# Optical OFDM Error Floor Estimation by Means of OTDR Enhanced by Front-End Optical Preamplifier
## 3 Test Results
### Preliminary Test Results  
Our preliminary test results are aimed to just verify the proposed concept, whereas the follow-up high-accuracy tests of this kind can be repeated as many times as needed. The exemplar OTDR setup screen shot and a trace with discovered and qualified events, are presented in Figure 9, followed by Tables 1 and 2 displaying the BER/BLER test results estimated by the proposed model (and indexed by \"T.DISP\" which stands for time dispersion, i.e., for large SNR), as well as the test results obtained by means of the BER tester. Figure 8: OTDR and the two-way BER test configuration. Figure 9: OTDR tests: (a) setup; (b) trace printout with discovered and qualified events (with distance [km], and power level [dB], written in blue font, and fiber loss [dB/km], in red one). Moreover, the below tables also contain the BER/BLER entries (indexed by \"ABSTR\") as the overpesimistic \"worst-case scenario\" values obtained by applying the well-known BER expression for the M-QAM signal transmission over the additive white Gaussian noise (AWGN) channel, as a function of the ratio of the energy \(E_{\text{b}}\) of a bit to noise spectral density \(N_{0}\), is [10]:  
\[BER=\frac{4\cdot Q\left(\sqrt{\frac{\frac{E_{b}}{N_{0}}\cdot\log_{2}M}{M-1}} \right)}{\log_{2}M}=4\cdot Q\left(\sqrt{3\frac{E_{b}}{N_{0}}}\right) \tag{21}\]  
where \(Q\) denotes the Gaussian tail function. From the OTDR trace, the actual _SNR_ (determining \(E_{\text{b}}/N_{0}\)) value at the far end, is read and substituted into (21) abstracting the actual BER by the AWGN-only based one (as a sum of a number of mutually independent and even non-Gaussian small distortions is subject to the application of Central Limit Theorem and can therefore be considered to have Gaussian distribution and the according mean and variance [10]. Then, we can use such an AWGN-modelled BER/BLER as another reference (in addition to the BER testing) for verification of the proposed BER/BLER predictions. As it is evident in Tables 1 and 2, there is good matching between the OTDR-aided residual BER and BLER estimations with the corresponding actually measured values, respectively, both with and without optical preamplifier (whose benefit for reducing BER and BLER was minor here due to relatively large SNR in both cases). Furthermore, in the above tables it is noticeable that the AWGN-abstracted BER and BLER are somewhat larger than the corresponding values obtained by both the proposed model and real life testing, with or without the preamplifier applied. This can be interpreted as the consequence of worst-case design of the AWGN abstraction (coming out of wide-sense stationary uncorrelated scattering (WSS-US) assumption, when no dominant reflective events are identified on the OTDR trace. With this regard, we considered the OTDR-identified reflective events as determining the standard time-dispersion indicator--mean delay spread of the power-delay profile, which is known to determine the BER floor (and thus BLER, too). Moreover, for the case when the high-SNR condition is not fulfilled for estimating the residual BER, we proposed the OTDR dynamic range extension by introducing a low-noise high-gain EDFA optical preamplifier in front of the OTDR, to reduce the noise floor of the cascade, and thus increase SNR. The theoretical model was preliminary validated experimentally, showing good matching between the OTDR-predicted and actually measured residual BER, for short transmitted pulses and large enough OTDR receiver bandwidth. This work was aimed to model, quantify, and verify predicting fiber OFDM transmission performance from OTDR trace, and so pave the way to high-accuracy measurements that can be repeated as many times as needed within professional R&D and field test campaigns, taking into account design and deployment issues as well, and using sophisticated hardware and industry-standard software simulation tools. Conceptualization, A.L. and V.L. ; methodology, A.L. ; software, A.L. and M.H. ; validation, A.L., V.L. and M.H. ; formal analysis, A.L. and V.L.