%MAC to BC Transformation%Authors: Nihar Jindal, Wonjong Rhee, Sriram Vishwanath, Syed Jafar, Andrea%Goldsmith%Date:  6/20/05function Downlink = MAC_to_BC(H, Uplink);%assumes users decoded in increasing order for uplink: 1,2,...,K,  %opposite encoding order for downlink (K, K-1,..., 1)%Function Inputs%H:             triply indexed UPLINK channel%               H(:,:,k) refers to the UPLINK channel of the kth receiver%               H(:,:,k) is an (M x N) matrix%Uplink:        triply indexed matrices containing the UPLINK covariance matrices%               Uplink(:,:,k) is the (N x N) covariance of user k%Function Outputs%Downlink:      triply indexed matrices containing the DOWNLINK covariance matrices%               Downlink(:,:,k) is the (M x M) covariance of user k%Other Variables%M:             # of transmit antennas in downlink channel%N:             # of receive antennas in downlink channel%K:             # of receivers%Determine # of antennas, users[M,N,K] = size(H);for k = 1:K    %Compute A_i (equation 34)    temp_sum = eye(M,M);    for l = (k+1):K        temp_sum = temp_sum + H(:,:,l) * Uplink(:,:,l) * H(:,:,l)';    end;    B(:,:,k) = temp_sum;    %Compute B_i (equation 34)    temp_sum = eye(N,N);    for l = 1:(k-1)        temp_sum = temp_sum + H(:,:,k)' * Downlink(:,:,l) * H(:,:,k);    end;    A(:,:,k) = temp_sum;    %take SVD of effective channel    Hk_eff = B(:,:,k)^(-0.5) * H(:,:,k) * A(:,:,k)^(-0.5);    [r,t] = size(Hk_eff);    if (t > r)        [F,D,G] = svd(Hk_eff',0);        Fk = G;        Gk = F;    else        [Fk,D,Gk] = svd(Hk_eff,0);    end;        %Compute downlink covariance (equation 35)    Downlink(:,:,k) = B(:,:,k)^(-0.5) * Fk * Gk' * A(:,:,k)^(0.5) * Uplink(:,:,k) *  A(:,:,k)^(0.5) * Gk * Fk' * B(:,:,k)^(-0.5);end;