## Mitigation of signal fading in radio over fiber transmission using fiber nonlinearity

Optics Express, Vol. 17, Issue 6, pp. 4518-4525 (2009)

http://dx.doi.org/10.1364/OE.17.004518

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### Abstract

Radio over fiber systems in a microwave/millimeter wave band experience a severe signal fading due to fiber dispersion. However, parametric amplification in transmission fibers, known as modulation instability, can compensate for the signal fading. In this paper, we experimentally demonstrate radio over fiber transmission of 111.689 Mbps BPSK signal with a carrier frequency of 10.804GHz, and measure bit error rates varying the optical transmission power. For the fiber launched power of 0dBm, we observe a power penalty of 5.8dB in the transmission over a 25km fiber, though by increasing the fiber launched power up to +10dBm, we successfully reduce the power penalty by 1.1dB.

© 2009 Optical Society of America

## 1. Introduction

2. H. Sotobayashi and K. Kitayama, “Cancellation of the signal fading for 60 GHz subcarrier multiplexed optical DSB signal transmission in nondispersion shifted fiber using midway optical phase conjugation,” J. Lightwave Technol. **17**, 2488–2497 (1999). [CrossRef]

3. G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming chromatic-dispersion effects in fiber-wireless System incorporating external modulators,” IEEE Trans. Micorowave Theory Tech. **45**, 1410–1415 (1997). [CrossRef]

4. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. **56**, 135–138 (1986). [CrossRef] [PubMed]

*χ*

^{(3)}nonlinearity pumped by the remaining carrier. By numerical simulations, we have demonstrated that the modulation instability can reduce a power penalty due to the fading in RoF systems [6]. This paper reports our experimental results that confirm our proposal, using a hand-made 111.689Mbps BPSK RF transmission system with carrier frequency of 10.804GHz.

## 2. Signal fading in radio over fiber transmission and modulation instability

*u*(

*z*,

*t*) is the SVA at a transmission distance

*z*and time

*t*, β

_{1}and β

_{2}are the group delay and the group velocity dispersion (GVD) parameter of the fiber, respectively, and γ is the nonlinear coefficient of the fiber. In this equation, we ignore fiber loss and higher order terms both of the dispersion and of the nonlinearity. If we introduce a moving time frame

*T*by

*U*(

*z*, ω) is the Fourier transform of

*u*(

*z*,

*T*). The equation can be easily solved as

_{m}. The SVA of the modulated optical field

*u*(0,

*T*) can be described as

*A*is the amplitude of the carrier component, and μ is a modulation index. Its Fourier transform

*U*(0, ω) becomes

*u*(

*z*,

*T*)|

^{2}is calculated as

*, we obtain the received RF amplitude as*

_{m}_{2}ω

_{m}

^{2}), which becomes shorter as the GVD parameter β

_{2}or modulation frequency ω

_{m}becomes greater.

*P*

_{0}=|

*u*

_{0}(0)|

^{2}is the optical transmission power. If we denote the propagating field with a small perturbation as

*a*(

*z*,

*T*), we obtain a linear equation for the perturbation

*a*(

*z*,

*T*):

*a*(

*z*,

*T*) using two real amplitude

*a*

_{1}(

*z*,

*T*) and

*a*

_{2}(

*z*,

*T*) as

*A*

_{1}(

*z*,

*w*) and

*A*

_{2}(

*z*,

*w*) are Fourier transforms of

*a*

_{1}(

*z*,

*T*) and

*a*

_{2}(

*z*,

*T*), respectively. Roots of the characteristic equation for this system, λ

_{+}and λ

_{-}, satisfy the following equation,

_{2}< 0 and

*P*

_{0}> β

_{2}ω

^{2}/(4γ), the roots are two real numbers:

*χ*

^{(3)}nonlinearity of the fiber, where the carrier component works as a pump. Because the gain is frequency-dependent, it causes distortion in the optical waveform, thus called modulation instability. However, the gain can be regarded almost constant for narrow-band signals, such as those in radio communications. Therefore we can expect the gain during propagation to reduce the decrease in modulation index due to fading.

_{2}=17ps

^{2}/km, and γ=2.2W

^{-1}km

^{-1}. Transmission powers are 0dBm, +5dBm and +10dBm, respectively. For the transmission power of +10dBm, we find that the gain band covers 10.804GHz, which is the modulation frequency of our experiment.

## 3. Change in optical envelope along transmission

7. R. H. Stolen, “Nonlinearity in Fiber Transmission,” Proc. IEEE **68**, 1232–1236 (1980). [CrossRef]

_{0}and μ

*are modulation indexes before and after the transmission, respectively. We measure the modulation index μ by using statistics functions of the sampling oscilloscope: we accumulate sampled data for five seconds, obtain a histogram in the proximity of the maximum, and find its peak as*

_{t}*V*

_{max}. Following the same process in the proximity of the minimum, we find

*V*

_{min}, and calculate μ by using the following equation

## 4. Experiments on radio over fiber transmission

^{9}–1 pseudo random bit stream of 111.689Mbps, with which a 10.804GHz carrier is BPSK-modulated through a ring modulator. This BPSK RF signal drives the LN intensity modulator which modulates the output of the DFB laser, the same laser as mentioned in section 3. The optical system is similar to that of Fig. 2, except the EDFA at the receiver side is omitted. The fiber launched power is controlled at the EDFA. The RF signal from the photodiode directly fed to a hand-made BPSK receiver.

^{-9}as a function of the launched power. At the transmission distance of 10km, the difference in the power penalty is small. This is because the influence of the chromatic dispersion is small. At the transmission distance 25km, on the other hand, the influence of the chromatic dispersion so greatly appears that the difference in the power penalty becomes remarkable. For the launched power of 0dBm, the power penalty is about 5.8dB, which almost coincides with theoretical penalty calculated from Eq. (11). The power penalty for the launched power of +10dBm is about 4.7dB, thus 1.1dB improvement is observed.

## 5. Conclusion

## Acknowledgment

## References and links

1. | H. Al-Raweshidy and S. Komaki, |

2. | H. Sotobayashi and K. Kitayama, “Cancellation of the signal fading for 60 GHz subcarrier multiplexed optical DSB signal transmission in nondispersion shifted fiber using midway optical phase conjugation,” J. Lightwave Technol. |

3. | G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming chromatic-dispersion effects in fiber-wireless System incorporating external modulators,” IEEE Trans. Micorowave Theory Tech. |

4. | K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. |

5. | G. P. Agrawal, |

6. | J. Maeda, T. Masuko, and A. Fujiwara, “A numerical study on signal degradation in radio over fiber transmission due to modulation instability,” Post deadline paper of Asia-Pacific Microwave Photonics Conference 2006, PD-3 (2006). |

7. | R. H. Stolen, “Nonlinearity in Fiber Transmission,” Proc. IEEE |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(060.4510) Fiber optics and optical communications : Optical communications

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 9, 2009

Revised Manuscript: March 3, 2009

Manuscript Accepted: March 3, 2009

Published: March 5, 2009

**Citation**

Joji Maeda, Kazutoyo Kusama, and Yutaka Fukuchi, "Mitigation of signal fading in radio over fiber transmission using fiber nonlinearity," Opt. Express **17**, 4518-4525 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-6-4518

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### References

- H. Al-Raweshidy and S. Komaki, Radio over Fiber Technologies for Mobile Communications Networks (Artech House, Boston, 2002).
- H. Sotobayashi and K. Kitayama, "Cancellation of the signal fading for 60 GHz subcarrier multiplexed optical DSB signal transmission in nondispersion shifted fiber using midway optical phase conjugation," J. Lightwave Technol. 17, 2488-2497 (1999). [CrossRef]
- G. H. Smith, D. Novak, and Z. Ahmed, "Overcoming chromatic-dispersion effects in fiber-wireless System incorporating external modulators," IEEE Trans. Micorowave Theory Tech. 45, 1410-1415 (1997). [CrossRef]
- K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986). [CrossRef] [PubMed]
- G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed., (Academic Press, San Diego, 2001)
- J. Maeda, T. Masuko and A. Fujiwara, "A numerical study on signal degradation in radio over fiber transmission due to modulation instability," Post deadline paper of Asia-Pacific Microwave Photonics Conference 2006, PD-3 (2006).
- R. H. Stolen, "Nonlinearity in Fiber Transmission," Proc. IEEE 68, 1232-1236 (1980). [CrossRef]

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