Digital Signal Processing Reference
In-Depth Information
Table 6.2
Statistics of the Faded SNR for the Three Fading Models under
Consideration
Model
Rayleigh
Rice/Nakagami-
n
Nakagami-
m
·
Parameter
K
=
n
2
≥ 0
m
≥
2
x
2
−
+
1
n
m
mx
2
1
γ
−
2
−
n
x
2
1
Γ()
m
−
−
(
1
+
ne
)
1
+
n
mx
m
e
e
γ
γ
PDF (
p
γ
(
x
))
e
γ
I
2
n
x
0
γ
γ
γ
x
γ
m
mx
1−
e
2
21
(
+
n
)
Γ
,
CDF (
F
γ
(
x
))
1
−
Qn
2
,
x
γ
1
γ
1−
Γ
()
m
during guard periods. The statistics of the received SNR for the SC-based joint design
are then derived before this result is applied to the performance and spectral efficiency
analysis.
6.3.1 Mode of Operation and Statistics
During each guard period, the receiver performs the following operations. First, the
receiver estimates the faded SNR of each antenna branch and selects the best branch
after proper comparisons. The combiner output SNR is then given by γ
c
= max[γ
1
, γ
2
, …,
γ
L
]. After that, the receiver determines the appropriate modulation scheme by sequen-
tially comparing the output SNR γ
c
with the threshold γ
T
n
,
n
=
N
,
N
- 1,
…
, 2. Whenever
the receiver finds that the output SNR is smaller than γ
T
n
+1
but greater than γ
T
n
, it selects
the modulation mode
n
for the subsequent data burst and feeds back that mode index to
the transmitter. If the combined SNR of all
L
available branches is below γ
T
2
, the receiver
may ask the transmitter to either (1) transmit using the lowest modulation mode, i.e.,
QPSK, in violation of the target instantaneous BER requirement (option 1), or (2) buf-
fer the data and wait until the next guard period for more favorable channel conditions
(option 2). Note that option 1 is useful in supporting delay-sensitive traffic with hard
delay constraint, especially when coupled with a powerful upper-layer error correction
mechanism.
Based on the mode of operation described above, we can see that the received SNR, γ
c
,
of the SC-based scheme is the same as the output SNR of a traditional
L
branch selection
combiner. In other words, the CDF of the received SNR,
F
γ
c
(·), is given by
SC
F
F
(),
(),
γ
foroption1;
γ
c
F
()
γ
=
SC
(6.2)
γ γ γ
>
γ
c
γ
T
foroption2,
c
2
F
SC
γ
γ
( ,
2
0<≤
γ γ
T
T
2
where
F
γ
SC
(·) denotes the CDF of the combined SNR with
L
branch SC, which is given for
i.i.d. fading environment by
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