BER performance analysis of radio over free-space optical systems considering laser phase noise under Gamma-Gamma turbulence channels

This paper analytically investigates a bit error rate (BER) performance of radio over free space optical (FSO) systems considering laser phase noise under Gamma-Gamma turbulence channels. An external modulation using a dual drive Mach-Zehnder modulator (DD-MZM) and a phase shifter is employed because a DD-MZM is robust against a laser chirp and provides high spectral efficiency. We derive a closed form average BER as a function of different turbulence strengths and laser diode (LD) linewidth, and investigate its analytical behavior under practical scenario. As a result, for a given average SNR with normalized perturbation, it is shown that the difference of average BER corresponding to two LDs (with linewidth of 624MHz and 10MHz) under weak turbulence is almost 3 times larger than that under strong turbulence. © 2009 Optical Society of America OCIS codes:(000.0000) General. References and links 1. V.W.S. Chan, “Free-Space Optical Communications,” J. Lightwave Technol. 24,4750–4762 (2006). 2. M.A. Al-Habash, L.C. Andrews, and R.L.Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40,1554–1562 (2001). 3. G.H. Smith and D. Novak, “Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators,” IEEE Trans. Microwave Theory Tech. 45,1410-1415 (1997). 4. R.W. Tkach and A.R. Chraplyvy, “Phase noise and linewidth in an InGaAsP DFB laser,” J. Lightwave Technol. LT-4, 1711–1716 (1986). 5. T. Cho, C. Yun, J. Song, and K. Kim, “Analysis of CNR penalty of radio-over-fiber systems including the effects of phase noise from laser and RF oscillator,” J. Lightwave Technol. 23,4093–4100 (2005). 6. J.R. Barry and E.A. Lee, “Performance of coherent optical receivers,” Proc. IEEE 78,1369–1394 (1990). 7. K. Kiasaleh, “Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence,” IEEE Trans. Commun. 54,604–607 (2006). 8. G.P. Agrawal,Fiber-Optic Communication Systems. (John Wiley and Sons, New York, 2002). 9. A.J. Viterbi,Principles of Coherent Communication. (McGraw-Hill, New York, 1966). 10. The Wolfram function site (2004), http://functions.wolfram.com/ .


Introduction
The volume of data traffic continues to increase due to the demand of subscribers for multimedia services that require the access network to support high data rates at any time, in any place inexpensively.Such demands require broadband communication systems.Free space optical (FSO) systems have been good candidates for next generation broadband services since FSO systems support large bandwidth, unlicensed spectrum, excellent security, and quick and inexpensive setup [1].In spite of these advantages, the performance of FSO systems can be unreliable due to atmospheric turbulence.The Gamma-Gamma distribution well represents atmospheric turbulence channels with a multiplication of two parameters of small-scale and large-scale irradiance fluctuations-of which pdfs are independent Gamma distributions-and provides excellent agreement between theoretical and simulation results [2].One of the well-known modulators of FSO systems is the external modulator, with a dual drive Mach-Zehnder modulator (DD-MZM), since it is robust against a laser chirp and provides high spectral efficiency [3].Fig. 1 represents the FSO system employing a DD-MZM.In this system, the laser phase noise from a laser diode (LD) is one of the decisive factors limiting the performance of FSO systems because the optical system is sensitive to laser phase noise.However, to the best of our knowledge, an analysis of the BER of FSO systems, with a DD-MZM impaired by the laser phase noise under turbulence channels, has not been carried out in the research due to the complexity of the analysis.
Therefore, in this paper, we first represent the optical signal model from a DD-MZM with laser phase noise using the Bessel expansion.We then analyze an average BER according to an average SNR, with normalized perturbation under atmospheric channels, where Gamma-Gamma distribution describes the turbulence-induced fading.Also, numerical results are provided to illustrate the degradation of performance according to the depth of scintillation and LD linewidth.

FSO System Architecture and Signal Model
Figure 1 shows the overall architecture of the FSO system.Data is modulated to a binary phase shift keying (BPSK) signal by the RF modulator.A BPSK signal from the RF modulator is split by a π/2 phase shifter.This BPSK signal is optically modulated by a LD with a DD-MZM.The output signal of the DD-MZM is transmitted via atmospheric turbulence channels between telescopes.The received signals are detected by the photodetector (PD), and the photocurrent corresponding to the transmitted BPSK signal is extracted by the bandpass filter (BPF).Finally, data is extracted by the RF demodulator module.The optical signal, x LD (t) [4] from the laser and the BPSK signal, x RF (t) from the RF modulator are modeled respectively, as follows: In ( 1), V LD and V RF are the optical carrier amplitude and the BPSK signal amplitude, respectively, and ω c and ω r f are angular frequencies of the signals from the LD and the RF modulator.The laser phase noise process Φ LD (t) is commonly characterized as a Wiener process [6].θ (t) = ∑ ∞ m=−∞ d m P(t − mT ) where P(t) is a unit amplitude pulse of the bit duration T and d m is the information of the m th bit duration, which takes on {0, π}.
After optically modulating x RF (t) by x LD (t) with a DD-MZM, the output signal of a DD-MZM is represented as [3], [5] L 20 where ε(= V RF /V π ) defines a normalized ac value, V π is the switching voltage of a DD-MZM, and L is the modulator insertion loss in decibels.Using the Bessel function, (2) can be expanded to ( We assume that high-order components of the Bessel function can be negligible since the value of επ in the Bessel function is very small due to the fact that V π V RF in general.The output signal at a DD-MZM is transmitted via turbulence channels experiencing different group delays due to the chromatic dispersion.After the transmission of turbulence channels, the received optical signal is expressed as where , and δ m is the turbulence channel coefficient for the m th data duration, τ 0 and τ 1 are group delays, and ψ 0 and ψ 1 are phase-shift parameters. Through direct detection, the optical signal can be detected at the PD, and the BPSK signal is extracted by the BPF.After the BPF, the photocurrent i(t) can be obtained as follows: where R is the responsivity of the PD and n th (t) is a random fluctuation which has an unit of current due to thermal noise in the load resistance.In general FSO systems, as thermal noise is dominant due to the high operating temperature [7], n th (t) is modeled as a Gaussian process [8].Also, Φ LD (t − τ 0 ) and Φ LD (t − τ 1 ) are independent-not of t-but of the differential delay (τ 1 − τ 0 ).Thus, using a Wiener process property, the difference of two random processes can be simplified as a zero mean Gaussian random variable Ψ with the variance σ2 of 2π∆ν∆τ where ∆ν is LD linewidth and ∆τ is the differential delay [6].Accordingly, (5) can be represented as where ϒ is 2 √ 2R(V LD /10 L/20 ) 2 J 0 (επ)J 1 (επ), ψ 2 = ψ 0 − ψ 1 .When we assume that the coherence time is larger than a bit time duration, {δ m } can be modeled as independent and identically distributed (i.i.d.) random variables, i.e., δ m = δ with Gamma-Gamma distribution.After the matched filter in the RF demodulator, T 0 i(t)d t , thermal noise becomes a random variable, n th with normal distribution, where k is the Boltzmann constant, R L is the load resistance, and ∆ f is the effective noise bandwidth [8].

Average SNR with (dB)
Linewidth: 624MHz Linewidth: 10MHz weak turbulence is almost 3 times larger than that under strong turbulence and the effect of the laser phase noise of LD linewidth 624MHz degrades almost 5dB to the SNR than that of LD linewidth 10MHz at all turbulence conditions.It is noteworthy that in (17), we use N = 10 for the Gauss-Hermite formula.

Conclusions
In this paper, we present an optical signal model from the transmitter output and the receiver input using the Bessel expansion.Also, we derive a close form average BER performance by considering the laser phase noise from LD under atmospheric turbulence channels with Gamma-Gamma distribution using the Gauss-Hermite quadrature formula and Meijer G function.As a result, we can more easily predict BER performance without complicated calculations.In practical terms, when we establish FSO systems, we can make an engineering table by using this derived BER formula according to each LD, which enables us to determine efficient LD under turbulence channel conditions.

Acknowledgment
This work was partially supported by the Center for Distributed Sensor Network at GIST, and by a grant (B01-03) from the Plant Technology Advancement Program funded by the Ministry of Construction and Transportation of the Korean government.

Fig. 1 .
Fig.1.Overall architecture of the FSO system considering of optical transmitter, turbulence channels, and optical receiver.