TECHNICAL FIELD The invention relates to the field of wireless communications, and more particularly to a multi-input multi-output (M IMO) system in a device-to-device (D2D) communication.

BACKGROUND In the massive multi-input multi-output (M IMO) systems, the transceivers can obtain through leveraging a large number of antennas a high power gain on the received signal as well as a large spatial multiplexing gain for parallel transmissions to a large number of users. However, the achievement of such a gain requires a lot of additional efforts on the design of the MIMO precoding. One of the most difficult challenges is the acquisition of channel state information (CSI), in particular in frequency-division multiplexing (FDD) systems, which still dominate the market although a dense literature focusing on precoding strategies in time-division duplexing (TDD) systems develops increasingly.

While the downlink CSI can be obtained from uplink transmission via channel reciprocity in TDD systems, channel reciprocity does not hold in FDD systems. As a result, to obtain the downlink CSI in an FDD system, the base station (BS) first sends a sequence of pilot symbols for each antenna, the users then estimate the channel and feedback the channel estimation to the BS for each antenna.

Such closed-loop feedback procedure raises a lot of overheads on channel training and feedback, which limits the throughput in massive MIMO systems. For example, using conventional techniques for CSI quantization and feedback, the number of bits required scales linearly according to both the number of antennas (Nt) and users (K) such that the feedback loading could exceed the tolerance of the massive MIMO systems.

Since CSI quality at the BS yields a great impact on the system performance, new strategies should be developed on CSI acquisition for massive M IMO precoding. In conventional MIMO systems wherein the number of antennas is not large, the channel quantization is an efficient approach for reducing the CSI feedback. Numerous quantization-based techniques, such as the Grassmannian quantization and the random vector (RVQ) quantization, have been developed. However, they rely on a pre- calculated codebook that scales exponentially according to the number of antennas such that they cannot be directly extended to massive MIMO systems. In another approach, the reduction in the CSI feedback exploits the low rank property of the transmit covariance matrix in massive MIMO systems. However, such an approach leads to a signal having a too small angular spread and a reduction in the antenna number from Nt to M where M remains still quite large. A device-to-device (D2D) communication enabled precoding technique has already been proposed in "Enabling massive MIMO systems in the FDD mode thanks to D2D communications", by H. Yin, L. Cottatellucci and D. Gesbert in Proceedings of Asilomar Conference on Signals, Systems and

Computers, Pacific Grove, CA, Nov. 2014, pp. 656-660. Therein, a massive MIMO BS serves a group of users, wherein one user is selected as a leader who collects the full CSI from all the other users via the D2D communication links. Upon obtaining the global CSI, the leader computes the precoder and feeds the set of chosen precoder indices back to the BS. Simulation results show that such a technique can significantly reduce the feedback loading from the users to the BS, while still achieving a good sum rate performance. However, two main issues persist. First, the method requires a central coordination among the users, which may not be a robust design in the multi-user networks. Second, the technique assumes that a perfect global CSI is known by the leader user, which requires very high data rates for the signaling among users. Thus, the resulting capacity required for the D2D CSI exchange may be far too large for the D2D network such that the D2D enabled massive MIMO precoding is hard to be implemented in existing systems without a smart design on the CSI exchange among the users.

SUMMARY

It is therefore an object of the present invention to provide methods and a user equipment device, which improve the existing techniques by reducing codebook and feedback overheads.

In particular the method and apparatus of the invention allows adaptively sharing or exchanging a channel state information and setting a distributed precoding amongst a plurality of users in a multi- input multi-output system over a device-to-device communication. The object is achieved by the features of the independent claims. Further embodiments of the invention are apparent from the dependent claims, the description and the drawings.

According to a first aspect, the invention relates to a method for adaptively sharing channel state information (CSI) in a multi-input multi-output system over a device-to-device (D2D) communication, the method, performed at a first transmitting device comprises the step of determining, a first transmitting device, a respective signal subspace; determining, at the first transmitting device whether the signal subspace of the first transmitting device overlaps the signal subspace of at least one second transmitting device as to form an overlapping signal su bspace; quantizing the portion of CSI lying in the overlapping signal subspace; and sharing the quantized portion of CSI with at least one second transmitting device over the D2D communication.

The transmitting device may by any device capable of transmitting and receiving data within the MIMO system. The step of sharing information, such as the quantized portion of CSI, may include exchanging information among the transmitting devices in the MIMO system.

According to an implementation, the method for adaptively sharing channel state information (CSI) in a multi-input multi-output system over a device-to-device (D2D) communication may comprise the step of determining, for each one amongst a plurality of user equipment devices, a respective signal subspace, the step of determining, for each one amongst a plurality of user equipment devices, whether the signal subspace of a user equipment device overlaps the signal subspace of another UE device as to form an overlapping signal subspace, the step of quantizing the portion of channel state information lying in the overlapping signal subspace, and the step of sharing the quantized portion of channel state information with each other amongst the plurality of user equipment devices over the device-to-device communication.

Thereby, only the channel state information in the overlapping signal subspace is shared or exchanged between the users (i.e., the user equipment devices) such that a partial CSI exchange between the users can be carried out. Thus, huge amount of signaling to share the CSI over the D2D is not needed. If two users have orthogonal signal subspaces, then they need to not exchange the CSI to each other because neither of them cause interference to the other, and if two users have identical signal subspaces, then they need to quantize their full CSI and exchange it to each other in high resolution.

According to a first implementation of the method according to the first aspect, the step of determining a respective signal subspace comprises sharing a respective CSI statistics information with at least one second transmitting device.

According to a further implementation, the step of determining a respective signal subspace may comprise the step of sharing a respective channel state information statistics information with each other amongst the plurality of user equipment devices. Thereby, a specific quantization is designed for each user individually, which takes the CSI statistics of all the users into consideration. Knowing that a user communicating its CSI to another user only needs to convey the portion of the CSI that lies on the overlapping signal subspace, if the overlapping signal subspace has rank 1, the "useful" portion of the CSI reduces to a scalar such that it is sufficient for the user to transmit the scalar to the other user.

According to a second implementation of the method according to the first implementation of the first aspect, the step of sharing the respective CSI statistics information comprises sharing a channel covariance matrix of the first transmitting device with the at least one second transmitting device.

According to a further implementation, the step of sharing the respective CSI statistics information may comprise sharing a channel covariance matrix of each user equipment device or transmitting device with each other amongst the plurality of user equipment devices or transmitting devices. Thereby, the need for a CSI exchange depends on topology and varies according to differences between the covariance matrices of two users (e.g., street corner situation). The portion of CSI that lies in the overlapping signal subspace with the other users can thus be quantized up to a specific resolution adaptive to the global channel statistics. Furthermore, the signal subspace of each user can correspond to the dominant eigenvector of each respective channel covariance matrix.

According to a third implementation of the method according to the second implementation of the first aspect, the step of determining an overlapping signal subspace comprises projecting the channel covariance matrix of each transmitting device onto the respective signal subspace of the other transmitting device as to obtain an interference covariance matrix.

The step of determining an overlapping signal subspace may comprise, in a further implementation, projecting the channel covariance matrix of each user equipment device onto the respective signal subspace of the other user equipment device as to obtain an interference covariance matrix. Thereby, the properties of the covariance matrices can be exploited. Furthermore, the overlapping signal subspace between a user and another one can correspond to the dominant eigenvector of the interference covariance matrix from the user to the other one.

According to a fourth implementation of the method according to the third implementation of the first aspect, the step of quantizing the portion of CSI comprises designing a respective channel codebook based on the interference covariance matrix in order to adapt the channel codebook to each one amongst the overlapping signal subspaces.

Thereby, the channel codebook can adapt to the interference covariance matrix and hence to the overlapping signal subspace within the D2D CSI sharing.

According to a fifth implementation of the method according to the fourth implementation of the first aspect, each channel codebook is designed to have an adaptive size in terms of bits, the size being limited by the signaling capacity of the whole D2D communication and adaptive according to the whole CSI statistics information.

Thereby, a smart allocation of bits for the D2D CSI sharing can be carried out, given that the total capacity for D2D CSI sharing is limited in terms of bits (B _d bits). Thus, the portion of CSI that lies in the overlapping signal subspace with the other users can be quantized up to a specific resolution adaptive not only to the global channel statistics but also to the D2D signaling capacity.

According to a sixth implementation of the method according to the fifth implementation of the first aspect, the size is adapted to minimize the whole interference leakage in the corresponding communication network.

Thereby, a smart partition of the D2D communication resources can be carried out. For example, if a first user needs to exchange a scalar with a second user, but a third user needs to exchange a long vector with a fourth user, then more D2D communication resource will be allocated to the latter user pair and it will result therefrom that they will have much larger channel codebooks.

According to a seventh implementation of the method according to the fifth implementation of the first aspect, the first transmitting device projects its own channel of direct communication between it and a base station, BS, onto its respective overlapping signal subspace with the at least second transmitting device, and quantizes the projected channel using the corresponding channel codebook in order to obtain the quantized portion of CSI.

In general, each user equipment device may project its own channel of direct communication between it and a BS onto its respective overlapping signal subspace with the other user equipment device, and quantizes the projected channel using the corresponding channel codebook in order to obtain the quantized portion of CSI. Thereby, only the portion of CSI on the overlapping signal subspace, i.e., the interference su bspace, needs to be quantized.

According to an eighth implementation of the method according to the seventh implementation of the first aspect, the transmitting device transmits the quantized projected channel towards the at least one second transmitting device over the D2D communication.

According to a further implementation, each user equipment device transmits the quantized projected channel towards another user equipment device over the D2D communication.

Thereby, a D2D CSI sharing can be carried out. The transmission from a user towards another user may be performed through a tunnel, which is directed from the user towards the other user. Using such a tunnel for D2D CSI exchange allows to significantly reduce the complexity of the channel quantization at the users.

The above object is also solved in accordance with a second aspect.

According to the second aspect, the invention relates to a method for adaptively setting a distributed precoding in a multi-input multi-output system over a device-to-device communication, the method comprising applying the steps of the method as specified in the first aspect and the implementations of the first aspect, designing a respective precoder codebook for each transmitting device amongst a plurality of transmitting devices based on the respective channel covariance matrix of each transmitting device, and computing a respective precoder for each transmitting device based on the own channel state information of each user equipment device and the quantized portion of channel state information shared by the other user equipment devices.

Thereby, a highly distributed D2D precoding can be obtained. Indeed, a precoder is computed based on the perfect direct link CSI and the partial cross link CSI from the other users, while being aware of the interference leakage to the other users in the corresponding communication network.

Furthermore, the precoder codebook of each user amongst the plurality of users can be adapted to the channel covariance matrix of either each respective user in a first embodiment or the plurality of users in a second embodiment. In the latter embodiment, the precoder codebook can be designed to place more vectors on the most likely transmission direction. According to a first implementation of the method according to the second aspect, the precoder is selected from the respective precoder codebook in order to maximize the signal-to-leakage-and- noise ratio. Thereby, the corresponding SLNR precoding can achieve a good performance in the multi-user MIMO system while providing a straightforward way for individual precoding. Furthermore, the selected precoder can then be transmitted from a user towards its serving base station.

The above object is also solved in accordance with a third aspect.

According to the third aspect, the invention relates to a user equipment device for adaptively sharing CSI in a multi-input multi-output system over a D2D communication, wherein the transmitting device is adapted to determine a signal subspace; determine whether its signal subspace overlaps the signal subspace of at least one second transmitting device as to form an overlapping signal subspace, quantize the portion of CSI lying in the overlapping signal subspace, and share the quantized portion of CSI with at least one second transmitting device over the D2D communication.

According to a further implementation, the transmitting user equipment device is adapted to determine a signal subspace; determine whether its signal subspace overlaps the signal su bspace of another user equipment device as to form an overlapping signal subspace, quantize the portion of CSI lying in the overlapping signal subspace, and share the quantized portion of CSI with each other amongst a plurality of user equipment devices over the D2D communication.

According to a first implementation of the transmitting device according to the third aspect, the transmitting device is adapted to design a precoder codebook based on its channel covariance matrix, and compute a precoder based on its own CSI and the quantized portion of CSI shared by the at least one second transmitting device.

According to a further implementation, the user equipment device is adapted to design a precoder codebook based on its channel covariance matrix, and compute a precoder based on its own CSI and the quantized portion of CSI shared by the other user equipment devices.

According to a second implementation of the transmitting device according to the first

implementation of the third aspect, the transmitting device is adapted to transmit the precoder towards a serving base station. The above object is also solved in accordance with a fourth aspect.

According to the fourth aspect, the invention relates to a computer program comprising program code for performing the method according to any one of the first and second aspects and/or any one of their respective implementation forms when executed on a computer. Thereby, the method can be performed in an automatic and repeatable manner.

The computer program can be performed by any one of the above apparatuses or devices. The apparatuses or devices can be programmably arranged to perform the computer program.

Embodiments of the invention can be implemented in hardware, software or in any combination thereof.

It shall further be understood that a preferred embodiment of the invention can also be any combination of the dependent claims or above embodiments with the respective independent claim.

These and other aspects of the invention will be apparent and elucidated with reference to the embodiments described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

In the following detailed portion of the present disclosure, the invention will be explained in more detail with reference to the exemplary embodiments shown in the drawings, in which: shows a signaling illustrating a distributive D2D enabled precoding for a single-cell multi-user massive MIMO system according to a first embodiment of the present invention;

Fig. 2 shows an overlapping signal subspace formed by the overlap between the signal subspaces of two UE devices according to a second embodiment of the present invention;

Fig. 3 shows a vector diagram illustrating the quantization of the partial channel ¾ of the UE device k into ¾ according to a third embodiment of the present invention; Fig. 4 shows a signaling illustrating a distributive D2D enabled precoding for a single-cell multi-user massive MIMO system according to a fourth embodiment of the present invention;

Fig. 5 shows a signaling illustrating a distributive D2D enabled precoding for a multi-cell multi-user massive MIMO system according to a fifth embodiment of the present invention;

Fig. 6 shows a schematic flow diagram for adaptively sharing CSI in a MIMO system over a D2D communication according to a sixth embodiment of the present invention; and

Fig. 7 shows a schematic flow diagram for adaptively setting a distributed precoding in a

MIMO system over a D2D communication according to a seventh embodiment of the present invention.

Possible identical reference signs are used for identical or at least functionally equivalent features. DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

A solution for obtaining an efficient CSI exchange amongst users might be to apply conventional channel quantization techniques to compress each user's channel and share it in the D2D network. However, a conventional codebook can only adapt to the spatial correlation of a particular user, but cannot jointly exploit the spatial correlations of the other users. This may lead to have large codebook and feedback overheads. Thus, it is still possible to optimize these techniques to fully exploit the channel statistics of all the users in the network.

Let us consider a single-cell multi-user massive MIMO system, wherein the single base station (BS) is equipped with Nt antennas and serves a plurality of K user equipment (UE) devices.

For simplification reasons, we consider K < Nt, where no user scheduling is performed. The single-cell multi-user massive MIMO system operates in a frequency-division duplexing (FDD) mode such that no channel reciprocity holds for a downlink CSI acquisition. The UE devices are assumed to be geographically close to each other such that they can communicate with each other by exploiting another air interface that does not interfere with the communication between the BS and the UE devices. It is clear, however, that the invention is not limited to the assumption a bove and that the principles described below apply to a more general system.

Let us denote the downlink channel of the UE device k (UEk) as h _k , where h _k 6 C ^Nt . The received signal of U Ek is given by the following equation (1): where Ik denotes the (deterministic) la rge-scale cha nnel gain of U Ek, Sk is the symbol for UEk, Wk ε C ^Nt is the precoder chosen by the U E device k (U Ek), rik ~ CN(0, 1) is the additive Gaussian noise, f the total transmission power and K is the number of U E devices served by the BS.

In addition, the channel covariance Rk = E {h _k h _k } satisfies tr { k} = N _t and the power allocation amongst the UE devices is considered equal.

A perfect CSI hk is assumed to be availa ble at each U Ek, but the knowledge of the global CSI requires an explicit signaling over a D2D communication between the U E devices.

Although the a bove UE devices are assumed to be geographically close to each other, it should be noted that the a bove simplified model of the single-cell multi-user massive M I MO system can also be extended to UE devices being distributed all over the area within the cell coverage. So, a two-layer precoding structure with user grouping may be used to justify the capa bility of inter-communication between the plurality of U E devices. With user grouping, we can guarantee that the UE devices in the same group can communicate with each other. With a two-layer precoding structure, the BS can process each group separately and the single-cell multi-user massive M I MO system degenerates to a single-user group case.

Moreover, the UE devices may share or exchange their respective CSI with each other in a point-to- point signaling, which is formally specified using the notion of tunnel, rather than in a one-to-many broadcast signaling. Thus, a tunnel, which is directed from a UE device k (U Ek) towards another U E device j (UE _j ) and is denoted by k -> j, is a point-to-point communication link for the U E device k (UEk) to transmit its message towards the U E device j (U E _j ). It should be noted that the data rate between the tunnels k -> j and j -> k can be different, those both tunnels being generally asymmetric. Using tunnels for D2D CSI exchange allows to significantly reduce the complexity of the cha nnel quantization at the UE devices. By considering that specific codebooks are designed for each tunnel, a UE device k (UEk) can, through the tu nnel k -> j, transmit a small amount of message dedicated to the U E device j (U E _j ) using a relatively small codebook Ckj. Then, UE _j can use the codebook Ckj to recover the respective message transmitted from UEk. It should be noted that the size of the codebook Ckj is small with respect to the size of the codebook Ck obtained in a one-to-many broadcast signaling beca use the codebook size scales exponentially to the num ber of bits a nd it only needs to capture the statistical information of the two UE devices k and j (U Ek, UE _j ) and not the statistical information between the U E device k (U Ek) and all the other UE devices. Furthermore, for each U E device j (U E _j ), the set of codebooks {CijJi i _j when in the point-to-point signaling is stored but not the set of codebooks {Ci}, ^ when in the one-to-many broadcast signaling. In other words, only the set of codebooks {Cij}, _{≠ j} when in the point-to-point signaling is stored.

In addition to the channel codebook Ckj on tunnel k -> j, which is a codebook used to quantize the channel of the U E device k (UEk), the precoder codebook C is a codebook that stores the precoding vectors, namely the precoders. Like each U E device, the UE device k (UEk) will select a precoder Wk from its respective precoder codebook C and will feed back the selected precoder Wk towards the BS. The proposed distributive D2D ena bled precoding consists of two steps: a CSI exchange and an individual precoding.

For each pair (k, j) of UE devices (UEk, UE _j ), the step of CSI exchange consists, for the U E device k (UEk), of quantizing its channel hk into and transmitting it towards the UE device j (UE _j ) through the tunnel k -> j. It should be noted that the U E devices can also excha nge or share the CSI in a straightforward way through broadcasting.

The step of individual precoding consists for each UE device k (UEk) to choose the precoder Wk based

(k) (k) (k)

on the perfect CSI of its own channel hk and the quantized cross link CSI {h^ , h ₂ , h ₃ , ...} shared by the other U E devices. In pa rticular, the UE device k (UEk) chooses the precoder Wk from the precoder codebook C in order to maximize a signal-to-leakage-a nd-noise ratio (SLN ) through a SLN R precoding according to the following equation (2): where P is the total transmission power, Ik denotes the (deterministic) large-scale channel gain of UEk, and K is the number of UE devices served by the BS.

It should be noted that there is a strong connection between the SLNR precoding and a minimum mean-square error (MMSE) precoding, which is considered to achieve a good performance from low to high signal-to-noise ratio (SNR). However, the SLNR precoding has the further advantage to provide a straightforward way for individual precoding while achieving a good performance.

Fig. 1 shows a signaling illustrating a distributive D2D enabled precoding for a single-cell multi-user massive MIMO system 100 according to an embodiment of the present invention. For only illustrative purpose, the depicted system comprises two users, namely two UE devices, which are respectively denoted as UE1 and UE2, in addition to the single cell, which is denoted as BS. Thus, it should be readily understood that the global number of users can be more than two. The channel quantization can be performed using an interference subspace projection method. An interference subspace or overlapping signal subspace between a UE device and another UE device exists when the signal subspace of the UE device overlaps the signal subspace of the other UE device, as depicted in Fig. 2. In the case that the UE device k (UE _k ) shares the CSI with the UE device j (UEj), the UE device k (UE _k ) first computes its partial channel by projecting its own channel h _k of direct communication between it and the BS onto the interference subspace Uj of the UE device j (UEj) according to the following relationship (3): where U _j ( <≡ C ^{Nt M} J) is a semi-orthogonal matrix. The matrix U _j , may contain the dominant eigenvectors Mj of the covariance matrix Rj of UEj. Then, the UE device k (UE _k ) quantizes its partial channel , as shown in Fig. 3, using b _k j bits from the corresponding channel codebook C _kj of the CSI tunnel k -> j in order to obtain the quantized portion of CSI, which corresponds to the CSI on the interference subspace U _kj . So, we obtain the following relationships (4, 5): ^a k Vk ^v fe (4)

V _f e - arg max _veCk .

(5)

where = is the gain of the channel, which is assumed to be perfectly transmitted to the

UE device k (UEk) such that only the channel direction h ,0 ^' ) needs to be quantized.

Afterwards, the UE device k (U Ek) transmits ¾ towards the UE device j (UE _j ) over the D2D commu nication.

As regards the cha nnel and precoder codebooks, their design can be performed using the random vector quantization (RVQ) feed back mechanism.

In the case that the UE device k (U Ek) shares the CSI with the U E device j (UE _j ), the signal su bspace Uk of the U E device k (UEk) ca n correspond to the dominant eigenvector of the cha nnel covariance matrix k. The interference cha nnel covariance matrix Rk _j from the U E device k (U Ek) to the U E device j (UE _j ) on the CSI tunnel k -> j is given by the following relationship (6):

The channel codebook is then designed to be adaptive to the interference channel covariance matrix R^ according to the following relationship (7): where ξ, is a random vector that has a standard complex Gaussian distribution and follows the distribution C (0, 1).

In a first em bodiment, the precoder codebook C can be designed to be adaptive to the channel covariance Rk of the UE device k (UEk) according to the following relationship (8): where ξ,, with i = 1, 2, 2 , is a random vector that has a standard complex Gaussian distribution and follows the distribution CN(0, 1), and Bf is the num ber of bits per UE device to feed back the precoder to the BS. Alternatively, the precoder codebook C _k can be designed to be adaptive to the channel covariance ∑¾ ¾ of all the U E devices according to the following relationship (9): where ξ,, with i = 1, 2, 2 ^Bf , is a random vector that has a standard complex Gaussian distribution and follows the distribution CN(0, 1), Bf is the number of bits per UE device to feed back the precoder to the BS and a llows to normalize the vector f, to have a unit norm.

It should be noted that in the case that the interference channel covariance matrix Rkj and the channel covariance Rk is rank deficient, the dimension of the codewords in the channel codebook Ckj within the point-to-point signaling and in the channel codebook Ck within the one-to-many broadcast signaling can be reduced by projecting them onto the dominant su bspaces of Rkj and k, respectively.

In order to have an efficient CSI exchange, we address the problem of how to allocate D2D commu nication resources. Thus, we consider that Bd bits per time frame are shared amongst the U E devices for the CSI exchange. Such a resource is to be partitioned amongst all the CSI transmission tunnels wherein a smart partition can strongly improve the system performance. In particular, we seek to minimize the total interference leakage. The D2D bit allocation problem for the CSI exchange can be formu lated by the following relationship (10): min∑ _{= 1} ∑ _j≠k I _kj (10) su bject to: ∑£ ₌₁ ∑ _j≠k log ₂ \ C _kj \ = B _d (11) , 2

where / _fej = pl _} \h" w _k \ represents the interference power at the U E device j due the signal intended for the UE device k, p = P/K represents the power allocation on each UE device k and Bd is the total capacity in bits for the D2D CSI sharing.

It should be noted that minimizing the interference according to the relationship (10) is asymptotically optimal in high SNR for a throughput maximization.

The case is now considered of a high SNR stating that the transmit power P is sufficiently high and thereby that the system operates in the interference limited region; and of a high resolution stating that the number of bits for D2D channel quantization is sufficiently large. An explicit derivation of an approximate lower bound of the interference leakage I _k j and an explicit formulation of the D2D bit allocation problem for the CSI exchange can be given through the following relationship (12) for explicative purposes: tr{R _kj ] ₂ -M _]k -1

min _s [b _kj ≥0 ∑fc = l∑y j≠k (12)

tr{R _k ] subject to: ∑ _f e=i∑ _j ≠fc b _k j— (13) where by is the size in bits of the channel codebook Cy, M _k j represents the number of strictly positive eigenvalues, and ||ff _j fe || _G is defined as the geometric mean of the eigenvalues of Rj _k .

Knowing that the D2D bit allocation problem is convex, an optimal bit allocation to minimize the approximated interference leakage can be derived from the relationships (12) and (13) according to the following relationship (14): h _{+ log2} - ^2

b* _k = (M _jk - 1) (14)

M where a _jfe = b is a parameter chosen to satisfy∑ _{k= 1} ∑j _≠k b _k j = B _d , and

is a projection operator defined as = max{0, x}. It should be noted that the parameter b can be found using a bisection search, which converges very fast.

The relationship (14) suggests that the optimal bit allocation for the D2D CSI exchange on each tunnel k -> j varies according to the dimension Mj _k of the interference subspace between the UE devices k and j (UE _k , UE _j ) as well as the eigenvalues of the covariance Rj _k of the overlapping subspace.

Thus, the invention has the advantage to save D2D signaling. For illustrative purposes, let us consider, for example, that the signal subspaces of a first UE device (UE1) and a second UE device (UE2) are only slightly overlapping due to small angular spreads (θι, Θ ₂ ) and large distance between each of both UE devices (UEl, UE2), as depicted in Fig. 4 showing a distributive D2D enabled precoding for a single-cell two-user massive MIMO system 200 according to an embodiment of the present invention. The teachings of the invention allow to only quantize a small portion of CSI that might interfere the other. In another example, let us consider that the second UE device (UE2) suffers from a much larger pathloss than the first UE device (UEl). That might be the case when UE2 is indoor and the signal is blocked, or when UEl is in an interference limited region and UE2 is in a noise limited region. In those scenarios, the invention allows to adaptively scale a much larger channel codebook C21 for UE2 and a smaller one Cu for UEl. Although the present invention has been described with reference to a single cell (BS) serving a plurality of users (i.e., UE devices), as shown in Fig. 1, the invention can be extended to a plurality of cells (BSs) serving a plurality of users (i.e., UE devices), as shown in the distributive D2D enabled precoding for a multi-cell multi-user massive MIMO system 300 of Fig. 5 wherein, for illustrative purpose, only two base stations (BS1, BS2) and two cell edge users (UEl, UE2) have been depicted and where h is the channel of direct communication between UEl and BS1 (hll), UEl and BS2 (hl2), UE2 and BS1 (h21) and UE2 and BS2 (h22), and h is the quantized channel of the channel h transmitted from UEl towards UE2 (hu) and from UE2 towards UEl (R21). In such a multi-cell multiuser massive MIMO system where a D2D communication is established for the cell edge users (UEl, UE2), the distributed precoding of the invention can be performed to mitigate the inter-cell interference without real-time backhaul signaling between the BSs (BS1, BS2). Thereby, the CSI sharing amongst the users from the adjacent cells can be much more efficient and more users can be supported under limited D2D communication capacity in the multiple access channel (MAC), the D2D communication being performed over MAC shared by all the users. Fig. 6 shows a schematic flow diagram for adaptively sharing CSI in a MIMO system over a D2D communication.

Fig. 7 shows a schematic flow diagram for adaptively setting a distributed precoding in a MIMO system over a D2D communication.

In summary, the present invention relates to a user equipment device and method for adaptively sharing channel state information and setting a distributed precoding in a multi-input multi-output system over a device-to-device communication. A plurality of user equipment devices shares the channel state information statistics with each other and cooperatively design individual channel codebooks and precoder codebooks for the device-to-device channel state information exchange. A respective precoder can then be computed and selected from the respective precoder codebook in order to maximize the signal-to-leakage-and-noise ratio. Only the portion of channel state information lying in the overlapping signal subspace is shared with each user equipment device and the shared portion of channel state information is quantized up to a resolution adaptive to the global channel state information statistics and the device-to-device signaling capacity.

While the invention has been illustrated and described in detail in the drawings and the foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments. From reading the present disclosure, other modifications will be apparent to a person skilled in the art. Such modifications may involve other features which are already known in the art and which may be used instead of or in addition to features already described herein. In particular, the transmission system is not restricted to an optical transmission system. Rather, the present invention can be applied to any wired or wireless transmission system. The receiver device of the proposed system can be implemented in discrete hardware or based on software routines for controlling signal processors at the reception side.

The invention has been described in conjunction with various embodiments herein. However, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Although the present invention has been described with reference to specific features and embodiments thereof, it is evident that various modifications and combinations can be made thereto without departing from the spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded simply as an illustration of the invention as defined by the appended claims, and are contemplated to cover any and all modifications, variations, combinations or equivalents that fall within the scope of the present invention.