Abstract:
A method according to the present invention is for selecting User Equipment (UE) for scheduling/precoding within the coverage area of a communications node having a predefined codebook. The method includes: receiving at the communications node feedback information from each of the UEs within the coverage area of the communications node wherein the feedback information includes at least one precoder matrix indicator (PMI); generating at the communications node a precoder matrix based on the reported precoder matrix indicator from each UE; determining at the communications node correlation values for each UE in the coverage utilizing the precoder matrix; identifying a pair of UEs having minimum correlation values; and selecting the identified UEs for scheduling/precoding if the minimum correlation value is less than or equal to a threshold value.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a national stage application of International Application No. PCT/JP2013/075604 entitled “Method for Improving Transmission Capacity in a DL MU-MIMO Communications System,” filed on Sep. 13, 2013, which claims the benefit of priority from Australian Patent Application 2012904070, filed on Sep. 18, 2012, the disclosures of which are incorporated herein in their entirety by reference thereto. 
     TECHNICAL FIELD 
     The present invention relates methods for improving transmission capacity in a communications system. In particular although not exclusively the present invention relates to methods for enhancing transmission capacity in MU-MIMO based Communication Systems. 
     BACKGROUND ART 
     MIMO technology has attracted attention in wireless communications as it offers significant increase in data throughput and link range without the need for additional bandwidth or increased transmit power. This increase in throughput is achieved by spreading the same total transmit power over the antennas to achieve an array gain that improves the spectral efficiency (more bits per second per hertz of bandwidth) or to achieve a diversity gain that improves the link reliability (reduced fading). Because of these properties, MIMO is an important part of modern wireless communication standards such as IEEE 802.11n (WiFi), HSPA+, 4G, 3GPP Long Term Evolution (LTE), LTE-Advanced (LTE-A), WiMAX, etc. 
     Multi-user MIMO or MU-MIMO is an enhanced form of MIMO technology that is gaining acceptance. MU-MIMO enables multiple independent radio terminals to access a system enhancing the communication capabilities of each individual terminal. MU-MIMO exploits the maximum system capacity by scheduling multiple users to be able to simultaneously access the same channel using the spatial degrees of freedom offered by MIMO. 
     SUMMARY OF INVENTION 
     Technical Problem 
     A general MU-MIMO system  100  is shown in  FIG. 1 . As shown the transmitter  101  transmits data to different receivers  102 ,  103  on the same time-frequency from multiple transmit antennas. To minimise interference between receivers  102 ,  103 , the transmitter creates transmission beams through pre-coding. At the receiving site, the receivers  102 ,  103  use post-coding (decoding) to take its data. Pre-coding is very much depended on the channel status. Mathematically, a MU-MIMO system is described as follows: 
                     y   ⁡     (   i   )       =         H   ⁡     (   i   )       ⁢     V   ⁡     (   i   )       ⁢     x   ⁡     (   i   )         +       ∑       k   =   1     ,     k   ≠   i         N   UE       ⁢           ⁢       H   ⁡     (   i   )       ⁢     V   ⁡     (   k   )       ⁢     x   ⁡     (   k   )           +     n   ⁡     (   i   )                 (   1   )               
where: y(i) is the received signal at the i-th user, x(i) is the data signal for the i-th user, H(i) is the channel matrix of the i-th user, V(i) is the precoder matrix of the i-th user and n(i) is the additive white Gaussian noise at the i-th user.
 
       FIG. 2  shows one possible transmission mechanism  200  utilised by the transmitter of  FIG. 1  to transmit data  201  to different receivers. To minimise inter-user interference, the receivers feedback their channel status information CSI  202  (which includes Precoder Matrix Indicator PMI) to the transmitter. In a system having 2-stage codebook of PMI, the i-th receiver reports 2 PMIs: PMI#1 and PMI#2 denoted by W(i) 1  and W(i) 2 . PMI#1 represents the long term or wideband channel and PMI#2 the short term or instant channel. 
     The transmitter then uses the reported PMIs to generate the precoder for the i-th receiver as:
 
 V ( i )= W ( i ) 1   ×W ( i ) 2   (2)
 
     While this form of pre-coding is effective it is not optimal. Additionally the use of such direct pre-coding can fail in some cases, particular where the receivers are too close to each other. 
     Clearly it would be to provide a method for pre-coding which mitigates the likelihood of failures. It would also be advantageous to provide a method for pre-coding which improves transmission capacity between transmitters and receivers. 
     Solution to Problem 
     Accordingly in one aspect of the present invention there is provided a method for selecting User Equipment (UE) for scheduling/precoding within the coverage area of a communications node having a predefined codebook said method including the steps of: 
     receiving at the communications node feedback information from each of the UEs within the coverage area of the communications node wherein the feedback information includes at least one precoder matrix indicator (PMI); 
     generating at the communications node a precoder matrix based on the reported precoder matrix indicator from each UE; 
     determining at the communications node correlation values for each UE in the coverage utilising the precoder matrix; 
     identifying a pair of UEs having minimum correlation values; and 
     selecting the identified UEs for scheduling/precoding if the minimum correlation value is less than or equal to a threshold value. 
     Suitably the predefined codebook is a 2-stage codebook and the feedback information includes a first precoder matrix indicator PMI 1  and second precoder matrix indicator PMI 2 . In such cases the procoder matrix W(i) for reported PMI 1  and PMI 2  from each UE may be generated by W(i)=W(i) 1 ×W(i) 2  where i=1, . . . , Φ. 
     Preferably the correlation values are given by C corr (i,j)=tr{[W H (i)W(j)] H [W H (i)W(j)]}, where i=1, . . . , Φ−1, j=i+1, . . . , Φ. The minimum correlation values may be determined by C corr (ĩ,{tilde over (j)})=min{C corr (i,j)}, for (ĩ,{tilde over (j)})=arg min{C corr (i,j)}. 
     In yet another aspect of the present invention there is provided a method of precoding data transmissions in a communications node servicing User Equipment within the node&#39;s coverage area the communications node having a predefined codebook servicing said method including the steps of: 
     selecting a User Equipment (UE) from within the coverage area as candidates for precoding wherein the selection of the UEs is based on correlation values calculated for each UE within the coverage area utilising a precoder matrix generated from precoder matrix indicators reported to the communications node by each UE; 
     determining correlation values for the selected UEs based on the reported precoder matrix indicator and Channel Matrix obtained from a fixed codebook of representative channel matrices; 
     selecting a Channel Matrix pair having the highest correlation values; and 
     generating precoders utilising the selected Channel Matrix pair. 
     Suitably the predefined codebook is a 2-stage codebook and the feedback information includes a first precoder matrix indicator PMI 1  and second precoder matrix indicator PMI 2 . In such cases the procoder matrix W(i) for reported PMI 1  and PMI 2  from each UE may be generated by W(i)=W(i) 1 ×W(i) 2  where i=1, . . . , Φ. 
     Preferably the correlation values are given by C corr (i,j)=tr{[W H (i)W(j)] H [W H (i)W(j)]}, where i=1, . . . , Φ−1, j=i+1, . . . , Φ. The minimum correlation values may be determined by C corr (ĩ,{tilde over (j)})=min{C corr (i,j)}, for (ĩ,{tilde over (j)})=arg min{C corr (i,j)}. 
     The fixed codebook of representative channel matrices may be generated from the long term PMI codebook and short term rank PMI codebook. Suitably the fixed codebook for Rank1, Ω RANK1  of representative channel matrices is generated from the long term PMI codebook and short term rank#1 PMI codebook. Preferably Ω RANK1  contains vectors of size N TX ×1. Suitably Rank 2 the fixed codebook Ω RANK2  of representative channel matrices (CM) is generated from the long term PMI codebook and short term rank#2 PMI codebook. Ω RANK2  contains matrices of size N TX ×N RX . 
     The fixed code books Ω RANK1  and Ω RANK2  may be utilised to identify the representative channels matrices. For Rank 2 the representative channel matrices may be given by 
     
       
         
           
             
               
                 
                   
                     
                       
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     For Rank1 a search may be conducted over Ω RANK1  for each of the i-th UE, from the PMI based matrix W(i) for N RX  vectors of size N TX ×1. These vectors may then utilised to form the channel matrix H(i) of size N RX ×N TX . 
     Suitably the correlation values for the selected UEs are calculated by C(i,n)=tr{[h(n) H W(i)] H [h(n) H W(i)]}, n=1, . . . , N vec    
     Preferably the step of selecting a Channel Matrix having the highest correlation includes sorting the correlation values C(i,n 1 )&gt;C(i,n 2 )&gt; . . . &gt;C(i,n N     vec   ) to identify the N RX  largest values corresponding to h(n 1 ), h(n 2 ), . . . , h(n N     RX   ) to form the channel matrix H(i)=[h(n 1 ), h(n 2 ), . . . , h(n N     RX   )] H . 
     The step of generating the precoders in one embodiment of the invention may include the steps of 
     a) initializing for all UEs the UE&#39;s post coder by setting G(i) (m=0) =J(i), i=1, . . . , N UE  where J(i) is RI(i)×N RX ; 
     b) calculating the precoder V(i) (m+1)  for all UEs using G(i) (m) ; 
     c) calculating post coder G(i) (m+1)  for all UEs using V(i) (m+1) ; 
     d) calculating 
             E   =       ∑     i   =   1       N   UE       ⁢           ⁢                G   ⁡     (   i   )         (     m   +   1     )       -       G   ⁡     (   i   )         (   m   )              F   2             
and comparing E to a convergence threshold ε;
 
e) setting m=m+1 if E≧ε and repeat steps b) to d) until
 
                   ∑     i   =   1       N   UE       ⁢           ⁢                G   ⁡     (   i   )         (     m   +   1     )       -       G   ⁡     (   i   )         (   m   )              F   2       &lt;   ɛ     ;         
and
 
f) outputting the precoder V(i) (m+1) .
 
     Suitably V(i) (m+1)  is calculated in accordance with 
               V   ⁡     (   i   )       =         [         ∑     j   =   1       N   UE       ⁢           ⁢         H   H     ⁡     (   j   )       ⁢       G   H     ⁡     (   j   )       ⁢     G   ⁡     (   j   )       ⁢     H   ⁡     (   j   )           +     υ   ⁢           ⁢   I       ]       -   1       ⁢       H   H     ⁡     (   i   )       ⁢       G   H     ⁡     (   i   )               
where υ is the Lagrange multiplier and G(i) (m+1)  is calculated in accordance with
 
               G   ⁡     (   i   )       =         V   H     ⁡     (   i   )       ⁢           H   H     ⁡     (   i   )       [         ∑     j   =   1       N   UE       ⁢           ⁢       H   ⁡     (   i   )       ⁢     V   ⁡     (   j   )       ⁢       V   H     ⁡     (   j   )       ⁢       H   H     ⁡     (   i   )           +         N   o     ⁡     (   i   )       ⁢   I       ]       -   1               
where N 0  is the noise variance.
 
     In some embodiments of the invention the Lagrange multiplier υ may be calculated according to the following steps: 
     a) calculating singular values λ i  of the decomposition 
                 U   ⁢           ⁢   Λ   ⁢           ⁢     U   H       =       ∑     i   =   1       N   UE       ⁢           ⁢           H   H     ⁡     (   i   )         m   +   1       ⁢         G   H     ⁡     (   i   )         m   +   1       ⁢       G   ⁡     (   i   )         (     m   +   1     )       ⁢       H   ⁡     (   i   )         (     m   +   1     )             ;         
b) setting minimum (υ min ) and maximum (υ max ) values of the Lagrange multiplier υ based on the calculated singular values λ i ;
 
c) setting the Lagrange multiplier as υ=(υ max +υ min )/2;
 
d) calculating
 
                 P   ^     =       ∑     i   =   1       N   TX       ⁢           ⁢       λ   i         (       λ   i     +   υ     )     2           ;         
c) calculating |{circumflex over (P)}−P| where P is the total transmit power;
 
d) comparing |{circumflex over (P)}−P| with the convergence threshold g;
 
e) setting υ max =υ if |{circumflex over (P)}−P| is greater than ε and if {circumflex over (P)} is less than P;
 
f) setting υ min =υ if |{circumflex over (P)}−P| is greater than ε and if {circumflex over (P)} is greater than P;
 
g) repeating steps c) to f) until |{circumflex over (P)}−P|&lt;ε and outputting the Lagrange multiplier υ.
 
     In some embodiments of the invention the noise variance N 0 (i) may be calculated by calculating the Signal to Interference plus Noise Ratio SINR (i,l) for all UEs based on the SINR threshold contained in the Channel Quality Indicator (CQI) table and then calculating the noise variance N 0 (i) for all UEs in accordance with the following: 
     
       
         
           
             
               
                 
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     In some embodiments of the invention G(i) (m+1)  may be calculated in accordance with G(i)=V H (i)H H (i)[H(i)V(i)V H (i)H H (i)+N o (i)I] −1  and the noise variance may be fixed to N o (i)=0, i=1, . . . , N UE . 
     The reference to any prior art in this specification is not, and should not be taken as an acknowledgement or any form of suggestion that the prior art forms part of the common general knowledge. 
     Advantageous Effects of Invention 
     According to each exemplary aspect of the present invention stated above, it is possible to provide a method for pre-coding which mitigates the likelihood of failures. It is also possible to provide a method for pre-coding which improves transmission capacity between transmitters and receivers. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       In order that this invention may be more readily understood and put into practical effect, reference will now be made to the accompanying drawings, which illustrate preferred embodiments of the invention, and wherein: 
         FIG. 1  is a schematic diagram general MU-MIMO system where the eNodeB transmits data to different UEs on the same time-frequency from multiple transmit antennas; 
         FIG. 2  is a schematic diagram depicting one possible transmission mechanism with UE feedback utilised by the transmitter of  FIG. 1  to transmit data to different receivers; 
         FIG. 3  is a flow chart depicting the process of User Equipment (UE) selection and precoding according to one embodiment of the present invention; 
         FIG. 4  is a flow chart depicting the process of producing precoders according to one embodiment of the present invention: 
         FIG. 5  is a flow chart depicting the process computing Lagrange multiplier for use in the production of the precoders as depicted in  FIG. 4  according to one embodiment of the present invention; 
         FIG. 6  is a flow chart depicting the process computing noise variance for use in the production of the precoders as depicted in  FIG. 4  according to one embodiment of the present invention. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     As will be appreciated by those of skill in the art in a MU-MIMO transmission scheme precoding is often applied based on the channel feedback received from UEs, including a channel rank indicator (RI), channel quality indicator (CQI), and precoding matrix indicator (PMI). The RI indicates the estimated number of simultaneous layers which can be received by the UE. One or more layers can be mapped to the same codeword and are jointly encoded for transmission to the target UE. In 3GPP LTE/LTE Advanced, different codebooks have been defined depending on the number of transmit antenna ports, and they provide precoding support for simultaneous transmission of variable number of layers (data stream) to the same target UE. For simplicity and ease of discussion the following description focuses on the case of two UEs and 2-stage codebook of PMI. 
     With reference to  FIG. 3  there is illustrated a process for User Equipment selection and precoding  300  according to one embodiment of the present invention. As shown the correlation values for of the UEs Precoder Matrix pairs are firstly calculated  301 . The Precoder Matrix (PM) being taken from the LTE codebook indexed at the UE&#39;s reported PMI. The UE pair with the minimum correlation value is then selected for further processing  302 . 
     In the present example the selection of the UE pair with minimum correlation value is performed as follows. Let W(i) denote the precoder matrix corresponding to the reported PMI#1 and PMI#2 of the i-th UE (i=1, . . . , Φ). Then
 
 W ( i )= W ( i ) 1   ×W ( i ) 2   (3)
 
     The correlation values can be calculated per equation (4) below
 
 C   corr ( i,j )= tr{[W   H ( i ) W ( j )] H   [W   H ( i ) W ( j )]}, i= 1, . . . ,Φ−1, j=i+ 1, . . . ,Φ  (4)
 
     The minimum correlation values are then provided by the following
 
 C   corr ( ĩ,{tilde over (j)} )=min{ C   corr ( i,j )},
 
( ĩ,{tilde over (j)} )=arg min{ C   corr ( i,j )}.  (5)
 
     The minimum correlation values are then compared against a correlation threshold T. If the minimum correlation value is greater than the threshold T i.e. C corr (ĩ,{tilde over (j)})&gt;T then the (ĩ,{tilde over (j)}) pair are not selected as pair for scheduling/precoding and the process is terminated  303 . If the minimum correlation value is less than the correlation threshold T i.e., C corr (ĩ,{tilde over (j)})≦T the correlation values of the reported PMI and CM are then calculated  304 . 
     The representative channel matrices (CM) in this instance are obtained utilising the fixed codebook of representative channels  305 . The fixed codebook of representative channels differs for the rank. For Rank 1 the fixed codebook Ω RANK1  of representative channel matrices is generated from the long term PMI codebook and short term rank#1 PMI codebook. Ω RANK1  contains vectors of size N TX ×1. For Rank 2 the fixed codebook Ω RANK2  of representative channel matrices (CM) is generated from the long term PMI codebook and short term rank#2 PMI codebook. Ω RANK2  contains matrices of size N TX ×N RX . 
     The fixed code books Ω RANK1  and Ω RANK2  are utilised to identify the representative channels matrices. For Rank 2 the representative channel matrices is given by 
     
       
         
           
             
               
                 
                   
                     
                       
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     For Rank1 a search is conducted over Ω RANK1  for each of the i-th UE, from the PMI based matrix W(i) for N RX  vectors of size N TX ×1. These vectors are then utilised to form the channel matrix H(i) of size N RX ×N TX . 
     Once the representative channel matrices are identified the correlation values are then calculated in accordance with the following
 
 C ( i,n )= tr{[h ( n ) H   W ( i )] H   [h ( n ) H   W ( i )]}, n= 1, . . . , N   vec   (7)
 
     The correlation values are then sorted to find the N RX  largest correlation values C(i,n 1 )&gt;C(i,n 2 )&gt; . . . &gt;C(i,n N     RX   ) corresponding to h(n 1 ), h(n 2 ), . . . , h(n N     RX   ) to form a channel matrix
 
 H ( i )=[ h ( n   1 ), h ( n   2 ), . . . , h ( n   N     RX   )] H   (8)
 
     The Channel Matrix pairs having the maximum correlation values are then selected  306  and the precoders then calculated  307  utilising values for N o (ĩ) N o ({tilde over (j)}) are then calculated using CQI(ĩ,l), CQI({tilde over (j)},l) (discussed in greater detail below). Then utilising the values for N o (ĩ), N o ({tilde over (j)}) and H(ñ(ĩ)), H(ñ({tilde over (j)})) with Lagrange multiplier (discussed in greater detail below) values for the precoders V(ĩ), V({tilde over (j)}) computed. 
     In this instance the resultant precoders are Minimum Mean Squared Error (MMSE) pecoders which are computed based on the PMI feedback. Consequently information on the channels is not required to produce the precoders. A more detailed discussion of the generation of the MMSE precoders in accordance with an embodiment of the present invention is discussed with respect to  FIG. 4  below. 
     With reference to  FIG. 4  there is illustrated one process for generating the MMSE precoders according to one embodiment of the present invention. The precoder is generated by firstly initializing the post coder for all UEs  401  as follows:
 
 G ( i ) (m=0)   =J ( i ), i= 1, . . . , N   UE .
 
     Here J(i) is the matrix RI(i)×N RX  the (a,b)-th element being zero for a≠b and being 1 for a=b and (m) denotes the m-th iteration. The precoder V(i) (m+1)  is then computed for all UEs  402  using G(i) (m)  for i=1, . . . , N UE . and the following equation: 
     
       
         
           
             
               
                 
                   
                     V 
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 N 
                                 UE 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 
                                   H 
                                   H 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   G 
                                   H 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 G 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 H 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             υ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             I 
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         H 
                         H 
                       
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         G 
                         H 
                       
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     In equation 9 the variable υ is the Lagrange multiplier obtained form step  505  in  FIG. 5  which is discussed in greater detail below. 
     The process then proceeds to compute for all UEs the post coder G(i) (m+1)    403  using V(i) (m+1)  for i=1, . . . , N UE  in accordance with the following equation. 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         V 
                         H 
                       
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             H 
                             H 
                           
                           ⁡ 
                           
                             ( 
                             i 
                             ) 
                           
                         
                         [ 
                         
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 N 
                                 UE 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 H 
                                 ⁡ 
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 V 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   V 
                                   H 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   H 
                                   H 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 N 
                                 o 
                               
                               ⁡ 
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                             ⁢ 
                             I 
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     For less complexity, the post coder G(i) (m+1)  for each UE can be calculated using the following:
 
 G ( i )= V   H ( i ) H   H ( i )[ H ( i ) V ( i ) V   H ( i ) H   H ( i )+ N   o ( i ) I]   −1   (11)
 
     In the case of equations 10 and 11 N 0 (i) is the noise variance obtained form step  602  in  FIG. 6 . The computation of the noise variance is discussed in greater detail below. 
     The process then computes 
               E   =       ∑     i   =   1       N   UE       ⁢           ⁢                  G   ⁡     (   i   )         (     m   +   1     )       -       G   ⁡     (   i   )         (   m   )              F   2     ⁢           ⁢   404         ,     here   ⁢           ⁢          .        F   2             
denotes Frobenius norm. The process then determines if E is greater than or equal to the convergent threshold ε i.e. E≧ε. If E≧ε then the process increments m  405  and repeats the calculations for V(i) (m+1)  and G(i) (m+1)  per steps  402 ,  403  to again calculate the value of E. This process is then repeated until
 
                 ∑     i   =   1       N   UE       ⁢           ⁢                G   ⁡     (   i   )         (     m   +   1     )       -       G   ⁡     (   i   )         (   m   )              F   2       &lt;   ɛ         
at which stage the precoder V(i) (m+1)  is outputted  406 .
 
     As can be seen form the above discussion the calculation of the precoder V(i) (m+1)  requires the use of a Lagrange multiplier v. The process of computing the Lagrange multiplier υ  500  is shown in  FIG. 5 . As shown singular values λ i  of the decomposition 
               U   ⁢           ⁢   Λ   ⁢           ⁢     U   H       =       ∑     i   =   1       N   UE       ⁢           ⁢           H   H     ⁡     (   i   )         m   +   1       ⁢         G   H     ⁡     (   i   )         m   +   1       ⁢       G   ⁡     (   i   )         (     m   +   1     )       ⁢       H   ⁡     (   i   )         (     m   +   1     )                 
are computed  501 . The minimum and maximum value of the Lagrange multiplier υ max υ min  are then set  502 . The Lagrange multiplier is then set  503  as υ=(υ max +υ min )/2.
 
     Once the Lagrange multiplier has been set the quantity 
               P   ^     =       ∑     i   =   1       N   TX       ⁢           ⁢       λ   i         (       λ   i     +   υ     )     2               
is then calculated  504 . The process then proceeds to calculate the absolute value {circumflex over (P)} less the total transmit power P which is then compared with the convergence threshold ε. If the absolute value of is less than ε i.e. |{circumflex over (P)}−P|≧ε the value of {circumflex over (P)} is compared with the value of P, if {circumflex over (P)} is less than P then υ max =υ  506  before resetting the Lagrange multiplier per step  503 . If {circumflex over (P)} is greater than P then υ min =υ  507  before resetting the Lagrange multiplier per step  503 .
 
     The steps of setting the Lagrange multiplier  503 , calculation of {circumflex over (P)}  504  and setting υ max =υ  506  or υ min =υ are repeated until |{circumflex over (P)}−P&lt;ε at which stage the Lagrange multiplier υ  505  for use in the calculation of the precoder V(i) (m+1)  at step  402  of  FIG. 4 . 
     In addition to the use of the Lagrange multiplier the process of generating the pre-coder information on the noise variance N 0 (i) is also required.  FIG. 6  show one possible procedure for the calculation of the noise variance N 0 (i)  600  according to one embodiment of the present invention. As shown the Signal to Interference plus Noise Ratio for all UEs SINR (i,l) is calculated  601  based on the SINR threshold contained in the Channel Quality Indicator (CQI) table. The SINR (i,l) is then utilised in conjunction the total power P to calculate the noise variance N 0 (i) for all TIES in accordance with the following: 
     
       
         
           
             
               
                 
                   N 
                   o 
                 
                 ⁡ 
                 
                   ( 
                   i 
                   ) 
                 
               
               = 
               
                 
                   P 
                   / 
                   
                     N 
                     UE 
                   
                 
                 
                   
                     ∑ 
                     
                       l 
                       = 
                       1 
                     
                     RI 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       SINR 
                       ⁡ 
                       
                         ( 
                         
                           i 
                           , 
                           l 
                         
                         ) 
                       
                     
                     / 
                     
                       RI 
                       ⁡ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               i 
               = 
               1 
             
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               N 
               UE 
             
           
         
       
     
     For less complexity, the noise variance can be fixed to zero i.e. N o (i)=0, i=1, . . . , N UE  in either case the value for N 0 (i) is then utilised in the calculation of G(i) (m+1)  at step  403  of the precoder calculation process discussed in relation to  FIG. 4  above. 
     As can be seen form the above discussion the present invention provides MMSE precoders based on the joint transmit &amp; receive optimization method in which utilises the PMI feedback. While the above examples have for the purposes of simplicity and ease of discussion focused on the case of two UEs and 2-stage codebook of PMI it will be appreciated by those of skill in the art that the proposed processes for the generation of precoders is not limited to the case of two UEs and 2-stage codebook of PMI and could be easily expanded to cover cases including multiple UEs and higher stage code books. 
     It is to be understood that the above embodiments have been provided only by way of exemplification of this invention, and that further modifications and improvements thereto, as would be apparent to persons skilled in the relevant art, are deemed to fall within the broad scope and ambit of the present invention described herein. 
     This application is based upon and claims the benefit of priority from Australian Patent Application No. 2012904070, filed on Sep. 18, 2012, the disclosure of which is incorporated herein in its entirety by reference. 
     REFERENCE SIGNS LIST 
     
         
           100  MU-MIMO system 
           101  transmitter 
           102 ,  103  receiver 
           200  transmission mechanism 
           201  transmit data 
           202  channel status information