10 -M-QAM bound Shannon bound (Rayleign) Shannon bound (AWGN) 64-QAM 32-QAM 16-0AM 0 20 Eb/NO (dB) Fig.7.13 Capacity limits of M-QAM signaling on the ii.d.Rayleigh channel with perfect CSI at receiver 7.4 Coding for Fading Channels 通过前面的容 分析，我们看到采用编码方法可以实现逼近衰落信道容量限的信息 传输，下面我们来讨论编码系统的设计准则与系统错误概率。作为对比，我们首先看 下衰落信道中未编码系统的性能。 7.4.1 Performance of Uncoded System in Independent Fading Channels Consider the independent fading channel: y=hx+n,x∈X (未编码信号是标量) The error probability with perfect CSI at receiver can be evaluated as follows. (a)We first compute the error probability P(eh)by assuming hconstant From Chapter 2,the pairwise error probability (PEP)conditioned onhis given by B6→xIM)=gx-） V2N Applying union bound,the conditional error probability P(exh)is upper-bounded by P(elx,h)s∑B(x→x'Ih) 2424 -5 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 Eb/N0 (dB) Capacity C (bits per 2D symbol) M-QAM bound Shannon bound (Rayleign) Shannon bound (AWGN) 64-QAM 32-QAM 16-QAM Fig. 7.13 Capacity limits of M-QAM signaling on the i.i.d. Rayleigh channel with perfect CSI at receiver 7.4 Coding for Fading Channels 通过前面的容量分析，我们看到采用编码方法可以实现逼近衰落信道容量限的信息 传输，下面我们来讨论编码系统的设计准则与系统错误概率。作为对比，我们首先看一 下衰落信道中未编码系统的性能。 7.4.1 Performance of Uncoded System in Independent Fading Channels Consider the independent fading channel: y hx n x    ,  (未编码信号是标量) The error probability with perfect CSI at receiver can be evaluated as follows. (a) We first compute the error probability ( | ) Pe h by assuming h constant. From Chapter 2, the pairwise error probability (PEP) conditioned on h is given by 2   0 | ( )| | 2 hx x Px xh Q N            Applying union bound, the conditional error probability ( | , ) Pe xh is upper-bounded by (|,) | 2   x x Pe xh P x x h     