depre_spatialmultiplexing.asv

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function x=pre_spatialMultiplexing(y)
if num(v) = 2;%num(v) is the numbers of layers v; 
    if index_codeBook==0;
        v1 = 1 /sqrt(2) * [1,1]';
        v2 = 1 /sqrt(2) * [1,0;0,1];
    elseif index_codeBook==1;
        v1 = 1 /sqrt(2) * [1,-1]';
        v2 = 1 /2 * [1,1;1,-1];
    elseif index_codeBook==2;
        v1 = 1 /sqrt(2) * [1,j].';
        v2 = 1 /2 * [1,1;j,-j];
    else index_codeBook==3;
        v1 = 1 /sqrt(2) * [1,-j].';
        v2 = [ ];
    end;
else num(v) = 4;%num(v) is the numbers of layers v; 
    I = eye(4);
   for  n = 1:16;
    W(n) = I - 2u(n) * u(n)' / (u(n)' * u(n));
   end;
    if index_codeBook==0;
        u(1) = [1,-1,-1,-1].';
        v1 = W1(;,1);
        v2 = W1(:,[1,4]) /sqrt(2) ;
        v3 =  W1(:,[1,2,4]) /sqrt(3);
        v4 =  W1(:,[1,2,3,4]) /2;
    elseif index_codeBook==1;
        u(2) = [1,-j,1,j].';
        v1 = W2(:,1);
        v2 = W2(:,[1,2]) /sqrt(2);
        v3 = W2(:,[1,2,3]) /sqrt(3) ;
        v4 = W2(:,[1,2,3,4]) /2 ;
    elseif index_codeBook==2;
        u(3)=[1,1,-1,1].';
        v1 = W3(:,1);
        v2 = W3(:,[1,2]) /sqrt(2) ;
        v3 = W3(:,[1,2,3]) /sqrt(3) ;
        v4 = W3(:,[3,2,1,4]) /2 ;   
    elseif index_codeBook==3;
        u(4) = [1,j,1,-j].';
        v1 = W4(:,1);
        v2 = W4(:,[1,2]) /sqrt(2) ;
        v3 = W4(:,[1,2,3]) /sqrt(3) ;
        v4 = W4(:,[3,2,1,4]) /2 ;   
    elseif index_codeBook==4;
        u(5) = [1,(-1-j)/sqrt(2),-j,(1-j)/sqrt(2)].';
        v1 = W5(:,1);
        v2 = W5(:,[1,4]) /sqrt(2) ;
        v3 = W5(:,[1,2,4]) /sqrt(3) ;
        v4 = W5(:,[1,2,3,4]) /2 ;
    elseif index_codeBook==5;
        u(6) = [1,(1-j)/sqrt(2),j,(-1-j)/sqrt(2)].';
        v1 = W6(:,1);
        v2 = W6(:,[1,4]) /sqrt(2) ;
        v3 = W6(:,[1,2,4])/sqrt(3) ;
        v4 = W6(:,[1,2,3,4])/2;    
    elseif index_codeBook==6;
        u(7) = [1,(1+j)/sqrt(2),-j,(-1+j)/sqrt(2)].';
        v1 = W7(:,1);
        v2 = W7(:,[1,3])/sqrt(2) ;
        v3 = W7(:,[1,3,4])/sqrt(3) ;
        v4 = W7(:,[1,3,2,4])/2;    
    elseif index_codeBook==7;
        u(8) = [1,(-1+j)/sqrt(2),j,(1+j)/sqrt(2)].';
        v1 = W8(:,1);
        v2 = W8(:,[1,3])/sqrt(2) ;
        v3 = W8(:,[1,3,4])/sqrt(3) ;
        v4 = W8(:,[1,3,2,4])/2;   
    elseif index_codeBook==8;
        u(9) = [1,-1,1,1].';
        v1 = W9(:,1);
        v2 = W9(:,[1,2])/sqrt(2);
        v3 = W9(:,[1,2,4])/sqrt(3);
        v4 = W9(:,[1,2,3,4])/2 ;    
    elseif index_codeBook==9;
        u(10) = [1,-j,-1,-j].';
        v1 = W10(:,1);
        v2 = W10(:,[1,4])/sqrt(2) ;
        v3 = W10(:,[1,3,4])/sqrt(3) ;
        v4 = W10(:,[1,2,3,4])/2 ;     
    elseif index_codeBook==10;
        u(11) = [1,1,1,-1].';
        v1 = W11(:,1);
        v2 = W11(:,[1,3])/sqrt(2) ;
        v3 = W11(:,[1,2,3])/sqrt(3);
        v4 = W11(:,[1,3,2,4])/2 ;  
    elseif index_codeBook==11;
        u(12) = [1,j,-1,j].';
        v1 = W12(:,1);
        v2 = W12(:,[1,3])/sqrt(2);
        v3 = W12(:,[1,3,4])/sqrt(3);
        v4 = W12(:,[1,3,2,4])/2 ; 
    elseif index_codeBook==12;
        u(13) = [1,-1,-1,1].';
        v1 = W13(:,1);
        v2 = W13(:,[1,2])/sqrt(2);
        v3 = W13(:,[1,2,3])/sqrt(3) ;
        v4 = W13(:,[1,2,3,4])/2 ;   
    elseif index_codeBook==13;
        u(14) = [1,-1,1,-1].';
        v1 = W14(:,1);
        v2 = W14(:,[1,3])/sqrt(2) ;
        v3 = W14(:,[1,2,3])/sqrt(3) ;
        v4 = W14(:,[1,3,2,4])/2 ;       
    elseif index_codeBook==14;
        u(15) = [1,1,-1,-1].';
        v1 = W15(:,1);
        v2 = W15(:,[1,3])/sqrt(2) ; 
        v3 = W15(:,[1,2,3])/sqrt(3) ;
        v4 = W15(:,[3,2,1,4])/2 ;    
    elseif index_codeBook==15;
        u(16) = [1,1,1,1].';
        v1 = W16(:,1);
        v2 = W16(:,[1,2])/sqrt(2);
        v3 = W16(:,[1,2,3])/sqrt(3) ;
        v4 = W16(:,[1,2,3,4])/2 ;  
    end;
end;   
for i=1:M_ap;
    M_ap=M_layer;
  %index_CDD由高层给出；
  if index_CDD=0;% without cyclic delay diversity ;
      [Q,R]=qr(W);
      x=R\(Q\y);
  else index_CDD=1;%large delay CDD;    
      switch v
          case 1
             U = [1];
             D(i) = [1];
          case 2
             U = 1/sqrt(2) * [1,1;1,exp(-j*pi)];
             D(i) = diag([1,exp(-j*pi*i)]);
          case 3   
             U = 1/sqrt(3) * [1,1,1;1,exp(-j*2*pi/3),exp(-j*4*pi/3);1,exp(-j*4*pi/3),exp(-j*8*pi/3)];
             D(i) = diag([1,exp(-j*2*pi*i/3),exp(-j*4*pi*i/3)]);
          case 4
             U = 1/2 * [1,1,1,1;1,exp(-j*2*pi/4),exp(-j*4*pi/4),exp(-j*6*pi/4);1,exp(-j*4*pi/4),exp(-j*8*pi/4),exp(-j*12*pi/4);1,exp(-j*6*pi/4),exp(-j*12*pi/4),exp(-j*18*pi/4)];
             D(i) = diag([1,exp(-j*2*pi*i/4),exp(-j*4*pi*i/4),exp(-j*6*pi*i/4)]);
      end;  
      y(i) = W * D(i) * U * x(i); x(i)=
  end;    
end;   
y;