objective function::: $$\mathop{\min}*{{ X,Y}}{ P}*{{\rm tot}}({ X})+\mu(\langle\bar{{ Y}}\rangle-\lambda_{\max} (\bar{{ Y}})) : $$

Constraint:: $$\eqalignno{ &\bar{{ Y}}:=\left[\matrix{{ Y} & {\cal L}({ X})\cr{\cal L}^{H}({ X}) & 1}\right] \succeq 0}$$

and

$$\eqalignno{ &\sigma_{s}^{2}{\bf Y}(i, i)\geq\cr&\alpha_{i}\Bigg(\sigma_{s}^{2}\sum_{j\neq i}\langle { l}*{i}{ l}*{i}^{H}{ Xh}*{j}{ h}*{j}^{H}{ X}^{H}\rangle+\sigma_{{\rm re}}^{2}\langle { l}*{i}{ l}*{i}^{H}{ XX}^{H}\rangle+\sigma_{{\rm de}}^{2}\Bigg),\cr&\quad i=1,2, \ldots, { M}.}$$

The above defined are the function to calculate optimized value:

$${ P}*{{\rm tot}}({ X})=\langle(\sigma*{s}^{2}{ HH}^{H}+\sigma_{{\rm re}}^{2}I_{N}){ X}^{H}{X}\rangle.$$ which is a convex quadratic function and $${\cal L}({ X})=({ l}*{1}^{H}{ Xh}*{1}, { l}*{2}^{H}{ Xh}*{2}, \ldots, { l}*{M}^{H}{ Xh}*{M})^{T}$$ where l_1,l_2…l_M and h_1,h_2,…h_M is a N * N matrix. H is a N * M matrix and Y is a M * M matrix. and all other sigma’s is a constant value. and alpha is a threshold.

The above described objective function is a difference of two conex fuction.

Thank you sir for your reply.Yes sir I have the original paper with me. “http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6463493” . File is not getting uploaded. Sir, the paper name is “Iterative D.C. Optimization of Precoding in

Wireless MIMO Relaying” , an ieee journal.

Sir I have written a code for this except of that second constraint because I am not getting that how should I code X * X^H. But thn also it is not working. I am attaching the code. It gives the error in quad_form.

```
M=3;
N=5;
R=1;
n_r=N/R;
%since N=R*n_r
sig=10^(20/10) ; %variance of signal
s_r=10^(0/10) ; %variance of received signal
iden=eye(N); %identity function of n*n matrix
sigde=10^(0/10);
SINR_db=[1:10];
%%
for i=1:M
l_temp=conj(transpose((randn(1,N) + sqrt(-1) * randn(1,N)) / sqrt(2)));
k(:,:,i)=l_temp;
down(:,i)=k(:,:,i);
h_temp=transpose((randn(1,N) + sqrt(-1) * randn(1,N)) / sqrt(2));
m(:,:,i)=h_temp;
upli(:,i)=m(:,:,i);
end
P=(sig*upli*conj(transpose(upli))+s_r*iden(N));
for i=1:M
lin=conj(transpose(down(:,i)))*upli(:,i);
li(i)=lin;
end
L=transpose(li);
Y=L*conj(transpose(L));
P=(sig*upli*conj(transpose(upli))+s_r*iden(N));
cvx_begin
variable X(N,N)
variable Y(M,M)
for i=1:M
li=conj(transpose(down(:,i)))*X*upli(:,i);
lit(i)=li;
end
L=transpose(lit);
%Y=L*conj(transpose(L));
Ycap=[ Y, L ; conj(transpose(L)), eye(1) ];
minimize(trace(real(quad_form(X,P))+0.5*(trace(Ycap)-lambda_max(Ycap))))
subject to
[ Y, L ; conj(transpose(L)), eye(1) ] == hermitian_semidefinite(M+1)
norm(X,Inf) <= 1;
norm(Y,INF)<=1;
%X>=0
cvx end
```

Sir, I need a favour from you… I have send the paper "Iterative D.c optimization of Precoding in Wireless MIMO Relaying " Please will you tell me that the objective function and constraint of equation 15, 22, 24, 25, 28 and 34 are either convex function or non convex. And also refer me some source from where I can easily differentiate between convex function and non convex function. Sir, its my kind request to you…