Digital Signal Processing Reference
In-Depth Information
6.3.2.2 Average Error Rate
The average BER for an adaptive modulation system can be calculated as [2, equation (35)]
N
1
∑
BER
=
nBER
n
,
(6.8)
η
n
=
2
where
BER
n
is the average error rate for constellation
n
, and which is given by
∫
()
γ
1
T
n
+
SC
c
BER
=
BER
γ γ γ
γ
p
()
d
,
(6.9)
n
n
γ
T
n
where
BER
n
(γ) is the conditional BER of the constellation
n
over an additive white
Gaussian noise (AWGN) channel given that its SNR is equal to γ, which is given in [30]
for uncoded
M
-QAM. Therefore, the average BER of the SC-based scheme under con-
sideration can be calculated as
∫
γ
∑
=
N
∫
γ
T
T
n
3
+
1
SC
SC
BERp d
()
γ
()
γ γ
+
n
BER
()
γ
p
( )
γγ
d
2
γ
n
γ
c
c
0
n
3
γ
T
n
,
for option 1;
∑
N
()
SC
N
−
F
γ
γ
T
c
n
n
=
3
BER
=
∑ ∫
+
2
N
γ
T
n
1
n
BER
()
γ
p
SC
( )
γ
d
γ
n
γ
c
n
=
γ
T
n
,
foroption2.
∑
2
N
()
SC
N
−
F
c
γ
γ
T
n
n
=
(6.10)
6.3.3
Numerical Examples
Figure 6.2
plots the average spectral efficiency of the SC-based scheme with both options
and for different numbers of receive antennas
L
. As we can see, as the number of receive
antennas increases, the average spectral efficiency of the system improves, but with
diminishing gain. If we compare the average spectral efficiency of the two options with
the same number of antennas, we can see that for a high-SNR region, both options have
nearly the same spectral efficiency, whereas for a low-SNR region, option 1 offers higher
efficiency than option 2. This is because when the channel condition is poor, option 2
will buffer the data while option 1 continues transmission at the cost of violating the
BER constraint.
The BER constraint violation can be immediately observed from
Figure 6.3
, where
we plot the average error rate of the SC-based scheme with both options and different
numbers of receive antenna
L
. The target BER is set to be 10
-3
in this figure. We also
observe that when the average SNR is greater than a certain value (10 dB for the
L
=
4 case), the average BER of the SC-based scheme with option 1 will always be smaller
than the target BER of 10
-3
. When the number of receive antennas increases, the SNR
region where the BER constraint is satisfied with option 1 also increases. For option 2,
however, more receive antennas will only lead to a better BER performance over the very
high-SNR region.
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