% 引入CVX，并设置求解器为Mosek
%addpath('/path/to/cvx');
%cvx_setup;
cvx_solver mosek;
% 清空CVX环境
cvx_clear;
% 定义问题数据
C = 64; % Quantization bits
q = 64;
V = 0.5; % Lyapunov weight
alpha = 1;
Round_num = 1000; % Total rounds of training
Device_num = 20; % Number of devices
Date_num = 128 * ones(1, Device_num); % Data amount for each device
d_c = 0.1; % Compute resource requirement
M = 878538;
%功率定义
% 生成服从正态分布的随机数向量
mu = 0;
sigma = 1;
rand_nums = mu + sigma * randn(1, Device_num);
% 对随机数向量进行标准化操作
rand_nums = (rand_nums - mean(rand_nums)) / max(abs(rand_nums)) * 1;
% 计算 Power_s
Power_s = 1.0 * ones(1, Device_num) - 0.05 * rand_nums;
% 计算 Power_ijD
Power_ijD = 1.0 * ones(Device_num, Device_num) - 0.05 * rand_nums;
% 计算 Power_jir
Power_jir = 1.0 * ones(Device_num, Device_num) - 0.05 * rand_nums;
a = zeros(20);
b = ones(1, Device_num);
Frequency = 1.5 * ones(1, Device_num) - 0.1 * rand_nums;
Band = 2e7;
Min_bandwidth = 0.1 / Device_num;
N0 = dBm_to_P(-174) * Band
%计算用户到基站的信道增益
H_i = zeros(1, Device_num);
% 假设 d 是距离，以千米为单位
d = 1; % 例如，假设距离为1千米
Device_num = 20;
% 先定义距离，信道增益根据距离计算
Distance_i = randi([0, 200], 1, 20);
% 计算信道增益
for k = 1:Device_num
H_i(k) = channel_gain(Distance_i(k)); % 调用 channel_gain 函数计算信道增益
end
%注：计算信道增益的公式，我不懂，但是都这么写：gain = 10^((-128.1 - 37.6 * log10(Distance_i / 1000)) / 10 - raylrnd(0.1));
%计算用户与用户之间的信道增益
H_ij = zeros(Device_num, Device_num); % 初始化信道增益矩阵
Distance_ij = randi([0, 200], Device_num, Device_num); % 生成随机距离矩阵，可以根据实际情况修改
for i = 1:Device_num
for j = 1:Device_num
H_ij(i, j) = channel_gain(Distance_ij(i, j)); % 调用 channel_gain 函数计算信道增益
end
end
T_total = [];
D2D_total = [];
E_final = [];
D2D_energy_total = [];
t_D2D = 0;
Energy_coefficient = 0.1; % Energy efficiency
% 定义CVX变量
cvx_begin
variable l_i_s(Device_num)
variable l_ij_d(Device_num, Device_num) symmetric % 定义对称矩阵变量
variable l_ji_r(Device_num, Device_num) symmetric
% 定义目标函数
for i = 1:Device_num
for j = 1:Device_num
k1 = Power_ijD(i) * H_ij(i, j) / (N0 * Band);
k2 = Power_jir(j, i) * H_i(j) / (N0 * Band);
k = (inv_pos(-rel_entr(l_ij_d(i, j), l_ij_d(i, j) + k1)) + inv_pos(-rel_entr(l_ji_r(j, i), l_ji_r(j, i) + k2))) * a(i, j) * q * M / Band;
D2D_total = [D2D_total; k] ;
end
t_D2D = sum(D2D_total);
T_total = [T_total;
d_c * Date_num(i) / Frequency(i) + ...
inv_pos(-rel_entr(l_i_s(i), l_i_s(i) + Power_s(i) * H_i(i) / (N0 * Band))) * ...
b(i) * q * M / Band + t_D2D];
D2D_total = [];
end
minimize(max(T_total));
% 添加约束条件
subject to
l_i_s >= 0 % 非负约束
l_ij_d >= 0
l_ji_r>=0
sum(l_i_s) + sum(l_ij_d) + sum(l_ji_r) ==1
cvx_end
% 打印结果
disp(['最小化目标函数值: ' num2str(V * max(T_total) + (1 - V) * sum(E_final))]);
function gain = channel_gain(d)
% 根据距离计算增益
rng('shuffle'); % 重新设置随机数种子，使得每次运行结果不同
gain = 10 ^ ((-128.1 - 37.6 * log10(d / 1000)) / 10 - raylrnd(0.1));
end
function p = dBm_to_P(b)
p = 10 ^ ((b - 30) / 10);
end
how do I solve this problem
My optimization goal is to minimize T, and the expression for T is as follows (the optimization variable is highlighted in yellow), I used rel_entr(x,x+k), but I kept getting the following error:
Disciplined convex programming error:
Illegal operation: {real affine} + {invalid}
k = (inv_pos(-rel_entr(l_ij_d(i, j), l_ij_d(i, j) + k1)) + inv_pos(-rel_entr(l_ji_r(j, i), l_ji_r(j, i) + k2))) * a(i, j) * q * M / Band