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Copy pathmain_snr_version1.m
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main_snr_version1.m
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close all; clear all; clc;
P0_dbm = 20;
P0 = 10^(P0_dbm/10) / 1e3;
N = 20; %antenna number
K = 4; %user number
M = 30; %symol number
L = 16; %RIS element number
SNR_dB = 20; %dB
SNR_dB_set = [0:2:10];
SNR = 10^(SNR_dB/10);
N0 = 1/SNR;
epsilon = 0.01;
Num_iter = 1e2;
max_iteration = 100;
rho = 0.01;
objective_notrade_all = [];
objective_tradeoff_all = [];
gamma_notrade = zeros(1, K); rate_notrade = zeros(1, K); rate_notrade_sum = zeros(size(SNR_dB_set)); rate_notrade_all = zeros(size(SNR_dB_set));
gamma_trade = zeros(1, K); rate_trade = zeros(1, K); rate_trade_sum = zeros(size(SNR_dB_set)); rate_trade_all = zeros(size(SNR_dB_set));
gamma0 = zeros(1, K); rate0 = zeros(1, K); rate0_sum = zeros(size(SNR_dB_set)); rate0_all = zeros(size(SNR_dB_set));
gamma0_trade = zeros(1, K); rate0_trade = zeros(1, K); rate0_trade_sum = zeros(size(SNR_dB_set)); rate0_trade_all = zeros(size(SNR_dB_set));
load Rd.mat;
F = chol(Rd);
for n_iter = 1: Num_iter
i_snr = 1;
S = randi(2,K,M)*2 - 3;
H_bu = (randn(K,N) + 1j* randn(K,N))/sqrt(2);
H_br = (randn(L,N) + 1j* randn(L,N))/sqrt(2);
H_ru = (randn(K,L) + 1j* randn(K,L))/sqrt(2);
for SNR_dB = SNR_dB_set
SNR = 10^(SNR_dB/10);
N0 = 1/SNR;
%% benchmark for given beampattern
FHS0 = F'*H_bu'*S;
[U0, S0, V0] = svd(FHS0);
X0 = sqrt(M) * F* U0* eye(N,M)* V0';
THETA = diag(ones(1,L));
H = H_bu + H_ru*THETA*H_br;
%% alternating optimization for given beampattern
delta = 100;
objective_old = 1e4;
n_ite = 1;
while (delta > epsilon) && (n_ite <= max_iteration)
n_ite = n_ite + 1;
FHS = F'*H'*S;
[U1, S1, V1] = svd(FHS);
X = sqrt(M) *F* U1 * eye(N, M) * V1';
objective = norm(H*X - S, 'fro')^2;
% for i = 1 : K
% MUI(i) = mean(abs(H(i,:)*X - S(i, :)).^2);
% gamma(i) = 1/(MUI(i)+N0);
% end
%%
B = H_ru' * H_ru;
C = H_br*X*X'*H_br';
T = H_bu * X - S;
D = H_br*X*T'*H_ru;
d = diag(D);
B_C = B.*C.';
manifold = complexcirclefactory(L);
problem.M = manifold;
problem.cost = @(x) x'*B_C*x + d.'*x + x'*conj(d);
problem.egrad = @(x) 2*B_C*x + 2*conj(d);
% checkgradient(problem);
options.verbosity = 0;
[x, xcost, info, options] = steepestdescent(problem, [], options);
THETA = diag(x);
H = H_bu + H_ru*THETA*H_br;
% for i = 1 : K
% MUI(i) = mean(abs(H(i,:)*X - S(i, :)).^2);
% gamma1(i) = 1/(MUI(i)+N0);
% end
objective_new = norm(H*X - S, 'fro')^2;
delta = objective_old - objective_new;
objective_old = objective_new;
objective_notrade_all = [objective_notrade_all, objective_new];
end
H_notrade = H; X_notrade = X;
%% benchmark for tradeoff
delta = 100;
objective_old = 1e4;
n_ite = 1;
b = 100;
U = X0;
while (delta > epsilon) && (n_ite <= max_iteration)
n_ite = n_ite + 1;
%% update X
A = [sqrt(rho)*H_bu; sqrt(1-rho)*eye(N)];
B = [sqrt(rho)*S; sqrt(1-rho)*U];
Q = A'*A; G = A'*B;
[V_Q, D_Q] = eig(Q);
lambda = diag(D_Q);
lambda_min = min(lambda);
u1 = -lambda_min; u2 = b;
while abs(u2-u1) > 1e-4
u3 = (u2+u1)/2;
u13 = (u1 + u3) / 2;
u23 = (u2 + u3) / 2;
P_u3 = norm(V_Q * inv(D_Q+u3*eye(N)) *V_Q' *G, 'fro')^2;
if P_u3 > M*P0
u1 = u3;
else
u2 = u3;
end
end
lambda_opt = u3;
X_opt = pinv(Q+lambda_opt*eye(N)) * G;
%% update U
FX = F'*X_opt;
[U_bar, S_bar, V_bar] = svd(FX);
U = sqrt(M)* F * U_bar * eye(N,M) * V_bar';
objective_new = norm(A*X_opt - B, 'fro')^2;
delta = objective_old - objective_new;
objective_old = objective_new;
end
X0_trade = X_opt;
% trace(X0_trade*X0_trade')
%% alternating for tradeoff
delta = 100;
objective_old = 1e4;
n_ite = 1;
U = X0;
b = 100;
THETA = eye(L,L);
% THETA = zeros(L,L)
H = H_bu + H_ru*THETA*H_br;
while (delta > epsilon) && (n_ite <= max_iteration)
n_ite = n_ite + 1;
%% update X
A = [sqrt(rho)*H; sqrt(1-rho)*eye(N)];
B = [sqrt(rho)*S; sqrt(1-rho)*U];
Q = A'*A; G = A'*B;
[V_Q, D_Q] = eig(Q);
lambda = diag(D_Q);
lambda_min = min(lambda);
u1 = -lambda_min; u2 = b;
while abs(u2-u1) > 1e-4
u3 = (u2+u1)/2;
u13 = (u1 + u3) / 2;
u23 = (u2 + u3) / 2;
P_u3 = norm(V_Q * inv(D_Q+u3*eye(N)) *V_Q' *G, 'fro')^2;
if P_u3 > M*P0
u1 = u3;
else
u2 = u3;
end
end
lambda_opt = u3;
X_opt = pinv(Q+lambda_opt*eye(N)) * G;
% trace(X_opt* X_opt')
%% update U
FX = F'*X_opt;
[U_bar, S_bar, V_bar] = svd(FX);
U = sqrt(M)* F * U_bar * eye(N,M) * V_bar';
%% update H
B1 = H_ru' * H_ru;
C = H_br*X_opt*X_opt'*H_br';
T = H_bu * X_opt - S;
D = H_br*X_opt*T'*H_ru;
d = diag(D);
B_C = B1.*C.';
manifold = complexcirclefactory(L);
problem.M = manifold;
problem.cost = @(x) x'*B_C*x + d.'*x + x'*conj(d);
problem.egrad = @(x) 2*B_C*x + 2*conj(d);
% checkgradient(problem);
options.verbosity = 0;
[x, xcost, info, options] = steepestdescent(problem, [], options);
THETA = diag(x);
H = H_bu + H_ru*THETA*H_br;
objective = norm(H*X - S, 'fro')^2;
objective_new = norm(A*X_opt - B, 'fro')^2;
delta = objective_old - objective_new;
objective_old = objective_new;
objective_tradeoff_all = [objective_tradeoff_all, objective_new];
end
H_trade = H; X_trade = X_opt;
for i = 1 : K
MUI0(i) = mean(abs(H_bu(i,:)*X0 - S(i, :)).^2);
gamma0(i) = 1/(MUI0(i)+N0);
rate0(i) = log2(1 + gamma0(i));
end
rate0_sum(i_snr) = sum(rate0);
for i = 1 : K
MUI(i) = mean(abs(H_notrade(i,:)*X_notrade - S(i, :)).^2);
gamma_notrade(i) = 1/(MUI(i)+N0);
rate_notrade(i) = log2(1 + gamma_notrade(i));
end
rate_notrade_sum(i_snr) = sum(rate_notrade);
for i = 1 : K
MUI0(i) = mean(abs(H_bu(i,:)*X0_trade - S(i, :)).^2);
gamma0_trade(i) = 1/(MUI0(i)+N0);
rate0_trade(i) = log2(1 + gamma0_trade(i));
end
rate0_trade_sum(i_snr) = sum(rate0_trade);
for i = 1 : K
MUI(i) = mean(abs(H_trade(i,:)*X_trade - S(i, :)).^2);
gamma_trade(i) = 1/(MUI(i)+N0);
rate_trade(i) = log2(1 + gamma_trade(i));
end
rate_trade_sum(i_snr) = sum(rate_trade);
i_snr = i_snr + 1;
end
rate0_all = rate0_all + rate0_sum;
rate_notrade_all = rate_notrade_all + rate_notrade_sum;
rate0_trade_all = rate0_trade_all + rate0_trade_sum;
rate_trade_all = rate_trade_all + rate_trade_sum;
disp(['Progress - ',num2str(n_iter),'/',num2str(Num_iter)]);
end
rate0_ave = rate0_all / Num_iter;
rate_notrade_ave = rate_notrade_all / Num_iter;
rate0_trade_ave = rate0_trade_all / Num_iter;
rate_trade_ave = rate_trade_all / Num_iter;
plot(SNR_dB_set, rate_trade_ave, '-r*', 'LineWidth', 1.2);
hold on;
plot(SNR_dB_set, rate_notrade_ave, '-r+', 'LineWidth', 1.2);
plot(SNR_dB_set, rate0_trade_ave, '-b>', 'LineWidth', 1.2);
plot(SNR_dB_set, rate0_ave, '-bo', 'LineWidth', 1.2);
grid on;
xlabel('SNR(dB)');
ylabel('Sum Rate(bit/s/Hz)');
legend('RIS-aided, trade-off', 'RIS-aided, strict', 'No RIS, trade-off', 'No RIS, strict');
save('results_SNR_rho_v2.mat','rho', 'L', 'SNR_dB_set', 'rate_trade_ave', 'rate_notrade_ave', 'rate0_trade_ave', 'rate0_ave')