Abstract:
Methods are provided. A method includes determining respective weighted likelihoods corresponding to a plurality of users in a multiple-input multiple-output communication system. The method further includes forming a plurality of user groups from the plurality of users using an iterative K-means clustering technique applied to the plurality of users. The iterative K-means clustering technique is responsive to the respective weighted likelihoods.

Description:
RELATED APPLICATION INFORMATION 
       [0001]    This application claims priority to provisional application Ser. No. 61/883,548 filed on Sep. 27, 2013, incorporated herein by reference. 
     
    
     BACKGROUND 
       [0002]    1. Technical Field 
         [0003]    The present invention relates to signal processing, and more particularly to two-stage precoding and user grouping for large scale multiple-input multiple-output (MIMO) systems. 
         [0004]    2. Description of the Related Art 
         [0005]    Most of the existing work directed to large scale MIMO (multi-input-multi-output) systems considers a Time Division Duplex (TDD) mode. However, there are as many FDD (Frequency Division Duplex) systems as TDD systems in real-world deployments. To equip a large amount of antennas in the base station (BS) of a FDD system, a two-stage precoding scheme has been proposed. In particular, all the users in the system are divided into several groups. The first stage precoding is designed to suppress the interferences among different groups. The second stage precoding is designed to suppress the interferences among different users within each group. Given the precoding methods, how to group users has a direct impact on the throughput performance. Fixing the number of groups, the existing grouping method may group too many users in some particular groups and group none or too few users to the other groups. Also, with groups being formed, scheduling which users of each group are to transmit and which users are to remain silent also has big impacts on the throughput. As is evident, such an approach is not a sufficient way to utilize the precious spectrum resources. 
       SUMMARY 
       [0006]    These and other drawbacks and disadvantages of the prior art are addressed by the present principles, which are directed to two-stage precoding and user grouping for large scale multiple-input multiple-output (MIMO) systems. 
         [0007]    According to an aspect of the present principles, a method is provided. The method includes determining respective weighted likelihoods corresponding to a plurality of users in a multiple-input multiple-output communication system. The method further includes forming a plurality of user groups from the plurality of users using an iterative K-means clustering technique applied to the plurality of users. The iterative K-means clustering technique is responsive to the respective weighted likelihoods. 
         [0008]    According to another aspect of the present principles, a method is provided. The method includes calculating respective rate gains for each of a plurality of users responsive to respectively adding each of the plurality of users to a given time slot in a multiple-input multiple-output communication system. The method further includes finding a maximum rate gain from among the respective rate gains. The method additionally includes scheduling a given one of the plurality of users with the maximum rate gain for the given time slot. 
         [0009]    These and other features and advantages will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0010]    The disclosure will provide details in the following description of preferred embodiments with reference to the following figures wherein: 
           [0011]      FIG. 1  shows an exemplary processing system  100  to which the present principles may be applied, in accordance with an embodiment of the present principles; 
           [0012]      FIG. 2  shows an exemplary system  200  for precoding, user grouping, and user scheduling in a large scale multiple-input multiple-output (MIMO) communication system, in accordance with an embodiment of the present principles; 
           [0013]      FIG. 3  shows an exemplary method  300  for assigning users to difference groups in a multiple-input multiple-output (MIMO) communication system using K-means clustering, in accordance with an embodiment of the present principles; 
           [0014]      FIG. 4  shows an exemplary method  400  for user scheduling in a multiple-input multiple-output (MIMO) communication system using K-means clustering, in accordance with an embodiment of the present principles; and 
           [0015]      FIG. 5  shows an exemplary method  500  for user grouping with joint group load balancing and precoding design in a multiple-input multiple-output (MIMO) communication system using K-means clustering, in accordance with an embodiment of the present principles. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0016]    The present principles are directed to two-stage precoding and user grouping for large scale multiple-input multiple-output (MIMO) systems. That is, various embodiments of the present principles are directed to user grouping, user scheduling, and load balancing problems relating to large scale MIMO systems. 
         [0017]    In an embodiment, we propose several user grouping methods to achieve higher throughput or better load balancing. For example, in an embodiment, we propose an improved K-means clustering algorithm for general user grouping. In an embodiment, we also propose a user grouping algorithm with joint load balancing and precoding (prebeamforming) design. 
         [0018]    In an embodiment, we also propose a dynamic user scheduling algorithm to enhance the system throughput. In an embodiment, the proposed dynamic user scheduling algorithm is a greedy algorithm, which achieves a local maximum at each step. Thus, a high throughput can be expected. 
         [0019]    The proposed improved K-means clustering algorithm and dynamic user scheduling algorithm advantageously achieve higher system throughput than existing approaches. In an embodiment, the proposed improved K-means clustering algorithm considers the weights of different Eigenmodes, which brings about better classification of different users. The proposed loading balancing algorithm advantageously solves the problem of unbalanced group loading for large scale MIMO system. 
         [0020]      FIG. 1  shows an exemplary processing system  100  to which the present principles may be applied, according to an embodiment of the present principles, is shown. The processing system  100  includes at least one processor (CPU)  104  operatively coupled to other components via a system bus  102 . A cache  106 , a Read Only Memory (ROM)  108 , a Random Access Memory (RAM)  110 , an input/output (I/O) adapter  120 , a sound adapter  130 , a network adapter  140 , a user interface adapter  150 , and a display adapter  160 , are operatively coupled to the system bus  102 . 
         [0021]    A first storage device  122  and a second storage device  124  are operatively coupled to system bus  102  by the I/O adapter  120 . The storage devices  122  and  124  can be any of a disk storage device (e.g., a magnetic or optical disk storage device), a solid state magnetic device, and so forth. The storage devices  122  and  124  can be the same type of storage device or different types of storage devices. 
         [0022]    A speaker  132  is operative coupled to system bus  102  by the sound adapter  130 . A transceiver  142  is operatively coupled to system bus  102  by network adapter  140 . A display device  162  is operatively coupled to system bus  102  by display adapter  160 . 
         [0023]    A first user input device  152 , a second user input device  154 , and a third user input device  156  are operatively coupled to system bus  102  by user interface adapter  150 . The user input devices  152 ,  154 , and  156  can be any of a keyboard, a mouse, a keypad, an image capture device, a motion sensing device, a microphone, a device incorporating the functionality of at least two of the preceding devices, and so forth. Of course, other types of input devices can also be used, while maintaining the spirit of the present principles. The user input devices  152 ,  154 , and  156  can be the same type of user input device or different types of user input devices. The user input devices  152 ,  154 , and  156  are used to input and output information to and from system  100 . 
         [0024]    Of course, the processing system  100  may also include other elements (not shown), as readily contemplated by one of skill in the art, as well as omit certain elements. For example, various other input devices and/or output devices can be included in processing system  100 , depending upon the particular implementation of the same, as readily understood by one of ordinary skill in the art. For example, various types of wireless and/or wired input and/or output devices can be used. Moreover, additional processors, controllers, memories, and so forth, in various configurations can also be utilized as readily appreciated by one of ordinary skill in the art. These and other variations of the processing system  100  are readily contemplated by one of ordinary skill in the art given the teachings of the present principles provided herein. 
         [0025]    Moreover, it is to be appreciated that system  200  described below with respect to  FIG. 2  is a system for implementing respective embodiments of the present principles. Part or all of processing system  100  may be implemented in one or more of the elements of system  200 . 
         [0026]    Further, it is to be appreciated that processing system  100  may perform at least part of the method described herein including, for example, at least part of any of methods  300 - 700  of  FIGS. 3-7 . Similarly, part or all of system  200  may be used to perform at least part of any of methods  300 - 700  of  FIGS. 3-7 . 
         [0027]      FIG. 2  shows an exemplary system  200  for precoding, user grouping, and user scheduling in a large scale multiple-input multiple-output (MIMO) communication system, in accordance with an embodiment of the present principles. 
         [0028]    The system  200  includes a K-means user clusterer  210 , a dynamic user scheduler  220 , and a joint load balancer and precoder  230 , all interconnected by a bus  266 . The K-means user clusterer  210  determines user groups. The dynamic user scheduler  220  determines user schedules. The joint load balancer and precoder  230  determines user groups. In an embodiment, at least the K-means clusterer  210  performs method  300  of  FIG. 3 , at least the dynamic user scheduler  220  performs method  400  of  FIG. 4 , and at least the joint load balancer and precoder  230  performs method  500  of  FIG. 5 . 
         [0029]      FIG. 3  shows an exemplary method  300  for assigning users to difference groups in a multiple-input multiple-output (MIMO) communication system using K-means clustering, in accordance with an embodiment of the present principles. Method  300  can be considered to correspond to algorithm 1 described herein. 
         [0030]    Method  300  uses weighted likelihood as a criterion to assign users. The weighted likelihood takes the weight of different Eigenmodes into consideration. The update of the group center and total likelihood also considers the weights of different Eigenmodes. 
         [0031]    At step  301 , find the covariance matrix for each user, and compute U k  using Eigen-decomposition R k =U k A k U k   H . 
         [0032]    At step  302 , for each group, randomly pick U k  as the group center V g . 
         [0033]    At step  303 , find the weighted likelihood L(R k , V g ) defined in Equation (1). 
         [0034]    At step  304 , assign the user to the group with the maximum weighted likelihood using Equation (2). 
         [0035]    At step  305 , update the group center V g  using Equation (3). 
         [0036]    At step  306 , compute the likelihood of each user to its assigned group. Add the likelihood as the total likelihood. 
         [0037]    At step  307 , determine whether or not the likelihood converges. If so, then the method terminates. Otherwise, the method returns to step  303 . 
         [0038]    The following equations apply to method  300 : 
         [0000]    
       
         
           
             
               
                 
                   
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         [0000]    where eig denotes the unitary matrix after Eigen-decomposition, S g  denotes the member set of group g, and |S g | denotes the number of group members in group g. 
         [0039]      FIG. 4  shows an exemplary method  400  for user scheduling in a multiple-input multiple-output (MIMO) communication system using K-means clustering, in accordance with an embodiment of the present principles. Method  400  can be considered to correspond to algorithm 2 described herein. 
         [0040]    Method  400  computes the throughput gains of adding each user given the set of users already scheduled (initially empty), and then finds the maximum one among them. Each time, the user with the maximum throughput gain is added to the set of users already scheduled. By doing this repeatedly, we can find the set of users to schedule. 
         [0041]    At step  401 , initially, define the user set as U={1, . . . , K}, where the group member set S g  is empty for all g. 
         [0042]    At step  402 , determine whether or not the total number of scheduled users in all groups is greater than or equal to the total number of beams of all groups. If so, then the method is terminated. Otherwise, the method proceeds to step  403 . 
         [0043]    At step  403 , determine whether or not U is empty. If so, then the method is terminated. Otherwise, the method continues to step  404 . 
         [0044]    At step  404 , begin a Loop A, for each unscheduled user. 
         [0045]    At step  405 , pick one user from U, and assume it is scheduled in its assigned group. 
         [0046]    At step  406 , perform zero forcing beamforming or regularized zero forcing beamforming given the group members already scheduled and the prebeamforming matrix for the user grouping. 
         [0047]    At step  407 , compute the rate gain K(k, g) as the difference of throughput with and without having user k scheduled. 
         [0048]    At step  408 , end Loop A. 
         [0049]    At step  409 , find the maximum of K(k, g) denoted as K(k * , g * ). 
         [0050]    At step  410 , determine whether or not K(k * , g * )&gt;0. 
         [0051]    At step  411 , schedule the user with the maximum rate gain K(k * , g * ), add k* into S g* , and eliminate k* from U. 
         [0052]    It is to be appreciated that steps  405 ,  406 , and  407  are repeated for all unscheduled users. 
         [0053]      FIG. 5  shows an exemplary method  500  for user grouping with joint group load balancing and precoding design in a multiple-input multiple-output (MIMO) communication system using K-means clustering, in accordance with an embodiment of the present principles. Method  500  can be considered to correspond to algorithm 3 described herein. 
         [0054]    At step  501 , find the covariance matrix for each user, and perform Eigen-decomposition to compute U k  as R k =U k A k U k   H . 
         [0055]    At step  502 , use K-means or improved K-means grouping algorithm to find the user association with each group. 
         [0056]    At step 503, update the group center V g  using Equation (3) or (5). 
         [0057]    At step 504, find pre-beamforming matrices. 
         [0058]    At step 505, approximate the average SINR(k, g) using Equation (4) or the large scale approximation method described herein. In an embodiment, the large scale approximation method is described with respect to algorithm 4. Of course, the present principles are not limited to solely the large scale approximation method described herein and, thus, other large scale approximation methods can also be used while maintaining the spirit of the present principles. 
         [0059]    At step  506 , optimize the utility using algorithm in Table 2. 
         [0060]    At step  507 , determine whether or not the utility has converged. If so, then the method is terminated. Otherwise, the method returns to step  503 . 
         [0061]    The following equations apply to method  500 : 
         [0000]    
       
         
           
             
               
                 
                   
                     SINR 
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         [0000]    where SINR is defined as the Signal to Interference plus Noise Ratio. 
         [0000]    
       
         
           
             
               
                 
                   
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         [0000]    (For K-means Clustering Algorithm), where eig denotes the unitary matrix after eigen-decompostion, S g  denotes the member set of group g, and |S g | denotes the number of group members in group g. 
         [0062]    TABLE 1 shows various notions applicable to the present principles, in accordance with an embodiment of the present principles. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Dimension 
                 Meaning 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 y 
                 K × 1 
                 Signals received by all users 
               
               
                   
                 yg 
                 K g  × 1 
                 Signals received by group g 
               
               
                   
                 d 
                 S × 1 
                 Signals transmitted for all users 
               
               
                   
                 dg 
                 S g  × 1 
                 Signals transmitted for group g 
               
               
                   
                 M 
                 1 × 1 
                 Number of antennas at the BS 
               
               
                   
                 H 
                 M × K 
                 Channel between BS and users 
               
               
                   
                 H 
                 b × K 
                 Effective channel between BS 
               
               
                   
                 S 
                 1 × 1 
                 Number of data stream 
               
               
                   
                 V 
                 M × S 
                 Precoding matrix 
               
               
                   
                 R k   
                 M × M 
                 Covariance matrix for user k 
               
               
                   
                 h k   
                 M × 1 
                 Instantaneous channel for user k 
               
               
                   
                 B 
                 M × b 
                 Pre-beamforming matrix 
               
               
                   
                 P 
                 b × S 
                 Precoding matrix 
               
               
                   
                 U k   
                 M × M 
                 Unitary matrix composed of 
               
               
                   
                 Λ k   
                 M × M 
                 Diagonal matrix composed of 
               
               
                   
                 V g   
                 M × M 
                 Group center of group g 
               
               
                   
                 Λ g   
                 M × M 
                 dominant eigenvalues for group 
               
               
                   
                 Bg 
                 M × b g   
                 Pre-beamforming matrix for 
               
               
                   
                 Pg 
                 b g  × S g   
                 Precoding matrix within each 
               
               
                   
                 z 
                 K × 1 
                 Noise vector 
               
               
                   
                 zg 
                 K g  × 1 
                 Noise vector within each group 
               
               
                   
                 θ 
                 1 × 1 
                 Azimuth angle of user 
               
               
                   
                 s 
                 1 × 1 
                 Distance between BS and user 
               
               
                   
                 Δ 
                 1 × 1 
                 Angle spread 
               
               
                   
                 r 
                 1 × 1 
                 Radius of scattering ring 
               
               
                   
                 G 
                 1 × 1 
                 Number of groups 
               
               
                   
                 α 
                 1 × 1 
                 Parameter for RZFBF precoding 
               
               
                   
                 p 
                 1 × 1 
                 Total transmit power of BS 
               
               
                   
                 N 
                 1 × 1 
                 Scaling factor for antenna and 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
               
                 Algorithm 1: Improved K-means Clustering Algorithm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  1 
                 Set n = 0, L tot   (n)  = 0 and S g   (0)  =  for g=1, . . . , G. 
               
               
                  2 
                 Randomly choose G different indices (denoted as π(g), ∀(g) from the  
               
               
                   
                 set {1, . . . , K} and set V g   (0)  = U π(g) , ∀g ; 
               
               
                  3 
                 while |L tot   (n)  − L tot   (n−1) | &gt; εL tot   (n−1)  do 
               
             
          
           
               
                  4 
                 | 
                 n = n + 1 ; S g   (n)  =  for g=1, . . . , G 
               
               
                  5 
                 | 
                 for k=1, . . . , K do 
               
             
          
           
               
                  6 
                 | 
                 | 
                 for g=1, . . . , G do 
               
               
                   
               
             
          
           
               
                    7   
                 | | | 
                 | | | 
                 | | | 
                 
                   
                     
                       
                         
                           Compute 
                            
                           
                               
                           
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                  8 
                 | 
                 | 
                 end 
               
             
          
           
               
                  9 
                 | 
                 end 
               
               
                 10 
                 | 
                 Assign user k to group g such that g = arg max g , L(R k , V g′ ) 
               
               
                   
               
             
          
           
               
                 12 
                 | 
                   
                 
                   
                     
                       
                         
                           S 
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                 11 
                 | 
                 for g=1, . . . , G do 
               
               
                   
               
             
          
           
               
                   13   
                 | | | 
                 | | | 
                 
                   
                     
                       
                         
                           V 
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                             ( 
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                         = 
                         
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                 14 
                 | 
                 end 
               
             
          
           
               
                 15 
                 Compute L tot   (n)  = Σ g=1   G Σ k∈S     g       (n)   L(R k , V g ) 
               
               
                 16 
                 end 
               
               
                 17 
                 Assign V g  = V g   (n)  and S g  = S g   (n) . 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Algorithm 2: Greedy algorithm for dynamic user selection and 
               
               
                 beamforming with determined user grouping 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 1 
                 User grouping {tilde over (g )}is given; 
               
               
                   
                 2 
                 Initially set u = {1, ..., K}, the weighted sum rate r ws  = 0 and 
               
               
                   
                   
                 S g   (0)  = Ø for g = 1, ..., G. ; 
               
               
                   
                 3 
                 While Termination conditions (Σ g  |S g | = Σ g  b g , K(k*,g k* ) ≦ 0, 
               
               
                   
                   
                 or u = Ø) are not satisfied do 
               
               
                   
                 4 
                  | For k ε u do 
               
               
                   
                 5 
                  | |  Let {tilde over (g )}= g k ; 
               
               
                   
                 6 
                  | | Set S′ g  = S g  ∪ {k}, and S′ g′  = S g′ , ∀g′ ≠ g ; 
               
               
                   
                 7 
                  | | Perform ZFBF or RZFBF based on {S′ g } and {B g } ; 
               
               
                   
                 8 
                  | | Compute the gain K(k,g) = max{0, r ws ({S′ g }, 
               
               
                   
                   
                  | | {B g }) − r ws ({S g },{B g })} ; 
               
               
                   
                 9 
                  | End 
               
               
                   
                 10 
                  | Obtain (k*,g k* ) = arg max kεu   K(k,g) ; 
               
               
                   
                 11 
                  | If K(k*,g k* ) &gt; 0 then 
               
               
                   
                 12 
                  | |  Let ← u\k* ; 
               
               
                   
                 13 
                  | |  Let S g     k*    ← S g     k*    ∪ {k*} ; 
               
               
                   
                 14 
                   End 
               
               
                   
                 15 
                 End 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Algorithm 3: User grouping with joint group load balancing and precoding 
               
               
                 design algorithm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 1 
                 Perform Algorithm 1 to obtain user group ID x ij . 
               
               
                   
                 2 
                 while Utility* (n)  − Utility* (n−1)  &gt; ∈Utility* (n−1)  do 
               
               
                   
                 3 
                  |  for g ∈ G do 
               
               
                   
                 4 
                  |   |  Find V g * (n)  using (21) or the proposed weighted 
               
               
                   
                   
                           likelihood (22) 
               
               
                   
                 5 
                  |  end 
               
               
                   
                 6 
                  |  for g ∈ G do 
               
               
                   
                 7 
                  |   |  Find Bg using Approximate BD approach 
               
               
                   
                 8 
                  |  end 
               
               
                   
                 9 
                  |  for k = 1,...,K do 
               
               
                   
                 10 
                  |   |  for g = 1,....,G do 
               
               
                   
                 11 
                  |   |   | Find SINR (k,g)using Algorithm 6 or (23) 
               
               
                   
                 12 
                  |   |  end 
               
               
                   
                 13 
                  |  end 
               
               
                   
                 14 
                  | 
               
               
                   
                 15 
                  | 
               
               
                   
                 16 
                  |  Optimize (19) using Algorithm 7 ; 
               
               
                   
                 17 
                  |  Update x ij  and Utility* (n)   
               
               
                   
                 18 
                 end 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
               
                 Algorithm 4: Large Scale SINR Approximation 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  1  
                 for g = 1, . . . , G do 
               
               
                   
               
             
          
           
               
                    2   
                 | | | 
                 
                   
                     
                       
                         
                           
                             Y 
                             g 
                           
                           = 
                           
                             
                               1 
                               
                                  
                                 
                                   S 
                                   g 
                                 
                                  
                               
                             
                              
                             
                               Σ 
                               
                                 k 
                                 ∈ 
                                 
                                   S 
                                   g 
                                 
                               
                             
                              
                             
                               U 
                               k 
                             
                              
                             
                               U 
                               k 
                               H 
                             
                           
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                  3 
                 | 
                   Y   g  = B g   H Y g B g ; 
               
               
                  4 
                 | 
                 while m g   (n)  − m g   (n−1)  &gt; εm g   (n−1)  do 
               
             
          
           
               
                  5 
                 | 
                 | 
                 Solve (24) iteratively to find m g  and updated T g . 
               
             
          
           
               
                  6 
                 | 
                 end 
               
             
          
           
               
                  7 
                 end 
               
               
                  8 
                 for k = 1, . . . , K do 
               
             
          
           
               
                  9 
                 | 
                 for g = 1, . . . , G do 
               
             
          
           
               
                 10 
                 | 
                 | 
                  Solve (25) iteratively to find m g     k    and updated T g . 
               
               
                 11 
                 | 
                 | 
                 Solve (26) and (27) with assumptions: (i) For target user, 
               
               
                   
                 | 
                 | 
                 the transmit correlation is R g     k   ; (ii) For intra group 
               
               
                   
                 | 
                 | 
                 co-scheduled users, the transmit correlation is same 
               
               
                   
                 | 
                 | 
                 as the average of the group; (iii) For inter group 
               
               
                   
                 | 
                 | 
                 co-scheduled users, the transmit correlation is same as 
               
               
                   
                 | 
                 | 
                 the average of the group. 
               
             
          
           
               
                 12 
                 | 
                 end 
               
             
          
           
               
                 13  
                 end 
               
               
                   
               
             
          
         
       
     
         [0063]    Embodiments described herein may be entirely hardware, entirely software or including both hardware and software elements. In a preferred embodiment, the present invention is implemented in software, which includes but is not limited to firmware, resident software, microcode, etc. 
         [0064]    Embodiments may include a computer program product accessible from a computer-usable or computer-readable medium providing program code for use by or in connection with a computer or any instruction execution system. A computer-usable or computer readable medium may include any apparatus that stores, communicates, propagates, or transports the program for use by or in connection with the instruction execution system, apparatus, or device. The medium can be magnetic, optical, electronic, electromagnetic, infrared, or semiconductor system (or apparatus or device) or a propagation medium. The medium may include a computer-readable medium such as a semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disk and an optical disk, etc. 
         [0065]    It is to be appreciated that the use of any of the following “/”, “and/or”, and “at least one of”, for example, in the cases of “A/B”, “A and/or B” and “at least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as readily apparent by one of ordinary skill in this and related arts, for as many items listed. 
         [0066]    The foregoing is to be understood as being in every respect illustrative and exemplary, but not restrictive, and the scope of the invention disclosed herein is not to be determined from the Detailed Description, but rather from the claims as interpreted according to the full breadth permitted by the patent laws. Additional information is provided in an appendix to the application entitled, “Additional Information”. It is to be understood that the embodiments shown and described herein are only illustrative of the principles of the present invention and that those skilled in the art may implement various modifications without departing from the scope and spirit of the invention. Those skilled in the art could implement various other feature combinations without departing from the scope and spirit of the invention.