From 8f3506b17e23349b18506445d116fca1c1de34dc Mon Sep 17 00:00:00 2001 From: Anatoly Date: Sat, 8 May 2021 17:48:49 +0300 Subject: [PATCH] =?UTF-8?q?=D0=97=D0=B0=D0=BA=D0=BE=D0=BD=D1=87=D0=B8?= =?UTF-8?q?=D0=BB=20=D0=B4=D0=B5=D0=BC=D0=BE=D0=B4=D1=83=D0=BB=D1=8F=D1=82?= =?UTF-8?q?=D0=BE=D1=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- decoder.tex | 18 ++-- images/demodulator.png | Bin 0 -> 101279 bytes term_paper.pdf | Bin 1084107 -> 1170340 bytes term_paper.tex | 234 +++++++++++++++++++++++++++++++++++++++-- 4 files changed, 237 insertions(+), 15 deletions(-) create mode 100644 images/demodulator.png diff --git a/decoder.tex b/decoder.tex index 0b1d92b..570eb01 100644 --- a/decoder.tex +++ b/decoder.tex @@ -1,4 +1,4 @@ -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=1.2cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -85,7 +85,7 @@ \caption{Решетка декодера} \label{fig:decoder} \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=2cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -152,7 +152,7 @@ \caption{Сегмент решетки декодера от $t=0$, до $t=3$} \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=2cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -236,7 +236,7 @@ \caption{Сегмент решетки декодера от $t=0$, до $t=4$} \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=2cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -336,7 +336,7 @@ \caption{Сегмент решетки декодера от $t=0$, до $t=5$} \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=1.8cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -452,7 +452,7 @@ \caption{Сегмент решетки декодера от $t=0$, до $t=6$} \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=1.58cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -583,7 +583,7 @@ \caption{Сегмент решетки декодера от $t=0$, до $t=7$} \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=1.36cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -727,7 +727,7 @@ \end{figure} -\begin{figure} +\begin{figure}[H] \begin{tikzpicture}[x=1.2cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; @@ -887,7 +887,7 @@ \end{figure} \begin{landscape} - \begin{figure} + \begin{figure}[H] \begin{tikzpicture}[x=1.4cm, y=-1cm] \node at (-0.5,0) [left] {$s_1=00$}; diff --git a/images/demodulator.png b/images/demodulator.png new file mode 100644 index 0000000000000000000000000000000000000000..572074b8182c68a9da7c890e2f2898200c153a69 GIT binary patch literal 101279 zcmd4&g-O@3%NS6rG-6bJuFe4!#h!TS2&?Vg>AT3C@QqoA5 z@LS_`KlgKe@B97%AKM0VGH0!Gtt0k*KaLZr{Xm8A2F(o&3=BdwRk$t&1~v=>1FHrf z7kpDWz|o3SNic76IZ+UBIo+a=Q(7TRa7cJE zAG9{--BRD`y_S0Yq}6>j?F{=H(ZTl-U2VrOeVsh<$(i&jMp%L(4XzYP_zOa|$8qti z6jZ;6jW6F{(=XLxydRv<%&Wfoa}`QxV(Ib{0|WWln5Ca2$7=RPMI)nT8UgW=qamW`RL%hdm%6LGiAa&KBH-kxQmfRjMz_VDQa zE#BijRSkzDFa?y~PX-s~_D`;S55k!r`E>i|m(%C>V`-0-t?#wK!q>TDbL(?)+73?y zs`@tj&~MNyFjHzY+L7 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ЛИСТА +\newpage +\tableofcontents \newpage Цель курсовой работы -- изучить и разработать систему цифровой связи, @@ -124,7 +131,7 @@ \end{figure} В систему входят следующие функциональные узлы с последующими назначениями: -\begin{enumerate} +\begin{itemize} \item Источник сообщений -- создает реализации $a(t)$ случайного процесса $A(t)$. \item Аналого-цифровой преобразователь -- преобразует аналоговый @@ -159,7 +166,7 @@ \item Цифро-аналоговый преобразователь -- для восстановления аналоговой формы сигнала $\hat{a}(t)$ из его цифрового представления; \item Получатель сообщений. -\end{enumerate} +\end{itemize} \section{Исходные данные} $m=41$ @@ -1178,15 +1185,230 @@ $n(t)$ типа гауссовского белого шума. Сигнал $Z( Требуется: \begin{enumerate} + \item Определить минимальную ширину полосы частот $F_k$ + непрерывного канала, необходимую для передачи по каналу сигнала + $S(t)$ с выхода модулятора. + \begin{equation} + \begin{split} + T_B=\frac{\Delta t}{2k}=2\,мкс\\ + T_S=4\cdot T_B=4\cdot2=8\,мкс + \end{split} + \end{equation} + \begin{equation} + F_k=4\cdot\frac{1}{T_S}=4\cdot\frac{1}{8\cdot10^{-6}}=5\cdot10^5\,Гц + \end{equation} + + \item Определить $P_с$ -- среднюю мощность информационного сигнала + $\mu\cdot S(t)$ на выходе канала. + \begin{equation} + P_с=\frac{E_{ср}}{T_S}=h^2=1\,В^2 + \end{equation} + + \item Определить $P_п$ -- среднюю мощность помехи $n(t)$ на выходе + канала и найти отношение $P_с/P_п$. + \begin{equation} + P_п=N_0\cdot F_k=2,3\cdot5\cdot10^{-2}=0,115\,В^2 + \end{equation} + \begin{equation} + P_с/P_п=1/0,115=8,7 + \end{equation} + \item Рассчитать пропускную способность $C$ (за секунду) + непрерывного канала. + \begin{equation} + C=F_k\log_2\biggr(1+\frac{P_c}{P_п}\biggr) + =5\cdot 10^5\cdot\log_2(1+8,7)=1,64\,Мбит/с + \end{equation} +\end{enumerate} + +\subsection{Демодулятор} +Требуется: +\begin{enumerate} + \item Изобразить структурную схему когерентного демодулятора, + оптимального по критерию максимального правдоподобия для заданного + сигнала квадратурной модуляции. + \begin{figure}[H] + \centering + \includegraphics{demodulator} + \caption{Структурная схема когерентного демодулятора + для сигнала КАМ-16} + \end{figure} + + \item Написать алгоритмы работы решающих устройств РУ1 и РУ2 в + составе когерентного демодулятора. + + В момент окончания каждого символьного интервала длительностью + $T_S$ решающее устройство определяет номер входа, на котором + напряжение максимально, и формирует соответствующий дибит в + параллельном формате. + + \item Определить вероятности ошибок на выходах РУ1 и РУ2 при + значениях символов $I_n$ и $Q_n$, равных $h$, $–h$, + $3h$, $-3h$, когда $h=1$ B. + + \begin{center} + \begin{tabular}{ | c | c | } + \hline + Передаваемая величина ИС&Вероятность ошибки в РУ\\ + \hline + $I_n=Q_n=\pm h$&$p(ош)=2Q\sqrt{\dfrac{2E_1}{N_0}}$\\ + \hline + $I_n=Q_n=\pm 3h$&$p(ош)=Q\sqrt{\dfrac{2E_1}{N_0}}$\\ + \hline + \end{tabular} + \end{center} + + \item На четырех символьных интервалах длительностью $T_S$ + нарисовать сигналы на выходах РУ1 и РУ2 демодулятора, + соответствующие сигналам на выходе блока ФМС, которые поступают на + два входа преобразователя параллельного кода в последовательный + код. Под двумя построенными графиками, используя сигнальное + созвездие для заданного вида модуляции, изобразить график сигнала + на выходе преобразователя кода в виде соответствующей + последовательности прямоугольных импульсов на входе блока ФМС + длительностью $T_B$. + + \begin{figure}[H] + \begin{tikzpicture}[x=0.8cm, y=-0.8cm] + \draw[->, very thick] (0,2) -- (16.2,2); + \draw[->, very thick] (0,4.2) -- (0,-0.2); + + \node at (-0.5,0) [left] {$3h$}; + \node at (-0.5,1) [left] {$h$}; + \node at (-0.5,2) [left] {$0$}; + \node at (-0.5,3) [left] {$-h$}; + \node at (-0.5,4) [left] {$-3h$}; + + \draw[blue] (0,4) -- (4,4) -- (4,1); + \draw[blue] (4,1) -- (8,1) -- (8,3); + \draw[blue] (8,3) -- (12,3) -- (12,0); + \draw[blue] (12,0) -- (16,0); + + \draw[red] (0,3) -- (4,3) -- (4,0); + \draw[red] (4,0) -- (8,0) -- (8,3); + \draw[red] (8,3) -- (12,3) -- (12,4); + \draw[red] (12,4) -- (16,4); + + \node at (16,0) [right] {РУ1}; + \node at (16,4) [right] {РУ2}; + \end{tikzpicture} + \caption{Сигналы на входе ФМС} + \end{figure} + + Сопоставив значения графика с рис. \ref{fig:cam_16} получим: + + \begin{figure}[H] + \hspace*{42pt}\begin{tikzpicture}[x=0.8cm, y=-1cm] + \draw[->, very thick] (0,1) -- (16.2,1); + \draw[->, very thick] (0,2.2) -- (0,-0.2); + + \draw (0,0) -- (3,0) -- (3,2); + \draw (3,2) -- (7,2) -- (7,0); + \draw (7,0) -- (9,0) -- (9,2); + \draw (9,2) -- (10,2) -- (10,0); + \draw (10,0) -- (11,0) -- (11,2); + \draw (11,2) -- (13,2) -- (13,0); + \draw (13,0) -- (16,0); + + \node at (0.5,-0.5) {$[1$}; + \node at (1.5,-0.5) {$1$}; + + \node at (2.5,-0.5) {$1$}; + \node at (3.5,-0.5) {$0]$}; + + \node at (4.5,-0.5) {$[0$}; + \node at (5.5,-0.5) {$0$}; + + \node at (6.5,-0.5) {$0$}; + \node at (7.5,-0.5) {$1]$}; + + \node at (8.5,-0.5) {$[1$}; + \node at (9.5,-0.5) {$0$}; + + \node at (10.5,-0.5) {$1$}; + \node at (11.5,-0.5) {$0]$}; + + \node at (12.5,-0.5) {$[0$}; + \node at (13.5,-0.5) {$1$}; + + \node at (14.5,-0.5) {$1$}; + \node at (15.5,-0.5) {$1]$}; + \end{tikzpicture} + \caption{Сигнал на выходе преобразователя кода} + \end{figure} + + \item Определить вероятности ошибок + \begin{equation} + p_{\ovund{I_n=h}{Q_n=h}}(ош.п);\, + p_{\ovund{I_n=3h}{Q_n=3h}}(ош.п);\, + p_{\ovund{I_n=h}{Q_n=3h}}(ош.п) + \end{equation} + на выходе преобразователя параллельного кода в последовательный код, + где $p_{\ovund{I_n=h}{Q_n=h}}(ош.п)$ -- обозначение вероятности + ошибочного приема, если $I_n=h$, $Q_n=h$. + \begin{equation} + E_1=\frac{h^2\cdot T}{2\cdot1,27^2}=2,48\cdot10^{-6} + \end{equation} + \begin{equation} + Q\sqrt{\dfrac{2E_1}{N_0}}=Q(4,64)\approx34\cdot10^{-7} + \end{equation} + + \begin{equation} + \begin{split} + p_{\ovund{I_n=h}{Q_n=h}}(ош.п)& + =p_{I_n=h}(ош)+p_{Q_n=h}(ош) + -p_{I_n=h}(ош)\cdot p_{Q_n=h}(ош)\\[-8pt] + &=13,6\cdot10^{-6}\\[10pt] + p_{\ovund{I_n=3h}{Q_n=3h}}(ош.п)& + =p_{I_n=3h}(ош)+p_{Q_n=3h}(ош) + -p_{I_n=3h}(ош)\cdot p_{Q_n=3h}(ош)\\[-8pt] + &=6,8\cdot10^{-6}\\[10pt] + p_{\ovund{I_n=h}{Q_n=3h}}(ош.п)& + =p_{I_n=h}(ош)+p_{Q_n=3h}(ош) + -p_{I_n=h}(ош)\cdot p_{Q_n=3h}(ош)\\[-8pt] + &=10^{-5} + \end{split} + \end{equation} + + \item Определить среднюю вероятность ошибки на выходе + преобразователя при условии, что имеют место равенства: + \begin{equation} + \begin{split} + &p_{\ovund{I_n=h}{Q_n=h}}(ош.п) + =p_{\ovund{I_n=-h}{Q_n=h}}(ош.п) + =p_{\ovund{I_n=h}{Q_n=-h}}(ош.п) + =p_{\ovund{I_n=-h}{Q_n=-h}}(ош.п);\\ + &p_{\ovund{I_n=3h}{Q_n=3h}}(ош.п) + =p_{\ovund{I_n=-3h}{Q_n=3h}}(ош.п) + =p_{\ovund{I_n=3h}{Q_n=-3h}}(ош.п) + =p_{\ovund{I_n=-3h}{Q_n=-3h}}(ош.п);\\ + &p_{\ovund{I_n=h}{Q_n=3h}}(ош.п) + =p_{\ovund{I_n=-h}{Q_n=3h}}(ош.п) + =p_{\ovund{I_n=h}{Q_n=-3h}}(ош.п) + =p_{\ovund{I_n=-h}{Q_n=-3h}}(ош.п)=\\ + &p_{\ovund{I_n=3h}{Q_n=h}}(ош.п) + =p_{\ovund{I_n=-3h}{Q_n=h}}(ош.п) + =p_{\ovund{I_n=3h}{Q_n=-h}}(ош.п) + =p_{\ovund{I_n=-3h}{Q_n=-h}}(ош.п); + \end{split} + \end{equation} + Средняя вероятность ошибки на выходе преобразователя: + \begin{equation} + p_{ср}=\frac{p_{\ovund{I_n=h}{Q_n=h}}(ош.п)+p_{\ovund{I_n=3h}{Q_n=3h}}(ош.п)+2p_{\ovund{I_n=h}{Q_n=3h}}(ош.п)}{4}=10^{-5} + \end{equation} \end{enumerate} \subsection{Декодер} -По каналу передавался код -\(\overline{u}=11 10 00 01 10 10 01 11 11...\). -Ошибка произошла на тактовом интервале \(q=3\). +Декодер формирует из непрерывной последовательности кодовых символов, +поступающих с выхода демодулятора (возможно, с ошибками), выходную +непрерывную последовательность декодированных кодовых символов, в +которых ошибки частично либо полностью исправлены. + +По каналу передавался код +$\overline{u}=11 10 00 01 10 10 01 11 11 10 11 00 00$. +Ошибка произошла на тактовом интервале $q=3$. Таким образом, на вход декодера поступает последовательность -\(\overline{Z}=11 \overset{\times}{0} 0 00 01 10 10 01 11 11...\). Крестиком обозначен ошибочно принятый символ. +$\overline{Z}=11 \overset{\times}{0} 0 00 01 10 10 01 11 11 10 11 00 00$. Крестиком обозначен ошибочно принятый символ. \subsubsection{Диаграмма декодера} \input{decoder}