From bab0df37d18d58a7a150ac6b9ab5ee0c73c1dc03 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Fri, 17 Dec 2021 19:43:04 +0100 Subject: Minor corrections in documentation --- doc/thesis/chapters/theory.tex | 10 +++------- 1 file changed, 3 insertions(+), 7 deletions(-) (limited to 'doc/thesis/chapters/theory.tex') diff --git a/doc/thesis/chapters/theory.tex b/doc/thesis/chapters/theory.tex index 6e0c3cc..bc69763 100644 --- a/doc/thesis/chapters/theory.tex +++ b/doc/thesis/chapters/theory.tex @@ -135,11 +135,6 @@ Phase shift keying (PSK) is another popular family of modulation schemes for dig \end{equation} \skelpar[3] -% \begin{figure} -% % TODO: Better Image -% % https://sites.google.com/site/billmahroukelec675/bipolar-phase-shift-keying -% \includegraphics[width=5cm]{./image/BPSK2.png} -% \end{figure} \subsection{Quadrature PSK (QPSK)} @@ -278,7 +273,8 @@ is different from \eqref{eqn:multipath-impulse-response} consider again the plot From a signal processing perspective \eqref{eqn:discrete-multipath-impulse-response} can be interpreted as a simple tapped delay line, schematically drawn in \figref{fig:tapped-delay-line}, which confirms that the presented mathematical model is indeed a FIR filter. Simple multipath channels can be simulated with just a few lines of code, for example the data for the static fading channel in \figref{fig:multipath-frequency-response-plots} is generated in just four lines of Python. The difficulty of fading channels in practice lies in the estimation of the constantly changing parameters \(c_k(t)\) and \(\tau_k(t)\). \subsection{Simulating multipath CIR with FIR filters} \label{sec:fractional-delay} -% TODO quelle: http://users.spa.aalto.fi/vpv/publications/vesan_vaitos/ch3_pt1_fir.pdf + +% TODO: cite sources \begin{figure} \centering @@ -402,7 +398,7 @@ Notice that by letting \(K = 0\), that is no power in the LOS path, \eqref{eqn:m \begin{equation} p(a)= 2a(1+K) \exp{\left(-K -a^2 (K+1) \right)} I_0 \left(2a\sqrt{K(1+K)} \right), \end{equation} -where \(I_0\) the zeroth order modified Bessel function. +where \(I_0\) the zeroth order modified Bessel function. Random variables with this probability density function are said to have a Rice or Rician distribution. % The Phase for the strait line component has no influences for the Random process therefore there set to zero. In the case when \(K = 0\). % the Rician distribution becomes a Rayleight distribution on the other hand when \(K\rightarrow \infty \) the distribution becomes an AWGN-channel model (additive white Gaussian noise). When \(K > 0 \) is the phase not equally distributed. -- cgit v1.2.1