应用介绍

此项目是六种检测门限的MATLAB仿真代码。

下面展示部分代码：

%假设二元信号模型为：

%H0: x = -1 + n

%H1: x = 1 + n

%n是均值为0，方差为0.5的高斯观测噪声

%H0和H1的先验概率分别为0.3和0.7

%代价因子:c00 = 1;c10 = 4; c11 = 2; c01 = 8

%观测次数为1

clear;close all;

syms x;%观测量

mu0 = -1;

mu1 = 1;

sigma = (0.5)^(0.5);

PH0 = 0.3;

PH1 = 0.7;

c00 = 1;

c10 = 4;

c11 = 2;

c01 = 8;

%计算似然比函数

lamdax = exp(4*x);

lx = x;%两边取对数

%计算似然比门限cita

cita = (PH0*(c10-c00))/(PH1*(c01-c11));

gama = 1/4*log(cita);%两边取对数，gama即为贝叶斯检测中的最佳门限

fprintf('贝叶斯判决的检测门限为\n%f\n',gama);

%计算四个条件概率和检测门限的关系

PH0_H1 = zeros(1,601);

PH0_H0 = zeros(1,601);

PH1_H1 = zeros(1,601);

PH1_H0 = zeros(1,601);

C = zeros(1,601);   %平均代价

for n=1:601

    PH0_H0(n) = normcdf(0.01*(n-301),mu0,sigma);

    PH1_H0(n) = 1-normcdf(0.01*(n-301),mu0,sigma);

    PH0_H1(n) = normcdf(0.01*(n-301),mu1,sigma);

    PH1_H1(n) = 1-normcdf(0.01*(n-301),mu1,sigma);

    C(n) = PH0*c10 + PH1*c11 + PH1*(c01-c11)*PH0_H1(n) - PH0*(c10-c00)*PH0_H0(n);

end

n=1:601;

figure(1)

plot(0.01*(n-301),PH0_H0);hold on;

plot(0.01*(n-301),PH1_H0);hold on;

plot(0.01*(n-301),PH0_H1);hold on;

plot(0.01*(n-301),PH1_H1);hold on;

title("条件概率和检测门限的关系");legend("P(H0|H0)","P(H1|H0)","P(H0|H1)","P(H1|H1)");

xlabel("检测门限");ylabel("概率");

figure(2)

plot(0.01*(n-301),C);hold on;

[~,t] = min(C);%寻找最小平均代价

plot(0.01*(n(t)-301),C(t),'rs','MarkerSize',6);%在图上标出该点

str = ['P(' num2str(0.01*(n(t)-301)) ',' num2str(C(t)) ')'];

text(0.01*(n(t)-301),C(t),str) %在图上标出平均代价和其对应的门限

title("平均代价和检测门限的关系");xlabel("检测门限");ylabel("平均代价");

.................想了解更多请下载附件。