Digital Signal Processing Reference
In-Depth Information
where
F
γ
SEC
(γ
T
2
)
(·) denotes the CDF of the combined SNR with
L
branch SEC and using γ
T
2
as an output threshold, which is given for the i.i.d. fading environment in (6.11). Cor-
respondingly, the PDF of the received SNR,
p
Γ
(·), is given by
SEC
( )
2
γ
p
T
(),
γ
foroption1;
γ
p
Γ
()
γ
=
c
(6.16)
SEC
SEC
(( )
−
( )
+
( )
γ
γ
p
T
()
γγγ
U
F
c
T
()(),
γ δγ
foroption2,
2
2
T
T
γ
γ
2
2
c
where
p
γ
SEC
(γ
T
2
)
(·) denotes the PDF of the combined SNR with
L
branch SSC/SEC and
using γ
T
2
as an output threshold, which is given for the i.i.d. fading environment by
(6.12).
Similarly, the CDF and PDF of the received SNR, Γ, of the minimum estimation
scheme based on SECps can be obtained as
SECps
( )
2
γ
F
T
(),
γ
foroption1;
γ
c
SECp
s
( )
F
Γ
()
γ
=
(6.17)
γ
F
T
(),
γ
γ γ
>
;
2
T
γ
2
foroption2,
c
SECps
( )
γ
F
T
( ,
γ
0
<≤
γ γ
2
T
T
γ
2
2
c
and
SECps
( )
2
γ
p
T
(),
γ
foroption1;
γ
p
Γ
()
γ
=
c
(6.18)
SECp
s
SECps
( )
−
( )
+
( )
γ
γ
p
T
()
γγγ
U
F
T
()(),
γ δγ
for option 2,
2
2
T
T
γ
γ
2
2
c
c
respectively, where
F
γ
SECps
(γ
T
2
)
(·) and
p
γ
SECps
(γ
T
2
)
(·) denote the CDF and PDF of the combined
SNR with
L
branch SECps and γ
T
2
as an output threshold, which is given for the i.i.d.
fading environment by (6.13) and (6.14), respectively.
6.4.2.3 Performance and Efficiency Analysis
With the statistics of the received SNR Γ derived for minimum estimation schemes
based on both SSC/SEC and SECps, we evaluate the performance and efficiency of the
system. Following an approach similar to the one used for the SC-based schemes in the
previous section, we obtain the average spectral efficiency of the SSC/SEC-based mini-
mum estimation scheme as
N
NF
SEC
( )
()
γ
−
T
γ
,
for option 1;
2
T
γ
n
c
n
=
3
η
=
(6.19)
N
∑
SEC
( )
()
γ
NF
−
T
γ
,
for option 2.
2
T
γ
n
c
n
=
2
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