## Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels

Optics Express, Vol. 17, Issue 23, pp. 20721-20726 (2009)

http://dx.doi.org/10.1364/OE.17.020721

Acrobat PDF (451 KB)

### Abstract

In this paper, we derive the average bit error rate (BER) of subcarrier multiplexing (SCM)-based free space optics (FSO) systems using a dual-drive Mach-Zehnder modulator (DD-MZM) for optical single-sideband (OSSB) signals under atmospheric turbulence channels. In particular, we consider the third-order intermodulation (IM3), a significant performance degradation factor, in the case of high input signal power systems. The derived average BER, as a function of the input signal power and the scintillation index, is employed to determine the optimum number of SCM users upon the designing FSO systems. For instance, when the user number doubles, the input signal power decreases by almost 2 dBm under the log-normal and exponential turbulence channels at a given average BER.

© 2009 Optical Society of America

## 1. Introduction

1. R. Olshansky, V. A. Lanzisera, and P. M. Hill, “Subcarrier multiplexed lightwave systems for broad-band distribution,” J. Lightwave Technol. **7**, 1329–1342 (
1989). [CrossRef]

2. V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol. **24**, 4750–4762 (
2006). [CrossRef]

3. T. Cho and K. Kim, “Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode machzehnder modulator with ODSB and OSSB signals,” J. Lightwave Technol. **24**, 2052–2058 (
2006). [CrossRef]

## 2. FSO system architecture and derivation of SNDR

*x*(

_{LD}*t*) is the optical signal from a laser diode (LD), we assume that the phase noise of LD is negligible,

*x*(

_{RF}*t*)=

*x*

_{1}(

*t*)+…+

*x*(

_{m}*t*)+…+

*x*(

_{M}*t*) is the group of input RF signals,

*x*(

_{m}*t*) is the tone signal allocated to one user in the SCM group, and PD is a photodetector. As shown in the Fig. 1, the optical signal

*x*(

_{LD}*t*) and the input RF signals

*x*(

_{RF}*t*) can be modulated using DD-MZM and a 900 phase shifter to generate optical single-sideband (OSSB) signals. Then, The input signals are

*x*(

_{LD}*t*)=

*A*·exp(

*jω*),

_{LD}t*x*(

_{RF}*t*)=∑

^{M}_{m=1}

*x*(

_{m}*t*), and

*x*(

_{m}*t*)=

*V*·cos(

_{RF}*ω*) where 1≤

_{m}t*m*≤

*M*,

*A*and

*V*are the optical carrier and RF signal amplitudes, respectively, and

_{RF}*w*and

_{LD}*w*are the angular frequencies of the signals. We assume that the frequency difference between users is larger than the bit duration; thus, we use tone for the user signal.

_{m}3. T. Cho and K. Kim, “Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode machzehnder modulator with ODSB and OSSB signals,” J. Lightwave Technol. **24**, 2052–2058 (
2006). [CrossRef]

*V*and

_{π}*β*=

*V*/(√2

_{RF}*V*) are the switching voltage and the normalized ac of DD-MZM, respectively. In addition,

_{µ}*x*√

*(*

_{RF}*t*) is the phase-shifted version of

*L*. From (1), the fundamental and IM3 components will be generated by beating each signal; then, after the transmission of the turbulence channels, the optical signal can be detected by the PD. In this paper, we focus our investigation on the worst performances among the SCM group due to the IM3 components, since the worst performance may limit the whole system. Specifically, we consider IM3 components having the same frequency as the user–at most by ⌊(

_{DM}*M*-1)/2⌋ times-because when

*M*is odd, the worst user has an (

*M*-1)/2 pair, and when

*M*is even the worst user has an

*M*/2-1 pair. In this case, the photocurrent

*i*(

*t*) after passing PD can be obtained as

*E*(

_{R}*t*) is the received optical signal at PD,

*M*-1)/2⌋ times,

*i*

_{s,o}(

*t*) are other spurious terms such as IM2, and

*n*(

*t*) are additive noises such as thermal and shot noises. Note, however, that IM2 terms are ignored in this paper since they are easily removed by utilizing an appropriate filter; hence, we concentrate on the fundamental frequency and IM3 components. Additionally, we assume that high-order components of the Bessel function are negligible since the value of

*βπ*in a Bessel function is very small due to the fact that

*V*≫

_{π}*V*in general. As such, using power

_{RF}*P*=|

*i*(

*t*)|

^{2}and

*J*(

_{n}*βπ*)≈(

*βπ*)

*/2*

^{n}*! for*

^{n}n*βπ*≪1 [3

3. T. Cho and K. Kim, “Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode machzehnder modulator with ODSB and OSSB signals,” J. Lightwave Technol. **24**, 2052–2058 (
2006). [CrossRef]

*δ*is the turbulence channel coefficient. Similarly, the power of

*ϕf*=

_{m}*πLDλ*

^{2}

*f*

^{2}

*/*

_{m}*c*due to dispersion [6] in the turbulence channel,

*λ*is the LD wavelength,

*L*is the communication distance,

*D*is the dispersion parameter, and c is the speed of light. Since the frequencies (

*f*,

_{w}*f*) of signals are much higher than the difference (|

_{m}*f*-

_{w}*f*|) [7], Y can be approximated as

_{m}*δ*can be modeled as [5

5. K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. **53**, 1455–1461 (
2005). [CrossRef]

*δ*=

*e*,

^{K}*µ*and σ

_{k}*denote the mean and standard deviation of*

_{k}*K*, respectively. Here, the scintillation index is defined as

5. K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. **53**, 1455–1461 (
2005). [CrossRef]

*δ*becomes the exponential distribution [5

5. K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. **53**, 1455–1461 (
2005). [CrossRef]

*δ*̄ is

*E*[

*δ*].

## 3. Average BER analysis of FSO systems

*k*=1.38×10

^{-23}

*J*/

*K*is the Boltzmann constant,

*q*=1.6×10

^{-19}

*C*is the electron charge,

*P*is the thermal noise power,

_{th}*P*is the shot noise power,

_{shot}*T*=300

*K*is the absolute temperature,

*B*is the effective noise bandwidth, and

*P*=

_{RF}*V*

^{2}

*/2 is the input signal power. Using the above SNDR and turbulence channels, we then derive the average BER (*

_{RF}*P*) as

_{b}*x*=(

*lnδ*-

*µ*)/√2σ

_{k}*and the Gauss-Hermite quadrature formula [8*

_{k}8. M. K. Simon and M. S. Alouini, *Digital Communication over Fading Channels*. (Wiley, New York,
2000). [CrossRef]

*N*is the order of approximation,

*x*,

_{i}*i*=1,…,

*N*are the zeros of the

*N*th-order Hermite polynormial and

*w*,

_{i}*i*=1,…,

*N*are weight factors for the

*N*th-order approximation;

*N*=10 is used for the analysis [5

**53**, 1455–1461 (
2005). [CrossRef]

## 4. Numerical results

*λ*) is 1550 nm, the switch voltage (

*V*) is 2.5 V, the DD-MZM insertion loss (

_{π}*L*) is 6 dB, the responsivity (ℜ) is 0.8 A/W, the communication distance (

_{DM}*L*) is 2 km, and the worst RF frequency (

*f*) is 25 GHz. Since SNDR is sensitive to the input signal power and the total number of users (

_{w}*M*), as shown in (14), in Fig. 2(a) we present the average BER as a function of the input signal power according to the total number of users under the log-normal and the exponential channels. In Fig. 2(b), we show the relationship between the scintillation index and the average BER.

## 5. Conclusions

*βπ*≪1. Thus, when we establish FSO systems practically, we should carefully consider the desired environment.

## Acknowledgment

## References and links

1. | R. Olshansky, V. A. Lanzisera, and P. M. Hill, “Subcarrier multiplexed lightwave systems for broad-band distribution,” J. Lightwave Technol. |

2. | V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol. |

3. | T. Cho and K. Kim, “Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode machzehnder modulator with ODSB and OSSB signals,” J. Lightwave Technol. |

4. | L. Besser and R. Gilmore, |

5. | K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. |

6. | G. P. Agrawal, |

7. | Y. Palaskas and Y. Tsividis, “Power-area-DR-frequency-selectivity trade-offs in weakly nonlinear active filters,” in Proceedings of ISCAS, (Bagnkok, Thailand, 2003), pp. I-453-I-456. |

8. | M. K. Simon and M. S. Alouini, |

**OCIS Codes**

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 5, 2009

Revised Manuscript: October 8, 2009

Manuscript Accepted: October 22, 2009

Published: October 27, 2009

**Citation**

Wansu Lim, Tae-Sik Cho, Changho Yun, and Kiseon Kim, "Average BER analysis of SCM-based
free-space optical systems by considering
the effect of IM3 with OSSB signals
under turbulence channels," Opt. Express **17**, 20721-20726 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-23-20721

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### References

- R. Olshansky, V. A. Lanzisera, and P. M. Hill, "Subcarrier multiplexed lightwave systems for broad-band distribution," J. Lightwave Technol. 7, 1329-1342 (1989). [CrossRef]
- V. W. S. Chan, "Free-space optical communications," J. Lightwave Technol. 24, 4750-4762 (2006). [CrossRef]
- T. Cho and K. Kim, "Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode machzehnder modulator with ODSB and OSSB signals," J. Lightwave Technol. 24, 2052-2058 (2006). [CrossRef]
- L. Besser and R. Gilmore, Practical RF Circuit Design For Modern Wireless Systems, (Artech House, Boston • London, 2003)
- K. Kiasaleh, "Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence," IEEE Trans. Commun. 53, 1455-1461 (2005). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001).
- Y. Palaskas and Y. Tsividis, "Power-area-DR-frequency-selectivity trade-offs in weakly nonlinear active filters," in Proceedings of ISCAS, (Bagnkok, Thailand, 2003), pp. I-453-I-456.
- M. K. Simon and M. S. Alouini, Digital Communication over Fading Channels, (Wiley, New York, 2000). [CrossRef]

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