3 files changed, 110 insertions, 10 deletions
diff --git a/chapter07/content_ch07.tex b/chapter07/content_ch07.tex
index f332b10..56871e7 100644
--- a/chapter07/content_ch07.tex
+++ b/chapter07/content_ch07.tex
@@ -1887,15 +1887,21 @@ However, not each $L_1$ code is orthogonal to any $L_2$ code. The relation of or
 	\label{fig:ch07:ovsf_code_tree}
 \end{figure}
 
-The rules for creating the \acs{OVSF} code tree are (derived from the construction rules of the Hadamard matrix):
-\begin{itemize}
-	\item The parent node in the tree is $\vect{C}_{n,k}$ ($n$ is the code length, $k$ is the index).
-	\item The child nodes are:
-	\begin{itemize}
-		\item $\vect{C}_{2n,2k-1} = \left[\vect{C}_{n,k}, \vect{C}_{n,k}\right]$
-		\item $\vect{C}_{2n,2k} = \left[\vect{C}_{n,k}, -\vect{C}_{n,k}\right]$
-	\end{itemize}
-\end{itemize}
+The rules for creating the \acs{OVSF} code tree are (derived from the construction rules of the Hadamard matrix):
+\begin{itemize}
+	\item The parent node in the tree is $\vect{C}_{n,k}$ ($n$ is the code length, $k$ is the index).
+	\item The child nodes are:
+	\begin{itemize}
+		\item $\vect{C}_{2n,2k-1} = \left[\vect{C}_{n,k}, \vect{C}_{n,k}\right]$
+		\item $\vect{C}_{2n,2k} = \left[\vect{C}_{n,k}, -\vect{C}_{n,k}\right]$
+	\end{itemize}
+\end{itemize}
+
+The different code lengths have benefits and drawbacks.
+\begin{itemize}
+	\item Longer codes have lower data rates. But they have a higher processing gain and better noise immunity. Data decoding works in noisy environments with low \ac{SNR}.
+	\item Short codes give a higher data rate. However, the processing gain is less as well as the noise immunity. Data decoding may not work in noisy environments. A proper \ac{SNR} is required.
+\end{itemize}
 
 \subsection{Asynchronous \acs{DS-CDMA}}
 
diff --git a/exercise06/exercise06.tex b/exercise06/exercise06.tex
index 9054ced..97c2b8a 100644
--- a/exercise06/exercise06.tex
+++ b/exercise06/exercise06.tex
@@ -122,7 +122,7 @@
 \begin{question}[subtitle={FFT}]
 	A series of the samples in the time-domain is given:
 	\begin{equation*}
-		x[n] = \left[2 \underline{-0.5} 1 -2 \right]
+		x[n] = \left[2, \underline{-0.5}, 1, -2 \right]
 	\end{equation*}
 	
 	\begin{remark}
diff --git a/exercise07/exercise07.tex b/exercise07/exercise07.tex
index be8f60a..a054be1 100644
--- a/exercise07/exercise07.tex
+++ b/exercise07/exercise07.tex
@@ -14,6 +14,100 @@
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{question}[subtitle={DS-CDMA}]
+	Two spreading codes are given.
+	\begin{itemize}
+		\item $\vect{C}_{4,1} = \left[1,1,-1,-1\right]$
+		\item $\vect{C}_{4,2} = \left[1,-1,-1,1\right]$
+	\end{itemize}
+
+	The data stream is $\vect{D} = \left[1,-1\right]$
+	
+	\begin{tasks}
+		\task
+		How much is the inner product of $\vect{C}_{4,1}$ and $\vect{C}_{4,2}$? What does the result mean?
+		\task
+		The data $\vect{D}$ is spread by $\vect{C}_{4,1}$. Calculate the transmitted chip sequence $\vect{S}$!
+		\task
+		Calculate the cross-correlation of $\vect{S}$ and $\vect{C}_{4,1}$!
+		\task
+		Calculate the cross-correlation of $\vect{S}$ and $\vect{C}_{4,2}$!
+		\task
+		Calculate the autocorrelation of $\vect{C}_{4,2}$!
+	\end{tasks}
+\end{question}
+
+\begin{solution}
+	\begin{tasks}
+	\end{tasks}
+\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{question}[subtitle={2G cell phone -- GSM}]
+	A GSM uses a FDMA/TDMA hybrid multiple access method. The TDMA part uses time-slots of \SI{546.5}{\micro{}s} length. Each time-slot is followed by a \SI{30.5}{\micro{}s} long guard interval. Eight time-slots are grouped into one frame. A user is assigned one of the time-slots in each frame for exclusive use.
+	
+	\SI{148}{bit} can be transported in one time-slot (excluding the guard interval). \SI{114}{bit} are usable for data.
+		
+	\begin{tasks}
+		\task
+		What purpose does the guard interval serve?
+		\task
+		How much is the frame length?
+		\task
+		How much is the raw symbol rate?
+		\task
+		How much is the data rate? One bit is encoded in one symbol.
+	\end{tasks}
+\end{question}
+
+\begin{solution}
+	\begin{tasks}
+	\end{tasks}
+\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{question}[subtitle={OFDM}]
+	An OFDM system has a sub-carrier spacing of \SI{15}{kHz}, a signal bandwidth of \SI{20}{MHz} and a guard band of \SI{2}{MHz}.
+	
+	\begin{tasks}
+		\task
+		How much is the symbol duration?
+		\task
+		How many sub-bands are available?
+		\task
+		Is the symbol duration affected if the modulation is changed from QPSK to 16-QAM?
+		\task
+		Give the data rate if a 16-QAM modulation is used. \SI{20}{\percent} of the sub-bands are pilots (for synchronization) and cannot be used for data transmission.
+	\end{tasks}
+\end{question}
+
+\begin{solution}
+	\begin{tasks}
+	\end{tasks}
+\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{question}[subtitle={3G cell phone -- UMTS}]
+	A UMTS system uses DS-CDMA with a constant chip rate of \SI{3.84}{MHz} for all users. The data is transmitted in frames with a length of 2560 chips. One frame occupies one time-slot. Each user is assigned a spreading code and a time-slot for transmitting his/her frame.
+	
+	\begin{tasks}
+		\task
+		The transmission of frames in time-slots makes the multiple access method of UMTS a hybrid of CDMA and which other technology? Explain this technology!
+		\task
+		How much is the time-slot length (duration) if guard intervals are neglected?
+		\task
+		A spreading factor of 8 is chosen. The modulation is QPSK. How much is the symbol rate? How much is the data rate?
+		\task
+		A voice data stream with \SI{15}{kbit/s} is transmitted using BPSK. How much is the processing gain?
+	\end{tasks}
+\end{question}
+
+\begin{solution}
+	\begin{tasks}
+	\end{tasks}
+\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\begin{question}[subtitle={Decibel}]
 %	\begin{tasks}
 %	\end{tasks}