Added content to Channel & Modulation slide

latex/presentations/midterm/sections/theoretical_background.tex

@@ -20,8 +20,40 @@
 \begin{frame}[t]
     \frametitle{Channel \& Modulation}
 
-    \todo{AWGN}
-    \todo{BPSK}
+    \tikzstyle{mapper} = [rectangle, minimum width=1.5cm, rounded corners=0.1cm, minimum height=0.7cm, text centered, draw=black, fill=KITgreen!80]
+    \begin{figure}[htpb]
+        \centering
+
+        \begin{tikzpicture}[scale=1, transform shape]
+            \node (in) {$c\left[ k \right] $};
+            \node[mapper, right=0.5cm of in] (bpskmap) {Mapper};
+            \node[right=1.5cm of bpskmap, draw, circle, inner sep=0pt, minimum size=0.5cm] (add) {$+$};
+            \node[right=0.5cm of add] (out) {$y\left[ k \right] $};
+            \node[below=0.5cm of add] (noise) {$n\left[ k \right] $};
+
+            \node at ($(bpskmap.east)!0.5!(add.west) + (0,0.3cm)$) {$x\left[ k \right] $};
+
+            \draw[->] (in) -- (bpskmap);
+            \draw[->] (bpskmap) -- (add);
+            \draw[->] (add) -- (out);
+            \draw[->] (noise) -- (add);
+        \end{tikzpicture}
+    \end{figure}
+
+    \begin{itemize}
+        \item All simulations are performed with BPSK Modulation:
+            \begin{align*}
+                x\left[ k \right]  = \left( -1 \right)^{c\left[ k \right] }, \hspace{5mm} \boldsymbol{c} \in \mathbb{F}_2^n, \hspace{2mm} k\in \left\{ 1, \ldots, n \right\} 
+            \end{align*}
+        \item The used channel model is AWGN:
+            \begin{align*}
+                \boldsymbol{y} = \boldsymbol{x} + \boldsymbol{n},
+                    \hspace{5mm}\boldsymbol{n}\sim \mathcal{N}
+                        \left(0,\frac{1}{2}\left(\frac{k}{n}\frac{E_b}{N_0}\right)^{-1}\right),
+                    \hspace{2mm} \boldsymbol{y}, \boldsymbol{n} \in \mathbb{R}^n
+            \end{align*}
+            \todo{Why $\frac{1}{2}$}
+    \end{itemize}
 \end{frame}