As you can see, it seems that the results are not correct. can you help me?
cvx_begin
variable q1(2,N)
variable gamma_k(N,K) nonnegative
variable rho(N,1) nonnegative
variable S(N,K) nonnegative
variable v(N,1) nonnegative
variable e(N,1) nonnegative
variable f(N,1) nonnegative
variable T_j(N,J) nonnegative
variable g(N,1) nonnegative
expression Gj_lb(J,N)
expression rate(K,N)
expression rate_temp(N,K)
% expression d_uk(2,1)
% expression d_tj(2,J)
% expression d_e(2,1)
for n=1:N
% Hk=(H_irs_users_hat(:,:,n)'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n))';
% he=(h_irs_eve_hat(:,n)'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n))';
for k=1:K
rate(k,n) = Alpha_k(k,n)*(log(1+gamma_k(n,k))-log(1+rho0(n))-(rho(n)-rho0(n))/(1+rho0(n)));
end
end
maximize (sum(sum(rate))/N/log(2))
subject to
%trajectory
q1(:,1)==q_s
q1(:,N)==q_f
for n=2:N
norm(q1(:,n)-q1(:,n-1))<=vmax*delta_T;
% norm([2*(q1(:,n)-q1(:,n-1));1-(vmax*delta_T)^2])<=1+(vmax*delta_T)^2;
norm([2*(q1(:,n)-q0(:,n));1-Delta])<=1+Delta;%trajectory approximation constraint
end
% time slot iteration
for n=1:N
% rho slack
he_n=[h_bs_eve_hat(:,n)'*W0(:,n);h_irs_eve'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n)*W0(:,n)];
% He_n=([h_bs_eve_hat(:,n)'*W0(:,n);h_irs_eve'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n)*W0(:,n)]*[h_bs_eve_hat(:,n)'*W0(:,n);h_irs_eve'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n)*W0(:,n)]');
% real([e(n),f(n)]*He_n*[e(n),f(n)]')<=rho(n);
norm([2*[e(n),f(n)]*he_n,1-rho(n)])<=1+rho(n);
%gamma_k slack
Hk=(H_irs_users'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n))';
for k=1:K
Huk_n=([H_bs_users_hat(:,k,n)'*W0(:,n);Hk(:,k)'*W0(:,n)]*[H_bs_users_hat(:,k,n)'*W0(:,n);Hk(:,k)'*W0(:,n)]');
d_uk0=[S0(n,k),v0(n)]';
real(d_uk0'*Huk_n*d_uk0+2*d_uk0'*Huk_n*([S(n,k),v(n)]'-d_uk0))>=gamma_k(n,k);
% gamma_k(n,k)>=0;
end
% target detection power constraint
Ht=(H_irs_targets'*diag(Phi0(:,n))*H_bs_irs_hat(:,:,n))';
for j=1:J
d_tj0=[T_j0(n,j),g0(n)]';
Htj_n=([H_bs_targets_hat(:,j,n)'*W0(:,n);Ht(:,j)'*W0(:,n)]*[H_bs_targets_hat(:,j,n)'*W0(:,n);Ht(:,j)'*W0(:,n)]');
% Gj_lb(j,n)= real(d_tj0'*Htj_n*d_tj0+2*d_tj0'*Htj_n*([T_j(n,j),g(n)]'-d_tj0));
Gj_lb(j,n)= real(2*d_tj0'*Htj_n*[T_j(n,j),g(n)]'-d_tj0'*Htj_n*d_tj0);
Beta_j(j,n)*(Gj_lb(j,n)-1)>=0;
end
% distance SCA constraint
for k=1:K
% Snk
square_pos(norm(q1(:,n)-P_u(:,k)))+H_u^2-eta^(4/alpha)*((4/alpha+1)*S0(n,k)^(-4/alpha)-4/alpha*S0(n,k)^(-4/alpha-1)*S(n,k))<=0;
S(n,k)>=eta*(2*norm(q_s-q_f)^2+2*H_u^2)^(-alpha/2);
end
% v
square_pos(norm(q1(:,n)-p_irs))+(H_u-H_i)^2-eta^(4/kappa)*((4/kappa+1)*v0(n)^(-4/kappa)-4/kappa*v0(n)^(-4/kappa-1)*v(n))<=0;
v(n)>=eta*(2*norm(q_s-q_f)^2+2*H_u^2)^(-kappa/2);
% g
square_pos(norm(q1(:,n)-p_irs))+(H_u-H_i)^2-theta^(4/kappa)*((4/kappa+1)*g0(n)^(-4/kappa)-4/kappa*g0(n)^(-4/kappa-1)*g(n))<=0;
g(n)>=theta*(2*norm(q_s-q_f)^2+2*H_u^2)^(-kappa/2);
% e
eta^(4/alpha)*pow_p(e(n),-4/alpha)-(norm(q0(:,n)-p_e)^2+H_u^2+2*(q0(:,n)-p_e)'*(q1(:,n)-q0(:,n)))<=0;
e(n)<=eta*H_u^(-2/alpha);
%f
eta^(4/kappa)*pow_p(f(n),-4/kappa)-(norm(q0(:,n))^2+(H_u-H_i)^2+2*q0(:,n)'*(q1(:,n)-q0(:,n)))<=0;
f(n)<=eta*(H_u-H_i)^(-2/kappa);
% tj
for j=1:J
square_pos(norm(q1(:,n)-P_t(:,j)))+H_u^2-theta^(4/alpha)*((4/alpha+1)*T_j0(n,j)^(-4/alpha)-4/alpha*T_j0(n,j)^(-4/alpha-1)*T_j(n,j))<=0;
T_j(n,j)>=theta*(2*norm(q_s-q_f)^2+2*H_u^2)^(-alpha/2);
end
end
% QoS constraint
for k=1:K
for n=1:N
rate_temp(n,k)=log(1+gamma_k(n,k))/log(2);
end
sum(Alpha_k(k,:).*rate_temp(:,k)')>=r_th*N;
end
cvx_end