## An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications |

Optics Express, Vol. 18, Issue 16, pp. 17346-17363 (2010)

http://dx.doi.org/10.1364/OE.18.017346

Acrobat PDF (2484 KB)

### Abstract

In free space optical (FSO) communication, atmospheric turbulence causes fluctuation in both intensity and phase of the received light signal what may seriously impair the link performance. Additionally, turbulent inhomogeneities may produce optical pulse spreading. In this paper, a simple rate adaptive transmission technique based on the use of variable silence periods and on-off keying (OOK) formats with memory is presented. This technique was previously proposed in indoor unguided optical links by the authors with very good performance. Such transmission scheme is now extensively analyzed in terms of burst error rate, and shown in this paper as an excellent alternative compared with the classical scheme based on repetition coding and pulse-position modulation (PPM), presenting a greater robustness to adverse conditions of turbulence.

© 2010 Optical Society of America

## 1. Introduction

1. J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. **44**, 46–51 (2006). [CrossRef]

## 2. Optical communication through turbulent atmosphere

*L*

_{0}, called the outer scale of turbulence, to a small scale size,

*l*

_{0}, denoted the inner scale of turbulence, the scale where the energy is dissipated into heat. It is assumed that each eddy is homogeneous, although with a different index of refraction. These atmospheric index-of-refraction variations produce fluctuations in the irradiance of the transmitted optical beam, what is known as

*atmospheric scintillation*. A widely used model with good accuracy to describe the spatial power spectrum of refractive index, Φ

_{n}(

*κ*) was proposed by Kolmogorov, which assumes the wavenumber spectrum to be:

*κ*is the spatial wave number and

*C*

^{2}

_{n}is the refractive-index structure parameter. Under the so-called Rytov approximation [14], the optical field,

*u*(

**r**), of an optical wave propagating at distance

*L*from the source can be expanded as [6

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

**r**is the observation point in the transverse plane at propagation distance

*L*,

*A*(

**r**,

*L*) is the amplitude of the electric vector of the optical wave and

*u*

_{0}(

**r**,

*L*) is the optical field amplitude without air turbulence expressed, from [6

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

*u*

_{0}(

**r**,

*L*) =

*A*

_{0}(

**r**,

*L*) · exp [

*jϕ*

_{0}(

**r**,

*L*)]. Finally, the exponent of the perturbation factor is:

*I*

_{0}= ∣

*A*

_{0}∣

^{2}is the level of irradiance fluctuation in the absence of air turbulence that ensures that the fading does not attenuate or amplify the average power, i.e.,

*E*[

*I*] = ∣

*A*

_{0}∣

^{2}. This may be thought of as a conservation of energy consideration and requires the choice of

*E*[

*χ*] =

*−σ*

^{2}

_{χ}, as was explained in [15, 16

16. D. L. Fried, “Aperture averaging of scintillation,” J. Opt. Soc. Am. **57**, 169–175 (1967). [CrossRef]

*E*[

*χ*] is the ensemble average of log-amplitude, whereas

*σ*

^{2}

_{χ}is its variance. ence, from the Jacobian statistical transformation, the probability density function of the intensity can be identified to have a log-normal distribution typical of weak turbulence regime [6

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

8. A. Jurado Navas, A. García Zambrana, and A. Puerta Notario, “Efficient lognormal channel model for turbulent FSO communications,” Electron. Lett. **43**, 178–179 (2007). [CrossRef]

*Y*(

*t*), can be written as

*Y*(

*t*) =

*α*(

_{sc}*t*)

*X*(

*t*) +

*N*(

*t*), with

*X*(

*t*) being the received optical power without scintillation, whereas

*α*(

_{sc}*t*) = exp[2

*χ*(

*t*)] is the temporal behavior of the scintillation sequence and represents the effect of the intensity fluctuations on the transmitted signal. To generate

*α*(

_{sc}*t*), a scheme based on a lowpass filtering of a random Gaussian signal is implemented as in [8

8. A. Jurado Navas, A. García Zambrana, and A. Puerta Notario, “Efficient lognormal channel model for turbulent FSO communications,” Electron. Lett. **43**, 178–179 (2007). [CrossRef]

*χ*(

*t*) is, as was explained above, the log-amplitude of the optical wave governed by Gaussian statistics. Finally, the additive white Gaussian noise,

*N*(

*t*), is assumed to include any front-end receiver thermal noise as well as shot noise caused by ambient light much stronger than the desired signal.

8. A. Jurado Navas, A. García Zambrana, and A. Puerta Notario, “Efficient lognormal channel model for turbulent FSO communications,” Electron. Lett. **43**, 178–179 (2007). [CrossRef]

*H*(

_{sc}*f*), we started with the covariance function for irradiance fluctuations,

*B*(

_{I}*r*), that for a plane wave and homogeneous and isotropic turbulence leads to [17

17. R. Lawrence and J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE **58**, 1523–1545 (1970). [CrossRef]

*k*is the wave number,

*L*is the propagation path length,

*κ*is the scalar spatial wave number, Φ

_{n}(

*κ*) is the spatial power spectrum of refractive index and

*J*

_{0}(·) is the Bessel function of the first kind and order zero. Based on the Kolmogorov spectrum given in Eq. (1) and after some mathematical manipulations indicated in [8

**43**, 178–179 (2007). [CrossRef]

*τ*

_{0}the turbulence correlation time, whereas

*u*

_{⊥}is the component of the wind velocity vector perpendicular to the propagation direction. Hence, the low-pass filter can be obtained from

**43**, 178–179 (2007). [CrossRef]

### 2.1. Propagation of Pulses Through Atmospheric Turbulence

18. Y. Ruike, H. Xiange, H. Yue, and S. Zhongyu, “Propagation Characteristics of Infrared Pulse Waves through Windblown Sand and Dust Atmosphere,” Int. J. Infrared Millim. Waves **28**, 181 (2007). [CrossRef]

19. C. H. Liu and K. C. Yeh, “Propagation of pulsed beam waves through turbulence, Cloud, Rain or Fog,” J. Opt. Soc. Am. **67**, 1261–1266 (1977). [CrossRef]

20. L. C. Lee, “Wave Propagation in a Random Medium: A Complete set of the moment equations with different wavenumbers,” J. Math. Phys. **15**, 1431–1435 (1974). [CrossRef]

21. C.Y. Young, A. Ishimaru, and L. C. Andrews, “Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution,” Appl. Opt. **35**, 6522–6526 (1996). [CrossRef] [PubMed]

22. I. Sreenivasiah and A. Ishimaru, “Beam wave two-frequency mutual coherence function and pulse propagation in random media: an analytic solution to the plane wave case,” Appl. Opt. **18**, 1613–1618 (1979). [CrossRef] [PubMed]

21. C.Y. Young, A. Ishimaru, and L. C. Andrews, “Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution,” Appl. Opt. **35**, 6522–6526 (1996). [CrossRef] [PubMed]

*T*

_{0}being the input pulse half-width at the 1/

*e*point [23

23. C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. **37**, 7655–7660 (1998). [CrossRef]

## 3. Rate-Adaptive Links Using Variable Silence Periods as a Promising Alternative

### 3.1. General Comments

**43**, 178–179 (2007). [CrossRef]

*u*

_{⊥}is taken to be 8 m/s, a typical magnitude, at least in southern Europe. This is the main reason to employ this concrete magnitude. On the other hand, the values of turbulence strength structure parameter,

*C*

^{2}

_{n}were set to 1.23 × 10

^{−14}and 1.23 × 10

^{−13}m

^{−2/3}for

*σ*

^{2}

_{χ}= 0.01 and 0.1, respectively and for plane waves; second, a three-pole Bessel high-pass filter with a −1 dB cut-off frequency of 500 kHz for natural (solar) light suppression; and last, a five-pole Bessel low-pass filter employed as a matched filter. The receivers employed here are point receivers whereas the weather-induced attenuation is neglected so that we concentrate our attention on turbulence effects. Furthermore, the atmospheric-induced beam spreading that causes a power reduction at the receiver is also neglected because we are considering a terrestrial link where beam divergence is typically on the order of 10

*µ*Rad.

**43**, 178–179 (2007). [CrossRef]

24. A. Christen, E. van Gorsel, and R. Vogt, “Coherent structures in urban roughness sublayer turbulence,” Int. J. Climatol. **27**, 1955–1968 (2007). [CrossRef]

9. A. Jurado-Navas and A. Puerta-Notario, “Generation of Correlated Scintillations on Atmospheric Optical Communications,” J. Opt. Commun. Netw **1**, 452–462 (2009). [CrossRef]

9. A. Jurado-Navas and A. Puerta-Notario, “Generation of Correlated Scintillations on Atmospheric Optical Communications,” J. Opt. Commun. Netw **1**, 452–462 (2009). [CrossRef]

*e*point [10

10. A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Numerical model for the temporal broadening of optical pulses propagating through weak atmospheric turbulence,” Opt. Lett. **34**, 3662–3664 (2009). [CrossRef] [PubMed]

23. C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. **37**, 7655–7660 (1998). [CrossRef]

*T*

_{2}≈

*T*

_{0}= 4.73 ns, being the broadening negligible, as we had anticipated above. To obtain an appreciable broadening on the order of 10% of

*T*

_{0}, we could use transmission rates up to 87.8 Gbps and 278 Gbps for

*C*

^{2}

_{n}= 1.23 × 10

^{−13}and 1.23 × 10

^{−14}m

^{−2/3}respectively with a 100% of duty-cycle (d.c.) and

*L*

_{0}= 30.34 m (this last value coincident with the height of our emplacement). These values let us utilize very high binary rates or ultrashort transmitted pulses and still neglecting the temporal broadening of the transmitted pulses. Thus, in this paper, we take advantage of this latter fact by adopting pulses with reduced duty cycle. As the criterion of limited average optical power is adopted, the signal amplitude can be increased as the duty cycle is decreased in order to maintain constant the average optical power, and then, the peak-to-average optical power ratio (PAOPR) can be higher. As shown through this section, a technique that increases the PAOPR parameter is preferred as it provides better performance in atmospheric optical links, overcoming the imposed distortion when a system bandwidth constraint is required. The obtained performance for all analyzed signaling techniques are in terms of burst error rate average. Hence, the impact of the atmospheric channel coherence on the behavior of the different signalling schemes can be taking into account, as was indicated in [8

**43**, 178–179 (2007). [CrossRef]

*L*= 5 as explained in [26]) any sequence of burst error.

_{b}### 3.2. Peak-to-average optical power ratio (PAOPR)

*x*(

*t*) the instantaneous optical power defined by

*a*is a random variable with values of 0 for the bit “0” (off pulse) and 1 for the bit “1” (on pulse),

_{k}*P*is the pulse peak power,

_{peak}*p*(

_{n}*t*) is the pulse shape with normalized peak power, and

*T*is the bit period. Then, the average transmitted optical power can be expressed as

_{b}*P*=

*P*·

_{peak}*P*·

_{n}*pr*(

*a*= 1), where

_{k}*P*is the optical power averaged over

_{n}*T*given by

_{b}*P*, depending on the adopted pulse shape, to improve the PAOPR while maintaining the average transmitted optical power at a constant level. Hereafter, to compare the different pulses performance, we define the increase factor in PAOPR as follows:

_{n}_{ref}is the PAOPR obtained with non-return to zero (NRZ) signaling and rectangular pulse shape, i.e.

*P*= 1. Note that Γ

_{nref}_{PAOPR}only depends on the pulse shape characteristics.

_{PAOPR}for a rectangular pulse with a duty cycle of

*ξ*, where 0 <

*ξ*≤ 1. In this case, from Eq. (12), it is easily derived that

*t*

_{0}=

*ξT*/2 is given by

_{b}*σ*=

_{p}*ξ · σ*

_{0}depends on the duty cycle,

*ξ*, and on

*σ*

_{0}=

*T*/

_{b}*n*, which characterizes the pulse width in relation to the bit period. In particular,

*n*defines the amount of optical energy contained within

*T*, so that for

_{b}*n*≥ 6 at least the 99.8% of the transmitted energy is within

*T*. In our analysis, we assume

_{b}*n*= 6 and, thus, from Eq. (12) and Eq. (14), the Γ

_{PAOPR}for the Gaussian pulse is given by

*P*transmitted more than compensates for the higher distortion induced on Gaussian pulse by a limited channel bandwidth.

_{peak}*ξ*, and, as expected, the Γ

_{PAOPR}offered by the Gaussian pulse is substantially higher than the one obtained by the rectangular pulse shape.

*σ*

^{2}

_{χ}= 0.1 and 0.01. In addition, a classic signalling technique based on variable-rate repetition coding is implemented, where

*RR*is the rate reduction factor. As we can observe, Gaussian pulse shapes obtain better performance than rectangular pulse shapes (for a same duty cycle and a same rate reduction factor). Moreover, when the duty cycle decreases a better performance is achieved, obtaining that an OOK-GS format and a 25%-duty cycle achieves a remarkable better performance than an identical OOK-GS format but with a higher duty cycle. In addition, a Gaussian pulse shape presents better performance than another one with a NRZ format. These two aspects confirms that an increase in the PAOPR parameter provides better performance in the atmospheric optical link as it is depicted in Fig. 1.

**43**, 178–179 (2007). [CrossRef]

9. A. Jurado-Navas and A. Puerta-Notario, “Generation of Correlated Scintillations on Atmospheric Optical Communications,” J. Opt. Commun. Netw **1**, 452–462 (2009). [CrossRef]

_{n}(

*κ*). It should be further noted that our Gaussian channel approach works perfectly not only for OOK-GS format but also for all the remaining cases in this paper so results obtained from the use of the more precise expression in Eq. (5) are omitted here for the sake of brevity.

*σ*

^{2}

_{χ}=0.1 and 0.01. Then, an OOK-GS format and a 25%-duty cycle already achieves similar performance than the 4PPM scheme, but with a lower complexity. Again, a classic signalling technique based on variable-rate repetition coding is implemented. The fact that broadening distortion does not affect to transmitted pulses until very reduced widths, and the better performance obtained in Fig. 2 for schemes with a reduced duty cycle are an interesting starting point to apply our rate-adaptive transmission technique as we explain below.

### 3.3. Rate Adaptive Links Using Variable Silence Periods

*RR*− 1 silence bit periods after an information bit so as to obtain an effective code rate with a rate reduction factor of

_{s}*RR*depending on the channel conditions. The average optical power is always maintained at a same constant level. So, in this scenario,

_{s}_{PAOPR}for the Gaussian pulse is now given by

*RR*we need to provide a significant improvement in terms of burst error rate. Thus, the increase in the PAOPR parameter is then used being the average optical power maintained at a constant level, and for a same system bandwidth constraint.

_{s}*σ*

^{2}

_{χ}= 0.1 and

*σ*

^{2}

_{χ}= 0.01. In such figure, all results are obtained for OOK-GS formats and a 25%-duty cycle. From Fig. 3, a remarkable improvement in performance can be noted when the rate adaptive technique based on inserting variable silence periods is adopted in relation to the classic variable-rate repetition coding, because there is no alteration in the statistics of occurrence of the transmitted pulses in this latter option and, consequently, Γ

_{PAOPR}is not increased. This superiority is even more relevant when the rate reduction factor is increased, showing a greater robustness to the more severe atmospheric turbulence conditions. For instance, the technique based on variable silence periods can achieve an improvement in average optical power requirements above 1 and 2 optical dB at a burst error rate of 10

^{−6}for a rate reduction of 2 and 4 respectively and

*σ*

^{2}

_{χ}= 0.1 in regard to classic variable-rate repetition coding.

### 3.4. Rate Adaptive Links Using Variable Silence Periods and Memory

*RR*represents the initial bit rate of the system,

_{b}*RR*is the rate reduction factor inherent to the OOK-GSc scheme,

_{c}*RR*is the rate reduction factor introduced by inserting

_{s}*RR*− 1 silence bit periods after an information bit, as explained above, and

_{s}*RR*=

*RR*·

_{c}*RR*is the total effective rate reduction factor of the system.

_{s}*RR*=2. Then, and when

_{c}*RR*=1,

_{s}_{PAOPR}for a Gaussian pulse shape is now given by

*RR*= 4. Hence,

_{c}*RR*= 1, so from Eq.(12) and Eq.(14), the Γ

_{s}_{PAOPR}for a Gaussian pulse is now given by

*RR*represents the initial bit rate of the system,

_{b}*RR*= 4 is the rate reduction factor inherent to the OOK-GScc scheme,

_{c}*RR*is the rate reduction factor introduced by inserting

_{s}*RR*− 1 silence bit periods after an information bit and

_{s}*RR*=

*RR*·

_{c}*RR*is the total effective rate reduction factor.

_{s}*σ*

^{2}

_{χ}= 0.1 and

*σ*

^{2}

_{χ}= 0.01. As it is shown, a remarkable improvement in performance can be observed when OOK-GS format with memory is adopted if compared with the OOK format without memory, where excellent agreement can be noted by using different rate reductions. Nevertheless, OOK-GSc and OOK-GScc formats present a very similar behavior in terms of burst error rate for an identical rate reduction factor. This fact may not comply with the Γ

_{PAOPR}heuristic law in the sense that the higher magnitude in Γ

_{PAOPR}we have the better performance we should expect from a signalling technique. However, the answer to this apparent incongruence raises from the definition adopted in this paper for a burst error in addition to the particular distribution of error bits in the different signalling techniques with memory analyzed in this paper in conjunction with the Viterbi algorithm employed in reception. In this sense, Fig. 6 shows the number of occurrences for different sets of consecutive correctly received bits for both the OOK-GSc scheme with a rate reduction factor of

*RR*=4 (where

*RR*=

*RR*·

_{c}*RR*, with

_{s}*RR*=2 and

_{c}*RR*=2); and the OOK-GScc format with its inherent rate reduction factor of 4, for different values of additive white Gaussian noise power.We can check that the occurrence of sequences consisting of an association of ten or more consecutive correct bits is higher when using an OOK-GScc scheme than employing an OOK-Gsc format. This fact is effectively confirmed when we change the definition of a burst error. Now, if any burst error can contain until 9 consecutive correct bits (

_{s}*L*= 10 as explained in [26]), then we can obtain the expected results in terms of burst error rate, as displayed in Fig. 7, where the superiority of OOK-GScc format versus OOK-GSc one is again established, as expected from the heuristic analysis of the Γ

_{b}_{PAOPR}parameter.

^{−6}for a rate reduction of 4 and 8 and

*σ*

^{2}

_{χ}=0.1, OOK-GScc obtains an improvement in average optical power requirements above 1.2 and 1.4 optical dB respectively with respect to OOK-GSc format.

27. A. García-Zambrana and A. Puerta-Notario, “Improving PPM schemes in wireless infrared links at high bit rates,” IEEE Commun. Lett. **5**, 95–97 (2001). [CrossRef]

*L*= 5). In this respect, the same conclusion that was obtained before for the OOK scheme is deduced now for the 4GPPM format: hence, when a Gaussian pulse shape is employed instead of a rectangular pulse for all values of

_{b}*RR*, then an improvement in performance is obtained, confirming that an increase in the PAOPR parameter provides better performance and a great robustness in the atmospheric optical link for a same system bandwidth constraint. The validity of this conclusion is extended not only for a ML detection procedure but also for a threshold (TD) detector, although with an important degradation in performance as a direct consequence of a more rudimentary detection algorithm. All in all, as was shown in Fig. 9, the inclusion of memory with OOK-GS formats provides a very attractive improvement in performance being, furthermore, the studied scheme with a higher PAOPR. Hence, this latter ratio can be used as a reliable figure of merit in IM/DD atmospheric optical links, where an increase in such ratio involves an increase in performance, as was effectively demonstrated through this paper.

## 4. Concluding Remarks

*pN*(

*t*), with a reduced duty cycle,

*ξ*, is presented in Fig. 10, showing that the solitonic pulse shape is narrower than rectangular and Gaussian pulses, so that we can increase the peak optical power to a higher lever maintaining the average optical power at the same constant level for all the pulse shapes under study. Then, as concluded in this paper, an increase in the peak-to-average optical power ratio involves higher performance. In this case, the higher pulse peak power transmitted,

*P*, compensates for the higher distortion induced on solitonic pulse by the system limited bandwidth, so a better performance is obtained when increasing the PAOPR parameter. In addition, we are currently researching about mode locking solitons [29

_{peak}29. T. Brabec, Ch. Spielmann, and E Krausz, “Mode locking in solitary lasers,” Opt. Lett. **16**, 1961–1963 (1991). [CrossRef] [PubMed]

30. F. X. Kärtner, D. Kopf, and U. Keller, “Solitary-pulse stabilization and shortening in actively mode-locked lasers,” J. Opt. Soc. Am. B **12**, 486–496 (1995). [CrossRef]

## Appendix I

*τ*= 0,

*B*(0) =

_{I}*σ*

^{2}

_{1}and

32. D. L. Fried and J. D. Cloud, “Propagation of an infinite plane wave in a randomly inhomogeneous medium,” J. Opt. Soc. Am. **56**, 1667–1676 (1966). [CrossRef]

*τ*= 0, the temporal covariance function written in Eq. (21) reduces to

*B*(0) = 1.23

_{I}*C*

^{2}

_{n}

*L*

^{11/6}

*k*

^{7/6}=

*σ*

_{2}

_{1}, i.e., the scintillation index. To obtain

*a*)

_{k}the Pochhammer symbol. Thus, to obtain

*k*=1 in Eq. (25). If

*r*=

*u*

_{⊥}

*τ*, and applying the chain rule that in the Leibniz notation is stated in the form

## Acknowledgment

## References and links

1. | J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. |

2. | A. Belmonte and J. M. Kahn, “Efficiency of complex modulation methods in coherent free-space optical links,” Opt. Express |

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5. | P. W. Nugent, J. A. Shaw, and S. Piazzolla, “Infrared cloud imaging in support of Earth-space optical communication,” Opt. Express |

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

7. | M. Al Naboulsi and H. Sizun, “Fog attenuation prediction for optical and infrared waves,” SPIE Optical Engineering |

8. | A. Jurado Navas, A. García Zambrana, and A. Puerta Notario, “Efficient lognormal channel model for turbulent FSO communications,” Electron. Lett. |

9. | A. Jurado-Navas and A. Puerta-Notario, “Generation of Correlated Scintillations on Atmospheric Optical Communications,” J. Opt. Commun. Netw |

10. | A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Numerical model for the temporal broadening of optical pulses propagating through weak atmospheric turbulence,” Opt. Lett. |

11. | A. García-Zambrana and A. Puerta-Notario, “Novel approach for increasing the peak-to-average optical power ratio in rate-adaptive optical wireless communication systems,” IEE Proc. Optoelectron.: Special Issue on Optical Wireless Communications |

12. | L. C. Andrews and R. L. Phillips, |

13. | A. Ishimaru, |

14. | V. I. Tatarskii, |

15. | J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in |

16. | D. L. Fried, “Aperture averaging of scintillation,” J. Opt. Soc. Am. |

17. | R. Lawrence and J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE |

18. | Y. Ruike, H. Xiange, H. Yue, and S. Zhongyu, “Propagation Characteristics of Infrared Pulse Waves through Windblown Sand and Dust Atmosphere,” Int. J. Infrared Millim. Waves |

19. | C. H. Liu and K. C. Yeh, “Propagation of pulsed beam waves through turbulence, Cloud, Rain or Fog,” J. Opt. Soc. Am. |

20. | L. C. Lee, “Wave Propagation in a Random Medium: A Complete set of the moment equations with different wavenumbers,” J. Math. Phys. |

21. | C.Y. Young, A. Ishimaru, and L. C. Andrews, “Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution,” Appl. Opt. |

22. | I. Sreenivasiah and A. Ishimaru, “Beam wave two-frequency mutual coherence function and pulse propagation in random media: an analytic solution to the plane wave case,” Appl. Opt. |

23. | C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt. |

24. | A. Christen, E. van Gorsel, and R. Vogt, “Coherent structures in urban roughness sublayer turbulence,” Int. J. Climatol. |

25. | A. Christen, M. W. Rotach, and R. Vogt, “Experimental determination of the turbulent kinetic energy budget within and above an Urban Canopy,” Fifth AMS Symposium on the Urban Environment, Vancouver (Canada), 23–27Aug. 2004. |

26. | L. Deutsch and R. Miller, “Burst statistics of Viterbi decoding,” The Telec. and Data Acquisition Progress Report, TDA PR 42–64, 187–193 (1981). |

27. | A. García-Zambrana and A. Puerta-Notario, “Improving PPM schemes in wireless infrared links at high bit rates,” IEEE Commun. Lett. |

28. | J. M. Garrido-Balsells, A. Jurado-Navas, M. Castillo-Vázquez, A. B. Moreno-Garrido, and A. Puerta-Notario, are preparing a manuscript to be called “Improving optical wireless links performance by solitonic shape pulses.” |

29. | T. Brabec, Ch. Spielmann, and E Krausz, “Mode locking in solitary lasers,” Opt. Lett. |

30. | F. X. Kärtner, D. Kopf, and U. Keller, “Solitary-pulse stabilization and shortening in actively mode-locked lasers,” J. Opt. Soc. Am. B |

31. | Q. Yao and M. Patzold, “Spatial-temporal characteristics of a half-spheroid model and its corresponding simulation model,” IEEE 59th Vehicular Technology Conference, VTC 2004-Spring , |

32. | D. L. Fried and J. D. Cloud, “Propagation of an infinite plane wave in a randomly inhomogeneous medium,” J. Opt. Soc. Am. |

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(070.4560) Fourier optics and signal processing : Data processing by optical means

(200.1130) Optics in computing : Algebraic optical processing

(290.5930) Scattering : Scintillation

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

(200.2605) Optics in computing : Free-space optical communication

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 4, 2010

Revised Manuscript: June 16, 2010

Manuscript Accepted: July 1, 2010

Published: July 30, 2010

**Citation**

Antonio Jurado-Navas, José María Garrido-Balsells, Miguel Castillo-Vázquez, and Antonio Puerta-Notario, "An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications," Opt. Express **18**, 17346-17363 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17346

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