(b)Next we take the expectation of P(elh)with respect to the r.v.h B(x→x)=E[B(x→xIh)] Under the assumption of Rayleigh fading,we have Ix-xP14N。 - Using the approximation 1 1-V+:2e→ we obtain,asN。→0 B(→)x-xP1N。SNR It is seen that the error probability is inversely proportional to SNR.In the following,we will show that coding can be used to improve the performance. Example:Consider BPSK transmission over the flat Rayleigh fading channel.With =(E-E,we have Ix-x'P=4E,.Hence Po- E,IN。 1+E,/No Fig.7.14 shows the error probability of this signaling over the Rayleigh fading channel and the awgn channel 从AwGN信道与independent Rayleigh信道的容量曲线对比、未编码系统的错误概 率曲线对比可以看出，它们在容量上的差别(g即)要比它们的错误概率曲线之间的 别小得多，this suggests that coding can be very beneficial to compensate for fading.(编码对 衰落信道非常重要、有用) 25 (b) Next we take the expectation of ( | ) Pe h with respect to the r.v. h Px x Px xh 2 2       h   |    E Under the assumption of Rayleigh fading, we have   2 0 2 2 0 1 | | /4 1 2 1 | | /4 xx N Px x x x N               Using the approximation 1 1 , ( ) 1 2 z z z z     we obtain, as 0 N  0 , 2   2 0 1 1 | |/ Px x xx N       SNR It is seen that the error probability is inversely proportional to SNR. In the following, we will show that coding can be used to improve the performance. Example: Consider BPSK transmission over the flat Rayleigh fading channel. With     E E s , s  , we have 2 | |4 s x   x E  . Hence 0 0 1 / () 1 2 1/ s s E N P e E N          Fig.7.14 shows the error probability of this signaling over the Rayleigh fading channel and the AWGN channel. 从 AWGN 信道与 independent Rayleigh 信道的容量曲线对比、未编码系统的错误概 率曲线对比可以看出，它们在容量上的差别（gap）要比它们的错误概率曲线之间的差 别小得多，this suggests that coding can be very beneficial to compensate for fading. (编码对 衰落信道非常重要、有用)