4.1  What You Will Learn

• Basic channel models and an introduction to the techniques used to mitigate the channel effects.
• Nyquist pulses such as the raised cosine for combating intersymbol interference (ISI). A shaping pulse is called a Nyquist pulse when it leads to zero-ISI.
• Equalization and system identification.
• Concepts related to synchronization techniques.

In practice, communication systems have to deal with several impairments: noise, interference, channel fading, etc. As discussed in Section 1.6.2, while noise is the term used for nature-made signals such as thermal noise, interference is typically adopted to describe signals created by humans but other than the signal(s) of interest. For example, in a binder of copper pairs used for DSL, one user receives interference signals from other users due to crosstalk.

In most channel models, added to the interference, there is thermal (or background) noise, which is typically modeled as AWGN, for example, with a unilateral PSD of $N_0=-140$ dBm/Hz.

Interference is not going to be considered here, and this chapter aims at studying how to deal with a channel that:

• implements a linear time-invariant (LTI) or time-variant filter $h_c(t)$ that may alter the spectrum of the transmitted signal $s(t)$,
• adds noise to the signal $g(t)$ at the output of $h_c(t)$ such as white Gaussian noise (WGN).