# Irregular Shifting of RF Driving Signal Phase to Overcome Dispersion Power Fading

^{*}

## Abstract

**:**

## 1. Introduction

_{TX}(t)) signals through optical fiber used to support wireless communication services. The X

_{TX}(t) in the RoF system is converted to an optical signal using an electro-optic (E/O) converter located at the central office (CO). The optical signal is later transmitted through a fiber link, and the RF signal is recovered using an opto-electric (O/E) converter positioned on the radio access point (RAP). The recovered RF signal (X

_{rec}(t)) is then transmitted wirelessly from the RAP to mobile station (MS). It is possible to convert RF signal to the optical one by modulating the optical source directly or externally, both of which serve as intensity modulation (IM) or phase modulation (PM). The intensity modulation is used most commonly because it has a simple system. Recovering RF signal can be done by direct detection (DD) using a photodetector [1].

_{TX}(t)) with double-sideband spectrum (double-sideband optical modulation, henceforth ODSB). When the ODSB signal is transmitted through a fiber link, the chromatic dispersion of the fiber causes the sideband and optical carrier to propagate at different speeds. This leads the modulated signal at the receiver (E

_{RX}(t)) to experience a phase difference between the sideband and optical carrier by φ. The proportion of φ follows the length of the fiber (L), the frequency of the RF signal (f

_{m}) and the wavelength (λ

_{c}) used. The phase difference causes the O/E process to generate two identical RF signals but with a different phase of 2φ, resulting in constructive and destructive interference on X

_{rec}(t). The destructive interference reduces the power of the recovered RF signal (P

_{rec}(t)), which is known as dispersion power fading. If φ = π, massive decrease in power will occur (deep fade). The proportion of power decrease is obtained by comparing the signal power with and without the fiber, something that is known as the carrier-to-noise (C/N) penalty [2].

_{rec}(t) is always in a constructive condition. However, the optical carrier phase before transmission should always be adjusted to the used L, f

_{m}, and λ

_{c}since the proportion of φ accords with L, f

_{m}, and λ

_{c}. In addition, successfully adjusting the optical carrier phase requires complex transmitter circuits.

_{TX}(t) consists only of upper and lower sidebands. The X

_{rec}(t) is thus generated only from the multiplication between the upper and lower sidebands, so no interference resulting in dispersion power fading is possible. The disadvantage of this method is that the X

_{rec}(t) frequency is twice the X

_{TX}(t) frequency, so the receiver has to do additional works to turn the X

_{rec}(t) frequency to its original frequency.

_{rec}(t) to have the same frequency as that of X

_{TX}(t), so it is not necessary for the receiver to adjust the X

_{rec}(t) frequency. The OSSB modulation scheme can be generated by biasing the dual-drive Mach–Zehnder modulator (DD-MZM) on the quadrature bias point (QBP) and at the phase difference of RF drive signal (θ) = 90° [19,30,40,43,44]. The DD-MZM is an electro-optic (E/O) converter that is commonly used on RoF links. The OSSB generated using DD-MZM manages to effectively overcome dispersion power fading if the X

_{TX}(t) spectrum is made up only of optical carriers and sideband fundamentals without harmonics. Otherwise, the phase shift occurring in the harmonics may result in a decrease of the X

_{rec}(t) power. To produce X

_{TX}(t) without harmonics, the DD-MZM must be operated at a modulation index (m) < 0.2. Hence, this method cannot overcome dispersion power fading efficiently at m ≥ 0.2.

_{TX}(t) spectrum. Different spectrum will also produce a different level of dispersion power fading. This paper proposes, as an update, the use of irregular θ to overcome dispersion power fading. The irregular θ is a θ that produces a minimum level of dispersion power fading, which is measured using (C/N) deviation factor. To calculate the (C/N) deviation factor, it is necessary, at first, to model the recovered RF signal’s power.

- A new method for dealing with dispersion power fading by using irregular θ.
- Generating a simple RoF link with standard DD-MZM as an E/O converter that can overcome dispersion power fading at all m. This link:
- (a)
- Can be used in any f
_{m}, L, and λ_{c}without having to re-adjust the transmitter. - (b)
- Has X
_{rec}(t) set at the same frequency as that of X_{TX}(t), thereby removing any additional work.

## 2. Principles of DD-MZM

_{in}(t)) produced by the laser diode (LD) is modulated by the RF signal (X

_{TX}(t)) to be transmitted later. The modulation is carried out by inserting X

_{TX}(t) into the upper and lower signal driver ports whose phases are differentiated using an electrical phase shifter (EPS) by θ. The upper bias port is given a V

_{bias}voltage, while the lower one is given 0 V voltage. The modulator output optical field is expressed as E

_{TX}(t).

_{in}(t) and X

_{TX}(t) are expressed in the following formula:

_{o}represents continuous optical wave amplitude, f

_{c}the continuous optical wave frequency, V

_{m}the amplitude of the RF signal, and f

_{m}the frequency of the RF signal. As such, the upper (V

_{up}(t)) and lower (V

_{down}(t)) driving signals of DD-MZM are expressed:

_{TX}(t)) can be approximated by the equation

_{π}is the switching voltage of MZM. By inserting the Equations (3) and (4) into (5), the following formula is obtained

_{n}(m) is the nth Bessel function of the first kind. Therefore, Equation (7) can be expressed as

- For $\theta ={180}^{o}$ and $\gamma =\frac{1}{2}$ (QBP, which is ${V}_{bias}=\frac{1}{2}{V}_{\pi}$), an ODSB modulation scheme is produced. The spectrum of this modulated signal is shown in Figure 2a.

## 3. Modeling of Recovered RF Signal Power

_{c}the optical wavelength, f the frequency offset of the optical carrier, c the speed of light in vacuum, and L the fiber length in km. When E

_{TX}(t) is transmitted through a dispersive link, a phase difference occurs between the first-order sideband and the optical carrier

_{RX}(t)) is formulated below:

_{RX}(t) is detected using a photodetector which is a squared-envelope operator, given by [2]

_{m}term, it is obtained

_{rec}(t) [47], so

_{rec}(t) power [2], so the formula below is used to measure the power of the recovered RF signal as a function of L

_{rec}(L) with and without fiber transmission. The calculation is mathematically stated as [2]

_{rec}(L). The minimum sample required for this calculation is one deep fade cycle, as shown in Figure 4a.

#### 3.1. (C/N) Penalty on ODSB

_{rec}(L) from the Equation (25), where P

_{rec}(L) without fiber = P

_{rec}(0), and (C/N) penalty (dB) = P

_{rec}(L) (dBm) − P

_{rec}(0) (dBm). The parameters used in this calculation are λ

_{c}= 1550 nm with D = 17 ps/(nm.km), and f

_{m}= 60 GHz. The range of fiber length L is 0 to 5 km with a step of 0.1 km. The calculations are made at m = 0.1, 0.5, 0.8, 1, 1.5, 2, 3, and 4. According to Bessel function, J

_{n}(4) is still significant until n = 10. Thus, the considered sideband in this calculation is that reaching until the 10th order (n = 10). The (C/N) penalty curve as the result of the calculation is shown in Figure 4.

_{m}, the researchers did a calculation of (C/N) penalty with m = 1, λ

_{c}= 1550 nm, D = 17 ps/(nm km) at L = 1 km to 5 km with a step of 0.1 km. The f

_{m}was varied at 30, 40, 50, 60, and 70 GHz. The results are shown in Figure 5a. On the other hand, to establish the effect of dispersion to the RoF link at different λ

_{c}, the researchers made a similar (C/N) penalty calculation at m = 1, f

_{m}= 60 GHz, at L = 1 km to 5 km with a step of 0.1 km. The λ

_{c}was also varied at 1540 nm (D = 16 ps/(nm km)), 1550 nm (D = 17 ps/(nm km)), 1560 nm (D = 17.5 ps/(nm km)), and 1570 nm (D = 18 ps/(nm km)), and the results of the calculation are given in Figure 5b. On the RoF link with variation f

_{m}, the bigger the f

_{m}used, the closer the distance of the deep fade. Likewise, on the RoF link with variation λ

_{c}, bigger λ

_{c}results in a closer distance of the deep fade.

#### 3.2. (C/N) Penalty on OSSB

_{m}and λ

_{c}respectively. The curve was obtained from calculations with m = 1, λ

_{c}= 1550 nm, and D = 17 ps/(nm km). Both figures illustrate the loss of power by 2.5 dB at different fiber length for different f

_{m}and λ

_{c}. This implies that the OSSB modulation scheme is also unable to overcome dispersion power fading effectively at other f

_{m}and λ

_{c}for m > 0.1.

## 4. Irregular Phase Shifted

_{TX}(t) spectrum to change as well. The X

_{TX}(t) with a different spectrum will result in a different (C/N) deviation factor. The proper shape of the spectrum will produce a small (C/N) deviation factor value, so choosing the right irregular θ will produce a minimum (C/N) deviation factor value.

- (a)
- Calculate P
_{rec}(L) using (24) with n = 10, m = 0.1, θ = 0 rad, λ_{c}= 1550 nm (D = 17 ps/(nm km)), and f_{m}= 60 GHz. The P_{rec}(L) is calculated at 0 ≤ L ≤ 5 km with step 0.1 km. - (b)
- From the obtained P
_{rec}(L) in a), calculate the (C/N) penalty using (26). - (c)
- Calculate the (C/N) deviation factor using (27) of all (C/N) penalties in b).
- (d)
- Repeat steps a) to c) for the value 0° ≤ θ ≤ 360° with step 1°.
- (e)
- Find θ in step d) which produces the smallest (C/N) deviation factor.
- (f)
- Repeat steps a) to e) for 0.1 ≤ m ≤ 4 with step 0.1. The value of m is limited to 4 since only in this condition can the sidebands of >10 order be ignored.

_{m}= 40 GHz. The results of the calculation, as shown in Figure 8b, conclude that at m = 1, the irregular θ I amounts to 69°. In other words, the irregular θ is the same with the same m despite different f

_{m}.

_{c}= 1550 nm (D = 17 ps/(nm km)), and f

_{m}= 60 GHz at 0.1 ≤ m ≤ 4. The results of this calculation are shown in Figure 9.

_{c}= 1550 nm (D = 17 ps/(nm.km)), and f

_{m}= 60 GHz. To validate these results, a comparison of calculation results of (C/N) penalty with the simulation results using Optisystem software was done. The simulation circuit is given in Figure 10.

_{π}used in the simulation is 4 V, the voltage of sine generator V

_{m}is set to 1.274 V to obtain m = 1. The output of the sine generator is then duplicated using fork 1x2. The first fork output is inserted into the electrical phase shift and utilized as an MZM top driver, while the second fork output is directly used as an MZM bottom driver. The electrical phase shift is used to differentiate the phase between the first RF signal and the second fork output by θ. The type of MZM used is LiNb-MZM. To produce γ = ½, MZM is set with the parameters as outlined in Table 2. MZM optical inputs are CW laser which is set to λ

_{c}= 1550 nm, power = 0 dBm, and line width = 10 MHz. The output of MZM is then transmitted through single-mode optical fiber. The optical fiber is configured with parameters in Table 3. In this simulation, the effect of fiber attenuation was ignored. At the receiver, the optical signal is detected using PIN photodetector under the parameter of responsivity (1 A/W) and dark current (10 nA). Because the output of photodetector consists of an electric signal with frequencies of 0, 60, 120 GHz, etc., it was filtered by means of a band pass rectangle filter. To obtain an RF signal at 60 GHz, the parameter filter was used by frequency of 60 GHz, bandwidth of 10 MHz, the insertion loss of 0 dB and a depth of 100 dB. The power of the recovered RF signal was measured using the electrical power meter. The simulation was performed in three scenarios, with the first one being for the RoF link with ODSB modulation scheme. To produce the ODSB modulation scheme, the electrical phase shift is set to θ = 180°. The second scenario is to set θ = 90° to produce OSSB modulation scheme, while the third scenario is for the RoF link with the irregular θ. Since m in this simulation is 1, the electrical phase shift is set to θ = 69 and 291°. The measurements of power for each scenario were performed for 0 to 5 km fiber lengths with a step of 0.1 km.

_{m}= 30 and 40 GHz at m = 1 to test whether the use of irregular θ can successfully handle the dispersion power fading of RoF link at different f

_{m}. The calculation is done with λ

_{c}= 1550 nm (D = 17 ps/(nm km)). The curve for the results of this calculation is shown in Figure 12.

_{m}= 30 GHz experienced a deep fade at L = 4.1 km, while that with f

_{m}= 40 GHz experienced it at L = 2.3 km. No deep fade was recorded on the RoF link with OSSB modulation, but there remained a power reduction of 2.5 dB at the same L. The reduction on the irregular θ of RoF link was incredibly small. The (C/N) deviation factor with ODSB was 7.8 at f

_{m}= 30 GHz and 7.5 at f

_{m}= 40 GHz. On the other hand, the (C/N) deviation factor of OSSB was 1.0 at f

_{m}= 30 GHz and 0.9 at f

_{m}= 40 GHz, while that of irregular θ was 0.1 at f

_{m}= 30 GHz and 0.1 at f

_{m}= 40 GHz. The figures suggest that the irregular θ handles dispersion power fading better than OSSB in every f

_{m}.

_{c}, the researcher conducted a (C/N) penalty calculation on the RoF link with λ

_{c}= 1540 nm (D = 16 ps/(nm km)) and λ

_{c}= 1570 nm (D = 18 ps/(nm km)) at m = 1. Figure 13 portrays the curve for the results of this calculation.

_{c}= 1570 nm experienced a deep fade at L = 0.9, 2.8 and 4.8 km, while that with λ

_{c}= 1540 nm experienced the fade at L = 1.1 and 3.3 km. The deep fade did not occur in the RoF link of OSSB or irregular θ, but a substantial power reduction of 2.5 dB occurred with OSSB modulation, whereas the reduction with the irregular θ was exceptionally small. The (C/N) deviation factor of RoF link with ODSB modulation was 8.6, OSSB modulation 0.9, and irregular θ 0.1, all at λ

_{c}= 1540 nm. The (C/N) deviation factor with λ

_{c}= 1570 nm for ODSB modulation was 7.3, OSSB modulation 0.9, and irregular θ 0.1. These numbers also imply that the use of irregular θ overcomes dispersion power fading better than OSSB does in any λ

_{c}.

## 5. Conclusions

_{m}and λ

_{c}, which is 0.1 at m = l. All in all, the irregular θ manages to overcome the dispersion power fading at any f

_{m}and λ

_{c}without having to re-adjust the transmitter.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**The spectrum of a modulated optical signal. (

**a**) DD-MZM as an optical double-sideband (ODSB) modulator and (

**b**) OSSB modulator.

**Figure 5.**The (C/N) penalty on the RoF link with ODSB modulation (

**a**) variation f

_{m}, (

**b**) variation λ

_{c}.

**Figure 6.**(C/N) penalty on the RoF link with OSSB modulation, (

**a**) m ≤ 1, (

**b**) m > 1, (

**c**) variation f

_{m}and (

**d**) variation λ

_{c.}

**Figure 9.**The (C/N) deviation factor of RoF link with ODSB, OSSB modulation schemes, and irregular θ.

**Figure 11.**(C/N) penalty of RoF link with ODSB, OSSB modulation, and irregular θ: The results of calculation and simulation.

**Figure 12.**(C/N) penalty of RoF link with ODSB, OSSB modulation, and irregular θ for f

_{m}= 30 and 40 GHz.

**Figure 13.**The (C/N) penalty for RoF link with ODSB, OSSB, and irregular θ modulation at λ

_{c}= 1540 nm and 1570 nm.

m | Irregular θ I (Degrees) | Irregular θ II (Degrees) | m | Irregular θ I (Degrees) | Irregular θ II (Degrees) |
---|---|---|---|---|---|

0.1 | 90 | 270 | 2.1 | 88 | 272 |

0.2 | 89 | 271 | 2.2 | 85 | 275 |

0.3 | 89 | 271 | 2.3 | 79 | 281 |

0.4 | 88 | 272 | 2.4 | 73 | 287 |

0.5 | 86 | 274 | 2.5 | 68 | 292 |

0.6 | 84 | 276 | 2.6 | 65 | 295 |

0.7 | 81 | 279 | 2.7 | 62 | 298 |

0.8 | 78 | 282 | 2.8 | 60 | 300 |

0.9 | 74 | 286 | 2.9 | 59 | 301 |

1.0 | 69 | 291 | 3.0 | 58 | 302 |

1.1 | 63 | 297 | 3.1 | 18 | 342 |

1.2 | 56 | 304 | 3.2 | 15 | 345 |

1.3 | 50 | 310 | 3.3 | 105 | 255 |

1.4 | 44 | 316 | 3.4 | 107 | 256 |

1.5 | 38 | 322 | 3.5 | 108 | 252 |

1.6 | 32 | 328 | 3.6 | 107 | 253 |

1.7 | 28 | 332 | 3.7 | 105 | 255 |

1.8 | 145 | 215 | 3.8 | 103 | 257 |

1.9 | 142 | 218 | 3.9 | 47 | 313 |

2.0 | 86 | 274 | 4.0 | 45 | 315 |

Parameter | Value | Units |
---|---|---|

Extinction ratio | 20 | dB |

Switching bias voltage | 4 | V |

Switching radio frequency (RF) voltage | 4 | V |

Insertion loss | 0 | dB |

Normalize electrical signal | unchecked | - |

Bias voltage1 | 0 | V |

Bias voltage2 | 2 | V |

Parameter | Value | Units |
---|---|---|

User-defined reference wavelength | Checked | - |

Reference wavelength | 1550 | nm |

Length | 0–5 | km |

Attenuation effect | Unchecked | - |

Group velocity dispersion | Checked | - |

Third-order dispersion | Unchecked | - |

Frequency domain parameter | Unchecked | - |

Dispersion | 17 | ps/nm/km |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ujang, F.; Firmansyah, T.; Priambodo, P.S.; Wibisono, G.
Irregular Shifting of RF Driving Signal Phase to Overcome Dispersion Power Fading. *Photonics* **2019**, *6*, 104.
https://doi.org/10.3390/photonics6040104

**AMA Style**

Ujang F, Firmansyah T, Priambodo PS, Wibisono G.
Irregular Shifting of RF Driving Signal Phase to Overcome Dispersion Power Fading. *Photonics*. 2019; 6(4):104.
https://doi.org/10.3390/photonics6040104

**Chicago/Turabian Style**

Ujang, Febrizal, Teguh Firmansyah, Purnomo S. Priambodo, and Gunawan Wibisono.
2019. "Irregular Shifting of RF Driving Signal Phase to Overcome Dispersion Power Fading" *Photonics* 6, no. 4: 104.
https://doi.org/10.3390/photonics6040104