AWGN channel model and Bandlimited AWGN one are not appropriate for modelling wireless propagation mechanisms:
There are three kinds of power losses in a radio communication link
more in general
Loss due to slow fading effects (distance scale is in the order of 50-100 m – shadow fading).
Loss due to short range fading: distance scale is in the order of λ/2 (<10m).
Short range fading is due to two phenomenons:
Time dispersion due to multipath.
Frequency dispersion due to radial mobility between TX and RX and/or to variability of the propagation channel properties (time-variant) → linear time-variant model.
s(t): transmitted signal with u(t) equivalent lowpass with band Bu
The received signal in the absence of noise can be expressed as:
n = 0 – LOS
n ≠ 0 - LOS
L(t) – number of paths
αn(t)- time – variant attenuation factor associated with the nth path
τn(t) - propagation delay associated with the nth path
ΦDn – phase shift due to doppler
The nth distinguishable path can be generated by a single scatterer or by a cluster of no-distinguishable scatterers.
If the delays τi and τj are very different:
the components i and j are distinguishable (wideband fading)
The i-th and j-th replica overlap → multipath non-distinguishable
If the τi and τj of two components are similar →
The paths are not distinguishable and the contributions combine in a single path (cluster of scatterers non- distinguishable).
Wideband channels (Bu>>1) have distinguishable paths → each term in the sum corresponds to a reflection or to a cluster of non-distinguishable paths.
If each term is due to a cluster of scatterers, αn(t) changes noticeably with the distance because of the phase changes of the single non-distinguishable contributions.
If the parameters are time-invariant:
The channel introduces only a time-dispersion and if L,τn are deterministic, the time-dispersion can be measured as the maximum delay with respect to the LOS contribution or to mean delay
RMS delay spread
rms of the kth path
Narrowband Fading : TM << 1/Bu ≅ T → non- distinguishable paths.
At the output we do not have a phasor because z(t) is not constant → Frequency dispersion
In general cn(t) is modeled as a complex gaussian process
Tm – multipath spread
where L is the numbers of paths, is the time resolution i.e. the duration of transmitted signal.
The phases Φn can give rise to constructive or destructive contributions that weaken or strengthening the amplitude of the transmitted signal, namely the presence of fading effects.
|z(t)| models the variation law of the attenuation.
The variability measure of z(t) allows us to valuate the amount of spectral dispersion.
z(t) is a random signal, hence let us consider the mean square value of the bandwidth of z(t) namely,Bd
Bd = doppler Bandwidth
If Bd >>1 → the channel “varies” rapidly
If Bd <<1 ← the channel “varies” slowly
Let us denote with Bu the bandwidth of the transmitted signal:
If Bd <<Bu → the channel can be assumed to be stationary since the spectral dispersion is negligible with respect to the signal bandwidth Bu.
In the time domain:
Bd<<Bu → 1/Bd >>1/Bu → TC>>TS Temporal Flat Fading, namely:
The signal duration is much smaller than the temporal scale TC of the channel variation.
13. Cyclic Codes