change_V_RF.m

function V_RF = change_V_RF()
global N N_RF
global H_t V_RF

A = cell(1,9);
B = cell(1,9);
D = cell(1,9);
zeta_B = zeros(N,N_RF);
zeta_D = zeros(N,N_RF);
eta_B = zeros(N,N_RF);
eta_D = zeros(N,N_RF);
c = zeros(N,N_RF);
z = zeros(N,N_RF);
phi = zeros(N,N_RF);

for j = 1:N_RF
    V_RF_bar = V_RF;
    V_RF_bar(:,j) = [];
    A{j} = H_t * V_RF_bar*(V_RF_bar')* H_t';
    % 计算B_j,D_j,用于计算zeta和eta
    B{j} = H_t'* (A{j}^(-2)) * H_t;
    D{j} = H_t'* (A{j}^(-1)) * H_t;
    for i = 1:N
        % 计算zeta和eta
        temp = 0;
        for m = 1:1:N
            if( m~=i )
                for n = 1:1:N
                    if(n~=i)
                        temp = temp + conj(V_RF(m,j))*B{j}(m,n)*V_RF(n,j);
                    end
                end
            end
        end
        zeta_B(i,j)= B{j}(i,i)+2*real(temp);
        temp = 0;
        for m = 1:1:N
            if( m~=i )
                for n = 1:1:N
                    if(n~=i)
                        temp = temp + conj(V_RF(m,j))*D{j}(m,n)*V_RF(n,j);
                    end
                end
            end
        end
        zeta_D(i,j)= D{j}(i,i)+2*real(temp);
        V_B = B{j} * V_RF;
        V_D = D{j} * V_RF;
        eta_B(i,j) = V_B(i,j) - B{j}(i,i)*V_RF(i,j);
        eta_D(i,j) = V_D(i,j) - D{j}(i,i)*V_RF(i,j);
        % 计算theta_1，theta_2
        c(i,j) = (1 + zeta_D(i,j)) * eta_B(i,j) - zeta_B(i,j) * eta_D(i,j);
        z(i,j) = imag( 2 * eta_B(i,j) * eta_D(i,j));
        phi(i,j) = 0;
        tt = asin(imag(c(i,j))/abs(c(i,j)));
        if(real(c(i,j))>=0) phi(i,j) = tt; 
        else phi(i,j) = pi - tt; 
        end
        theta_1 = -phi(i,j) + asin(z(i,j)/abs(c(i,j)));
        theta_2 = pi - phi(i,j) - asin(z(i,j)/abs(c(i,j)));
        % 判断最优theta
        V_RF1 = exp(-1j * theta_1);
        V_RF2 = exp(-1j * theta_2);
        f1 = N * trace(A{j}^(-1)) - ...
            N * ( zeta_B(i,j) + 2 * real(conj(V_RF1)*eta_B(i,j)))/...
            (1+zeta_D(i,j)+2*real(conj(V_RF1)*eta_D(i,j)));
        f2 = N * trace(A{j}^(-1)) - ...
            N * ( zeta_B(i,j) + 2 * real(conj(V_RF2)*eta_B(i,j)))/...
            (1+zeta_D(i,j)+2*real(conj(V_RF2)*eta_D(i,j)));
        if(f1 < f2) theta_opt = theta_1; 
        else theta_opt = theta_2;
        end
        V_RF(i,j) = exp(-1j*theta_opt);
    end
end