Fading Multipath Channels
Published:
Abstract: Most of the edge research in wireless communication is based on theory studies. It is extremely difficult to model a truly wireless communication as it is happening in the real world. However, there are very well accurated mathematical models that aims to represent some specific scenarios.
Fading Multipath Channels
To characterize the time-variant multipath channel statistically. So, let us examine the effects of the channel on a transmitted signal that is represented as
Assuming a multiple propagation paths, a propagation delay and an attenuation factor is considered for each path, both are time-variant because the changes in the medium. For this reason, the received band-pass may be expressed as
it follows that the equivalent low-pass received signal is
when the equivalent low-pass received signal, is analyzed as a tropospheric scatter channel, the previous model is replicated, but in the continuum multipath domain. It is expected that and
change sufficiently at different rates and in an unpredictable manner. When there are a large number of paths, the central limit theorem can be applied. That is, the equivalent low-pass received signal (
) may be modeled as a complex-valued Gaussian random process. This means that the time-variant impulse response
is a complex-valued Gaussian random process in the
variable.
As a consequence on signal , the multiplath propagation model will result in signal fading. The fading phenomenon is a result of time variant of the phase and in the amplitude ( signal fading ). Which are due to the time-variant multipath characteristics of the channel.
When the impulse response aims to model a moving scattererers scenario, it is modeled as a zero-mean complex-valued Gaussian process, the envelope
is Rayleigh-distributed ( Rayleigh fading channel). In the event that there are fixed scatterers or signal reflectors in the medium, in addition to randomly moving scatterers, the envelope
has a Rice distribution ( Ricean fading channel).
It is important to remark that these distribution functions aims to model the envelope of fading signals.