Digital Signal Processing Reference
In-Depth Information
uses that path for data burst reception, and informs the transmitter to use 2
N
-QAM
as the modulation mode for the subsequent data burst. If the received SNRs of all the
available paths are below γ
T
N
, the receiver selects the modulation mode corresponding
to the SNR interval in which the combined SNR falls. With SSC/SEC, the combined
SNR is the SNR of the last unacceptable path, whereas with SECps, it is the SNR of
the best unacceptable path. In particular, the receiver sequentially compares the output
SNR with the thresholds, γ
T
N
-1
, γ
T
N
-2
,
…
, γ
T
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 this selected mode to the transmitter. If, in the
worst case, the combined SNRs of all the available paths ends up being below γ
T
2
, the
receiver has the same two termination options as for the minimum estimation scheme
(i.e., to transmit using the lowest modulation mode [option 1] or to wait until the next
guard period [option 2]).
6.4.3.2 Statistics of the Received SNR
Based on the mode of operation described above, we can see that the received SNR, Γ, of
the bandwidth-efficient scheme is the same as the combined SNRs of SSC/SEC or SECps
diversity with γ
T
N
as the output threshold. Therefore, the CDF of the received SNR of this
bandwidth-efficient scheme based on SEC is given by
SEC
( )
γ
F
T
N
(),
γ
foroption1;
γ
c
SEC
(( )
F
Γ
()
γ
=
(6.22)
γ
F
T
N
(),
γ γ γ
>
;
T
γ
2
c
for option 2,
SEC
( )
γ
F
c
T
N
( ,
γ
0
<≤
γ γ
T
T
γ
2
2
where
F
γ
SEC
(γ
T
N
)
(·) denotes the CDF of the combined SNR with
L
branch SEC and γ
T
N
as an
output threshold. Correspondingly, the PDF of the received SNR is given by
SEC
( )
γ
p
T
N
(),
γ
foroption1;
γ
p
Γ
()
γ
=
(6.23)
c
SEC
SEC
(( )
( )
−
( )
+
γ
γ
p
T
N
()
γγγ
U
F
c
T
N
()(),
γ δγ
foroption2,
T
T
γ
γ
2
2
c
where
p
γ
SEC
(γ
T
N
)
(·) denotes the PDF of the combined SNR with
L
branch SEC and γ
T
N
as
output threshold. The CDF and PDF of received SNR with the SECps-based bandwidth-
efficient scheme can be similarly obtained, but are omitted here for conciseness.
6.4.3.3 Performance and Efficiency Analysis
With the statistics of the received SNR at hand, we study the performance, efficiency, and
complexity of the bandwidth-efficient scheme as we did for the minimum estimation.
For conciseness, we just list the analytical results in what follows for the SSC/SEC-based
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