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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} |