Channel state information reporting for precoder coefficient scaling in wireless communications

Abstract

According to an aspect of some embodiments, there is provided a method performed by a wireless device (300) in a wireless communications network The method comprises receiving (501) configuration information associated with a channel state information, CSI, report, wherein the configuration information indicates a number of antenna ports,N 1,in a first dimension, and a number of antenna ports,N 2,in a second dimension. The method further comprises determining (502), based on the configuration information, a precoding vector comprising a plurality of scaling coefficients, for 2 N 1 N 2 antenna ports, wherein each entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or a phase value, or an amplitude and phase value. The method further comprises generating (503) a CSI report comprising a Precoder Matrix Indicator, PMI, indicating the precoder vector. The method further comprises reporting (504) to a network node (400) the CSI report.

Description

[0001]Channel State Information Reporting for Precoder CoefficientScaling in Wireless Communications TECHNICAL FIELD The present disclosure relates to the field of wireless communications, and in particular to methods and apparatuses for Channel State Information (CSI) reporting in a wireless communications network such as advanced 5G networks. BACKGROUND The radio access technology (RAT) in fifth generation (5G) mobile communications system, also known as 5G new radio (NR), provides a higher level of performance and flexibility than the previous generations of mobile communications systems.5G mobile communications has been driven by the need to provide ubiquitous connectivity for applications as diverse automotive communication, remote control with feedback, video downloads, as well as data applications for Internet-of-Things (IoT) devices, machine type communication (MTC) devices, etc. 5G wireless technology brings several main benefits, such as faster speed, shorter delays and increased connectivity. The third-generation partnership project (3GPP) provides the complete system specification for the 5G network architecture, which includes at least a radio access network (RAN), core transport networks (CN) and service capabilities.The present invention proposes methods and apparatuses for channel stateinformation, CSI, reporting at a wireless device (e.g., a user equipment, UE), with theaim to reduce signaling or feedback overhead and to improve performance over knownCSI reporting schemes of mobile communications systems, such as 5G NR systems.SUMMARYIt is an objective of the embodiments herein to provide methods and apparatuses forCSI feedback reporting for wireless communications networks such as advanced 5G networks. According to an aspect of some embodiments herein, there is provided a methodperformed by a wireless device in a wireless communications network. The methodcomprises:- receiving configuration information associated with a channel state information,CSI, report, wherein the configuration information indicates a number ofantenna ports, ^^, in a first dimension, and a number of antenna ports, ^^, in asecond dimension, -determining based on the configuration information a precoding vector,comprising a plurality of scaling coefficients, for 2^^^^antenna ports, wherein each entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or aphase value, or an amplitude and phase value,- generating a CSI report comprising a Precoder Matrix Indicator, PMI, indicatingthe precoder vector, and -reporting to a network node the CSI report.According to another aspect of some embodiments herein, there is provided a methodperformed by a network node (e.g., a gNB), for receiving, from a wireless device, achannel state information, CSI, report in a wireless communications network. Themethod comprising: ^transmitting to a wireless device, configuration information associated with achannel state information, CSI, report, wherein the configuration informationindicates a number of antenna ports, ^^, in a first dimension, and a number ofantenna ports, ^^, in a second dimension, for enabling the wireless device to: odetermine based on the configuration information a precoding vectorcomprising a plurality of scaling coefficients for 2^^^^antenna ports, wherein each entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or a phase value, or an amplitude andphase value, ogenerate a CSI report comprising a Precoder Matrix Indicator, PMI,indicating the precoder vector, and^ receiving, from the wireless device an uplink control information, UCI, includingthe CSI report over an uplink, UL, channel. According to another aspect of embodiments herein, there is also provided a wirelessdevice (e.g., a UE) comprising a processor and a memory containing instructionsexecutable by the processor, whereby said wireless device is operative or configured to perform any one of the embodiments presented in the detailed description related to the actions performed by the wireless device. According to yet another aspect of embodiments herein, there is provided a network node comprising a processor and a memory containing instructions executable by the processor, whereby said network node is operative or configured to perform any one of the embodiments presented in the detailed description related to the actions performed by the network node. There is also provided a computer program comprising instructions which whenexecuted on at least one processor of the wireless device (e.g., a UE), cause the atleast said one processor to carry out the actions or method steps presented herein. There is also provided a computer program comprising instructions which when executed on at least one processor of the network node, cause the at least said one processor to carry out the method steps presented herein. A carrier is also provided containing the computer program, wherein the carrier is one of a computer readable storage medium, an electronic signal, optical signal, or a radio signal. An advantage of the embodiments herein is to significantly reduce the feedback overhead and the computational complexity at the wireless device for codebook-based CSI reporting. Another advantage is to reduce latency of the CSI reporting. Additional advantages of the embodiments herein are provided in the detailed description of this disclosure. BRIEF DESCRIPTION OF THE DRAWINGS Embodiments of the present invention are now described in further detail with reference to the accompanying drawings, in which:Fig. 1 shows a schematic representation of a wireless communications network,wherein embodiments herein may be applied;Fig. 2 shows a block-based model of a MIMO DL transmission using codebook-based-precoding in accordance with LTE Release 8;Fig. 3 is a block diagram depicting a wireless device (e.g., a UE) according toexemplary embodiments herein.Fig. 4 is a block diagram depicting a network node (e.g., a gNB) according toexemplary embodiments herein.Fig. 5 illustrates a flowchart of a method performed by a wireless device (e.g., aUE) according to some embodiments herein;Fig. 6 illustrates a flowchart of a method performed by a network node (e.g., agNB) according to some embodiments herein;Fig. 7 illustrates the association of the ^ vectors and ^ scaling coefficients of theprecoding vector ^ for ^ = 2, ^ = 4 and ^ = 4, ^ = 2.Fig. 8 illustrates an example of grouping ^^ subbands to ^ = 6 subband groupswith each subband group comprises three consecutive subbands.Fig. 9 illustrates an example for a vector index selection for a first subband froma (full-sized) codebook and for a second subband from a restricted set ofcodebook indices.Fig. 10 illustrates an example vector index selection for a second subband fromtwo restricted sets of codebook indices. DETAILED DESCRIPTION In the following, a detailed description of the exemplary embodiments is described in conjunction with the drawings, in several scenarios to enable easier understanding of the solution(s) described herein. Figure 1 illustrates a simplified schematic view of an example of a wireless communications network 100 including a core network (CN) 110 and a radio access network (RAN) 120. The RAN 120 is shown including a plurality of network nodes orradio base stations, which in 5G are called gNBs. Three radio base stations aredepicted gNB1, gNB2 and gNB3. Each gNB serves an area called a coverage area or a cell. Figure 1 illustrates 3 cells 121, 122 and 123, each served by its own gNB, gNB1, gNB2 and gNB3, respectively. It should be mentioned that the network 100 may include any number of cells and gNBs. The radio base stations, or network nodes serve users within a cell. In 4G or LTE, a radio base station is called an eNB, in 3G or UMTS, a radio base station is called an eNodeB, and BS in other radio access technologies. A user equipment (UE) may be a wireless or a mobile terminal device ora stationary communication device. A wireless device may be a UE, an Internet ofThings (IoT) device, a Machine-type communication (MTC) device, etc. IoT devicesmay include wireless sensors, software, actuators, and computer devices. The IoTdevices can be imbedded into mobile devices, motor vehicle, industrial equipment,environmental sensors, medical devices, aerial vehicles and more, as well as network connectivity that enables these devices to collect and exchange data across an existing network infrastructure.Referring back to Figure 1, each cell as shown includes UEs and IoT devices. gNB1in cell 121 serves UE1121A, UE2121B and IoT device 121C. Similarly, gNB2 in cell 121 serves UE3122A, UE4122B and IoT device 122C, and gNB3 in cell 123 serves UE5 123A, UE6123B and IoT device 123C. The wireless communications network 100 may include any number of UEs and IoT devices or any other types of devices. The devices communicate with the serving gNB(s) in the uplink and the gNB(s)communicate with the devices in the downlink. The respective base stations gNB1 to gNB3 may be connected to the CN 110, e.g., via the S1 interface, via respectivebackhaul links 111, 121D, 122D, 123D, which are schematically depicted in Fig. 1 bythe arrows pointing to “core”. The core network 110 may be connected to one or more external networks, such as the Internet. The gNBs may be connected to each other via the S1 interface or the X2 interface or the XN interface in 5G, via respective interface links 121E, 122E and 123E, which is depicted in the figure by the arrows pointing to gNBs. For data transmission, a physical resource grid may be used. The physical resource grid may comprise a set of resource elements (REs) to which various physical channels and physical signals are mapped. For example, the physical channels may include the physical downlink, uplink and / or sidelink (SL) shared channels (PDSCH, PUSCH, PSSCH) carrying user specific data, also referred to as downlink, uplink or sidelink payload data, the physical broadcast channel (PBCH) carrying for example a master information block (MIB) and a system information block (SIB), the physical downlink, uplink and / or sidelink control channels (PDCCH, PUCCH, PSCCH) carrying for example the downlink control information (DCI), the uplink control information (UCI) or the sidelink control information (SCI). For the uplink, the physical channels may further include the physical random-access channel (PRACH or RACH) used by UEs for accessing the network once a UE is synchronized and obtains the MIB and SIB. The physical signals may comprise reference signals (RS), synchronization signals (SSs) and the like. The resource grid may comprise a frame or radio frame having a certain duration, like 10 milliseconds, in the time domain and having a given bandwidth in the frequency domain. The radio frame may have a certain number of subframes of a predefined length, e.g., 2 subframes with a length of 1 millisecond. Each subframe may include two slots of a number of OFDM symbols depending on the cyclic prefix (CP) length. IN 5G, each slot consists of 14 OFDM symbols or 12 OFDM symbols based on normal CP and extended CP respectively. A frame may also consist of a smaller number of OFDM symbols, e.g., when utilizing shortened transmission time intervals (TTIs) or a mini-slot / non-slot-based frame structure comprising just a few OFDM symbols. Slot aggregation is supported in 5G NR and hence data transmission can be scheduled to span one or multiple slots. Slot format indication informs a UE whether an OFDM symbol is downlink, uplink or flexible.The wireless communications network may be any single-tone or multicarrier systemusing frequency-division multiplexing, like the orthogonal frequency-division multiplexing (OFDM) system, the orthogonal frequency-division multiple access(OFDMA) system, or any other Discrete Fourier Transform (DFT) based signal with orwithout CP, e.g., DFT-spread OFDM (DFT-s-OFDM). Other waveforms, like non- orthogonal waveforms for multiple access, e.g., filter-bank multicarrir (FBMC), generalized frequency division multiplexing (GFDM) or universal filtered multi carrier (UFMC), may also be used. The wireless communication system may operate, e.g., in accordance with the LTE-Advanced Pro standard, the 5G or NR (New Radio) standard or any other standard using any of the aforementioned waveforms. The wireless communications network depicted in Figure 1 may be a heterogeneous network having two distinct overlaid networks, a network of macro cells with each macro cell including a macro base station, like base station gNB1 to gNB3, and anetwork of small cell base stations (not shown in Figure 1), like femto- or pico-basestations. In addition to the above described wireless network also non-terrestrial wireless communication networks exist including spaceborne transceivers, like satellites, and / or airborne transceivers, like unmanned aircraft systems. The non- terrestrial wireless communication network or system may operate in a similar way as the terrestrial system described above with reference to Figure 1, for example in accordance with the LTE-advanced pro standard or the 5G or NR, standard. In the wireless communications network such as the one depicted schematically inFigure 1, multi-antenna techniques may be used, e.g., in accordance with LTE, NR orany other communication system, to improve user data rates, link reliability, cellcoverage and network capacity. To support multi-stream or multi-layer transmissions,linear precoding is used in the physical layer of the communication system. Linear precoding is performed by a precoder matrix which maps layers of data to antenna ports. The precoding may be seen as a generalization of beamforming, which is a technique to spatially direct or focus a data transmission towards an intended receiver. The precoder matrix to be used at the gNB to map the data to the transmit antenna ports is decided using channel state information, CSI. In the wireless communications network system as described above, such as LTE or New Radio (5G), various physical channels are defined for the communication of data payload and control information. In addition, various reference signals are also designed for purposes such as link adaptation and management, demodulation, frame synchronization, cell search, phase tracking, among others. A gNodeB (gNB) or eNodeB (eNB), which could also be a base station, transmits to one or more users in the downlink. A user equipment (UE) or mobile terminal transmits to one or more base stations in the uplink. In the sidelink, two or more user equipments may be involved incommunication. The data payload is transmitted via the physical downlink sharedchannel (PDSCH) in the downlink (DL), via the physical uplink shared channel (PUSCH) in the uplink (UL) and via the physical sidelink shared channel (PSSCH) in the sidelink (SL), of a wireless network. The control information is typically transmitted via the physical downlink control channel (PDCCH) or the enhanced PDCCH (ePDCCH) in certain LTE releases in the downlink (DL), via the physical uplink control channel (PUCCH) in the uplink (UL) and via the physical sidelink control channel (PSCCH) in the sidelink (SL), of a wireless network. The physical broadcast channel (PBCH) is transmitted along with the synchronization signals (SS) in the downlink as a SS / PBCH block to aid in cell search and downlink synchronization. The SS / PBCH block may also be called as a synchronization signal block (SSB). The physical sidelink broadcast channel (PSBCH) in the sidelink is similar in structure and functionality to the PBCH. The physical random-access channel (PRACH) in the uplink is characterized by the PRACH preamble and is used for uplink synchronization. The PDSCH, PDCCH, PBCH, PUSCH, PUCCH, PSSCH, PSCCH and PSBCH are provided with DeModulation Reference Signals (DMRS) for coherent demodulation of the channel. The number of DMRS antenna ports during a given instance of transmission of the channel is equal to the number of layers transmitted. A layer of the transmission of a channel can be referred to using the DMRS port associated with it. In LTE, the common reference signals (CRS) may be used for DL demodulation, channel estimation, etc. The channel state information reference signal (CSI-RS) is transmitted with a reduced density in the time and frequency domain compared to CRS and plays a crucial role in initiating, maintaining, adapting, and recovering communication links. The following are some uses of the CSI-RS in a wireless network: estimation of the DL channel for adaptation of link parameters such a spatial precoder, modulation order and coding scheme, measurement and reporting of suitable spatial beam(s) for communication,tracking of various parameters required for communication such as average delay,delay spread, Doppler shift / spread, DL pathloss, etc. and recovering a link after its “failure”. For signal precoding at the gNB, several CSI-RS reporting mechanisms are used such as non-precoded CSI-RS and beamformed CSI-RS reporting. For a non- precoded CSI-RS, a one-to-one mapping between a CSI-RS port and a transceiver unit, TXRU, of the antenna array at the gNB is utilized. Therefore, non-precoded CSI- RS provides a cell-wide coverage where the different CSI-RS ports have the same beam direction and beam width. For beamformed / precoded UE-specific or non-UE- specific CSI-RS, a beamforming operation is applied over a single antenna port or over multiple antenna ports to have several narrow beams with high gain in different directions and, therefore, no cell-wide coverage. In a wireless communications network system employing time division duplexing, TDD, due to channel reciprocity, the CSI is available at the base station (gNB). However, when employing frequency division duplexing, FDD, due to the absence of channel reciprocity, the channel is estimated at the UE and the estimate is fed back tothe gNB. Figure 2 shows a block-based model of a Multiple Input Multiple Output(MIMO) DL transmission using codebook-based-precoding in accordance with LTErelease 8. Fig. 2 shows schematically the base station 200, gNB, the user equipment,UE, 202 and the channel 204, like a radio channel for a wireless data communication between the base station 200 and the user equipment 202. The base station includes an antenna array ANTThaving a plurality of antennas or antenna elements, and a precoder 206 receiving a data vector 208 and a precoder F from a codebook 210. Theterm “precoder” means, without limitation, a precoding matrix or a precoder matrix.The channel 204 may be described by the channel tensor / matrix 212. The userequipment 202 receives the data vector 214 via an antenna or an antenna array ANTRhaving a plurality of antennas or antenna elements. A feedback channel 216 between the user equipment 202 and the base station 200 is provided for transmitting feedback information. The previous releases of 3GPP up to Release 15 support the use ofseveral downlink reference symbols (such as CSI-RS) for CSI estimation at the UE. In FDD systems (up to Rel.15), the estimated channel at the UE is reported to the gNB implicitly where the CSI report transmitted by the UE over the feedback channel includes the rank index (RI), the precoding matrix index (PMI) and the channel quality index (CQI) (and the CRI from Rel.13) allowing, at the gNB, to decide the precoding matrix, and the modulation order and coding scheme (MCS) of the symbols to be transmitted. The PMI and the RI are used to determine the precoding matrix from apredefined set of matrices, also referred to as codebook. A codebook comprisesvectors or indices indicating vectors. A UE may select a vector from the codebook andindicates the selected vector or the index of the selected vector (i.e., a precodingvector) in the CSI report. The codebook, e.g., in accordance with LTE, may be a look- up table with matrices in each entry of the table, and the PMI and RI from the UE decide from which row and column of the table the precoder matrix to be used is obtained. The precoders and codebooks are designed up to Rel.15 for gNBs equipped with one-dimensional Uniform Linear Arrays (ULAs) having ^^dual-polarizedantennas (in total ^^ = 2^^ antennas or antenna ports), or with two-dimensionalUniform Planar Arrays (UPAs) having dual-polarized antennas at ^^^^positions (intotal ^^ = 2^^^^ antennas or antenna ports). The ULA allows controlling the radiowave in the horizontal (azimuth) direction only, so that azimuth-only beamforming at the gNB is possible, whereas the UPA supports transmit beamforming on both vertical (elevation) and horizontal (azimuth) directions, which is also referred to as full- dimension (FD) MIMO. The codebook, e.g., in the case of massive antenna arrays such as FD-MIMO, may be a set of beamforming weights that forms spatially separated electromagnetic transmit / receive beams using the array response vectors of the array. The beamforming weights (also referred to as the array steering vectors) of the array are amplitude gains and phase adjustments that are applied to the signal fed to the antennas (or the signal received from the antennas) to transmit (or obtain) a radiation towards (or from) a particular direction. The components of the precoder matrix are obtained from the codebook, and the PMI and the RI are used to read thecodebook and obtain the precoder. The array steering vectors may be described bythe columns of a two-dimensional Discrete Fourier Transform (DFT) matrix when ULAsor UPAs are used for signal transmission. The precoder matrices used in the Type-I, Type-I multi-panel and Type-II CSI reporting schemes in 3GPP NR standards are defined by a dual-stage structure (i.e., twocomponents codebook), ^ = ^^^^. The first component or the so-called first stageprecoder or matrix, ^^, is used to select a number of beam vectors from a Discrete Fourier Transform-based (DFT-based) matrix, which is also called the spatialcodebook. Moreover, the first stage precoder, ^^, corresponds to a wide-band matrixand contains a number of spatial beamforming vectors (the so-called spatial beams) selected from a DFT-based codebook matrix for the two polarizations of the antenna array. The second component or the so-called second stage precoder is used to combine the selected beam vectors. This means the second stage precoder or matrix, ^^, corresponds to a selection / combining / co-phasing matrix to select / combine / co-phase the beams defined in ^^. For rank-^ transmission, ^ contains ^ vectors, wherein^ denotes the transmission rank, where the entries of each vector are chosen tocombine single or multiple beams within each polarization. The selection of thematrices ^^ and ^^ is performed by the wireless device (e.g., a UE) based on referencesignals such as CSI-RS and the knowledge of the channel conditions. The selected matrices are indicated in a CSI report in the form of a RI (the RI denotes the rank of the precoding matrix) and a PMI and are used at the gNB to update the multi-user precoder for the next transmission time interval.The present invention proposes methods and apparatuses for channel stateinformation, CSI, reporting at a wireless device (i.e., a user equipment, UE) that aimto reduce signaling or feedback overhead and improve performance over known CSI reporting schemes of 5G NR systems. A codebook approach that enhances Type-I 5G NR CSI reporting is proposed where a precoding vector or matrix is selected by the wireless device from a codebook that comprises a pre-defined set of vectors and / ormatrices. It is proposed that the precoding vector or matrix selected from the codebookmay comprise additional scaling coefficients which are associated with the entries of the precoding vector or matrix. Such a scaling of the entries of the precoding vector or matrix may improve the overall system performance. The precoding vector or matrix is indicated in the CSI report by the wireless device and transmitted or reported toanother wireless device or a network node. The CSI report may comprise additionalinformation related to the scaling coefficients. This additional information includeseither amplitude information, phase information or both amplitude and phase information of the scaling coefficients. The term ‘higher layer’ in the following, when used in isolation, denotes any communication layer above the physical layer in the protocol stack. When the term is used in connection with a specific layer, it denotes any communication in the protocol stack above said layer. The term serving cell and carrier component (CC) may be used interchangeably in this disclosure as a serving cell configured for a UE and is usually a separate physical carrier centered around a particular carrier frequency. Depending on the frequency ofa component carrier / serving cell, the size of the cell and the beamformed referencesignals may vary. The term ‘PDxCH’ or ‘PDXCH’ may indicate either the physical downlink shared channel (PDSCH) or the physical downlink control channel (PDCCH), while ‘PUxCH’ or ‘PUXCH’ may indicate either the physical uplink shared channel (PUSCH) or the physical uplink control channel (PUCCH). The term ‘PxxCH’ or ‘PXXCH’ may denote a PDSCH, a PDCCH, a PUSCH, a PRACH, a PBCH, a PSSCH, or a PSCCH. The phrase ‘fixed / predetermined / provided in the specifications’ in this invention disclosure may mean the following: one or more rules and / or methods and / or particulars regarding certain parameter(s) are provided in the standard specifications that the UE and / or any network node is supposed to follow or implement. The term ‘configured’ may mean the following: one or more rules and / or methods and / or particulars regarding one or more parameters as provided in the standard specifications that the UE is supposed to follow or implement are provided to the UE by one or more network entities, e.g., via higher layer signaling, like radio resource control, RRC, signaling.A precoding vector or matrix is determined by the wireless device based onmeasurements of one or more received reference resources (e.g., channel stateinformation reference signal, CSI-RS, resource). The reference resources areprovided by another wireless device or a network node. A CSI-RS resource or anumber of CSI-RS reference resources, ^, is / are configured to the wireless device viaa configuration information from another wireless device or the network node. Thewireless device performs channel state information, CSI, measurements on the one ormore configured CSI-RS resources (e.g., ^) received over one or more slots, ^, andto determine based on the CSI measurements a precoding vector or a precodingmatrix (in short, a precoder). The precoding vector or matrix is indicated via aprecoding matrix identifier, PMI, in the CSI report. The CSI report is transmitted by thewireless device to the other wireless device or a network node. A reference (eg., CSI-RS) resource is associated with a subset of 2^^^^ antenna ports or CSI-RS ports,wherein ^^ and ^^ are the number of antenna ports in a first and a second dimension,respectively. In some examples, ^ = 1 and ^ = 1. In some other examples, ^ > 1and ^ = 1. In some other examples, ^ > 1 and ^ > 1.In certain embodiments, the PMI indicates a precoding matrix, comprising a pluralityof precoding vectors for ^ transmission layers, wherein each precoding vector isassociated with a transmission layer.In certain embodiments, the precoding vector for a transmission layer comprises aDFT-based vector of size ^^^^ × 1. The DFT-based vector can be a product or aKronecker product of a DFT-based vector of dimension ^^ × 1 selected from a firstDFT-based codebook (comprising DFT-based vectors) and a DFT-based vector ofdimension ^^ × 1 selected from a second DFT-based codebook (comprising DFT-based vectors). In some examples, the first DFT-based codebook (comprising DFT-based vectors) has a size of ^^ In some examples, the second DFT-basedcodebook (comprising DFT-based vectors) has a size of ^^ × ^^^^. Alternatively, theprecoding vector is selected from a 2D-DFT codebook of size ^^^^ × ^^^^^^^^.In certain embodiments, the wireless device is configured to select one or morevectors or precoding vectors from a codebook or DFT-based codebook and to indicate the selected vector(s) or precoding vector(s) (i.e., the PMI) in the CSI report.In certain embodiments, the wireless device is configured to indicate a precodingmatrix and the rank of the precoding matrix (in other words, a precoder) in the CSIreport. When the precoder or precoding matrix has rank ^, the precoding matrixcomprises ^ precoding vector(s) for ^ transmission layers of the precoder.In certain embodiments, a precoding vector ^ is associated with a transmission layerand defined by a product of a vector ^, selected from a codebook or DFT-basedcodebook, and an amplitude ^ and / or phase value ^. This means, ^ = ^^, or ^ = ^^^,or ^ = ^^, wherein ^ is a real-valued amplitude, and ^ = exp (√−12^^) is a phase orphase value with ^ ∈ {0,2^}. In some options, ^ = 1 and is hence not indicated in theCSI report, and only information about ^ is reported. In another option, ^ and ^ areindicated in the CSI report. In certain embodiments, a precoding vector associated with a transmission layercomprises ^ vectors ^^. The ^ vectors ^^ are from a codebook or DFT-basedcodebook. This means, in some examples, the ^ vectors are DFT-based vectors. Insome examples the ^ vectors are identical. Note that each entry of a precoding vectoris associated with an antenna or CSI-RS port. Therefore, when the precoding vectorcomprises ^ = 2 vectors, a first vector is associated with a first subset of the 2^^^^antenna ports and a second vector is associated with a second subset of the 2^^^^antenna ports. The antenna ports of the first subset are different to the antenna ports of the second subset. In some examples, the first subset of antenna ports, in otherwords the first antenna port subset, is associated with a first polarization of thetransmission and the second subset of antenna ports, in other words, the secondantenna port subset, is associated with a second polarization of the transmission. Insome examples, the ^-th vector is associated with an ^-th antenna port subset withindices wherein ^ ∈ {0, … , ^ − 1}. The antenna port indicesof the ^ subsets are different and non-overlapping. The first ^ / 2 antenna port subsetsare associated with a first polarization of the antenna ports or transmission and theremaining ^ / 2 antenna port subsets are associated with a second polarization of theantenna ports or transmission.Each of the ^ vectors ^^ can be a product or a Kronecker product of a DFT-basedvector of dimension ^× 1 selected from a first DFT-based codebook and a DFT-based vector of dimension ^^ × 1 selected from a second codebook. In some^^ examples, the first codebook has a size of^and the second codebook hasa size of ^^ × ^^^^. Alternatively, the vector can be a product or a Kronecker productof a DFT-based vector of dimension ^^ × 1 selected from a DFT-based codebook ofsize ^^ × ^^^^ and a DFT-based vector of dimension^^^^× 1 selected from a DFT-based codebook of si Scaling of precoding vector entriesIn certain embodiments, the precoding vector of a transmission layer comprises ^ real-or complex-valued scaling coefficients, wherein each scaling coefficient is associated with one or more entries of the precoding vector. Such scaling coefficients allow a scaling in amplitude and / or phase of the antenna ports used for a precodedtransmission. A scaling coefficient can be based on an amplitude value, or a phasevalue, or an amplitude and phase value. Note that each entry of the precoding vectoris associated with an antenna port. The entries of the precoding vector are groupedinto ^ subsets, wherein each subset comprises one or more entries of the precodingvector. In some examples, the one or more entries of the precoding vector is / are associated with all antenna or CSI-RS ports of a single CSI-RS resource out of the ^CSI-RS resources, wherein ^ > 1. In some examples, the subsets are non-overlapping. This means the entry / entries of one subset is / are different to the entry / entries of any other subset. Hence, each scaling coefficient is associated with a subset or proper subset of the 2^^^^antenna ports, and therefore, for the 2^^^^antenna ports, there are ^ antenna port subsets. Each antenna port subset comprising^^^^^^ antenna ports or antenna port indices is associated with a scaling coefficient.The antenna port indices of the ^ antenna port subsets are different and non-overlapping.In some examples, the 2^^^^ antenna ports associated with the precoding vector aredivided into a number of antenna port subsets, ^, wherein the ^-th antenna port subset ^^ ^ comprises^ ^^ antenna ports and is associated with a scaling coefficient and with the local antenna port indices − 1}, wherein ^ ∈ {0, … , ^ − 1}.In some examples, the 2^^^^ antenna ports associated with the precoding vector aredivided into a number of antenna port subsets, ^, wherein the ^-th antenna port subset ^^ omprises^^ c^antenna ports and is associated with a scaling coefficient and with thelocal antenna port indices ^^, ^ + ^, ^ + 2^, ^ + 3^, … , ^ + − 1^ ^^, wherein ^ ∈{0, … , ^ − 1}.In some examples, the 2^^^^ antenna ports associated with the precoding vector aredivided into a number of antenna port subsets, ^, wherein the ^-th antenna port subset ^^ comprises^^^ antenna ports each denoted by index ^ and is associated with ascaling coefficient and with the local antenna port indices + In certain embodiments, the ^-th antenna port subset index is associated with a ^-th scaling coefficient. In certain embodiments, the ^-th antenna port subset index isassociated with a ^′-th scaling coefficient, wherein ^′ is a rotated or remapped indexwith respect to an antenna port subset index associated with the strongest scaling coefficient. In certain embodiments, the phase difference between a scaling coefficient of a precoding vector of a transmission layer associated with a first antenna port and a scaling coefficient of the precoding vector of the same transmission layer associatedwith a second antenna port is given by ^^, wherein the first antenna port is associatedwith index ^ and the second antenna port is associated with an index ^ + ^^^^ of theprecoding vector, wherein ^ = 0, … , ^^^^ − 1. In some examples, ^^ = and ^ = 0,1, … , 2^^^^ − 1 or ^ = 0,1, … , 2^^^^^^ − 1. In some examples, ^^^^ ∈{1,2,3, … }.In certain embodiments, the phase difference between two scaling coefficients associated with a precoding vector of a transmission layer is given by ^^, wherein thefirst scaling coefficient is associated with an antenna port with index ^ of the precodingvector and the second scaling coefficient is associated with an antenna port with index^ + ^^^^ of the precoding vector, and ^ = 0, … , ^^^^ − 1. In some examples, ^^ =and ^ = 0,1, ^^^^ ^^^^^^ … , 2 − 1 or ^ = 0,1, … , 2 − 1. In some examples,^^^^ ∈ {1,2,3, … }. In certain embodiments, a precoding vector associated with a transmission layercomprises ^ vectors ^^ and ^ real- or complex-valued scaling coefficients, whereineach vector is associated with a plurality of entries of the precoding vector, andwherein each scaling coefficient is associated with one or more entries of theprecoding vector. In some examples, the number of vectors, ^, and the number ofscaling coefficients, ^, is identical. In another example, the number of vectors, ^, isgreater than the number of scaling coefficients, ^. In yet another example, the number of scaling coefficients, ^, is greater than the number of vectors, ^. In some examples, the precoding vector associated with a transmission layer is givenby ^ = [^^^^^^^^^^ … ^^^^^ ^^^^ ]^, wherein ^^ = [^^^^^^ … ^^^^^]^is an 2^^^^-lengthvector, and ^^, ^^, … , ^^^^ are the scaling coefficients with ^^ being either a phasevalue, an amplitude value or an amplitude and a phase value. In some options, thevector ^^ = [^^^^^^ … ^ ^^^^ ]^ = [^^^^^^]^comprises the two ^^^^-length vectors ^^and^^. In some options, the two vectors ^^, ^^ are identical. This means, ^^ = ^^ = ^. Insome options, the vector ^ is selected from a codebook or DFT-based codebook. Insome options ^^and ^^are different. The vectors ^^and ^^are selected from acodebook or DFT-based codebook. In some options, the vector ^^ = [^^^^^^ … ^^^^^]^=[^^^^^^^^^^^^]^ comprises the four ^^^^ / 2-length vectors ^^, ^^, ^^, ^^. In some options,the vectors ^^, ^^, ^^, ^^ are identical. This means, ^^ = ^^ = ^^ = ^^ = ^. In someoptions, the vector ^ is selected from a codebook or DFT-based codebook. In someoptions ^^and ^^are identical, ^^and ^^are identical and ^^and ^^are different. Thevectors ^^, ^^, ^^, ^^ are selected from a codebook or DFT-based codebook. In someoptions, the vector ^^ = [^^^^^ ^^ … ^^^^ ]^ = [^^^^^^^^^^^^^^^^^^]^comprises the six^^^^ / 3-length vectors ^^, ^^, ^^, ^^, ^^, ^^. In some options, the vectors ^^, ^^, ^^, ^^, ^^,^^ are identical. This means, ^^ = ^^ = ^^ = ^^ = ^^ = ^^ = ^. In some options, thevector ^ is selected from a codebook or DFT-based codebook. In some options ^^, ^^and ^^are identical, and ^^, ^^and ^^are identical and ^^and ^^are different. Thevectors ^^, ^^, ^^, ^^, ^^, ^^ are selected from a codebook or DFT-based codebook. Insome options, the vector ^^ = [^^^^^ ^ ^^ … ^^^^ ] = [^^^^^^^^^^^^^^^^^^^^^^^^]^comprisesthe eight ^^^^ / 4-length vectors ^^, ^^, ^^, ^^, ^^, ^^, ^^, ^^. In some options, the vectors^^, ^^, ^^, ^^, ^^, ^^, ^^, ^^, are identical. This means, ^^ = ^^ = ^^ = ^^ = ^^ = ^^ =^^ = ^^ = ^. In some options, the vector ^ is selected from a codebook or DFT-basedcodebook. In some options ^^, ^^, ^^ and ^^ are identical, ^^, ^^, ^^ and ^^, are identicaland ^^ and ^^ are different. The vectors ^^, ^^, ^^, ^^, ^^, ^^, ^^, ^^, are selected from acodebook or DFT-based codebook.In some examples, for ^ = 2 and ^ = 2, the precoding vector associated with atransmission layer is given by ^ = [^^^^^^^^^^]^, wherein[^^^^^^ ]^ = [^^^^^^]^, ^^, ^^are the ^ = 2 scaling coefficients, and ^^ and ^^ are the ^ = 2 vectors each having oflength ^^^^.In some examples, for ^ = 4 and ^ = 2, the precoding vector associated with atransmission layer is given by ^ = [^^^^^^^^^^^^^^^^^^^^]^with[^^^^^^^^^^^^]^=[^^^^^^]^and 1^^, and ^^ = − 1)^, wherein ^^, ^^, ^^, ^^ are the ^ = 4 scalingcoefficients, and ^^ and ^^ are the ^ = 2 vectors each of length ^^^^. Here, ^^(^)denotes the ^-th entry of vector ^^. In Figure 7, the association of the ^ = 2 vectorsand ^ = 4 scaling coefficients to the precoding vector ^ is illustrated.In some examples, for ^ = 6 and ^ = 2, the precoding vector associated with atransmission layer is given by ^ = [^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^]^with ^^ − 1)^, wherein ^^, ^^, ^^, ^^, ^^, ^^, are the ^ = 6 scalingcoefficients, and ^^ and ^^ are the ^ = 2 vectors each of length ^^^^. Here, ^^(^)denotes the ^-th entry of vector ^^.In some examples, for ^ = 8 and ^ = 2, the precoding vector associated with atransmission layer is given by ^ =[^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^]^with wherein ^^, ^^, ^^, ^^, ^^, ^^, ^^, ^^ are the ^ = 8 scalingcoefficients, and ^^ and ^^ are the ^ = 2 vectors each of length ^^^^. Here, ^^(^)denotes the ^-th entry of vector ^^.In some examples, for ^ = 2 and ^ = 4, the precoding vector associated with atransmission layer is given by ^ = [^^^^^^^^^^^^^^^^^^^^ ]^, wherein ^^ = ^^ , ∀^ ∈{0,1,2,3} is a vector of length^^^^^ and ^⌊^^ / ^⌋is the scaling coefficient associated withthe ^-th vector. In some options, the vectors ^^, ^^, ^^, ^^ are identical. This means,^^ = ^^ = ^^ = ^^ = ^. In some options, the vector ^ is selected from a codebook orDFT-based codebook. In some options ^^and ^^are identical, ^^and ^^are identicaland ^^ and ^^ are different. The vectors ^^, ^^, ^^, ^^ are selected from a codebook orDFT-based codebook. In Figure 7, the association of the ^ = 4 vectors and ^ = 2scaling coefficients to the precoding vector ^ is illustrated.In some examples, for ^ = 2 and ^ = 6, the precoding vector associated with atransmission layer is given by ^ = [^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^] , wherein ^^ =^^ , ∀^ ∈ {0,1,2,3,4,5} is a vector of length^^^^^and ^⌊^^ / ^⌋, is the scaling coefficientassociated with the ^-th vector. In some options, the vectors ^^, ^^, ^^, ^^, ^^, ^^ areidentical. This means, ^^ = ^^ = ^^ = ^^ = ^^ = ^^ = ^. In some options, the vector ^ isselected from a codebook or DFT-based codebook. In some options ^^and ^^and ^^are identical, ^^ and ^^ and ^^, are identical and ^^ and ^^ are different. The vectors ^^,^^, ^^, ^^, ^^, ^^ are selected from a codebook or DFT-based codebook.In some examples, for ^ = 2 and ^ = 8, the precoding vector associated with atransmission layer is given by ^ = [^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^]^,wherein ^ = ^ , ∀^ ∈ {0,1 }^^^^^ ^ ,2,3,4,5,6,7 is a vector of length^ and ^⌊^^ / ^⌋is thescaling coefficient associated with the ^-th vector. In some examples, for ^ = 4 and^ = 8, the precoding vector associated with a transmission layer is given by ^ =[^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^]^, wherein ^^ = ^^ , ∀^ ∈ {0,1,2,3,4,5,6,7}is a vector of length and ^⌊^^ / ^⌋is the scaling coefficient associated with the ^-thvector. In some options, the vectors ^^, ^^, ^^, ^^, ^^, ^^, ^^, ^^, are identical. Thismeans, ^^ = ^^ = ^^ = ^^ = ^^ = ^^ = ^^ = ^^ = ^. In some options, the vector ^ isselected from a codebook or DFT-based codebook. In some options ^^, ^^, ^^and ^^are identical, ^^, ^^, ^^ and ^^, are identical and ^^ and ^^ are different. The vectors ^^,^^, ^^, ^^, ^^, ^^, ^^, ^^, are selected from a codebook or DFT-based codebook.In certain embodiments, each scaling coefficient of the D scaling coefficients isassociated with an amplitude value and a phase value. This means ^^ =^^exp (√−12^^^), wherein ^^ is an amplitude (real value) and exp (√−12^^^) is aphase value with ^^ ∈ {0,2^}.In certain embodiments, each scaling coefficient of the D scaling coefficients isassociated only with a phase value. This means ^^ = exp (√−12^^^) with ^^ ∈ {0,2^}.Note that phase value and phase factor of a scaling coefficient is interchangeably usedin the following. In some examples, for ^ = 2 scaling coefficients, the phase factorsassociated with the two scaling coefficients of the precoding vector of a transmissionlayer are given by the vector [^^ ^^]^, where ^^ , ^ = 0,1 is the phase factor of a ^-thscaling coefficient. In some examples, [^^ ^^]^ = and wherein ^^ = with ^ and ^^^^ being integer values. In someexamples, for ^ = 4 scaling coefficients, the phase factors associated with the fourscaling coefficients of the precoding vector of a transmission layer are given by vector[^^ ^^ ^^ where ^^ , ^ = 0,1,2,3 is the phase factor of a ^-th scalingcoefficient. In some examples, [^^ ^^ ^^ ^^]^ = [1 ^^ ^^ ^^^^]^ or In some examples, the phase factors of the ^ scaling coefficients associated with theprecoding vector of a first transmission layer are given by a vector[^^ ^^ ^^ In some examples, the phase factors of the^ scaling coefficients associated with the precoding vector of a second transmissionlayer is given by a vector [^^ ^^ ^^ ^^]^ = [1 −^^ ^^ −^^^^]^. In someexamples, the phase factors of the ^ scaling coefficients associated with the precodingvector of a third transmission layer is given by a vector [^^ ^^ ^^ ^^]^ =^1 ^^ −^^ −^^ ^^^^^ . In some examples, the phase factors of the ^ scalingcoefficients associated with the precoding vector of a fourth transmission layer is givenby a vector [^^ ^^ ^^ ^^]^ = [1 −^^ −^^ ^^^^]^.In certain embodiments, the selected indices of ^ and / or ^ associated with the phasefactors of the scaling coefficients of the precoding vector of a transmission layer areindicated in the CSI report. In some examples, the indices ^ and / or ^ are indicated inthe CSI report in a subband or wideband manner. When the indices ^ and / or ^ areindicated in the CSI report in a subband manner, the indices are indicated for each subband or one or more subsets (or proper subsets) of subbands or all subbandsassociated with the precoding vector or matrix. When the indices ^ and / or ^ areindicated in the CSI report in a wideband manner, the indices are identical for all subbands with the precoding vector or matrix and hence only a single set of indices is indicated in the CSI report. In some examples, the value of ^^^^is either given by two or three or four. In some examples, the value of ^^^^is either given by two or three or four or five. In someexamples, ^^^^ < ^^^^.In certain embodiments, the index ^ of a phase value of a scaling coefficient is selectedfrom a restricted set comprising less than 2^^^^indices. In some examples, therestricted set comprises a proper subset of indices {0,1, … , 2^^^^^^ − 1}.In certain embodiments, the index ^ of a phase value of a scaling coefficient is selectedfrom a restricted set comprising less than 2^^^^indices. In some examples, therestricted set comprises a proper subset of indices {0,1, … , 2^^^^^^ − 1}.In certain embodiments, the phase factors of the ^ scaling coefficients associated withthe precoding vector of a transmission layer are cyclically rotated with respect to the index of a reference scaling coefficient such that the phase factor of the reference scaling is one (and phase is zero). In some examples, the cyclic rotation of the phasefactors of the ^ scaling coefficients associated with the precoding vector of atransmission layer is realized by using the equation ^′ = ^^^(^ − ^^, ^), wherein ^is the scaling coefficient index, ^′ is the rotated index of the scaling coefficient withrespect to index ^, and ^^ is the index of the reference scaling coefficient, wherein ^ =0, … , ^ − 1, ^′ = 0, … , ^ − 1 and ^^ ∈ {0, … , ^ − 1}.In some examples, the reference scaling coefficient is the scaling coefficient with unitamplitude and unit phase factor (this means the phase factor ^^ = exp (√−12^^^) isequal to one, ^^ = 1). In some examples, for ^ = 4, assuming the phase factors of the^ scaling coefficients associated with the precoding vector of a transmission layer aregiven by the vector [1 ^^ ^^ ^^^^]^. If the reference coefficient with amplitudeone and unit phase factor is associated with ^^ = 2, the phase factors of the ^ scalingcoefficients are rotated such that the scaling coefficient associated with ^^ = 2 has aunit phase factor resulting in the vector with new phase factors [^^ ^^^^ 1 ^^]^ forthe ^ scaling coefficients. In another example, for ^^ = 3, the new or rotated phasevalues associated with the ^ scaling coefficients is given by the vector[^^ ^^ ^^^^ 1]^. Here, ^^ is the phase factor associated with the first scalingcoefficient with index ^ = 0, ^^ is the phase factor associated with the second scalingcoefficient with index ^ = 1, ^^^^ is the phase factor associated with the third scalingcoefficient with index ^ = 2 and a unit phase factor associated with the fourth scalingcoefficient with index ^ = 3.In certain embodiments, each scaling coefficient in a first subset of the D scalingcoefficients is associated only with a phase (and unit-magnitude) value, and eachscaling coefficient in a second subset of the D scaling coefficients is associated withan amplitude and a phase value.In some examples, a scaling coefficient is based on a product of two different phasevalues. In yet another example, a scaling coefficient is based on a product of two different phase values and an amplitude value. In yet another example, a scalingcoefficient is based on a product of two different phase values and two amplitudevalues. In one example, the first amplitude value is a wideband amplitude value, andthe second amplitude value is an amplitude value defined per PRB or a group of PRBs or a subband or a subband group. Indication of scaling coefficients in CSI reportIn certain embodiments, the amplitude and / or phase information of the ^ scalingcoefficients associated with a precoding vector are indicated by the wireless device(e.g., a UE) in the CSI report.In certain embodiments, one of the ^ scaling coefficients is associated with a unitmagnitude and zero phase. This scaling coefficient is not indicated in the CSI report. In some options, the first scaling coefficient ^^has unit magnitude and zero phase,i.e., ^^ = 1.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindex of the scaling coefficient associated with unit amplitude and zero phase and / or the index of the antenna port subset associated with the scaling coefficient having unitamplitude and zero phase in the CSI report. In some examples, this index is indicatedvia a ⌈log^^⌉-bit indicator or a ^-bit bitmap.In one example, the wireless device (e.g., a UE) indicates the amplitude and / or phaseinformation of ^ − 1 or a subset of ^ − 1 scaling coefficients of the precoder vector fora PRB, or a group of PRBs, or a subband, or a subband group in the CSI report. Inanother example, the wireless device (e.g., a UE) reports ^ − 1 or a subset of ^ − 1scaling coefficients of a precoder vector for a PRB or a group of PRBs or a subbandor a subband group associated with a subset of transmission layers ^^, wherein ^^ < ^.In certain embodiments, the amplitude value for a scaling coefficient is selected from an amplitude set comprising a number of amplitude values, wherein each amplitude value is associated with an index. In certain embodiments, the UE is configured to indicate an index of the amplitudevalue from the amplitude set selected for each of the ^ or ^ − 1 amplitude values inthe CSI report.In some examples, indicating the amplitude information of the ^ or ^ − 1 scalingcoefficients in the CSI report comprises the indication of an index associated with eachof the ^ or ^ − 1 scaling coefficients. The index is associated with a specific amplitudevalue and is selected from an amplitude set comprising a number of amplitude values. In some examples, the amplitude set is given by a subset or a proper subset of the ^^^^^^^^^^^^^^ ^ ^ ^^ ^1, 2 ^, 2 ^, 2 ^, 2 ^, 2 ^, 2 ^, 2 ^, 2^ ^, 2^ ^, 2^ ^ , … , 0 ^,wherein ^ ∈ {1,2,3,4 … } is the step size.In some examples, the first amplitude value is common for all subbands and is selected from an amplitude set which is given by a subset or a proper subset of the amplitude values from the set wherein ^^ ∈ {1,2,3,4 … } is the step size. In some examples, the second amplitude value is selectedfrom an amplitude set which is given by a subset or a proper subset of the amplitude ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^values from the set ^1, 2^^^ , 2^^^, 2^^^ , 2^^^, 2^^^ , 2^^^, 2^^^ , 2^^^, 2^^^ , 2^^^ , … , 0 ^,wherein ^^ ∈ {1,2,3,4 … } is the step size. In some examples, the step size of the firstamplitude set ^^is greater than the step size of the second amplitude set ^^. In some examples, the second amplitude value is common for all subbands. Hereafter, the scaling coefficient associated with unit amplitude and zero phase is referred to as the strongest scaling coefficient. In certain embodiments, the scaling coefficients are segmented into two coefficient ^ subsets, wherein each coefficient subset comprises ^ scaling coefficients. A firstcoefficient subset is associated with the antenna ports {0, … , ^^^^ − 1} and a secondcoefficient subset is associated with the antenna ports {^^^^, … , 2^^^^ − 1}. One ofthe coefficient subsets comprises the strongest scaling coefficient. For the coefficient subset comprising the strongest scaling coefficient only the amplitude and / or phase ^− 1 or le^ information related to ^ss than^− 1 scaling coefficients other than thestrongest scaling coefficient are indicated in the CSI report. For the coefficient subset not comprising the strongest scaling coefficient, the amplitude and / or phase ^ information related the to ^ or less than ^ scaling coefficients are indicated in the CSI report.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindex of the coefficient subset associated with the strongest scaling coefficient in theCSI report. For example, for two coefficient subsets of scaling coefficients, the wirelessdevice (e.g., a UE) uses a single bit, wherein a ‘0’ indicates that the first coefficientsubset of scaling coefficients associated with the antenna ports {0, … , ^^^^ − 1} isassociated with the strongest scaling coefficient and a ‘1’ indicates that the second coefficient subset of scaling coefficients associated with the antenna ports{^^^^, … , 2^^^^ − 1} is associated with the strongest scaling coefficient or vice versa.^ In one example, the ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient are associated with a unit amplitude and a zero phase^ and the ^scaling coefficients of the other coefficient subset are associated with a unit magnitude and non-zero phase. Hence, the non-zero phase information of the or ^ less than ^scaling coefficients of the other coefficient subset is indicated in the CSIreport. ^ In one example, the ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient are associated with a unit amplitude and a non-zero^ phase and the ^ scaling coefficients of the other coefficient subset are associated with a unit magnitude and non-zero phase. Hence, the non-zero phase information of the −1 or less than^ ^ ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient and the non-zero phase information of the^ or less than ^ ^scaling coefficients of the other coefficient subset is indicated in the CSI report.^ In one example, the ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient are associated with a unit amplitude and a zero phase^ and the ^ scaling coefficients of the other coefficient subset are associated with a non- unit magnitude and non-zero phase. Hence, the non-unit amplitude and non-zero ^ phase information of the or less than ^ scaling coefficients of the other coefficient subset is indicated in the CSI report. ^ In one example, the ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient are associated with a unit amplitude and a non-zero^ phase and the ^ scaling coefficients of the other coefficient subset are associated with a non-unit magnitude and non-zero phase. Hence, the non-zero phase information of the− 1 or less than ^− 1 scaling coefficients of the coefficient subset comprisingthe strongest scaling coefficient and the non-unit amplitude and non-zero phase^ ^ information of the ^ or less than ^ scaling coefficients of the other coefficient subset is indicated in the CSI report. ^ In one example, the ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient are associated with a non-unit amplitude and a zero^ phase and the ^ scaling coefficients of the other coefficient subset are associated with a non-unit magnitude and non-zero phase. Hence, the non-unit amplitude information of the− 1 or less than^ ^− 1 scaling coefficients of the coefficient subset comprisingthe strongest scaling coefficient and the non-unit amplitude and non-zero phase ^ ^ information of the ^ or less than ^ scaling coefficients of the other coefficient subset is indicated in the CSI report. ^ In one example, the ^− 1 scaling coefficients of the coefficient subset comprising thestrongest scaling coefficient are associated with a non-unit amplitude and a non-zero^ phase and the ^ scaling coefficients of the other coefficient subset are associated with a non-unit magnitude and non-zero phase. Hence, the non-unit amplitude and the non- − 1 or less than zero phase information of the ^− 1 scaling coefficients of thecoefficient subset comprising the strongest scaling coefficient and the non-unit ^ amplitude and non-zero phase information of the ^ or less than ^ scaling coefficients of the other coefficient subset is indicated in the CSI report. In some examples, the index of the scaling coefficient associated with unit amplitude ^ ^ ^ and zero phase is indicated via a ^log^^ ^-bit indicator or a ^-bit bitmap, wherein the ^ scaling coefficients are associated with the antenna ports or local port indices associated with the strongest scaling coefficient.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindex of the antenna port subset associated with the scaling coefficient having unit amplitude and zero phase. In some examples, this index is indicated via a⌈log^^⌉-bit indicator or a ^-bit bitmap. In some examples, this index is indicated via a ^log - ^ ^ indicator or a ^-bit bitmap, wherein the ^ antenna port subsets or subset indices are associated with the antenna ports or port indices of the strongest polarization. In certain embodiments, the scaling coefficients are segmented in ^^ amplitudesubsets, wherein the amplitude values of ^′ scaling coefficients in an amplitude subsetare identical, wherein 1 < ^^ < ^. The wireless device (e.g., a UE) is configured toindicate ^^ ^^− 1 amplitude values in the CSI report.The advantage of the segmentation of the amplitude information of the ^ scaling^ coefficients into ^^ amplitude subsets is to reduce the feedback overhead by a factor In some examples, for ^ = 8 and ^^ = 2, there are four amplitude subsets, and eachamplitude subset comprises two scaling coefficients associated with an identicalamplitude value and the wireless device (e.g., a UE) indicates either three or fouramplitude values in the CSI report for the ^ = 8 scaling coefficients. In someexamples, for ^ = 4 and ^^ = 2, there are two amplitude subsets, and each amplitudesubset comprises two scaling coefficients associated with an identical amplitude valueand the wireless device (e.g., a UE) indicates either one or two amplitude values inthe CSI report for the ^ = 4 scaling coefficients. In certain embodiments, the scaling coefficients are segmented in phase subsets,wherein the phase values of ^′′ scaling coefficients in a phase subset are identical,wherein 1 ≤ ^^^ < ^. The wireless device (e.g., a UE) is configured to indicate or −of the segmentation of the phase phase subsets is to reduce thefeedback overhead by a factor of ^ − ^^^.In some examples, for ^ = 8 and ^^^ = 2, there are four phase subsets, and eachphase subset comprises two scaling coefficients associated with an identical phasevalue and the wireless device (e.g., a UE) indicates either three or four phase valuesin the CSI report for the ^ = 8 scaling coefficients. In some examples, for ^ = 4 and^^^ = 2, there are two phase subsets, and each phase subset comprises two scalingcoefficients associated with an identical phase value and the wireless device (e.g., aUE) indicates either one- or two-phase values in the CSI report for the ^ = 4 scalingcoefficients.In some examples, the value of ^′ and / or ^’’ is determined by the wireless device (e.g.,a UE) and is indicated in the CSI report. In another example, the value of ^′ and / or ^’’is configured by higher layer configuration (RRC configuration) or MAC-CE or DCI signaling or fixed in the specification.In some examples, the values of ^′ and / or ^’’ are determined based on otherconfigured parameters. For example, the values of ^′ and / or D’’ are dependent on thevalue of ^ or the number of CSI-RS resources, ^ or on the number of time slots, ^,on which the wireless device (e.g., a UE) measures the ^ CSI-RS resources.Configuration / reporting of the parameter DIn one example, the number of scaling coefficients ^ is configured to the wirelessdevice (e.g., a UE) by the network node. In another example, the number of scalingcoefficients ^ is determined by the wireless device (e.g., a UE) and reported in theCSI report. In yet another example, the number of scaling coefficients ^ is determinedby the wireless device (e.g., a UE) and not reported. In yet another example, thenumber of scaling coefficients ^ is derived by the wireless device (e.g., a UE) basedon other configured or fixed parameters. In yet another example, ^ is implicitly givenor derived by the wireless device (e.g., a UE) based on the number of configured CSI-RS resources, ^. In yet another example, the value of ^ is implicitly given or derivedby the wireless device (e.g., a UE) using the number of slots on which the ^ CSI-RSresources related to 2^^^^ antenna ports. In yet another example, the value of ^ isdetermined by the wireless device (e.g., a UE) as ^ =^ ^ ^or ^ =^, wherein ^ is thetotal number of CSI-RS resources and ^ is the number of slots on which the ^ CSI-RS resources related to 2^^^^ antenna ports are measured. In yet another example,the value of ^ is given by the number of slots, ^, on which the ^ CSI-RS resourcesrelated to 2^^^^ antenna ports are measured. In yet another option, the value of ^ isfixed in the specification.Variation of scaling coefficients with respect to rank or over transmission layersIn certain embodiments, the number of scaling coefficients, ^, are dependent on therank of the precoder matrix. In some examples, the number of scaling coefficients, ^,decreases for increasing rank values. In some other examples, the number of scalingcoefficients, ^, increases for increasing rank values.In certain embodiments, for a rank ^ precoder matrix, the number of scalingcoefficients, ^, are identical or different over the ^ transmission layers. In someexamples, the number of scaling coefficients increases with increasing transmission layer index. In some other examples, the number of scaling coefficients decreaseswith increasing transmission layer index.Selection of vectors {^, ^^, ^^} with respect to transmission layersIn the following, some schemes for the selection of the vectors ^^, ^^ and ^ (asmentioned above) are proposed.In certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to select a single vector (the vector ^) from a codebook (e.g., a DFT-based codebook) for each transmission layer of the precoder matrix (in short precoderin the following). The selected vector can be identical for all transmission layers. Insome examples, the wireless device (e.g., a UE) selects different vectors for the ^transmission layers. Note that in general, the selected vectors for the ^ transmissionlayers can be identical, different, or partly identical.In certain embodiments, the wireless device (e.g., a UE) is configured to select a singlevector from a codebook for a first transmission layer subset, wherein the firsttransmission layer subset comprises ^′ transmission layers of the precoding matrix,and wherein ^’ < ^. For the transmission layer(s) not comprised in the first subset, thewireless device (e.g., a UE) is configured to select a single vector per layer or subsetof transmission layers of the precoding matrix. In one example, for rank ^ = 3, thewireless device (e.g., a UE) selects a first vector for transmission layers {1,2} and asecond vector for transmission layer {3}, wherein the first vector is not identical to thesecond vector. In another example, for rank ^ = 7, the wireless device (e.g., a UE)selects a first vector for transmission layers {1,2,3,4}, a second vector for transmissionlayer {5}, and a third vector for transmission layer {6}, and a fourth vector fortransmission layer {7}, wherein the first, second, third and fourth vectors are notidentical to each other.In certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to select a first vector for a first transmission layer subset comprising ^’transmission layers of the precoding matrix, wherein ^’ < ^, and a second vector for atransmission layer subset comprising ^’’ transmission layers of the precoding matrix,wherein ^’′ < ^ and ^’ + ^′^ = ^. The first vector can be different or identical to thesecond vector. In one example, for ^ = 3, the wireless device (e.g., a UE) selects afirst vector for a first transmission layer subset comprising transmission layers {1,2}and a second vector for a second transmission layer subset comprising transmissionlayer {3}. In another example, for ^ = 4, the wireless device (e.g., a UE) selects a firstvector for a first transmission layer subset comprising transmission layers {1,2} and asecond vector for a second transmission layer subset comprising transmission layers{3,4}. In yet another example, for ^ = 5, the wireless device (e.g., a UE) selects a firstvector for a first transmission layer subset comprising transmission layers {1,2,3}, anda second vector for a second transmission layer subset comprising transmission layers{4,5}. In yet another example, for ^ = 6, the wireless device (e.g., a UE) selects a firstvector for a first transmission layer subset comprising transmission layers {1,2,3}, anda second vector for a second transmission layer subset comprising transmission layers{4,5,6}. In yet another example, for ^ = 7, the wireless device (e.g., a UE) selects afirst vector for a first transmission layer subset comprising transmission layers{1,2,3,4}, and a second vector for a second transmission layer subset comprisingtransmission layers {5,6,7}. In yet another example, for ^ = 8, the wireless device(e.g., a UE) selects a first vector for a first transmission layer subset comprisingtransmission layers {1,2,3,4}, and a second vector for a second transmission layersubset comprising transmission layers {5,6,7,8}. In the above examples, the first andthe second vectors are not identical. In some examples, the possible values of {^’, ^’’}for a rank ^ precoder matrix are given by {^ − ^, ^}, where ^ ∈ {1, … , ^ − 1}.In certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to select a first vector for a first transmission layer subset comprising ^’transmission layers of the precoding matrix, wherein ^’ < ^, a second vector for asecond transmission layer subset comprising ^’’ transmission layers of the precodingmatrix, wherein ^’′ < ^, and third vector for a third transmission layer subsetcomprising ^’’′ transmission layers of the precoding matrix, wherein ^’′′ < ^, and ^^ +^^^ + ^^^^ = ^. Note that the subsets are not identical. In some options, the first, secondand third vectors can be identical or not identical. In one example, for ^ = 4, thewireless device (e.g., a UE) selects a first vector for a first transmission layer subsetcomprising transmission layers {1,2}, a second vector for a second transmission layersubset comprising transmission layer {3}, and a third vector for a third transmissionlayer subset comprising transmission layer {4}. In another example, for ^ = 5, thewireless device (e.g., a UE) selects a first vector for a first transmission layer subsetcomprising transmission layers {1,2}, a second vector for a second transmission layersubset comprising transmission layers {3,4} and a third vector for a third transmissionlayer subset comprising transmission layer {5}. In yet another example, for ^ = 6, thewireless device (e.g., a UE) selects a first vector for a first transmission layer subsetcomprising transmission layers {1,2}, and a second vector for a second transmissionlayer subset comprising transmission layers {3,4} and a third vector for a thirdtransmission layer subset comprising transmission layer {5,6}. In yet another example,for ^ = 7, the wireless device (e.g., a UE) selects a first vector for a first transmissionlayer subset comprising transmission layers {1,2,3}, a second vector for a secondtransmission layer subset comprising transmission layers {4,5} and a third vector for athird transmission layer subset comprising transmission layer {6,7}. In yet anotherexample, for ^ = 8, the wireless device (e.g., a UE) selects a first vector for a firsttransmission layer subset comprising transmission layers {1,2,3}, a second vector fora second transmission layer subset comprising transmission layers {4,5,6} and a thirdvector for a third transmission layer subset comprising transmission layer {7,8}. In allexamples, the first, second and third vectors are not identical. In some examples, thepossible values of {^’, ^’’, ^′′′} for a rank ^ precoder matrix are given by {^ − ^ − ^, ^, ^},where ^ ∈ {1, … , ^ − 2} and ^ ∈ {1, … , ^ − ^ − 1}.In certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to select a first vector for a first transmission layer subset comprising ^’transmission layers of the precoding matrix, wherein ^’ < ^, a second vector for asecond transmission layer subset comprising ^’′ transmission layers of the precodingmatrix, wherein ^’′ < ^, a third vector for a third transmission layer subset comprising^’′′ transmission layers of the precoding matrix, wherein ^’′′ < ^, and a fourth vectorfor a fourth transmission layer subset comprising ^’′′′ transmission layers of theprecoding matrix, wherein ^’^^^ < ^, and ^^ + ^^^ + ^^^^ + ^′′′′ = ^. In one example, for^ = 5, the wireless device (e.g., a UE) selects a first vector for a first transmissionlayer subset comprising transmission layers {1,2}, a second vector for a secondtransmission layer subset comprising transmission layer {3}, a third vector for a thirdtransmission layer subset comprising transmission layer {4}, and a fourth precodingvector for a fourth transmission layer subset comprising transmission layer {5}. Inanother example, for ^ = 6, the wireless device (e.g., a UE) selects a first precodingvector for a first transmission layer subset comprising transmission layers {1,2}, asecond vector for a second transmission layer subset comprising transmission layers{3,4}, a third precoding vector for a third transmission layer subset comprisingtransmission layer {5}, and a fourth vector for a fourth transmission layer subsetcomprising transmission layer {6}. In yet another example, for ^ = 7, the wirelessdevice (e.g., a UE) selects a first vector for a first transmission layer subset comprisingtransmission layers {1,2}, a second vector for a second transmission layer subsetcomprising transmission layers {3,4}, a third vector for a third transmission layer subsetcomprising transmission layers {5,6}, and a fourth vector for a fourth transmission layersubset comprising transmission layer {7}. In yet another example, for ^ = 8, thewireless device (e.g., a UE) selects a first vector for a first transmission layer subsetcomprising transmission layers {1,2}, a second vector for a second transmission layersubset comprising transmission layers {3,4}, a third vector for a third transmission layersubset comprising transmission layers {5,6}, and a fourth vector for a fourthtransmission layer subset comprising transmission layer {7,8}. In some examples, thepossible values of {^’, ^’’, ^^^^ , ^′′′′} for a rank ^ precoder matrix are given by {^ − ^ −^ − ^, ^, ^, ^}, where ^ ∈ {1, … , ^ − 3}, ^ ∈ {1, … , ^ − ^ − 2} and ^ ∈ {1, … , ^ − ^ − ^ −1}.Selection of vectors {^, ^^, ^^} with respect to rankIn certain embodiments, for a precoder matrix of rank ^ > ^, the wireless device (e.g.,a UE) is configured to select a first vector ^ or {^^, ^^} for a first transmission layersubset comprising ^’ transmission layers of the precoding matrix, wherein ^’ < ^, anda second vector ^ or {^^, ^^} for a second transmission layer subset comprising ^’’transmission layers of the precoding matrix, wherein ^’′ < ^ and ^’ + ^′^ = ^, andwherein ^ ∈ {2,3,4,5,6,7,8}.In certain embodiments, for a precoder matrix of rank ^ > ^, the wireless device (e.g.,a UE) is configured to select a first vector for a first transmission layer subsetcomprising ^’ transmission layers of the precoding matrix, wherein ^’ < ^, and asecond vector for a second transmission layer subset comprising ^’′ transmissionlayers of the precoding matrix, wherein ^’ < ^, and third vector for a third transmissionlayer subset comprising ^’′′ transmission layers of the precoding matrix, wherein ^’′′ <^, and ^^ + ^^^ + ^^^^ = ^, and wherein ^ ∈ {2,3,4,5,6,7,8}.In certain embodiments, for a precoder matrix of rank ^ > ^, the wireless device (e.g.,a UE) is configured to select a first vector for a first transmission layer subsetcomprising ^’ transmission layers of the precoding matrix, wherein ^’ < ^, and asecond vector for a second transmission layer subset comprising ^’′ transmissionlayers of the precoding matrix, wherein ^’′ < ^, and a third vector for a thirdtransmission layer subset comprising ^’′′ transmission layers of the precoding matrix,wherein ^’′′ < ^, wireless device (e.g., a UE)and a fourth vector for a fourthtransmission layer subset comprising ^’’^^ layers of the precoding matrix, wherein^’^^^ < ^, and ^^ + ^^^ + ^^^^ + ^′′′′ = ^, and wherein ^ ∈ {2,3,4,5,6,7,8}.Let “^” or “(^, ^)” be the index / indices associated with a selected vector associatedwith a transmission layer subset. In some examples, ^ ∈ {0, … . , ^^^^ − 1} or ^ ∈{0, … . ^^^^^^^^ − 1}, and ^ ∈ {0 … , ^^^^ − 1}, ^ ∈ {0 … , ^^^^ − 1}. Here, ^ is the indexfrom the codebook comprising ^^^^or ^^^^^^^^indices or vector indices associatedwith the ^^ antenna ports in a first dimension and ^^ antenna ports in a seconddimension. Here, ^ is the index from the codebook associated with the ^^ antennaports in the first dimension and ^ is the index from the codebook associated with the^^ antenna ports in the second dimension.In some examples, for a rank ^ of the precoder matrix, the number of transmissionlayer subsets is ⌈^ / 2⌉. For odd ^, the first ^ / 2 transmission layer subsets comprise twotransmission layers each and the last transmission layer comprises the last or theremaining transmission layer. For even ^, all ⌈^ / 2⌉ transmission layer subsetscomprise two transmission layers each. In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindices ^^, ^ = 0, … , ⌈^ / 2⌉ − 1 of the selected vectors of the ⌈^ / 2⌉ transmission layersubsets in the CSI report, wherein ^^ ∈ {0, … . , ^^^^ − 1} or ^^ ∈ {0, … . − 1}.In one option, the indices ^^, ^ = 0, … , ⌈^ / 2⌉ − 1 of the selected vectors of the ⌈^ / 2⌉ transmission layers subsets are indicated separately for each transmission layer subset in the CSI report. In one example, the index ^^of the selected vector is indicatedby an ⌈log^ ^^^^^^^^⌉-bit indicator. In another example, the index ^^ of the selectedvector is indicated by an ⌈log^ ^^^^⌉-bit indicator. In another option, the indices ^^ ofthe selected vectors associated with the ⌈^ / 2⌉ transmission layer subsets are indicatedjointly in the CSI report. In one example, the ⌈^ / 2⌉ selected vectors associated withthe ⌈^ / 2⌉ transmission layer subsets are jointly indicated using abit indicator. In addition, the mapping of the ⌈^ / 2⌉ indices to the ⌈^ / 2⌉ transmission layersubsets can be indicated using a ⌈log^(⌈^ / 2⌉!)⌉-bit indicator. Note that for the indicationof the indices ^^in this example, the rotation factors associated with the selected vector need to be indicated in addition, as discussed below.For ⌈^ / 2⌉ trasmission layer subsets, the feedback overhead associated with theindication of the selected vectors is given by ⌈^ / 2⌉ ⋅ ⌈log^(^^^^)⌉-bits for the separateindication andbits for the joint indication. For example, when (^^, ^^) = (8,4) and ^ = 8, the overhead of the separate indication and the jointindication is 20 bits and 21 bits, respectively. Both indications result in a similarfeedback overhead which is quite high for Type-I codebooks. As the main advantageof the Type-I codebook is the low feedback overhead compared to the other codebooktypes specified in 5G NR, the feedback overhead shall be kept small even for large(^^, ^^) values. Therefore, overhead reduction schemes are proposed in the following.In certain embodiments, the wireless device (e.g., a UE) is configured to select thevector indices ^^, ∀^ = 0, … , − 1 for the transmission layers subsets such thatthe vector index ^^ of a transmission layer subset ^ is smaller than a vector index ^^^of transmission layer subset ^′, wherein ^^ > ^ and ^^ ∈ {0, … , ^^^^^^^^ − 1}. Theindices ^^ of the selected vectors of the ⌈^ / 2⌉ transmission layers subsets can beindicated jointly in the CSI report using abit indicator, wherein the ^-th index of the indicated ⌈^ / 2⌉ indices is associated with the ^-th transmission layersubset. Additionally, the rotation factors associated with the selected vectors areindicated in the CSI report. For example, when (^^, ^^) = (8,4) and ^ = 8, the overhead is given by 16 bits resulting in 20% lower feedback overhead compared tothe separate and joint indications of the selected vectors.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindices = 0, … , ⌈^ / 2⌉ − 1 associated with the selected vectors for the ⌈^ / 2⌉transmission layer subsets in the CSI report. Here, ^^ ∈ {0 … , ^^^^ − 1} and ^^ ∈{0 … , ^^^^ − 1}. In one example, the selected indices ^^ and ^^ associated with aselected vector are indicated by a ⌈log^ ^^^^⌉-bit indicator and a ⌈log^ ^^^^⌉-bitindicator, respectively, in the CSI report for ^ = 0, … , ⌈^ / 2⌉ − 1.In another example, the selected indices ^^ and ^^ associated with a selected vectorare indicated by a ⌈log^^^⌉-bit indicator and ⌈log^^^⌉-bit indicator, respectively, in theCSI report for ^ = 0, … , ⌈^ / 2⌉ − 1. Note that for this indication, the rotation factorsassociated with a selected vector needs to be indicated in the CSI report as well as discussed below.For ⌈^ / 2⌉ transmission layer subsets, the total feedback overhead for the indication ofthe ⌈^ / 2⌉ vector indices of the selected vectors is ⌈^ / 2⌉ ⋅ (⌈log^ ^^^^⌉ + ⌈log^ ^^^^⌉)-bits. For example, when ^ = 8 and (^^, ^^) = (8,8), the feedback overhead is 40 bitswhich is high for a Type-I codebook. Therefore, in the following more feedback overhead reduction schemes are proposed.In certain embodiments, the selected vector of the ^-th transmission layer subset (^ >0) is associated with two indices (^^, ^^). The index ^^ is either selected from a fullset ^^comprising indices or from a restricted set ^^^comprising ^^indices. The index ^^is either selected from a full set ^^comprising ^^^^indices or from a restricted set ^^^ comprising ^^ indices. The indices {0, … , ^^^^} from the full set^^ are associated vectors. The ^^ indices {0, … , ^^} from the restricted set^^^are associated with ^^orthogonal vectors, wherein the orthogonal vectors are associated with a rotation factor in a first dimension of a reference transmission layersubset. The ^^^^ indices {0, … , ^^^^} from the full set ^^ are associated with ^^^^vectors. The ^^ indices {0, … , ^^} from the restricted set ^^^are associated with ^^orthogonal vectors, wherein the orthogonal vectors are associated with a rotation factor in a second dimension of a reference transmission layer subset. In some examples, the reference transmission layer subset is the first transmission layer subset comprising the first two transmission layers (i.e., the transmission layer subsetwith index ^ = 0).In some examples, the selected index ^^, ^ = 0 and the selected index ^^, ^ = 0 areindicated separately using a ⌈log^ ^^^^⌉-bit indicator and ⌈log^ ^^^^⌉-bit indicator,respectively, in the CSI report or jointly indicated by a ⌈log^ ^^^^⌉-bit indicator and theselected rotation factors are indicated using a ⌈log^ ^^^^⌉-bit indicator in the CSIreport.In a first option, for the ^-th transmission layer subset (^ > 0), the index ^^ is selectedfrom a restricted set and index ^^is selected from a full set ^^. In another option,for the ^-th transmission layer subset (^ > 0), the index ^^ is selected from a full set^^and index ^^is selected from a restricted set ^^^ . In another option, for the ^-thtransmission layer subset (^ > 0), the index ^^ is selected from a restricted set ^^^and index ^^is selected from a restricted set ^^^.In some examples, if ^ , ^ > 0 is selected from a restricted set , the selected^^ is indicated by a ⌈log^ ^^⌉-bit indicator in the CSI report. In some examples, if ^^, ^ >0 is selected from a restricted set ^^^, the selected index ^^is indicated by a ⌈log^^^⌉-bit indicator in the CSI report. In some examples, if ^^, ^ > 0 is selected from a full set^^, the selected index ^^, ^ > 0 is indicated by a ⌈log^ ^^^^⌉-bit indicator or by a⌈log^ ^^(^^ − 1)⌉-bit indicator or by ⌈log^(^^ − 1)(^^ − 1)⌉-bit indicator or by a⌈log^(^^ − 1) ^^⌉-bit indicator in the CSI report. In some examples, if ^^, ^ > 0 isselected from a full set ^^, the selected index ^^, ^ > 0 is indicated by a ⌈log^ ^^^^⌉-bit indicator or by a ⌈log^ ^^(^^ − 1)⌉-bit indicator or by ⌈log^(^^ − 1)(^^ − 1)⌉-bitindicator or by a ⌈log^(^^ − 1) ^^⌉-bit indicator in the CSI report. The selected rotationfactors associated with indices ^^, ^ > 0 and ^^, ^ > 0 are jointly indicated by a⌈log^ ^^^^⌉-bit indicator in the CSI report. In some examples, if ^^, ^ > 0 is selectedfrom a restricted set ^^^ and ^^, ^ > 0 is selected from a full set ^^, the selected indices^^, ^ > 0 and ^^, ^ > 0 are jointly indicated by a ⌈log^ ^^^^⌉-bit indicator or by a⌈log^(^^ − 1)^^⌉-bit indicator or by a ⌈log^(^^ − 1)^^⌉-bit indicator or by a⌈log^(^^ − 1)(^^ − 1)⌉-bit indicator in the CSI report. The selected rotation factorassociated with ^^, ^ > 0 is indicated by a ⌈log^ ^^⌉-bit indicator in the CSI report. Insome examples, if ^^, ^ > 0 is selected from a full set ^^ and ^^, ^ > 0 is selectedfrom a restricted set ^^^ , the selected indices ^^, ^ > 0 and ^^, ^ > 0 are indicatedjointly indicated by a ⌈log^ ^^^^⌉-bit indicator or by a ⌈log^(^^ − 1)^^⌉-bit indicator orby a ⌈log^(^^ − 1)^^⌉-bit indicator or by a ⌈log^(^^ − 1)(^^ − 1)⌉-bit indicator in theCSI report. The selected rotation factor associated with ^^, ^ > 0 is indicated by a⌈log^ ^^⌉-bit indicator in the CSI report.In certain embodiments, the wireless device is configured to apply for eachtransmission layer subset ^, (^ > 0) the restricted set for the selection of indices ^^and / or the restricted set ^^^for the selection of indices ^^. The vectors associated with the indices of the restricted set are associated with the same rotation factor as the vector associated with index ^^selected by the wireless device for transmission layersubset ^ = 0. The vectors associated with the indices of the restricted set ^^^are associated with the same rotation factor as the vector associated with index ^^selected by the wireless device for transmission layer subset ^ = 0. The wirelessdevice is configured to indicate by an index indicator in the CSI report if the indices ofthe vectors of each transmission layer subset ^ > 0 are associated with the restrictedset ^^^ for the selection of indices ^^ and / or if the indices of the vectors of alltransmission layer subsets ^, (^ > 0) are associated with the restricted set ^^^for the selection of indices ^^. In some examples, this is indicated by a single bit in the CSIreport for all transmission layer subsets (^ > 0) or per transmission layer subset. Insome examples, a codepoint ‘1’ may indicate the usage of the restricted set for theselection of indices ^^, and a codepoint ‘0’ may indicate the usage of the restricted set^^^for the selection of indices ^^. In some examples, a two-bit indicator is used to indicate if the restricted set ^^^is used for the selection of indices ^^, or the restricted set ^^^is used for the selection of indices ^^, or if the restricted set is used for the selection of indices ^^and the restricted set ^^^is used for the selection of indices ^^.In some options, for a transmission layer subset ^, (^ > 0), the index indicatorindicates if the indices of the vectors of each transmission layer subset ^ > 0 areassociated with the restricted set ^^^for the selection of indices ^^and / or if the indicesof the vectors of all transmission layer subsets ^, (^ > 0) are associated with the restricted set ^^^for the selection of indices ^^, and in addition, the rotation factor in one dimension associated with the indices of the selected vector for a transmissionlayer subset ^ by a ^log^ ^^ + 1^-bit indicator. Here, ^^ = ^^ if the restricted set isused for the selection and ^^ = ^^ if the restricted set ^^^is used for the selection.In some examples, the restricted set ^^^ is used for the selection of the indices ^^, ^ > 0for all transmission layer subsets ^ > 0 and the same rotation factor is used for theselection of indices ^^, ^ > 0 for all transmission layer subsets ^ > 0. In this case,^^ = ^^, ∀^ a ⌈log^ ^^⌉-bit indicator is indicated once in the CSIreport for all transmission layer subsets associated with indices ^ > 0. In someexamples, the restricted set ^^^ is used for the selection of the indices ^^, ^ > 0 for alltransmission layer subsets ^ > 0 and the same rotation factor is used for the selectionof indices ^^, ^ > 0 for all transmission layer subsets ^ > 0. In this case, ^^ = ^^, ∀^ =1, … , − 1 and a ⌈log^ ^^⌉-bit indicator is indicated once in the CSI report for alltransmission layer subsets associated with indices ^ > 0.In certain embodiments, the wireless device is configured to indicate in the CSI reportthe selected indices ^^, ^ > 0 across all ⌈^ / 2⌉ − 1 transmission layer subsets jointly. Insome examples, if indices ^ , ^ > 0 are selected from a restricted set , such indication is given by one of the following indicators: a bit bit indicator. In some examples, if indices ^^, ^ > 0 are from a full set ^^ , such joint indication is given by one of the following indicators: a^ ^log ^^⌈ ⌉ − 1 bit indicator, or aindicator or ^ ^log^^^^^⌈ ⌉ − 1 bit indicator, or a indicator, or a ^log(^^)(^^ − 1)^^⌈^ / 2⌉ − 1 ^^-bit indicator, or a ^log (^^ − 1)(^^ − 1)^ ^ ⌈^ / 2⌉ − 1^^-bit indicator. In someoptions, the mapping between the ⌈^ / 2⌉ − 1 indices ^^ and the ⌈^ / 2⌉ − 1 transmissionlayer subsets can be indicated by a ⌈log^(⌈^ / 2⌉ − 1)!⌉-bit indicator.In certain embodiments, the wireless device is configured to indicate in the CSI reportthe selected indices ^^, ^ > 0 across the ⌈^ / 2⌉ − 1 transmission layer subsets jointly.In some examples, if indices ^^, ^ > 0 are selected from a restricted set ^^^, such jointindication is given by one of the following indicators: abit or a bit indicator. In some examples, if indices ^^, ^ > 0 are selected from a full set ^^, such joint indication is given by one of the followingindicators: a ^log ^^^ ^^-bit indic ^^ − 1^ ⌈^ / 2⌉ − 1 ator, or a ^log^ ^ ⌈^ / 2⌉ − 1^^-bit indicator or aor aIn options, the mapping between the ⌈^ / 2⌉ − 1 indices and the ⌈^ / 2⌉ − 1 transmissionlayer subsets can be indicated by a ⌈log^(⌈^ / 2⌉ − 1)!⌉-bit indicator.In certain embodiments, the wireless device is configured to indicate in the CSI reportthe selected indices ^^, ^ > 0 and ^^, ^ > 0 across the ⌈^ / 2⌉ − 1 transmission layersubset jointly by a combined index ^^, ^ > 0 . In some examples, such joint indication^ iven by one of the following indicators: a ^log^^ is g^^^⌈^ / 2⌉ − 1^^-bit indicator, or a^log^^^^ − 1^^⌈ ⌉ − 1 bit indicator, or a ^(^^ − 1)(^ − 1)⌈^ / 2 − 1 ^^-bit indicator, or a^log ^(^^)(^^ − 1)⌈ ⌉ − 1^^-bit indicator, or abit indicator. In some examples, the indices In some other examples, the combined index ^ = ^^^^ + ^^, where ^^ = 0, … , −and ^^ = 0, … , ^^ − 1. In some options, the mapping between the indicated ⌈^ / 2⌉ − 1index pairs (^^, ^^) and the ⌈^ / 2⌉ − 1 transmission layers subsets are indicated by a⌈log^((⌈^ / 2⌉ − 1)!)⌉-bit indicator in the CSI report.In certain embodiments, the wireless device (e.g., a UE) selects the index ^^, ^ > 0such that the index ^^ of a transmission layer subset ^ is smaller than an index ^^^ oftransmission layer subset ^′, wherein ^^ > ^. The indices ^^, ∀^ > 0 of the ⌈^ / 2⌉ − 1transmission layers subsets may be indicated jointly in the CSI report. In someexamples, if indices ^^, ^ > 0 are selected from a restricted set ^^^, such joint indicationis given by one of the following indicators: ^l ^-bit indicator, or a^log^^ − 1^^⌈^ / 2⌉ − 1^^-bit indicator. In some examples, if indices ^^, ^ > 0 are selected froma full set ^^ , such joint indication is given by one of the following indicators: a^ ^log^^^⌈^ / 2⌉ − 1^^-bit indicator, or a ^log^ ^ ^^ − 1⌈^ / 2⌉ − 1^^-bit indicator or a ^ ^log^^^^^⌈^ / 2⌉ − 1^^-bit indicator, or a indicator, or a ^log ^(^^)(^^ − 1)⌈ ⌉ − 1 ^^-bit indicator, or abit In certain embodiments, the wireless device (e.g., a UE) is configured to select theindices ^^, ^ > 0 such that the index ^^ of a transmission layer subset ^ is smallerthan an index ^ of transmission laye ^^^ r subset ^′, wherein ^ > ^. The indices^^, ∀^ > 0 of the ⌈^ / 2⌉-1 transmission layers subsets may be indicated jointly in theCSI report. In some examples, if indices ^^, ^ > 0 are selected from a restricted set^, such joint indication is given by one of the following indicators: a bit indicator or abit indicator. In some examples, if indices ^^, ^ > 0 are selected from a full set ^^ , such joint indication is given by one of the followingindicators: a ^log ^^^1^^- ^^ − 1^ ⌈^ / 2⌉ − bit indicator, or a ^log^ ^ ⌈^ / 2⌉ − 1^^-bit indicator or a^ ^log^^^^^⌈^ / 2⌉ − 1^^-bit indicator or a ^log(^^ − 1)^^^^⌈^ / 2⌉ − 1 ^^-bit indicator or a^log ^(^^)(^^ − 1)⌈ ⌉ − 1 ^^-bit indicator or abit In certain embodiments, the wireless device (e.g., a UE) is configured to select theindices ^^, ^ > 0 and ^^, ^ > 0 such that the combined index ^^, ^ > 0 of atransmission layer subset ^ is smaller than a combined index ^^^ of transmission layersubset ^′, wherein ^^ > ^. The combined indices ^^ , ∀^ > 0 of the ⌈^ / 2⌉ − 1transmission layers subsets may be indicated jointly in the CSI report. In someexamples, such joint indication is given by one of the following indicators: a ^ ^log ^^^^^^-bit in^^^^ − 1^ ⌈^ / 2⌉ − 1dicator or a ^log^^⌈^ / 2⌉ − 1^^-bit indicator or a)^^-bit indicator or a ^log(^^)(^^ − 1)^^⌈^ / 2⌉ − 1 ^^-bit indicator or abit indicator. In some examples, the combined index ^^ = some other examples,the combined index ^^ = ^^^^ + ^^, where ^^ = 0, … , ^^ − 1 and ^^ = 0, … , ^^ − 1.In certain embodiments, the wireless device (e.g., a UE) is configured to select therotation factors such that the rotation factor ^^, ^ > 0 selected for transmission layersubset ^, ^ > 0 is smaller than a rotation factor index ^^^ of a transmission layersubset ^′, wherein ^^ > ^. The rotation factors selected for the ^^ ^^ − 1 transmissionlayer subsets are indicated jointly in the CSI report by a bit indicator or bybit indicator. Here, ^^ = ^^ if the full set ^^ is used for the selection of the indices ^^, ^ > 0 and ^^ = ^^ if the full set ^^ is used for the selectionof the indices ^^, ^ > 0.Selection of vectors {^, ^^, ^^} with respect to frequency subbandsIn certain embodiments, the wireless device is configured with a number of subbands,^^, in the frequency domain, wherein a subband may comprise one or more PRBs.The wireless device is further configured to determine a precoding vector or matrix forthe ^^ subbands and indicate the precoder vector or matrix in the CSI report. In currentCSI reporting schemes for 5G NR systems, the precoding vector for a transmissionlayer is typically kept constant over the ^^ subbands and only a single precoding vectorfor a transmission layer is indicated in the CSI report. However, when the number of subbands and the associated CSI reporting bandwidth of the precoding vector ormatrix is large, it may be beneficial for an improved overall performance to indicate aprecoding vector for each subband. However, such an approach would drasticallyincrease the feedback overhead of the CSI report. Therefore, it is proposed to groupthe ^^ subbands into N subband groups, wherein a subband group is a proper subsetof the ^^ subbands configured to the wireless device. In general, ^ < ^^. A subbandgroup may be associated with an index ^, ^ ∈ {0, … , ^ − 1}. The ^-th subband groupmay comprise ^^ subbands, such that ∑^^^ ^^^ ^^ = ^^. In some examples, the number ofsubband groups, ^, is at least two. In some examples, the number of subbands in asubband group, ^, is at least two. The precoding vectors associated with a subband ina subband group can be identical. This means there is a single precoding vector persubband group which is indicated in the CSI report. The precoding vectors associatedwith different subband groups can be identical or not. In some options, the precodingvector(s) selected by the wireless device (e.g., a UE) for the ^ subband groups areindicated in the CSI report and reported or transmitted to the network node.In one example, ^^ = ^ for several subband groups or for all ^ subband groups. In oneexample, ^ =^^^. In another example, ^^ = ^ for the first ^ − 1 subbands, and ^^^^ =^^ − ∑^^^ ^^^ ^ , and ^ = In yet another example, the first ^ − 1 subband groups(^ = 0, … , ^ − 2) comprise identical number of subbands, ^, and the last subbandgroup comprises the remaining subbands given by ^^^^ = ^^ In Figure 8,an example of grouping ^^ subbands to ^ = 6 subband groups is shown, whereineach subband group comprising three consecutive subbands. In one option, the number of subband groups, ^, is configured to the wireless device(e.g., a UE) by the network node. In another option, the number of subband groups,^, is reported by the wireless device (e.g., a UE) to the network node in the CSI report.In yet another option, the number of subband groups, ^, is determined by the wirelessdevice (e.g., a UE) based on the number of subbands, ^^. In yet another example, thenumber of subband groups, ^, is determined by the wireless device (e.g., a UE) usingthe number of subbands, ^^and the number of subbands in each group ^^or ^. In one option, the number of subbands in a subband group, ^, is configured to thewireless device (e.g., a UE) by the network node. In another example, number ofsubbands in a subband group, ^, is reported by the wireless device (e.g., a UE) to thenetwork node in the CSI report. In yet another option, the number of subbands in asubband group, ^, is determined by the wireless device (e.g., a UE) based on thenumber of subbands, ^^. In yet another option, the number of subbands in a subbandgroup, ^, is determined by the wireless device (e.g., a UE) based on the number ofsubbands, ^^and the number of subband groups, ^.In certain embodiments, the number of subband groups, ^, is layer common andidentical for all transmission layers of the precoder or precoder matrix. In certainembodiments, the number of subband groups, ^, is layer specific and varies for eachtransmission layer of the precoder matrix.Layer grouping and variation of the number of subbands groups with respect to rankIn certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to segment the ^ transmission layers into two transmission layer subsets,wherein the first transmission layer subset comprises ^′ transmission layers and thesecond transmission layer subset comprises the remaining ^ − ^’ transmission layers,and wherein the number of subband groups for the first transmission layer subset is^(^), and the number of subband groups for the second transmission layer subset is^(^). For calculating the precoder, the ^^ subbands are grouped into ^(^)subband groups for the first transmission layer subset, and the ^^subbands are grouped into^(^) subband groups for the second transmission layer subset. In some examples, asubband group can be a proper subset of the ^^subbands configured to the wirelessdevice (e.g., a UE). In some examples, ^(^) = ^ (^)^ or ^ = ^^. In some examples,^(^) = 1 or ^(^) = 1.The numbers of subband groups for the two transmission layer subsets are notidentical or only partly identical (in other words, overlapping). In one example, ^(^)≠^(^). In another example, ^(^) = ^(^). In yet another example, ^(^) < ^(^), or ^(^) >^(^). In yet another example, ^(^) is derived from ^(^), or is derived from ^(^). Inyet another example, ^(^) = and ^ is a positive rational number less than 1.In yet another example, ^(^) = and ^ is a positive rational number greaterthan 1 or a positive integer.In certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to segment the ^ transmission layers into three transmission layersubsets, wherein the first transmission layer subset comprises ^′ transmission layers,the second transmission layer subset comprises ^′′ transmission layers, and the thirdtransmission layer subset comprises the remaining ^ − ^^ − ^′′ transmission layers,wherein the number of subband groups for the transmission layers of the firsttransmission layer subset is ^(^), the number of subband groups for the transmissionlayers of the second transmission layer subset is ^(^), and the number of subbandgroups for the transmission layers of the third transmission layer subset is ^(^). In oneexample, ^(^) ≠ ^(^) ≠ ^(^). In another example, ^(^) = ^(^) = ^(^). In yet anotherexample, ^(^) < ^(^) < ^(^). In yet another example, ^(^) > ^(^) > ^(^). In yetanother example, ^(^)is derived from ^(^)or ^(^). In yet another example, ^(^)is derived from ^(^)or ^(^). In yet another example, ^(^)is derived from ^(^)or ^(^). Inyet another example, and ^ is a positive rationalnumber less than 1 or a positive rational number greater than 1 or a positive integer.In yet another example, ^(^) = or ^(^) = ^^(^)^^ and ^ is a positive rationalnumber less than 1 or a positive rational number greater than 1 or a positive integer.In yet another example, ^(^) = or ^(^) = ^^(^)^^ and ^ is a positive rationalnumber less than 1 or a positive rational number greater than 1 or a positive integer.In certain embodiments, for a rank ^ precoder matrix, the wireless device (e.g., a UE)is configured to segment the ^ transmission layers into four transmission layersubsets, wherein the first transmission layer subset comprises ^′ transmission layers,the second transmission layer subset comprises ^′′ transmission layers, the thirdtransmission layer subset comprises ^′′′ transmission layers and the fourthtransmission layer subset comprises the remaining ^ − ^^ − ^^^ − ^′′′ transmissionlayers, and wherein the number of subband groups for the transmission layers of thefirst transmission layer subset is ^(^), the number of subband groups for thetransmission layers of the second transmission layer subset is ^(^), the number ofsubband groups for the transmission layers of the third transmission layer subset is^(^), and the number of subband groups for the transmission layers of the fourthtransmission layer subset is . In one example, ^(^) ≠ ^(^) ≠ ^(^) = ^(^). Inanother example, ^(^) = ^(^) = ^(^) = ^(^). In yet another example, ^(^) < ^(^) <^(^) < ^(^). In yet another example, ^(^) > ^(^) > ^(^) > ^(^). In yet another example, ^(^)is derived from ^(^)or ^(^)or ^(^). In yet another example, ^(^)is derived from or ^(^)or ^(^). In yet another example, ^(^)is derived from or ^(^)or ^(^). In yet another example, is derived from ^(^)or ^(^)or ^(^). In yetanother example, and ^ is apositive rational number less than 1 or a positive rational number greater than 1 or apositive integer. In yet another example, ^(^) = (^) or ^ = ^^(^)^^ or ^(^) =^^(^)^^, and ^ is a positive rational number less than 1 or a positive rational numbergreater than 1 or a positive integer. In yet another example, ^(^) = (^) or ^ =^^(^)^^ or ^(^) = ^^(^)^^, and ^ is a positive rational number less than 1 or a positiverational number greater than 1 or a positive integer. In yet another example, ^(^)= and ^ is a positive rational number lessthan 1 or a positive rational number greater than 1 or a positive integer.Selection of vectors {^, ^^, ^^} with respect to frequency subbands and rankFor higher CSI reporting bandwidths configured to the wireless device (e.g., a UE), aselection of vectors ^ or {^^, ^^} per subband group incurs a high reporting overhead,especially when the number of subband groups is high. Therefore, it is proposed to support only a vector selection per subband group for specific transmission rankvalues. Here, the rank indicates the number of transmission layers ^, for which theprecoder or precoding matrix indicated by the PMI is calculated.In certain embodiments, the vector selection for each subband group is rank specific.In one example, the vector selection per subband group is supported only for rank ^ <^ of the precoding matrix. In some examples, ^ ∈ {2,3,4,5,6,7,8}. In some examples,the value of ^ is configured to the wireless device (e.g., a UE) by the network node.In another example, the value of ^ is determined and reported by the wireless device(e.g., a UE) in the CSI report. In some examples, the vector selection per subbandgroup can be set to ‘ON’ or ‘OFF’ and is indicated to the wireless device (e.g., a UE)by higher level RRC configuration, or by MAC-CE, or by physical layer signaling.Indication of {^, ^^, ^^} in the CSI reportIn certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindex ^ of the selected vector of a subband group in the CSI report. In one example,the index of the selected vector of a subband group is indicated by a ⌈log^ ^^^^^^^^⌉-bit indicator. In another example, the selected index of a subband group is reported bya ⌈log^ ^^^^⌉-bit indicator and the rotation factor is indicated using a ⌈log^ ^^^^⌉-bitindicator.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindices (^, ^) of the selected vector for a subband group in the CSI report. In oneexample, the selected indices ^ and ^ per subband group are reported by a⌈log^ ^^^^⌉-bit indicator and ⌈log^ ^^^^⌉-bit indicator, respectively. In another example,the selected indices ^ and ^ per subband group are reported using ⌈log^ ^^⌉-bits and⌈log^ ^^⌉-bits, respectively. The rotation factors associated with the indices ^ and ^are reported by a⌈log^^^⌉-bit indicator and⌈log^^^⌉-bit indicator, respectively or by a⌈log^^^^^⌉-bit indicator. In one option, the rotation factors are reported in a wideband manner, wherein a single indicator of ⌈log^^^^^⌉-bits or two indicators of ⌈log^^^⌉-bits and ⌈log^^^⌉-bits are identical for all subbands or subband groups and are reported only once in the CSI report.To reduce feedback overhead related to the reporting of the selected vectors for asubband, several reporting overhead reduction schemes are provided in the following.In certain embodiments, the wireless device (e.g., a UE) is configured with ^^subbands, and to select a first vector from a codebook for a first subband of the precoding matrix, and to select a second vector from a restricted codebook for a second subband of the precoding matrix.In some options, the restricted codebook may comprise a set of ^ vectors, or a windowof ^ consecutive or non-consecutive indices indicating the ^ vectors. In some options,the restricted codebook may comprise a set of ^ vectors, or a first window associatedwith ^^consecutive or non-consecutive indices, and a second window associated with^^ consecutive or non-consecutive indices, indicating the ^ vectors. Note that the size (i.e., the number of entries) of the restricted codebook is smaller than the size of the codebook (i.e., the non-restricted codebook). In some examples, the codebook comprises ^^^^or ^^^^^^^^vectors or indices associated with ^^^^or ^^^^^^^^vectors as described above. In some options, the first and second vector are indicated in the CSI report. Moreover, in some options, the selection of the second vector associated with the second subband can be restricted or may depend on the selected first vector associated with the first subband. In the following, some examples of such a restriction or dependency are provided.Let “^” or be the index / indices associated with the selected vector ^^ of a firstsubband, wherein examples for the index range are ^ ∈ {0, … . , ^^^^ − 1} or ^ ∈ Here, ^ is the indexfrom the codebook comprising ^^^^or ^^^^^^^^indices or vector indices associated with the ^^antenna ports in a first dimension and ^^antenna ports in the seconddimension. Here, ^ is the index from the codebook associated with the ^^ antennaports in a first dimension and ^ is the index from the codebook associated with the ^^antenna ports in a second dimension.In general, the value of ^ can be given by any positive integer value less than ^^^^.In some examples, the value of ^ is given by any odd number less than ^^^^, or byany even number less than ^^^^.In one example, ^ = 1 and the window comprises a single index ^ + 1 or ^ − 1 or ^ + ^,wherein ^ is any positive integer or negative integer less than or equal to ^^^^ − 1. Inanother example, ^ = 2 and the window comprises the two indices {^ + 1, ^ + 2}, or{^ − 1, ^ + 1}, or {^ + ^, ^ + ^}, wherein In yetanother example, the value of ^ = 2 and the window comprises two values {^ − ^, ^ +^}, wherein {^, ^} ∈ {0, … , ^. In yet another example, ^ = 3 and thewindow comprises three consecutive values {^ + 1, ^ + 2, ^ + 3}, or {^ + ^, ^ + ^, ^ + ^},or {^ − ^, ^ + ^, ^ + ^}, or {^ − ^, ^ − ^, ^ + ^}, wherein ^ ^. In yet another example, ^ = 4 and the window comprise four consecutive values{^ + 1, ^ + 2, ^ + 3, ^ + 4}, or {^ + ^, ^ + ^, ^ + ^, ^ + ^}, or {^ − ^, ^ + ^, ^ + ^, ^ + ^}, or{^ − ^, ^ − ^, ^ + ^, ^ + ^}, or ^ − ^, ^ − ^, ^ − ^, ^ + ^}, wherein {^, ^, ^, ^} ∈{0, … , ^^^^ − 1} and ^ ≠ ^ ≠ ^ ≠ ^. The values of ^ and / or ^ and / or ^ and / or ^ areeither configured to the wireless device (e.g., a UE) by the network node or determinedand reported by the wireless device (e.g., a UE) to the network node in the CSI reportor fixed in the specification or derived from any other parameter.In Figure 9, it is shown that for a first subband, the vector index is selected from a (full-sized) codebook, e.g., comprising ^^^^ or ^^^^^^^^ indices or vector indices,whereas for a second subband, the vector index is selected from a restricted codebookcomprising ^ = 4 indices or vector indices {^, ^ + 1, ^ + 2, ^ + 3}, wherein ^ is the indexof the selected vector for the first subband from a codebook comprising ^^^^or ^^^^^^^^indices or vector indices.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindex of the second vector associated with the second subband in the CSI report by a⌈log^^⌉-bit indicator. In one example, the value of ^^is given by any integer value less than or equal to ^^. In another example, the value of ^^is given by any integer value less than or equal to ^^. In yet another example, the value of ^^is given by any integer value less than or equal to ^^or ^^^^. In another example, the value of ^^is given by any integer value less than or equal to to ^^or ^^^^.In one example, ^^ = 1 and the window comprises a single value ^ + ^^, or ^ + ^^^^,wherein ^^is any positive integer less than or equal to ^^or ^^or ^^^^. In anotherexample, ^^ = 1 and the window comprises a single value ^ + ^^, or ^ + ^^^^,wherein ^^is any positive integer less than or equal to ^^or ^^or ^^^^.In one example, ^^ = 2 and the window comprise two values {^ + ^^, ^ + 2^^}. Inanother example, ^^ = 2 and the window comprise two values {^ + ^^^^, ^ + ^^^^},wherein {^, ^} ∈ {0, … , ^^^^ − 1} and ^^ ^^. In yet another example, ^^ = 2 and thewindow comprise two values {^ − ^^^^, ^ + ^^^^}, wherein {^^, ^^} ∈ {0, … , ^^^^ − 1}and ^^ ≠ ^^ or ^^ = ^^.In one example, ^^ = 2 and the window comprise two values {^ + ^^, ^ + 2^^}. Inanother example, ^^ = 2 and the window comprise two values {^ + ^^^^, ^ + ^^^^},wherein {^^, ^^} ∈ {0, … , ^^^^ − 1} and ^^ ≠ ^^. In yet another example, ^^ = 2 and thewindow comprise two values {^ − ^^^^, ^ + ^^^^}, wherein {^^, ^^} ∈ {0, … , ^^^^ − 1}and ^^ ≠ ^^ or ^^ = ^^.In one example, ^^ = 3 and the window comprise three consecutive values {^ + ^^, ^ +2^^, ^ + 3^^}. In another example, ^^ = 3 and the window comprise three consecutivevalues {^ + ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein ^^ ^^. In yet another example, ^^ = 3 and the window comprise three consecutivevalues {^ − ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein ^^. In yet another example, ^^ = 3 and the window comprise three{^ − ^^^^, ^ − ^^^^, ^ + ^^^^}, wherein ∈ {0, … , ^^^^ − 1} In one example, ^^ = 3 and the window comprise three consecutive values {^ +^^, ^ + 2^^, ^ + 3^^}. In another example, ^^ = 3 and the window comprise threeconsecutive values {^ + ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein {^^, ^^, ^^} ∈{0, … , ^^^^ − 1} and ^^ ^^. In yet another example, ^^ = 3 and the windowcomprise three consecutive values {^ − ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein yet another example,^^ = 3 and the window comprise three consecutive values {^ − ^^^^, ^ − ^^^^, ^ +^^^^}, wherein {^^, ^^ , ^^} ∈ {0, … , ^^^^ − 1} and ^^ ≠ ^^ ≠ ^^.In one example, ^^ = 4 and the window comprise four consecutive values {^ + ^^, ^ +2^^, ^ + 3^^, ^ + 4^^}. In another example, ^^ = 4 and the window comprise fourconsecutive values {^ + ^^^^, ^ + ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein {^^, ^^, ^^, ^^} ∈{0, … , ^^^^ − 1} and ^^ ≠ ^^ ≠ ^^ ≠ ^^. In another example, ^^ = 4 and the windowcomprise four consecutive values {^ − ^^^^, ^ + ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein{^^, ^^, ^^, ^^} ∈ {0, … , ^^^^ − 1} and ^^ ≠ ^^ ≠ ^^ ≠ ^^ or ^^ = ^^ ≠ ^^ ≠ ^^. Inanother example, ^^ = 4 and the window comprise four consecutive values {^ −^^^^, ^ − ^^^^, ^ + ^^^^, ^ + ^^^^}, wherein {^^, ^^, ^^, ^^} ∈ {0, … , ^^^^ − 1}. In oneexample, ^^ = 4 and the window comprise four consecutive values {^ + ^^, ^ +2^^, ^ + 3^^, ^ + 4^^}. In another example, ^^ = 4 and the window comprise fourconsecutive values {^ + ^^^^, ^ + ^^^^, ^ + 2^^, ^ + ^^^^}, wherein another example, ^^ = 4and the window comprise four consecutive values {^ − ^^^^, ^ + ^^^^, ^ + 2^^, ^ +^^^^}, wherein ^^ ^^. In another example, ^^ = 4 and the window comprise four consecutive values{^ − ^^^^, ^ − ^^^^, ^ + 2^^, ^ + ^^^^}, wherein {^^, ^^, ^^, ^^} ∈ {0, … , ^^^^ − 1}.In Figure 10, it is shown that for the first subband the vector index ^ is selected from a(full-size) codebook comprising ^^ indices or vector indices and the vectorindex ^ is selected from a (full-size) codebook comprising ^^ or ^^^^ indices or vectorindices, whereas for the second subband, the vector index for the ^^ antenna ports inthe first dimension is selected from a restricted codebook comprising ^^ = 2 indices orvector indices {^, ^ + 1} and the vector index for the ^^ antenna ports in the seconddimension is selected from a restricted codebook comprising ^^ = 2 indices or vectorindices given by {^, ^ + 1}.The values of ^^and / or ^^and / or ^^and / or ^^are either configured to the wirelessdevice (e.g., a UE) by the network node or determined and reported by the wirelessdevice (e.g., a UE) and to the network node in the CSI report or fixed in thespecification or derived from any other parameter. The values of ^^and / or ^^and / or^^ and / or w^ are either configured to the wireless device (e.g., a UE) by the networknode or determined and reported by the wireless device (e.g., a UE) and to the networknode in the CSI report or fixed in the specification or derived from any other parameter.In some examples, ^^ = ^^, ^^ = ^^, ^^ = ^^ and ^^ = ^^.In certain embodiments, the wireless device (e.g., a UE) is configured to indicate theindices of the second vector associated with the second subband in the CSI report by a ⌈log^^^⌉-bit indicator and ⌈log^^^⌉-bit indicator. Power scaling across layers In certain embodiments, the precoding vector associated with a transmission layer isassociated with a transmission layer-specific power scaling factor. In some examples,the precoding vector associated with a transmission layer ^ is given by ^^ =^ ^√^^ ^^^^^, wherein ^^ = [^^^^^^^ ^^^^ … ^^^^^^^^ ]^, ^ ′ = [^^^^^^ … ^^^^^]^is an 2^^^^-length vector, ^^, ^^, … , ^^^^ are the scaling coefficients with ^^ (^ = 0, … , ^ − 1, ^indicates the number of scaling coefficients) being either a phase value, an amplitudevalue or an amplitude and a phase value, ^^, ^ = 1, … , ^ is a transmission layer powerscaling factor, and ^ is a normalization factor. In some examples, it is assumed thatthe sum power of the precoding vector ^^ is one before applying the power scalingfactor per transmission layer ^^and normalization factor ^.When using the per transmission layer power scaling factors across layers, the sumpower of the precoder can be either one or less than one. In some options, the sumpower of the precoder of all transmission layers is equal to one, and it is assumed thatthe PDSCH (after applying the precoder at the network node (e.g., gNB) side to thetransmission) is transmitted with full transmit power ^^. When the sum power of the precoder of all transmission layers is less than one, the PDSCH is transmitted withpartial transmit power which is smaller than ^^.By introducing the per transmission layer power scaling factors, the total transmitpower ^^ (transmit power of the PDSCH applied at the network side) is divided equallyor unequally among the ^ transmission layers of the precoder. For simplicity, it isassumed in the following that ^^ is equal to one or less than one.Typically, for the Type-I and Type-II codebooks specified in the 3GPP standards [seeTS 38.214, version 16.10.0, 2022-06-23], the sum power of a precoder comprising ^transmission layers is one and the power is equally distributed among the ^transmission layers, i.e., each transmission layer ^ is allocated with a power of^ ^,where ^ denotes the rank or the number of transmission layers of the precoder. Sinceit is assumed that the sum power of the precoder is equal to one before applying the ^ power scaling factor per transmission layer ^^= ^, ∀^ = 1, … , ^.In certain embodiments, the wireless device determines the per transmission layerpower scaling factors for ^ transmission layers based on a certain measure(maximizing throughput, or signal-to-noise ratio (SNR), or capacity etc.,). In someoptions, the transmission layer power scaling factor of a transmission layer can be anyvalue between 0 and 1 or any value less than 1. In certain embodiments, the wireless device indicates the per transmission layer powerscaling factors for the ^ transmission layers of the precoder in the CSI report. In oneoption, the transmission layer power scaling factors are indicated using an ^-bitindicator in the CSI report. In some examples, the ^ bits are associated with 2^ or2^ − 1 power values. In some examples, the 2^ or 2^ − 1 power values are uniformlyor non-uniformly spaced between 0, or any other number, and 1, either in linear scale or decibel scale. In one option, the per transmission layer power scaling factors areselected from a set comprising 2^ or 2^ − 1 power values. In one example, the 2^power values are given In some examples, the normalization factor ^ associated with each of the ^^ transmission layers is given by Each DFT-based vector used in the precoder is associated with a set of antenna portsand used to spatially focus the power of the (precoded) transmission to a desireddirection. Therefore, the DFT-based vectors used in the precoder can also be calledas beams. These beams may have strong sidelobes depending on the antenna arrayused at the network node. This may cause interference with other co-existing terrestrial systems or satellite systems. According to the ‘WRC 23 Resolution COM4 / 7: Terrestrial component of IMT within the frequency band 6425–7125 MHz,’ the level ofthe expected Effective Isotropically Radiated Power (EIRP) spectral density as afunction of the vertical angle above the horizon is limited. Therefore, it is desired tocontrol the transmit power of the precoder so that the interference is limited in desireddirections to a certain threshold value.For this purpose, it was agreed in RAN1#118 to configure the wireless device (e.g.,UE) with a threshold value per DFT-based vector or a group of DFT-based vectorsused by the precoder. The threshold values are indicated using a 3-bit scaling factorselected from the following set ^√1, For example, if the precoder uses a DFT-based vector configured with a threshold value^^ ^, the power ofthe associated transmission layer of the precoder cannot exceed ½.In certain embodiments, the wireless device is configured with a threshold power valuefor each DFT-based vector, or a group of DFT-based vectors, wherein a group maycomprise at least one vector, used by the precoder via a higher layer configurationfrom the network node. The threshold power value associated with a DFT-basedvector or a group of DFT-based vectors may be denoted by ^ in the following. Thevalue ^ may be different for different DFT-based vectors, or different groups of DFT-based vectors. The configured maximum power values are considered by the wirelessdevice when calculating the precoder.In certain embodiments, a maximum power value associated with a DFT-based vectoror a group of DFT-based vectors is configured to the wireless device using a ^^-bitindicator and is chosen from a set comprising 2^^ or less than 2^^ values. In someexamples, the values of the set are uniformly or non-uniformly spaced in linear scaleor in decibel scale. In some examples, the threshold power value ^ associated with aDFT-based vector or a group of DFT-based vectors is configured using a 3-bit indicatorand is chosen from the set ^1, In certain embodiments, the wireless device determines the per transmission layerpower scaling factor such that the total power of the precoding vector of a transmissionlayer does not exceed the threshold power value ^ associated with the DFT-basedvector used for the precoder for that transmission layer. In some examples, the power^ scaling factor is given by a smallest value among ^ and ^. In this case, as the networkis aware of the rank and the configured value ^, there is no need to indicate the pertransmission layer power scaling factors in the CSI report. In certain embodiments, the wireless device determines the per transmission layer power scaling factor such that the total power of the precoding vector of a transmissionlayer does not exceed the threshold power value ^ associated with the DFT vectorused for the precoder for that transmission layer, and indicates the values of ^^, ∀^ =1, … , ^ in the CSI report. In some examples, ^^ is any value greater than zero and / orless than or equal In certain embodiments, the wireless device determines the per transmission layer power scaling factor such that the total power of the precoding vector of a transmission ^ layer does not exceed the threshold power value ^ associated with the DFT-basedvector configured with a threshold power value ^. Here, ^ is the number oftransmission layers using the same DFT-based vector. In some examples, the value^ of ^^is given by smallest value among ^ and ^. In this case, as the network is awareof the rank, the configured threshold power value ^ and the value of ^, there is no needto indicate the per transmission layer power scaling factors in the CSI report. In certain embodiments, the wireless device determines the per transmission layer power scaling factor such that the total power of the precoding vector of a transmission ^ layer does not exceed the maximum power value ^ associated with the DFT-basedvector configured with a maximum power value ^, and indicates the values of ^^, ∀^ =1, … , ^ in the CSI report. Here, ^ is the number of transmission layers using the sameDFT-based vector. In some examples, ^^ is any value greater than zero and less thanor equal to min ^^ ^ ^ , ^ ^. In certain embodiments, the wireless device determines the transmission layer powerscaling factors of ^ transmission layers such that the total power of the precodingvector of the ^ transmission layers does not exceed the maximum power value ^, andindicates the per transmission layer power scaling factors in the CSI report. In someexamples, for ^ = 4, the first two layers i.e., layer 1 and layer 2 are associated with afirst DFT-based vector configured with a threshold power value 1 / 2 and the remainingtwo layers i.e., layer 3 and layer 4 are associated with a second DFT-based vectorconfigured with a threshold power value ¼. In this case, the sum power of the per transmission layer power scaling factors of layer 1 and layer 2 should not exceed ½ and the sum power of the per transmission layer power scaling factors of layer 3 and layer 4 should not exceed ¼. Reporting and quantization of the power scaling factors In certain embodiments, the wireless device is configured to indicate the per transmission layer power scaling factor in the CSI report using an ^^-bit indicator. In some examples, the ^^-bit indicator indicates a power value selected by the wirelessdevice from a set of 2^^ or 2^^ − 1 power values.In some examples, when a DFT-based vector associated with a threshold power value^ is used for the precoder of a transmission layer, the transmission layer power scalingfactors are selected from the 2^^ or 2^^ − 1 power values which lie between 0 and ^(or 1).In some examples, the 2^^ or 2^^ − 1 power values are uniformly or non-uniformlyspaced between 0 and ^ either in linear scale or decibel scale. In some otherexamples, the 2^^ or 2^^ − 1 power values are uniformly or non-uniformly spacedbetween 0 and 1 either in linear scale or decibel scale.Rank specific configuration of power scaling valuesIn some examples, for ^ = 4, the configured threshold power values for the DFT-basedvectors used for the precoding vectors of layer 1, layer 2, layer 3 and layer 4 are given by ½, ¼, and 1 / 3, 1 / 8, respectively. The per transmission layer power scaling factor isdetermined by the wireless device (e.g., UE) Therefore, the determinedtransmission layer power scaling factor for layer 1, layer 2, layer 3 and layer 4 are ¼, ¼, ¼, and 1 / 8, respectively. It can be observed that for layers 1,2, and 3, the configured maximum power values are either larger or equal to 1 / ^. As the transmission layerpower scaling factor is determined by the wireless device there is noneed for the network node to configure the threshold power values which are greaterthan 1 / ^ for a rank ^ transmission. Therefore, the following is proposed. In certainembodiments, the range of the threshold power values is dependent on the rank. Insome examples, for ^ = 2, the range of the allowable maximum power values isbetween 0 and ½. In some examples, for ^ = 2, the range of the allowable maximumpower values is between 1 / 16 and ½. In some examples, for ^ = 2, the range of the ^ ^ allowable maximum power values is between ^^ and ^. In some examples, for ^ = 4,^ ^ the range of the allowable maximum power values is between ^^ and ^. In certain embodiments, the number of allowable threshold power values used for the configuration of threshold power values for a first rank value is greater than the number of allowable threshold power values used for the configuration of threshold power values for a second rank value, wherein the first rank value is smaller than the second rank value. In some examples, the number of threshold power values used for rank 1 is given by 8, whereas for rank 4, the number of threshold power values is given by 4. In some examples, the number of threshold power values for rank 1 are whereas the number of threshold power values for rank 4 are^^ ^ ^ ^ ^ , ^ , ^^ , ^^ ^. In certain embodiments, the allowable threshold power values used for the configuration of threshold power values for a first rank value is given by a proper subset of the allowable threshold power values used for the configuration of threshold power values for a second rank value. In one option, the first rank value is greater than the second rank value. In some examples, the first rank value is given by 4, whereas the second rank value is either 1 or 2. In one option, the allowable threshold power ^ values for rank 4 , ^^^ is a proper subset of the allowable power values forrank Phase coefficient vector across frequency domain unitsIn certain embodiments, a precoding vector comprises ^ DFT-based vectors and oneor more of the ^ DFT-based vectors are associated with one or more phase coefficientvector in the frequency domain. This means an ^-th DFT-based vector can beassociated with a phase coefficient vector. In some options, the phase coefficientvector can be, in some examples, a DFT-based vector, defined across a number ofPRBs, subbands, or subband groups. This means, an entry of the phase coefficientvector is associated with a PRB, subband, or a subband group (in an increasing or decreasing order). Such a phase coefficient vector allows a precoding of one or moreof the ^ DFT-based vectors in the frequency domain. In some examples, ^ = 2, andonly the vector associated with indices {^^^^, … , 2^^^^ − 1} is associated with a phasecoefficient vector. In some examples, ^ = 2, and only the vector associated withindices {0, … , ^^^^ − 1} is associated with a phase coefficient vector. In someexamples, a first phase coefficient vector is associated with a first vector and a second phase coefficient vector is associated with a second vector, wherein the first and second vectors are associated with different indices of the precoding vector. In some options, a phase coefficient vector is also associated with a scaling coefficient, whereinthe scaling coefficient is at least one of an amplitude value and a phase value.In certain embodiments, a selected phase coefficient vector is indicated by thewireless device in the CSI report, and / or the information of the amplitude value orphase value or both amplitude and phase value of the scaling coefficient associatedwith a selected phase coefficient vector is indicated by the wireless device in the CSIreport.In certain embodiments, a phase coefficient vector is selected by the wireless devicefrom a full-size DFT-based codebook, wherein the dimensions of the codebook areeither dependent on the number of PRBs, or subbands. In some examples, the sizeof the codebook, or codebook matrix is either ^^ × ^^ or ^^ × ^^^^ or ^^^^ × ^^^^ or^^^^ × ^^^^^^. Here, ^^, ^^^^ , ^^ are the number of subbands, number of PRBs andthe oversampling factor of the DFT-based codebook, respectively. Each vector orindex in the codebook is associated with a phase coefficient vector.In certain embodiments, a phase coefficient vector is selected by the wireless devicefrom a reduced size codebook comprising ^ vectors or DFT-based vectors or indicesassociated with ^ vectors, wherein ^ < ^^ or ^ < ^^^^, and wherein the ^ vectors areassociated with consecutive or non-consecutive indices from the full-size codebook.In some examples, for ^ = 4, the ^ vectors are associated with the indices {0,1,2,3}or {0,2,4,6} of the full-size codebook. In some other examples, the ^ vectors may beassociated with the first few indices and last few indices of the codebook. In certainembodiments, the ^ vectors in the reduced size codebook may not be associated witha zero index of the full-size codebook. In some examples, for ^ = 4, the ^ vectors areassociated with the indices {1,2,3,4} or {1,3,5,7} of the full-size DFT codebook. In someexamples, the wireless device indicates the selected phase coefficient vector via a⌈log^ ^⌉-bit indicator in the CSI report. In some examples, the value of ^ is determinedby the wireless device (e.g., a UE) and indicated in the CSI report or derived by thewireless device using the information related to the configured parameters such as thenumber of PRBs or the number of subbands. In another example, the value of ^ isconfigured to the wireless device (e.g., a UE) by higher level RRC configuration or viaMAC-CE or DCI signaling. In yet another example, the value of ^ is fixed in thespecification. Referring to Figure 5, there is illustrated a method performed by a wireless device (300) according to some of the previously described embodiments. The method isperformed by the wireless device (300) in a wireless communications network. Themethod comprises: -receiving (501) configuration information associated with a channel stateinformation, CSI, report, wherein the configuration information indicates anumber of antenna ports, ^^, in a first dimension, and a number of antennaports, ^^, in a second dimension, -determining (502) based on the configuration information a precoding vector,comprising a plurality of scaling coefficients, for 2^^^^ antenna ports, whereineach entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or aphase value, or an amplitude and phase value,- generating (503) a CSI report comprising a Precoder Matrix Indicator, PMI,indicating the precoder vector, and -reporting (504) to a network node the CSI report.In certain embodiments, the precoding vector comprises ^ DFT-based vectors.In certain embodiments, the precoding vector comprises ^ real- or complex-valuedscaling coefficients. In certain embodiments, the number of scaling coefficients, ^, is greater than the number of DFT-based vectors, ^. In certain embodiments, each scaling coefficient is associated with an antenna port subset, wherein the antenna port subset is a subset or proper subset of the 2^^^^antenna ports. In certain embodiments, the method further comprising at least one of the following: indicating an index of the scaling coefficient associated with unit amplitude value andzero phase value, or indicating an index of the antenna port subset associated withthe scaling coefficient having unit amplitude value and zero phase value in the CSI report.In certain embodiments, the scaling coefficients ^ are segmented in ^ 1 < ^ < ^,amplitude subsets, and the amplitude values of ^′ scaling coefficients in an amplitudesubset are identical.In certain embodiments, the PMI indicates a rank ^ precoding matrix comprising ^precoding vectors for ^ transmission layers.In certain embodiments, the number of scaling coefficients, ^, are dependent on therank ^ of the precoding matrix.In certain embodiments, for the rank ^ precoding matrix, the method further comprises:selecting a first vector for a first transmission layer subset comprising ^’ transmissionlayers of the precoding matrix, wherein ^’ < ^, and selecting a second vector for asecond transmission layer subset comprising ^’’ transmission layers of the precodingmatrix, wherein ^’′ < ^ and ^’ + ^′^ = ^.In certain embodiments, a plurality of precoding vectors is determined for ^^subbands. The ^^ subbands are grouped into N subband groups, wherein a subbandgroup is a subset of the ^^ subbands, and wherein a precoding vector for a subbandgroup is indicated in the CSI report.In certain embodiments, for the rank ^ precoding matrix, the method further comprises:segmenting the ^ transmission layers into two transmission layer subsets, wherein afirst transmission layer subset comprises ^′ transmission layers and a secondtransmission layer subset comprises the remaining ^ − ^’ transmission layers, andwherein a number of subband groups for the first transmission layer subset is ^(^), and a number of subband groups for the second transmission layer subset is ^(^),wherein In certain embodiments the method further comprises: selecting a first precodingvector for a first subband from a codebook comprising a number of vectors or indicesindicating the vectors, and selecting a second precoding vector for a second subband from a restricted codebook, wherein a size (e.g., number of elements or entries) of the restricted codebook is smaller than a size (e.g., number of elements or entries) of the codebook. In order to perform the previously described process or method steps performed bythe wireless device (e.g., a UE or an IoT device), there is also provided a wirelessdevice. Figure 3 illustrates a simplified block diagram depicting a wireless device (e.g.,a UE or an IoT device) 300. The wireless device 300 comprises a processor 310 orprocessing circuit or a processing module or a processor means 310; a receiver circuit or receiver module 340; a transmitter circuit or transmitter module 350; a memory module 320, a transceiver circuit or transceiver module 330 which may include the transmitter circuit 350 and the receiver circuit 340. The wireless device 300 further comprises an antenna system 360 which includes antenna circuitry for transmitting and receiving signals to / from at least the network node or other wireless device(s). The antenna system employs beamforming as previously described.The wireless device 300 may belong to any radio access technology including 4G orLTE, LTE-A, 5G, advanced 5G or a combination thereof that support beamforming technology. The wireless device 300 may be a UE or an IoT device. The wireless device comprising the processor and the memory contains instructions executable by the processor, whereby the wireless device 300 is operative or is configured to perform any one of the embodiments related to the wireless device as previously described. The processing module / circuit 310 includes a processor, microprocessor, an application specific integrated circuit (ASIC), field programmable gate array (FPGA), or the like, and may be referred to as the “processor.” The processor 310 controls the operation of the wireless device and its components. Memory (circuit or module) 320 includes a random-access memory (RAM), a read only memory (ROM), and / or another type of memory to store data and instructions that may be used by processor310. In general, it will be understood that the wireless device 300 in one or moreembodiments includes fixed or programmed circuitry that is configured to carry out the operations in any of the embodiments disclosed herein. In at least one such example, the processor 310 includes a microprocessor, microcontroller, DSP, ASIC, FPGA, or other processing circuitry that is configured to execute computer program instructions from a computer program stored in a non- transitory computer-readable medium that is in or is accessible to the processing circuitry. Here, “non-transitory” does not necessarily mean permanent or unchanging storage, and may include storage in working or volatile memory, but the term does connote storage of at least some persistence. The execution of the program instructions specially adapts or configures the processing circuitry to carry out the operations disclosed in this disclosure relating to the wireless device. Further, it will be appreciated that the wireless device 300 may comprise additional components. The wireless device 300 by means of processor 310 executes instructions contained in the memory 320 whereby the wireless device is operative to perform any one of the previously described embodiments related to the actions performed by the wirelessdevice, some of which are presented in appended claims.There is also provided a computer program comprising instructions which when executed by the processor 310 of the wireless device 300 cause the processor 310 to carry out the method according to any one of the previously described embodiments. There is also provided a computer program comprising instructions which whenexecuted by the processor 310 of the wireless device 300 cause the processor 310 tocarry out the method according to any one of claims 1-13. Referring to Figure 6, there is illustrated a method performed by a network node (400) according to some of the previously described embodiments. The method performedby the network node (400) is used for receiving, from a wireless device (300), achannel state information, CSI, report in a wireless communications network. Themethod comprises: ^transmitting (601), to a wireless device (300), configuration informationassociated with a channel state information, CSI, report, wherein theconfiguration information indicates a number of antenna ports, ^^, in a firstdimension, and a number of antenna ports, ^^, in a second dimension, for enabling the wireless device to: odetermine based on the configuration information a precoding vectorcomprising a plurality of scaling coefficients for 2^^^^antenna ports, wherein each entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or a phase value, or an amplitude andphase value, ogenerate a CSI report comprising a Precoder Matrix Indicator, PMI,indicating the precoder vector, and ^receiving (602), from the wireless device (300) an uplink control information,UCI, including the CSI report over an uplink, UL, channel.In order to perform the previously described process or method steps performed bythe network node there is also provided a network node. Figure 4 illustrates a blockdiagram depicting a network node 400. The network node 400 comprises a processor 410 or processing circuit or a processing module or a processor means 410; a receivercircuit or receiver module 440; a transmitter circuit or transmitter module 450; amemory module 420, a transceiver circuit or transceiver module 430 which may include the transmitter circuit 450 and the receiver circuit 440. The network node 400 further comprises an antenna system 460 which includes antenna circuitry for transmitting and receiving signals to / from at least the wireless device. The antenna system employs beamforming as previously described. The network node 400 may belong to any radio access technology including 4G or LTE, LTE-A, 5G, advanced 5G or a combination thereof that support beamforming technology. The network node may be a gNB. The network device comprising the processor and the memory contains instructions executable by the processor, whereby the network node 400 is operative or is configured to perform any one of the embodiments related to the network node 400 as previously described. The processing module / circuit 410 includes a processor, microprocessor, an application specific integrated circuit (ASIC), field programmable gate array (FPGA), or the like, and may be referred to as the “processor.” The processor 410 controls the operation of the network node and its components. Memory (circuit or module) 420 includes a random-access memory (RAM), a read only memory (ROM), and / or another type of memory to store data and instructions that may be used by processor410. In general, it will be understood that the network node in one or moreembodiments includes fixed or programmed circuitry that is configured to carry out the operations in any of the embodiments disclosed herein. In at least one such example, the processor 410 includes a microprocessor, microcontroller, DSP, ASIC, FPGA, or other processing circuitry that is configured to execute computer program instructions from a computer program stored in a non- transitory computer-readable medium that is in or is accessible to the processing circuitry. Here, “non-transitory” does not necessarily mean permanent or unchanging storage, and may include storage in working or volatile memory, but the term does connote storage of at least some persistence. The execution of the program instructions specially adapts or configures the processing circuitry to carry out the operations disclosed in this disclosure relating to the network node. Further, it will beappreciated that the network node 400 may comprise additional components. Thenetwork node 400 may also be viewed as a Transmitter and Receiver Point (TRP). The network node 400 by means of processor 410 executes instructions contained in the memory 420 whereby the network node 400 is operative to perform any one of the previously described embodiments related to the actions performed by the networknode, some of which are presented in appended claim 14. There is also provided a computer program comprising instructions which when executed by the processor 410 of the network node cause the processor 410 to carry out the method according to claim 14.Several advantages of the described embodiments in this disclosure are achieved aspreviously described and which include significantly reducing the feedback overhead and the computational complexity at the wireless device for codebook-based CSI reporting. Another advantage is to reduce latency in the CSI reporting. Reference throughout this specification to “an example” or “exemplary” means that a particular feature, structure, or characteristic described in connection with the example is included in at least one embodiment of the present technology. Thus, appearances of the phrases “in an example” or the word “exemplary” in various places throughout this specification are not necessarily all referring to the same embodiment. Throughout this disclosure, the word "comprise" or “comprising” has been used in a non-limiting sense, i.e. meaning "consist at least of". Although specific terms may be employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation. The embodiments herein may be applied in any wireless systems including LTE or 4G, LTE-A (or LTE-Advanced), 5G, advanced 5G, WiMAX, WiFi, satellite communications, TV broadcasting etc.

Claims

CLAIMS1. A method performed by a wireless device (300) in a wireless communicationsnetwork, the method comprising: -receiving (501) configuration information associated with a channel stateinformation, CSI, report, wherein the configuration information indicates anumber of antenna ports, ^^, in a first dimension, and a number of antennaports, ^^, in a second dimension, -determining (502) based on the configuration information a precoding vector,comprising a plurality of scaling coefficients, for 2^^^^ antenna ports, whereineach entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or aphase value, or an amplitude and phase value,- generating (503) a CSI report comprising a Precoder Matrix Indicator, PMI,indicating the precoder vector, and -reporting (504) to a network node (400) the CSI report.

2. The method of claim 1, wherein the precoding vector comprises ^ DFT-basedvectors.

3. The method of claim 2, wherein the precoding vector comprises ^ real- or complex-valued scaling coefficients.

4. The method of claim 3, wherein, the number of scaling coefficients, ^, is greaterthan the number of DFT-based vectors, ^.

5. The method of claim 1, wherein each scaling coefficient is associated with anantenna port subset, wherein the antenna port subset is a subset of the 2^^^^antenna ports.

6. The method of claims 1-5, wherein the method further comprising at least one ofthe following: indicating an index of the scaling coefficient associated with unitamplitude value and zero phase value, or indicating an index of the antenna portsubset associated with the scaling coefficient having unit amplitude value and zero phase value in the CSI report.

7. The method of claim 3, wherein the scaling coefficients ^ are segmented in1< ^^ < ^, amplitude subsets, and wherein the amplitude values of ^′ scalingcoefficients in an amplitude subset are identical.

8. The method of claim 1, wherein the PMI indicates a rank ^ precoding matrixcomprising ^ precoding vectors for ^ transmission layers.

9. The method of claim 3 and claim 8, wherein the number of scaling coefficients, ^,are dependent on the rank ^ of the precoding matrix.

10. The method of claim 8, wherein for the rank ^ precoding matrix, the method furthercomprising: selecting a first vector for a first transmission layer subset comprising^’ transmission layers of the precoding matrix, wherein ^’ < ^, and selecting asecond vector for a second transmission layer subset comprising ^’’ transmissionlayers of the precoding matrix, wherein ^’′ < ^ and ^’ + ^′^ = ^.11.The method of claim 1, wherein a plurality of precoding vectors is determined for^^ subbands, and wherein the ^^ subbands are grouped into N subband groups,wherein a subband group is a subset of the ^^ subbands, and wherein a precodingvector for a subband group is indicated in the CSI report.12.The method of claim 11, wherein for the rank ^ precoding matrix, the method furthercomprising: segmenting the ^ transmission layers into two transmission layersubsets, wherein a first transmission layer subset comprises ^′ transmission layersand a second transmission layer subset comprises the remaining ^ − ^’transmission layers, and wherein a number of subband groups for the firsttransmission layer subset is ^(^), and a number of subband groups for the secondtransmission layer subset is ^(^), wherein13.The method of claim 11, wherein the method further comprising: selecting a firstprecoding vector for a first subband from a codebook comprising a number of vectors or indices indicating the vectors, and selecting a second precoding vectorfor a second subband from a restricted codebook, wherein a size of the restrictedcodebook is smaller than a size of the codebook.14.A method performed by a network node (400), for receiving, from a wireless device(300), a channel state information, CSI, report in a wireless communicationsnetwork, the method comprising: ^transmitting (601) to a wireless device (300), configuration informationassociated with a channel state information, CSI, report, wherein theconfiguration information indicates a number of antenna ports, ^^, in a firstdimension, and a number of antenna ports, ^^, in a second dimension, for enabling the wireless device (300) to: odetermine based on the configuration information a precoding vectorcomprising a plurality of scaling coefficients for 2^^^^antenna ports, wherein each entry of the precoding vector is associated with an antenna port and each scaling coefficient is associated with one or more entries of the precoding vector, and wherein a scaling coefficient is based on an amplitude value, or a phase value, or an amplitude andphase value, ogenerate a CSI report comprising a Precoder Matrix Indicator, PMI,indicating the precoder vector, and ^receiving (602), from the wireless device (300) an uplink control information,UCI, including the CSI report over an uplink, UL, channel.15.A network node (400) comprising a processor (410) and a memory (420) containinginstructions executable by said processor (410), whereby the network node (400) is operative to perform the method according to claim 14.16.The network node (400) of claim 15, wherein the network node (400) is a gNB.A wireless device (300) comprising a processor (310) and a memory (320)containing instructions executable by said processor (310), whereby the wirelessdevice (300) is operative to perform the method according to any of claims 1-13.The wireless device (300) of claim 17, wherein the wireless device (300) is a User Equipment, UE.

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