Digital Signal Processing Reference
In-Depth Information
Angle spread is an important quantity in characterizing the radio channel.
It causes space-selective fading. This effect is due to the spread of directions
of the incoming paths and is caused by scattering in the vicinity of the trans-
mitter or receiver. A large angle spread is caused by rich scattering and will
allow spatial diversity, meaning that the signals propagate via independent
channels to different antenna elements, and the correlation between antenna
elements is low. This property is exploited in MIMO systems to improve
spectral efficiency via spatial multiplexing and link reliability.
In a macrocell environment, the motion of the mobile will give rise to
Doppler spread, which causes time selectivity of the channels. Taking into
account both time-selectivity and frequency-selectivity of the channel, fading
channels may be categorized into one of the following four types:
1. Flat fading channels (channels are both time and frequency flat)
2. Frequency-selective fading channels (channels are frequency selec-
tive but time flat)
3. Time-selective fading channels (channels are time selective but
frequency flat)
4. Doubly selective fading channels (channels are both frequency and
time selective)
The wide-sense stationary uncorrelated scattering (WSSUS) linear time-
variant channel model is widely used to model signal propagation in the
mobile communications environment. The WSSUS model was introduced by
Bello
7
and was further investigated, for example, in Reference 16. The channel
may be modeled as follows:
16
N
l
1
√
N
l
e
j
(
2
π
f
d,l
t
+
θ
l
)
h
RF
h
ij
(
t,
τ)
=
(τ
−
τ
)
,
(8.1)
l
l
=
1
where
N
l
is the number of echo paths,
f
d,l
is the Doppler spread,
θ
l
is the
angular spread, and
h
RF
(
t
)
is the impulse response of the receive filter. For
each delay
τ
, the channel is given by selecting:
1.
N
l
Doppler frequencies
f
d,l
from a random variable with classical
Jakes pdf in
(
−
f
d,
max
,f
d,
max
)
. The maximum Doppler spread can be
expressed as
f
d,
max
=
v/λ
w
, where
v
is the mobile station speed and
is the signal wavelength.
2.
N
l
initial phases
λ
w
θ
l
from a uniform distributed random variable in
].
3.
N
l
echo delay times
[0
,
2
π
l
. Each delay spread is a random variable with
probability density function proportional to the mean power delay
profile of the propagation environment.
τ
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