## 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

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OSA Recommended Articles SPM-GVD effect on radio-over-fiber transmissions using OSSB+C signals

Joji Maeda and Satoshi Ebisawa
J. Opt. Soc. Am. B 31(7) 1443-1450 (2014) ### References

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1. H. Al-Raweshidy and S. Komaki, Radio over Fiber Technologies for Mobile Communications Networks (Artech House, Boston, 2002).
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]
5. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)
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 68, 1232–1236 (1980).
[Crossref]

#### 1997 (1)

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]

#### 1986 (1)

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

#### 1980 (1)

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

#### Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)

#### Ahmed, Z.

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]

#### Al-Raweshidy, H.

H. Al-Raweshidy and S. Komaki, Radio over Fiber Technologies for Mobile Communications Networks (Artech House, Boston, 2002).

#### Fujiwara, A.

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).

#### Hasegawa, A.

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

#### Komaki, S.

H. Al-Raweshidy and S. Komaki, Radio over Fiber Technologies for Mobile Communications Networks (Artech House, Boston, 2002).

#### Maeda, J.

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).

#### Masuko, T.

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).

#### Novak, D.

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]

#### Smith, G. H.

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]

#### Stolen, R. H.

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

#### Tai, K.

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

#### Tomita, A.

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

#### IEEE Trans. Micorowave Theory Tech. (1)

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]

#### Phys. Rev. Lett. (1)

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

#### Proc. IEEE (1)

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

#### Other (3)

H. Al-Raweshidy and S. Komaki, Radio over Fiber Technologies for Mobile Communications Networks (Artech House, Boston, 2002).

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).

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### Figures (8)

Fig. 1. Calculated parametric gain coefficient in a typical single mode fiber. See text for parameters.
Fig. 2. Experimental setup for observation of optical waveform. LD: laser diode, SG: signal generator, LNM: LN intensity modulator, EDFA: erbium-doped fiber amplifier, PD: photodetector, OSC: sampling oscilloscope.
Fig. 3. Optical waveforms. (1-a,b,c): 0km transmission, (2-a,b,c): 10km transmission, (3-a,b,c): 25km transmission. Suffixes -a, -b, and -c stand for fiber launched power of 0dBm, +5dBm, and +10dBm, respectively.
Fig. 4. Measured figure of merit of degradation in modulation index as a function of transmission distance. Fiber launched powers are 0dBm (solid line with square), +5dBm (broken line with filled circle), and +10dBm (dotted line with triangle).
Fig. 5. Experimental setup for bit error rate measurement. PPG: pulse pattern generator, BERT: bit error rate tester. See Fig. 2 for other abbreviations.
Fig. 6. Block diagram of hand-made BPSK receiver. DBM: double balanced mixer, LO: local oscillator, AGC: automatically gain-controlled amplifier, IF: intermediate frequency, LIA: limiting amplifier.
Fig. 7. Measured bit error rate after 0km (dashed dotted line), 10km and 25km transmission. Fiber launched powers are 0dBm (solid line with square), +5dBm (broken line with filled circle), and +10dBm (dotted line with triangle).
Fig. 8. Measured power penalty of fiber transmission at bit error rate of 10-9. Fiber launched powers are 0dBm (solid line with square), +5dBm (broken line with filled circle), and +10dBm (dotted line with triangle).

### Equations (21)

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$i ∂ u ( z , t ) ∂ z = − i β 1 ∂ u ( z , t ) ∂ z + β 2 2 ∂ 2 u ( z , t ) ∂ t 2 − γ ∣ u ( z , t ) ∣ 2 u ( z , t ) ,$
$T = t − β 1 z ,$
$i ∂ u ( z , T ) ∂ z = β 2 2 ∂ 2 u ( z , t ) ∂ T 2 − γ ∣ u ( z , t ) ∣ 2 u ( z , t ) .$
$i ∂ U ( z , ω ) ∂ z = − β 2 2 ω 2 U ( z , ω ) ,$
$U ( z , ω ) = U ( 0 , ω ) exp ( i β 2 2 ω 2 z ) .$
$u ( 0 , T ) = A ( 1 + μ cos ω m T ) = A + Aμ 2 [ exp ( − i ω m T ) + exp ( − i ω m T ) ] ,$
$U ( 0 , ω ) = A δ ( ω ) + Aμ 2 [ δ ( ω + ω m ) + δ ( ω − ω m ) ] ,$
$U ( z , ω ) = A δ ( 0 ) + Aμ 2 exp ( i β 2 2 ω 2 z ) [ δ ( ω + ω m ) + δ ( ω − ω m ) ] .$
$u ( z , T ) = A + Aμ 2 exp ( i β 2 2 ω 2 z ) cos ω m t .$
$∣ u ( z , T ) ∣ 2 = A 2 + Aμ cos β 2 2 ω m 2 × cos ω m t + A 2 μ 2 4 cos 2 ω m t .$
$Aμ cos β 2 2 ω m 2 z × cos ω m t .$
$u 0 ( z ) = u 0 ( 0 ) exp ( i γ ∣ u 0 ( 0 ) ∣ 2 z ) ≡ P 0 exp ( i γ P 0 z ) ,$
$u ( z , T ) = ( P 0 + a ( z , t ) ) exp ( i γ P 0 z ) ,$
$i ∂ a ( z , T ) ∂ z = β 2 2 ∂ 2 a ( z , T ) ∂ t 2 − 2 γ P 0 ( a ( z , T ) + a * ( z , T ) ) .$
$a ( z , T ) = a 1 ( z , T ) + i a 2 ( z , T ) ,$
$∂ a 1 ( z , T ) ∂ z = β 2 2 ∂ 2 a 2 ( z , T ) ∂ T 2 , ∂ a 2 ( z , T ) ∂ z = − β 2 2 ∂ 2 a 1 ( z , T ) ∂ T 2 + 2 γ P 0 a 1 ( z , T ) .$
$∂ A 1 ( z , ω ) ∂ z = − β 2 2 ω 2 A 2 ( z , ω ) , ∂ A 1 ( z , ω ) ∂ z = ( β 2 2 ω 2 + 2 γ P 0 ) A 1 ( z , ω ) ,$
$λ ± 2 = − β 2 2 ω 2 ( β 2 2 ω 2 + 2 γ P 0 ) .$
$λ ± = ± ∣ β 2 ∣ 2 ω 2 ( 2 γ P 0 − ∣ β 2 ∣ 2 ω 2 ) .$
$− 10 log μ t μ 0 ,$
$μ = V max − V max V max + V max .$
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