless devices, with serving beams. In 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE), base stations, which may be referred to as eNodeBs or even eNBs, may be directly connected to one or more core networks. In the context of this disclosure, the expression Downlink (DL) may be used for the transmission path from the base station to the wireless device. The expression Uplink (UL) may be used for the transmission path in the opposite direction i.e., from the wireless device to the base station.

[0007] The standardization organization 3GPP is currently in the process of specifying a New Radio Interface called NR or 5G-UTRA, as well as a Fifth Generation (5G) Packet Core Network, which may be referred to as Next Generation (NG) Core Network, abbreviated as NG-CN, NGC or 5G CN.

[0008] Large antenna arrays for wireless cellular communications may be used in a mobile radio network in order to increase capacity and performance. The use of multiple antennas combined with adequate processing may be understood to be one way to improve the spectral efficiency of a communication system.

[0009] When using multiple antennas, e.g., in the form of large antenna arrays at base stations in a mobile radio network, transmissions between nodes of the radio network, such as between said base stations and wireless devices, may pass over several antenna elements. Therefore, a radio channel between, e.g., a wireless device and a serving base station having a plurality of antenna elements may be understood to be multi-dimensional in that there may be understood to be a plurality of propagation paths between the wireless device and the different antenna elements of the serving base station, where each path may be associated with a gain and a phase, relative to the other paths or to a reference value. It may be understood to be important for many reasons to be able to characterize this multi-dimensional channel.

[0010] A traditional way of characterizing this type of multi-dimensional channel may be by a covariability matrix of the channel. A co-variability matrix of the channel may be used herein to refer to any of a covariance matrix or a correlation matrix, which may provide information on a stochastic relationship between signals passing over the different antenna elements. This covariability matrix may be often signalled between nodes of the network and also used in signal processing in the communication system, e.g., in beamforming applications. In multi-antenna processing it is very common to estimate spatial channel co-variability matrices and use these to determine beamforming weights. For an N-element antenna array, the spatial channel co-variability matrix R may be typically of size N x N where each element may be understood to represent the channel co-variability between element i and element j. As known in the art, R may be estimated using reference signals such as Demodulation Reference Signals (DM-RS) or Sounding Reference Signals (SRS).

[0011] The channel co-variability between two elements in an antenna array may be understood to be a function of the distribution of incoming, or, by reciprocity, outgoing, radio waves and the spatial separation of the two elements. The spatial separation between two elements in an antenna array may be indicated by a so-called displacement vector as will be illustrated next.

[0012] Each antenna array may be understood to comprise a set of antenna elements. Figure 1 is a schematic representation depicting an example of a periodic antenna array with 2 x 3 antenna elements. In Figure 1, the antenna elements are represented by black dots. The respective positions, e.g., in relation to an arbitrary origin, of the antenna elements m and n of any pair of antenna elements in a spatial layout of the antenna array may be described by position vectors rmand rn, respectively, which are schematically represented in the figure by arrows. A geometrical relationship dmnbetween the antenna elements of the pair of antenna elements may be defined by rm-rn, as illustrated in Figure 1. The geometrical relationship dmn=rm-rndescribing how one antenna element may be displaced with respect to another may be hereinafter referred to as a displacement vector.

[0013] Figure 2 is a schematic representation depicting an example of a recurring displacement vector, depicted with arrows, in a periodic antenna array with 2 x 3 antenna elements, in panel a), and the recurring instances of the opposite of this displacement vector, depicted with arrows in panel b). A recurring displacement vector may be understood to mean that the distance and direction from one antenna x to another antenna y exactly the same as the distance and direction from antenna z to antenna w. The number of displacement vectors in an array may be understood to equal the number of elements in the co-variability matrix and may be N2for an antenna array with N antennas.

[0014] The size of the above-mentioned co-variability matrix may be understood to grow with the square of the number of elements in the antenna array. Large antenna array sizes may hence tax resources concerning computational power and memory storage, even for simple sample covariance estimators. Furthermore, in cases where the channel state information (CSI) that may be passed e.g., between nodes in a communication network may include covariability matrix information, the transmission bandwidth of the inter-node link may be overloaded. While this may be manageable for a single link or for moderately-sized arrays, the size of the matrix in combination with a large number of concurrent communication links may become unmanageable.

[0015] WO 2018124950 and US 10,547,370 teach the fact that if the incoming radio waves to an antenna array are essentially planar and the same for every observation point on the array, there may be significant redundant information in R. In particular, for an N x N uniform planar array there may only be 2MN — M — N + 1 unique elements in the matrix, and these may correspond to the unique spatial displacement vectors between pairs of elements in the array.

[0016] As taught by WO 2018124950 and US 10,547,370, the spatial co-variability between pairs of antenna elements that have the same displacement vector may be understood to be equal, while pairs with opposite but equal length displacement vectors may be understood to have spatial co-variability that may only differ by a complex conjugate.

[0017] WO 2018124950 and US 10,547,370 teach how these observations may be used to compactly represent R, with applications for better estimation of R, for more efficient storage and Channel State Information (CSI) reporting involving R, and less computationally complex matrix algebra involving R.

[0018] WO 2018124950 discloses a method whereby a radio node may measure one or more reference signals transmitted from antenna elements of a transmit antenna array. The radio node may then determine a subset of coefficients of a channel correlation matrix that may characterize channel correlation between two or more of the antenna elements of the transmit antenna array according to the measurement. This subset may include, for each of one or more antenna element separation distances, a coefficient from which channel correlation between any of the two or more antenna elements that are separated by that distance may be derivable. The radio node may then transmit the subset of coefficients as channel correlation feedback that parameterizes the channel correlation matrix.

[0019] US 10,547,370 discloses a method which includes obtaining geometrical relationships between any pair of antenna elements in a spatial layout of the antenna array. All pairs of antenna elements may be classified into sets based on the obtained geometrical relationships, so that all pairs of antenna elements in a set may have a substantially equal geometrical relationship in the spatial layout. The method also includes determining a representation of channel characteristics as P(P), wherein argument p is a vector of elements, each element relating to a magnitude and / or phase of covariance between the antenna elements in the set, and P is a mapping function based on the classifying. Antenna characteristics may then be processed based on the representation P(P).

[0020] Existing methods to handle antenna characteristics in large antenna arrays may result, under certain circumstances, in erroneous beamforming weights being used which may cause performance losses. SUMMARY

[0021] It is an object of embodiments herein to improve the handling coefficients of co-variability of antenna elements.

[0022] According to a first aspect of embodiments herein, the object is achieved by a method, performed by a first node. The method is for handling coefficients of co-variability of antenna elements. The first node operates in a wireless communications network. The first node determines, within each subset of one or more subsets of coefficients of co-variability between pairs of antenna elements comprised in an antenna array, a first indication. The first indication is of a similarity between pairs of coefficients of co-variability within a same subset. Each of the one or more subsets corresponds to antenna elements sharing a geometrical relationship in a spatial layout of the antenna array. Each of the one or more subsets comprises at least two coefficients of co-variability selected to represent the respective subset. The determining is based on measurements of one or more reference signals transmitted from, or received by, the antenna elements. The first node determines one or more subgroups of coefficients of covariability for each of the subsets of coefficients comprising at least one coefficient having the first indication below the first threshold, so that within the determined one or more subgroups, the coefficients have a respective first indication within a respective range below the first threshold. The first node then provides a second indication indicating the determined one or more subgroups.

[0023] According to a second aspect of embodiments herein, the object is achieved by a method, performed by a second node. The method is for handling the coefficients of covariability of antenna elements. The second node operates in the wireless communications network. The second network node receives the second indication from the first node operating in the wireless communications network. The second indication indicates the one or more subgroups of coefficients of co-variability for each of the one or more subsets of coefficients of co-variability between the pairs of antenna elements comprised in an antenna array. Each of the one or more subsets corresponds to the antenna elements sharing the geometrical relationship in the spatial layout of the antenna array. Each of the one or more subsets comprises at least two coefficients of co-variability selected to represent the respective subset. Each of the one or more subsets comprise the at least one coefficient having the first indication, of the similarity between the pairs of coefficients of co-variability within the same subset, below the first threshold. The first indication is based on the measurements of the one or more reference signals transmitted from, or received by, the antenna elements, so that within the one or more subgroups, the coefficients have the respective first indication within the respective range below the first threshold. The second node then initiates using the second indication. According to a third aspect of embodiments herein, the object is achieved by the first node. The first node may be understood to be for handling the coefficients of co-variability of antenna elements. The first node is configured to operate in the wireless communications network. The first node is configured to determine, within each subset of the one or more subsets of coefficients of co-variability between the pairs of antenna elements configured to be comprised in the antenna array, the first indication. The first indication is of the similarity between the pairs of coefficients of co-variability within the same subset. Each of the one or more subsets is configured to correspond to the antenna elements configured to share the geometrical relationship in the spatial layout of the antenna array. Each of the one or more subsets is configured to comprise at least two coefficients of co-variability configured to be selected to represent the respective subset. The determining is configured to be based on the measurements of the one or more reference signals configured to be transmitted from, or received by, the antenna elements. The first node is also configured to determine the one or more subgroups of coefficients of co-variability for each of the subsets of coefficients configured to comprise at the least one coefficient having the first indication below the first threshold, so that within the determined one or more subgroups, the coefficients have the respective first indication within the respective range below the first threshold. The first node is further configured to provide the second indication configured to indicate the one or more subgroups configured to be determined.

[0024] According to a fourth aspect of embodiments herein, the object is achieved by the second node. The second node may be understood to be for handling the coefficients of covariability of antenna elements. The second node is configured to operate in the wireless communications network. The second node is configured to receive the second indication from the first node configured to operate in the wireless communications network. The second indication is configured to indicate the one or more subgroups of coefficients of co-variability for each of the one or more subsets of coefficients of co-variability between pairs of antenna elements configured to be comprised in the antenna array. Each of the one or more subsets is configured to correspond to the antenna elements sharing the geometrical relationship in the spatial layout of the antenna array. Each of the one or more subsets is configured to comprise at least two coefficients of co-variability configured to be selected to represent the respective subset. Each of the one or more subsets is configured to comprise at least one coefficient having the first indication, of the similarity between pairs of coefficients of co-variability within the same subset, below the first threshold. The first indication is configured to be based on the measurements of the one or more reference signals configured to be transmitted from, or received by, the antenna elements, so that within the one or more subgroups, the coefficients have the respective first indication within the respective range below the first threshold. The second node is also configured to initiate using the second indication. According to a fifth aspect of embodiments herein, the object is achieved by a computer program, comprising instructions which, when executed on at least one processing circuitry, cause the at least one processing circuitry to carry out the method performed by the first node.

[0025] According to a sixth aspect of embodiments herein, the object is achieved by a computer-readable storage medium, having stored thereon the computer program, comprising instructions which, when executed on at least one processing circuitry, cause the at least one processing circuitry to carry out the method performed by the first node.

[0026] According to a seventh aspect of embodiments herein, the object is achieved by a computer program, comprising instructions which, when executed on at least one processing circuitry, cause the at least one processing circuitry to carry out the method performed by the second node.

[0027] According to an eighth aspect of embodiments herein, the object is achieved by a computer-readable storage medium, having stored thereon the computer program, comprising instructions which, when executed on at least one processing circuitry, cause the at least one processing circuitry to carry out the method performed by the second node.

[0028] By the first node determining the first indication of the similarity between the pairs of coefficients of co-variability within each subset corresponding to antenna elements sharing the geometrical relationship in the spatial layout of the antenna array, the first node may be enabled to identify possible deviations from plane wave incidence via comparison of covariability coefficients corresponding to pairs of antenna elements with identical displacement vectors but located in different parts of the array. This may enable to address that there may be situations where the different parts of the antenna array may be differently illuminated by the incoming radio waves. For example, objects near the antenna array, such as roof edges, chimneys, etc may shadow only part of the array, or some of the incoming waves may originate from a nearby point or line sources resulting in non-planar wavefronts at the array.

[0029] By then determining the one or more groups of coefficients of co-variability for each of the subsets of coefficients comprising at least one coefficient having the first indication below the first threshold, the first node may be enabled to adjust the compression level of the representation, e.g., R, of the characteristics of a radio channel wherein the one or more reference signals may be transmitted from, or received by, the antenna elements to account for the different parts of the antenna array that may be differently illuminated by the incoming radio waves or by line sources resulting in non-planar wavefronts at the array. One possible adjustment may be to reduce the compression level for the representation of R.

[0030] By then providing the second indication indicating the determined one or more subgroups, the first node may enable to use the representation, e.g., R, of the characteristics of the radio channel wherein the one or more reference signals may be transmitted from, or received by, the antenna elements, while transmitting the representation in a more efficient than representing the full spatial representation, e.g., R, of the characteristics of the radio channel, yet enabling to avoid issues with the compact representation when there may be non- planar waves or partial shadowing of the antenna array.

[0031] By providing the second indication indicating the one or more subgroups, the first node may enable, for example, that the channel co-variability matrix may be reconstructed by the receiver of the second indication, e.g., the second node. The receiver of the second indication may then be enabled to e.g., precode a transmission, e.g., of user data, based on the reconstructed channel correlation matrix R. By providing the second indication indicating the one or more subgroups, the first node may enable that the reconstruction of R may be performed with similar quality, but lower complexity. Furthermore, since a communication link may be understood to be associated with a certain capacity in terms of, e.g., bits / sec, by providing the second indication indicating the one or more subgroups, the first node may enable that less of this capacity may be taken up by transmissions of channel characteristics, leaving more room for payload transmissions, e.g., user data. The signal processing operations using the representation according to the one or more subgroups may be reduced in complexity, leading to faster processing times and reduced load on memory and bandwidth. A yet further advantage may be understood to be that memory requirements may be reduced when storing channel characteristics. Yet another advantage may be understood to be that signal processing operations relating to channel characteristics may be made more efficient in terms of implementation.

[0032] BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Examples of embodiments herein are described in more detail with reference to the accompanying drawings, and according to the following description.

[0034] Figure 1 is a schematic representation depicting an example of a uniform planar array with 2x3 elements, according to existing methods.

[0035] Figure 2 is a schematic representation depicting an example of a) a recurring displacement vector in a regular array, and b) the recurring instances of the opposite of this displacement vector, according to existing methods.

[0036] Figure 3 is a schematic diagram illustrating a wireless communications network, according to embodiments herein.

[0037] Figure 4 is a flowchart depicting an example of a method performed by a first node, according to embodiments herein.

[0038] Figure 5 is a schematic diagram illustrating an example of aspects of a method performed by a first node, according to embodiments herein. Figure 6 is a schematic diagram illustrating an example of a covariance matrix with structure corresponding to a six-element uniform linear array, according to embodiments herein.

[0039] Figure 7 is a schematic representation depicting a non-limiting example of group belongings for the covariance matrix elements, according to a) existing methods, and b) embodiments herein.

[0040] Figure 8 is a flowchart depicting an example of a method performed by a second node, according to embodiments herein.

[0041] Figure 9 is a schematic block diagram illustrating two non-limiting examples, a) and b), of a first node, according to embodiments herein.

[0042] Figure 10 is a schematic block diagram illustrating two non-limiting examples, a) and b), of a second node, according to embodiments herein.

[0043] DETAILED DESCRIPTION

[0044] As part of the development of embodiments herein, one or more challenges with the existing technology will first be identified and discussed.

[0045] For very large antenna arrays, there may be situations where the different parts of the array are differently illuminated by the incoming radio waves. For example, objects near the antenna array such as roof edges, chimneys, etc may shadow only part of the array, or some of the incoming waves may originate from a nearby point or line sources resulting in non-planar wavefronts at the array. The basic assumption behind WO 2018124950 and US 10,547,370, namely that the incoming radio waves are planar, then no longer holds in such scenarios, and applying the solutions taught by these references may lead to errors in the representation of R. This may then lead to erroneous beamforming weights being used which may cause performance losses.

[0046] Another situation that may create different co-variability coefficients for different pairs of antenna elements with the same spatial separation is if the radiation properties of the antennas, such as amplitude, phase, and polarization as a function of angle, may not be identical for all elements in the array. Practical antenna arrays, in contrast to theoretical antenna arrays, may experience such differences due to manufacturing tolerances and mutual coupling, which may affect centralized antenna elements and edge antenna elements differently.

[0047] Certain aspects of the present disclosure and their embodiments may provide solutions to these challenges or other challenges. There are, proposed herein, various embodiments which address one or more of the issues disclosed herein. Embodiments herein may be understood to be related to an effective co-variability handling for large antenna arrays.

[0048] Particular embodiments herein may relate to identifying possible deviations from plane wave incidence via comparison of co-variability coefficients corresponding to pairs of antenna elements with identical displacement vectors but located in different parts of the array, and using this information to adjust the representation of R. One possible adjustment may be to reduce the compression level for the representation of R.

[0049] Some of the embodiments contemplated will now be described more fully hereinafter with reference to the accompanying drawings, in which examples are shown. In this section, the embodiments herein will be illustrated in more detail by a number of exemplary embodiments. 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 by way of example to convey the scope of the subject matter to those skilled in the art. It should be noted that the exemplary embodiments herein are not mutually exclusive. Components from one embodiment may be tacitly assumed to be present in another embodiment and it will be obvious to a person skilled in the art how those components may be used in the other exemplary embodiments.

[0050] Note that although terminology from LTE / 5G has been used in this disclosure to exemplify the embodiments herein, this should not be seen as limiting the scope of the embodiments herein to only the aforementioned system. Other wireless systems with similar features, may also benefit from exploiting the ideas covered within this disclosure.

[0051] Figure 3 depicts two non-limiting example of a wireless communications network 100, sometimes also referred to as a wireless communications system, cellular radio system, or cellular network, in which embodiments herein may be implemented. The wireless communications network 100 may typically be a 5G system, 5G network, NR-U or Next Gen System or network, Licensed-Assisted Access (LAA), MulteFire. The wireless communications network 100 may support a younger system than a 5G system. The wireless communications network 100 may support other technologies, such as, for example Long- Term Evolution (LTE), LTE-Advanced I LTE-Advanced Pro, e.g. LTE Frequency Division Duplex (FDD), LTE Time Division Duplex (TDD), LTE Half-Duplex Frequency Division Duplex (HD-FDD), LTE operating in an unlicensed band, etc... Other examples of other technologies the wireless communications network 100 may support may be Wideband Code Division Multiple Access (WCDMA), Universal Terrestrial Radio Access (UTRA) TDD, Global System for Mobile communications (GSM) network, GSM / Enhanced Data Rates for GSM Evolution (EDGE) Radio Access Network (GERAN) network, Ultra-Mobile Broadband (UMB), EDGE network, network comprising of any combination of Radio Access Technologies (RATs) such as e.g. Multi-Standard Radio (MSR) base stations, multi-RAT base stations etc., any 3rd Generation Partnership Project (3GPP) cellular network, WiFi networks, Worldwide Interoperability for Microwave Access (WiMax), loT, NB-loT, or any cellular network or system. Thus, although terminology from 5G / NR and LTE may be used in this disclosure to exemplify embodiments herein, this should not be seen as limiting the scope of the embodiments herein to only the aforementioned systems.

[0052] The wireless communications network 100 comprises a first node 101 , a second node 102 and a third node 103, as depicted in the non-limiting example Figure 3. Any of the first node 101, the second node 102 and the third node 103 may be a radio network node, such as any of the first radio network node 111 and the second radio network node 112 described below, a core network node, such as the core network node 120 described below, or a wireless device, such as any of the first wireless device 131 and the second wireless device 132 described below.

[0053] The first node 101, the second network node 102 and the third network node 103 may, in some examples, be co-located or be the same network node. In the non-limiting example depicted in panel a) of Figure 3, the first node 101 is co-localized with the third node 103. In other examples, such as in non-limiting example depicted in Figure 3 b), the first node 101 , the second node 102 and the third node 103 may be different nodes.

[0054] The wireless communications network 100 comprises a first radio network node 111 and a second radio network node 112, as depicted in the non-limiting example Figure 3. A radio network node may be understood as a transmission point such as a radio base station, for example a gNB, an eNB, or any other network node with similar features capable of serving a wireless device, such as a user equipment or a machine type communication device, in the wireless communications network 100. In other examples, any of the first node 101 and the second node 102 may be a distributed node, such as a virtual node in the cloud 115, and may perform its functions entirely on the cloud 115, or partially, in collaboration with a radio network node.

[0055] The wireless communications network 100 covers a geographical area which may be divided into cell areas, wherein each cell area may be served by a radio network node, although, one radio network node may serve one or several cells. Cells are not represented in Figure 3 to simplify the figure.

[0056] Any of the first radio network node 111 and the second radio network node 112 may be of different classes, such as, e.g., macro base station, home base station or pico base station, based on transmission power and thereby also cell size. Any of the first radio network node 111 and the second radio network node 112 may support one or several communication technologies, and its name may depend on the technology and terminology used. In 5G / NR, any of the first radio network node 111 and the second radio network node 112 may be referred to as a gNB and may be directly connected to one or more core networks.

[0057] In the non-limiting example depicted in Figure 3 b), the first node 101 is a core network node in the cloud 115.

[0058] One or more wireless devices such as a first wireless device 131 and a second wireless device 132 may be comprised in the wireless communication network 100. Any of the first wireless device 131 and the second wireless device 132 comprised in the wireless communications network 100 may be a wireless communication device such as a 5G UE, or a UE, which may also be known as e.g., mobile terminal, wireless terminal and / or mobile station, a mobile telephone, cellular telephone, or laptop with wireless capability, just to mention some further examples. Any of the first wireless device 131 and the second wireless device 132 comprised in the wireless communications network 100 may be, for example, portable, pocket- storable, hand-held, computer-comprised, or a vehicle-mounted mobile device, enabled to communicate voice and / or data, via the RAN, with another entity, such as a server, a laptop, a Personal Digital Assistant (PDA), or a tablet, Machine-to-Machine (M2M) device, device equipped with a wireless interface, such as a printer or a file storage device, modem, or any other radio network unit capable of communicating over a radio link in a communications system. Any of the first wireless device 131 and the second wireless device 132 comprised in the wireless communications network 100 may be enabled to communicate wirelessly in the wireless communications network 100. The communication may be performed e.g., via a RAN, and possibly the one or more core networks, which may be comprised within the wireless communications network 100.

[0059] Any of the one or more wireless devices such as the first wireless device 131 and the second wireless device 132, and the second radio network node 112 may be referred to as a plurality of nodes 131 , 132, 112.

[0060] The first radio network node 111 may be configured to communicate within the wireless communications network 100 with the first wireless device 131 over a first link 141, e.g., a radio link. The first radio network node 111 may be configured to communicate within the wireless communications network 100 with the second wireless device 132 over a second link 142, e.g., a radio link. The first radio network node 111 and the second radio network node 112 may be configured to communicate within the wireless communications network 100 over a third link 143, e.g., a wired link, a radio link or an X2 interface. The first radio network node 111 may be configured to communicate within the wireless communications network 100 with the core network node 120 over a fourth link 144, e.g., a radio link or a wired link.

[0061] Any of the first node 101 , the second node 102 and the third node 103 may comprise an antenna array 150. In some embodiments, one of the second node 102 and the third node 103 may comprise the antenna array 150. The antenna array 150 may comprise a plurality of antenna elements. In the non-limiting example of Figure 3, for illustration purposes only, the antenna array 150 is depicted as comprising four antenna elements depicted as black dots. The antenna elements may be arranged in the antenna array 150 in one or more spatial dimensions. Also, in the non-limiting example of Figure 3, and for illustration purposes only, the antenna array 150 is depicted as being comprised in the third node 103, which is the same node as the first node 101 in panel a) and is the first radio network node 111. In panel b), and also for illustration purposes only, the antenna array 150 is depicted as being comprised in the second node 102, which is the first radio network node 111. It may be understood that these examples are non-limiting. The antenna array 150 may be comprised in any of e.g., the first wireless device 131, the second wireless device 132 and the second network node 112. All the combinations are not depicted in Figure 3 to simplify the Figure.

[0062] In general, the usage of “first”, “second”, “third” and / or “fourth” herein may be understood to be an arbitrary way to denote different elements or entities, and may be understood to not confer a cumulative or chronological character to the nouns they modify.

[0063] Several embodiments are comprised herein. It should be noted that the examples herein are not mutually exclusive. Components from one embodiment may be tacitly assumed to be present in another embodiment and it will be obvious to a person skilled in the art how those components may be used in the other exemplary embodiments.

[0064] Embodiments of a method, performed by a first node, such as the first node 101 , will now be described with reference to the flowchart depicted in Figure 4. The method is for handling coefficients of co-variability of antenna elements. The first node 101 operates in the wireless communications network 100.

[0065] Several embodiments are comprised herein. In some embodiments all the actions may be performed. In some embodiments, some of the actions may be performed. It should be noted that the examples herein are not mutually exclusive. One or more embodiments may be combined, where applicable. All possible combinations are not described to simplify the description. Components from one embodiment may be tacitly assumed to be present in another embodiment and it will be obvious to a person skilled in the art how those components may be used in the other exemplary embodiments. A non-limiting example of the method performed by the first node 101 is depicted in Figure 4. Some actions may be performed in a different order than that shown Figure 4. For example, in some examples, the order of Action 402 and Action 403 may be changed. In some examples, Action 401 may be performed before Action 403 but Action 402 may be performed before or after, not necessarily in between. Action 401

[0066] In this Action 401 , the first node 101 may obtain measurements of one or more reference signals transmitted from or received by antenna elements. The antenna elements are comprised in the antenna array 150. The one or more reference signals are transmitted from, or received by, the antenna elements.

[0067] Obtaining in this Action 401 may comprise performing the measurements or receiving the measurements from another node, such as from the second node 102 or from the third node 103.

[0068] That is, in some examples, the first node 101 may be the receiver of the one or more reference signals, wherein the one or more reference signals may be transmitted via the antenna elements, or received via the antenna elements. In other examples, the first node 101 may be the transmitter of the one or more reference signals via the antenna elements, or transmitted by the first node 101 and then received via the antenna elements by another node, e.g., any of the second node 102 and the third node 103. Yet in other examples, the first node 101 may be a node that may neither transmit nor receive the one or more reference signals, but which may receive the measurements performed by the other node, e.g., any of the second node 102 and the third node 103, see the non-limiting example depicted in panel b) of Figure 3.

[0069] The one or more reference signals may be, for example, one or more Sounding Reference Signals (SRS), or one or more Demodulation Reference Signal (DMRS), if transmitted by any of the first wireless device 131 and the second wireless device 132, or one or more channel state information reference signals (CSI-RS), if transmitted by any of the first radio network node 111 and the second radio network node 112.

[0070] The measurements may be, for example, estimates of the amplitude ratio of and the phase shift between the transmitted reference signals and the received reference signals.

[0071] By obtaining the one or more measurements in this Action 401, the first node 101 may be then enabled to estimate the coefficients of co-variability between pairs of antenna elements comprised in the antenna array 150, as will be described in Action 403.

[0072] Action 402

[0073] The one or more reference signals may be understood to be transmitted from transmitter to receiver via a radio channel. In some embodiments, one of the second node 102 and the third node 103 may comprise the antenna array 150. The radio channel may therefore in such embodiments be between the second node 102, and the third node 103 operating in the communications network 100. As mentioned earlier, the radio channel may be understood to be multi-dimensional, in that there may be understood to be a plurality of propagation paths between the transmitter or receiver of the reference signals and the different antenna elements of the of the antenna array 150, where each path may be associated with a gain and a phase, relative to the other paths or to a reference value.

[0074] This multi-dimensional radio channel may be characterized by a co-variability matrix of the channel. The co-variability may be one of: covariance and correlation. Hence, the covariability matrix of the radio channel may be any of a covariance matrix or a correlation matrix.

[0075] The co-variability matrix, as also stated earlier, may provide information on a stochastic relationship between signals passing over the different antenna elements.

[0076] For an N-element antenna array, the spatial channel co-variability matrix R may be typically of size N x N where each element of the matrix may be understood to represent the channel co-variability between element i and element j. R may be estimated in the next Action 403 using the measurements of one or more reference signals obtained in Action 401. It may be noted that, as mentioned earlier, in some cases, the order of Action 402 and Action 403 may be changed. In some examples, Action 401 may be performed before Action 403 but Action 402 may be performed before or after, not necessarily in between. The channel covariability between two elements in an antenna array may be understood to be a function of the distribution of incoming, or, by reciprocity, outgoing, radio waves and the spatial separation of the two elements. The spatial separation between two elements in an antenna array may be indicated by a displacement vector.

[0077] In this Action 402, the first node 101 may determine a structure of the co-variability matrix of the radio channel.

[0078] Determining may be understood as assessing, calculating, estimating, deriving or similar.

[0079] The determining in this Action 402 of the structure of the co-variability matrix of the radio channel may comprise obtaining geometrical relationships between any pair of antenna elements in a spatial layout of the antenna array 150. The geometrical relationships may be obtained by, for each pair of antenna elements in the antenna array 150, relating a distance and direction of one antenna element of a pair to that of the other antenna element of the same pair. A pair of antenna elements may be understood to also comprise so-called autopairs, meaning the geometrical relationship of a single antenna with itself.

[0080] The structure of the co-variability matrix may be based on respective positions of the antenna elements m and n of any pair of antenna elements in a spatial layout of the antenna array 150. The respective positions may be described by position vectors rmand rn, respectively. A geometrical relationship dmnbetween the antenna elements of the pair of antenna elements may be defined by rm-rn. As explained earlier, the geometrical relationship dmn=rm-rndescribing how one antenna element may be displaced with respect to another may be referred to as a displacement vector. The number of displacement vectors in an array may be understood to equal the number of elements in the co-variability matrix and may be N2for an antenna array with N antennas.

[0081] For an auto-pair, elements m and n refer to the same antenna element, rmand rn, may be understood to be identical and a displacement vector dmn=rm-rnmay be understood to be a null vector.

[0082] When elements m and n refer to different antenna elements, rmand rn, may be understood to be different, and displacement vectors dmnand dnmmay be understood to be vectors of the same magnitude, but with opposite directions. That is, as taught by WO 2018124950 and US 10,547,370, the spatial co-variability between pairs of antenna elements that have the same displacement vector may be understood to be equal, while pairs with opposite but equal length displacement vectors may be understood to have spatial covariability that may only differ by a complex conjugate.

[0083] The determining in this Action 402 of the structure of the co-variability matrix of the radio channel may comprise specifically determining which antenna elements may nominally share the same value of the coefficient of co-variability, e.g., the same real part and, except for the sign, the same imaginary part, based on a geometry of the antenna array 150 and assuming ideal equal radiation patterns of all antenna elements and a set of plane waves incident on the antenna array 150. In particular, if the incoming radio waves to an antenna array are essentially planar and the same for every observation point on the array, for an N x N uniform planar array there may only be 2MN — M — N + 1 unique elements in the matrix, and these may correspond to the unique spatial displacement vectors between pairs of elements in the array.

[0084] All pairs of antenna elements may be classified into sets based on the obtained geometrical relationships, so that all pairs of antenna elements in a set may have a substantially equal geometrical relationship in the spatial layout. All pairs of antenna elements having the same relative position with respect to each other in the spatial layout of the antenna array 150, up to a sign or direction of the displacement vector, may be classified to belong to the same set.

[0085] The determining in this Action 402 may comprise identifying one or more subsets of coefficients of co-variability between pairs of antenna elements comprised in the antenna array 150. Each of the one or more subsets may be understood to correspond to antenna elements sharing a geometrical relationship in the spatial layout of the antenna array 150. The geometrical relationship may be a displacement vector value.

[0086] The coefficients of co-variability may be comprised in the co-variability matrix of the radio channel. Hence, even it at this stage the coefficients of co-variability may not have been estimated yet, their identification in this Action 402 may be based on their correspondence to the antenna elements in the spatial layout, that is, to their position in the co-variability matrix. That is, the coefficients of variability may be identified as R^, R52, R&3, etc.

[0087] The determining in this Action 403 may comprise identifying some or all subsets of coefficients of co-variability.

[0088] The determining in this Action 402 of the structure of the co-variability matrix of the radio channel may further comprise forming groups of such antenna elements, e.g., in the form of the function p( ) described in US 10,547,370. Argument p may be understood to be a vector of elements, each element relating to a magnitude and / or phase of co-variability between the antenna elements in the set, and p may be understood to be a mapping function based on classifying all pairs of antenna elements into sets based on the obtained geometrical relationships, which may map the set of unique values ft to the full covariance matrix R.

[0089] Determination of the function p([J)

[0090] The determination of the function p(fl) as described in Figure 5 of US 10,547,370 is reproduced herein as Figure 5 to facilitate understanding of the method.

[0091] Figure 5 schematically illustrates the determination of the function p(fl) with a nonlimiting example for a uniform linear array comprising four antenna elements.

[0092] Figure 5a schematically illustrates a uniform linear array comprising four antenna elements, wherein the antenna elements are represented by black dots, labelled 1, 2, 3 and 4. According to an aspect, geometrical relationships between all pairs of antenna elements in a spatial layout of the antenna array 150 may be obtained. The geometrical relationships may be obtained using displacement vectors dmn=rm-rn, where rmand rn, may be understood to be position vectors of the respective antenna element m and n of a pair of antennas, as is illustrated in Figure 5b and Figure 5c.

[0093] According to a further aspect, all pairs of antenna elements may be classified into sets based on the obtained geometrical relationships, wherein all pairs of antenna elements in a set may be understood to have substantially equal geometrical relationship in the spatial layout. Pairs of antenna elements in a set having substantially equal geometrical relationships may be based on the displacement vectors, wherein two pairs may be considered having substantially equal geometrical relationships if they are represented by substantially equal displacement vectors, up to a sign. The term “substantially” may be understood as that the geometrical relationships may be understood to not be required to be exactly equal, but only to within a norm or measure relating to a metric.

[0094] Figures 5d-g illustrate sets comprising subsets of the geometrical relationships of Figures 5b and c, wherein each set comprises geometrical relationships that have been classified to have substantially equal geometrical relationship in the spatial layout, up to a sign. The first node 101 may determine a representation of channel characteristics as p( ?), wherein argument / 3 may be understood to be a vector of elements, each element relating to a magnitude and / or phase of covariance between the antenna elements in the set, and p may be understood to be a mapping function based on the classifying.

[0095] Representative geometrical relationships of the sets defined in the classifying may be used as a basis for representing channel covariance.

[0096] Figure 5h illustrates representative geometrical relationships corresponding to a respective set of Figures 5d-5g. Each representative geometrical relationship may be understood to be an element of a respective set of Figures 5d-5g.

[0097] Figure 5i illustrates a set comprising the unique representative geometrical relationships of Figure 5h. The elements of the set of Figure 5i may be used as a basis for representing channel covariance.

[0098] A detailed aspect is described below in relation to Figures 5j-5i for an antenna as illustrated in Figure 5a, using the obtained geometrical relationships, as illustrated in Figures 5b and 5c, and the classification of the obtained geometrical relationships, as illustrated in Figures 5d -5g.

[0099] According to an aspect, p may be understood to be a matrix defined by

[0100] VeC{ Rmn}= p / 3 (1) wherein covariance between antenna elements may be represented by a covariance matrix 7?mn, vec{ / ?mn} denoting the vectorization of 7?mn, m and n being indices running over the number of antenna elements of the antenna array.

[0101] Figure 5j illustrates a representation of channel covariance, the representation comprising the elements of the set of Figure 5i.

[0102] Figure 5k illustrates a parametrization of the representative geometrical relationships of Figure 5i. The four displacement vectors of the set illustrated in Figure 5 k may be represented by the real valued parameters a, b, c, d, e, f and g, such that the null vector may be represented by a and the others may be represented by b-ic, d-ie, f-ig, respectively, where i may be understood to be the imaginary unit, such that i2=— 1.

[0103] Figure 5I illustrates a covariance matrix based on the parametrization illustrated in Figure 5k of the representative geometrical relationships of Figure 5i and the representation of channel covariance illustrated in Figure 5j.

[0104] According to this aspect, as illustrated in Figure 5I , the covariance matrix / ?mnmay be represented by wherein the numbers 1-4 may indicate the respective antenna element, as numbered in Figure 5a , have been added for clarity. Then, using p and / 3 as determined by equation (1) above, may be, according to an aspect, defined by

[0105]

[0106] Since p may be based on the geometrical relationships, p may be based on the structure of the antenna array 150. To further the understanding of embodiments herein, a non-limiting example of a covariability matrix with structure corresponding to a uniform linear array with six elements is shown in Figure 6. All coefficients of co-variability belonging to the same group may be understood to nominally have exactly the same value. Coefficients of co-variability above the main diagonal will be the complex conjugate of coefficients of co-variability below the main diagonal in the same group. In this example, there may be understood to always exist six unique values for the coefficients Rj7, hence these coefficients may be understood to belong to one of six different sets or groups. Of these six groups, three different group belongings, a first group or subset, a second group or subset, and a fourth group or subset are indicated, for the co-variability matrix elements. In this non-limiting example of Figure 6, the three elements f?41, f?52, and / ?63belong to the same subset or group, as do their complex conjugate counterparts R14, R25, and R36.

[0107] The determined coefficients of co-variability between pairs of antenna elements comprised in the antenna array 150 may be understood to effectively compress, or parameterize the channel co-variability matrix R , in the sense that / 3 may be understood to be a compressed representation of R, in a way that may be understood to enable the channel covariability matrix R to be reconstructed from that subset of coefficients.

[0108] By determining the structure of the co-variability matrix of the radio channel in this Action 402, the first node 101 may enable that estimation of channel characteristics in the form of channel co-variability may be performed with similar quality, but lower complexity. A yet further advantage may be understood to be that memory requirements may be reduced when storing channel characteristics. Yet another advantage may be understood to be that signal processing operations relating to channel characteristics may be made more efficient in terms of implementation.

[0109] Action 403

[0110] In this Action 403, the first node 101 may estimate the coefficients of co-variability based on the obtained measurements in Action 401. The first node 101 may estimate covariance or correlation coefficients Rj7between pairs of antennas in the antenna array 150, including at least two coefficients belonging to the same group, that is, the same subset of coefficients of co-variability that may have been assessed to nominally have the same value in Action 402.

[0111] In some examples, at least two coefficients of co-variability may be estimated for every subset.

[0112] In particular examples, at least two coefficients with nominally the same value may need to be calculated.

[0113] In other examples, all coefficients of co-variability in the co-variability matrix may be estimated.

[0114] The estimation of the coefficients of co-variability in this Action 403 may be performed according to known methods.

[0115] In some embodiments, the first node 101 may refrain from performing Action 402 and in this Action 403, the first node 101 may estimate all correlation coefficients Rj7.

[0116] Action 404

[0117] In this Action 404, the first node 101 may determine at least two coefficients of covariability selected to represent each respective subset.

[0118] The determination in this Action 404 may be performed, e.g., randomly, since within each respective subset the coefficients may be understood to be the nominally same, or sufficiently similar. In other examples, the determination in this Action 404 may be performed based on a relation to a location in the antenna array 150. Channel co-variability between any antenna elements that may be separated by a certain distance may be derivable from the at least two coefficients of co-variability selected to represent for that distance.

[0119] Action 405

[0120] The basic premise of WO 2018124950 and US 10,547,370 may be understood to be that different pairs of antenna elements in the antenna array 150 that share the same spatial displacement vector may be understood to have the same co-variability coefficient. While this may be understood to be applicable to idealized, e.g., theoretical, antenna arrays and for a superposition of plane waves incident from different directions, it may not be generally expected to always hold in practical situations. As explained earlier, there may be situations where the different parts of the antenna array 150 may be differently illuminated by the incoming radio waves. For example, objects near the antenna array 150, such as roof edges, chimneys, etc may shadow only part of the array, or some of the incoming waves may originate from a nearby point or line sources resulting in non-planar wavefronts at the array. In order to address this issue, in this Action 405, the first node 101 determines, within each subset of the one or more subsets of coefficients of co-variability between pairs of antenna elements comprised in the antenna array 150, as determined in Action 402, a first indication of a similarity between pairs of coefficients of co-variability within a same subset. Each of the one or more subsets corresponds to antenna elements sharing a geometrical relationship in the spatial layout of the antenna array 150. Each of the one or more subsets comprises the at least two coefficients of co-variability selected to represent the respective subset, as e.g., performed in Action 404.

[0121] That the first node 101 determines the first indication within each subset of the one or more subsets of coefficients of co-variability in this Action 406 may be understood to mean that the first indication may be determined for all the possible subsets of coefficients of covariability that may be determined, for if there are more than two, for at least one or more of them, as described in Action 402.

[0122] The determining in this Action 405 is based on the measurements of the one or more reference signals transmitted from, or received by, the antenna elements, as e.g., performed in Action 401. This may be understood to mean that the coefficient of co-variabilities may have been estimated based on the measurements of the one or more reference signals transmitted from, or received by, the antenna elements.

[0123] In other words, in this Action 405, the first node 101 may determine the similarity of the coefficients of co-variability belonging to the same subset, also referred to herein as group, that is, those coefficients of co-variability that nominally may have the same values, up to a complex conjugate as known in existing methods. The first indication indicating the degree of similarity may be determined in different ways, e.g., by comparing the real and imaginary parts of the difference between the coefficients of co-variability to some relative or absolute threshold, which may be referred to herein as a first threshold, or by comparing the amplitude and phase of the at least two coefficients of co-variability selected to represent the respective subset, as e.g., performed in Action 404. The first threshold may be one common value for all comparisons, or it may be adjusted to be more sensitive to errors in larger groups or groups corresponding to nominally larger magnitudes of the coefficients. The latter may increase the fidelity of the computed beamforming weights based on the resulting compact representation of the covariance matrix.

[0124] By the first node 101 determining the first indication of the similarity between the pairs of coefficients of co-variability within each subset corresponding to antenna elements sharing the geometrical relationship in the spatial layout of the antenna array 150, the first node 101 may be enabled to identify possible deviations from plane wave incidence via comparison of co-variability coefficients corresponding to pairs of antenna elements with identical displacement vectors but located in different parts of the array. This may enable to address that there may be situations where the different parts of the antenna array may be differently illuminated by the incoming radio waves. For example, objects near the antenna array, such as roof edges, chimneys, etc may shadow only part of the array, or where some of the incoming waves may originate from a nearby point or line sources resulting in non-planar wavefronts at the array.

[0125] Action 406

[0126] To address the issue with existing methods described in the previous Action 405, in this Action 406, the first node 101 determines one or more subgroups of coefficients of covariability for each of the subsets of coefficients comprising at least one coefficient having the first indication below the first threshold, so that within the determined one or more subgroups, the coefficients have a respective first indication within a respective range below the first threshold.

[0127] That at least one coefficient may have the first indication below the first threshold may be understood to mean that the at least one coefficient may not be sufficiently similar to the other coefficients of co-variability in the subset. Or put differently, that the at least one coefficient may not sufficiently dissimilar to the other coefficients of co-variability in the subset. In other words, in this Action 406, the first node 101 may split subsets, that is, groups, which may containing dissimilar coefficients of co-variability into two or more distinct subgroups, where the coefficients of co-variability within each new and smaller subgroup may be sufficiently similar to be represented by a single common value. An non-limiting example is shown in Figure 7 (b). Figure 7 depicts a non-limiting example of subset or group belongings for the co-variability matrix elements depicted in Figure 6. Every subset is represented by a same number from 1 to 6 in Figure 7 (a). The example in Figure 7 (a) shows a typical Toeplitz structure according to existing methods e.g., WO 2018124950 and US 10,547,370. In the example of Figure 7(b), one coefficient in the fourth group, circled, has been deemed to be dissimilar to the others and has been reassigned into a new sub-group 7.

[0128] The usage of “subset” and “subgroup” herein may be understood to refer to some type of grouping of coefficients. Subset and subgroup are used to indicate these refer to different types of groupings.

[0129] In some examples of embodiments herein wherein the first node 101 may have refrained from performing Action 402, and may have estimated all correlation coefficients in Action 403, the first node 101 may, in this Action 406, determine the subgroups instead using the first indication, that is, the similarity metric from Action 405, so that all coefficients of co-variability that may be sufficiently similar may be grouped together, irrespective of which antenna pairs they may relate to.

[0130] As described earlier in relation to Figure 3, the plurality of nodes 131 , 132, 112 may have a plurality of communication links 141 , 142, 143 with the antenna array 150. That is, each of the nodes in the plurality of nodes 131 , 132, 112 may be understood to have a respective link with the antenna array 150.

[0131] In some examples, the grouping may be shared between multiple communication links 141 , 142, 143. This may be preferable when the grouping may be primarily dependent on the configuration of the antenna array 150.

[0132] In other embodiments, the determining in this Action 406 of one or more subgroups of coefficients may be performed per respective communication link of the plurality of communication links 141, 142, 143. In such embodiments, different groupings may be determined for different communication links. This may be preferable if the grouping may be also dependent on the direction or distance to the other end of the communication link, e.g., any of the first wireless device 131 or the second wireless device 132. For instance, one wireless device 131, 132 may be in a direction where parts of the antenna array 150 may be blocked, or at a shorter distance. In both cases, the plane wave assumption leading to the Toeplitz structure may be understood to not be valid. Other wireless devices at longer distances or in unblocked locations, may be located such that the plane wave assumption and the Toeplitz structure may hold.

[0133] In some examples, the determining in this Action 406 may be modified such that instead of splitting Toeplitz groups into smaller subgroups, the deviation from the Toeplitz structure may be captured by an uncompressed delta matrix 5|j_7| , e.g., with entries for all i and j, such that Rtj = RT(]i - j|) + <5|i-7|(i - |i - / I) , where RTmay be understood to be the Toeplitz matrix coefficients, e.g., the 1 ,2, 3, 4, 5, 6 in the example in Figure 7(a). Since the deviations <5|i_7l from the Toeplitz structure may be understood to likely be smaller than the Toeplitz matrix coefficients RT, these deviations may be encoded more efficiently, either with fewer bits or with variable-length encoding, where the number of bits used for each 5|j_7| may depend on the magnitude.

[0134] By determining the one or more groups of coefficients of co-variability for each of the subsets of coefficients comprising at least one coefficient having the first indication below the first threshold, the first node 101 may be enabled to adjust the compression level of the representation, e.g., R, of the characteristics of a radio channel wherein the one or more reference signals may be transmitted from, or received by, the antenna elements to account for the different parts of the antenna array 150 that may be differently illuminated by the incoming radio waves or by line sources resulting in non-planar wavefronts at the array. One possible adjustment may be to reduce the compression level for the representation of R. One advantage compared to existing methods may be understood to be that the reduced compression level may lead to a more accurate representation of R, which may lead to improved gains from e.g. beamforming. At the same time, the R representation may still retain most of its compression which may keep much of the benefits of existing methods.

[0135] Action 407

[0136] In this Action 407, the first node 101 provides a second indication indicating the determined one or more subgroups in Action 407.

[0137] Providing may be understood as outputting, displaying, or sending.

[0138] In some embodiments, the second indication may be provided to at least one of: i) the second node 102, and ii) the plurality of nodes 131 , 132, 112 having communication links 141 , 142, 143 with the antenna array 150.

[0139] The sending in this Action 407 may be performed, e.g., on a feedback channel, such as a physical uplink shared channel (PUSCH) or physical uplink control channel (PUCCH) in Long Term Evolution (LTE) or in NR embodiments.

[0140] In particular embodiments, the first node 101 may be the second node 102.

[0141] In some embodiments, the second indication may further indicate any remaining subsets of the one or more subsets wherein no subgroups may have been determined.

[0142] In some embodiments, the second indication may indicate which of at least one of the one or more subgroups and the one or more subsets may have to be used. In a particular example, the providing of the second indication in this Action 407 may comprise signaling to a different node which groups may need to be used. In particular embodiments, in agreement with some of the examples described in the previous Action 406, the second indication may indicate a matrix of delta values, each delta value indicating a respective deviation of each of the coefficients of co-variability from a Toeplitz structure.

[0143] By providing the second indication indicating the determined one or more subgroups, the first node 101 may enable to use the representation, e.g., R, of the characteristics of the radio channel wherein the one or more reference signals may be transmitted from, or received by, the antenna elements, while transmitting the representation in a more efficient form than representing the full spatial representation, e.g., R, of the characteristics of the radio channel, yet enabling to avoid issues with the compact representation when there may be non-planar waves or partial shadowing of the antenna array.

[0144] By providing the second indication indicating the one or more subgroups in this Action 407, the first node 101 may enable, for example, that the channel co-variability matrix may be reconstructed by the receiver of the second indication. The receiver of the second indication may then be enabled to e.g., precode a transmission, e.g., of user data, based on the reconstructed channel correlation matrix R. By providing the second indication indicating the one or more subgroups in this Action 407, the first node 101 may enable that the reconstruction of R may be performed with similar quality, but lower complexity. Furthermore, since a communication link may be understood to be associated with a certain capacity in terms of, e.g., bits / sec, by providing the second indication indicating the one or more subgroups in this Action 407, the first node 101 may enable that less of this capacity may be taken up by transmissions of channel characteristics, leaving more room for payload transmissions, e.g., user data. The signal processing operations using the representation according to the one or more subgroups in this Action 407 may be reduced in complexity, leading to faster processing times and reduced load on memory and bandwidth. A yet further advantage may be understood to be that memory requirements may be reduced when storing channel characteristics. Yet another advantage may be understood to be that signal processing operations relating to channel characteristics may be made more efficient in terms of implementation.

[0145] Action 408

[0146] In this Action 408, the first node 101 may determine a difference between a first beamforming gain of the antenna array 150 calculated with all the coefficients of variance of the co-variability matrix and a second beamforming gain of the antenna array 150. The second beamforming gain may be calculated with at least two coefficients of co-variability for each of the determined one or more subgroups and any remaining subsets of the one or more subsets wherein no subgroups may have been determined indicated in the second indication. With the proviso the difference may exceed a second threshold, that is, with the proviso the difference may be too big according to a reference value, the first node 101 may then repeat the determining in Action 405 of the first indication, the determining in Action 406 of the one or more subgroups of coefficients of co-variability and the providing in Action 407 of the second indication, iteratively until the difference may be lower than the second threshold. In other words, if the beamforming gain obtained using the compressed co-variability matrix is too different, e.g., much lower, than the beamforming gain obtained with the subsets, the first node 101 may re-calculate the subgroups until the beamforming gain obtained may no longer differ, that is, until no beamforming gain may be lost by compressing the co-variability matrix according to embodiments herein.

[0147] In this Action 408, the first node 101 may optionally determine the beamforming gain in two ways: by using the full covariance matrix with all elements Rj7, and by using the compressed co-variability matrix represented by the output of Action 406. If the difference between the two beamforming gains is unacceptably large, that is, exceeds the specified second threshold, then the first threshold, that is, the similarity threshold used in Action 405 may be tightened and steps 405, 406 and 407, and optionally Action 408, may be repeated.

[0148] Embodiments of a method, performed by a second node, such as the second node 102, will now be described with reference to the flowchart depicted in Figure 8. The method may be understood to be for handling the coefficients of co-variability of the antenna elements. The second node 102 operates in the wireless communications network 100.

[0149] Several embodiments are comprised herein. In some embodiments all the actions may be performed. In some embodiments, one or more actions may be performed. It should be noted that the examples herein are not mutually exclusive. One or more embodiments may be combined, where applicable. All possible combinations are not described to simplify the description. Components from one embodiment may be tacitly assumed to be present in another embodiment and it will be obvious to a person skilled in the art how those components may be used in the other exemplary embodiments. A non-limiting example of the method performed by the second node 102 is depicted in Figure 8. Some actions may be performed in a different order than that shown Figure 8. The detailed description of some of the following corresponds to the same references provided above, in relation to the actions described for the first node 101 and will thus not be repeated here to simplify the description. For example, the one or more reference signals may be, for example, one or more SRS, or one or more DMRS, if transmitted by any of the first wireless device 131 and the second wireless device 132, or one or more CSI-RS, if transmitted by any of the first radio network node 111 and the second radio network node 112. Action 801

[0150] In some embodiments, in this Action 801 , the second node 102 may transmit or receive the one or more reference signals via the antenna elements. The antenna elements are comprised in the antenna array 150.

[0151] Although not necessary, in some embodiments, the second node 102 may be the transmitter of the one or more reference signals or the receiver of the one or more reference signals.

[0152] Action 802

[0153] In some embodiments, in this Action 802, the second node 102 may optionally obtain the measurements of the one or more reference signals transmitted from or received by the antenna elements.

[0154] This Action 802 may be performed in embodiments wherein the first node 101 may not determine the measurements itself.

[0155] Action 803

[0156] In some embodiments, in this Action 803, the second node 102 may optionally provide the obtained measurements to the first node 101.

[0157] This Action 803 may be performed in embodiments wherein the first node 101 may not determine the measurements itself.

[0158] Action 804

[0159] In this Action 804, the second node 102 may optionally estimate the coefficients of covariability based on the obtained measurements.

[0160] This Action 804 may be performed in embodiments wherein the first node 101 may not estimate the coefficients of co-variability itself.

[0161] Action 805

[0162] In this Action 805, the second node 102 may optionally provide the estimated coefficients of co-variability to the first node 101 .

[0163] This Action 805 may be performed in embodiments wherein the first node 101 may not estimate the coefficients of co-variability itself.

[0164] Action 806

[0165] In this Action 806, the second node 102 receives the second indication from the first node 101 operating in the wireless communications network 100. The second indication indicates the one or more subgroups of coefficients of co-variability for each of the one or more subsets of coefficients of co-variability between the pairs of antenna elements comprised in an antenna array 150. Each of the one or more subsets corresponds to the antenna elements sharing the geometrical relationship in the spatial layout of the antenna array 150. Each of the one or more subsets comprises at least two coefficients of co-variability selected to represent the respective subset. Each of the one or more subsets comprise the at least one coefficient having the first indication, of the similarity between the pairs of coefficients of covariability within the same subset, below the first threshold. The first indication is based on the measurements of the one or more reference signals transmitted from, or received by, the antenna elements, so that within the one or more subgroups, the coefficients have the respective first indication within the respective range below the first threshold.

[0166] In some embodiments, at least one of the following may apply: a) the coefficients of covariability may be comprised in the co-variability matrix of the radio channel, b) the covariability may be one of: covariance and correlation, c) the radio channel may be between the second node 102, and the third node 103 operating in the communications network 100, d) one of the second node 102 and the third node 103 may comprise the antenna array 150, e) the first node 101 may be the second node 102, and f) the geometrical relationship may be the displacement vector value, and g) the second indication may further indicate any remaining subsets of the one or more subsets wherein no subgroups may have been determined.

[0167] In some embodiments, the one or more subgroups of coefficients may be determined per respective communication link of the plurality of communication links 141 , 142, 143.

[0168] In some embodiments, the second indication may indicate which of at least one of the one or more subgroups and the one or more subsets may have to be used.

[0169] In some embodiments, the second indication may indicate the matrix of delta values. Each delta value may indicate the respective deviation of each of the coefficients of covariability from a Toeplitz structure.

[0170] In some embodiments, the received second indication may be based on the provided measurements in Action 803.

[0171] Action 807

[0172] In this Action 807, the second node 102 initiates using the second indication.

[0173] Initiating using may be understood to comprise beginning using, or triggering, enabling, facilitating another node to perform the using.

[0174] Using the second indication in this Action 807 may comprise using the extended set of subsets or groups, that is, the one or more subgroups of coefficients of co-variability and any remaining subsets of the one or more subsets wherein no subgroups may have been determined, when creating and using a compact representation of the co-variability matrix as described existing methods e.g., WO 2018124950 and US 10,547,370. As a summarized overview of the foregoing, embodiments herein may be understood to disclose methods that may enable to detect deviations from the Toeplitz structure of R, adjust the compression level of the representation of R, and / or communicate the selected / updated compression level of R.

[0175] Certain embodiments disclosed herein may provide one or more of the following technical advantage(s), which may be summarized as follows. Embodiments herein may be understood to enable a method that may be more efficient than representing the full spatial covariability matrix of a radio channel, yet that may avoid issues with the compact representation according to WO 2018124950 and US 10,547,370 when there may be non-planar waves or partial shadowing of the antenna array.

[0176] Figure 9 depicts an example of the arrangement that the first node 101 may comprise to perform the method described in Figure 4, Figure 5, Figure 6 and / or Figure 7(b). The first node 101 may be understood to be for handling the coefficients of co-variability of antenna elements. The first node 101 is configured to operate in the wireless communications network 100.

[0177] Several embodiments are comprised herein. It should be noted that the examples herein are not mutually exclusive. One or more embodiments may be combined, where applicable. All possible combinations are not described to simplify the description. Components from one embodiment may be tacitly assumed to be present in another embodiment and it will be obvious to a person skilled in the art how those components may be used in the other exemplary embodiments. The detailed description of some of the following corresponds to the same references provided above, in relation to the actions described for the first node 101 and will thus not be repeated here. For example, the one or more reference signals may be configured to be, for example, one or more SRS, or one or more DMRS, if configured to be transmitted by any of the first wireless device 131 and the second wireless device 132, or one or more CSI-RS, if configured to be transmitted by any of the first radio network node 111 and the second radio network node 112.

[0178] The first node 101 is configured to determine, within each subset of the one or more subsets of coefficients of co-variability between the pairs of antenna elements configured to be comprised in the antenna array 150, the first indication. The first indication is of the similarity between the pairs of coefficients of co-variability within the same subset. Each of the one or more subsets is configured to correspond to the antenna elements configured to share the geometrical relationship in the spatial layout of the antenna array 150. Each of the one or more subsets is configured to comprise at least two coefficients of co-variability configured to be selected to represent the respective subset. The determining is configured to be based on the measurements of the one or more reference signals configured to be transmitted from, or received by, the antenna elements.

[0179] The first node 101 is also configured to determine the one or more subgroups of coefficients of co-variability for each of the subsets of coefficients configured to comprise at the least one coefficient having the first indication below the first threshold, so that within the determined one or more subgroups, the coefficients have the respective first indication within the respective range below the first threshold.

[0180] The first node 101 is further configured to provide the second indication configured to indicate the one or more subgroups configured to be determined.

[0181] In some embodiments, at least one of the following may apply: a) the coefficients of covariability may be configured to be comprised in the co-variability matrix of the radio channel, b) the co-variability may be configured to be one of: covariance and correlation, c) the radio channel may be configured to be between the second node 102, and the third node 103 configured to operate in the communications network 100, d) one of the second node 102 and the third node 103 may be configured to comprise the antenna array 150, e) the first node 101 may be configured to be the second node 102, f) the geometrical relationship may be configured to be the displacement vector value, g) the second indication may be further configured to indicate any remaining subsets of the one or more subsets wherein no subgroups may have been determined, and h) the second indication may be configured to be provided to at least one of: i) the second node 102, and ii) the plurality of nodes 131 , 132, 112 configured to have communication links 141 , 142, 143 with the antenna array 150.

[0182] In some embodiments, the determining of the one or more subgroups of coefficients may be configured to be performed per respective communication link of the plurality of communication links 141, 142, 143.

[0183] In some embodiments, the first node 101 may be further configured with at least one of the following three configurations.

[0184] In some embodiments, the first node 101 may be further configured to obtain the measurements of the one or more reference signals configured to be transmitted from or received by the antenna elements.

[0185] In some embodiments, the first node 101 may be further configured to determine the structure of the co-variability matrix of the radio channel. The determining of the structure may be configured to comprise identifying the one or more subsets of coefficients of co-variability between the pairs of antenna elements configured to be comprised in the antenna array 150.

[0186] In some embodiments, the first node 101 may be further configured to estimate the coefficients of co-variability based on the measurements configured to be obtained. In some embodiments, the first node 101 may be further configured to determine the at least two coefficients of co-variability selected to represent each respective subset.

[0187] In some embodiments, the second indication may be configured to indicate which of at least one of the one or more subgroups and the one or more subsets may have to be used.

[0188] In some embodiments, the first node 101 may be further configured to determine the difference between the first beamforming gain of the antenna array 150 configured to be calculated with all the coefficients of variance of the co-variability matrix and the second beamforming gain of the antenna array 150 configured to be calculated with at least two coefficients of co-variability for each of the determined one or more subgroups and any remaining subsets of the one or more subsets wherein no subgroups may have been determined, indicated in the second indication. With the proviso the difference exceeds the second threshold, the second node 102 may be further configured to repeat the determining of the first indication, the determining of the one or more subgroups of coefficients of covariability and the providing of the second indication, iteratively, until the difference may be lower than the second threshold.

[0189] In some embodiments, the second indication may be configured to indicate the matrix of delta values. Each delta value may be configured to indicate the respective deviation of each of the coefficients of co-variability from the Toeplitz structure.

[0190] The embodiments herein in the first node 101 may be implemented through one or more processors, such as a processing circuitry 901 in the first node 101 depicted in Figure 9, together with computer program code for performing the functions and actions of the embodiments herein. A processor, as used herein, may be understood to be a hardware component. The program code mentioned above may also be provided as a computer program product, for instance in the form of a data carrier carrying computer program code for performing the embodiments herein when being loaded into the first node 101. One such carrier may be in the form of a CD ROM disc. It is however feasible with other data carriers such as a memory stick. The computer program code may furthermore be provided as pure program code on a server and downloaded to the first node 101.

[0191] The first node 101 may further comprise a memory 902 comprising one or more memory units. The memory 902 is arranged to be used to store obtained information, store data, configurations, schedulings, and applications etc. to perform the methods herein when being executed in the first node 101.

[0192] In some embodiments, the first node 101 may receive information from, e.g., the second node 102, the third node 103, the first radio network node 111 , the second radio network node 112, the core network node 120, the first wireless device 131, the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100, through a receiving port 903. In some embodiments, the receiving port 903 may be, for example, connected to one or more antennas in the first node 101. In other embodiments, the first node 101 may receive information from another structure in the wireless communications network 100 through the receiving port 903. Since the receiving port 903 may be in communication with the processing circuitry 901, the receiving port 903 may then send the received information to the processing circuitry 901. The receiving port 903 may also be configured to receive other information.

[0193] The processing circuitry 901 in the first node 101 may be further configured to transmit or send information to e.g., the second node 102, the third node 103, the first radio network node 111, the second radio network node 112, the core network node 120, the first wireless device 131, the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100, through a sending port 904, which may be in communication with the processing circuitry 901, and the memory 902.

[0194] Those skilled in the art will also appreciate that the units comprised within the first node 101 described above as being configured to perform different actions, may refer to a combination of analog and digital circuits, and / or one or more processors configured with software and / or firmware, e.g., stored in memory, that, when executed by the one or more processors such as the processing circuitry 901 , perform as described above. One or more of these processors, as well as the other digital hardware, may be included in a single Application-Specific Integrated Circuit (ASIC), or several processors and various digital hardware may be distributed among several separate components, whether individually packaged or assembled into a System-on-a-Chip (SoC).

[0195] The first node 101 may be configured to perform any of the Actions described in relation to Figure 4, Figure 5, Figure 6 and / or Figure 7(b), e.g., by means of the processing circuitry 901 within the first node 101 , configured to perform any of such actions.

[0196] Also, in some embodiments, different units comprised within the first node 101 may be configured to perform the different actions described above, implemented as one or more applications running on one or more processors such as the processing circuitry 901.

[0197] Thus, the methods according to the embodiments described herein for the first node 101 may be respectively implemented by means of a computer program 905 product, comprising instructions, i.e. , software code portions, which, when executed on at least one processing circuitry 901 , cause the at least one processing circuitry 901 to carry out the actions described herein, as performed by the first node 101. The computer program 905 product may be stored on a computer-readable storage medium 906. The computer-readable storage medium 906, having stored thereon the computer program 905, may comprise instructions which, when executed on at least one processing circuitry 901, cause the at least one processing circuitry 901 to carry out the actions described herein, as performed by the first node 101. In some embodiments, the computer-readable storage medium 906 may be a non-transitory computer- readable storage medium, such as a CD ROM disc, or a memory stick. In other embodiments, the computer program 905 product may be stored on a carrier containing the computer program 905 just described, wherein the carrier is one of an electronic signal, optical signal, radio signal, or the computer-readable storage medium 906, as described above.

[0198] The first node 101 may comprise a communication interface configured to facilitate, or an interface unit to facilitate, communications between the first node 101 and other nodes or devices, e.g., the second node 102, the third node 103, the first radio network node 111, the second radio network node 112, the core network node 120, the first wireless device 131 , the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100. The interface may, for example, include a transceiver configured to transmit and receive radio signals over an air interface in accordance with a suitable standard.

[0199] In other embodiments, the first node 101 may comprise a radio circuitry 907, which may comprise e.g., the receiving port 903 and the sending port 904.

[0200] The radio circuitry 907 may be configured to set up and maintain at least a wireless connection with the second node 102, the third node 103, the first radio network node 111 , the second radio network node 112, the core network node 120, the first wireless device 131 , the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100. Circuitry may be understood herein as a hardware component.

[0201] Hence, embodiments herein also relate to the first node 101 operative to operate in the wireless communications network 100. The first node 101 may comprise the processing circuitry 901 and the memory 902, said memory 902 containing instructions executable by said processing circuitry 901 , whereby the first node 101 is further operative to perform the actions described herein in relation to the first node 101 , e.g., in Figure 4, Figure 5, Figure 6 and / or Figure 7(b).

[0202] Figure 10 depicts an example of the arrangement that the second node 102 may comprise to perform the method described in Figure 8, Figure 5, Figure 6 and / or Figure 7(b). The second node 102 may be understood to be for handling the coefficients of co-variability of antenna elements. The second node 102 is configured to operate in the wireless communications network 100.

[0203] Several embodiments are comprised herein. It should be noted that the examples herein are not mutually exclusive. One or more embodiments may be combined, where applicable. All possible combinations are not described to simplify the description. Components from one embodiment may be tacitly assumed to be present in another embodiment and it will be obvious to a person skilled in the art how those components may be used in the other exemplary embodiments. The detailed description of some of the following corresponds to the same references provided above, in relation to the actions described for the second node 102 and will thus not be repeated here. For example, the one or more reference signals may be configured to be, for example, one or more SRS, or one or more DMRS, if configured to be transmitted by any of the first wireless device 131 and the second wireless device 132, or one or more CSI-RS, if configured to be transmitted by any of the first radio network node 111 and the second radio network node 112.

[0204] The second node 102 is configured to receive the second indication from the first node 101 configured to operate in the wireless communications network 100. The second indication is configured to indicate the one or more subgroups of coefficients of co-variability for each of the one or more subsets of coefficients of co-variability between pairs of antenna elements configured to be comprised in the antenna array 150. Each of the one or more subsets is configured to correspond to the antenna elements sharing the geometrical relationship in the spatial layout of the antenna array 150. Each of the one or more subsets is configured to comprise at least two coefficients of co-variability configured to be selected to represent a respective subset. Each of the one or more subsets is configured to comprise at least one coefficient having the first indication, of the similarity between pairs of coefficients of covariability within the same subset, below the first threshold. The first indication is configured to be based on the measurements of the one or more reference signals configured to be transmitted from, or received by, the antenna elements, so that within the one or more subgroups, the coefficients have the respective first indication within the respective range below the first threshold.

[0205] The second node 102 is also configured to initiate using the second indication.

[0206] In some embodiments, at least one of the following may apply: a) the coefficients of covariability may be configured to be comprised in the co-variability matrix of the radio channel, b) the co-variability may be configured to be one of: covariance and correlation, c) the radio channel may be configured to be between the second node 102, and the third node 103 configured to operate in the communications network 100, d) one of the second node 102 and the third node 103 may be configured to comprise the antenna array 150, e) the first node 101 may be configured to be the second node 102, f) the geometrical relationship may be configured to be the displacement vector value, g) the second indication may be further configured to indicate any remaining subsets of the one or more subsets wherein no subgroups may have been determined, and h) the second indication may be configured to be provided to at least one of: i) the second node 102, and ii) the plurality of nodes 131 , 132, 112 configured to have communication links 141, 142, 143 with the antenna array 150. In some embodiments, the one or more subgroups of coefficients may be configured to be determined per respective communication link of the plurality of communication links 141, 142, 143.

[0207] In some embodiments, the second node 102 may be further configured with at least one of the following two configurations.

[0208] In some embodiments, the second node 102 may be configured to obtain the measurements of the one or more reference signals configured to be transmitted from or received by the antenna elements.

[0209] In some embodiments, the second node 102 may be configured to provide the measurements configured to be obtained to the first node 101 , and the second indication configured to be received may be configured to be based on the measurements configured to be provided.

[0210] In some embodiments, the second node 102 may be further configured with at least one of the following two configurations.

[0211] In some embodiments, the second node 102 may be configured to estimate the coefficients of co-variability based on the measurements configured to be obtained.

[0212] In some embodiments, the second node 102 may be configured to provide the coefficients of co-variability configured to be estimated to the first node 101.

[0213] In some embodiments, the second node 102 may be configured to transmit or receive the one or more reference signals via the antenna elements.

[0214] In some embodiments, the second indication may be configured to indicate which of at least one of the one or more subgroups and the one or more subsets may have to be used.

[0215] In some embodiments, the second indication may be configured to indicate the matrix of delta values. Each delta value may be configured to indicate the respective deviation of each of the coefficients of co-variability from the Toeplitz structure.

[0216] The embodiments herein in the second node 102 may be implemented through one or more processors, such as a processing circuitry 1001 in the second node 102 depicted in Figure 10, together with computer program code for performing the functions and actions of the embodiments herein. A processor, as used herein, may be understood to be a hardware component. The program code mentioned above may also be provided as a computer program product, for instance in the form of a data carrier carrying computer program code for performing the embodiments herein when being loaded into the second node 102. One such carrier may be in the form of a CD ROM disc. It is however feasible with other data carriers such as a memory stick. The computer program code may furthermore be provided as pure program code on a server and downloaded to the second node 102.

[0217] The second node 102 may further comprise a memory 1002 comprising one or more memory units. The memory 1002 is arranged to be used to store obtained information, store data, configurations, schedulings, and applications etc. to perform the methods herein when being executed in the second node 102.

[0218] In some embodiments, the second node 102 may receive information from, e.g., the first node 101 , the third node 103, the first radio network node 111 , the second radio network node 112, the core network node 120, the first wireless device 131 , the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100, through a receiving port 1003. In some embodiments, the receiving port 1003 may be, for example, connected to one or more antennas in second node 102. In other embodiments, the second node 102 may receive information from another structure in the wireless communications network 100 through the receiving port 1003. Since the receiving port 1003 may be in communication with the processing circuitry 1001, the receiving port 1003 may then send the received information to the processing circuitry 1001. The receiving port 1003 may also be configured to receive other information.

[0219] The processing circuitry 1001 in the second node 102 may be further configured to transmit or send information to e.g., the first node 101, the third node 103, the first radio network node 111, the second radio network node 112, the core network node 120, the first wireless device 131, the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100, through a sending port 1004, which may be in communication with the processing circuitry 1001, and the memory 1002.

[0220] Those skilled in the art will also appreciate that the units comprised within the second node 102 described above as being configured to perform different actions, may refer to a combination of analog and digital circuits, and / or one or more processors configured with software and / or firmware, e.g., stored in memory, that, when executed by the one or more processors such as the processing circuitry 1001 , perform as described above. One or more of these processors, as well as the other digital hardware, may be included in a single Application-Specific Integrated Circuit (ASIC), or several processors and various digital hardware may be distributed among several separate components, whether individually packaged or assembled into a System-on-a-Chip (SoC).

[0221] The second node 102 may be configured to perform any of the Actions described in relation to Figure 8, Figure 5, Figure 6 and / or Figure 7(b), e.g., by means of the processing circuitry 1001 within the second node 102, configured to perform any of such actions.

[0222] Also, in some embodiments, different units comprised within the second node 102 may be configured to perform different actions described above, implemented as one or more applications running on one or more processors such as the processing circuitry 1001.

[0223] Thus, the methods according to the embodiments described herein for the second node 102 may be respectively implemented by means of a computer program 1005 product, comprising instructions, i.e., software code portions, which, when executed on at least one processing circuitry 1001, cause the at least one processing circuitry 1001 to carry out the actions described herein, as performed by the second node 102. The computer program 1005 product may be stored on a computer-readable storage medium 1006. The computer- readable storage medium 1006, having stored thereon the computer program 1005, may comprise instructions which, when executed on at least one processing circuitry 1001, cause the at least one processing circuitry 1001 to carry out the actions described herein, as performed by the second node 102. In some embodiments, the computer-readable storage medium 1006 may be a non-transitory computer-readable storage medium, such as a CD ROM disc, or a memory stick. In other embodiments, the computer program 1005 product may be stored on a carrier containing the computer program 1005 just described, wherein the carrier is one of an electronic signal, optical signal, radio signal, or the computer-readable storage medium 1006, as described above.

[0224] The second node 102 may comprise a communication interface configured to facilitate, or an interface unit to facilitate, communications between the second node 102 and other nodes or devices, e.g., the first node 101, the third node 103, the first radio network node 111, the second radio network node 112, the core network node 120, the first wireless device 131, the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100. The interface may, for example, include a transceiver configured to transmit and receive radio signals over an air interface in accordance with a suitable standard.

[0225] In other embodiments, the second node 102 may comprise a radio circuitry 1007, which may comprise e.g., the receiving port 1003 and the sending port 1004.

[0226] The radio circuitry 1007 may be configured to set up and maintain at least a wireless connection with the first node 101, the third node 103, the first radio network node 111 , the second radio network node 112, the core network node 120, the first wireless device 131 , the second wireless device 132, another node or user equipment, and / or another structure in the wireless communications network 100. Circuitry may be understood herein as a hardware component.

[0227] Hence, embodiments herein also relate to the second node 102, operative to operate in the wireless communications network 100. The second node 102 may comprise the processing circuitry 1001 and the memory 1002, said memory 1002 containing instructions executable by said processing circuitry 1001, whereby the second node 102 is further operative to perform the actions described herein in relation to the second node 102, e.g., in Figure 8, Figure 5, Figure 6 and / or Figure 7(b).

[0228] As used herein, the expression “at least one of:” followed by a list of alternatives separated by commas, and wherein the last alternative is preceded by the “and” term, may be understood to mean that only one of the list of alternatives may apply, more than one of the list of alternatives may apply or all of the list of alternatives may apply. This expression may be understood to be equivalent to the expression “at least one of:” followed by a list of alternatives separated by commas, and wherein the last alternative is preceded by the “or” term. When using the word "comprise" or “comprising” it shall be interpreted as non- limiting, i.e. meaning "consist at least of".

[0229] A processor may be understood herein as a hardware component.

[0230] The embodiments herein are not limited to the above described preferred embodiments. Various alternatives, modifications and equivalents may be used. Therefore, the above embodiments should not be taken as limiting the scope of the invention.

Claims

CLAIMS:

1. A method performed by a first node (101), the method being for handling coefficients of co-variability of antenna elements, the first node (101) operating in a wireless communications network (100), and the method comprising:- determining (405), within each subset of one or more subsets of coefficients of co-variability between pairs of antenna elements comprised in an antenna array (150), a first indication of a similarity between pairs of coefficients of covariability within a same subset, wherein: i. each of the one or more subsets corresponds to antenna elements sharing a geometrical relationship in a spatial layout of the antenna array (150), ii. each of the one or more subsets comprises at least two coefficients of co-variability selected to represent a respective subset, and iii. the determining (405) is based on measurements of one or more reference signals transmitted from, or received by, the antenna elements,- determining (406) one or more subgroups of coefficients of co-variability for each of the subsets of coefficients comprising at least one coefficient having the first indication below a first threshold, so that within the determined one or more subgroups, the coefficients have a respective first indication within a respective range below the first threshold, and- providing (407) a second indication indicating the determined one or more subgroups.

2. The method according to claim 1, wherein at least one of:- the coefficients of co-variability are comprised in a co-variability matrix of a radio channel,- the co-variability is one of: covariance and correlation,- the radio channel is between a second node (102), and a third node (103) operating in the communications network (100),- one of the second node (102) and the third node (103) comprises the antenna array (150),- the first node (101) is the second node (102),- the geometrical relationship is a displacement vector value,- the second indication further indicates any remaining subsets of the one or more subsets wherein no subgroups have been determined, and- the second indication is provided to at least one of: i. the second node (102), and ii. a plurality of nodes (131, 132, 112) having communication links (141, 142, 143) with the antenna array (150).

3. The method according to claim 2, wherein the determining (406) of one or more subgroups of coefficients is performed per respective communication link of the plurality of communication links (141 , 142, 143).

4. The method according to any of claims 2-3, further comprising at least one of:- obtaining (401) the measurements of the one or more reference signals transmitted from or received by the antenna elements,- determining (402) a structure of the co-variability matrix of the radio channel, the determining (402) comprising identifying the one or more subsets of coefficients of co-variability between the pairs of antenna elements comprised in the antenna array (150), and- estimating (403) the coefficients of co-variability based on the obtained measurements.

5. The method according to any of claims 1-4, further comprising:- determining (404) the at least two coefficients of co-variability selected to represent each respective subset.

6. The method according to any of claims 1-5, wherein the second indication indicates which of at least one of the one or more subgroups and the one or more subsets are to be used.

7. The method according to any of claims 2-6, further comprising:- determining (408) a difference between a first beamforming gain of the antenna array (150) calculated with all the coefficients of variance of the covariability matrix and a second beamforming gain of the antenna array (150) calculated with at least two coefficients of co-variability for each of the determined one or more subgroups and any remaining subsets of the one or more subsets wherein no subgroups have been determined indicated in the second indication, and with the proviso the difference exceeds a second threshold, repeating the determining (405) of the first indication, the determining (406) of the one or more subgroups of coefficients of co-variability and theproviding (407) of the second indication, iteratively until the difference is lower than the second threshold.

8. The method any of claims 1-7, wherein the second indication indicates a matrix of delta values, each delta value indicating a respective deviation of each of the coefficients of co-variability from a Toeplitz structure.

9. A method performed by a second node (102), the method being for handling coefficients of co-variability of antenna elements, the second node (102) operating in a wireless communications network (100), and the method comprising:- receiving (806) a second indication from a first node (101) operating in the wireless communications network (100), the second indication indicating one or more subgroups of coefficients of co-variability for each of one or more subsets of coefficients of co-variability between pairs of antenna elements comprised in an antenna array (150), wherein: i. each of the one or more subsets corresponds to antenna elements sharing a geometrical relationship in a spatial layout of the antenna array (150), ii. each of the one or more subsets comprises at least two coefficients of co-variability selected to represent a respective subset, and iii. each of the one or more subsets comprise at least one coefficient having a first indication, of a similarity between pairs of coefficients of co-variability within a same subset, below a first threshold, wherein the first indication is based on measurements of one or more reference signals transmitted from, or received by, the antenna elements, so that within the one or more subgroups, the coefficients have a respective first indication within a respective range below the first threshold, and- initiating (807) using the second indication.

10. The method according to claim 9, wherein at least one of:- the coefficients of co-variability are comprised in a co-variability matrix of a radio channel,- the co-variability is one of: covariance and correlation,- the radio channel is between the second node (102), and a third node (103) operating in the communications network (100),- one of the second node (102) and the third node (103) comprises the antenna array (150),- the first node (101) is the second node (102), and- the geometrical relationship is a displacement vector value, and- the second indication further indicates any remaining subsets of the one or more subsets wherein no subgroups have been determined.

11. The method according to claim 10, wherein the one or more subgroups of coefficients are determined per respective communication link of a plurality of communication links (141 , 142, 143).

12. The method according to any of claims 10-11, further comprising at least one of:- obtaining (802) the measurements of the one or more reference signals transmitted from or received by the antenna elements, and- providing (803) the obtained measurements to the first node (101), and wherein the received second indication is based on the provided measurements.

13. The method according to claim 12, further comprising:- estimating (804) the coefficients of co-variability based on the obtained measurements, and- providing (805) the estimated coefficients of co-variability to the first node (101).

14. The method according to any of claims 10-13, further comprising:- transmitting or receiving (801) the one or more reference signals via the antenna elements.

15. The method according to any of claims 9-14, wherein the second indication indicates which of at least one of the one or more subgroups and the one or more subsets are to be used.

16. The method any of claims 9-15, wherein the second indication indicates a matrix of delta values, each delta value indicating a respective deviation of each of the coefficients of co-variability from a Toeplitz structure.

17. A first node (101), for handling coefficients of co-variability of antenna elements, the first node (101) being configured to operate in a wireless communications network (100), and the first node (101) being further configured to:- determine, within each subset of one or more subsets of coefficients of covariability between pairs of antenna elements configured to be comprised in an antenna array (150), a first indication of a similarity between pairs of coefficients of co-variability within a same subset, wherein: i. each of the one or more subsets is configured to correspond to antenna elements configured to share a geometrical relationship in a spatial layout of the antenna array (150), ii. each of the one or more subsets is configured to comprise at least two coefficients of co-variability configured to be selected to represent a respective subset, and iii. the determining is configured to be based on measurements of one or more reference signals configured to be transmitted from, or received by, the antenna elements,- determine one or more subgroups of coefficients of co-variability for each of the subsets of coefficients configured to comprise at least one coefficient having the first indication below a first threshold, so that within the determined one or more subgroups, the coefficients have a respective first indication within a respective range below the first threshold, and- provide a second indication configured to indicate the one or more subgroups configured to be determined.

18. The first node (101) according to claim 17, wherein at least one of:- the coefficients of co-variability are configured to be comprised in a covariability matrix of a radio channel,- the co-variability is configured to be one of: covariance and correlation,- the radio channel is configured to be between a second node (102), and a third node (103) configured to operate in the communications network (100),- one of the second node (102) and the third node (103) is configured to comprise the antenna array (150),- the first node (101) is configured to be the second node (102),- the geometrical relationship is configured to be a displacement vector value,- the second indication is further configured to indicate any remaining subsets of the one or more subsets wherein no subgroups have been determined, and- the second indication is configured to be provided to at least one of:i. the second node (102), and ii. a plurality of nodes (131, 132, 112) configured to have communication links (141, 142, 143) with the antenna array (150).

19. The first node (101) according to claim 18 wherein the determining of the one or more subgroups of coefficients is configured to be performed per respective communication link of the plurality of communication links (141 , 142, 143).

20. The first node (101) according to any of claims 18-19, being further configured to at least one of:- obtain the measurements of the one or more reference signals configured to be transmitted from or received by the antenna elements,- determine a structure of the co-variability matrix of the radio channel, the determining of the structure being configured to comprise identifying the one or more subsets of coefficients of co-variability between the pairs of antenna elements configured to be comprised in the antenna array (150), and- estimate the coefficients of co-variability based on the measurements configured to be obtained.

21. The first node (101) according to any of claims 17-20, being further configured to:- determine the at least two coefficients of co-variability selected to represent each respective subset.

22. The first node (101) according to any of claims 17-21, wherein the second indication is configured to indicate which of at least one of the one or more subgroups and the one or more subsets are to be used.

23. The first node (101) according to any of claims 18-22, being further configured to:- determine a difference between a first beamforming gain of the antenna array (150) configured to be calculated with all the coefficients of variance of the covariability matrix and a second beamforming gain of the antenna array (150) configured to be calculated with at least two coefficients of co-variability for each of the determined one or more subgroups and any remaining subsets of the one or more subsets wherein no subgroups have been determined indicated in the second indication, and with the proviso the difference exceeds a second threshold, the second node (102) is further configured to repeat the determining of the first indication, the determining of the one or more subgroupsof coefficients of co-variability and the providing of the second indication, iteratively until the difference is lower than the second threshold.

24. The first node (101) any of claims 17-23, wherein the second indication is configured to indicate a matrix of delta values, each delta value being configured to indicate a respective deviation of each of the coefficients of co-variability from a Toeplitz structure.

25. A second node (102), for handling coefficients of co-variability of antenna elements, second node (102) being configured to operate in a wireless communications network (100), and the second node (102) being further configured to:- receive a second indication from a first node (101) configured to operate in the wireless communications network (100), the second indication being configured to indicate one or more subgroups of coefficients of co-variability for each of one or more subsets of coefficients of co-variability between pairs of antenna elements configured to be comprised in an antenna array (150), wherein: i. each of the one or more subsets is configured to correspond to antenna elements sharing a geometrical relationship in a spatial layout of the antenna array (150), ii. each of the one or more subsets is configured to comprise at least two coefficients of co-variability configured to be selected to represent a respective subset, and iii. each of the one or more subsets is configured to comprise at least one coefficient having a first indication, of a similarity between pairs of coefficients of co-variability within a same subset, below a first threshold, wherein the first indication is configured to be based on measurements of one or more reference signals configured to be transmitted from, or received by, the antenna elements, so that within the one or more subgroups, the coefficients have a respective first indication within a respective range below the first threshold, and- initiate using the second indication.

26. The second node (102) according to claim 25, wherein at least one of:- the coefficients of co-variability are configured to be comprised in a covariability matrix of a radio channel,- the co-variability is configured to be one of: covariance and correlation,- the radio channel is configured to be between the second node (102), and a third node (103) configured to operate in the communications network (100),- one of the second node (102) and the third node (103) is configured to comprise the antenna array (150),- the first node (101) is configured to be the second node (102), and- the geometrical relationship is configured to a displacement vector value, and- the second indication is further configured to indicate any remaining subsets of the one or more subsets wherein no subgroups have been determined.

27. The second node (102) according to claim 26, wherein the one or more subgroups of coefficients are configured to be determined per respective communication link of a plurality of communication links (141 , 142, 143).

28. The second node (102) according to any of claims 26-27, being further configured to at least one of:- obtain the measurements of the one or more reference signals configured to be transmitted from or received by the antenna elements, and- provide the measurements configured to be obtained to the first node (101), and wherein the second indication configured to be received is configured to be based on the measurements configured to be provided.

29. The second node (102) according to claim 28, being further configured to:- estimate the coefficients of co-variability based on the measurements configured to be obtained, and- provide the coefficients of co-variability configured to be estimated to the first node (101).

30. The second node (102) according to any of claims 26-29, being further configured to:- transmit or receive the one or more reference signals via the antenna elements.

31. The second node (102) according to any of claims 25-30, wherein the second indication is configured to indicate which of at least one of the one or more subgroups and the one or more subsets are to be used.

32. The second node (102) any of claims 25-31, wherein the second indication is configured to indicate a matrix of delta values, each delta value being configured toindicate a respective deviation of each of the coefficients of co-variability from a Toeplitz structure.

33. A computer program (905), comprising instructions which, when executed on at least one processing circuitry (901), cause the at least one processing circuitry (901) to carry out the method according to any of claims 1-8.

34. A computer-readable storage medium (906), having stored thereon a computer program (905), comprising instructions which, when executed on at least one processing circuitry (901), cause the at least one processing circuitry (901) to carry out the method according to any of claims 1-8.

35. A computer program (1005), comprising instructions which, when executed on at least one processing circuitry (1001), cause the at least one processing circuitry (1001) to carry out the method according to any of claims 9-16.

36. A computer-readable storage medium (1006), having stored thereon a computer program (1005), comprising instructions which, when executed on at least one processing circuitry (1001), cause the at least one processing circuitry (1001) to carry out the method according to any of claims 9-16.

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