/
clock_synchronize_algorithm.m
246 lines (237 loc) · 10.2 KB
/
clock_synchronize_algorithm.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
%On clock synchronization algorithm for wireless sensor network under unknowm delay
%autor:Mei Leng and Yik-Chung Wu
%2016.12.23 by xu
%==========================================================================
close all;
%==========================================================================
%%
clear;
clc;
N = 11;%measures times
h = 1;
for SNR = 0:15:30
%parameters setting
O = 30;%simulation runs times
H = 25;%中心节点发送时间间隔
w_sigma = 0.3 * H;%中心节点发送时刻噪声的方差
G = 30;%参考节点发送时间间隔
v_sigma = 0.3 * G;%参考节点发送时刻噪声的方差
d_lb = 0 + eps;%lower bound of fixed delay(open interval)
d_ub = 10;%upper bound of fixed delay
beta1_lb = 0.9;%lower bound of relative skew
beta1_ub = 1.1;%upper bound of relative skew
beta0_lb = -10;%lower bound of relative offset
beta0_ub = 10;%upper bound of relative offset
sigma = (H^2+G^2)/(power(10,SNR/10));%variance of random delay Xi and Yi
k = 1;
for alpha = 1:10%measures times
%time stamps
T_1 = zeros(N,O);
T_2 = zeros(N,O);
T_3 = zeros(N,O);
T_4 = zeros(N,O);
d = zeros(1,O);%real fixed delay
beta1 = zeros(1,O);%real clock skew
beta0 = zeros(1,O);%real clock offset
beta1_mle = zeros(1,O);%estimates clock skew
beta0_mle = zeros(1,O);%estimates clock offset
for o = 1:O
d(1,o) = unifrnd(d_lb,d_ub);
beta1(1,o) = unifrnd(beta1_lb,beta1_ub);
beta0(1,o) = unifrnd(beta0_lb,beta0_ub);
%produce measures
for i = 1:N
T_1(i,o) = i * H + normrnd(0,sqrt(w_sigma));
T_3(i,o) = i * G + normrnd(0,sqrt(v_sigma));
T_2(i,o) = beta1(1,o) * T_1(i,o) + beta0(1,o) + beta1(1,o) * (d(1,o) + normrnd(0,sqrt(sigma)));
T_4(i,o) = (T_3(i,o) - beta0(1,o)) / beta1(1,o) + d(1,o) + normrnd(0,sqrt(sigma));
end
%MLLE <2>alpha= alpha star
%produce alpha star
j = mod(N,3);
n = (N - j)/3;
alpha_star_star = 2*n+ceil(j/2);
for alpha_star = 1:10
for m = 1:N-alpha_star
D_1(m,alpha_star,o) = T_1(alpha_star+m,o)-T_1(m,o);
D_2(m,alpha_star,o) = T_2(alpha_star+m,o)-T_2(m,o);
D_3(m,alpha_star,o) = T_3(alpha_star+m,o)-T_3(m,o);
D_4(m,alpha_star,o) = T_4(alpha_star+m,o)-T_4(m,o);
end
beta1_mlle_PB2(alpha_star,o) = 2*sigma*beta1(1,o)^4/...
(sum(beta1(1,o)^2*D_1(:,alpha_star,o).^2+D_3(:,alpha_star,o).^2+6*beta1(1,o)^2*sigma));
end
end
%MLLE <2>alpha = alpha star
beta1_mlle_PB2_mes(h,k) = sum(beta1_mlle_PB2(k,:),2)/O;
k = k + 1;
end
figure(2)
semilogy(1:10,beta1_mlle_PB2_mes(h,:),'ok-');
hold on;
semilogy(alpha_star_star,beta1_mlle_PB2_mes(h,alpha_star_star),'rx','MarkerSize',20);
gtext(['SNR = ',num2str(SNR),' bB']);
h=h+1;
end
figure(2)
grid on;
legend('N = 11');
xlabel('\alpha');
ylabel('PB_g of the clock skew(\beta_1)');
%==========================================================================
%%
clear;
clc;
%parameters setting
O = 10000;%simulation runs times
H = 25;%中心节点发送时间间隔
w_sigma = 0.3 * H;%中心节点发送时刻噪声的方差
G = 30;%参考节点发送时间间隔
v_sigma = 0.3 * G;%参考节点发送时刻噪声的方差
d_lb = 0 + eps;%lower bound of fixed delay(open interval)
d_ub = 10;%upper bound of fixed delay
beta1_lb = 0.9;%lower bound of relative skew
beta1_ub = 1.1;%upper bound of relative skew
beta0_lb = -10;%lower bound of relative offset
beta0_ub = 10;%upper bound of relative offset
SNR = 30;%dB
sigma = (H^2+G^2)/(power(10,SNR/10));%variance of random delay Xi and Yi
k = 1;
for N = 6:2:18%measures times
%time stamps
T_1 = zeros(N,O);
T_2 = zeros(N,O);
T_3 = zeros(N,O);
T_4 = zeros(N,O);
d = zeros(1,O);%real fixed delay
beta1 = zeros(1,O);%real clock skew
beta0 = zeros(1,O);%real clock offset
beta1_mle = zeros(1,O);%estimates clock skew
beta0_mle = zeros(1,O);%estimates clock offset
beta1_CRLB = zeros(1,O);
beta0_CRLB = zeros(1,O);
d_CRLB = zeros(1,O);
beta1_mlle_1 = zeros(1,O);
beta0_mlle_1 = zeros(1,O);
beta1_mlle_PB1 = zeros(1,O);
beta0_mlle_PB1 = zeros(1,O);
beta1_mlle_2 = zeros(1,O);
beta0_mlle_2 = zeros(1,O);
beta1_mlle_PB2 = zeros(1,O);
beta0_mlle_PB2 = zeros(1,O);
beta1_my = zeros(1,O);
beta0_my = zeros(1,O);
beta1_my_PB = zeros(1,O);
beta0_my_PB = zeros(1,O);
for o = 1:O
d(1,o) = unifrnd(d_lb,d_ub);
beta1(1,o) = unifrnd(beta1_lb,beta1_ub);
beta0(1,o) = unifrnd(beta0_lb,beta0_ub);
for i = 1:N
T_1(i,o) = i * H + normrnd(0,sqrt(w_sigma));
T_3(i,o) = i * G + normrnd(0,sqrt(v_sigma));
T_2(i,o) = beta1(1,o) * T_1(i,o) + beta0(1,o) + beta1(1,o) * (d(1,o) + normrnd(0,sqrt(sigma)));
T_4(i,o) = (T_3(i,o) - beta0(1,o)) / beta1(1,o) + d(1,o) + normrnd(0,sqrt(sigma));
end
%MLE
%matrix form
Ts = [T_1(:,o);-T_4(:,o)];
Tp = [T_2(:,o) -ones(N,1);-T_3(:,o) ones(N,1)];
P = eye(2*N) - Tp * inv(Tp' * Tp) * Tp';
d_est = -(ones(1,2*N) * P * Ts + Ts' * P * ones(2*N,1))/(2 * ones(1,2*N) * P * ones(2*N,1));
theta_est = inv(Tp' * Tp)*Tp'*(Ts + d_est * ones(2*N,1));
beta1_mle(1,o) = 1/theta_est(1,1);
beta0_mle(1,o) = theta_est(2,1)/theta_est(1,1);
%CRLB
A = beta1(1,o)*beta1(1,o)*(T_1(:,o)+d(1,o))'*(T_1(:,o)+d(1,o)) +...
N*beta1(1,o)^2*sigma + (T_3(:,o)-beta0(1,o))'*(T_3(:,o)-beta0(1,o))/(beta1(1,o)^4);
B = sum(beta1(1,o)*(T_1(:,o)+d(1,o)) + (T_3(:,o)-beta0(1,o)))/(beta1(1,o)^3);
C = sum(beta1(1,o)*(T_1(:,o)+d(1,o))-(T_3(:,o)-beta0(1,o)))/(beta1(1,o)^2);
beta1_CRLB(1,o) = 2 * N *sigma/(2*N*A-beta1(1,o)^2*B^2-C^2);
beta0_CRLB(1,o) = sigma*beta1(1,o)^2*(2*N*A-C^2)/(2*N*(2*N*A-beta1(1,o)^2*B^2-C^2));
d_CRLB(1,o) = sigma*(2*N*A-beta1(1,o)^2*B^2)/(2*N*(2*N*A-beta1(1,o)^2*B^2-C^2));
%MLLE <1>alpha = N-1
alpha = N - 1;
W_1 = T_1(N,o) - T_1(1,o);
W_2 = T_2(N,o) - T_2(1,o);
W_3 = T_3(N,o) - T_3(1,o);
W_4 = T_4(N,o) - T_4(1,o);
beta1_mlle_1(1,o) = (W_2^2+W_3^2)/(W_1*W_2+W_4*W_3);
beta0_mlle_1(1,o) = sum(T_2(:,o) + T_3(:,o)-beta1_mlle_1(1,o)*(T_1(:,o)+T_4(:,o)))/(2*N);
beta1_mlle_PB1(1,o) = 2*sigma*beta1(1,o)^4/(beta1(1,o)^2*W_1^2+W_3^2+6*beta1(1,o)^2*sigma);
beta0_mlle_PB1(1,o) = sigma*beta1(1,o)^2/(2*N)+beta1_mlle_PB1(1,o)/...
(4*N^2)*(sum(beta1(1,o)*(T_1(:,o)+d(1,o))+(T_3(:,o)-beta0(1,o)))*...
sum(beta1(1,o)*(T_1(:,o)+d(1,o))+(T_3(:,o)-beta0(1,o)))/(beta1(1,o)^2)+N*sigma);
%MLLE <2>alpha= alpha star
%produce alpha star
j = mod(N,3);
n = (N - j)/3;
alpha_star = 2*n+ceil(j/2);
for m = 1:N-alpha_star
D_1(m,o) = T_1(alpha_star+m,o)-T_1(m,o);
D_2(m,o) = T_2(alpha_star+m,o)-T_2(m,o);
D_3(m,o) = T_3(alpha_star+m,o)-T_3(m,o);
D_4(m,o) = T_4(alpha_star+m,o)-T_4(m,o);
end
beta1_mlle_2(1,o) = (D_2(:,o)'*D_2(:,o)+D_3(:,o)'*D_3(:,o))/(D_1(:,o)'*D_2(:,o)+D_4(:,o)'*D_3(:,o));
beta0_mlle_2(1,o) = sum(T_2(:,o) + T_3(:,o)-beta1_mlle_2(1,o)*(T_1(:,o)+T_4(:,o)))/(2*N);
beta1_mlle_PB2(1,o) = 2*sigma*beta1(1,o)^4/(sum(beta1(1,o)^2*D_1(:,o).^2+D_3(:,o).^2+6*beta1(1,o)^2*sigma));
beta0_mlle_PB2(1,o) = sigma*beta1(1,o)^2/(2*N)+beta1_mlle_PB2(1,o)/...
(4*N^2)*(sum(beta1(1,o)*(T_1(:,o)+d(1,o))+(T_3(:,o)-beta0(1,o)))*sum(beta1(1,o)*(T_1(:,o)+d(1,o))+(T_3(:,o)-beta0(1,o)))/(beta1(1,o)^2)+N*sigma);
%Proposed algorithm
Ts_1 = T_1(:,o)+T_4(:,o);
Tp_1 = [T_2(:,o)+T_3(:,o) -2*ones(N,1)];
theta_1 = inv(Tp_1'*Tp_1)*Tp_1'*Ts_1;
beta1_my(1,o) = 1/theta_1(1,1);
beta0_my(1,o) = theta_1(2,1)/theta_1(1,1);
K = sum((T_1(:,o) + d(1,o) + (T_3(:,o)-beta0(1,o)/beta1(1,o))).^2+3*sigma)/beta1(1,o)^2;
beta1_my_PB(1,o) = 2*N*sigma/(N*K-beta1(1,o)^2*B^2);
beta0_my_PB(1,o) = sigma*beta1(1,o)^2*K/(2*N*K-2*beta1(1,o)^2*B^2);
end
%MLE
beta1_mle_mes(1,k) = (beta1 - beta1_mle)*(beta1 - beta1_mle)'/O;
beta0_mle_mes(1,k) = (beta0 - beta0_mle)*(beta0 - beta0_mle)'/O;
beta1_CRLB_mes(1,k) = sum(beta1_CRLB,2) / O;
beta0_CRLB_mes(1,k) = sum(beta0_CRLB,2) / O;
%MLLE <1>alpha = N-1
beta1_mlle_mes1(1,k) = (beta1 - beta1_mlle_1)*(beta1 - beta1_mlle_1)'/O;
beta0_mlle_mes1(1,k) = (beta0 - beta0_mlle_1)*(beta0 - beta0_mlle_1)'/O;
beta1_mlle_PB1_mes(1,k) = sum(beta1_mlle_PB1,2)/O;
beta0_mlle_PB1_mes(1,k) = sum(beta0_mlle_PB1,2)/O;
%MLLE <2>alpha = alpha star
beta1_mlle_mes2(1,k) = (beta1 - beta1_mlle_2)*(beta1 - beta1_mlle_2)'/O;
beta0_mlle_mes2(1,k) = (beta0 - beta0_mlle_2)*(beta0 - beta0_mlle_2)'/O;
beta1_mlle_PB2_mes(1,k) = sum(beta1_mlle_PB2)/O;
beta0_mlle_PB2_mes(1,k) = sum(beta0_mlle_PB2)/O;
%proposed algorithm
beta1_my_mes(1,k) = (beta1 - beta1_my)*(beta1 - beta1_my)'/O;
beta0_my_mes(1,k) = (beta0 - beta0_my)*(beta0 - beta0_my)'/O;
beta1_my_PB_mes(1,k) = sum(beta1_my_PB)/O;
beta0_my_PB_mes(1,k) = sum(beta0_my_PB)/O;
k = k + 1;
end
t = 6:2:18;
figure(3);
hold on;
plot(t,beta0_mlle_mes1,'sk-',t,beta0_mlle_PB1_mes,'dr--');
plot(t,beta0_mlle_mes2,'dk-',t,beta0_mlle_PB2_mes,'+r--');
plot(t,beta0_my_mes,'<k-',t,beta0_my_PB_mes,'xr--');
plot(t,beta0_mle_mes,'>k-',t,beta0_CRLB_mes,'or--');
legend('GE-(\alpha=N-1)','PB_g-(\alpha=N-1)','GE-(\alpha=\alpha^*)',...
'PB_g-(\alpha=\alpha^*)','Proposed','PB_p','MLE','CRLB');
grid on;
xlabel('N');
ylabel('MSE of the clock offset(\beta_0)');
axis([6,18,0.2,1]);
figure(4);
semilogy(t,beta1_mlle_mes1,'sk-',t,beta1_mlle_PB1_mes,'dr--');
hold on;
semilogy(t,beta1_mlle_mes2,'dk-',t,beta1_mlle_PB2_mes,'+r--');
plot(t,beta1_my_mes,'<k-',t,beta1_my_PB_mes,'xr--');
semilogy(t,beta1_mle_mes,'>k-',t,beta1_CRLB_mes,'or--');
legend('GE-(\alpha=N-1)','PB_g-(\alpha=N-1)','GE-(\alpha=\alpha^*)',...
'PB_g-(\alpha=\alpha^*)','Proposed','PB_p','MLE','CRLB','location','Best');
grid on;
xlabel('N');
ylabel('MSE of the clock skew (\beta_1)')
axis([6,18,1e-6,1e-4]);