# 0.3 Modelling corruption

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The next layer encompasses [link] through [link] . This gives a closer look at the idealized receiver—how things work when everythingis just right: when the timing is known, when the clocks run at exactly the right speed, when there are no reflections,diffractions, or diffusions of the electromagnetic waves. This layer also introduces a few M atlab tools that are needed to implement the digital radio.The order in which topics are discussed is precisely the order in which they appear in the receiver:

$\begin{array}{c}\\ \text{channel}\\ Chapter\phantom{\rule{4.pt}{0ex}}\text{4}\end{array}\to \begin{array}{c}\text{frequency}\\ \text{translation}\\ Chapter\phantom{\rule{4.pt}{0ex}}\text{5}\end{array}\to \begin{array}{c}\\ \text{sampling}\\ Chapter\phantom{\rule{4.pt}{0ex}}\text{6}\end{array}\to$
$\begin{array}{c}\underbrace{\begin{array}{c}\text{receive}\\ \text{filtering}\end{array}\to \text{equalization}}\\ Chapter\phantom{\rule{4.pt}{0ex}}\text{7}\end{array}\to \begin{array}{c}\underbrace{\begin{array}{c}\text{decision}\\ \text{device}\end{array}\to \text{decoding}}\\ Chapter\phantom{\rule{4.pt}{0ex}}\text{8}\end{array}$
$\begin{array}{cc}\text{Channel}\phantom{\rule{4.pt}{0ex}}\text{impairments}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}\text{linear}\phantom{\rule{4.pt}{0ex}}\text{systems}\hfill & \hfill \text{Chapter}\phantom{\rule{4.pt}{0ex}}\text{4}\\ \text{Frequency}\phantom{\rule{4.pt}{0ex}}\text{translation}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}\text{modulation}\hfill & \hfill \text{Chapter}\phantom{\rule{4.pt}{0ex}}\text{5}\\ \text{Sampling}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}\text{gain}\phantom{\rule{4.pt}{0ex}}\text{control}\hfill & \hfill \text{Chapter}\phantom{\rule{4.pt}{0ex}}\text{6}\\ \text{Receive}\phantom{\rule{4.pt}{0ex}}\text{(digital)}\phantom{\rule{4.pt}{0ex}}\text{filtering}\hfill & \hfill \text{Chapter}\phantom{\rule{4.pt}{0ex}}\text{7}\\ \text{Symbols}\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}\text{bits}\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}\text{signals}\hfill & \hfill \text{Chapter}\phantom{\rule{4.pt}{0ex}}\text{8}\end{array}$

Chapter  [link] provides a complete (though idealized) software-defined digital radio system.

From there to here, from here to there, funny things are everywhere.

—Dr. Seuss, One Fish, Two Fish, Red Fish, Blue Fish, 1960

If every signal that went from here to there arrived at its intended receiver unchanged, the life of a communications engineerwould be easy. Unfortunately, the path between here and there can be degraded in several ways, including multipath interference,changing (fading) channel gains, interference from other users, broadband noise, and narrowband interference.

This chapter begins by describing these problems, which are diagrammed in [link] . More important than locating the sources of the problems isfixing them. The received signal can be processed using linear filters to help reduce the interferencesand to undo, to some extent, the effects of the degradations. The central question is how to specify filters that can successfullymitigate these problems, and answering this requires a fairly detailed understanding of filtering.Thus, a discussion of linear filters occupies the bulk of this chapter, which also provides a background for other uses of filtersthroughout the receiver, such as the lowpass filters used in the demodulators of Chapter  [link] , the pulse shaping and matched filters of Chapter  [link] , and the equalizing filters of Chapter  [link] .

## When bad things happen to good signals

The path from the transmitter to the receiver is not simple, as [link] suggests. Before the signal reaches the receiver, it is subjectto a series of possible “funny things,” events that may corrupt the signal and degrade the functioning of the receiver.This section discusses five kinds of corruption that are used throughout the chapter to motivate and explain the various purposesthat linear filters may serve in the receiver.

## Other users

Many different users must be able to broadcast at the same time. This requires that there be a way for areceiver to separate the desired transmission from all the others (for instance, to tune to a particular radio or TV station among a largenumber that may be broadcasting simultaneously in the same geographical region). One standard method is to allocate different frequencybands to each user. This was called frequency division multiplexing (FDM) in Chapter  [link] , and was shown diagrammatically in [link] . The signals from the different users can be separatedusing a bandpass filter, as in [link] . Of course, practical filters do not completely remove out-of-bandsignals, nor do they pass in-band signals completely without distortions. Recall the three filters in [link] .

#### Questions & Answers

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Joseph
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Giriraj
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revolt
da
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narayan
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Damian
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Professor
I think
Professor
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Alexandre
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Rafiq
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Damian
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LITNING
scanning tunneling microscope
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Rafiq
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