diff --git a/documents/thesis/chapters/appendix-random-phasor.tex b/documents/thesis/chapters/appendix-random-phasor.tex
index f0da3db..507256a 100644
--- a/documents/thesis/chapters/appendix-random-phasor.tex
+++ b/documents/thesis/chapters/appendix-random-phasor.tex
@@ -13,7 +13,7 @@
 %\section{Random Phasor Distribution}
 
 This section gives a short derivation of \eqref{eq:random_phasor_sum:phase:sine} using two frequency-domain phasors.
-Further reading can be found in Ref.~\cite[Chapter 2.9]{goodman1985:2.9} under ``Constant Phasor plus Random Phasor Sum``.
+Further reading can be found in Ref.~\cite[Chapter 2.9]{goodman1985:2.9} under ``Constant Phasor plus Random Phasor Sum''.
 \\
 
 Write the noise phasor as $\vec{m} = a \, e^{i\pTrue}$ with phase $-\pi < \pTrue \leq \pi$ and amplitude $a \geq 0$,
@@ -26,14 +26,14 @@ The noise phasor is fully described by the joint probability density function
 	\phantom{,}
 	p_{A\PTrue}(a, \pTrue; \sigma)
 	=
-	\frac{a}{s\pi\sigma^2} e^{-\frac{a^2}{2\sigma^2}}
+	\frac{a}{2\pi\sigma^2} e^{-\frac{a^2}{2\sigma^2}}
 	,
 \end{equation}
 for $-\pi < \pTrue \leq \pi$ and $a \geq 0$.
 \\
 
 Integrating \eqref{eq:noise:pdf:joint} over the amplitude $a$, it follows that the phase is uniformly distributed.
-
+\\
 Likewise, the amplitude follows a Rayleigh distribution
 \begin{equation}
 	\label{eq:noise:pdf:amplitude}
@@ -49,10 +49,9 @@ for which the mean is $\bar{a} = \sigma \sqrt{\frac{\pi}{2}}$ and the standard~d
 
 % Random phasor sum
 Adding the signal phasor, the mean in \eqref{eq:noise:pdf:joint} shifts
-from $\vec{a}^2 = a^2 {\left( \cos \pTrue + \sin \pTrue \right)}^2$
-to ${\left(\vec{a} - \vec{s}\right)}^2 = {\left( a \cos \pTrue -s \right)}^2 + {\left(\sin \pTrue \right)}^2$
-,
-resulting in a new joint distribution
+	from $\vec{a}^2 = a^2 {\left( \cos \pTrue + \sin \pTrue \right)}^2$
+	to ${\left(\vec{a} - \vec{s}\right)}^2 = {\left( a \cos \pTrue -s \right)}^2 + {\left(\sin \pTrue \right)}^2$,
+	resulting in a new joint distribution
 \begin{equation}
 	\label{eq:phasor_sum:pdf:joint}
 	\phantom{.}
@@ -84,43 +83,28 @@ a Rice (or Rician) distribution for the amplitude,
 	,
 \end{equation}
 where $I_0(z)$ is the modified Bessel function of the first kind with order zero.
+\\
 
+\begin{figure}
+	\centering
+	\includegraphics[width=0.5\textwidth]{beacon/phasor_sum/pdfs-amplitudes.pdf}
+	\caption{
+		A signal phasor's amplitude in the presence of noise will follow a Rician distribution~\eqref{eq:phasor_sum:pdf:amplitude}.
+		For strong signals, this approximates a gaussian distribution, while for weak signals, this approaches a Rayleigh distribution.
+	}
+	\label{fig:phasor_sum:pdf:amplitude}
+\end{figure}
 For the Rician distribution, two extreme cases can be highlighted (as can be seen in Figure~\ref{fig:phasor_sum:pdf:amplitude}).
 In the case of a weak signal ($s \ll a$), \eqref{eq:phasor_sum:pdf:amplitude} behaves as a Rayleigh distribution~\eqref{eq:noise:pdf:amplitude}.
 Meanwhile, it approaches a gaussian distribution around $s$ when a strong signal ($s \gg a$) is presented.
-
 \begin{equation}
 	\label{eq:strong_phasor_sum:pdf:amplitude}
 	p_A(a; \sigma) = \frac{1}{\sqrt{2\pi}} \exp[-\frac{{\left(a - s\right)}^2}{2\sigma^2}]
-\end{equation}
+\end{equation}\\
 
-\begin{figure}
-	\begin{subfigure}{0.45\textwidth}
-		\includegraphics[width=\textwidth]{beacon/phasor_sum/pdfs-phases.pdf}
-		\caption{
-			The Random Phasor Sum phase distribution \eqref{eq:phase_pdf:random_phasor_sum}.
-			For strong signals, this approximates a gaussian distribution, while for weak signals, this approaches a uniform distribution.
-		}
-		\label{fig:random_phasor_sum:pdf:phase}
-	\end{subfigure}
-	\hfill
-	\begin{subfigure}{0.45\textwidth}
-		\includegraphics[width=\textwidth]{beacon/phasor_sum/pdfs-amplitudes.pdf}
-		\caption{
-			A signal phasor's amplitude in the presence of noise will follow a Rician distribution.
-			For strong signals, this approximates a gaussian distribution, while for weak signals, this approaches a Rayleigh distribution.
-		}
-		\label{fig:phasor_sum:pdf:amplitude}
-	\end{subfigure}
-	\caption{
-		\protect \Todo{expand captions}
-	}
-	\label{fig:phasor_sum:pdf}
-\end{figure}
-
-\bigskip
-Like the amplitude distribution \eqref{eq:phasor_sum:pdf:amplitude}, the marginal phase distribution of \eqref{eq:phasor_sum:pdf:joint} results in two extremes cases;
-weak signals correspond to the uniform distribution for \eqref{eq:noise:pdf:joint}, while strong signals are well approximated by a gaussian distribution.
+Like the amplitude distribution \eqref{eq:phasor_sum:pdf:amplitude}, the marginal phase distribution of \eqref{eq:phasor_sum:pdf:joint} results in two extreme cases;
+weak signals correspond to the uniform distribution for \eqref{eq:noise:pdf:joint}, while strong signals are well approximated by a gaussian distribution (see Figure~\ref{fig:random_phasor_sum:pdf:phase}).
+\\
 
 The analytic form takes the following complex expression,
 \begin{equation}
@@ -144,5 +128,13 @@ where
 	,
 \end{equation}
 is the error function.
-
+\begin{figure}
+	\centering
+	\includegraphics[width=0.5\textwidth]{beacon/phasor_sum/pdfs-phases.pdf}
+	\caption{
+		The Random Phasor Sum phase distribution \eqref{eq:phase_pdf:random_phasor_sum}.
+		For strong signals, this approximates a gaussian distribution, while for weak signals, this approaches a uniform distribution.
+	}
+	\label{fig:random_phasor_sum:pdf:phase}
+\end{figure}
 \end{document}