# 正交幅度调制

（重定向自QAM

SSB · DSB
FMPM

OOK · QAM
FSK
MSK · GFSK
PSK
CPM

CSS · DSSS · THSS · FHSS

## 概述

M-QAM信号波形的表达式为：

${\displaystyle s_{m}(t)=\Re [(A_{mc}+jA_{ms})g(t)e^{j2\pi f_{c}t}]=A_{mc}g(t)\cos 2\pi f_{c}t-A_{ms}g(t)\sin 2\pi f_{c}t{\mbox{ ,where }}m=1,2,\ldots ,M}$

${\displaystyle s_{m}(t)=\Re [V_{m}e^{j\theta m}g(t)e^{j2\pi f_{c}t}]=V_{m}g(t)\cos(2\pi f_{c}t+\theta _{m})}$

## 性能

• ${\displaystyle M}$  = 星座点的个数
• ${\displaystyle E_{b}}$  = 平均比特能量
• ${\displaystyle E_{s}}$  = 平均符号能量 = ${\displaystyle E_{b}\cdot \log _{2}{M}}$
• ${\displaystyle N_{0}}$  = 噪声功率谱密度
• ${\displaystyle P_{b}}$  = 误比特率
• ${\displaystyle P_{bc}}$  = 每个正交载波上的误比特率
• ${\displaystyle P_{s}}$  = 误符号率
• ${\displaystyle P_{sc}}$  = 每个正交载波上的误符号率
• ${\displaystyle Q(x)={\frac {1}{\sqrt {2\pi }}}\int _{x}^{\infty }e^{-t^{2}/2}dt={\frac {1}{2}}\operatorname {erfc} \left({\frac {x}{\sqrt {2}}}\right),\ x\geq {}0}$
${\displaystyle Q(x)}$ 表示有着零均值和单位方差的高斯随机变量t 大于x的概率。它与高斯误差补函数的关系是：${\displaystyle Q(x)={\frac {1}{2}}\operatorname {erfc} \left({\frac {x}{\sqrt {2}}}\right)}$

## 矩形QAM

### 误码率性能

${\displaystyle P_{sc}=P_{{\sqrt {M}}{\mbox{-PAM}}}=2\left(1-{\frac {1}{\sqrt {M}}}\right)Q\left({\sqrt {{\frac {3}{M-1}}{\frac {E_{s}}{N_{0}}}}}\right)}$ ,

${\displaystyle \,P_{s}=1-\left(1-P_{sc}\right)^{2}}$ .

${\displaystyle P_{bc}={\frac {4}{k}}\left(1-{\frac {1}{\sqrt {M}}}\right)Q\left({\sqrt {{\frac {3k}{M-1}}{\frac {E_{b}}{N_{0}}}}}\right)}$ ,

${\displaystyle P_{b}=P_{bc}}$

${\displaystyle P_{s}\leq {}4Q\left({\sqrt {\frac {3kE_{b}}{(M-1)N_{0}}}}\right)}$ .

## 非矩形QAM

QAM本身有许多可以使用的排列，这里只列出两种为例。

${\displaystyle P_{s}<(M-1)Q\left({\sqrt {d_{min}^{2}/2N_{0}}}\right)}$ .