# Optical OFDM Error Floor Estimation by Means of OTDR Enhanced by Front-End Optical Preamplifier

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis

#### 2.1. OFDM BER Floor Model

_{S}) of the channel delay power profile (describing time dispersion), whereas the modulation coefficient ${k}_{\mathrm{MOD}}$, is given by the ratio of the symbol error rate (SER) for the M-QAM modulation to BER:

#### 2.2. OTDR Trace as Power-Delay Profile

_{BS}(z), which we consider to conform to the OTDR backscatter trace (as describing time dispersion alike).

_{T}

^{1/2}(z), is its convolution with the fiber impulse response h(τ) of an OTDR system, where:

_{BS}

^{1/2}(τ) = P

_{T}

^{1/2}(τ) * h(τ); τ = (2z ⸱ n)/c

_{T}

^{1/2}(τ), i.e., solve (5) per h(τ), which leads to [12]:

_{i}⸱S⸱η

_{i}⸱exp(−2αz)

_{i}and η

_{i}are speed of light, laser energy, fiber average refractive index, and quantum efficiency of the avalanche photodiode detector, respectively, whereas S < 1 denotes the efficiency to confine the incident light (so only a certain part of the scattered light travels back to the OTDR), and α stands for fiber loss.

_{T}(z) = δ(−2αz)

_{BS}

^{1/2}(z) = δ(−2αz)

_{*}h(z) = h(z); z = c · τ/2

#### 2.3. OTDR Dynamic Range

_{BS}(0) at the input of the fiber, and the effective noise equivalent power NEP

_{eff}—the noise floor where SNR = 1 [9], can be presented as:

_{BS}(0) − NEP

_{eff}]

_{eff}, with visual outcome similar to the one illustrated in Figure 5.

#### 2.4. OTDR Receiver Noise Floor Reduction

_{eff}of a receiver cascade of blocks by the more common noise figure F relating the (shot) noise power spectral density P

_{no}at the receiver output to the input noise power spectral density P

_{ni}multiplied by the receiver gain G [12]:

_{no}/G ·P

_{ni}= 1 + NEP

_{eff}/G · P

_{ni}

_{eff}with the noise figure F [12]:

_{eff}= (F − 1) G · P

_{ni}

#### 2.4.1. Noise Figure of ODC Coupled OTDR

_{1,2}of the cascaded two blocks is, to the large extent, determined by the noise figure F

_{1}of the first block (with large gain G

_{1}>> 1) in the series:

_{1,2}=F

_{1}+ (F

_{2}− 1)/G

_{1}≈ F

_{1}

_{2}(unless it is very large), does not contribute significantly to F

_{1,2}characterizing the whole cascade [12].

_{DC}(equal to its own NF), deteriorates the noise figure (13) of the cascade even further to [12]:

_{OTDR}=A

_{DC}+ (F

_{APD}− 1) · A

_{DC}= A

_{DC}· F

_{APD}

#### 2.4.2. OA/OC/OTDR Dynamic Range Prediction Model

_{OC+OA+OTDR}=F

_{OC+OA}+ (F

_{OTDR}− 1)/G

_{OC+OA}≈ F

_{OC}

_{OC+OA}≈ G

_{OA}>> A

_{OC}(quite justifiably as G

_{OA}is of the order of 10

^{3}and thereby much larger than the OC insertion loss A

_{OC}).

_{OC+OA+OTDR}≈ A

_{OC}·F

_{OA}<< F

_{OTDR}= A

_{DC}· F

_{APD}

_{BS}(0) − NEP

_{OC+OA+OTDR}] − [P

_{BS}(0) − NEP

_{OTDR}] = NEP

_{OTDR}− NEP

_{OC+OA+OTDR}

_{ni}, the noise floor NEP

_{OTDR}for the OTDR alone is:

_{OTDR}= (F

_{OTDR}− 1) · G

_{OTDR}

_{OC+OA+OTDR}≈ NEP

_{OA}= (F

_{OA}− 1) · G

_{OA}· P

_{ni}

_{sOA+OTDR}/P

_{nOA+OTDR})/1 = G

_{OA}⸱NEP

_{OTDR}/(G

_{OTDR}⸱NEP

_{OA}+NEP

_{OTDR})

_{OTDR}to be close to −50 dBm, G

_{OA}of 30 dB and F

_{OA}of 6 dB, resulting with NEP

_{OA}= 447 × 10

^{−5}nW, whereas considering G

_{OTDR}= 10 dB, (20) provides the predicted dynamic range extension value of ΔDR ≈ 30 dB [12].

## 3. Test Results

#### 3.1. Test System

#### 3.2. Preliminary Test Results

_{b}of a bit to noise spectral density N

_{0}, is [10]:

_{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].

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**OTDR trace; (

**a**) with short pulse for better event resolution; (

**b**) with longer pulse for larger dynamic range.

**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).

**Table 1.**OTDR trace-based estimate vs. measured bit-error-rate (BER) floor; 50 and 80 km fiber link, 1 Gbit/s.

Link Length | 50 km | 80 km |
---|---|---|

BER_OTDR_{T.DISP} | 4.13 × 10^{−12} | 6.31 × 10^{−12} |

BER_OTDR_{T.DISP}/OA | 4.08 × 10^{−12} | 6.22 × 10^{−12} |

BER_OTDR_{ABSTR} | 4.84 × 10^{−12} | 6.97 × 10^{−12} |

BER_OTDR_{ABSTR}/OA | 4.77 × 10^{−12} | 6.83 × 10^{−12} |

BER_BERT | 4.49 × 10^{−12} | 6.89 × 10^{−12} |

BER_BERT/OA | 4.46 × 10^{−12} | 6.7 × 10^{−12} |

Link Length | 50 km | 80 km |
---|---|---|

BER_OTDR_{T.DISP} | 5.02 × 10^{−8} | 7.63 × 10^{−8} |

BER_OTDR_{T.DISP}/OA | 4.96 × 10^{−8} | 7.32 × 10^{−8} |

BER_OTDR_{ABSTR} | 5.52 × 10^{−8} | 8.42 × 10^{−8} |

BER_OTDR_{ABSTR}/OA | 5.48 × 10^{−8} | 8.24 × 10^{−8} |

BER_BERT | 5.45 × 10^{−8} | 8.37 × 10^{−8} |

BER_BERT/OA | 5.42 × 10^{−8} | 8.14 × 10^{−8} |

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**MDPI and ACS Style**

Lipovac, A.; Lipovac, V.; Hamza, M.; Batoš, V.
Optical OFDM Error Floor Estimation by Means of OTDR Enhanced by Front-End Optical Preamplifier. *Sensors* **2021**, *21*, 7303.
https://doi.org/10.3390/s21217303

**AMA Style**

Lipovac A, Lipovac V, Hamza M, Batoš V.
Optical OFDM Error Floor Estimation by Means of OTDR Enhanced by Front-End Optical Preamplifier. *Sensors*. 2021; 21(21):7303.
https://doi.org/10.3390/s21217303

**Chicago/Turabian Style**

Lipovac, Adriana, Vlatko Lipovac, Mirza Hamza, and Vedran Batoš.
2021. "Optical OFDM Error Floor Estimation by Means of OTDR Enhanced by Front-End Optical Preamplifier" *Sensors* 21, no. 21: 7303.
https://doi.org/10.3390/s21217303