From fd55df1b53c97b7e12a440c56cb5859cf1a8c391 Mon Sep 17 00:00:00 2001 From: Philipp Le 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