## Dimensioning of OFDMA PON with non-preselected independent ONUs sources and wavelength-control |

Optics Express, Vol. 20, Issue 1, pp. 607-613 (2012)

http://dx.doi.org/10.1364/OE.20.000607

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### Abstract

A simple and low cost method for wavelength control of economical random non-preselected independent ONU sources is shown to increase the number of users in an OFDMA-PON. The method is based on OLT monitoring and thermal tuning control; it has been validated through Monte-Carlo simulations and a probabilistic model. The minimum optical spectral gap between the ONUs wavelengths that guarantees a tolerable amount of optical beat interference has been determined through an experiment.

© 2011 OSA

## 1. Introduction

2. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “A novel OFDMA-PON architecture with source-free ONUs for next-generation optical access networks,” IEEE Photon. Technol. Lett. **21**(17), 1265–1267 (2009). [CrossRef]

3. S. Soerensen, “Optical beat noise suppression and power equalization in subcarrier multiple access passive optical networks by downstream feedback,” J. Lightwave Technol. **18**(10), 1337–1347 (2000). [CrossRef]

5. S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol. **15**(5-6), 407–413 (2009). [CrossRef]

3. S. Soerensen, “Optical beat noise suppression and power equalization in subcarrier multiple access passive optical networks by downstream feedback,” J. Lightwave Technol. **18**(10), 1337–1347 (2000). [CrossRef]

6. C. Desem, “Optical interference in subcarrier multiplexed systems with multiple optical carriers,” IEEE J. Sel. Areas Comm. **8**(7), 1290–1295 (1990). [CrossRef]

7. C. H. Chang, “Interference of multiple optical carriers in subcarrier-multiplexed systems,” IEEE Photon. Technol. Lett. **5**(7), 848–850 (1993). [CrossRef]

3. S. Soerensen, “Optical beat noise suppression and power equalization in subcarrier multiple access passive optical networks by downstream feedback,” J. Lightwave Technol. **18**(10), 1337–1347 (2000). [CrossRef]

## 2. Optical Beat Interference experimental results

_{1}and ONU

_{2}, with different wavelengths transmit an OFDM signal consisting of 256 subcarriers with 4-PSK coded data. ONU

_{1}used the first 128 subcarriers, while ONU

_{2}used the last ones. Data was generated randomly for a total length of 2

^{18}bits. The Hermitian symmetry property was employed in order to get a real valued OFDM signal. The data was loaded to an arbitrary waveform generator (AWG) to get two analogue waveforms at 6.5 GSa/s, giving an effective bandwidth (BW) for ONU

_{1}and ONU

_{2}of 3.125 GHz each. Each electrical signal modulates the light source by means of a Mach-Zehnder modulator (MZM) biased at quadrature. The ONU

_{1}light source was a DFB whose wavelength was left static at 1550.83 nm, while the ONU

_{2}wavelength was swept from 0 to 0.8 nm with respect to the ONU

_{1}emission wavelength. The total unmodulated laser linewidth was about 30 MHz. The optical OFDM signal then travelled through 6 km of fibre; it was detected with an avalanche photodiode (APD) and captured with a real-time 50 GSa/s oscilloscope. The signal was then post-processed in Matlab® performing the FFT and PSK decoding for measuring the bit error ratio (BER) of ONU

_{1}data.

^{−3}when the optical gap is more than 0.075 nm (9.375 GHz in C-band). It is a consistent result since it nearly corresponds to the sum of the modulated BWs of each ONU. This equals the situation where the two spectra have crossed each other completely and almost no overlap is present. Following the results of the experiment, in case more ONUs are transmitting simultaneously at the same bit rate, a spectral gap of at least 0.1nm would be needed between their emission wavelengths to reduce OBI and be properly detected.

## 3. Laser wavelength distribution algorithm

### 3.1 Description

9. S. Uchiyama, N. Yokouchi, and T. Ninomiya, “Continuous-wave operation up to 36°C of 1.3-μm GaInAsP-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. **9**(2), 141–142 (1997). [CrossRef]

### 3.2 Theoretical approach

*k*bands with a width equal to the needed OBI spectral safe margin. The ONU wavelengths are considered to fall in any of these sub-bands with equal probability. A total of

*y*wavelengths are generated following an uniform probability distribution, and the number of lasers that are found in each sub-band

*h*is denoted as

*w*. OBI occurs when any of these

_{h}*w*is greater than one. We first analyze the case in which the number of sub-bands equals the total number of lasers to be allocated (y = k). For example, consider the total band is divided into 3 sub-bands (

_{h}*k*= 3,

*h*= {1,2,3}) and 3 lasers (

*y*= 3) are generated. The only OBI-free case is having all ONUs in different sub-bands, therefore the probability of this situation can be modeled as following a multinomial distribution with all

*w*= 1:

_{h}*x*of the

*y*ONUs transmit in different frequency, Eq. (1) has to be modified. Following the example, this refers to the case when we consider that only 2 ONUs (

*x*=2) out of the 3 available (

*y*=3) have enough separation between their emission frequency (

*w*=1,

_{1}*w*=2, and

_{2}*w*=0 and their permutations). Having these remarks on mind, Eq. (1) is modified as:

_{3}*y*ONUs, we should consider all the possible situations that result in

*x*active ONUs, indicated in the values of

*w*. As an example, if only 2 ONUs (

_{h}*x*=2) transmit out of a total of 4 of them (

*y*=4), the options are

*w*=

_{1}*w*=2,

_{2}*w*=

_{3}*w*=0 and

_{4}*w*=1,

_{1}*w*=3,

_{2}*w*=

_{3}*w*=0 with their corresponding permutations. As can be inferred, the sum of all

_{4}*w*should result in

_{h}*y*:

*W*. Equation (2) when

*x*≠

*y*is adjusted as follows:

*y*generated lasers (

*y*≤

*k*) the combinations of

*k*in

*y*are incorporated too. For example, having a grid where 4 users (

*k*= 4) can transmit, but only 3 (

*y*=3) are active. The OBI free probability is obtained as:

*w*are changed to

_{k}*w*to consider the available tuning. Following with the example of the previous paragraph if lasers can be tuned 1 band, then the possibility that the three of them interfere in the same sub-band

_{k,tun}*h*is avoided, and if the users can be tuned up to 2 bands, then no interference should happen (w

_{1}= w

_{2}= w

_{3}= 1). Having these considerations in mind, only the denominator of Eq. (4) when

*x*≠

*y*changes and turns into:

*tun*refers to the number of slots that the laser can be displaced and needs to be solved recursively. We simplify it by using the concept of compositions from number theory in the summation:

*x*numbers whose sum is equal to

*y*[10]. As an approximation, we consider only the total number of compositions of a number along with the possible combinations inside each composition. The simplified result is plotted in Fig. 4 (left) for a total of 64 lasers. As noted, the amount of active lasers approaches the total lasers when the tuning increases, giving an acceptance ratio of around 99% with full tuning. These results were generated using Eq. (5) and provide a first estimation of the rejection ratios that can be expected, which are further validated through a Monte Carlo analysis next section.

### 3.3 Simulation results

## 4. Conclusion

## Acknowledgments

## References and links

1. | W. Wei, L. Zong, and D. Qian, “Wavelength-based sub-carrier multiplexing and grooming for optical networks bandwidth virtualization,” in Proceedings OFC 2008, paper PDP35 (2008). |

2. | D. Qian, N. Cvijetic, J. Hu, and T. Wang, “A novel OFDMA-PON architecture with source-free ONUs for next-generation optical access networks,” IEEE Photon. Technol. Lett. |

3. | S. Soerensen, “Optical beat noise suppression and power equalization in subcarrier multiple access passive optical networks by downstream feedback,” J. Lightwave Technol. |

4. | I. Cano, M. C. Santos, V. Polo, and J. Prat, “Dimensioning of OFDMA PON with non-preselected independent ONUs sources and wavelength-control,” in Proceedings ECOC 2011, paper Tu.5.C.2 (2011). |

5. | S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol. |

6. | C. Desem, “Optical interference in subcarrier multiplexed systems with multiple optical carriers,” IEEE J. Sel. Areas Comm. |

7. | C. H. Chang, “Interference of multiple optical carriers in subcarrier-multiplexed systems,” IEEE Photon. Technol. Lett. |

8. | A. Papoulis, |

9. | S. Uchiyama, N. Yokouchi, and T. Ninomiya, “Continuous-wave operation up to 36°C of 1.3-μm GaInAsP-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. |

10. | S. Heubach and T. Mansour, |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

**ToC Category:**

Access Networks and LAN

**History**

Original Manuscript: September 30, 2011

Revised Manuscript: October 29, 2011

Manuscript Accepted: November 5, 2011

Published: December 23, 2011

**Virtual Issues**

European Conference on Optical Communication 2011 (2011) *Optics Express*

**Citation**

I. Cano, M. C. Santos, V. Polo, F. X. Escayola, and J. Prat, "Dimensioning of OFDMA PON with non-preselected independent ONUs sources and wavelength-control," Opt. Express **20**, 607-613 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-607

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### References

- W. Wei, L. Zong, and D. Qian, “Wavelength-based sub-carrier multiplexing and grooming for optical networks bandwidth virtualization,” in Proceedings OFC 2008, paper PDP35 (2008).
- D. Qian, N. Cvijetic, J. Hu, and T. Wang, “A novel OFDMA-PON architecture with source-free ONUs for next-generation optical access networks,” IEEE Photon. Technol. Lett.21(17), 1265–1267 (2009). [CrossRef]
- S. Soerensen, “Optical beat noise suppression and power equalization in subcarrier multiple access passive optical networks by downstream feedback,” J. Lightwave Technol.18(10), 1337–1347 (2000). [CrossRef]
- I. Cano, M. C. Santos, V. Polo, and J. Prat, “Dimensioning of OFDMA PON with non-preselected independent ONUs sources and wavelength-control,” in Proceedings ECOC 2011, paper Tu.5.C.2 (2011).
- S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol.15(5-6), 407–413 (2009). [CrossRef]
- C. Desem, “Optical interference in subcarrier multiplexed systems with multiple optical carriers,” IEEE J. Sel. Areas Comm.8(7), 1290–1295 (1990). [CrossRef]
- C. H. Chang, “Interference of multiple optical carriers in subcarrier-multiplexed systems,” IEEE Photon. Technol. Lett.5(7), 848–850 (1993). [CrossRef]
- A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).
- S. Uchiyama, N. Yokouchi, and T. Ninomiya, “Continuous-wave operation up to 36°C of 1.3-μm GaInAsP-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett.9(2), 141–142 (1997). [CrossRef]
- S. Heubach and T. Mansour, Combinatorics of Compositions and Words (CRC Press, Boca Raton, FL, 2009).

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