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| -rw-r--r-- | chapter05/content_ch05.tex | 5 | ||||
| -rw-r--r-- | chapter07/content_ch07.tex | 95 |
2 files changed, 87 insertions, 13 deletions
diff --git a/chapter05/content_ch05.tex b/chapter05/content_ch05.tex index 2716023..f598e65 100644 --- a/chapter05/content_ch05.tex +++ b/chapter05/content_ch05.tex @@ -1980,7 +1980,8 @@ All digital modulation techniques take time-discrete and value-discrete data. \item Each instantaneous value of the time-discrete data points is prolonged to the symbol period $T_{sym}$. In fact, it becomes a rectangle function. \item The result is a series of symbols $x_{sym}(t)$. \end{itemize} -\end{itemize} +\end{itemize}% +\nomenclature[St]{$T_{sym}$}{Symbol period, smybol duration} The process of converting time-discrete symbols to time-continuous rectangle functions can be mathematically described by: \begin{equation} @@ -2581,7 +2582,7 @@ The number $K_m$ of the $K_m$-\acs{QAM} selects the number of possible symbols i \vspace{1em} - The transmission bandwidth is related symbol rate $f_{sym}$. + The transmission bandwidth is related symbol rate $f_{sym}$. \nomenclature[St]{$f_{sym}$}{Transission bandwidth} \begin{itemize} \item Simple approximations set the symbol rate $f_{sym}$ and transmission equal. \item However, the exact transmission bandwidth depends on the selection of filters and the modulation technique. diff --git a/chapter07/content_ch07.tex b/chapter07/content_ch07.tex index 0716aa2..648e5e2 100644 --- a/chapter07/content_ch07.tex +++ b/chapter07/content_ch07.tex @@ -11,9 +11,52 @@ \chapter{Spread Spectrum and Multiple Access} \begin{refsection} + +The electromagnetic spectrum is a sparse resource. It must be used as efficient as possible because it is shared with numerous users and applications. However, modern digital communication systems use spread spectrum technologies that occupy a relatively wide frequency band + +The purpose of spread spectrum is amongst others: +\begin{itemize} + \item Immunity against noise and disturbances + \item Encryption and confidentiality of the communication + \item Plausible deniability that the communication had ever taken place + \item Coexistence with other services (multiple access) +\end{itemize} + +Especially, the multiple access is an important reason for employing spread spectrum technologies. In modern communication systems, the resource \emph{frequency} is not only allocated to a single user. For example, \ac{LTE} allows many users to access the service with high data rates and low latency. The resource \emph{frequency} must be shared. Efficient medium access relies on spread spectrum to achieve this. \section{Spread Spectrum} +In the modulation techniques considered so far, are \emph{plain} or \emph{non-spread spectrum}. For the definition of spread spectrum signals, the symbol duration and the transmission bandwidth is investigated. +\begin{itemize} + \item The signal duration is the amount of time required to convey an information. In digital communication system, an information is a symbol modulated onto a carrier. The signal duration is the symbol period $T_{sym}$. + \item The signal bandwidth $\Delta f_{sym}$ is the minimum bandwidth required by the receiver to receive the signal. In the case of modulation, it is the \emph{transmission bandwidth}. +\end{itemize} +In the \ac{ASK}, \ac{PSK} and \ac{QAM} modulation of Chapter 5, the signal duration and the bandwidth are inversely proportional. +\begin{equation} + \Delta f_{sym} = \frac{1}{T_{sym}} +\end{equation} + +The product of the bandwidth and the duration -- the \index{time-bandwidth product} \textbf{time-bandwidth product} -- is constantly $1$.\footnote{This is the ideal case. For real implementations, the constant may differ from $1$ depending on the modulation technique. However, it will be close to $1$.} +\begin{equation} + T_{sym} \cdot \Delta f_{sym} = 1 +\end{equation} + +\paragraph{Time-Bandwidth Product.} + +The time-bandwidth product is used for the definition of spread spectrum: +\begin{definition}{Spread spectrum} + The time-bandwidth product of \index{spread spectrum} \textbf{spread spectrum} signals is significantly greater than $1$. + \begin{equation} + T_{sym} \cdot \Delta f_{sym} \gg 1 + \end{equation} +\end{definition} + +Typically, this means that the bandwidth $\Delta f_{sym}$ is increased while the symbol duration and thereby the symbol rate is kept constant. +\begin{itemize} + \item The symbol sequence (time-bandwidth product of $1$) is altered in a way which distributes the signal power over a wider frequency band. This process is called \index{spreading} \textbf{spreading}. + \item The inverse process is \index{despreading} \textbf{despreading}. The original symbol sequence is reconstructed from the wide-band spread spectrum signal. +\end{itemize} + \begin{figure}[H] \centering \begin{tikzpicture} @@ -55,17 +98,41 @@ \caption[PSD of a narrow-band and spread spectrum signal]{\acs{PSD} of a narrow-band and spread spectrum signal. Both signals carry the same information and have the equal power. The narrow-band signal concentrates the whole signal power in a narrow frequency band. In contrast, the spread spectrum signal distributes the signal power over a wide frequency band.} \end{figure} -\todo{Purpose: Noise immunity} - -\todo{Noise like} - -\todo{Purpose: Immunity against narrowband disturbances} - -\todo{Purpose: Coexistence with other services, multiple access} - -\todo{Purpose: Plausible deniability} - -\todo{Purpose: Encryption, confidentiality} +\paragraph{Noise-like Signal.} + +The signal power remains constant while the signal is spread. +\begin{itemize} + \item The \ac{PSD} is reduced. + \item But, the \ac{PSD} is integrated over a wider frequency range. + \item The overall power remains constant. +\end{itemize} + +The \ac{PSD} of the spread spectrum signal is flat in approximation. +\begin{itemize} + \item The flat \ac{PSD} resembles the \ac{PSD} of noise. + \item Spread spectrum signal are therefore \emph{noise-like}. +\end{itemize} + +A third party who has no knowledge of neither the existence of the spread spectrum signal nor the technology used cannot detect the signal. +\begin{itemize} + \item The spread spectrum signal looks like noise or a wide-band disturbance from the view of the receiver which does not participate in the communication. + \item This circumstance can be used to conceal the existence of the signal (plausible deniability of its existence). +\end{itemize} + +\paragraph{Despreading.} + +\index{despreading} Despreading reconstructs the symbols -- and thereby the data -- from the spread spectrum signal. +\begin{itemize} + \item The spreading is reversed. + \item The symbols (time-bandwidth product of $1$) are reconstructed. This can be seen like re-concentrating the spread signal power in a narrow-band symbol sequence. + \item The disturbances which are uncorrelated to the spread spectrum signal are converted into the wide-band noise with a low \ac{PSD}. + \begin{itemize} + \item The wide-band noise floor (like thermal noise or quantization noise) remains wide-band. + \item Strong but narrow-band disturbing signals (like other users of the electromagnetic spectrum) are spread to low-\acs{PSD} wide-band noise during the despreading. The \ac{SNR} is increased by spreading the signal power of the disturbance. + \end{itemize} +\end{itemize} + +\todo{Despreading in frequency-domain, suppression of noise and disturbances} \subsection{Direct-Sequence Spread Spectrum} @@ -77,6 +144,12 @@ \subsection{Time-Hopping Spread Spectrum} +\subsection{Symbol Reconstruction} + +\todo{Reception under noise} + +\todo{Cross-correlation} + \section{Multi-carrier Modulation} \todo{OFDM} |