Digital Signal Processing Reference
In-Depth Information
input symbols is encoded by a space-time encoding function into an
M
T
× 1 discrete-
time complex baseband sequence
x
[
n
] (
n
is a discrete-time index). The
x
[
n
] sequence is
subsequently transformed by a pulse-shaping filter into an
M
T
× 1 continuous-time com-
plex baseband sequence
x
(
t
), and then the baseband signal is modulated with a transmis-
sion carrier. The transmission channel
H
superposes the transmitted signal due to the
distortions of environment. At the reception side, under the assumption of synchronous
sampling, the received signal
y
(
t
) with additive noise is downconverted to baseband and
sampled to produce a discrete-time signal sequence. Finally, the estimated symbols are
decoded by the space-time decoding block.
If the channel is time invariant, the equivalent received signal at the receiving antenna
with
M
T
elements at the transmitter (Tx) and
M
R
elements at the receiver (Rx) can be
written as
−
∑
H
L
1
y
()
t
=
x
(
t
− +
τη
)
()
t
.
(4 .1)
l
l
l
=
0
If the channel is time variant, the overall MIMO relation can be formulated as
∫
H
τ τ η
τ
(4.2)
y
()
t
=
(, )(
t
x
t
− +
)(),
t
where
x
(
t
) and
y
(
t
) represent the transmitted and received signals,
x() [(),
t
=
xtxt
(),
…
,
x
()],
t
T
(4.3)
1
2
M
T
T
y() [(),
t
=
ytyt
(),
…
,
y
()],
t
(4.4)
1
2
M
R
and
L
denotes the number of resolvable multipaths, τ is the propagation delay,
H
(
t
,
τ
) is
the
M
R
×
M
T
time-variant channel matrix,
H
l
is the
M
R
×
M
T
channel matrix of resolv-
able path
l
, and finally, η(
t
) is an additive noise.
4.2.2
MIMO Channel Stationarity Definition
In wireless communication, a stochastic time-variant linear channel usually employs
wide-sense stationarity uncorrelated scattering (WSSUS) for stationary property
[2, 3]. This WSSUS channel expresses uncorrelated attenuation in both time-delay and
Doppler-shift domains. The quasi-WSSUS channel [2] is usually applied to real radio
systems. It has the properties of a WSSUS channel for a limited bandwidth and for a
limited time or within a limited environment. This kind of assumption is exceptionally
useful in communication systems. For example, ergodic MIMO channel performance
can be given by averaging the channel performances over many independent channel
realizations considering that they have the same statistics.
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