vice issues
4.4.1
Guard interval and spectral efficiency
The burst-mode NFDM system is resilient to the dispersion effects by insert- ing a very long guard interval (GI), to prevent the inter-symbol interference (ISI). However, the large GI overhead compromises the spectral efficiency benefit of NFDM transmission, and also leads to an increased complexity in the computation of the NFT and INFT of the signal. In NFDM systems, dispersion effects can only be removed at the receiver in the NFT domain, while the pulse is still broadens in the temporal-domain upon propagation. The Authors of [124] have evaluated both in a numerical study and in its ex- perimental validation, the spectral efficiency gain in pre-compensated NFDM
4.4. DSP implementation and transmission device issues
as a function of a variable size GI. As per [124], the normalized spectral ef- ficiency in symbol/s/Hz as a function of the guard interval size, taking both CD and PMD into account [124], is given as:
SE = Ts
Ts+ 2πBβ2L+ 3 ⋅ Dp
√
L (4.14) Neglecting the PMD term and using the relation Ts = Nsc/B, where Nsc is
the number of useful subcarriers, Ts is the useful NFDM symbol duration
and B is the bandwidth of the transmitted signal, Eq.(4.14) is reduced to: SE = 1
1+ 2πB2β
2L/Nsc
(4.15) In this section, the effect of variable GI size on NFDM systems is investigated numerically.
4.4.1.1 B2B Performance
To analyze the impact of the GI, the NFDM signal is designed with a variable GI size in a B2B configuration. At the receiver, it is essential to minimize the error associated with synchronization, CFO and the split-step Fourier method. Fig.(4.14) shows the optimal Q-factor performance of the NFDM system for different sizes of the normalized guard interval GI/T0, i.e. the
guard interval length is normalized to the symbol duration. It can be ob- served that high-power NFDM symbols perform as good as low power sym- bols, for normalized guard intervals (NGI) from 2 to 3. However, the high power symbols performance decreases sharply for NGIs less that 1.5. This is due to the fact that, at high power, the NFDM symbol exhibits longer tails, due to its increasing energy leakage towards the decaying tails, when compared with lower power symbols. Moreover, a reduced guard interval also induces a performance penalty as a result of increasing numerical errors in the NFT-INFT computation, due to increased sample size in the nonlinear frequency domain.
4.4.1.2 Transmission Performance
The transmission performance of NFDM systems subject to variable NGI size is presented in Fig.(4.15). Here, the simulation was done for both a noise-free and a noisy amplified optical fiber channel. Fig.(4.15) shows the Q-factor performance as a function of the input launch burst power for different sizes of NGI in noise-free (thick lines) and noisy (dashed lines) transmissions.
1 1.5 2 2.5 3 10
15 20
Normalized Guard Interval (GI/T0)
Q-factor
[dB]
Pin=−2 dBm
Pin= 1 dBm
Figure 4.14: Simulation result of a B2B Q-factor performance as a function of NGI for NFDM transmissions with input power of −4 dBm and −1 dBm.
−8
−6
−4
−2
0
5
10
15
Input Launch Power [dBm]
Q-factor
[dB]
N GI = 3w/o ASE noise N GI = 2w/o ASE noise N GI = 1.5w/o ASE noise N GI = 1w/o ASE noise
N GI = 3with ASE noise N GI = 2with ASE noise N GI = 1.5with ASE noise N GI = 1with ASE noise
Figure 4.15: Q-factor vs burst input power for NFDM transmissions with dif- ferent NGIs in a noise-free (solid lines) and noisy (dashed lines) fiber transmis- sions.
In Fig.(4.15), the noise-free transmission performance of a NFDM system with a short guard interval perform slightly worse when compared with a NFDM system with a longer guard intervals. This penalty is attributed
4.4. DSP implementation and transmission device issues
to the growth of the signal-noise interaction in the region near the lower end of the input power; moreover, the noisy performance curve fall down as the impact of ASE noise increase. The noisy transmission performance demonstrates that noise has significant impact on the NFDM transmission with a shorter NGI. Compared with NFDM transmission with NGI = 3, the NFDM system with NGI = 1 exhibits a Q-factor penalty of 3.4 dB at input burst power of −2 dBm, and a comparable performance for an input burst power lower that −4 dBm and. However, spectral efficiency will increase by a factor of 2 when compared with the NFDM transmissions with NGI = 1.
4.4.2
Oversampling and numerical accuracy
While the idea of using the continuous spectrum for NFDM transmissions is attractive due to analogies with OFDM, errors in the generated continuous spectrum and run-time of the NFT/INFT algorithms, make the NFDM more complex in practical implementations. This sub-section investigates the de- pendence of the accuracy of a NFDM system on the oversampling factor and signal power.
4.4.2.1 B2B performance
For the oversampling investigation, a NFDM system with variable oversam- pling factor is used. NFDM symbols in the linear spectrum are over-sampled, before mapping them to the continuous part of the nonlinear spectrum. Since the NLSE is solved by using the INFT numerically, oversampling is essential for minimizing the numerical errors associated with the information-bearing signal at the output of the INFT block, q (0, τ). The B2B noise-free perfor- mance is illustrated in the Fig.(4.16).
The performance of the NFDM transmission in Fig.(4.16) shows a significant Q-factor gain as the oversampling factor is increased from a value of 4 to a value of 32. This gain can be attributed to improved accuracy in the computation of the nonlinear spectral amplitude, as illustrated in inset of Fig.(4.16).
4.4.2.2 Transmission performance
For transmission performance investigation of the oversampling factor, an oversampling factor of 4 and 8 was used. Here, the simulation was done for both a noise-free and a noisy amplified optical fiber channel. Fig.(4.17) shows the Q-factor performance remain similar for the oversampling factor of 4 and 8. This is the main reason behind our decision to reduce the oversampling
2 4 8 16 32 15 20 25 Oversampling Factor Q-factor [dB]
Figure 4.16: Illustration of B2B performance of the oversampling factor.
factor from 32, in single polarization first experiment, to factor of 8, in a dual polarization experimental validation.
−8 −6 −4 −2 0 2 4 6 Pin[dBm] Q-factor [dB] OSF=4 OSF=8
Figure 4.17: Q-factor performance as function of input launch power for the oversampling factor of 4 and 8.