The Fading Channel

The Fading Channel In designing a communications system, the communications
engineer needs to estimate the effects of multipath fading and noise on the
mobile channel. The simplest channel model, from the point of view of analysis, is
the additive white Gaussian noise (AWGN) channel. In this channel, the desired
signal is degraded by thermal noise associated with the physical channel itself as
well as electronics at the transmitter and receiver (and any intermediate amplifiers
or repeaters). This model is fairly accurate in some cases, such as space communications
and some wire transmissions, such as coaxial cable. For terrestrial wireless
transmission, particularly in the mobile situation, AWGN is not a good guide for
the designer.
Rayleigh fading occurs when there are multiple indirect paths between transmitter
and receiver and no distinct dominant path, such as an LOS path. This represents a
worst case scenario. Fortunately, Rayleigh fading can be dealt with analytically, providing
insights into performance characteristics that can be used in difficult environments,
such as downtown urban settings.
Rician fading best characterizes a situation where there is a direct LOS path in
addition to a number of indirect multipath signals. The Rician model is often applicable
in an indoor environment whereas the Rayleigh model characterizes outdoor
settings. The Rician model also becomes more applicable in smaller cells or in more
open outdoor environments. The channels can be characterized by a parameter K,
defined as follows:



K=power in the dominant path/power in the scattered paths



When K = 0 the channel is Rayleigh (i.e., numerator is zero) and when
K = 00, the channel is AWGN (i.e., denominator is zero). Figure 5.14, based on
[FREE98a] and [SKLA01], shows system performance in the presence of noise.
Here bit error rate is plotted as a function of the ratio Eb/No. Of course, as that ratio
increases, the bit error rate drops. The figure shows that with a reasonably strong signal,
relative to noise, an AWGN exhibit provides fairly good performance, as do
Rician channels with larger values of K, roughly corresponding to microcells or an
open country environment. The performance would be adequate for a digitized
voice application, but for digital data transfer efforts to compensate would be
needed. The Rayleigh channel provides relatively poor performance; this is likely to
be seen for flat fading and for slow fading; in these cases, error compensation mechanisms
become more desirable. Finally, some environments produce fading effects
worse than the so-called worst case of Rayleigh. Examples are fast fading in an
urban environment and the fading within the affected band of a selective fading
channel. In these cases, no level of Eb/No will help achieve the desired performance,
and compensation mechanisms are mandatory. We turn to a discussion of those
mechanisms next.