# 正交振幅調變

(重新導向自 QAM)

SSB · DSB
FMPM

OOK · QAM
FSK
MSK · GFSK
PSK
CPM

CSS · DSSS · THSS · FHSS

## 概述

M-QAM訊號波形的表達式為：

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

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

## 性能

• ${\displaystyle M}$ = 星座點的個數
• ${\displaystyle E_{b}}$ = 平均位元能量
• ${\displaystyle E_{s}}$ = 平均符號能量 = ${\displaystyle E_{b}\cdot \log _{2}{M}}$
• ${\displaystyle N_{0}}$ = 雜訊功率譜密度
• ${\displaystyle P_{b}}$ = 誤位元率
• ${\displaystyle P_{bc}}$ = 每個正交載波上的誤位元率
• ${\displaystyle P_{s}}$ = 誤符號率
• ${\displaystyle P_{sc}}$ = 每個正交載波上的誤符號率
• ${\displaystyle Q(x)={\frac {1}{\sqrt {2\pi }}}\int _{x}^{\infty }e^{-t^{2}/2}dt={\frac {1}{2}}\operatorname {erfc} \left({\frac {x}{\sqrt {2}}}\right),\ x\geq {}0}$
${\displaystyle Q(x)}$表示有著零均值和單位方差的高斯隨機變量t 大於x的機率。它與高斯誤差補函數的關係是：${\displaystyle Q(x)={\frac {1}{2}}\operatorname {erfc} \left({\frac {x}{\sqrt {2}}}\right)}$

## 矩形QAM

### 誤碼率性能

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

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

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

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

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

## 非矩形QAM

QAM本身有許多可以使用的排列，這裡只列出兩種為例。

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