# Convex Approximation Techniques for Joint Multiuser Downlink Beamforming and Admission Control

Dear,

We have the following problem: http://www.ece.umn.edu/~nikos/MatSidLuoTasTWC2008.pdf.

We have just started working with CVX tool. However, we didn’t get the expected results for the first algorithm defined in the paper(D-SDR).

``````            cvx_clear;
cvx_quiet(true);
cvx_solver sedumi
cvx_begin
variable W(N*K,N*K) symmetric;
variable S(2*K,2*K) symmetric;

minimize(e*trace(W)+(1-e)*trace(One_matrix*S));
subject to
%the constraints

%the power constraint
trace(W)<=P;

%the SINR constraint
for i=1:K
trace(H(1+(i-1)*N:i*N,1+(i-1)*N:i*N)*W(1+(i-1)*N:i*N,1+(i-1)*N:i*N))  +  1/delta*trace(ones(2)*S(2*i-1:2*i,2*i-1:2*i))  >=  c*(trace(H_k(:,:,i)*W)-trace(H(1+(i-1)*N:i*N,1+(i-1)*N:i*N)*W(1+(i-1)*N:i*N,1+(i-1)*N:i*N))+sigma);
end
%Construction of the beamforming big matrix
W(1:N,N+1:N*K) == zeros(N,N*(K-1));
W(N*(K-1)+1:N*K,1:N*(K-1)) == zeros(N,N*(K-1));
for i=N+1:N:N*(K-2)+1
W(i:i+N-1,1:i-1) == zeros(N,i-1);
W(i:i+N-1,i+N:N*K) == zeros(N,N*(K-1)-i+1);
end

%Construction of the admission control big matrix
S(1:2,3:2*K) == zeros(2,2*K-2);
S(2*K-1:2*K,1:2*(K-1)) == zeros(2,2*K-2);
for i=3:2:2*K-3
S(i:i+1,1:i-1) == zeros(2,i-1);
S(i:i+1,i+2:2*K) == zeros(2,2*K-i-1);
end
for i=1:2*K
S(i,i) == 1 ;
end

%The semidefiniteness constraint
W == semidefinite(N*K);
S == semidefinite(2*K);

cvx_end
``````

Can you please help me to know if it is useful to optimize this code with this tool and how can i change it in order to be near the given solution or I have to use another tool(SeDuMi, YALMIP).