数字基带传输系统商洪涛

<span class="equation-text" contenteditable="false" data-index="0" data-equation="s_n(t)=\begin{cases} g_1(t-nT_B) \quad 以概率P出现\\g_2(t-nT_B) \quad 以概率1-P出现 \end{cases}"><span></span><span></span></span>

稳态波：<span class="equation-text" contenteditable="false" data-index="0" data-equation="v(t)=\sum\limits_{s=-\infty}\limits^{\infty}[Pg_1(t-nT_B)+(1-P)g_2(t-nT_B)]=\sum\limits_{s=-\infty}\limits^{\infty}v_n(t)"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="v(t)的功率谱密度"><span></span><span></span></span>：<span class="equation-text" contenteditable="false" data-index="1" data-equation="P_v(f)=\sum\limits_{s=-\infty}\limits^{\infty}|f_B[PG_1(mf_B)+(1-P)G_2(mf_B)]|^2 \delta (f-mf_B)"><span></span><span></span></span>

交变波：<span class="equation-text" contenteditable="false" data-index="0" data-equation="u(t)=a_n[g_1(t-nT_B)+g_2(t-nT_B)]"><span></span><span></span></span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;其中<span class="equation-text" contenteditable="false" data-index="1" data-equation="a_n=\begin{cases} 1-P\quad 以概率P出现\\-P\quad \ \ \ \ 以概率1-P出现 \end{cases}"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="u(t)"><span></span><span></span></span>的功率谱密度：<span class="equation-text" contenteditable="false" data-index="1" data-equation="P_u(f)=f_BP(1-P)|G_1(f)-G_2(f)|^2"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="s(t)"><span></span><span></span></span>的功率谱密度：<span class="equation-text" contenteditable="false" data-index="1" data-equation="P_s(f)=P_u(f)+P_v(f)=f_BP(1-P)|G_1(f)-G_2(f)|^2+ \sum\limits_{s=-\infty}\limits^{\infty}|f_B[PG_1(mf_B)+(1-P)G_2(mf_B)]|^2 \delta (f-mf_B)"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="P_s(f)"><span></span><span></span></span>表明

单极性

双极性

单极性归零(RZ)波形

双极性归零波形

相对码波形

差分波形

多电平波形

对代码的要求：原始消息代码必须编成适合于传输<br>用的码型

对所选码型的电波形要求：电波形应适合于基带系<br>统的传输

不含直流，且低频分量尽量少<br>

应含有丰富的定时信息，以便于从接收码流中提取定时信号<br>

&nbsp;功率谱主瓣宽度窄，以节省传输频带<br>

&nbsp;不受信息源统计特性的影响，即能适应于信息源的变化<br>

具有内在的检错能力，即码型应具有一定规律性，以便利用这一规律性进行宏观监测<br>

&nbsp;编译码简单，以降低通信延时和成本

AMI码：传号交替反转码

<font color="#ff0000">HDB3码</font>：&nbsp;3阶高密度双极性码

双相码：也称曼彻斯特（&nbsp;Manchester）码

差分双相码

密勒码：又称延迟调制码

CMI码：&nbsp;CMI码是传号反转码的简称

块编码<br>

码间串扰

信道加性噪声

接收滤波器输出信号：<span class="equation-text" contenteditable="false" data-index="0" data-equation="r(t)=d(t)*h(t)+n_R(t)=\sum\limits_{n=-\infty}\limits^{\infty}a_nh(t-nT_s)+n_R(t)"><span></span><span></span></span><br>nR(t)是加性噪声n(t)经过接收滤波器后输出的噪声<br>

抽样判决：抽样判决器对r(t)进行抽样判决<br>在<span class="equation-text" contenteditable="false" data-index="0" data-equation="r(t)"><span></span><span></span></span>上抽样判决输出：<span class="equation-text" contenteditable="false" data-index="1" data-equation="r(kTs+t_0)=a_kh(t_0)+\sum\limits_{n\neq k}a_nh[(k-n)T_s+t_0]+n_R(kTs+t_0)"><span></span><span></span></span>

基本思想：<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sum\limits_{n\neq k}a_nh[(k-n)T_s+t_0]=0"><span></span><span></span></span>

无码间串扰的传输特性的设计

总误码率：<span class="equation-text" contenteditable="false" data-index="0" data-equation="P(e)=P(1)P(0|1)+P(0)P(1|0)"><span></span><span></span></span>

令<span class="equation-text" contenteditable="false" data-index="0" data-equation="\frac{\partial P_e}{\partial V_d}=0"><span></span><span></span></span>&nbsp; 有最佳门限电平：<span class="equation-text" contenteditable="false" data-index="1" data-equation="V^*_d=\frac{\sigma^2_n}{2A}\ln \frac{P(0)}{P(1)}"><span></span><span></span></span>

二进制双极性信号且<span class="equation-text" data-index="0" data-equation="P(1)=P(0)=\frac{1}{2}" contenteditable="false"><span></span><span></span></span><br><font color="#ff0000">最佳门限电平：<span class="equation-text" data-index="1" data-equation="V^*_d=0" contenteditable="false"><span></span><span></span></span></font><br>总误码率：<span class="equation-text" data-index="2" data-equation="P_e=\frac{1}{2}[P(0|1)+P(1|0)]=\frac{1}{2}[1-erf(\frac{A}{\sqrt{2} \sigma_n})]=\frac{1}{2}erfc(\frac{A}{\sqrt{2} \sigma_n})" contenteditable="false"><span></span><span></span></span><br>

二进制单极性信号且<span class="equation-text" data-index="0" data-equation="P(1)=P(0)=\frac{1}{2}" contenteditable="false"><span></span><span></span></span><br><font color="#ff0000">最佳门限电平：<span class="equation-text" data-index="1" data-equation="V^*_d=\frac{A}{2} +\frac{\sigma^2_n}{A}\ln \frac{P(0)}{P(1)}=\frac{A}{2}" contenteditable="false"><span></span><span></span></span></font><br>总误码率：<span class="equation-text" data-index="2" data-equation="P_e=\frac{1}{2}erfc(\frac{A}{2\sqrt{2} \sigma_n})" contenteditable="false"><span></span><span></span></span><br>