From b0307201182f7222402b8d767fd851ce5b9434fd Mon Sep 17 00:00:00 2001 From: Philipp Le Date: Tue, 30 Jun 2020 02:02:05 +0200 Subject: Exercise 7 --- chapter07/content_ch07.tex | 24 +++++++++++++++--------- 1 file changed, 15 insertions(+), 9 deletions(-) (limited to 'chapter07') diff --git a/chapter07/content_ch07.tex b/chapter07/content_ch07.tex index f332b10..56871e7 100644 --- a/chapter07/content_ch07.tex +++ b/chapter07/content_ch07.tex @@ -1887,15 +1887,21 @@ 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} +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} + +The different code lengths have benefits and drawbacks. +\begin{itemize} + \item Longer codes have lower data rates. But they have a higher processing gain and better noise immunity. Data decoding works in noisy environments with low \ac{SNR}. + \item Short codes give a higher data rate. However, the processing gain is less as well as the noise immunity. Data decoding may not work in noisy environments. A proper \ac{SNR} is required. +\end{itemize} \subsection{Asynchronous \acs{DS-CDMA}} -- cgit v1.1