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and
⎡
⎤
x
2
x
1
−
⎣
⎦
x
4
x
3
−
|
|
C
OF DM
2
=
(2)
|
|
|
|
x
2
N
x
2
N−
1
−
where
N
is the number of subcarriers and (
.
)
∗
denotes the complex conjugate.
The two codewords take two time instances and each row represents transmission
over one subcarrier. Hence, the two codewords together form a 2
2O-STBC
for each subcarrier. In such a design, we gain spatial diversity but no frequency
diversity.
The signal model at the
j
-th receive antenna for the
n
-th subcarrier at time
t
(
t
=1
,
2) is given as
y
t
(
n
)=
ρ
M
t
×
M
t
c
t
(
n
)
h
ij
(
n
)+
η
t
(
n
)
,
(3)
i
=1
where
ρ
is the channel SNR,
c
t
(
n
) is the energy-normalized transmitted symbol
from the
i
-th transmit antenna at the
n
-th tone, and
η
t
(
n
) are independent
Gaussian random variables with zero mean and variance 1.
h
ij
(
n
) is the channel
frequency response from the
i
-th transmit antenna to the
j
-th receive antenna
at the
n
-th tone.
t
takes values 1 and 2 since there are two codewords that
take two time instances, as mentioned earlier. The fading channel is assumed
to be quasi-static. We assume that perfect channel state information is known
at the receiver, and the ML decoding is used to detect the transmitted symbols
independently.
3 Scalable H.264 Codec
In this work, the scalable extension of H.264/AVC is used for video coding.
We will use the acronym “SVC” to specifically refer to the scalable extension
of H.264/AVC and not to scalable video coding in general. SVC is based on a
hierarchical prediction structure in which a GOP consists of a key picture and
all other pictures temporally located between the key picture and the previously
encoded key picture. These key pictures are considered as the lowest temporal
resolution of the video sequence and are called temporal level zero (TL0) and
the other pictures encoded in each GOP define different temporal levels (TL1,
TL2, and so on). Each of these pictures is represented by a non-scalable base
layer (FGS0) and zero or more quality scalable enhancement fine granularity
scalability (FGS) layers. The hierarchical coding structure of SVC is shown in
Figure 1.
4 Optimal Bandwidth Allocation
The bandwidth allocation problem is defined as the minimization of the expected
end-to-end distortion by optimally selecting the application layer parameter, QP
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