The invention relates to wireless communication systems, and more particularly to the pre- coding of data to be transmitted in a multiuser multi-input multi-output (MU-MIMO) wireless communication system.

In MU-MIMO downlink transmissions, multiple user equipments are served at the same time on the same transmission channel. The suppression of co-channel interference can be achieved by using properly configured pre-coders at the transmitter side, in other words by choosing carefully beamforming vectors, or pre-coding weights, before the transmission of the signal to multiple user equipments.

Several methods exist currently for choosing such beamforming vectors. For instance, the beamforming vectors are chosen optimally in order to maximize the output signal to interference plus noise ratio (SINR) for each user equipment.

It is known from PCT patent application PCT/CN 2011/071707, filed in the name of the assignee, a rate-maximizing (RAM) beamforming method. Such a method iteratively adjusts the beamforming vector associated with a user equipment to maximize the sum data rate of the communication system comprising said user equipment. This is achieved by tuning the user equipment transmission parameters to maximizing the data rate for said user equipment while minimizing the degradation in throughput for the other user equipments of the communication system.

One drawback of this method is that it needs perfect channel state information to compute the beamforming vectors. Hence, the performance of said method deteriorates if limited channel feedback is used and perfect channel state information is , therefore, not available.

Therefore, there is a need for an alternative pre-coding scheme which overcomes the drawbacks of the above-mentioned method and can offer improved performances in terms of data rate sum throughput without increasing excessively the complexity of the system.

The object of the present invention is to propose a sum-throughput maximizing beamforming approach for the pre-coding scheme in MIMO systems.

A first object of the invention is a method for transmitting a signal carrying data from a network equipment to a user equipment in a multiple input-multiple output communication system, said method comprising the steps of:

Receiving from the user equipment information related to a covariance matrix associated with a vector transmission channel established between the user equipment and the network equipment, Re-constructing the covariance matrix associated with a vector transmission channel established between the user equipment and the network equipment , using said information

Determining a beamforming vector associated with the vector transmission channel using at least the covariance matrix associated to th e vector transmission channel, the beamforming vector maximizing the difference between the sum data rate throughput achieved by the user equipment and at least one other user equipment and the sum data rate throughput achieved by the other user equipment without the user equipment,

- Computing the signal carrying data to be transmitted by pre-coding the data in accordance with the determined beamforming vector associated with the vector transmission channel.

In such a transmitting method, the network equipment receives, for each user equipment belonging to the M IMO system, information related to a covariance matrix associated to a vector transmission channel established between the network equipment and each user equipment of the communication system.

A vector transmission channel comprises all the transmission channels established between each radio transceivers of the network equipment and each radio transceivers of the user equipment. For example, if the network equipment has four transmit antennas and the user equipment has two receive antennas, then the vector transmission channel established between the network equipment and the user equipment comprises eight transmission channels.

Such a method enables the calculation of the beamforming vectors with limited vector transmission channel feedback information. The performance of such a method is not impacted by the quality of the feedback information obtained, or its availability as it is the case in the prior art.

According to one characteristic of the transmission method of the invention, the beamforming vector associated with the vector transmission channel is determined for each other user equipment.

The method of the invention is an iterative method to compute a beamforming vector for a given user equipment of the communication system, in which the impact of every user equipment of the communication system on the vector transmission channel is taken into account.

An other object of the invention is a method of communication between a user equipment and a network equipment in a multiple input-multiple output communication system, said method comprising the steps of: Determining at least an eigen-vector and an eigen-value representing a covariance matrix associated to a vector transmission channel established between the user equipment and the network equipment, by computing an eigen- decomposition of the covariance matrix associated to the vector transmission channel,

Selecting from a predetermined codebook, a codeword approximating a subspace spanned by the eigen-vector,

Transmitting the codewords and eigen-values associated to the covariance matrix for the vector transmission channel to the network equipment.

The communication method of the invention proposes to use codebook based feedback back scheme to transmit information related to the covariance matrix associated to a vector transmission channel established between a network equipment and a user equipment.

Another object of the invention is a network equipment transmitting a signal carrying data to a user equipment in a multiple input-multiple output communication system , said network equipment comprising :

Means for receiving from the user equipment information related to a covariance matrix associated with a vector transmission channel established between the user equipment and the network equipment,

Means for re-constructing the covariance matrix associated with a vector transmission channel established between the user equipment and the network equipment, using said information ,

Means for determining a beamforming vector associated with the vector transmission channel using at least the covariance matrix associated with the vector transmission channel, the beamforming vector maximizing the difference between the sum data rate throughput achieved by the user equipment and at least an other user equipment and the sum data rate throughput achieved by the other user equipment without the user equipment,

Means for computing the signal carrying data to be transmitted by pre-coding the data in accordance with the determined beamforming vector associated with the vector transmission channel.

Such a network equipment is, for example an eNodeB.

Still another object of the invention is a user equipment communicating with a network equipment in a multiple input-multiple output communication system , said user equipment comprising :

- Means for determining at least an eigen-vector and an eigen-value representing a covariance matrix associated to a vector transmission channel established between the user equipment and the network equipment, by computing an eigen- decomposition of the covariance matrix associated to the vector transmission channel,

Means for selecting from a predetermined codebook, a codeword approximating a subspace spanned by the eigen-vector,

Means for transmitting the codewords and eigen-values associated to the covariance matrix for the vector transmission channel to the network equipment.

Such a user equipment is for example a mobile phone.

A multiple input-multiple output communication system comprising a network equipment transmitting a signal carrying data to a user equipment, said network equipment comprising :

Means for receiving from the user equipment information related to a covariance matrix associated with a vector transmission channel established between the user equipment and the network equipment,

- Means for re-constructing the covariance matrix associated with a vector transmission channel established between the user equipment and the network equipment, using said information,

Means for determining a beamforming vector associated with the vector transmission channel using at least the covariance matrix associated with the vector transmission channel, the beamforming vector maximizing the difference between the sum data rate throughput achieved by the user equipment and at least an other user equipment and the sum data rate throughput achieved by the other user equipment without the user equipment,

Means for computing the signal carrying data to be transmitted by p re-coding the data in accordance with the determined beamforming vector associated with the vector transmission channel ,

and at least a user equipment communicating with the network equipment, said user equipment comprising :

Means for determining at least an eigen-vector and an eigen-value representing the covariance matrix associated with the vector transmission channel, by computing an eigen-decomposition of the covariance matrix associated to the vector transmission channel,

Means for selecting from a predetermined codebook, a codeword approximating a subspace spanned by the eigen-vector, Means for transmitting the codewords and eigen-values associated to the covariance matrix for the vector transmission channel to the network equipment.

Finally, one object of the invention concerns computer programs, in particular computer programs on or in an information medium or memory, suitable for implementing the method transmitting a signal carrying data and the communication method object of the invention. These programs can use any programming language, and be in the form of source code, binary code, or of code intermediate between source code and object code such as in a partially compiled form, or in any other desirable form for implementing the methods according to the invention.

The information medium may be any entity or device capable of storing the program. For example, the medium can comprise a storage means, such as a ROM, for example a CD ROM or a microelectronic circuit ROM, or else a magnetic recording means, for example a diskette (floppy disk) or a hard disk.

Moreover, the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means. The program according to the invention may in particular be downloaded from a network of Internet type.

The present system and method are explained in further detail, and by way of example, with reference to the accompanying drawings wherein:

Figure 1 represents a simplified wireless communication system which illustrates the principle of the invention,

Figure 2 represents the vector transmission channel established between a network equipment and a user equipment,

Figure 3 represents block diagram of the iterative algorithm to determine the beamforming vectors of the invention,

Figure 4 represents a network equipment capable of running the method of transmission of the invention,

Figure 5 represents a user equipment capable of running the communication method of the invention.

Figure 1 represents a simplified wireless communication system which illustrates the principle of the invention.

The upper part of figure 1 shows the cell of a wireless multiuser-multiple input multiple output MU-MIMO communication system with only two co-channel user equipments u-i and u ₂ , which achieve individual data rate throughputs r _l/k and r _{2/ k} , respectively. Here, the back slash in the subscript of these data rate throughputs parameters denotes that these data rate are achieved without the presence of any third user equipment u _k . The sum data rate throughput for these two user equipments is thus U _llk — r _llk + r _2lk in such a cell. When a new user equipment u _k comes into consideration for this cell, as shown in the lower part of figure 1 , the data rate throughputs of the different users equipments within the cell are modified. The new data rate throughputs for user equipments u1 and u2 are respectively designated by r _x and r ₂ , and user equipment u _k achieves itself a data rate throughput r _k . The sum data rate throughput of the user equipments in this situation becomes U— r _k + r _x + r ₂ in this cell.

The present invention seeks to maximize the sum throughput gain of all three user equipments, when compared to the previous situation with only two user equipments, which is given by the following equation: (1 ) S = U-U _lk = r _k + (r _l -r _llk )+ (r ₂ -r _2lk )

In other words, in this equation (1 ), the first part r _k is the individual data rate throughput, or gain realized by the third user equipment u _k and the second part, ( — r _l/k )+ (r ₂ —r _{2/ k} ) , is the gain caused to co-channel user equipments u-i and u ₂ by the introduction of user equipment u _k in the cell.

Thus, the beamforming vector optimization, for user equipment u _k , consists of maximizing the sum of these two parts such that the total sum data rate throughput is maximized.

Such a method of transmitting a signal carrying data is performed in a multiple-input multiple-output (MIMO) communication system involving a plurality of K user equipments u-i , ...,u _k , . . . , UK having a plurality of receiving antennas and a network equipment, such as an eNodeB, having a plurality of transmitting antennas. The K user equipments define thus a user equipment set L {k} .

This method comprises first a beamforming determination stage wherein beamforming vector(s) w _k are determined respectively for one or more user equipment(s) belonging to this user equipment set L ^j {k} . Such a beamforming vector w _k is associated with a vector transmission channel VTC established between the network equipment and the user equipment u _k . Said vector transmission channel VTC comprises all the transmission channels C, established between each transmitting antennas N _t of the network equipment eNodeB and each receiving antennas N _r of the user equipment u _k . For example, if the network equipment eNodeB has four transmit antennas N _t and the user equipment u _k has two receive antennas N _r , as represented on figure 2, then the vector transmission channel VTC established between the network equipment eNodeB and the user equipment u _k comprises eight transmission channels Q.

In particular, the determination of the beamforming vector w _k for a user equipment u _k of the set L {k) comprises the step of computing the beamforming vector w _k which maximizes the sum throughput gain S corresponding to the difference between, on the one hand, the sum data rate throughput U achieved by this user equipment u _k and one or more other user equipment(s) of the user equipment set L {k} _, and, on the other hand, the sum data rate throughput achieved by these one or more other user equipments of the user equipment set L vj {k} without said user equipment u _k .

Hence, to come back to the example of the figure 1 , the beamforming vector w _k for user equipment u _k is thus the beamforming vector which maximizes the equation:

S = U-U _lk = r _k + (r _l -r _Vk )+ (r ₂ -r _2lk ) .

Once the beamforming vector(s) have been determined, the data to be transmitted by the network equipment are pre-coded in accordance with the beamforming vector(s) which have been determined.

Finally, once the data have been pre-coded, a signal carrying on the pre-coded data is transmitted from the plurality of transmitting antennas of the network equipment towards the user equipments u-|-u _K .

The maximization of the sum throughput gain S can be reformulated as follows using a covariance matrix associated with a vector transmission channel.

In such a multi-user MIMO system involving a user equipment comprising a plurality of transmitting antennas and user equipments u-i ,...,u _k each having a a plurality of receiving antennas, the received signal for user u _k can be expressed by the following receiving vector y _k :

(2) y* = Η _Λ + Η,∑ _Χ/ + ιι,

l≠k

where : - n^. ~ CN(0, σ ² Ι) is the Gaussian noise vector with white covariance matrix, with σ ² being the noise variance normalized with respect to the transmit power; x _k = , χ ₂ , · · · , χ _Ν ] ^r is the transmitted waveform vector with N _t being the number of transmit antennas; and

H _k is the ( N _r x N _f ) vector transmission channel matrix, with N _r being the number of receive antennas. Assuming that transmit power is uniformly distributed among the user equipments, the transmitted waveform can be expressed as:

(3) ¾ = w _t ¾ where w _t is the normalized beamforming vector for the k-th user equipment, i.e., fw I ² = 1 , and

I 1 2

s _k is the transmitted data symbol associated with this k-th user such that E s^. = 1 . The Covariance Matrix R _k of the interferences -plus-noise affecting user equipment u _k can be then defined as follows:

Here, a beamforming user equipment set L of user equipments is defined which comprises user equipments of L u {k} which are properly configured, i.e. which are already associated with a beamforming vector.

When a new user equipment u _k of L {k) , which does not belong to such a beamforming user equipments set ( u _k <£ L ), is taken into consideration, as mentioned before, the sum data rate throughput achieved, on one hand, by the user equipments of the beamforming user set L {k) and the user equipment u _k (in other words the sum data rate throughput for L {k} ), and the sum data rate throughput achieved, on the other hand, by the user equipments of the beamforming user equipment set L without the user equipment u _k (i.e. the sum data rate throughput for L), are respectively defined as follows:

(5) U = r _{k +} ∑ _ri

leL (6) U _{/ k} =∑i k

leL

Where: - r _{1/ k} is the data rate throughput (i.e. the achievable capacity) of user equipment U| without the presence of user equipment u _k ; and

Γ) is the data rate for user equipment U| .

Considering equations (5) and (6), the beamforming vector w _k for user equipment u _k is obtained by computing the beamforming vector W ^opt which maximizes the sum data rate throughput gain introduced by the user equipment u _k , in other words which solves the following equation:

(7) y ^pt = arg

An expression of the data rate for user equipment u _k is readily obtained by employing the Shannon capacity for the vector transmission channel of user equipment u _k as :

r _k = log(l + SINR _k ) (8) where SNIR _k is the signal plus interference to noise ration for user equipment u _k . The signal plus interference to noise ration for user equipment u _k is given by SINRt (9)

l≠k l≠k where R .

In equation (9), the value of the signal plus interference to noise ration for user equipment u _k is approximated with pre-processing values, such as the signal plus interference to noise ratio SINR of received signals at user equipment prior to any pre-processing, i.e. calculation of a beamforming vector. The degradation in the transmission channel capacity of user equipment / caused by user equipment k is given by :

SINR, - SINR _l

1 - I l k

'/ 'I l k dog

l + SlNR _I/k j dog SlNR _l/k ^w i R/ ^w i (10)

l + SlNR _l/k

SINR U, k (1 1 )

(l + SINR,,, )!,

In equation (10), the expression 7 _; = N _r a ² + y,w^R _m presents the interference-plus-

noise caused to user equipment /.

Upon combining equations (8) and (10), the following expression of the net gain in sum throughput NGST introduced by user equipment k in the cell is obtained :

where μ _ι = κ _ι Ι _]ί SINR„k - (13)

(l + SINR _l/k )l, In equation (12), the two approximations are satisfied by assuming that Κ _/ wf R w* « 1 .

Beamforming vector for new user equipment u _k is then determined to maximize the net gain in sum throughput NGST introduced by user equipment k as follows :

(14)

Hence, the beamforming vector w^ that maximize the net gain in sum throughput NGST introduced by user equipment k is shown to be the generalized eigenvector corresponding to the maximum eigen-value of matrixes I _k I _Nt + ^ / _/ R _/ ^A and I _{k Ni} + R _¾ ■ Since the matrix l≠k

I _k \ _Nt + ^ _/ u _/ R _/ ^A is invertible, the generalized eigen-value problem is reduced down to a standard l≠k

eigen-value problem.

As a result, the optimal beamforming vector for user equipment k obtained in solving this eigen-value problem is given by: wV ^Fl oc max eigenvector! (¾ + R* ) (15)

l≠k where max eigenvecto r (τ) denotes the eigenvector corresponding to the largest eigen-value of Z _> where Z refers to a generic Hermitian matrix. It is observed from equation (15) that user equipment beamforming weights depend on user equipment vector transmission channel covariance matrixes, rather than on explicit channel state information CSI as it is the case in prior art. This makes employment of codebook-based channel feedback feasible.

Thus the invention also concerns a codebook-based channel feedback method allowing the transmission of information related to the covariance matrix of the vector transmission channel from the user equipment u _k to the network equipment.

A crucial enabler of the proposed MU-MIMO beamforming is the codebook-based feedback scheme to provide accurate channel state information CSI, which, in the invention, is the vector transmission channel covariance. Assuming that N _t > N _r eigen-decomposition of vector transmission channel covariance is be expressed as : R* = V _t ∑ _t V = fvi V, ⁰ ] (16)

where ∑[ e C ^{Nr xNr} is a diagonal matrix containing non-zero eigen-values of the covariance matrix R* .

Then, a codeword Ψ = {ψ _ί }, ψ _ί e C ^N ' ^xNr is selected from a codebook in order to approximate the subspace spanned by the vector ..

In a first embodiment of the invention, the codeword selected to approximate the subspace spanned by the vector is :

In this first embodiment, the codeword choosen is the codeword the codework having the minimum chordal distance to the subspace spanned by .

In a second embodiment of the invention, the codeword selected to approximate the subspace spanned by the vector is

Once the network equipment receives all channel feedback information, it conducts the iterative algorithm to determine the beamforming vectors of user equipments object of the invention.

Figure 3 represents a block diagram of the iterative algorithm to determine the beamforming vectors of the invention.

In a step E1 , the network equipment receives least an eigen-vector and an eigen-value representing the covariance matrix associated to the vector transmission channel established between the user equipment and the network equipment and resulting from the eigen- decomposition of the covariance matrix.

In a step E2, the network equipment re-constructs the vector transmission channel covariance as = - -K using the eigen-vector and an eigen-value resulting from the eigen-decomposition, where K = L {k)

In a step E3, the network e uipment initializes a user equipment beamforming vector :

In step E4, the network equipment computes the interference-plus-noise for user equipments u _k :

In a step E5 a first iteration index n is set to 1 . This first iteration index n is an integer comprise between 1 , 2, , N. The greater the total number of iterations N the more optimized the beamforming vector.

In a step E6 a second iteration index A- is set to 1 . This first iteration index k is an integer comprise between 1 , 2, , K, K being the total number of user equipments of the cell.

During a step E7, the network equipment determines if the index k of the current user equipment is higher or lower than the index / of the already processed user equipments.

If k>\, the network equipment computes, in a step E8, the signal plus interference ratio of user U| excluding the interference caused by user equipment u^ on the other user equipments of the cell using a first formula :

SINR _l/k =

If l>k, the network equipment computes, in a step E9, the signal plus interference ratio excluding the interference caused by user equipment u _k on the other user equipments of the cell using a second formula :

SINR ^■

During a step E10, the network equipment computes μ, = -< —— f— for /≠k

(l + SINRi _/k )Ii

Knowing the value μ, from step E10, the network equipment computes the beamforming vector for user equipment u _k as expressed in equation (15) in a step E1 1 : oc max eigenvector! I _k l _Ni +2 R?

l≠k

In a step E12, the network equipment updates user equipment interference value using the beamforming vector in step E1 1 :

This updated value of the user equipment interference is destined to be used in the following iteration. In a step E13, the second iteration index k \s set to k+1. When the second iteration index k is equal to K, the first iteration index n is set to n +1 in a step E14. Steps E5 to E14 are executed until the first iteration index n is equal to N.

Figure 4 represents a network equipment capable of running the method of transmission of the invention.

The network equipment comprises means for receiving 10 information related to a covariance matrix associated with a vector transmission channel established between the user equi pment and the network equipment.

The information received comprises at least an eigen-vector and an eigen-value representing the covariance matrix associated to the vector transmission channel established between a user equipment and the network equipment and resulting from the eigen- decomposition of the covariance matrix.

The network equipment comprises means for re-constructing 1 1 the vector transmission channel covariance as = - -K using the eigen-vector and an eigen-value resulting from the eigen-decomposition, where K = L vj {k}

The means for re-constructing 1 1 the vector transmission channel are connected to the means for receiving information 10.

The network equipment comprises, connected to the means of re-constructing 1 1 , means for initializing 12 a user equipment beamforming vector : w^ ⁰ -* oc max eigenvector (R^ \ k = 1,2, - K

The network equipment comprises, connected to the means for initializing 12, means for computing 13 the interference-plus-noise for user equipments u _k : = N _r a ² +∑(wL ⁰⁾ f wL ⁰⁾ , * = 1,2,-*

m≠k

The network equipment comprises means 14 for incrementing a first iteration index n. This first iteration index n is an integer comprise between 1 , 2, , N. The greater the total number of iterations N the more optimized the beamforming vector.

The network equipment comprises means 15 for incrementing a second iteration index k.

This first iteration index k is an integer comprise between 1 , 2, , K, K being the total number of user equipments of the cell.

The network equipment comprises means for determining 16 if the index k of the current user equipment is higher or lower than the index / of the already processed user equipments. The means for determining 16 are connected to the means for incrementing an iteration index 14 and 15. The network equipment comprises, connected to the means for determining 16, means for computing 17 the signal plus interference ratio excluding the interference caused by user equipment u _k on the other user equipments of the cell.

The user equipment comprises, connected to the means for computing 17, means for computing 18 _μ! :

The network equipment comprises, connected to the means for computing 18, means for computing 19 the beamforming vector for user equipment u _k as expressed in equation (15) : oc max eigenvector! I _k l _Ni +2 R?

l≠k

The network equipment comprises, connected to the means for computing 19, means for updating 20 user equipment interference value using the beamforming vector : A (η) > h M ί (η-\) _Ώ ίι (n-\) '≠k

This updated value of the user equipment interference is destined to be used in the following iteration.

The user equipment comprises, connected the means for updating 20, means for computing 21 the signal carrying data to be transmitted by pre-coding the data in accordance with the determined beamforming vector associated with the vector transmission channel .

Figure 5 represents a user equipment capable of running the communication method of the invention.

The user equipment comprises means for running an eigen-decomposition 100 of vector transmission channel covariance. Assuming that N _t > N _r this eigen-decomposition is be expressed as : where ∑{ e C ^{Nr xNr} is a diagonal matrix containing non-zero eigen-values of the covariance matrix .

The user equipment comprises, connected to the means running an eigen-decomposition 100, means for selecting 1 10 a codeword Ψ = {ψ _ι ,}, ψ _{ι :} e C ^N ' ^Nr from a codebook in order to approximate the subspace spanned by the vector . Such a codebook is store in a data base DB connected to the means for selecting a codeword 1 10. The user equipment comprises, connected to the means for selecting a codeword 1 10, means for transmitting 120 the codewords and eigen-values associated to the covariance matrix for the vector transmission channel to the network equipment.