%multiuser_dectect.m

clear all;
close all;

%gold squence
N=31;
step=2000;
K=10;
S1=[1 1 1 1 1 -1 -1 -1 1 1 -1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 -1 1 1 -1 -1];%a(n)=a(2)+a(-1)
S2=[1 -1 -1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 -1 -1 1 1 1 -1 1 1 1 1 1 -1 -1 1 -1 -1 1];%a(n)=a(3)+a(2)+a(1)+a(-1)
for i=1:N
    SS(i,:)=(S1~=[S2(i:N),S2(1:i-1)]);
end
SS=SS*2-1;
S=SS(1:K,:);%K*N

C(1,:)=SS(1,:);
C(2:N,:)=rand(N-1,N)*2-1;
for i=2:N
    rou=C(i,:)*C(1:i-1,:).'./dot(C(1:i-1,:),C(1:i-1,:),2).';
    C(i,:)=C(i,:)-rou*C(1:i-1,:);
end
for i=1:N
    C(i,:)=C(i,:)/sqrt(dot(C(i,:),C(i,:)));
end
C_null=C(2:N,:);

SINR_LMS=zeros(1,step);
P1_LMS=zeros(1,step);
P_i_n_LMS=zeros(1,step);
E_ex_LMS=zeros(1,step);

SINR_RLS=zeros(1,step);
P1_RLS=zeros(1,step);
P_i_n_RLS=zeros(1,step);
E_ex_RLS=zeros(1,step);

SINR_Kalman=zeros(1,step);
P1_Kalman=zeros(1,step);
P_i_n_Kalman=zeros(1,step);
E_ex_Kalman=zeros(1,step);

SNR_db=[20,30,30,30,30,30,40,40,40,50];  %SNR (in dB)
SNR=10.^(SNR_db./10);
A=sqrt(SNR./SNR(1));%1×K

repeat_time=500;
for repeat=1:repeat_time
    repeat
    %through the channel
    b=zeros(K,step);
    b=sign(rand(K,step)-0.5);
    noiseN_step=randn(N,step);  % Noise
    noiseN_step=sqrt(10./SNR(1))*noiseN_step;
    for i=1:K
        Ab(i,:)=A(i)*b(i,:);
    end
    yN_step=(Ab.'*S).';
    yN_step=yN_step+noiseN_step;
    
    [P1_temp,P_i_n_temp,y,correct,E_ex_temp]=LMS_S(b,N,K,step,yN_step,S,SNR);
    P1_LMS=P1_LMS+P1_temp;
    P_i_n_LMS=P_i_n_LMS+P_i_n_temp;
    E_ex_LMS=E_ex_LMS+E_ex_temp;

    [P1_temp,P_i_n_temp,y,correct,E_ex_temp]=RLS_S(b,N,K,step,yN_step,S,SNR);
    P1_RLS=P1_RLS+P1_temp;
    P_i_n_RLS=P_i_n_RLS+P_i_n_temp;
    E_ex_RLS=E_ex_RLS+E_ex_temp;
     
    [P1_temp,P_i_n_temp,y,correct,E_ex_temp]=Kalman_S(b,N,K,step,yN_step,S,SS,C_null,SNR);
    P1_Kalman=P1_Kalman+P1_temp;
    P_i_n_Kalman=P_i_n_Kalman+P_i_n_temp;
    E_ex_Kalman=E_ex_Kalman+E_ex_temp;   
end

SINR_LMS=P1_LMS./P_i_n_LMS;
SINR_db_LMS=10*log10(SINR_LMS);
figure(1);
hold on;
plot(SINR_db_LMS,'b');
E_ex_LMS=E_ex_LMS/repeat_time;
E_ex_LMS=abs(E_ex_LMS);
figure(2);
hold on;
plot(E_ex_LMS,'b');

SINR_RLS=P1_RLS./P_i_n_RLS;
SINR_db_RLS=10*log10(SINR_RLS);
figure(1);
hold on;
plot(SINR_db_RLS,'r');
E_ex_RLS=E_ex_RLS/repeat_time;
E_ex_RLS=abs(E_ex_RLS);
figure(2);
hold on;
plot(E_ex_RLS,'r');

SINR_Kalman=P1_Kalman./P_i_n_Kalman;
SINR_db_Kalman=10*log10(SINR_Kalman);
figure(1);
hold on;
plot(SINR_db_Kalman,'g');
E_ex_Kalman=E_ex_Kalman/repeat_time;
E_ex_Kalman=abs(E_ex_Kalman);
figure(2);
hold on;
plot(E_ex_Kalman,'g');

figure(1);
title('SIR');
legend('LMS','RLS','Kalman');
figure(2);
title('EOE');
legend('LMS','RLS','Kalman');