## 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

In recent years, information traveling across the Internet has been growing both in quality and in quantity. In addition, a growing number of users are expecting broadband access to the Internet regardless of their locations. Mobile communications in the near future are expected to achieve a bit rate over 100Mbps, which will be realized by multiplexing techniques and/or by shifting carrier frequencies beyond microwave band. However, the transmission loss of microwave/millimeter wave limits the size of a service cell, and increases the number of base stations necessary to cover the whole service area.

Radio over fiber (RoF) transmission is one of the key techniques to realize such services [1]. Radio frequency (RF) signals used in radio communications are directly used to modulate the intensity of the laser light, which is transmitted through the optical fiber. The received optical signal is converted again to RF signals. Since RoF systems work irrespective of modulation formats of radio waves, they can be cost-effective solutions for systems running various types of modulation. In addition, advantages of optical fibers, e.g., light weight, small diameter, low loss, reasonable price, etc., makes RoF systems attractive for systems employing many base stations. RoF transmission systems are new commercially available for cellular phone systems and for terrestrial digital television systems.

When the operation frequency of RoF systems is extended towards microwave/millimeter wave band, the chromatic dispersion of fibers causes significant distortion in transmitted signals [2, 3]. More precisely, the index of amplitude modulation periodically varies along the transmission. This phenomenon is known as a fading due to fiber dispersion, and becomes the more significant for the higher modulation frequency.

On the other hand, fibers in an anomalous dispersion regime show a class of nonlinear phenomena called modulation instability [4, 5]. The modulation instability can be understood as a parametric amplification of the modulation sidebands through *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

In this section, we briefly review the mechanism of fading due to fiber dispersion and that of modulation instability.

The slowly varying amplitude (SVA) of a light field in fibers with the second order dispersion and self-phase modulation obeys the following nonlinear Schrödinger equation [5],

where *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

the Eq. (1) can be written as

Let us first consider the linear case: γ=0. Fourier transform of Eq. (3) gives

where *U*(*z*, ω) is the Fourier transform of *u*(*z*, *T*). The equation can be easily solved as

For an incident optical field, we consider an amplitude-modulated field, the modulation angular frequency of which is ω_{m}. The SVA of the modulated optical field *u*(0, *T*) can be described as

where *A* is the amplitude of the carrier component, and μ is a modulation index. Its Fourier transform *U*(0, ω) becomes

where δ(ω) is Dirac’s delta function. Substituting Eq. (7) into Eq. (5), we obtain

The inverse Fourier transform of Eq. (8) yields the time domain amplitude *u*(*z*, *T*) as

The received optical power |*u*(*z*, *T*)|^{2} is calculated as

If we filter out frequency component around ω* _{m}*, we obtain the received RF amplitude as

The RF received amplitude periodically varies along the transmission. The phenomenon is thus considered as a class of fading. The period of the fading is 4π/(β_{2}ω_{m}
^{2}), which becomes shorter as the GVD parameter β_{2} or modulation frequency ω_{m} becomes greater.

Next, we consider the nonlinear case: γ > 0, where we assume the field as a continuous wave with a small perturbation. The steady state solution of Eq. (3) is

where *P*
_{0}=|*u*
_{0}(0)|^{2} is the optical transmission power. If we denote the propagating field with a small perturbation as

substitute Eq. (13) into Eq. (3), and ignore the second and higher order terms of *a*(*z*, *T*), we obtain a linear equation for the perturbation *a*(*z*, *T*):

Writing the complex amplitude *a*(*z*, *T*) using two real amplitude *a*
_{1}(*z*, *T*) and *a*
_{2}(*z*, *T*) as

we obtain a set of equations:

Fourier transforms of these equations are

where *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,

In case β_{2} < 0 and *P*
_{0} > β_{2}ω^{2}/(4γ), the roots are two real numbers:

This implies that a small modulation of frequency ω in the SVA can be amplified during propagation. Physically, this phenomenon is regarded as a parametric amplification of modulation sidebands through *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.

Figure 1 shows the gain coefficient given by Eq. (19) as a function of modulation frequency [=ω/(2π)], where we use β_{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

In this section, we show the change in a sinusoidally-modulated optical envelope along transmission in a fiber. The experimental setup is shown in Fig. 2. A frequency synthesizer generates a sinusoidal wave of 10.804GHz, which drives an LN intensity modulator modulating the output of a DFB laser oscillating at a wavelength of 1559.5nm. An erbium-doped fiber amplifier (EDFA1) is used to control the fiber launched power. Another erbium-doped fiber amplifier (EDFA2) is used to amplify the optical signal after transmission. Converting the received optical signal to the electric signal by using a photodetector (bandwidth about 20GHz), we observe the optical waveform using a sampling oscilloscope.

For convenience of experimental instruments, the fiber launched power is limited below + 10dBm. In this power regime, we have not observed any obvious symptom of stimulated Brillouin scattering [7].

Observed optical waveforms are shown in Fig. 3, where we varied the fiber launched powers as 0dBm, +5dBm and +10dBm and the transmission distance as 1m (patch cord), 10km and 25km, respectively. For comparison, the optical power at the photodetector is controlled to the same value for each transmission distance. We find asymmetrical distortions after 10km and 25km transmission (total dispersion 190ps/nm, 424ps/nm, respectively). In figures after the 25km transmission, we also find that the signal amplitude for the +10dBm launched power is larger than that for the 0dBm launched power.

To quantitatively evaluate the degradation of the modulation index from the optical waveforms, we define the figure of merit for the degradation in the modulation index as

where μ_{0} and μ* _{t}* 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

*V*

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

*V*

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

Figure 4 shows the result, from which we notice that the figure of merit decreases as the fiber launched power increases.

## 4. Experiments on radio over fiber transmission

In this section, we discuss our experimental results on RoF transmission. The experimental setup is shown in Fig. 5. A pulse pattern generator produces 2^{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.

Figure 6 shows the block diagram of the BPSK receiver. The intermediate frequency is 304MHz, the carrier of which is recovered by means of a multiplication method. The obtained binary data are reshaped by a limiting amplifier.

Using this experimental system, we measure the bit error rate after transmission through single mode fibers, the same fibers as mentioned in section 3.

The bit error rate measurement is performed as follows. The EDFA is operated in the output power constant mode. The received optical power is varied by using the optical variable attenuator. We measure the bit error rate as a function of the received optical power for each fiber launched power.

Figure 7 shows the bit error rate as a function of the received optical power, where the fiber launched powers are 0dBm, +5dBm and +10dBm, respectively. The curves of 10km and 25km transmission show that the bit error rate is improved by increasing the launched power.

Figure 8 shows the power penalty at the BER of 10^{-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.

Comparing Fig. 8 with Fig. 4, they are almost the same, i.e., the change in the modulation index is directly related to the change in the power penalty. Thus, we conclude that the power penalty during transmission is due to the fading along the fiber transmission, and the decrease in the penalty associated with increasing the power is caused by the parametric gain in the modulation sidebands.

## 5. Conclusion

In this paper, we have experimentally shown that the power penalty in the radio over fiber transmission due to dispersion-induced signal fading can be reduced by the parametric gain in the transmission fiber. The 111.689Mbps BPSK signal with a carrier frequency of 10.804GHz transmitted in a 25km single mode fiber has experienced the penalty of 5.8dB for the fiber launched power of 0dBm, though the penalty has been reduced by 1.1dB for the fiber launched power of +10dBm.

Our recent experiments with higher optical power confirm the reduction of the power penalty up to 2.3dB, though the reduction is limited by the increase in the optical noise due to Brillouin scattering that appears for the fiber launched power higher than +15dBm. We will report on this issue in another place.

## Acknowledgment

This work is supported by KAKENHI, Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (18560387).

## References and links

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