diff options
| -rw-r--r-- | doc/thesis/chapters/implementation.tex | 19 | ||||
| -rw-r--r-- | doc/thesis/chapters/theory.tex | 4 |
2 files changed, 14 insertions, 9 deletions
diff --git a/doc/thesis/chapters/implementation.tex b/doc/thesis/chapters/implementation.tex index 5e253de..05bb545 100644 --- a/doc/thesis/chapters/implementation.tex +++ b/doc/thesis/chapters/implementation.tex @@ -156,7 +156,7 @@ Thus the tagged stream is processed with a custom block, of which a simplified v \subsubsection{Performance of the implementation}\label{sec:preforming-implementation} The phase and frequency correction block was implemented with the design goal of being able to correct under ideal conditions a maximal frequency offsets of \(\hat{\epsilon} = 0.1\%\), which is sufficient to take into account small Doppler shifts at walking speed (\(v = \SI{2}{\meter\per\second}\)) with carrier at \(f_c = 2.4\) GHz. The USRP B210 devices have an internal clock frequency accuracy of \(\epsilon = 1\text{ ppm} = 10^{-6}\), which results in a total frequency offset of -\begin{equation} +\begin{equation}\label{eq:doppler} \Delta f = f_c \left( \frac{v}{c_0} + \epsilon \right) = \SI{2.4}{\giga\hertz} \left( \frac{\SI{2}{\meter\per\second}}{\SI{3e8}{\meter\per\second}} + 10^{-6} @@ -357,13 +357,20 @@ When nothing mentioned the number of how many FIR- filter taps are used is eight %TODO: Other Plots? \subsubsection{Real value example} -In order to obtain a realistic simulation the values for multi-path fading propagation condition for a Extended Typical Urban (ETU) model from the ETSI (European Telecommunication Standards Institute) where used. This +In order to obtain a realistic simulation the values for multipath fading propagation condition for a Extended Typical Urban (ETU) model, from the ETSI (European Telecommunication Standards Institute), where used\cite{ETSI}. For those values shown in \tabref{tab:etsi-tap-values} the maximum Doppler frequency possibilities are predefined. In the following examples \figref{fig:dynamic-exp-real} either \(\SI{5}{\hertz}\) or \(\SI{70}{\hertz}\) were used, as in \eqref{eq:doppler} \(\SI{16}{\hertz}\) calculated for a walking speed of \(\SI{2}{\meter\per\second}\). Those predefined values had a speed of +\begin{equation} + v = \frac{\Delta f}{f_c}\cdot c_0 = \frac{\SI{5}{\hertz}}{\SI{2.4}{\giga\hertz}}\cdot \SI{3e8}{\meter\per\second}= \SI{0.625}{\meter\per\second} +\end{equation} +and +\begin{equation} + v = \frac{\Delta f}{f_c}\cdot c_0 = \frac{\SI{70}{\hertz}}{\SI{2.4}{\giga\hertz}}\cdot \SI{3e8}{\meter\per\second}= \SI{8.75}{\meter\per\second} +\end{equation}. \skelpar[5]{ - Simulate an example from the skript + More simulation plots. } + \begin{table}[b] - \centering \begin{tabular}{rr} \toprule @@ -387,7 +394,7 @@ In order to obtain a realistic simulation the values for multi-path fading propa \centering \input{figures/tikz/qpsk-sim-constellations-dynamic-exp-NLOS-5} \caption{ - TODO + Constellation diagrams for a simulated link using QPSK and Rayleighan fading. With the ETU model and a Doppler frequency of \(\SI{5}{\hertz}\). } \label{fig:dynamic-exp-real} \end{figure} @@ -457,7 +464,7 @@ For generating the Byte error rate it is focus on byte-blocks of a specific leng \input{figures/tikz/qpsk-sim-constellations-static-symb-NLOS} \caption{ Constellation diagrams for a simulated link using QPSK with the discrete time model block. - The parameters are: delay of samples per symbol, amplitude of 0.2 and LOS. + The parameters are: delay of samples per symbol, amplitude of 0.2 and NLOS. } \label{fig:static-symb-special-case-NLOS} \end{figure} diff --git a/doc/thesis/chapters/theory.tex b/doc/thesis/chapters/theory.tex index bc69763..0f1b13e 100644 --- a/doc/thesis/chapters/theory.tex +++ b/doc/thesis/chapters/theory.tex @@ -274,8 +274,6 @@ From a signal processing perspective \eqref{eqn:discrete-multipath-impulse-respo \subsection{Simulating multipath CIR with FIR filters} \label{sec:fractional-delay} -% TODO: cite sources - \begin{figure} \centering \begin{subfigure}{.4\linewidth} @@ -293,7 +291,7 @@ From a signal processing perspective \eqref{eqn:discrete-multipath-impulse-respo } \end{figure} -As mentioned in \ref{sec:discrete-time-model} a FIR filter can be used to simulate discrete-time models of multipath fading. But with FIR filters the delays can only be integer multiples of the sample rate. When the delays are non integer an approximation needs to be done, that is because FIR filters have a transfer function of the form +As mentioned in \ref{sec:discrete-time-model} a FIR filter can be used to simulate discrete-time models of multipath fading. But with FIR filters the delays can only be integer multiples of the sample rate. When the delays are non integer an approximation needs to be done \cite{Valimaki1995}, that is because FIR filters have a transfer function of the form \begin{equation} \label{eqn:transfer-function-fir} H(j\omega) = \sum_{n = 0}^{N} h(n) e^{-j\omega nT} \quad \text{commonly written as} \quad |