The need to co-propagate an idler, containing no additional information, along with the signal, normally leads to a reduction of the spectral efficiency (SE) in PSA links. However, PSA-based links can actually reach higher SE than PIA links when operating at low SNRs. PSAs with higher SE than PIAs have already been demonstrated for deep-space communication applications where the benefit of low-noise amplification was exploited [195]. This can be extended to fiber links. A preliminary numerical study is performed here with single-channel 10 GBaud QPSK data signal.
The SE is plotted against the SNR of the PIA (SNRPIA) in terms of the Shannon limit and for the QPSK format in Fig. 5.1. The SE corresponding to the Shannon limit [52] is plotted for PIA (red-dotted curve) with log2(1 + SN RPIA)whereas for the PSA (red-solid curve) it is 12log2(1 + 4SN RPIA). In case of the PSA, the factor of 4 comes from the SNR improvement due to the low-noise amplification and the factor of 12 accounts for the extra bandwidth occupied by the idler. The PIA and PSA links are studied at low SNRs, where FECs are required to provide error free transmission (post-FEC BER
< 10−15). It has been shown that a better metric to predict the post-FEC BER of soft-decision (SD) FECs is generalized mutual information (GMI) [196]. In this study, the GMI provides the maximum number of information bits per transmitted symbol over a memoryless AWGN auxiliary channel with bit-wise decoder [197,198]. The GMI is obtained by Monte Carlo simulations [199]. The GMI is equal to the SE for PIAs. In case of the PSA, the SE curve is shifted to left by 6 dB due to the SNR improvement and divided by 2 as the PSA requires the signal and a copy. The PIA and PSA Shannon SE cross at SNRPIA = 3 dB. Therefore, the PSA links have higher SE than PIA links below 3 dB SNR.
For the QPSK modulation format, since the upper bound SE in case of PSAs is 1 (bits/s/Hz), the PIA and PSA curves cross at SNRPIA = -0.6 dB. At high
5.2. PSA fiber links at low SNR
Figure 5.1: Spectral efficiency versus signal-to-noise ratio (SNR) of the PIA. The red curves correspond to Shannon and the blue curves correspond to quadrature phase shift keying (QPSK). The dotted and solid lines cor-respond to phase-insensitive amplifiers (PIAs) and phase-sensitive am-plifiers (PSAs), respectively. For Shannon, the PIA and PSA curves cross at 3 dB whereas for QPSK it happens at -0.6 dB.
SNRs, the SE of PIAs are twice that of the PSAs. As the SNR decreases, the ratio of the SEP SA to SEP IA increases and becomes one at SNRs which correspond to the crossing point of PIA and PSA curves. The PSAs become more spectrally efficient than the PIAs for SNRs below the crossing point as the ratio of SEP SA to SEP IA starts to increase. Moving to still lower SNRs, the ratio of SEP SA to SEP IA reaches two.
Simulations were performed with single- and multi-span links utilizing PIAs and PSAs. A 80 km SSMF was used as the transmission span. The propaga-tion was modelled by solving NLSE using SSFM. The transmission span was dispersion managed and optimized for both PIA and PSA links. Additional span losses were emulated using variable-optical attenuator assuming linear propagation. The NF for the PIA was 4 dB. The PSA was emulated as in [C]
where the NF of the PSA was 1 dB. In the single-span links, the GMI was calculated at optimum launch powers (PIN) for different span losses and the SE was obtained from the GMI. The SE for the PIA links is equal to the simu-lated GMI. However, we divide the GMI by two to take into account the extra bandwidth occupied by the idler for the PSA. The spectral efficiency is plotted for a single-span PIA and PSA links against the span loss in Figure 5.2. The SE of PIA starts to decrease at lower span losses and crosses the SE of PSA at approximately 70.4 dB span loss. This shows us that the SE of PSA links is larger than the PIA links at span losses above 70.4 dB.
The multi-span transmission links were simulated with PIA and PSA as inline amplifiers. For the PIA, dispersion unmanaged links are considered as they have less penalties from nonlinear distortions. For each span, the GMI was calculated for different PIN. The GMI is obtained from the optimum PIN
55 60 65 70 75
Figure 5.2: Spectral efficiency (SE) is against the span loss for single-span links for phase-insensitive amplifier (PIA) and phase-sensitive amplifier (PSA).
The maximum spectral efficiency for the phase-insensitive amplifier uti-lizing single-polarization (SP) quadrature phase shift keying (QPSK) signal is two whereas for PSA it is one due to the need for the conju-gated copy of the signal. The SE curves for PIA and PSA crosses at approximately 70.4-dB span loss. This also shows that the single-span links using PSAs as preamplifier has higher SE than PIA links when the span loss is greater than 70.4 dB.
0 1000 2000 3000 4000 5000 6000 7000 8000 Distance (km)
Figure 5.3: Spectral efficiency (SE) is against the distance for phase-insensitive am-plifier (PIA) and phase-sensitive amam-plifier (PSA) used inline in multi-span links with different multi-span losses. The maximum spectral effi-ciency for the phase-insensitive amplifier utilizing single-polarization (SP) quadrature phase shift keying (QPSK) signal is two whereas for PSA it is one due to the need for the conjugated copy of the signal.
The SE decreases with distance for both PIA and PSA links. As the span loss increases, the SE curves of PIA and PSA crosses at shorter distances after which the PSA links are spectrally efficient than the PIA links.
5.3. Nonlinearity mitigation