In this chapter we examine fading models for the constructive and destructive addition of different multipath components introduced by the channel. Although these multipath effects are captured in the ray-tracing models from Chapter 2 for deterministic channels, in practice deterministic channel models are rarely available and so we must characterize multipath channels statistically. In this chapter we model the multipath channel by a random time-varying impulse response. We will develop a statistical characterization of this channel model and describe its important properties.

If a single pulse is transmitted over a multipath channel then the received signal will appear as a pulse train, with each pulse in the train corresponding to the line-of-sight component or a distinct multipath component associated with a distinct scatterer or cluster of scatterers. The time delay spread of a multipath channel can result in significant distortion of the received signal. This delay spread equals the time delay between the arrival of the first received signal component (LOS or multipath) and the last received signal component associated with a single transmitted pulse. If the delay spread is small compared to the inverse of the signal bandwidth, then there is little time spreading in the received signal. However, if the delay spread is relatively large then there is significant time spreading of the received signal, which can lead to substantial signal distortion.