## Free space optical ultra-wideband communications over atmospheric turbulence channels |

Optics Express, Vol. 18, Issue 16, pp. 16618-16627 (2010)

http://dx.doi.org/10.1364/OE.18.016618

Acrobat PDF (1021 KB)

### Abstract

A hybrid impulse radio ultra-wideband (IR-UWB) communication system in which UWB pulses are transmitted over long distances through free space optical (FSO) links is proposed. FSO channels are characterized by random fluctuations in the received light intensity mainly due to the atmospheric turbulence. For this reason, theoretical detection error probability analysis is presented for the proposed system for a time-hopping pulse-position modulated (TH-PPM) UWB signal model under weak, moderate and strong turbulence conditions. For the optical system output distributed over radio frequency UWB channels, composite error analysis is also presented. The theoretical derivations are verified via simulation results, which indicate a computationally and spectrally efficient UWB-over-FSO system.

© 2010 OSA

## 1. Introduction

1. W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. **17**(11), 2418–2420 (2005). [CrossRef]

3. M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. **26**(15), 2594–2603 (2008). [CrossRef]

1. W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. **17**(11), 2418–2420 (2005). [CrossRef]

2. F. Zeng and J. Yao, “An approach to ultra-wideband pulse generation and distribution over optical fiber,” IEEE Photon. Technol. Lett. **18**(7), 823–825 (2006). [CrossRef]

4. F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. **18**(19), 2062–2064 (2006). [CrossRef]

5. P. C. Peng, W. R. Peng, J. H. Lin, W. P. Lin, and S. Chi, “Generation of wavelength- tunable optical pulses using EDFA as external-injection light source and amplifier for Fabry-Pérot laser diode,” IEEE Photon. Technol. Lett. **16**(11), 2553–2555 (2004). [CrossRef]

6. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. **50**(8), 1293–1300 (2002). [CrossRef]

7. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. **6**(8), 2813–2819 (2007). [CrossRef]

6. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. **50**(8), 1293–1300 (2002). [CrossRef]

7. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. **6**(8), 2813–2819 (2007). [CrossRef]

6. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. **50**(8), 1293–1300 (2002). [CrossRef]

## 2. Proposed system model

3. M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. **26**(15), 2594–2603 (2008). [CrossRef]

4. F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. **18**(19), 2062–2064 (2006). [CrossRef]

_{k}}’s are TH PPM modulated via Gaussian pulse train and passed through a bias-tee circuit to drive the FPLD into gain-switched operation. The 1550-nm FPLD operates with a threshold current of 18 mA at 25° C with 0.8 nm mode spacing and in this configuration, it is biased at 16 mA and gain-switched at 4 GHz. The generated optical signal is fed to the EDFA which serves both as an external-injection source and an amplifier for the FPLD output and it consists of a 980-nm pump laser diode that pumps 50 mW output power to couple an erbium-doped fiber via 980/1550-nm wavelength division multiplexer (WDM) and an isolator to reduce back reflections. The output of EDFA is passed through TF which operates in the range of 1527 to 1562 nm. The central wavelength of the TF is chosen to be close to that of FPLD output so that the system has a single wavelength output before it is sent to FSO channel.

*E*denotes the pulse energy amplified by EDPA,

_{p}*p(t)*denotes the Gaussian pulse,

*d*and {

_{n}*c*} are the binary information and pseudo-random code sequences for time hopping, respectively.

_{j}*T*,

_{d}*T*,

_{f}*T*and

_{c}*T*represent the symbol, bit, chip and pulse durations, respectively and bits are repeated

_{p}*N*times in a symbol period.

_{s}*h(t) = I(t) + I*where

_{b}*I(t)*and

*I*are the instantaneous light intensity and the background radiation whose effects are removed at the receiver as in [6

_{b}**50**(8), 1293–1300 (2002). [CrossRef]

*η*(

*n(t)*represents the combined effects of both the thermal noise and the shot noise, which can jointly be modeled as an additive white Gaussian noise (AWGN) with zero mean and variance

*N*. Assuming perfect synchronization, the received signal is passed through the matched filter

_{0}/2*x*which can be written asresulting in the sampled outputwhere the noise term

_{r}(t)*N*. Zero-threshold detection is employed at the matched filter output. Notice that the decision output of the FSO subsystem can be used directly or can be to the users over an UWB channel. In this case,

_{0}/2*E*denotes the energy pulse,

_{F}*q(t)*denotes the Gaussian monocycle pulse train. The UWB channel can be modeled aswhere

*κ*denotes the RF log-normal fading random variable,

*N*and

*K(j)*denotes the number of observed clusters and multipaths within each cluster, respectively.

*T*is the delay of the

_{j}*j*

^{th}cluster.

*α*denotes the channel coefficient of the

_{jk}*j*

^{th}cluster and the

*k*

^{th}multipath and can be expressed as

*α*, where

_{jk}= p_{jk}β_{jk}*p*is a Bernoulli random variable taking values of ± 1 and

_{jk}*β*is the log-normal distributed channel coefficient. To normalize each channel realization to unity requires that

_{jk}## 3. Detection error probability analysis

*γ*where

_{RF}= (κ^{2}N_{s}γ_{p})*γ*denotes the pulse SNR and results in error probability ofwhere erfc(⋅) is the complementary error function. After averaging out the probability density function (PDF) over

_{p}= E_{F}/N_{0}*κ*

*y*and

_{i}*ω*,

_{i}*i*= 1,…,

*n*, are the

*i*root (abscissa) and associated weight, respectively [8]. After the change of variables such that

^{th}*γ*and

_{FSO}= N_{s}γ_{p}*γ*are the symbol and pulse SNRs, respectively. Notice that due to the random fluctuations in its amplitude, the light intensity is modeled as a random variable whose distribution is dependent on the turbulence region. Therefore, in order to find the average DEP of the FSO link, one needs to evaluate the expectation over the distribution of the light intensity such that

_{p}= E_{p}/(N_{0}/2)*d*is the minimum free distance of the convolutional code, and

_{free}*N*is the sum of the Hamming weight of all the input sequences whose associated convolutional codeword have a Hamming weight of

_{b}*d*

_{free}_{.}

### 3.1 Error performance of FSO system in weak turbulence

### 3.2 Error performance of FSO system in moderate turbulence

11. The Wolfram Function Site, (2004), http://functions.wolfram.com/.

_{n}(⋅) in Eq. (25) can be expressed in terms of Meijer's G-function as

11. The Wolfram Function Site, (2004), http://functions.wolfram.com/.

### 3.3 Error performance of FSO system in strong turbulence

12. S. G. Wilson, M. B. Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Comm. **23**(9), 1901–1910 (2005). [CrossRef]

## 4. Simulation results

*N*= 1000 symbols,

*N*= 2 and

_{s}*η*= 0.9, respectively. The channel parameters change at every 200 symbols, i.e.,

*τ*/(

_{c}*NT*) = 0.2 where

_{d}*τ*is the channel coherence time and

_{c}*NT*is the total duration of a frame.

_{d}^{−15}for weak turbulence. For link distances over 2, 2.5, 3 and 4 km, the corresponding channel parameters are

*μ*= 0 and

_{x}*σ*= 0.3, 0.37, 0.44 and 0.57. From Eq. (19), these values correspond to

_{X}^{−14}and consider link distances over 2, 2.5 and 3 km. Using the formulation in Eq. (24), the (

*α,β*) parameter pairs are (4.16,2.21), (4.00,1.75) and (4.05,1.51). These values correspond to the following scintillation index values

*I*] = 1 and

*A*and

_{0}*Λ*in LOS environment chosen as 47 dB and 1.7, respectively. The two cases where the UWB signals are transmitted over a FSO link of 2 km length at 30 and 45 dB, respectively, are considered. For weak and moderate conditions, we assume constant

^{−15}and 1.76x10

^{−14}and the corresponding channel parameters are

*σ*= 0.3 and (

_{X}*α,β*) = (4.16,2.21), respectively. The RF UWB simulations adopt CM1 conditions and assume a link distance of

*D*= 2 meters and

*σ*is taken as 3 dB. The results are shown in Fig. 3 . The error performance of the UWB transmission over CM1 channels without any FSO link errors is included as a reference curve. Our results show that for weak turbulence conditions, FSO channel does not introduce additional performance degradation up to 10

_{g}^{−6}BER limit at 30 dB. On the other hand, for moderate and strong turbulence conditions, error floors appear at relatively high BER levels due to the high error rates carried from the FSO subsystem.

_{8}and

*N*= 2,

_{b}*d*= 7 ([9], pp. 540) is employed together with a Viterbi decoder. The coded system performance under each turbulence regime is shown in Fig. 4 . Notice that the use of even a very simple code reduces the error floors significantly. For instance, error floors are decreased to the 9x10

_{free}^{−20}at 32 dB and 4.8x10

^{−43}at 42 dB for weak turbulence, 6.5x10

^{−8}at 24 dB and 2.2x10

^{−13}at 30 dB for moderate turbulence, 7.4x10

^{−5}at 20 dB and 2x10

^{−7}at 24 dB for strong turbulence. In Fig. 4, only the error floors under strong turbulence conditions are shown for comparison purposes with uncoded signaling scheme.

## 5. Conclusion

## Acknowledgments

## References and links

1. | W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. |

2. | F. Zeng and J. Yao, “An approach to ultra-wideband pulse generation and distribution over optical fiber,” IEEE Photon. Technol. Lett. |

3. | M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. |

4. | F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. |

5. | P. C. Peng, W. R. Peng, J. H. Lin, W. P. Lin, and S. Chi, “Generation of wavelength- tunable optical pulses using EDFA as external-injection light source and amplifier for Fabry-Pérot laser diode,” IEEE Photon. Technol. Lett. |

6. | X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. |

7. | S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. |

8. | M. Abramowitz, and I. A. Stegun, |

9. | S. Lin, and D. J. Costello, |

10. | E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of free-space optical systems in Gamma-Gamma fading,” in |

11. | The Wolfram Function Site, (2004), http://functions.wolfram.com/. |

12. | S. G. Wilson, M. B. Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Comm. |

13. | S. S. Ghassemzadeh, L. J. Greenstein, A. Kavcic, T. Sveinsson, and V. Tarokh, “An empirical indoor path loss model for ultra-wideband channels,” J. Commun. Network |

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(060.4510) Fiber optics and optical communications : Optical communications

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 22, 2010

Revised Manuscript: May 3, 2010

Manuscript Accepted: July 1, 2010

Published: July 23, 2010

**Citation**

Kemal Davaslıoğlu, Erman Çağıral, and Mutlu Koca, "Free space optical ultra-wideband communications over atmospheric turbulence channels," Opt. Express **18**, 16618-16627 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16618

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### References

- W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. 17(11), 2418–2420 (2005). [CrossRef]
- F. Zeng and J. Yao, “An approach to ultra-wideband pulse generation and distribution over optical fiber,” IEEE Photon. Technol. Lett. 18(7), 823–825 (2006). [CrossRef]
- M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. 26(15), 2594–2603 (2008). [CrossRef]
- F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]
- P. C. Peng, W. R. Peng, J. H. Lin, W. P. Lin, and S. Chi, “Generation of wavelength- tunable optical pulses using EDFA as external-injection light source and amplifier for Fabry-Pérot laser diode,” IEEE Photon. Technol. Lett. 16(11), 2553–2555 (2004). [CrossRef]
- X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]
- S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. 6(8), 2813–2819 (2007). [CrossRef]
- M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).
- S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).
- E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of free-space optical systems in Gamma-Gamma fading,” in Global Telecommunications Conference 2008. GLOBECOM `08 (IEEE, 2008), 1–6.
- The Wolfram Function Site, (2004), http://functions.wolfram.com/ .
- S. G. Wilson, M. B. Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Comm. 23(9), 1901–1910 (2005). [CrossRef]
- S. S. Ghassemzadeh, L. J. Greenstein, A. Kavcic, T. Sveinsson, and V. Tarokh, “An empirical indoor path loss model for ultra-wideband channels,” J. Commun. Network 5, 303–308 (2003).

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