Patent ID: 11876589
Assignee: FRAUNHOFER GESELLSCHAFT ZUR FÖRDERUNG DER ANGEWANDTEN FORSCHUNG E.V.
Field: Telecommunications (Electrical engineering)
Classification: CPC H | IPC H

Claim 10:
11. The communication device of claim 10, wherein the processor is configured to apply, after the construction of the 3D channel tensor, a transformation/compression with respect to
all three dimensions of the 3D channel tensor  of dimension Nr×Nt×S represented by a (column-wise) Kronecker product as

=(1,2,3)(), vec
    ⁡
    (
    ℋ
    )
   
   =
   
    
     vec
     ⁡
     (
     
      
       ℱ
       
        (
        
         1
         ,
         2
         ,
         3
        
        )
       
      
      (
      
       ℋ
       ^
      
      )
     
     )
    
    =
    
     
      ∑
      
       
        n
        r
       
       =
       0
      
      
       
        N
        r
        ′
       
       -
       1
      
     
      
     
      
       ∑
       
        
         n
         t
        
        =
        0
       
       
        
         N
         t
         ′
        
        -
        1
       
      
       
      
       
        ∑
        
         s
         =
         0
        
        
         
          S
          ′
         
         -
         1
        
       
        
       
        
         γ
         
          
           n
           r
          
          ,
          
           n
           t
          
          ,
          s
         
        
        ⁢
           
        
         
          b
          
           3
           ,
           
            n
            r
           
           ,
           
            n
            t
           
           ,
           s
          
         
         ⊗
         
          b
          
           2
           ,
           
            n
            r
           
           ,
           
            n
            t
           
           ,
           s
          
         
         ⊗
         
          b
          
           1
           ,
           
            n
            r
           
           ,
           
            n
            t
           
           ,
           s
          
         
        
       
      
     
    
   
  
  ,
 

where
b1,nr,nt,s is a transformation vector of size Nr×1 with respect to the first dimension of the 3D channel tensor , selected from a codebook matrix Ω1;
b2,nr,nt,s is a transformation vector of size Nt×1 with respect to the second dimension of the 3D channel tensor , selected from a codebook matrix Ω2;
b3,nr,nt,s is a transformation vector of size S×1 with respect to the third dimension of the 3D channel tensor , selected from a codebook matrix Ω3;
γnr,nt,s is the transformed/compressed channel coefficient associated with the vectors b1,nr,nt,s, b2,nr,nt,s, and b3,nr,nt,s, and
N′r, N′t, and S′ (N′r≤Nr, N′t≤Nt, S′≤S) represents the value of the first, second and third dimension of the transformed/compressed 3D channel tensor , respectively, or

the space dimensions of the 3D channel tensor, represented by, ℋ
    =
    
     
      ℱ
      
       (
       
        1
        ,
        2
       
       )
      
     
     (
     
      ℋ
      ^
     
     )
    
   
   ,
   

   
    
     vec
     ⁡
     (
     ℋ
     )
    
    =
    
     
      vec
      ⁡
      (
      
       
        ℱ
        
         (
         
          1
          ,
          2
         
         )
        
       
       (
       
        ℋ
        ^
       
       )
      
      )
     
     =
     
      
       ∑
       
        
         n
         r
        
        =
        0
       
       
        
         N
         r
         ′
        
        -
        1
       
      
       
      
       
        ∑
        
         
          n
          t
         
         =
         0
        
        
         
          N
          t
          ′
         
         -
         1
        
       
        
       
        
         ∑
         
          s
          =
          0
         
         
          
           S
           ′
          
          -
          1
         
        
         
        
         
          γ
          
           
            n
            r
           
           ,
           
            n
            t
           
           ,
           s
          
         
         ⁢
            
         
          
           b
           
            3
            ,
            s
           
          
          ⊗
          
           b
           
            2
            ,
            
             n
             r
            
            ,
            
             n
             t
            
            ,
            s
           
          
          ⊗
          
           b
           
            1
            ,
            
             n
             r
            
            ,
            
             n
             t
            
            ,
            s
           
          
         
        
       
      
     
    
   
   ,
  
 

where
b3,s is a transformation vector of all zeros with the s-th element being one,
b2,nr,nt,s is a vector of size Nt×1 with respect to the second dimension of the 3D channel tensor , selected from a codebook matrix Ω2, and
b1,nr,nt,s is a transformation vector of size Nr×1 with respect to the first dimension of the 3D channel tensor , selected from a codebook matrix Ω1, N′r≤Nr, N′t≤Nt, S′=S, or

the frequency dimension of the 3D channel tensor, represented by

=(3)(),, vec
    ⁡
    (
    ℋ
    )
   
   =
   
    
     vec
     ⁡
     (
     
      
       ℱ
       
        (
        3
        )
       
      
      (
      
       ℋ
       ^
      
      )
     
     )
    
    =
    
     
      ∑
      
       
        n
        r
       
       =
       0
      
      
       
        N
        r
        ′
       
       -
       1
      
     
      
     
      
       ∑
       
        
         n
         t
        
        =
        0
       
       
        
         N
         t
         ′
        
        -
        1
       
      
       
      
       
        ∑
        
         s
         =
         0
        
        
         
          S
          ′
         
         -
         1
        
       
        
       
        
         γ
         
          
           n
           r
          
          ,
          
           n
           t
          
          ,
          s
         
        
        ⁢
           
        
         
          b
          
           3
           ,
           
            n
            r
           
           ,
           
            n
            t
           
           ,
           s
          
         
         ⊗
         
          b
          
           2
           ,
           
            n
            r
           
          
         
         ⊗
         
          b
          
           1
           ,
           
            n
            t
           
          
         
        
       
      
     
    
   
  
  ,
 

where
b2,nr is a transformation vector of all zeros with the nr-th element being one, b1,nt is a vector of all zeros with the nt-th element being one, and
b3,nr,nt,s is a transformation vector of size S×1 with respect to the third dimension of the 3D channel tensor , selected from a codebook matrix Ω3, N′r=Nr and N′t=Nt, S′≤S.