※ 引述《shiyoung (睽违已久的ID)》之铭言： : ※ 引述《supsymmetry (supsymmetry)》之铭言： : : A binary communication system transmits signals s_i(t)(i=1,2).The receiver t : : est statistic z(T)=a_i+n_0, where the signalcomponent a_i is either a_1=1 or : : a_2=-1 and the noise component n_0 is uniformly distributed, yielding the c : : onditional density functions p(z|s_i) given by : : p(z|s_1)=1/2 for -0.2<=z<=1.8 : : 0 otherwise : : and : : p(z|s_2)=1/2 for -1.8<=z<=0.2 : : 0 otherwise : : Find the probability of a bit error, P_B, for the case of equally likely sig : : naling and the use of an optimum decision threshold. : : 我才判决水平应该是\gamma=0,然后bit error probability 应该是 : : \int_{-0.2}^{0}1/2dz=0.1的. : : 但是怎么都不能从原来的题目的已知中推导出来. : : 求求解思路.谢谢. .... Should be Bayesian. choose S1 if P(s1 | Z ) > P(s2 | Z) , where Z is the observation. Assume S1, S2 are equally likely.. etc. Prob. of Error = 0.1 is a correct answer, However, you can choose arbitary decision boundary between [-0.2 , 0.2] and achieve the same prob of error. Or,in other words, what happens if the likelihood ration is equal to the threshold ? : From MAP criterion : 1 : > : p(z|s_1) p(z|s_2) : < : -1 : therefore P_B = Pr(s_1-s_2 < 0) what's your symbol Pr(s_1-s_2 < 0) here ? : s_1 : s_2 ┌─────┐ : ┌──┼──┐ │ : ─┴──┴──┴──┴── : -1.8 -0.2 0.2 1.8 : P_B = int_{-0.2}^{0.2} int_{x}^{0.2} 0.5 dydx : = int_{-0.2}^{0.2} 0.5(0.2-x) dx : = 0.1x - 0.25x^2 |_{-0.2}^{0.2} : = 0.01 - (-0.03) : = 0.04 No idea what's talk about. : 囧rz....跟你算的不一样 : 我不保证我的就对 : 参考看看吧 : 有错也指正一下 : 很久没算这玩意儿了 -- 赵客缦胡缨，吾钩霜雪明。银鞍照白马，飒沓如流星。 十步杀一人，千里不留行。是了拂衣去，深藏身与名。 闲过信陵饮，脱剑膝前横。将炙啖朱亥，持觞劝侯赢。 三杯吐然诺，五岳倒为轻。眼花耳热後，意气素霓生。 就赵挥金锤，邯郸先震惊。千秋二壮士，烜赫大梁城。 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 76.171.3.196