Wireless Network Design: Optimization Models and Solution ...

60 K. V. S. Hari
3.5.2.4 Dominant Reflectors Model
In this model [33], it is assumed that there are Lr dominant reflectors and the received
signal vector is defined as
x(t) =
Lr(t)−1
∑ a(θ)αl(t)s(t − τ) + n(t) (3.24)
l=0
α j is the complex amplitude of the lth dominant reflector given by
αl(t) = βl(t) � Γlψ(τl) (3.25)
where Γl denotes lognormal fading and ψ(τl) represents the power delay profile and
βl(t) = Kr
Nr
∑
r=1
Cr(θl) exp( jωd cos(Ωr,lt)) (3.26)
where Nr is the number of signal components adding to the lth dominant reflector.
Cr(θl) is the complex amplitude of the rth component of the lth dominant reflector.
Simulations using this model have shown that the results are close to measured data.
3.5.2.5 Typically Urban (TU) and Bad Urban (BU) Models
TU and BU models are specifically specified for GSM and PCS systems where the
scatterers are assumed to be away at a certain distance and the scatterer positions
are kept fixed for a certain amount of time and then moved to a new position based
on the velocity profile and random phases assigned to the scatterers. These models
have been successfully used for practical system design [44]. Both models assume
that the received array vector. In the TU model, 120 scatterers are assumed to be
randomly placed 1km away. The positions of the scatterers are kept fixed for every
interval of 5m movement of the mobile. During this time duration, random phases
are assigned to the scatterers as well as randomized shadowing losses are assigned
with a log-normal distribution. For the BU model, an additional cluster of 120 scatterers
are assumed to be located at an angular offset of 45 degrees with respect to
the first cluster of scatterers. The average power for this second cluster of scatterers
is assumed to be 5dB lower than that of the first cluster. Thus, the BU channel introduces
more angular spread and increases the delay spread of the channel. These
models have been compared with actual measurements and found to be in close
agreement with the models used by GSM system designers.