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Novel ROF/FTTX/CATV hybrid three-band transport system

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Abstract

A novel cost-effective radio-over-fiber (ROF)/fiber-to-the-X (FTTX)/CATV hybrid three-band transport system based on direct modulation of a distributed feedback laser diode (DFB LD) with multi-wavelength output characteristic is proposed and experimentally demonstrated. Radio-frequency (RF) (1.25Gbps/6GHz) signal with direct modulation, as well as baseband (BB) (622 Mbps) and CATV (channels 2-78) signals with external remodulation are successfully transmitted simultaneously. Low bit error rate (BER) and clear eye diagram were achieved for ROF and FTTX applications; as well as good performances of carrier-to-noise ratio (CNR), composite second-order (CSO) and composite triple beat (CTB) were obtained for CATV signals over an 80-km single-mode fiber (SMF) transport.

©2011 Optical Society of America

1. Introduction

With the ubiquitous popularity of handheld devices, the demands on wireless and wired-line capacity have grown rapidly. The next generation communication systems require high data rate and large broadband services. Radio-over-fiber (ROF), fiber-to-the-X (FTTX), and fiber optical CATV systems are promising candidates to satisfy the requirements in wireless and wire-lined optical access networks. ROF transport systems have the ability to offer significant mobility, economic advantage, and large capacity due to the characteristics of broad bandwidth and low transmission loss of fiber. FTTX networks have provided the last mile solution in optical access networks. In addition, fiber optical CATV systems are deployed widely to offer broad bandwidth to the subscribers. Several papers have been studied towards the simultaneous transmission of radio-frequency (RF) and baseband (BB) [1,2], CATV and RF [3,4], as well as CATV and BB signals [5]. However, hybrid three-band transmission of ROF/FTTX/CATV combined signals has not been reported. A hybrid three-band transport system that uses different optical wavelength to transmit the combined ROF RF/FTTX BB/CATV analog signals would be quite useful for fiber networks providing telecommunication, Internet, and CATV services. Nevertheless, it is a challenge to transmit RF, BB, and CATV signals simultaneously by using one optical fiber in a cost-effective way. A single-wavelength system where the different signals are multiplexed in the electrical domain may be a solution. However, the interactions among ROF RF, FTTX BB, and CATV analog signals are the major concern of systems. Multiplexing these three signals in the electrical domain will introduce distortions after beating among these three electrical signals. For example, the highest carrier frequency for CATV signal is 550 MHz, which is close to the fundamental frequency of 622 Mbps BB signal (622 MHz). Thus, CATV and 622 Mbps BB signals will be interfered each other, in which resulting in system performance degradation. Hybrid multi-band transport systems are envisioned to have a multiple number of distributed feedback laser diodes (DFB LDs) which are wavelength-selected for each channel and controlled to operate at a specific wavelength, this process will increase the cost and complexity of the systems. For a practical implementation of hybrid multi-band transport systems, it is necessary to develop a cost-effective multi-wavelength light source. Several approaches have been proposed to solve the problem. Lightwave transport systems employing spectrum-sliced light sources such as light-emitting diodes (LEDs) or amplified spontaneous emission (ASE) sources were proposed [6,7]. However, the output power of LED is insufficient to accommodate many channels. Moreover, although the spectrum-sliced ASE source provides much higher output power than that of the LED, it requires expensive erbium-doped fiber (EDF) and pumping LD. Recently, there has been a proposal of a multi-wavelength light source based on direct modulation of a DFB LD [8]. When a DFB LD is directly modulated with large optical modulation index (OMI), the single wavelength characteristic of the DFB LD will be changed into multi-wavelength one, and thus it can be used as a cost-effective light source in a hybrid multi-band transport system. In this paper, we proposed and experimentally demonstrated a novel cost-effective ROF/FTTX/CATV hybrid three-band transport system based on direct modulation of a DFB LD with multi-wavelength output characteristic. One DFB LD with large OMI is a feasible scheme in which selected wavelength is filtered out, directly transmitted and externally remodulated individually. It is attractive because it avoids the need of multiple DFB LDs with selected wavelengths. Our proposal reveals a prominent one than those of systems with multiple DFB LDs. Transmission performances over an 80-km single-mode fiber (SMF) transport were studied. With the help of only one optical sideband and optical single sideband (SSB) schemes at the receiving site, low bit error rate (BER) and clear eye diagram were achieved for ROF and FTTX applications; as well as good performances of carrier-to-noise ratio (CNR), composite second-order (CSO), and composite triple beat (CTB) were obtained for CATV signal. Such a hybrid three-band transport system would be very attractive for trunk applications in advanced optical fiber transport and distribution networks, for provisioning full services including telecommunication, Internet, and CATV broadband integrated services.

2. Experimental setup

The schematic architecture of our proposed novel ROF/FTTX/CATV hybrid three-band transport systems based on direct modulation of a DFB LD with multi-wavelength output characteristic is shown in Fig. 1 . The hybrid three-band transport systems consist of one directly modulated DFB laser transmitter, and an 80-km SMF with two cascaded broadband erbium-doped fiber amplifiers (EDFAs). The output power of the DFB LD is 4.77 dBm, at a bias current of 25 mA. Furthermore, the optical characteristics of the DFB LD including threshold current and 3-dB bandwidth of frequency response are 17 mA and 7.8 GHz, respectively. The output power and noise figure of each EDFA are ~17 dBm and ~4.5 dB, at an input power of 0 dBm, respectively. For the transmitting site, it is composed of one DFB LD with a central wavelength of 1532.14 nm, three optical band-pass filters (OBPFs; OBPF1-OBPF3), two external modulators, and one EDFA. A 1.25-Gbps data stream is mixed with a 6-GHz RF carrier to generate the data signal. The resulting data signal is directly modulated into the DFB LD with a large OMI of 9% to generate the multi-wavelength output characteristic. The modulated optical signal is efficiently split into three parts by three OBPFs, directly transmitted and externally remodulated individually. Each OBPF is composed of one optical circulator (OC) and one fiber Bragg grating (FBG). The wavelength variation of the FBG with temperature controller is ~0.003 nm/°C. The OBPF1, with a 3-dB bandwidth of 0.06 nm, is used to pick up two modes (0 and + 1) from the output of the DFB LD. As to the OBPF2 and OBPF3, with a 3-dB bandwidth of 0.02 nm, each is employed to pick up one mode (−1 and −2) from the one. To ensure only one mode is pick up, OBPF2 and OBPF3 exhibit a sharp cutoff in the transmission spectrum. A data signal of 622 Mbps, with a pseudorandom binary sequence (PRBS) length of 223-1, is fed into an external modulator for remodulation. A multi-carrier generator (Matrix SX-16; NTSC) is employed to feed RF subcarriers (channels 2-78) into the other external modulator for remodulation. To compare with the three DFB LDs configuration, in which each DFB LD is directly modulated with ROF, FTTX, and CATV applications, it is noted that we have applied two additional external modulators in our proposed systems. DFB laser transmitter with direct modulation exhibits an optical frequency that varies with output power, referred to as chirp. As chirp is combined with fiber dispersion, signal degradation accumulates along the fiber length. For this reason, nearly all 1550 nm optical transmitters currently in operation use external modulation, a technique which provides minimal chirp. The composite signals are now a combination of ROF (1.25Gbps/6GHz, RF), FTTX (622 Mbps, BB), and CATV (CH2-78) signals. The hybrid three-band signals are multiplexed back into the EDFA-I through a 3 × 1 optical combiner. Since the optical power level of the CATV channel is much higher than that of the ROF and FTTX channels, yet the output of the ROF and FTTX channels are through a variable optical attenuator (VOA). Thereby, the ROF RF and FTTX BB signals compared to the CATV signal have only a very small effect on the input power of EDFA-I.

 figure: Fig. 1

Fig. 1 The schematic architecture of our proposed novel ROF/FTTX/CATV hybrid three-band transport systems.

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System link with a transmission length of 80 km consists of two SMF spans (40 + 40 km, with an attenuation of ~0.24 dB/km, and a dispersion coefficient of ~17 ps/km/nm). The VOA was introduced after each EDFA, this would have resulted in less distortions since the optical power launched into the fiber would have been less. The stimulated Brillouin scattering (SBS) suppression ability is ~17 dBm, so the optical power launched into each fiber span should be kept at ≤ + 17 dBm by using a VOA to avoid degradation caused by the SBS effect. The optical powers launched into the first and the second fiber spans are 9.6 and 12.7 dBm, respectively. Both are operated in the linear regime. After transmission over a total length of 80 km, the received optical signal is split using a 1 × 3 optical splitter, passed through three OBPFs (OBPF4-OBPF6) to select the appropriate optical mode, and detected by two photodiodes (PDs; PD1-PD2) and one analog optical receiver, respectively. Each OBPF is also composed of one OC and one FBG. The OBPF4 and OBPF5, with a 3-dB bandwidth of 0.02 nm, are used to pick up one mode ( + 1 and −1) from the transmitted optical signal. The function of OBPF4 is employed to filter out the upper mode ( + 1) of ROF RF signal; i.e., to convert signal format into only one optical sideband format. RF signal usually needs the beating process to obtain the 6 GHz signal at the receiving site in order to serve it directly to the antenna. Since the zone radius between the receiving site and the end user is limited, the BER performance evaluated at the receiving site is similar to that measured at the end user. To ensure good BER performance is obtained by the end user, direct-detection technique for monitoring BER performance is deployed at the receiving site. After BER performance evaluation, the 3-dB bandwidth of OBPF4 can be adjusted from 0.02 nm to 0.06 nm to pick up two modes (0 and + 1). These two modes are detected by a PD, and applied to an antenna for wireless transmission between the receiving site and the end user. The frequency of the RF carrier comes from the beating between two modes (0 and + 1) after PD detection. Direct-detection technique is worth employing due to expensive and high-bandwidth RF demodulator is not required at the receiving site. The OBPF6, with a 3-dB bandwidth of 0.06 nm, is used to convert the double sideband (DSB) format (lower sideband, main mode (−2 mode), and upper sideband) into the single sideband (SSB) format (main mode (−2 mode) and lower sideband). The optical spectra of the different signals at some interesting points in the optical path are shown in the Fig. 2(i)-(x) (insert (i)-(x) of Fig. 1). To evaluate the BER performance at the receiving site, the 1.25 Gbps data signal is directly fed into a BER tester (BERT). For the 622 Mbps data (FTTX) and CATV signals, 1 GHz RF low-pass filters (LPFs) are used to remove the spurious (1.25Gbps/6GHz) before BER and CATV parameters measured by BER tester and HP-8591C CATV analyzer. Moreover, for better performance of the analog CATV receiver, the received optical power level needs to be kept at −3 ~ + 3 dBm. If we arrange the fiber link as (EDFA + 80-km SMF + EDFA), then the received optical power level of the analog CATV receiver will be <-3 dBm. It is the reason why we arrange the fiber link as (EDFA + 40-km SMF + EDFA + 40-km), rather than (EDFA + 80-km SMF + EDFA).

 figure: Fig. 2

Fig. 2 The optical spectral of the different signals at some interesting points in the optical path.

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3. Experimental results and discussions

The optical spectra for a directly modulated DFB LD at various OMI are present in Fig. 3(a), (b), and (c) , respectively. As OMI values are 3.8% (Fig. 3(a)) and 5.7% (Fig. 3(b)), the optical spectra possess only a few wavelengths. However, as OMI value is increased up to 9% (Fig. 3(c)), the optical spectrum possesses multiple wavelengths with adequate flatness (−2, −1, 0, and + 1 modes). Figure 4 shows the measured side-mode suppression ratio (SMSR) values under different OMI for mode 0. The SMSR value is defined as a power level comparison between the mode 0 and the other mode. It is clear that the SMSR is inversely proportional to the OMI. Moreover, the marked solid triangle (a), (b), and (c) three cases in Fig. 4 are correspondent with Fig. 3(a), (b), and (c), respectively. Large OMI not only results in small SMSR, but also results in directly modulated DFB LD with flat multi-wavelength output characteristic. The spectrum of the output light from a directly modulated DFB LD using a small signal approximation is given by [9]:

S(f)=Σ|Jn(Δffm)M4{Jn+1(Δffm)ejφ+Jn1(Δffm)ejφ}|2δ(f(f0+nfm)),
where Jn(x) is the nth order Bessel function of the first kind, n is the number of side modes, M is the OMI, f0 is the optical frequency under CW operation, Δf is the peak frequency deviation caused by the modulation, fm is the modulation frequency, Δf/fm is the FM index, and φis the phase delay between the intensity and the phase modulation. It is clear that, from the Eq. (1), the amplitude of each sideband is mainly affected by the OMI value. As we observed in the Fig. 3(a)-(c), the sideband optical power is proportionally increased with the increasing OMI value. A large OMI allows a directly modulated DFB LD to obtain a multi-wavelength output with flat power level.

 figure: Fig. 3

Fig. 3 The optical spectrum for a directly modulated DFB LD at various OMI (a) 3.8% (b) 5.7% (c) 9% .

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 figure: Fig. 4

Fig. 4 The measured SMSR values under different OMI for mode 0.

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The measured BER curves for the ROF (1.25Gbps/6GHz) and the FTTX (622 Mbps) applications as a function of received optical power level are plotted in the Fig. 5 . At a BER of 10−9, for ROF RF transmission, the received optical power level is −23 dBm; for FTTX BB transmission, the received optical power level is −24.2 dBm. Good BER performances are achieved over an 80-km SMF transport, it verifies that the proposed ROF/FTTX transport systems can be constructed by employing by a DFB LD with direct modulation. The back-to-back (BTB) BER curves are also given in Fig. 5. At a BER of 10−9, there exists a large power penalty of 14.6 dB (ROF) between BTB case and optical DSB scheme due to RF power degradation induced by fiber dispersion. And at a BER of 10−9, there exist small power penalties of 6.8 (ROF) and 6.1 (FTTX) dB between BTB cases and only one optical sideband schemes due to the suppression of RF power degradation induced by fiber dispersion [10]. These >6 dB power penalties are the results of the fiber dispersion-induced distortions. Fiber dispersion is one of the most severe limiting factors in long-haul lightwave transport systems. If the fiber transmission length exceeds several tens of kilometers, dispersion effect can cause intolerable amounts of distortion. In lightwave transport systems with chirp parameter α, the received RF power Pf can be stated as [11]:

Pfcos2{πLDλc2fc2c[12πtan1(α)]},
where L is the fiber length, D is the fiber dispersion coefficient, λc is the optical carrier wavelength, fc is the frequency for which the power fading is evaluated, and c is the light velocity in vacuum. Over an 80-km SMF transport, fiber dispersion causes severe power degradation due to optical DSB scheme. The RF power degradation because of fiber dispersion degrades the BER performance.

 figure: Fig. 5

Fig. 5 The measured BER curves for the ROF (1.25Gbps/6GHz) and the FTTX (622 Mbps) applications as a function of the received optical power level.

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The eye diagrams of the transmitted RF and BB (after 1 GHz LPF) signals at the receiving site are demonstrated in Fig. 6(a) and (b) , respectively. In Fig. 6(a), the corresponding jitter and SNR are 3.9 ps and 30.5 dB; in Fig. 6(b), the corresponding jitter and SNR are 3.5 ps and 31 dB. In addition, the corresponding jitter and SNR for RF and BB signals (BTB) are 0.4ps/36dB and 0.3ps/36.3dB, respectively. Although little and undesired jitter and amplitude fluctuations are introduced; nevertheless, clear and open eye diagrams for both RF and BB signals are still observed. Furthermore, the corresponding jitter and SNR for RF signal (DSB) are 7.8 ps and 24.4 dB. More undesired jitter and amplitude fluctuations are induced because of fiber dispersion-induced distortion.

 figure: Fig. 6

Fig. 6 The eye diagrams of the transmitted (a) RF and (b) BB (after 1 GHz LPF) signals at the receiving site.

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Figure 7 shows the measured CNR, CSO and CTB values under NTSC channel number, respectively. Since CNR value results from the relative intensity noise of LD, thermal and shot noise of optical receiver, as well as signal-spontaneous and spontaneous-spontaneous beat noise of EDFA; CNR values (>50 dB) of systems with optical DSB and SSB scheme are almost the same due to the use of an identical LD, the same input optical power levels of EDFA and analog receiver. For CSO and CTB performances, the CSO (<-70 dBc) and CTB (<-69 dBc) values of systems with optical SSB scheme can be improved significantly. The improved results seen are due to the use of optical SSB filter (OBPF6) to decrease the linewidth of the optical signal, in which leading to the reduction of the fiber dispersion. The dispersion coefficient D follows that

D=1Lτωωλc,
where τ is the group delay, and ω is the angular frequency. Since τ/ω=Lβ¨, ω/λc=2πc/λc2(β¨ is the second order dispersion coefficient in the frequency expansion), thus

 figure: Fig. 7

Fig. 7 The measured CNR, CSO and CTB values under NTSC channel number.

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D=2πcλc2β¨.

Finally, the differential group delay (Δτ) can be expressed by

Δτ=DLΔλc,
where Δλc is the linewidth of the optical signal. It is effective to introduce an optical SSB filter to reduce the optical linewidth so that total fiber dispersion is reduced. The second and third order harmonic distortions (2HD and 3HD) due to fiber dispersion are [12]:
2HD=10log[mDλc2Lf4c16(Δτ)2+4λc4L2π2f6c2],
3HD=10log[9m2D2λc4L2f24c(4(Δτ)2+4π2f)],
where m is the OMI, and f is the RF carrier frequency. Moreover, according to the analysis in [13], CSO and CTB distortions can be stated as:
CSO=2HD+10logNCSO+6,
CTB=3HD+10logNCTB+6,
where NCSO and NCTB are the product counts of CSO and CTB. It can be concluded that, from these above equations, CSO and CTB degradations are proportional to the linewidth of the optical signal. The use of an optical SSB filter makes the optical linewidth to change from a broad linewidth into a narrow one. Then there would be significant reductions in the CSO and CTB distortions, since the CSO and CTB distortions are due to fiber dispersion. From the experimental results we can see that large CSO and CTB improvements of about 6 dB have been achieved compared to optical DSB system.

OBPFs with tight and sharp cutoff characteristics are used in systems. Probably, the cost of OBPFs will increase the cost of systems. However, they are worth employing because a multiple number of DFB LDs are replaced by a single DFB LD at the transmitting site, as well as only one optical sideband and optical SSB formats are obtained at the receiving site. For ROF RF signal with only one optical sideband format, since optical carrier and one of the sidebands are eliminated before detecting, the RF power degradation induced by fiber dispersion can be cancelled. In this way, the BB data signal is obtained directly from the optical sideband. It is shown to be a promising solution since expensive and sophisticated RF devices (for example, local oscillator for RF signal down-conversion) are not required at the receiving site. For CATV signal with optical SSB format, since one of the sidebands is deleted before receiving, the RF power degradation induced by fiber dispersion can be suppressed. In this way, the optical spectral efficiency is improved and the fiber dispersion-induced distortion is reduced.

FTTX networks are usually implemented with different fiber lengths. To show a more direct association with our proposed systems and the fiber lengths, we measure the BER/CNR/CSO/CTB values at different fiber lengths, and the results are given in Table 1 . It is obvious that longer fiber length leads to worse system performances, due to the accumulations of noise and fiber dispersion.

Tables Icon

Table 1. Measured BER/CNR/CSO/CTB Values at Different Fiber Lengths

4. Conclusions

We have proposed a novel cost-effective ROF/FTTX/ CATV hybrid three-band transport system based on direct modulation of a DFB LD with multi-wavelength output characteristic. From the serious discussions and the demonstrated experimental results, we can declare that such a novel system not only reveals simple and economic advantages by employing a DFB LD with direct modulation to replace multiple LDs, but also demonstrates an efficient and practical architecture to serve broadband integrated services. With the assistance of only one optical sideband and optical SSB schemes, low BER and clear eye diagram were achieved for ROF and FTTX applications; as well as good performances of CNR, CSO and CTB were obtained for CATV signals. Such a hybrid three-band transport system would be very attractive for trunk applications in advanced optical fiber transport and distribution networks, it reveals a prominent alternative with advantages in simplicity and cost to provide triple-play services for wide areas.

References and links

1. C. H. Chang, H. H. Lu, H. S. Su, C. L. Shih, and K. J. Chen, “A broadband ASE light source-based full-duplex FTTX/ROF transport system,” Opt. Express 17(24), 22246–22253 (2009). [CrossRef]   [PubMed]  

2. R. Llorente, T. Alves, M. Morant, M. Beltran, J. Perez, A. Cartaxo, and J. Marti, “Ultra-wideband radio signals distribution in FTTH nettworks,” IEEE Photon. Technol. Lett. 20(11), 945–947 (2008). [CrossRef]  

3. H. H. Lu, H. C. Peng, W. S. Tsai, C. C. Lin, S. J. Tzeng, and Y. Z. Lin, “Bidirectional hybrid CATV/radio-over-fiber WDM transport system,” Opt. Lett. 35(3), 279–281 (2010). [CrossRef]   [PubMed]  

4. A. Murakoshi, K. Tsukamoto, and S. Komaki, “High-performance RF signals transmission in SCM/WDMA radio-on-fiber bus link using optical FM method in presence of optical beat interference,” IEEE Trans. Microw. Theory Tech. 54(2), 967–972 (2006). [CrossRef]  

5. T. F. Fent, S. Shaari, and B. Y. Majlis, “Distributed CATV inputs in FTTH-PON system,” IEEE International Conf. on Semiconductor Electron. (ICSE). 58–61 (2006).

6. S. Gao, C. Yang, X. Xiao, Y. Tian, Z. You, and G. Jin, “Wavelength conversion of spectrum-sliced broadband amplified spontaneous emission light by hybrid four-wave mixing in highly nonlinear, dispersion-shifted fibers,” Opt. Express 14(7), 2873–2879 (2006). [CrossRef]   [PubMed]  

7. K. H. Han, E. S. Son, K. W. Lim, H. Y. Choi, S. P. Jung, and Y. C. Chung, “Bi-directional WDM passive optical network using spectrum-sliced light-emitting diodes,” Opt. Fiber Commun. 1, 23–27 (2004) (OFC).

8. M. Yoshino, N. Miki, N. Yoshimoto, and K. Kumozaki, ““Multiwavelength optical source for OCDM using sinusoidally modulated laser diode,” IEEE/OSA J,” J. Lightwave Technol. 27(20), 4524–4529 (2009). [CrossRef]  

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10. W. I. Lin, H. H. Lu, H. C. Peng, and C. H. Huang, “Direct-detection full-duplex radio-over-fiber transport systems,” Opt. Lett. 34(21), 3319–3321 (2009). [CrossRef]   [PubMed]  

11. G. H. Smith and D. Novak, “Broad-band millimeter-wave (38 GHz) fiber-wireless transmission system using electrical and optical SSB modulation to overcome dispersion effects,” IEEE Photon. Technol. Lett. 10(1), 141–143 (1998). [CrossRef]  

12. M. R. Phillips, T. E. Darcie, D. Marcuse, G. E. Bodeep, and N. J. Frigo, “Nonlinear distortion generated by dispersive transmission of chirped intensity-modulated signals,” IEEE Photon. Technol. Lett. 3(5), 481–483 (1991). [CrossRef]  

13. W. I. Way, Broadband Hybrid Fiber/Coax Access System Technologies, San Diego: CA: Academic, ch. 2, 33–37 (1999).

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Figures (7)

Fig. 1
Fig. 1 The schematic architecture of our proposed novel ROF/FTTX/CATV hybrid three-band transport systems.
Fig. 2
Fig. 2 The optical spectral of the different signals at some interesting points in the optical path.
Fig. 3
Fig. 3 The optical spectrum for a directly modulated DFB LD at various OMI (a) 3.8% (b) 5.7% (c) 9% .
Fig. 4
Fig. 4 The measured SMSR values under different OMI for mode 0.
Fig. 5
Fig. 5 The measured BER curves for the ROF (1.25Gbps/6GHz) and the FTTX (622 Mbps) applications as a function of the received optical power level.
Fig. 6
Fig. 6 The eye diagrams of the transmitted (a) RF and (b) BB (after 1 GHz LPF) signals at the receiving site.
Fig. 7
Fig. 7 The measured CNR, CSO and CTB values under NTSC channel number.

Tables (1)

Tables Icon

Table 1 Measured BER/CNR/CSO/CTB Values at Different Fiber Lengths

Equations (9)

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S ( f ) = Σ | J n ( Δ f f m ) M 4 { J n + 1 ( Δ f f m ) e j φ + J n 1 ( Δ f f m ) e j φ } | 2 δ ( f ( f 0 + n f m ) ) ,
P f cos 2 { π L D λ c 2 f c 2 c [ 1 2 π tan 1 ( α ) ] } ,
D = 1 L τ ω ω λ c ,
D = 2 π c λ c 2 β ¨ .
Δ τ = D L Δ λ c ,
2 H D = 10 log [ m D λ c 2 L f 4 c 16 ( Δ τ ) 2 + 4 λ c 4 L 2 π 2 f 6 c 2 ] ,
3 H D = 10 log [ 9 m 2 D 2 λ c 4 L 2 f 2 4 c ( 4 ( Δ τ ) 2 + 4 π 2 f ) ] ,
C S O = 2 H D + 10 log N C S O + 6 ,
C T B = 3 H D + 10 log N C T B + 6 ,
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