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整个通信模型 信源---信源编码---加密编码---信道编码---调制---信道---解调---信道译码---解密---信源译码---信宿 我们抽离出调制子系统 调制---信道---解调 对该部分进行可靠性分析 以连续波作为载波分析，只考虑信道加性高斯白噪声。在调制子系统中，只有解调部分对噪声进行了处理，因此可以用解调器的输出信噪比衡量系统的可靠性，（随想：输出信噪比体现了对信号放大和噪声抑制程度，输出信噪比越大，噪声对信号的幅值的影响越小，信号越纯）。因此分析可靠性只需把注意力关注在解调器即可 调制信号（有用信号+噪声）-----LPF------解调器 函数乘 <span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="cos" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑐𝑜𝑠 ,有效值变为原 <span class="MathJax_SVG" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="2" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">2 ，相应能量变为 <span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="12" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">12 ，乘 <span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="cos2ωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑐𝑜𝑠2𝜔𝑐𝑡 ,有效值变为原来<span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="12" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">12，能量变为原来 <span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="14" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">14，对于均值为0，方差为δ的窄带高斯白噪声 <span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="nc(t)cosωct−ns(t)sinωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑛𝑐(𝑡)𝑐𝑜𝑠𝜔𝑐𝑡−𝑛𝑠(𝑡)𝑠𝑖𝑛𝜔𝑐𝑡 , <span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="nc(t)" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑛𝑐(𝑡) 与 <span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="ns(t)" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑛𝑠(𝑡) 的自相关函数相等，且 <span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="Rc(0)=Rs(0)=R(0)" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑅𝑐(0)=𝑅𝑠(0)=𝑅(0) ，均值为0，故总功率（R(0)）-直流功率（均值）=交流功率（方差），故 <span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="E[nc2(t)]=E[ns2(t)]" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝐸[𝑛𝑐2(𝑡)]=𝐸[𝑛𝑠2(𝑡)] =δ。 对于DSB系统：解调器输入信号 <span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="m(t)cosωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑚(𝑡)𝑐𝑜𝑠𝜔𝑐𝑡 ,采用相干解调，输出信号 <span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="m(t)∗cos2ωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑚(𝑡)∗𝑐𝑜𝑠2𝜔𝑐𝑡 ,能量变为原来<span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="12" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">12 噪声 <span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="nc(t)cosωct−ns(t)sinωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑛𝑐(𝑡)𝑐𝑜𝑠𝜔𝑐𝑡−𝑛𝑠(𝑡)𝑠𝑖𝑛𝜔𝑐𝑡 ,采用相干解调，输出信号变为<span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="nc(t)cos2ωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑛𝑐(𝑡)𝑐𝑜𝑠2𝜔𝑐𝑡 ,能量变为原来 <span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="1212" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">1212(正交分量与同向分量的能量相同，正交分量消去，又乘了个cos) 故制度增益为2. 对于SSB系统：解调器输入信号为 <span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="nc(t)cosωct−ns(t)sinωct" role="presentation" style="display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap-mode: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">𝑛𝑐(𝑡)𝑐𝑜𝑠𝜔𝑐𝑡−𝑛𝑠(𝑡)𝑠𝑖𝑛𝜔𝑐𝑡 ，成个cos，正弦那一部分在一个周期上积分就没了，能量变为原来1/2，余弦那一部分乘cos，能量再变为1/2,总的能量变为输入的1/4,而噪声跟DSB一样都是1/4,故制度增益为1.
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发表于 2025-5-8 11:15:28