From fd55df1b53c97b7e12a440c56cb5859cf1a8c391 Mon Sep 17 00:00:00 2001
From: Philipp Le <philipp-le-prviat@freenet.de>
Date: Mon, 29 Jun 2020 00:01:00 +0200
Subject: Added rules for OVSF code tree generation

---
 chapter07/content_ch07.tex | 10 ++++++++++
 1 file changed, 10 insertions(+)

(limited to 'chapter07/content_ch07.tex')

diff --git a/chapter07/content_ch07.tex b/chapter07/content_ch07.tex
index e436e1a..f332b10 100644
--- a/chapter07/content_ch07.tex
+++ b/chapter07/content_ch07.tex
@@ -1887,6 +1887,16 @@ 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}
+
 \subsection{Asynchronous \acs{DS-CDMA}}
 
 Welsh code have excellent cross-correlation properties. But, Welsh codes \underline{do not} have good autocorrelation properties.
-- 
cgit v1.1

