Devices and methods for exchanging channel state information

Abstract

The application relates to a communication device comprising: a communication interface configured to transmit a pilot signal via a communication channel to a second communication device and to receive a plurality of data elements representing channel state information (CSI) from the second communication device, wherein the plurality of data elements are a subset of a set of data elements representing the full channel state information (CSI) being available at the second communication device; and a processing unit configured to generate the full channel state information (CSI) on the basis of the plurality of data elements by applying a fitting scheme to the plurality of data elements received from the second communication device.

Claims

1. A first communication device, comprising: a communication interface configured to transmit a pilot signal via a communication channel to a second communication device and to receive a plurality of data elements representing channel state information (CSI) from the second communication device, wherein the plurality of data elements are generated by selecting a subset of a set of data elements representing the full CSI over at least one of a predefined time and a predefined frequency range being available at the second communication device; and a processor configured to generate the set of data elements representing the full CSI based on the plurality of data elements by applying a fitting scheme to the plurality of data elements received from the second communication device.

2. The first communication device of claim 1, wherein the processor is configured to generate the full CSI based on the plurality of data elements by applying a piecewise linear fitting scheme to the plurality of data elements received from the second communication device.

3. The first communication device of claim 1, wherein the processor is further configured to determine a respective frequency or a respective time associated with each data element of the plurality of data elements based on data received from the second communication device.

4. The first communication device of claim 1, wherein the full CSI comprises at least one of a frequency response, a time response and a spatial response of the communication channel to the pilot signal.

5. The first communication device of claim 1, wherein each of the plurality of data elements comprises phase information, amplitude information, a complex value, at least one of a real part of a complex value and an imaginary part of a complex value.

6. A method of operating a first communication device, wherein the method comprises: transmitting a pilot signal via a communication channel to a second communication device and receiving a plurality of data elements representing channel state information (CSI) from the second communication device, wherein the plurality of data elements are generated by selecting a subset of a set of data elements representing the full CSI over at least one of a predefined time and a predefined frequency range being available at the second communication device; and generating the set of data elements representing the full CSI based on the plurality of data elements by applying a fitting scheme to the plurality of data elements received from the second communication device.

7. A first communication device, comprising: a communication interface configured to receive a pilot signal from a second communication device; and a processor configured to generate a plurality of data elements representing channel state information (CSI) by selecting a subset of a set of data elements representing the full CSI over at least one of a predefined time and a predefined frequency range being available at the first communication device; wherein the communication interface is further configured to transmit the plurality of data elements representing the CSI to the second communication device.

8. The first communication device of claim 7, wherein the processor is configured to select a predefined number of data elements from the set of data elements representing the full CSI for generating the plurality of data elements.

9. The first communication device of claim 8, wherein the processor is configured to select predefined data elements from the set of data elements representing the full CSI for generating the plurality of data elements.

10. The first communication device of claim 8, wherein the processor is configured to select the predefined number of data elements from the set of data elements representing the full CSI for generating the plurality of data elements in such a way that a fitting scheme applied to the selected predefined number of data elements results in minimal residual fitting errors.

11. The first communication device of claim 8, wherein the processor is further configured to dynamically adapt the number of data elements to be selected from the set of data elements representing the full CSI for generating the plurality of data elements based on a quality measure of the CSI.

12. The first communication device of claim 8, wherein the processor is configured to select the number of data elements as well as the selected number of data elements from the set of data elements representing the full CSI for generating the plurality of data elements in such a way that a fitting scheme applied to the selected predefined number of data elements results in a-minimal residual fitting errors.

13. The first communication device of claim 10, wherein the fitting scheme comprises fitting by a piecewise linear function.

14. The first communication device of claim 7, wherein the processor is further configured to quantize the subset of the set of data elements with a variable bit width.

15. The first communication device of claim 7, wherein each of the plurality of data elements comprises phase information, amplitude information, a complex value, at least one of a real part of a complex value and an imaginary part of a complex value.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) Further embodiments of the invention will be described with respect to the following figures, wherein:

(2) FIG. 1 shows a schematic diagram of a transmitter communication device according to an embodiment in communication with a receiver communication device according to an embodiment;

(3) FIG. 2 shows a diagram illustrating steps of a method implemented in a transmitter communication device according to an embodiment;

(4) FIG. 3 shows a diagram illustrating steps of a method implemented in a receiver communication device according to an embodiment;

(5) FIG. 4 shows a schematic diagram illustrating a first stage of a CSI exchange scheme implemented in communication devices according to an embodiment;

(6) FIG. 5 shows a schematic diagram illustrating a second stage of a CSI exchange scheme implemented in communication devices according to an embodiment;

(7) FIG. 6 shows a schematic diagram illustrating a third stage of a CSI exchange scheme implemented in communication devices according to an embodiment;

(8) FIG. 7 shows a schematic diagram illustrating different aspects of the invention;

(9) FIG. 8 shows a schematic diagram illustrating a sixth stage of a CSI exchange scheme implemented in communication devices according to an embodiment; and

(10) FIG. 9 shows a schematic diagram illustrating a seventh stage of a CSI exchange scheme implemented in communication devices according to an embodiment.

(11) In the various figures, identical reference signs will be used for identical or at least functionally equivalent features.

DETAILED DESCRIPTION OF EMBODIMENTS

(12) In the following description, reference is made to the accompanying drawings, which form part of the disclosure, and in which are shown, by way of illustration, specific aspects in which the present invention may be placed. It will be appreciated that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following detailed description, therefore, is not to be taken in a limiting sense, as the scope of the present invention is defined by the appended claims.

(13) For instance, it will be appreciated that a disclosure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding device may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures.

(14) Moreover, in the following detailed description as well as in the claims embodiments with different functional blocks or processing units are described, which are connected with each other or exchange signals. It will be appreciated that the present invention covers embodiments as well, which include additional functional blocks or processing units that are arranged between the functional blocks or processing units of the embodiments described below.

(15) Finally, it is understood that the features of the various exemplary aspects described herein may be combined with each other, unless specifically noted otherwise.

(16) FIG. 1 shows a communication system 100 comprising a communication device 101 according to an embodiment and a communication device 131 according to an embodiment configured to communicate via a communication channel 120. In the following the communication device 101 will be also referred to as transmitter communication device 101 and the communication device 131 will be also referred to as receiver communication device 131. In an embodiment, the communication system 100 can be a wireless communication system 100. In an embodiment, the transmitter communication device 101 can be a base station 101. In an embodiment, the receiver communication device 131 can be a user equipment (UE) 131. As will be appreciated, the communication system 100 can comprise more than one transmitter communication device 101 and/or more than one receiver communication device 131.

(17) As can be taken from FIG. 1 and as will be described in more detail further below, the transmitter communication device 101 comprises a communication interface 103 configured to transmit a pilot signal via the communication channel 120 to the receiver communication device 131. In an embodiment, the communication interface 103 of the transmitter communication device 101 can comprise one or more antennas. In an embodiment, the communication interface 103 is a MIMO communication interface 103.

(18) The communication interface 103 of the transmitter communication device 101 is further configured to receive a plurality of data elements representing channel state information (CSI) defined, for instance, over a predefined time and/or frequency range from the receiver communication device 131, wherein the plurality of data elements are a subset of a set of data elements representing the full channel state information (CSI) over the predefined time and/or frequency range being available at the receiver communication device 131.

(19) Furthermore, the transmitter communication device 101 comprises a processing unit 105 configured to generate the full channel state information (CSI) on the basis of the plurality of data elements by applying a fitting scheme to the plurality of data elements received from the receiver communication device 131, as will be described in more detail further below.

(20) As can be taken from FIG. 1 and as will be described in more detail further below, the receiver communication device 131 comprises a communication interface 133 configured to receive a pilot signal from the transmitter communication device 101. In an embodiment, the communication interface 133 of the receiver communication device 131 can comprise one or more antennas.

(21) Furthermore, the receiver communication device 131 comprises a processing unit 135 configured to generate the plurality of data elements representing the channel state information (CSI) by selecting a subset of the set of data elements representing the full channel state information (CSI) being available at the receiver communication device 131. The communication interface 133 of the receiver communication device 131 is further configured to transmit the plurality of data elements representing channel state information (CSI), i.e. the selected subset of the full CSI, to the transmitter communication device 101. For instance, in an embodiment the receiver communication device can sample a channel response functions over a predefined frequency range at 20 different frequencies (which defines the full channel state information (CSI) being available at the receiver communication device 131) and selecting 5 of these samples for transmission to the transmitter communication device 101.

(22) FIG. 2 shows a diagram illustrating steps of a method 200 for operating the transmitter communication device 101 according to an embodiment. The method 200 comprises the steps of: transmitting 201 a pilot signal via the communication channel 120 to the receiver communication device 131 and receiving the plurality of data elements representing channel state information (CSI) from the receiver communication device 131, wherein the plurality of data elements are a subset of a set of data elements representing the full channel state information (CSI) being available at the receiver communication device 131; and generating 203 the full channel state information (CSI) on the basis of the plurality of data elements by applying a fitting scheme to the plurality of data elements received from the receiver communication device 131.

(23) FIG. 3 shows a diagram illustrating steps of a method 300 for operating the receiver communication device 131 according to an embodiment. The method 300 comprises the steps of: receiving a pilot signal from the receiver communication device 101; generating 303 a plurality of data elements representing channel state information (CSI) by selecting a subset of a set of data elements representing the full channel state information (CSI) being available at the receiver communication device 131; and transmitting 305 the plurality of data elements representing channel state information (CSI) to the transmitter communication device 101.

(24) Further embodiments of the transmitter communication device 101, the receiver communication device 131 and the methods 200 and 300 will be described in the following. In several of these embodiments the communication network 100 comprises more than one receiver communication devices, in particular user equipments 131.

(25) In an embodiment, the channel 120 observed after the estimation by the i-th receiver communication device 131 can be expressed by means of one or multiple vectors
h.sub.ij=[h.sub.ij,1, . . . ,h.sub.ij,R]∈S.sup.R  (1)

(26) wherein: S denotes a normed subspace. h.sub.ij,k∈S, ∀k∈[1, R]∩. j∈[1,J]∩, with J denoting the number of estimated channel vectors, and J≥1 independently of the processing/estimation procedures performed by the receiver communication device(s) 131 on the received pilot signal or training sequences. For example, each receiver communication device 131 could estimate one channel vector per transmit/receive antenna pair, or per antenna port. Alternatively, J could be the number of virtual/equivalent channel vectors obtained through combining operations. R denotes the amount of resources over which a channel vector is measured. For example, R could be the number of sub-carriers/resource blocks/resource block groups, if the estimation is performed in the frequency domain, or alternatively the duration of the channel impulse response in terms of number of sampling periods at the receiver communication device 131, if the estimation is performed in the time domain.

(27) In an embodiment, the operations performed on h.sub.ij by the i-th receiver communication device 131 can be divided in two categories: 1. Selection/sampling/processing of the elements of h.sub.ij along R to reduce their number or guarantee that they satisfy a specific property/metric, which has been described above as selecting a subset of the set of data elements representing the full channel state information (CSI) being available at the receiver communication device 131. 2. Quantization of the components obtained after the selection/sampling/processing.

(28) As will be appreciated, each element of a channel vector as defined in above equation (1) can always be mapped into several dependent or independent components, without loss of information if the mapping is invertible. The inverse mapping can be applied even on sampled versions of the components obtained at the previous step, even if the latter are independently sampled. Each component of a vector, evaluated across the entirety or the available resources over which it is measured, i.e., R, can be seen as a set of data that can be approximated by means of function fitting. Technically, fitting, or approximation in general, is to find under certain constraints the approximation of a function or a set of data with other functions that are more elementary or more manageable. In other words, the goal of this operation is to take known values of a function (possibly calculated by means of complex procedures) and identify a new function, or a set of functions, that is easier to evaluate and that can interpolate between, or extrapolate beyond, the known values. In embodiments of the application, this approximation can be targeted for a continuous domain or for a set of discrete points.

(29) Accordingly, embodiments of the application are based on a CSI exchange scheme, which can be broken down into seven stages, as illustrated in FIGS. 3 to 9.

(30) In a first stage of the CSI exchange scheme implemented in embodiments of the application, all the elements of each vector h.sub.ij can be remapped to yield an alternative representation of these elements, suitable for the subsequent operations. In an embodiment, this can be done by applying an invertible mapping f: S>.sup.L, where L≥1, and is a normed subspace, in general but not necessarily different from . For instance, if = and L=2 then f could the invertible map that for any h.sub.ij,k yields h.sub.ij,k (1)=|h.sub.ij,k| and h.sub.ij,k(2)=e.sup.j∠h.sup.ij, i.e., two quantities carrying information on the amplitude and the phase of h.sub.ij,k. Alternatively, f could be the invertible map that for any h.sub.ij,k yields h.sub.ij,k (1)={h.sub.ij,k} and h.sub.ij,k(2)={h.sub.ij,k} (with {⋅} and {⋅} defined as operators that yield the real and imaginary parts of their complex argument, respectively). In a further embodiment, for a generic normed subspace S and L=1, f could also be the identity function mapping h.sub.ij,k to itself, i.e., f(h.sub.ij,k)=h.sub.ij,k.

(31) In general, the operation described above can be mathematically expressed by defining f as an invertible map that for any h.sub.ij,k yields

(32) $f\left(h_{\mathrm{ij},k}\right)=\left[\begin{array}{c}{h}_{\mathrm{ij},k}\left(1\right)\\ h_{\mathrm{ij},k}\left(2\right)\\ \mathrm{.Math.}\\ h_{\mathrm{ij},k}\left(L\right)\end{array}\right]$
and its natural extension to S.sup.R, induced by the Cartesian product, as the canonical invertible mapping

(33) $g\text{:}{𝒮}^R->\underset{\underset{R}{︸}}{{𝒯}^L\times {𝒯}^L\times \mathrm{.Math.}\times {𝒯}^L}={𝒯}^{L\times R}$
such that

(34) $\begin{array}{cc}g\left(h_{\mathrm{ij}}\right)=H_{\mathrm{ij}}=\left[\begin{array}{cccc}{h}_{\mathrm{ij},1}\left(1\right)& h_{\mathrm{ij},2}\left(1\right)& & h_{\mathrm{ij},R}\left(1\right)\\ h_{\mathrm{ij},1}\left(2\right)& h_{\mathrm{ij},2}\left(2\right)& \mathrm{.Math.}& h_{\mathrm{ij},R}\left(2\right)\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ h_{\mathrm{ij},1}\left(L\right)& h_{\mathrm{ij},2}\left(L\right)& \mathrm{.Math.}& h_{\mathrm{ij},R}\left(L\right)\end{array}\right].& \left(2\right)\end{array}$

(35) Finally, a set of vectors is defined as follows:
h.sub.ij.sup.(m)=[h.sub.ij,1(m), . . . ,h.sub.ij,R(m)], ∀m∈[1,L]

(36) which is obtained as the result of the projection proj.sub.m:.sup.L×R.fwdarw..sup.R. In this regard, it is noted that both f, g and proj.sub.m are known at both sides of the communication channel 120, i.e., by the transmitter communication device 101 and the receiver communication device 131. If this were not the case, the transmitter communication device 101 would not be able to reconstruct an estimation of all the vectors h.sub.ij using the selected subset received from the receiver communication device(s) 131. A graphical representation of the first stage of the CSI exchange scheme implemented in embodiments of the application is shown in FIG. 4.

(37) In a second stage of the CSI exchange scheme implemented in embodiments of the application, which is illustrated in FIG. 5, each h.sub.ij.sup.(m) can be processed to extract, i.e. select, a number R.sub.m≥0 of its elements, where all the R.sub.m may or may not be identical. This operation is not invertible and in general yields m vectors of different lengths, which are denoted as .sup.(m). According to embodiments of the application, both the number and the selection of the R.sub.m elements constituting the vectors .sup.(m), ∀m∈[1, L] and for each vector, can be determined by means of a fitting procedure where each vector h.sub.ij.sup.(m) is seen as a data set to be approximated by means of a piecewise function. Accordingly, R.sub.m is in general different for all the vectors h.sub.ij.sup.(m) and can be determined, for instance, according to one of the following embodiments.

(38) In a first embodiment based on minimum square errors, both the value of R.sub.m, ∀m∈[1, L] and the choice of the retained elements after the selection, i.e., the elements in .sup.(m), are determined by the processing unit 135 of the receiver communication device 131 in order to minimize the mean square error of the fitting. The indices of the retained elements are then stored in separate vectors .sup.(m)∈[1, R]∩. This embodiment yields a couple of output vectors (.sup.(m), .sup.(m)) for each input vector h.sub.ij.sup.(m).

(39) In a further embodiment relating to a dynamic choice or selection of the data elements, R.sub.m is a user-defined parameter, which in general can be different for all the vectors h.sub.ij.sup.(m), ∀m∈[1, L]. The retained elements are independently selected from each vector h.sub.ij.sup.(m) by the receiver communication device(s) 131, and sequentially chosen to yield the vectors .sup.(m) in order to minimize the residual fitting error after each choice. The indices of the retained elements are then stored in separate vectors .sup.(m)1 ∈[1, R]∩. This embodiment yields a couple of output vectors (.sup.(m), .sup.(m)) for each input vector h.sub.ij.sup.(m).

(40) In a further embodiment relating to a static choice or selection of the data elements, R.sub.m is again a user-defined parameter, which in general can be different for all the vectors h.sub.ij.sup.(m), ∀m∈[1, L]. In this embodiment, however, the R.sub.m retained elements from h.sub.ij.sup.(m) are statically chosen by the receiver communication device(s) 131 in order for their indices to follow a pattern known and agreed upon by both the transmitter communication device 101 and the receiver communication device(s) 131 in the context of the underlying communication protocol/standard. Accordingly, this pattern does not need to be part of the signaling message(s) sent from the receiver communication device(s) 131 to the transmitter communication device 101. For instance, let R=13, m=1 and R.sub.1=3. In this case, .sup.(1) could carry only the 1.sup.st, 7.sup.th and 13.sup.th element of h.sub.ij.sup.(1), or other elements according to an alternative pattern. This embodiment yields one output vector .sup.(m) for each input vector h.sub.ij.sup.(m).

(41) In a third stage of the CSI exchange scheme implemented in embodiments of the application, which is illustrated in FIG. 6, a parametric quantization can be performed over all the vectors .sup.(m) (and .sup.(m), whenever present) to yield vectors .sup.(m) (resp. .sup.(m)). In particular, B.sub.h.sup.(m) and B.sub.i.sup.(m) bits can be used to quantize each element of .sup.(m) and .sup.(m) (whenever present), respectively. In other words, embodiments of the application make use of a numerical quantizer which supports different bit widths, and thus different levels of precision. More precisely, the quantizer can operate on each input vector using different B.sub.h.sup.(m) and B.sub.i.sup.(m), and yields output vectors .sup.(m) (resp. .sup.(m)) of length B.sub.h.sup.(m)R.sub.m (resp. B.sub.i.sup.(m)R.sub.m), ∀m∈[1, L].

(42) In a fourth stage of the CSI exchange scheme implemented in embodiments of the application, the signaling for transmission to the transmitter communication device 101 is generated. The size of the signaling depends on the adopted policy to build the vectors .sup.(m). In particular, if a fitting procedure is adopted in the second stage, then the signaling carries information related to at least the vectors .sup.(m) and .sup.(m), ∀m∈[1, L], which implies the transmission of at least Σ.sub.m=1.sup.L(B.sub.h.sup.(m)+B.sub.i.sup.(m))R.sub.m bits per signaling period. Alternatively, if a static selection is applied in the second stage, then the signaling carries information related to at least the vectors .sup.(m), ∀m∈[1, L], which implies the transmission of at least Σ.sub.m=1.sup.LB.sub.h.sup.(m)R.sub.m bits per signaling period. A summary of the signaling for each of the aforementioned cases is provided in FIG. 7.

(43) In a fifth stage of the CSI exchange scheme implemented in embodiments of the application, the signaling comprising the selected subset of data elements is performed by the receiver communication device(s) 131 via the communication channel 120 to the transmitter communication device 101 according to the underlying communication protocol/standard implemented in the communication network 100.

(44) In embodiments of the application, the stages 1 to 5 described above can be part of an even more sophisticated CSI exchange scheme which accounts for interactions between the communication devices aiming at optimizing the performance of the communication network 100 in terms of reduction of redundancy for the CSI signaling overhead. Accordingly, embodiments of the application comprise the following further stages.

(45) In a sixth stage of the CSI exchange scheme implemented in embodiments of the application, the transmitter communication device 101 reconstructs an estimate of the vectors h.sub.ij.sup.(m) by means of a piecewise fitting of the plurality of data elements provided by the receiver communication device(s) 131.

(46) Depending on the procedure adopted by the receiver communication device(s) 131 for determining the number and the selection of the R.sub.m elements constituting the vectors .sup.(m), ∀m∈[1, L], the piecewise fitting can be implemented, for instance, on the basis of either one of the two following approaches.

(47) In an embodiment based on a dynamic fitting approach, each couple (.sup.(m), .sup.(m)) can be processed by the processing unit 105 of the transmitter communication device 101 independently of the other couples. First, a vector .sup.(m) with R elements set to zeros is initialized. Then, the R.sub.m elements of .sup.(m) corresponding to the R.sub.m indices carried in .sup.(m) (after transforming them in their natural number representation) are set to the corresponding elements of .sup.(m) (previously transformed in their real number representation). The resulting .sup.(m) then carries the real number representation of the R.sub.m elements of .sup.(m), and R−R.sub.m zeros.

(48) In an embodiment based on a static fitting approach, each vector .sup.(m) is processed by the processing unit 105 of the receiver communication device 101 independently of the other vectors. First, a vector .sup.(m) with R elements set to zeros is initialized. Then, the R.sub.m elements of .sup.(m) corresponding to the R.sub.m static indices, known and agreed upon by both the transmitter communication device 101 and the receiver communication device(s) 131 in the context of the underlying communication protocol/standard, are set to the real number representation of the corresponding elements of .sup.(m). The resulting .sup.(m) then carries the real number representation of the R.sub.m elements of .sup.(m), and R−R.sub.m zeros.

(49) In both embodiments, a piecewise fitting (preferably a piecewise linear fitting) is performed by the processing unit 105 of the transmitter communication device 101 on .sup.(m) to yield h.sub.ij,E.sup.(m), i.e., the reconstructed estimate of h.sub.ij.sup.(m) at the transmitter communication device 101.

(50) In a last stage of the CSI exchange scheme implemented in embodiments of the application, the processing unit 105 of the receiver communication device 101 takes all the vectors h.sub.ij,B.sup.(m) and reconstructs an estimate of the matrices H.sub.ij, as per equation (2) and denoted in the following as H.sub.ij,E, given by

(51) $H_{\mathrm{ij},E}=\left[\begin{array}{c}{\stackrel{\_}{h_{\mathrm{ij},E}}}^{\left(1\right)}\\ {\stackrel{\_}{h_{\mathrm{ij},E}}}^{\left(2\right)}\\ \mathrm{.Math.}\\ {\stackrel{\_}{h_{\mathrm{ij},E}}}^{\left(L\right)}\end{array}\right].$

(52) Finally, the vectors h.sub.ij,E, i.e., the reconstructed version of the vectors h.sub.ij,E, are obtained by the processing unit 105 of the transmitter communication device 101 by application of the inverse map g.sup.−1, that is
h.sub.ij,E=g.sup.−1(H.sub.ij,E).

(53) In an embodiment, the considered wireless communication system 100 is a Massive MIMO system 100 operating in FDD, in which the transmitter communication device 101 in the form of a base station 101 requires one or more receiver communication devices 131 in the form of one or more user equipments 131 to feedback signaling on their estimated downlink CSI. In this embodiment, the one or more user equipments 131 estimate the response of one or a plurality of downlink channels 120, over R time or frequency resources, by means of any conventional channel estimation technique, possibly including additional processing performed in the context of the estimation (by means of linear or non-linear operations). This yields the vectors h.sub.ij∈, ∀j∈[1,J]∩, with J≥1 denoting the number of estimated channel vectors, independently of the processing/estimation performed by the user equipment(s) 131 on the received pilot sequences. Alternatively J could be the number of virtual/equivalent channel vectors obtained through combining operations. In this embodiment, the CSI exchange scheme can comprise the following stages.

(54) The one or more user equipments 131 map the vector h.sub.ij into the vectors h.sub.ij.sup.(1) =|h.sub.ij| and h.sub.ij.sup.(2)=e.sup.j∠h.sup.ij (or alternatively h.sub.ij.sup.(1)={h.sub.ij} and h.sub.ij.sup.(2)={h.sub.ij}).

(55) The one or more user equipments 131 extract R.sub.1 and R.sub.2 elements from h.sub.ij.sup.(1) and h.sub.ij.sup.(2), respectively, in which R.sub.1 and R.sub.2 are not necessarily identical, and according to a static pattern known and agreed upon by the base station 101 and the user equipment(s) 131. This operation yields the two vectors .sup.(1) and .sup.(2), which carry R.sub.1 elements of h.sub.ij.sup.(1) and R.sub.2 elements of h.sub.ij.sup.(2), respectively.

(56) The one or more user equipments 131 perform a variable-bit-width numerical quantization of .sup.(1) and .sup.(2) to yield the vectors .sup.(1) and .sup.(2), respectively. In particular, B.sub.h.sup.(1) bits are used to quantize each element of .sup.(1), whereas B.sub.h.sup.(2) bits are used to quantize each element of .sup.(2). Hence, .sup.(2) and .sup.(2) carry B.sub.h.sup.(1)R.sub.1 and B.sub.h.sup.(2)R.sub.2 bits, respectively.

(57) The one or more user equipments 131 generate the signaling which carries at least information related to the vectors .sup.(1) and .sup.(2). This implies the transmission of at least B.sub.TOT=B.sub.h.sup.(1)R.sub.1+B.sub.h.sup.(2)R.sub.2 bits per user equipment 131 per signaling period.

(58) The one or more user equipments 131 perform the signaling towards the at least one base station 101 according to the underlying communication protocol/standard implemented in the communication network 100.

(59) In particular, above-described five steps/stages can be included in a larger procedure which accounts for interactions between the devices aiming at optimizing the performance of the system in terms of reduction of redundancy for the CSI signaling overhead.

(60) Upon reception of the signaling from the one or more user equipments 131 the base station 101 reconstructs an estimate of the vectors h.sub.ij.sup.(1), h.sub.ij.sup.(2) by means of a piecewise fitting of the vectors .sup.(1) and .sup.(2), respectively. To this end, the base station can initialize two vectors with R elements set to zeros, i.e., .sup.(1) and .sup.(2). Then, the base station 101 sets the R.sub.1 (resp. R.sub.2) elements of the vector .sup.(1) (resp. .sup.(2)) corresponding to the R.sub.1 (resp. R.sub.2) static indices, known and agreed upon by both the base station 101 and the one or more user equipments 131 in the context of the underlying communication protocol/standard, to the real number representation of the corresponding elements of .sup.(1) and .sup.(2). The resulting vector .sup.(1) (resp. .sup.(2)) then carries the real number representation of the R.sub.1 (resp. R.sub.2) elements of .sup.(1) (resp. .sup.(2)), and R−R.sub.1 (resp. R−R.sub.2) zeroes. Finally, the base station 101 performs a piecewise fitting on .sup.(2) and .sup.(2) to obtain h.sub.ij,E.sup.(m)and h.sub.ij,E.sup.(2), respectively, i.e., the reconstructed estimates of h.sub.ij.sup.(1) and h.sub.ij.sup.(2).

(61) In an embodiment, the processing unit 105 of the transmitter communication device 101 is configured to map h.sub.ij,E.sup.(1) and h.sub.ij,E.sup.(2) into the reconstructed estimates of h.sub.ij, i.e., h.sub.ij,E, by means of the following operation:

(62) $h_{\mathrm{ij},E}={\stackrel{\_}{h_{\mathrm{ij},E}}}^{\left(1\right)}{e}^{j\angle {\stackrel{\_}{h_{\mathrm{ij},E}}}^{\left(2\right)}}.$

(63) In an alternative embodiment, the processing unit 105 of the transmitter communication device 101 is configured to use the operation h.sub.ij,E=h.sub.ij,E.sup.(1)+jh.sub.ij,E.sup.(2), depending on which map has been adopted in the second stage of the CSI exchange scheme described above.

(64) While a particular feature or aspect of the disclosure may have been disclosed with respect to only one of several implementations or embodiments, such feature or aspect may be combined with one or more other features or aspects of the other implementations or embodiments as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms “include”, “have”, “with”, or other variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term “comprise”. Also, the terms “exemplary”, “for example” and “e.g.” are merely meant as an example, rather than the best or optimal. The terms “coupled” and “connected”, along with derivatives may have been used. It should be understood that these terms may have been used to indicate that two elements cooperate or interact with each other regardless whether they are in direct physical or electrical contact, or they are not in direct contact with each other.

(65) Although specific aspects have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific aspects shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific aspects discussed herein.

(66) Although the elements in the following claims are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence.

(67) Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, those skilled in the art readily recognize that there are numerous applications of the invention beyond those described herein. While the present invention has been described with reference to one or more particular embodiments, those skilled in the art recognize that many changes may be made thereto without departing from the scope of the present invention. It is therefore to be understood that within the scope of the appended claims and their equivalents, the invention may be practiced otherwise than as specifically described herein.