8.4 Coherent Detection Schemes
349
N 1 = (A L O + A s )
2 T b
(8.61)
Consequently, the voltage seen by the decoder in the receiver is
V = N 1 − N 0 = (A L O + A s )
2 T b − (A L O − A s )
2 T b = 4 A L O A s T b
(8.62)
and the associated rms noise is
σ =
A
2
L O T b
(8.63)
Again, as in the case of homodyne OOK detection, the condition V/ σ = 12 for a
BER of 10
−9 yields
A
2
L O T b = 9
(8.64)
This says that for ideal PSK homodyne detection (η = 1), an average of 9 photons
per bit is required to achieve a 10
−9 BER. Note that here it is not necessary to consider
the difference between photons per pulse and photons per bit as in the OOK case,
because a PSK optical signal is on all the time.
Again using Eq. (7.16),
BER =
1
2
erfc
2ηN p
(8.65)
for PSK homodyne detection.
Heterodyne Detection Schemes
The analysis for heterodyne receivers is more complicated than in the homodyne
case because the photodetector output appears at an intermediate frequency ω IF . The
detailed derivations of the BER for various modulation schemes are given in the
literature [36–39] so only the results are given here.
An attractive feature of heterodyne receivers is that they can employ either
synchronous or asynchronous detection. Figure 8.19 shows the general receiver
configuration. In synchronous PSK detection (Fig. 8.19a) one uses a carrier-recovery
circuit, which is usually a microwave phase-locked loop (PLL), to generate a local
phase reference. The intermediate-frequency carrier is recovered by mixing the
output of the PLL with the intermediate-frequency signal. One then uses a lowpass filter to recover the baseband signal. The BER for synchronous heterodyne PSK
is given by
BER =
1
2
erfc
ηN p
(8.66)
349
N 1 = (A L O + A s )
2 T b
(8.61)
Consequently, the voltage seen by the decoder in the receiver is
V = N 1 − N 0 = (A L O + A s )
2 T b − (A L O − A s )
2 T b = 4 A L O A s T b
(8.62)
and the associated rms noise is
σ =
A
2
L O T b
(8.63)
Again, as in the case of homodyne OOK detection, the condition V/ σ = 12 for a
BER of 10
−9 yields
A
2
L O T b = 9
(8.64)
This says that for ideal PSK homodyne detection (η = 1), an average of 9 photons
per bit is required to achieve a 10
−9 BER. Note that here it is not necessary to consider
the difference between photons per pulse and photons per bit as in the OOK case,
because a PSK optical signal is on all the time.
Again using Eq. (7.16),
BER =
1
2
erfc
2ηN p
(8.65)
for PSK homodyne detection.
Heterodyne Detection Schemes
The analysis for heterodyne receivers is more complicated than in the homodyne
case because the photodetector output appears at an intermediate frequency ω IF . The
detailed derivations of the BER for various modulation schemes are given in the
literature [36–39] so only the results are given here.
An attractive feature of heterodyne receivers is that they can employ either
synchronous or asynchronous detection. Figure 8.19 shows the general receiver
configuration. In synchronous PSK detection (Fig. 8.19a) one uses a carrier-recovery
circuit, which is usually a microwave phase-locked loop (PLL), to generate a local
phase reference. The intermediate-frequency carrier is recovered by mixing the
output of the PLL with the intermediate-frequency signal. One then uses a lowpass filter to recover the baseband signal. The BER for synchronous heterodyne PSK
is given by
BER =
1
2
erfc
ηN p
(8.66)