The problem from the paper whose doi is “10.1109/TWC.2017.2789293” is as follows:

I don’t know how to express the formula in the red box. And I have learnt about this one http://ask.cvxr.com/t/log-convex/9169. but it didn’t work, I ran the code in this way only to get a wrong conclusion. And my code is as follows:

%SCA

epsilon_Traj = 1;

obj1 = 0;

t = 0;

Q_t = Q_0;

V_t = V_0;

Grad =zeros(M,N+1,K);

tmp1 = zeros(K,N+1);

for k = 1:K

for m =1:M

tmp1(k,: ) = tmp1(k,:)+Pbeta0./(Heig^2+norms(Q_t(:,:,m)-W(:,:,k),2).^2);beta0./((Heig^2+norms(Q_t(:,:,m)-W(:,:,k),2).^2).^2)./tmp1(k,:)/log(2);

end

end

tmp1 = tmp1+sigma2;

item1 = log2(tmp1);

for k = 1:K

for m = 1:M

Grad(m,:,k) = P

end

end

while epsilon_Traj >= 1e-4

t = t+1;

cvx_begin quiet

variable Q(2,N+1,M);

variable V(2,N+1,M);

variable A(2,N+1,M);

variable yita;

variable S(M,N+1,K);

variable y(M,N+1,K);

variable R_lb2(M,N+1,K);

expression varia(M,N+1,K)

expression R_lb1(K,N+1);

expression Tmp(M,N+1);

expression cons1(K,N+1);

maximize(yita)

subject to

for k = 1:K

for m = 1:M

y(m,:,k) >= rel_entr(1,(Heig^2+S(m,:,k))/(Pbeta0));beta0./((Heig^2+norms(Q_t(:,:,m)-W(:,:,k),2).^2).^2)./tmp1(k,:)/log(2);

end

end

for k = 1:K

for m = 1:M

varia(m,:,k) = norms(Q_t(:,:,m)-W(:,:,k).ones(2,N+1),2).^2-pow_pos(norms(Q(:,:,m)-W(:,:,k).(V(:,:,m)-V_t(:,:,m))).’ >= Vmin^2;ones(2,N+1),2),2);V_t(:,:,m).’

if M > 1

if m == 1

R_lb2(m,:,k) >= log_sum_exp([y(2:M,:,k);ones(1,N+1)log(sigma2)],1);(Q(:,:,m)-Q_t(:,:,m))).’

elseif m == M

R_lb2(m,:,k) >= log_sum_exp([y(1:M-1,:,k);ones(1,N+1)log(sigma2)],1);diag((Q_t(:,:,m)-W(:,1,k)).’

else

R_lb2(m,:,k) >= log_sum_exp([y(1:M-1,:,k);y(m+1:M,:,k);ones(1,N+1)log(sigma2)],1);1e-5

end

end

end

R_lb1(k,: ) = sum(Grad(:,:,k).varia(:,:,k),1)+item1(k,:);(R_lb1(k,:)-R_lb2(m,:,k));

end

for k = 1:K

for m = 1:M

cons1(k,: ) = cons1(k,:)+Alp(m,:,k).

end

end

sum(cons1,2)/(N+1) >= yita

for k = 1:K

for m = 1:M

S(m,:,k) <= norms(Q_t(:,:,m)-W(:,1,k),2,1).^2+ …

2

end

end

for m = 1:M

norms(V(:,:,m),2,1) <= Vmax;

norms(V_t(:,:,m),2,1).^2+diag(2

norms(A(:,:,m),2,1) <= amax;

Q(:,2:N+1,m) == Q(:,1:N,m)+V(:,1:N,m)deltat+1/2A(:,1:N,m)deltat^2;beta0./(Heig^2+norms(Q_t(:,:,m)-W(:,:,k),2).^2);

V(:,2:N+1,m) == V(:,1:N,m)+A(:,1:N,m)deltat;1e-5;

end

cvx_end

if ~contains(cvx_status,‘Solved’)

break;

end

obj2 = yita

epsilon_Traj = abs(obj2-obj1)/abs(obj2)

obj1 = obj2;

%update

Q_t = Q;

V_t = V;

Grad =zeros(M,N+1,K);

tmp1 = zeros(K,N+1);

for k = 1:K

for m =1 :M

tmp1(k,: ) = tmp1(k,:)+P

end

end

tmp1 = tmp1+sigma2;

item1 = log2(tmp1);

for k = 1:K

for m = 1:M

Grad(m,:,k) = P

end

end

end

This problem has confused me for too long, I would appreciate it if anyone can help me.