TECHNICAL FIELD

The present disclosure relates to channel state information (CSI) for a transmission channel between a transmitter (Tx) and receiver (Rx). The disclosure presents a device and a method for generating compressed CSI. Further, the disclosure provides a device and a method for reconstructing CSI from compressed CSI. The compressed CSI may be fed back over the transmission channel with a reduced overhead compared to feeding back the CSI.

BACKGROUND

CSI feedback or reporting, for example, in wireless/mobile multiple input multiple output (MIMO) communications systems, is a very important topic, as it provides channel knowledge from the receiver to the transmitter. This knowledge allows the transmitter to make more accurate decisions, for example, for beamforming transmission and scheduling. CSI is a key issue in feedback based systems (for instance, in frequency division duplex (FDD) and Cloud-RAN architectures), in which for a certain circumstance the processing/transmitting unit (transmitter), for instance, a base station (BS) or a centralized cloud server, cannot measure by itself the channel, and thus requires a CSI feedback report from another intermediate unit, for instance, a radio head unit (RRH), or from a final end/receiving unit (receiver), for example, a user equipment (UE), that has access to such channel measurement information. For instance, in the FDD case, feedback is necessary because the system uses, respectively, Downlink (DL) and Uplink (UL) bands with a certain frequency gap. Due to this, channel reciprocity cannot be directly assumed, as it typically happens in time division duplex (TDD) systems. Notably, as an UL feedback channel has limited capacity, the CSI report must be small enough to avoid a depletion of resources, if multiple UE intend to send simultaneously CSI updates.

A communication channel in a MIMO system, with multiple antennas at the transmitter side and the receiver side and defined for a certain portion of the spectrum, can be modelled by a tensor matrix H of complex channel coefficients that represent channel path attenuations and phases shift of the different antenna Tx-Rx paths. More broadly speaking, a channel/beamforming tensor H may be composed of channel coefficients for N Tx antennas, F frequency sub-bands, and M layers (as shown as an example in Fig. la). The M layers can represent either, in a channel representation, measurements associated to each antenna at the receiver side (i.e., M receiver antennas or antenna ports of the receiver), or if having a beamforming precoding matrix, M may also represent a certain number of spatial streams or transmission layers with a respective spectral efficiency associated to number of layers given by M (i.e., M transmission layers).

Mechanisms to transmit CSI information in a feedback based system have been extensively studied in the past years, and are also the focus of constant study inside standardization bodies like the 3 ^rd generation partnership project (3GPP). The vision of industry and academy has always been to find a representation of each of the M layers, which requires only a reduced bit overhead, for example, by exploiting alternatives ways of channel description based on ideas like the quite well known space beam Fourier based decomposition and other directions like time delay representation for frequency domain compression (see Fig. lb).

However, little attention has yet been given to: (1) the way how to report a channel with a plurality of M antenna layers (also referred to as high rank representation) in a single and compact set of channel coefficients; and (2) a way to reduce the CSI radio resources for pilot mapping, which would provide scalability for a higher number of antenna ports (see Fig. lc).

These two issues are of significant importance, because in a not very long term future, the UE might support a very high rank transmission (up to rank 8) and the MIMO BS arrays are constantly evolving, ever requiring a larger number of antenna ports (32, 64, 128Tx and beyond). It would require a larger number of mapped resources for CSI-RS pilots for cell specific implementations, or even worse in UE specific cases, in which each user requires its own independent CSI-RS pilots set. Such mapped radio resources are precious for data transmission, and the amount of overhead related to reference signals in the physical downlink shared channel (PDSCH) should be reduced as much as possible. SUMMARY

Accordingly, it is a general goal of this disclosure to reduce the amount of overhead in CSI reporting. The solutions presented in this disclosure are, however, based also on the following considerations made by the inventors.

Considering the progress of CSI techniques for the case of FDD in standardization, a rapid development could be observed in the last 5 years with the advent of the 5G New Radio. Initially the Release 15 Type II codebook was proposed, wherein this codebook consists of a selection of L _s = 4 wideband beams, which are common for both polarizations of an antenna array. Then, for each subband, amplitude and phase shift of the 2 Ls projections (Ls beams, assuming an array with 2 polarizations) on each of these L _s beams for the F selected subband precoders are obtained. The main issue of the Release 15 Type II is a very significant overhead per layer (~ 350-400 bits). For this reason it was decided to limit the Release 15 Type II to only a rank 2 transmission (~800 bits for 2 layers).

Later on, Release 16 Enhanced Type II included the frequency compression by additionally including a codebook, in order to obtain frequency-to-time delay response. Thus, for each of the 2L _S projections for space, it may be considered that for frequency-to-time delay there are M _v taps associated. This frequency compression reduced the bit overhead per layer to a figure slightly between 250-300 bits, and transmission up to rank 4 was enabled (~4 x 250 = 1000 bits). Despite the fact that Release 16 Enhanced Type II allows having L _s =6 beams for rank 1 , in a multirank case it is possible only to keep L _s =4. This restriction limits the performance of the FDD network system.

Currently, Release 17 is being discussed, the strongest proposal at this moment being based on the assumption that long term spatial channel characteristics can be obtained from UL sounding, what is called UL-DL reciprocity. This idea has many advantages, as it may provide a very compact and precise CSI report with less than 300 bits per layer, while complexity for calculating the CSI in the UE is reduced. In contrast, the computational complexity is transferred to the BS, which needs to derive the spatial-frequency basis that is used for precoding the CSI-RS pilots, which are UE specific. Moreover, the fact that the CSI-RS pilots are actually UE specific, brings another issue. As each user requires its own CSI-RS pilot signals set, this poses a problem due to the significant radio resource overhead necessary for that scheme.

Moreover, the current paradigm of CSI reporting in 3GPP schemes requires one report slice for each of the M layers. This might become an issue, if each of the layers is constantly updated in a short term window requiring M times fold bit overhead with respect to a single transmission layer. Exemplary schemes consider a common spatial basis or a fixed grid of beams for all layers. By such a scheme, however, the flexibility of the CSI representation may be reduced, which would give as a result losses of system performance.

In view of this, an objective of the present disclosure is to provide a way to compress CSI (specifically to compress multirank or multilayered CSI). This would achieve the general goal of this disclosure to reduce the amount of overhead in CSI reporting. However, the flexibility of the CSI representation should not be reduced, in order to avoid losses of system performance.

These and other objectives are achieved by the solutions of this disclosure as described in the enclosed independent claims. Advantageous implementations are further defined in the dependent claims.

A first aspect of this disclosure provides a device for generating compressed CSI based on C pilots transmitted over a channel between a transmitter and a receiver, the device being configured to: obtain a 3D channel tensor for the channel, the 3D channel tensor having C x F x M channel coefficients for the C pilots, F frequency subbands, and M transmission layers or M receiving antenna ports of the receiver; calculate a 2D channel matrix based on the 3D channel tensor, the 2D channel matrix having K x T channel coefficients for K spatial beam directions and T time delay taps, wherein the channel coefficients for the K spatial beam directions are calculated by jointly performing a spatial transformation based on the channel coefficients for the C pilots for all the M transmission layers or M receiving antenna ports, and/or the channel coefficients for the T time delay taps are calculated by jointly performing a frequency-to-time transformation based on the channel coefficients for the F frequency subbands for all the M transmission layers or M receiving antenna ports; and generate the compressed CSI based on the K x T channel coefficients of the 2D channel matrix. The compressed CSI is generated by the device of the first aspect based on K x T channel coefficients, while the 3D channel tensor for the channel - based on which CSI would be generated - has C x F x M channel coefficients. Accordingly, the amount of channel coefficients is reduced in the compressed CSI, and thus the amount of overhead in CSI reporting can be reduced. Thereby, the representation of the CSI by the K x T channel coefficients accurately represents the channel, and thus avoids losses of system performance.

Notably, M being the number of transmission layers may be applicable, if speaking of an eigenvector precoder weights CSI, and a number of layers M may be selected. This is called a rank based CSI. M being the number of receiver antennas may be applicable, when the channel coefficients are purely obtained directly from measurement, and no eigenvectors are obtained as an intermediate step, and when there is further a fixed number of M receiving antennas. This is called an antenna based CSI.

In an implementation form of the first aspect, the frequency-to-time transformation comprises a discrete Fourier transformation (DFT), or a fast Fourier transformation (FFT).

In an implementation form of the first aspect, the transmitter comprises N transmitting antenna ports, and wherein C = N.

The disclosure thus provides a solution for the case, when the number of transmitter pilots equals the number of transmitter antennas, which may be considered a normal case. The following implementations lead to an efficient and accurate calculation of the compressed CSI and the channel coefficients, on which it is based.

In an implementation form of the first aspect, the 3D channel tensor has N x F x M channel coefficients for the N transmitting antenna ports, the F frequency subbands, and the M transmission layers or M receiving antenna ports.

In an implementation form of the first aspect, the frequency-to-time transformation is performed before the spatial transformation, and the device is configured to calculate the channel coefficients for the T time delay taps by: obtaining M matrices based on the 3D channel tensor, each of the M matrices having N x F channel coefficients; performing the frequency-to-time transformation on the channel coefficients of each of the M matrices; and selecting T common time delay taps from the M frequency-to-time transformed matrices.

In an implementation form of the first aspect, the spatial transformation is performed before the frequency-to-time transformation, and the device is configured to calculate the channel coefficients for the T time delay taps by: performing the frequency-to-time transformation on a 2D matrix with K x F channel coefficients obtained after spatial transformation from N transmitting antenna ports to K spatial components, in order to obtain a resulting 2D matrix having K x T channel coefficients.

In an implementation form of the first aspect, the device is configured to calculate the channel coefficients for the K. spatial beam directions for each of the T delay taps if the frequency-to-time transformation is performed before the spatial transformation or for each of the F frequency subbands if the frequency-to-time transformation is performed after the spatial transformation, by: obtaining the spatial vector basis, each of the K vectors including the most significant spatial components from the N transmitting antenna ports and the M transmission layers or M receiving antenna ports, wherein the spatial vector basis corresponds to an extended 2D matrix having K x N*M spatial vector basis coefficients; if the frequency-to-time transformation is performed before the spatial transformation, multiplying the spatial vector basis by M matrices having N x T channel coefficients in their concatenated 2D form N*M x T, in order to obtain a resulting 2D matrix with K x T channel coefficients; and if the spatial transformation is performed before the frequency-to-time transformation, multiplying the spatial vector basis by M matrices having N x F channel coefficients in their concatenated 2D form N*M x F, in order to obtain the resulting 2D matrix with K x F channel coefficients.

In an implementation form of the first aspect, the spatial transformation comprises at least one of: a principal component analysis (PCA) based transformation, for instance a Singular Value Decomposition (SVD) or an Eigenvalue Decomposition (EVD); a DFT based transformation; a FFT based transformation. In an implementation form of the first aspect, the transmitter comprises N transmitting antenna ports, and wherein C < N.

The disclosure thus provides a solution for the case, when the number of transmitter pilots is less than the number of transmitter antennas, which may be beneficial in case there is a very large number of transmitter antennas and/or the receiver can handle a limited number of pilot signals. The following implementations lead to an efficient and accurate calculation of the compressed CSI and the channel coefficients, on which it is based.

In an implementation form of the first aspect, the spatial transformation comprises a compressive sensing algorithm, for instance, an orthogonal match pursuit (OMP) algorithm, in order to find the K most significant spatial vector components associated to the N transmitting antenna ports of the transmitter from the coefficients of the C pilots.

In an implementation form of the first aspect, the frequency-to-time transformation is performed after the spatial transformation, and the device is configured to calculate the channel coefficients for the K spatial beam directions for each of the selected T time delay taps by: constructing a concatenated 2D matrix having C*F x M channel coefficients; performing the spatial transformation on the channel coefficients of the concatenated 2D matrix to obtain a reduced 2D matrix having K x F*M channel coefficients; performing the frequency-to-time transformation on the channel coefficients of the reduced 2D matrix; and selecting the T time delay taps from the frequency-to-time transformed reduced 2D matrix to obtain K x T channel coefficients.

In an implementation form of the first aspect, the frequency-to-time transformation is performed before the spatial transformation, and the device is configured to calculate the channel coefficients for the K spatial beam directions for each of the selected T time delay taps by: constructing a concatenated 2D matrix having C*M x F channel coefficients; and performing the frequency-to-time transformation on the channel coefficients of the concatenated 2D matrix to obtain a reduced 2D matrix having C*M x T channel coefficients after selecting the T time delay taps from the frequency-to-time transformed reduced 2D matrix; and performing the spatial transformation on the channel coefficients of the reduced 2D matrix to obtain K x T channel coefficients. In an implementation form of the first aspect, the device is further configured to: determine L channel coefficients from the K x T channel coefficients of the 2D channel matrix; quantize each of the L channel coefficients; index the L quantized channel coefficients; and generate the compressed CSI using the L quantized and indexed channel coefficients.

A second aspect of this disclosure provides a device for reconstructing CSI from compressed CSI, the CSI being related to a channel between a transmitter and a receiver, and the device being configured to: calculate a 2D channel matrix based on the compressed CSI, the 2D channel matrix having K x T channel coefficients for K spatial beam directions and T time delay taps; calculate a 3D channel tensor for the channel based on the 2D channel matrix, the 3D channel tensor having N x F x M channel coefficients for N transmitting antenna ports of the transmitter, F frequency subbands, and M transmission layers or M receiving antenna ports of the receiver; wherein the channel coefficients for the N transmitting antenna ports and the M transmission layers or M receiving antenna ports are calculated by performing an inverse spatial transformation based on K spatial beam direction vector components, and/or the channel coefficients for the F frequency subbands are calculated by performing a time-to-frequency transformation based on basis vector components selected for the T time delay taps common for the M transmission layers or M receiving antenna ports; and determine the CSI based on the 3D channel tensor.

The device of the second aspect, enables a decompression of the compressed CSI (e.g., compressed by the device of the first aspect), and thus allows implementing the scheme with its advantages. That is, it supports the reduction of the overhead without substantially sacrificing accuracy.

In an implementation form of the second aspect, the device is configured to: obtain a number of L quantized and indexed channel coefficients from the compressed CSI; and dequantize and rearrange the L quantized and indexed channel coefficients to obtain the 2D channel matrix.

In an implementation form of the second aspect, the device is configured to calculate the 3D channel tensor by: multiplying the channel coefficients of the 2D channel matrix by corresponding K and T basis components of the respective spatial and frequency domains. In an implementation form of the second aspect, the transmitter comprises N transmitting antenna ports, wherein the time-to-frequency transformation comprises at least one of: an inverse discrete Fourier transformation (IDFT), and an inverse fast Fourier transformation (IFFT).

In an implementation form of the second aspect, the transmitter comprises N transmitting antenna ports, and wherein the inverse spatial transformation comprises at least one of: a PCA based inverse transformation, for instance, based on a SVD or an EVD; a DFT based inverse transformation; a FFT based inverse transformation.

A third aspect of this disclosure provides a method for generating compressed CSI based on C pilots transmitted over a channel between a transmitter and a receiver, the method comprising: obtaining a 3D channel tensor for the channel, the 3D channel tensor having C x F x M channel coefficients for the C pilots, F frequency subbands, and M transmission layers or M receiving antenna ports of the receiver; calculating a 2D channel matrix based on the 3D channel tensor, the 2D channel matrix having K x T channel coefficients for K spatial beam directions and T time delay taps, wherein the channel coefficients for the K spatial beam directions are calculated by jointly performing a spatial transformation based on the channel coefficients for the C pilots and for all the M transmission layers or M receiving antenna ports, and/or the channel coefficients for the T time delay taps are calculated by jointly performing a frequency-to-time transformation based on the channel coefficients for the F frequency subbands for all the M transmission layers or M receiving antenna ports; and generating the compressed CSI based on the K x T channel coefficients of the 2D channel matrix.

The method of the third aspect may be performed by the device of the first aspect. The method of the third aspect can have implementation forms according to the implementation forms of the device of the first aspect, i.e., each additional step that the device of the first aspect is configured to carry out may be an additional step of the method of the third aspect. Accordingly the method of the third aspect and its implementation forms provide the same advantages as the device of the first aspect and its respective implementation forms.

A fourth aspect of this disclosure provides a method for reconstructing CSI from compressed CSI, the CSI being related to a channel between a transmitter and a receiver, and the method comprising: calculating a 2D channel matrix based on the compressed CSI, the 2D channel matrix having K x T channel coefficients for K spatial beam directions and T time delay taps; calculating a 3D channel tensor for the channel based on the 2D channel matrix, the 3D channel tensor having N x F x M channel coefficients for N transmitting antenna ports of the transmitter, F frequency subbands, and M transmission layers or M receiving antenna ports of the receiver; wherein the channel coefficients for the N transmitting antenna ports and the M transmission layers or M receiving antenna ports are calculated by performing an inverse spatial transformation based on K spatial beam direction vector components, and/or the channel coefficients for the F frequency subbands are calculated by performing a time-to-frequency transformation based on basis vector components selected for the T time delay taps common for the M transmission layers or M receiving antenna ports; and determining the CSI based on the 3D channel tensor.

The method of the fourth aspect may be performed by the device of the second aspect. The method of the fourth aspect can have implementation forms according to the implementation forms of the device of the second aspect, i.e., each additional step that the device of the second aspect is configured to carry out may be an additional step of the method of the fourth aspect. Accordingly the method of the fourth aspect and its implementation forms provide the same advantages as the device of the second aspect and its respective implementation forms.

A fifth aspect of this disclosure provides a computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to the third aspect or the fourth aspect or any implementation form thereof.

It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

BRIEF DESCRIPTION OF DRAWINGS

The above described aspects and implementation forms will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

FIG. la shows an exemplary 3D channel tensor with channel coefficients for N Tx antennas, F frequency bands, and M Rx antennas or M transmission layers.

FIG. lb shows a generalization of a CSI concept, wherein each tensor component of the exemplary 3D channel tensor can be represented in a simpler and sparser form, if a different representation is used. For example, beam domain, timedelay domain, or combinations thereof may be used. The number of M layers can be either a set of measurements for each Rx antenna or a set of beamforming precoder (transmission) layers.

Fig. 1 c . shows a certain number of CSI-RS pilots that are required to enable channel measurements in the receiving unit (e.g., the UE). With the increase of the number of antenna ports, a larger number of CSI-RS pilots is typically required.

FIG. 2 shows an exchange of pilots and compressed CSI, respectively, over a channel between a transmitter and a receiver.

FIG. 3 shows a device for generating the compressed CSI according to an embodiment of this disclosure.

FIG. 4 shows a device for reconstructing CSI from the compressed CSI according to an embodiment of this disclosure.

FIG. 5 illustrates a conversion of the 3D channel tensor into a 2D channel matrix. FIG. 6a shows an embodiment, in which the number of pilots is equal to the number of antenna ports of the transmitter (C N).

FIG. 6b shows an embodiment, in which the number of pilots is less than the number of antenna ports of the transmitter (C < N).

FIG. 7a shows a typical FDD CSI feedback scheme.

FIG. 7b illustrates a CSI DL pilot reduction.

FIG. 8 shows an exemplary CSI scheme in FDD D-MIMO/Cloud RAN infrastructure, wherein: dotted arrow shows CSI flow from UE toward central servers; solid lines reference signal transmission toward UE; dashed connection represents limited capacity backhaul.

FIG. 9 shows an exemplary mm- wave transceiver having different RF -chains for DL/UL for specific multipath configuration (no channel reciprocity assumed).

FIG. 10 shows an embodiment for C = N, in particular, an example of a compression process of CSI based on a DFT based frequency-to-time delay transform and SVD/EVD based spatial transform implementation.

FIG. 11 shows an embodiment for C = N, in particular, an example of a decompression process of CSI based on a DFT based frequency-to-time delay transform and SVD/EVD based spatial transform implementation.

FIG. 12 shows an embodiment for C < N, in particular, a compression process of CSI using OMP with DFT dictionary spatial transform and DFT based frequency-to-time delay transform.

FIG. 13 shows an embodiment for C < N, in particular, an example of a detailed OMP loop and interaction with the other further steps. FIG. 14 shows an embodiment for C < N, in particular, an example of a reconstruction process of CSI, which can be used for channel recovery/acquisition or CSI decompression.

FIG. 15 shows a numerical example, in particular, of a calculation of a bit overhead for an embodiment of this disclosure (implementation SVD and DFT for spatial and frequency-to time transformations respectively). The case of a single slice update (embodiment) is compared to an approach in which each of the M layers require its own short term update.

FIG. 16 shows exemplary simulation parameters.

FIG. 17a shows compression performance of multilayer CSI using the example of an implementation with PCA spatial transform and FFT/DFT frequency-to- time delay channel tensor processing.

FIG. 17b shows compression performance of multilayer CSI using the example of OMP(2D-DFT) spatial transform and DFT based frequency-to-time delay transform channel tensor processing for C=8-12 CSI-RS pilots.

FIG. 18 shows a method for generating compressed CSI according to an embodiment of this disclosure.

FIG. 19 shows a method for reconstructing compressed CSI according to an embodiment of this disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 2 shows a scenario, according to which devices and methods according to this disclosure may be used. In particular, FIG. 2 shows a transmitter 201 (e.g., a single BS or a set of transmit and receive points (TRP) working jointly as single transmitter) and a receiver 202 (e.g., a UE), and a channel 204 between the transmitter 201 and the receiver 202. The channel 204 may be a wireless channel, e.g., the transmitter 201 and receiver 202 may be in a wireless and/or mobile network. Further, FIG. 2 shows that C pilots 205 (wherein C > 1) are transmitted over the channel 204 from the transmitter 201 to the receiver 202. In response, the receiver 202 may transmit CSI (in this disclosure compressed CSI 203) over the channel 204 to the transmitter 201. In the following will be shown, how the compressed CSI 203 is generated at the side of the receiver 202, and how it can be reconstructed at the side of the transmitter 201 .

FIG. 3 shows a device 300 according an embodiment of this disclosure. The device 300 is configured to generate the compressed CSI 203 based on the C pilots 205 shown in FIG. 1 and FIG. 2. The device 300 may be located at the side of the receiver 202. For example, it may be implemented in the receiver 202. The device 300 may, however, be only in communication with the receiver 202.

The device 300 is configured to obtain a 3D channel tensor 301 for the channel 204. For instance, the device 300 may obtain this 3D channel tensor 301 from the receiver 202, or it may generate the 3D channel tensor 301 based on information obtained from at least one of the transmitter 201 and the receiver 202. The 3D channel tensor 301 has C x F x M channel coefficients, which are for the C pilots 205, for F > 1 frequency subbands, and for M > 1 transmission layers or M receiving antenna ports of the receiver 202. That is, there is one channel coefficient per pilot, per frequency subband and per transmission layer or receiving antenna port. The 3D channel tensor 301 may be as shown in FIG. 1.

Further, the device 300 is configured to calculate a 2D channel matrix 302 based on the 3D channel tensor 301. The 2D channel matrix 302 has K x T channel coefficients, which are for K > 1 spatial beam directions and T > 1 time delay taps. That is, there is one channel coefficient per spatial beam direction and per time delay tap in the 2D channel matrix. Thereby, the channel coefficients for the K spatial beam directions are calculated by the device 300 by jointly performing a spatial transformation based on the channel coefficients for the C pilots 205 for all the M transmission layers or M receiving antenna ports. In addition or alternatively, the channel coefficients for the T time delay taps are calculated by the device 300 by jointly performing a frequency-to-time transformation based on the channel coefficients for the F frequency subbands for all the M transmission layers or M receiving antenna ports. For this, the frequency-to-time transformation may comprise a DFT or a FFT. The spatial transformation may comprises at least one of a PCA based transformation, for instance a SVD or an EVD, a DFT based transformation, and a FFT based transformation. The spatial transformation may also comprise a compressive sensing algorithm, for instance, an OMP algorithm. How the 2D channel matrix may specifically be obtained from the 3D channel tensor is shown further below (and is also described in the summary part with respect to the implementation forms of the first aspect).

The device 300 is further configured to generate the compressed CSI 203 based on the K x T channel coefficients of the 2D channel matrix 302. For example, the device 300 may determine L > 1 channel coefficients from the K x T channel coefficients of the 2D channel matrix. Then, the device 300 may quantize each of the L channel coefficients. Then, the device 300 may index the L quantized channel coefficients. Then, the device 300 may generate the compressed CSI 203 using the L quantized and indexed channel coefficients. Then, the device 300 may be configured to output the compressed CSI 203 (e.g., to the receiver 202) or transmit the compressed CSI 203 over the channel 204 to the transmitter 201, as indicated by the dashed arrow in FIG. 3.

FIG. 4 shows a device 400 for reconstructing CSI 403, which is related to the channel 204, from the compressed CSI 203. The device 400 may be located at the side of the transmitter 201. For example, the device 400 may be implemented in the transmitter 201. The device 400 may, however, be only in communication with the transmitter 201.

The device 400 is configured to calculate a 2D channel matrix 401 based on the compressed CSI 203. The 2D channel matrix 401 has K x T channel coefficients, which are for K > 1 spatial beam directions and T > 1 time delay taps. That is, there is one channel coefficient per spatial beam direction and per time delay tap.

Further, the device 400 is configured to calculate a 3D channel tensor 402 for the channel 204 based on the 2D channel matrix 401. For example, the device 400 may be configured to obtain a number of L > 1 quantized and indexed channel coefficients from the compressed CSI 203, and to de-quantize and rearrange the L quantized and indexed channel coefficients to obtain the 2D channel matrix 401. The 3D channel tensor has N x F x M channel coefficients for the N transmitting antennas of the transmitter 201, F > 1 frequency subbands, and M > 1 transmission layers or M receiving antenna ports of the receiver 202. That is, there is one channel coefficient per antenna, per frequency subband, and per transmission layer or receiving antenna port.

The channel coefficients for the N transmitting antenna ports and the M transmission layers or the M receiving antenna ports are calculated by the device 400 by performing an inverse spatial transformation based on K spatial beam direction vector components. In addition or alternatively, the channel coefficients for the F frequency subbands are calculated by the device 400 by performing a time-to-frequency transformation based on basis vector components selected for the T time delay taps common for the M transmission layers or M receiving antenna ports. The time-to-frequency transformation may comprise at least one of an IDFT and an IFFT. The inverse spatial transformation may comprise at least one of a PC A based inverse transformation, for instance, based on a SVD or an EVD; a DFT based inverse transformation; a FFT based inverse transformation.

Then, the device 400 is configured to determine the CSI 403 based on the 3D channel tensor 402, and may be configured to output the CSI 403 (e.g., to the transmitter 201) as indicated by the dashed arrow in FIG. 4.

Notably, the device 300 and the device 400 (for instance, included in receiver 202 and the transmitter 201, respectively) may form a system. The system is able to perform CSI feedback based on pilots sent from transmitter 201 to receiver 202, wherein a compressed CSI 203 is fed back from the receiver 202 to the transmitter 201. Accordingly, the device 300 and device 400 may together perform a compressed CSI feedback method, which includes sending the C pilots 205 over the channel 204 from transmitter 201 to receiver 202, and then sending in return the compressed CSI 203 from the receiver 202 to the transmitter 201 over the channel 204. This has reduced overhead compared to a conventional CSI feedback method.

The device 300 and/or the device 400 may comprise a processor or processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the respective device 300, 400 described herein. The processing circuitry may comprise hardware and/or the processing circuitry may be controlled by software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multipurpose processors. The device 300 and/or the device 400 may further comprise memory circuitry, which stores one or more instruction(s) that can be executed by the processor or by the processing circuitry, in particular under control of the software. For instance, the memory circuitry may comprise a non-transitory storage medium storing executable software code which, when executed by the processor or the processing circuitry, causes the various operations of the respective device 300, 400 to be performed. In one embodiment, the processing circuitry comprises one or more processors and a non- transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the respective device 300, 400 to perform, conduct or initiate the operations or methods described herein.

The blocks shown inside the device 300 of FIG. 3 are optional, and may include processing circuitry configured to, respectively, calculate the 2D channel matrix 302, generate the compressed CSI 203, and output or transmit the compressed CSI 203.

The blocks shown inside the device 400 of FIG. 4 are optional, and may include processing circuitry configured to, respectively, calculate the 2D channel matrix 401, calculate the 3D channel tensor 402, and determine and optionally output the CSI 403.

The device 300 is particularly configured to compress a multirank or multi-layered CSI, e.g. including the multirank 3D channel tensor 301 (including channel coefficients for M transmission layers or M receiving antennas). The channel tensor 301 may in total be composed of channel coefficients for C pilots 205, F frequency sub-bands, and M layers (either corresponding to the receiving antennas or spatial transmission layers). If M > 1 , the 3D channel tensor 301, and the CSI that it would lead to, are of multirank. According to this disclosure, it is possible to represent this 3D channel tensor 301 in a reduced single slice composed of channel coefficients for K spatial beam directions and T time delays, i.e., by the 2D channel matrix 302. Thus, the compressed CSI 203 can be generated based on the 2D channel matrix 302. The compressed CSI 203 greatly reduces the amount of information that needs to be transmitted from the receiver 202 to the transmitter 201 over the channel 204 (see FIG. 2). The compressed CSI 203 can, in particular, be generated by obtaining a set of channel coefficients based on two basis for space and time-delay respectively, wherein these two basis can describe full characteristics for a plurality of M layers (transmission layers or receiver antenna ports) simultaneously. For doing this, one of the basis of the 3D channel tensor 301 may be extended, in order to be able to project all M layers. In the example shown in FIG. 5 (which illustrates the 3D channel tensor 301 being transformed into the 2D channel matrix 302 by such a basis extension), there is a spatial basis with K selected components of size N x M, which contains all spatial long-term information related to each of the M transmission layers or receiving antenna ports. Regarding to frequency, a number of common selected T time delay taps can be selected, in order to create a set of K x T projection channel coefficients, which may form the 2D channel matrix 302.

This compression approach of the present disclosure provides advantages over the conventional techniques for reporting CSI, the advantages being summarized in the below table. This disclosure considers the CSI compression regarding two cases. First, a standard case when the number N of antenna ports of the MIMO array (transmitter) is equal to the number C of CSI-RS pilots 205 (C = N). Second, a case in which the number C of CSI-RS pilots 205 is smaller than N (C < N). The described solutions of this disclosure are also based on the following considerations.

MIMO channel properties usually obey to a certain structure, in which a correlation in space, frequency and time can be found for 2D channel slices with N transmitter antenna ports and F frequency subbands. Most research by industry and academy is done on studying these properties at the 2D level, while forgetting that a real channel - or its derived beamforming precoding tensor - is composed of a set of multiple layers (receiver antennas or transmission layers). When considering that the 3D channel tensor 301 has M layers, it turns out to be possible to find a way to represent this 3D channel tensor 301 by means of a joint space-frequency common support, if one the basis is extended (either in space or frequency) to represent the M layers. That is, the 3D channel tensor 301 can be represented by the 2D channel matrix 302.

Just as conceptual reminder, the mathematical relationship between a channel slice Hr - with Mfuii Rx antennas and N Tx antennas at a certain frequency subband f from the set of F frequency subbands, and its ideal beamforming matrix Vf with N Tx antennas and Mop, layers (with M _op t < Mfuii), is given by the relationship Hf=U fVf*, obtained from a SVD. It is well known that the effective channel obtained from the product Hr, _e ff = HfVrmay yield the optimal capacity, as energy is specifically beamformed toward the user with an optimal number of layers. If H is a tensor with full size M/ _a // Rx antennas, N Tx antennas, and F frequency subbands, and if its associated beamforming tensor V consists of N Tx antennas, Mop/ layers, and F frequency subbands, then both tensors can have correlation characteristics between the layers, and thus a single common support can be found if the tensor is studied, and if it is imaginarily reshaped as a long 2D Matrix with one of the dimensions - either space or frequency - being extended by the total number of layers, i.e. M (Mop or Mfaii respectively). In that case, a single set of K spatial projections with T delay taps can be obtained (2D matrix 302) in order to represent the full tensor structure (3D channel tensor 301).

FIG. 6a shows schematically an example implementation for the case C = N. In this case, the spatial transformation may be performed, by the device 300, by obtaining the projections on a spatial basis (e.g., dictionary-aided or not), in order to select the main K spatial components. Each component contains N x M coefficients. The following variants of the spatial transformation, and the way to obtain each of these K components, may be a DFT/FFT and/or PC A implemented either with SVD/EVD. However other spatial transformations may also be considered.

FIG. 6b shows schematically another example implementation for the case C < N. In this case, the spatial transformation may be performed, by the device 300, by obtaining the projections in a dictionary, in order to select the main K spatial components. Each dictionary codeword may have a size of N. Further, a compressive sensing related algorithm may be performed, for example an OMP based algorithm, to obtain the common sparse support from a limited set of measurements C. This enables to reconstruct the space domain to components of size N.

Notably, in both example implementations, frequency-to-time delay taps can be easily obtained by using a discrete Fourier Matrix (DFT) or FFT. Nonetheless, any other type of frequency-to-time transformation can be considered.

In the following, some specific application embodiments are now described. In particular, CSI feedback reporting is required in a large variety of scenarios. The most popular scenario is the classic FDD case, in which due to the lack of direct reciprocity between the DL and the UL channels, a CSI feedback mechanism is required. In that case, a set of pilots, particularly CSI reference signal pilots, are sent by the BS (transmitter 201) to the UE (receiver(s) 202). Each UE senses and estimates the channel, and at the end a CSI feedback is reported back to the BS (see schematically FIG. 7a).

It has a great importance for future network transmission schemes to consider also cases, in which the BS-UE transmission requires high-rank transmissions, particularly, much beyond the typical single rank case. In a not so remote future, a receiver 202 i.e., a UE may be equipped with more than 4 receiver antennas, maybe with 8 antennas or more, and thus a very high rank may become reality. In the same way, the increase of the number of antenna ports at the transmitter 201, in particular, from cases like 32T or 64T to cases with many tens or hundreds of antenna ports, is also a possibility. This means that the CSI-RS overhead cannot be neglected. For that reason, it is sensible to propose CSI schemes not only for C = N (wherein the number of C pilots the same as number of N transmitter antenna ports) but also for C < N. This may also be sensible for some UE manufacturers that desire to keep their channel estimation implementation simple enough for a reduced number of pilot signals (see schematically illustrated in FIG. 7b).

Moreover, FDD CSI is not the only case where a CSI feedback is needed in a wireless network system. Another typical case is the D-MIMO/ Cloud RAN scenario, in which: (1) backhaul CSI compression is required to transmit CSI to a central processing server (both for FDD and TDD schemes); and (2) the CSI associated to a number of distributed antenna panels or radio head units with a different number of antennas is collected via radio from the feedback of UEs deployed in the mobile network (only FDD, see, for instance, illustrated in FIG. 8). This type of architecture has actually become a very important topic for Cooperative Multipoint Joint Transmission (COMP-JT), which is to be studied also for standardization.

Last but not least, mm-waves are also of great interest for current and future wireless communication scenarios. The issue of CSI for mm-wave equipment can occur not only for FDD but also for TDD. This is due to the fact that a mm-wave phased array can be composed by independent RF chains and/or antenna panels for DL or UL. This is, because an independent UL/DL gives more flexible Tx/Rx configuration to support different multipath characteristics in each direction, however, it clearly compromises channel reciprocity (see exemplary in FIG. 9).

In the first case of this disclosure, the number of pilots C is equal to the number of transmitter antenna ports N. An exemplary implementation is now described for this case. In a first step, a 3D channel/beamforming tensor 301 with a size of N transmitting antenna ports, F frequency bands, and M transmission layers or receiving antenna ports (including a channel coefficient per antenna port, frequency band and layer) is about to be processed. In this implementation, a PCA may be used as the spatial transformation, while for the time delay tap selection a DFT/FFT can be considered. Arbitrarily, the frequency-to time delay transformation can be done first, and then then spatial transformation. Nonetheless these two transformations could be performed in different order.

Compression stage in this implementation: reference is made to FIG. 10. The compression stage may be performed by the device 300. Step I: Reshape the 3D channel tensor 301, and separate M channel slices (M matrices 1000) each with size N x F. That is, obtain the M matrices 1000 based on the 3D channel tensor 301, each of the M matrices having N x F channel coefficients.

Step 2: Performing the frequency-to-time transformation on the channel coefficients of each of the M matrices 1000. For example, for each of the channel layers, perform a Fourier transform (either DFT or FFT) for each of the N rows of each matrix/slice 1000 with size N x F. After the Fourier processing, a representation of time delay taps may be obtained for each antenna port. For example, a common set of T delay taps may be selected in all of the M layers, which concentrate most of the signal energy (common support calculation). That is, T common time delay taps may be selected from the M frequency-to-time transformed matrices 1001. The new M channel slices will become of size N x T, with T < F. The index of each tap may be saved with respect to the total length of the DFT/FFT operation.

Step 3: Create an extended 2D matrix, which comprises the set of M transformed matrices with size N x T each (from step 2), and calculate the auto-correlation matrix. Apply a SVD/EVD operation on such resulting auto-correlation matrix. From that, obtain a resulting spatial vector basis with (N*M) x (N*M). Select the first K principal components to derive a (truncated) spatial vector basis with size (N*M) x K. Obtain the projections (with Hermitian product) of the 2D transformed matrix with size (N*M) x T on the obtained spatial vector basis with size (N*M) x K. As a result, a resulting 2D matrix with size K x T is obtained, which corresponds to the short term feedback to all M layers. Long term information is contained in the spatial vector basis with size (N*M) x K.

Step 4: Optionally, further DFT/FFT Fourier processing (2D-DFT/ 2D-FFT if MIMO Array has Horizontal and Vertical dimensions) can be applied into the eigenvectors of the (N*M) x K long term basis, in order to obtain a sparse representation of eigenvectors and select only most significant amplitude coefficients in each vector. Regarding short term, it can be further reduced by selecting only some points of the K x T slice with significant amplitude values, but this is optional. All points can be taken, further assuming that K x T corresponds to a very few number of coefficients. In addition, each complex coefficient (amplitude and phase) is quantized and a way of indexing delay taps and spatial components is provided to place them back later during decompression. The way of indexing depends on specific implementation, it can be a single indicator, a duplet (row and column indexes associated to spatial beam and/or time delay dimensions) or a bitmap. Similarly for the long term SVD/EVD derived basis with K components, a mechanism of update may be implemented, however, the update of this information can be done in a more spread frame of time. In other implementations in which spatial basis is known by the two communication nodes associated to the CSI feedback process (e.g. User Equipment and Base Station), for example, with a DFT /2D-DFT dictionary or FFT/2D-FFT transform, there is no need to transfer the long term basis in contrast to the SVD/EVD case aforementioned described.

Decompression stage: reference is made to FIG. 11. The decompression stage is performed by the device 400.

In order to reconstruct the CSI from the compressed CSI 203, it is enough firstly to dequantize the coefficients and then, re-use the spatial basis (long term) with size (N*M) x K. and frequency basis (inverse transform to the respective frequency-to-time delay compression stage with length F), and multiply the K x T projected coefficients back on the respective indexed components of each basis (spatial and frequency basis). As a result, a reconstructed channel with dimensions N*M x F is obtained, which can be easily reshaped into a 3D tensor 402 with size N x F x M.

In the second case of this disclosure, the number of C pilots 205 is less than the number of the N transmitter antenna ports. An exemplary implementation is now described for this case. In a first step, a 3D channel/beamforming tensor 301 with size C CSI-RS precoded ports, F frequency bands, and M layers (M receiver antenna ports or M transmission layers) is about to be processed. For this implementation, one may assume that for the spatial transformation an OMP algorithm with a DFT dictionary for compressive sensing can be used. For the time delay tap selection, DFT/FFT can be considered. Arbitrarily, first the spatial transformation may be made and then the frequency-to-time transformation. Nonetheless these two transformations could be performed in any order.

In order to enable compressive sensing, the C pilots may be randomly precoded for each subband f in F, with a mapping matrix A'f, _p for each subband f and a polarization p of the transmitter antenna array (+/- 45 degrees polarizations typically). Also in this example, it may be considered that the two communication nodes - transmitter 201 and receiver 202 - associated to the CSI feedback process (e.g., UE and BS) have knowledge of a dictionary matrix D with £2 oversampled 2D-DFT components with size N/2 (half antenna array size corresponding to single polarization).

Channel acquisition with reduced pilots and compression stage: reference is made to Fig. 12. The compression stage may be performed by the device 300.

Step 1 : Reshape the 3D channel tensor 301, and separate the M channel slices/matrices with size C x F. Construct from a 2D matrix by concatenating the matrix to have as a result a matrix with size C*M x F.

Step 2: Obtain a common support with K channel coefficients by means of an OMP loop on all frequency subbands f in F and for each polarization p (the OMP loop will be explained in detail later). As result, a reduced 2D matrix with size K x F*M is obtained.

Step 3 : Effectuate a frequency-to-time delay transformation (with DFT or FFT) and select T time delay taps. The resulting matrix has a size of K x T channel coefficients, which corresponds a single slice CSI update.

Step 4: Similarly as in the first case of C = N, a short term CSI update can be further reduced by selecting only points of the K x T slice/matrix with significant amplitude values (as mentioned before, this is optional). Likewise, as in the previous example each complex coefficient (amplitude and phase) is quantized and a way of indexing delay taps and spatial components is provided to place them back during decompression and match with the corresponding space and frequency codewords of the codebooks/dictionaries for the respective inverse transforms. The way of indexing can be a single indicator, a duplet (row and column indexes associated to spatial beam and/or time delay dimensions) or a bitmap. Notably, in this case such an indexing would correspond to selected indexes in the spatial dictionary D and frequency-to-time delay DFT/FFT transform.

Regarding the OMP loop (see illustrated in FIG. 13), the procedure comprises sweeping all subbands f in F and each polarization p, in order to obtain the spatial common support (indexes from the dictionary) and associated projections (i.e., channel coefficients). In each iteration i, an index may be added to a set S, which contains the common support in space. In iteration zero, each signal set Yf (size C x M) is measured for each subband fin F, which initializes what is called a residual matrix Resf. Likewise, S is empty at the start (no indexes). In order to calculate the common support, the accumulated correlation in all subbands f in F and in each polarization p may be calculated with respect to what is called the sensing matrix d>. The sensing matrix corresponds to the product of the random pilot mapping matrix X and the spatial dictionary D, i.e. <Df, _p =Xf, _p *D for each subband f in F and polarization p. As can be seen, the relationship between Yr -measured signals with size C x M for each f in F, and hn, f- sparse representation of the channel/beamforming matrix with size 2 x M for each f in F is given by Yt= <Dr hn, r. Notice that dfr operates as a mapping interface between the measured signal and the sparse channel/beamforming matrix representation. Notice also that d>r is a block diagonal matrix with <I>f, _P for each polarization p. By accumulating the sum of the projected values of the residual matrix on the sensing matrix (by means of the norm of Hermitian product) and selecting the indexes with best accumulated resulting correlation, it is possible to find the hidden spatial components of D (vectors of size N/2) which approximate the channel/beamforming matrix to its full spatial representation with size N. In each iteration i, the selected sensing matrix components are progressively stacked for each subband f in F and polarization p. Then a least square solution may be used and the equation, hn,f,i= (<Df,i* fj) ¹ 4>f,i‘Yf is solved for each iteration i as the spatial component knowledge is gradually accumulated. Notice that at the end of each iteration, the matrix Resr is updated by removing the sparse spatial components already found from the signal Yf in the previous iterations. Resf converges to zero and it may stop at some iteration point. This iterative converging process can guarantee that such spatial components are removed from the loop, and significant but less dominant spatial components may successively be found. Last but not least, notice that the OMP loop is done for K/2 iterations. This is due to the fact that it may be assumed that the two polarizations share the same common support. At the end of the process, K channel coefficients for each of the F subbands and M layers may be obtained. After that, Step 3 and 4 of this implementation are performed.

Regarding the reconstruction or decompression, the principle (see FIG. 14) is very similar to what was already illustrated for the first case. As can be seen, in order to recover the full 3D channel/beamforming tensor 402 it may be considered to multiply the single slice update with size K x T by the respective set of vectors selected from the spatial and frequency basis. The spatial basis is composed of K Fourier vectors (DFT/2D-DFT) with size N/2 selected from D to create a block diagonal matrix (K/2 components for one polarization and another K/2 for the second one) with full size K x N. On the other hand, for the frequency domain, as mentioned, DFT or FFT operation can be used. In any case, it may be considered to effectuate the inverse transform to come back from T delay taps to M*F frequency components. Notice that this mechanism can be used for simple channel recovery/acquisition in a receiving node, alternatively to the proposed main utilization described in this document as a CSI compression approach. The only remarkable difference is that in decompression case it would be necessary to deal with quantized coefficients as an additional step to reconstruct channel/beamforming tensor from a CSI report exchanged between two nodes. Finally as a result, we have recovered the 3D channel/beamforming tensor 402 with size N x F x M from a set of original measurements limited by C CSI-RS pilots.

Numerical Examples for the two cases (C = N; C < N)

In the first case, the spatial transformation may be performed with SVD/EVD and the frequency-to-time delay transformation may be performed by means of a DFT/FFT based procedure. For calculating the bit overhead in this case (see FIG. 15), further processing inside channel coefficients of the long and short term to exploit further internal sparsity is not considered, i.e. long term consists of N* M x K channel coefficients and short term has K x T coefficients. If the configuration in FIG. 15 is considered, with long term update each 30 ms and single short term slice update every 5 ms, it is clear that by using a single slice of size K x T (2D channel matrix 302) for the short term update, the bit overhead becomes much less than in the case in which each layer requires an independent update for long term and short term. At a first glance, it may be thought that long term is the major component of bit overhead, however, its influence is rapidly reduced if the periodicity is decreased while assuming the stability of long term information. In contrast, it is actually the short term bit overhead that influences the most the global bit overhead of the CSI report. This is quite clear by comparing the right picture of FIG. 15, in which each of the M layers require an individual short term update, with the left picture in which a single short term update is required. Now, some additional numerical results from simulations with the two aforementioned cases are presented. Simulation parameters are presented in FIG. 16.

In FIG. 17a, some results of the described implementation example for the first case (C = N) are shown, with PCA (SVD/EVD) for spatial transform and DFT/FFT for frequency- to-time delay transform. As observed for a channel tensor with N=32 Tx antennas, M=4 Rx antennas, and F=50 RB granularity, the single K x T slice scheme outperforms a similar scheme with M slices. For the low bit overhead regime below 1000 bits, there is a correlation gain of 2-4% between reconstructed channel to ideal channel. Clearly, a major advantage of the proposed scheme is that it can truly exploit the long term properties of the channel 204 (W = periodicity of long term/ short term CSI) and interlayer correlation to update a single slice of spatial and time delay taps with a more relaxed bit overhead. In contrast, the second scheme with M layers requires to sacrifice CSI resolution in order to accommodate same bit overhead which bring losses as a result. Notice that for the bit overhead between 1000-2000bits the proposed single short term slice update allows to reach same reconstruction level with up to 30% less bit overhead.

For the example implementation in the second case (C < N), numerical results are presented in FIG. 17b. OMP with 2D-DFT dictionary and extended DFT dictionary for frequency- to-time delay transform were used. For comparison, a typical configuration for Rell6 32 CSI-RS pilots with DFT based codebook was used. The ratio of effective channel correlation can be calculated with a reconstructed set of precoders at full rank M=4. It can be seen, that correlation values for all numerical results bring very close correlation value ~0.8, but the approach of this disclosure uses only C=8-12 CSI-RS pilots, in comparison to the Release 16 which uses 32 CSI-RS cell specific pilots. These results shows not only lower bit overhead, but also a reduction of radio resource overhead.

FIG. 18 shows a method 1800 according to an embodiment of this disclosure. The method 1800 may be performed by the device 300. The method 1800 is for generating compressed CSI 203 based on C pilots 205 transmitted over a channel 204 between a transmitter 201 and a receiver 202 (see e.g. FIG. 2).

The method 1800 comprises a step 1801 of obtaining a 3D channel tensor 301 for the channel 204. The 3D channel tensor 301 has C x F x M channel coefficients for the C pilots 205, F frequency subbands, and M transmission layers or M receiving antenna ports of the receiver 202.

The method 1800 further comprises a step 1802 of calculating a 2D channel matrix 302 based on the 3D channel tensor 301, the 2D channel matrix 302 having K x T channel coefficients for K spatial beam directions and T time delay taps. The channel coefficients for the K spatial beam directions may be calculated by jointly performing a spatial transformation based on the channel coefficients for the C pilots 205 and for all the M transmission layers or M receiving antenna ports. The channel coefficients for the T time delay taps may be calculated by jointly performing a frequency-to-time transformation based on the channel coefficients for the F frequency subbands for all the M transmission layers or M receiving antenna ports.

The method 1800 further comprises a step 1803 of generating the compressed CSI 203 based on the K x T channel coefficients of the 2D channel matrix 302.

FIG. 19 shows a method 1900 according to an embodiment of this disclosure. The method 1900 may be performed by the device 400. The method 1900 is for reconstructing CSI 403 from compressed CSI 203, wherein the CSI 403 is related to a channel 204 between a transmitter 201 and a receiver 202 (see FIG. 2)

The method 1900 comprises a step 1901 of calculating a 2D channel matrix (401) based on the compressed CSI, the 2D channel matrix having K x T channel coefficients for K spatial beam directions and T time delay taps.

The method 1900 further comprises a step 1902 of calculating a 3D channel tensor 402 for the channel 204 based on the 2D channel matrix 401. The 3D channel tensor 402 has N x F x M channel coefficients for N transmitting antenna ports of the transmitter 201, F frequency subbands, and M transmission layers or M receiving antenna ports of the receiver 202. The channel coefficients for the N transmitting antenna ports and the M transmission layers or M receiving antenna ports may be calculated by performing an inverse spatial transformation based on K spatial beam direction vector components. The channel coefficients for the F frequency subbands may be calculated by performing a time-to- frequency transformation based on basis vector components selected for the T time delay taps common for the M transmission layers or M receiving antenna ports.

The method 1900 further comprises a step 1903 of determining the CSI 403 based on the 3D channel tensor 402.

The present disclosure has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed matter, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.