## Rate-adaptive FSO links over atmospheric turbulence channels by jointly using repetition coding and silence periods |

Optics Express, Vol. 18, Issue 24, pp. 25422-25440 (2010)

http://dx.doi.org/10.1364/OE.18.025422

Acrobat PDF (1388 KB)

### Abstract

In this paper, a new and simple rate-adaptive transmission scheme for free-space optical (FSO) communication systems with intensity modulation and direct detection (IM/DD) over atmospheric turbulence channels is analyzed. This scheme is based on the joint use of repetition coding and variable silence periods, exploiting the potential time-diversity order (TDO) available in the turbulent channel as well as allowing the increase of the peak-to-average optical power ratio (PAOPR). Here, repetition coding is firstly used in order to accomodate the transmission rate to the channel conditions until the whole time diversity order available in the turbulent channel by interleaving is exploited. Then, once no more diversity gain is available, the rate reduction can be increased by using variable silence periods in order to increase the PAOPR. Novel closed-form expressions for the average bit-error rate (BER) as well as their corresponding asymptotic expressions are presented when the irradiance of the transmitted optical beam follows negative exponential and gamma-gamma distributions, covering a wide range of atmospheric turbulence conditions. Obtained results show a diversity order as in the corresponding rate-adaptive transmission scheme only based on repetition codes but providing a relevant improvement in coding gain. Simulation results are further demonstrated to confirm the analytical results. Here, not only rectangular pulses are considered but also OOK formats with any pulse shape, corroborating the advantage of using pulses with high PAOPR, such as Gaussian or squared hyperbolic secant pulses. We also determine the achievable information rate for the rate-adaptive transmission schemes here analized.

© 2010 Optical Society of America

## 1. Introduction

1. J. M. Kahn and J. R. Barry, “Wireless Infrared Communications,” Proc. IEEE **85**, 265–298 (1997). [CrossRef]

*“last mile” problem*, as well as a supplement to radio-frequency (RF) links [2

2. L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid Optical RF Airborne Communications,” Proc. IEEE **97**(6), 1109–1127 (2009). [CrossRef]

3. W. Lim, C. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under Gamma-Gamma turbulence channels,” Opt. Express **17**(6), 4479–4484 (2009). [CrossRef] [PubMed]

*atmospheric scintillation*, severely degrading the link performance [4

4. L. Andrews, R. Phillips, and C. Hopen, *Laser Beam Scintillation with Applications* (Bellingham, WA: SPIE Press, 2001). [CrossRef]

5. X. Zhu and J. M. Kahn, “Free-Space Optical Communication through Atmospheric Turbulence Channels,” IEEE Trans. Commun. **50**(8), 1293–1300 (2002). [CrossRef]

6. J. Anguita, I. Djordjevic, M. Neifeld, and B. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. **4**(9), 586–601 (2005). [CrossRef]

10. F. Xu, A. Khalighi, P. Caussé, and S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express **17**(2), 872–887 (2009). [CrossRef] [PubMed]

11. S. G. Wilson, M. Brandt-Pearce, Q. Cao, I. Leveque, and J. H., “Free-Space Optical MIMO Transmission With *Q*-ary PPM,” IEEE Trans. Commun. **53**(8), 1402–1412 (2005). [CrossRef]

13. T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. **8**(2), 951–957 (2009). [CrossRef]

14. M. Simon and V. Vilnrotter, “Alamouti-Type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. **4**(1), 35–39 (2005). [CrossRef]

16. C. Abou-Rjeily, “Orthogonal Space-Time Block Codes for Binary Pulse Position Modulation,” IEEE Trans. Commun. **57**(3), 602–605 (2009). [CrossRef]

17. E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. **58**(1), 58–62 (2010). [CrossRef]

18. A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection Transmit Diversity for FSO Links Over Strong Atmospheric Turbulence Channels,” IEEE Photon. Technol. Lett. **21**(14), 1017–1019 (2009). [CrossRef]

19. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express **18**(6), 5356–5366 (2010). [CrossRef] [PubMed]

23. N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Optical Wireless Communications with Adaptive Subcarrier PSK Intensity Modulation,” (2010). Accepted for publication in IEEE Global Telecommunications Conference (GLOBECOM ’10), URL http://users.auth.gr/nestoras.

21. I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express **17**(20), 18,250–18,262 (2009). [CrossRef]

22. I. B. Djordjevic, “Adaptive Modulation and Coding for Free-Space Optical Channels,” IEEE/OSA Journal of Optical Communications and Networking **2**(5), 221–229 (2010). [CrossRef]

23. N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Optical Wireless Communications with Adaptive Subcarrier PSK Intensity Modulation,” (2010). Accepted for publication in IEEE Global Telecommunications Conference (GLOBECOM ’10), URL http://users.auth.gr/nestoras.

24. A. A. Ali and I. A. Al-Kadi, “On the use of repetition coding with binary digital modulations on mobile channels,” IEEE Trans. Veh. Technol. **38**(1), 14–18 (1989). [CrossRef]

25. S. Trisno, I. I. Smolyaninov, S. D. Milner, and C. C. Davis, “Delayed diversity for fade resistance in optical wireless communication system through simulated turbulence,” in Proc. SPIE , pp. 385–394 (2004). [CrossRef]

27. C. H. Kwok, R. V. Penty, and I. H. White, “Link Reliability Improvement for Optical Wireless Communication Systems with Temporal-Domain Diversity Reception,” IEEE Photon. Technol. Lett. **20**(9), 700–702 (2008). [CrossRef]

15. A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett. **11**(5), 390–392 (2007). [CrossRef]

18. A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection Transmit Diversity for FSO Links Over Strong Atmospheric Turbulence Channels,” IEEE Photon. Technol. Lett. **21**(14), 1017–1019 (2009). [CrossRef]

19. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express **18**(6), 5356–5366 (2010). [CrossRef] [PubMed]

## 2. Atmospheric turbulence channel model

4. L. Andrews, R. Phillips, and C. Hopen, *Laser Beam Scintillation with Applications* (Bellingham, WA: SPIE Press, 2001). [CrossRef]

15. A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett. **11**(5), 390–392 (2007). [CrossRef]

*E*[

*I*] = 1 and the second moment is given by

*E*[

*I*

^{2}] = 2, the scintillation index is

*SI*=

*E*[

*I*

^{2}]/(

*E*[

*I*])

^{2}– 1 = 1. This distribution can be seen as the gamma-gamma distributed turbulence model in Eq. (2) when the channel parameters are

*β*= 1 and

*α*→ ∞. From the point of view of scintillation index, it is easy to deduce the fact that the strength of atmospheric fading represented by the gamma-gamma distributed turbulence model with channel parameters

*β*= 1 and increasing

*α*tends to be closer and closer to that corresponding to the negative exponential distributed turbulence model.

15. A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett. **11**(5), 390–392 (2007). [CrossRef]

18. A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection Transmit Diversity for FSO Links Over Strong Atmospheric Turbulence Channels,” IEEE Photon. Technol. Lett. **21**(14), 1017–1019 (2009). [CrossRef]

*L*, or both, pulse shape distortion is assumed to be negligible for the typical FSO scenario here analyzed [32

32. R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE **63**(12), 1669–1692 (1975). [CrossRef]

33. 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**(33), 7655–7660 (1998). [CrossRef]

*ϕ*(

*t*) is defined as

*g*(

*t*) represents any normalized pulse shape satisfying the non-negativity constraint, with 0 ≤

*g*(

*t*) ≤ 1 in the bit period and 0 otherwise, and

*G*(

*f*= 0) represents the Fourier transform of

*g*(

*t*) evaluated at frequency

*f*= 0, i.e. the area of the employed pulse shape, and

*T*parameter is the bit period. The random variable (RV)

_{b}*a*follows a Bernoulli distribution with parameter

_{k}*p*= 1/2, taking the values of 0 for the bit “0” (off pulse) and 1 for the bit “1” (on pulse). From this expression, it is easy to deduce that the average optical power transmitted is

*P*, defining a constellation of two equiprobable points in a one-dimensional space with an Euclidean distance of

*ξ*=

*T*/

_{b}E_{g}*G*

^{2}(

*f*= 0) represents the square of the increment in Euclidean distance due to the use of a pulse shape of high PAOPR, alternative to the classical rectangular pulse.

6. J. Anguita, I. Djordjevic, M. Neifeld, and B. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. **4**(9), 586–601 (2005). [CrossRef]

7. M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. **5**(6), 1229–1233 (2006). [CrossRef]

34. H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average Capacity of Optical Wireless Communication Systems Over Atmospheric Turbulence Channels,” IEEE/OSA Journal of Lightwave Technology **27**(8), 974–979 (2009). [CrossRef]

10. F. Xu, A. Khalighi, P. Caussé, and S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express **17**(2), 872–887 (2009). [CrossRef] [PubMed]

*i*

_{1}and

*i*

_{2}per frame, perfect interleaving can be done by simply sending the same information delayed by the expected fade duration, as shown experimentally in [27

27. C. H. Kwok, R. V. Penty, and I. H. White, “Link Reliability Improvement for Optical Wireless Communication Systems with Temporal-Domain Diversity Reception,” IEEE Photon. Technol. Lett. **20**(9), 700–702 (2008). [CrossRef]

## 3. Proposed rate-adaptive transmission scheme

*R*= 1/

_{b}*T*, for a rate reduction (

_{b}*RR*) parameter as

*R*/

_{b}*RR*in order to satisfy a predefined BER requirement. In this section, we firstly explain the case corresponding to the rate-adaptive transmission only based on variable silence periods; secondly, we present the case corresponding to the rate-adaptive transmission only based on repetition coding and, finally, we consider the adaptive transmission scheme here proposed and based on the joint use of repetition coding and variable silence periods, exploiting the potential time-diversity order available in the turbulent channel as well as allowing the increase of the PAOPR, which has shown to be a favorable characteristic in IM/DD links.

35. A. García-Zambrana and A. Puerta-Notario, “Large change rate-adaptive indoor wireless infrared links using variable silence periods,” IEE Electronics Letters **37**(8), 524–525 (2001). [CrossRef]

36. A. García-Zambrana and A. Puerta-Notario, “RZ-Gaussian pulses reduce the receiver complexity in wireless infrared links at high bit rates,” IEE Electronics Letters **35**(13), 1059–1061 (1999). [CrossRef]

**11**(5), 390–392 (2007). [CrossRef]

**21**(14), 1017–1019 (2009). [CrossRef]

19. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express **18**(6), 5356–5366 (2010). [CrossRef] [PubMed]

37. A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications,” Opt. Express **18**(**16**), 17,346–17,363 (2010). [CrossRef]

38. A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient lognormal channel model for turbulent FSO communications,” IEE Electronics Letters **43**(3), 178–179 (2007). [CrossRef]

*RR*– 1 is the number of silence bit periods added in order to accomodate the transmission rate to the channel conditions, so that the higher rate reduction (

_{s}*RR*=

*RR*), the larger silence time. From this expression, it is easy to deduce that an increase of the PAOPR is required in order to maintain the average optical power at the same constant level of

_{s}*P*.

*RR*=

*RR*·

_{rc}*RR*. In this adaptive transmission technique, repetition coding is firstly used in order to accomodate the transmission rate to the channel conditions until the whole time diversity order available in the turbulent channel by interleaving is exploited, i.e.

_{s}*RR*≤ TDO and

_{rc}*RR*= 1. Then, once no more diversity gain is available, the rate reduction can be increased by using variable silence periods in order to increase the PAOPR, i.e.

_{s}*RR*= TDO and

_{rc}*RR*> 1. For the sake of simplicity, we here consider values multiples of 2 for

_{s}*RR*when rate reduction is applied, i.e

*RR*= {1,2,4,8, ···} as well as for the time-diversity order effective TDO which is provided by interleaving, i.e. TDO = {1,2,4}, in this fashion, allowing to satisfy different latency requirements in the system [10

10. F. Xu, A. Khalighi, P. Caussé, and S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express **17**(2), 872–887 (2009). [CrossRef] [PubMed]

## 4. BER performance analysis

### 4.2. Exponential atmospheric turbulence channel

4. L. Andrews, R. Phillips, and C. Hopen, *Laser Beam Scintillation with Applications* (Bellingham, WA: SPIE Press, 2001). [CrossRef]

**11**(5), 390–392 (2007). [CrossRef]

*μ*= 1 and

*λ*= 1 [42], i.e.

*I ∼ G*(

*μ*= 1,

*λ*= 1), the sum of Ω

*i.i.d. RVs represented by*

_{d}*μ*= Ω

*and*

_{d}*λ*= 1, i.e.

*I*∼

_{T}*G*(

*μ*= Ω

*,*

_{d}*λ*= 1) as

41. Wolfram Research Inc., “The Wolfram functions site,” URL http://functions.wolfram.com.

_{2}

*F*

_{2}(

*a*

_{1},

*a*

_{2};

*b*

_{1},

*b*

_{2};

*z*) is a generalized hypergeometric function [31, Eq. (9.14.1)]. The results corresponding to this FSO scenario are illustrated in Fig. 2, where rectangular pulse shapes with

*ξ*= 1 are used for values of TDO = {1, 2, 4} and rate reductions of

*RR*= {1,2, 4, 8}. BER simulation results are furthermore included as a reference. Due to the long simulation time involved, simulation results only up to BER=10

^{−6}are included. Simulation results demonstrate an excellent agreement with the analytical results in Eq. (24) for the different rate-adaptive transmission schemes here analyzed. As in previous subsection, with the purpose of analyzing the diversity order achieved for the rate-adaptive here proposed, making use in Eq. (24) of the fact that the series expansion corresponding to a generalized hypergeometric function can be simplified by

_{2}

*F*

_{2}(

*a*

_{1},

*a*

_{2};

*b*

_{1},

*b*

_{2};

*z*) ∝ 1+

*O*(

*z*), the asymptotic BER can be expressed after some algebraic manipulations as Results corresponding to this asymptotic analysis are also illustrated in the Fig. 2 for different cases: no rate reduction {

*RR*= 1}, scheme Sil-{

*RR*= 2}, scheme Rep-{

*RR*= 4, TDO = 2} and, finally, scheme Rep&Sil-{

*RR*= 8, TDO = 4}. In this way, it is straightforward to show that the average BER behaves asymptotically as

*G*and

_{d}*G*denote diversity order and coding gain, respectively, corroborating a diversity gain of Ω

_{c}*in relation to the absence of rate reduction or rate-adaptive transmission only based on variable silence periods, wherein the average BER varies as*

_{d}14. M. Simon and V. Vilnrotter, “Alamouti-Type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. **4**(1), 35–39 (2005). [CrossRef]

**11**(5), 390–392 (2007). [CrossRef]

*κ*= 1 and rate reductions of

*RR*= {1, 2, 4, 8}, when different levels of turbulence strength of (

*α,β*) = (4, 1), (

*α,β*) = (10, 1) and (

*α,β*) = (20, 1) are assumed, corresponding to values of scintillation index of

*SI*= 1.5,

*SI*= 1.2 and

*SI*= 1.1, respectively, are displayed in Fig. 3(b) together with the corresponding analytical results in Eq. (24). As previously commented in section 2, it can be deduced from this figure that the BER performance corresponding to the FSO scenario where the strength of atmospheric fading is represented by the gamma-gamma distributed turbulence model with channel parameters

*β*= 1 and increasing

*α*tends to be closer and closer to that corresponding to the negative exponential distributed turbulence model.

## 5. Achievable information rate performance analysis

*R*= 1/

_{b}*T*, for a

_{b}*RR*parameter as

*R*/

_{b}*RR*in order to achieve a target BER requirement

*P*, the achievable information rate,

_{b}*R*, in bits/channel use, can be defined as

*R*= 1/

*RR*. While the required value of

*RR*to satisfy a target BER requirement can be numerically solved from analytical results in Eqs. (20) or (24), we can significantly simplify this analysis when target BER requirements and levels of turbulence imply a sufficiently tight performance for the corresponding asymptotic BER in Eqs. (21) or (25). From results displayed in Fig. 1 and Fig. 2, it can be deduced that the asymptotic BER expressions are closer and closer upper bounds for the BER performance as the level of turbulence is increased. This is an expected conclusion since a greater value of average SNR is required to satisfy the same predefined target BER requirement. In this sense, particularizing with the negative exponential distributed turbulence model and making use of the asymptotic BER in Eq. (25), the achievable information rate can be written as

*Y*by

*Y*/

*σ*and now considering

*X*∈ {0,1}. In this way, our channel model can be rewritten as where

*I*(

*X*;

*Y*|

*i*) for this channel is derived as in [43

43. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “On the Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels Using OOK Signaling,” EURASIP Journal on Wireless Communications and Networking **2010**. Article ID 127657, 9 pages, 2010. [CrossRef] .

45. A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express **18**(**19**), 20,445–20,454 (2010). [CrossRef]

*P*(

_{X}*x*= 0) =

*P*(

_{X}*x*= 1) = 1/2,

*C*(

*γ*), can be numerically obtained by averaging (30) over the PDF in (6) as follows This expression is computed using a symbolic mathematics package [46]. Figure 4 depict the mutual information in (31) for the exponential atmospheric turbulent optical channel together with the results corresponding to the achievable information rate in (26), (27) and (28) corresponding to the rate-adaptive transmission schemes Sil, Rep and Rep&Sil, respectively, for two different target BER requirements,

*P*= 10

_{b}^{−4}and

*P*= 10

_{b}^{−8}, and TDO={2, 4}. It can be noted that obtained results corroborate previous results presented in terms of BER performance in Fig. 2. For example, it can be observed that the required value of SNR to satisfy a target BER requirement of

*P*= 10

_{b}^{−8}is about 30 dB when using the rate-adaptive transmission scheme Rep&Sil with RR=8 and TDO=4; while, however, this value is about 70 dB when the rate-adaptive transmission scheme Rep with RR=4 and TDO=2 is assumed. These values can be contrasted in Fig. 4(b) from the point of achievable information rate, where capacity values of 1/8 bits/channel use and 1/4 bits/channel use are achieved, respectively.

27. C. H. Kwok, R. V. Penty, and I. H. White, “Link Reliability Improvement for Optical Wireless Communication Systems with Temporal-Domain Diversity Reception,” IEEE Photon. Technol. Lett. **20**(9), 700–702 (2008). [CrossRef]

21. I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express **17**(20), 18,250–18,262 (2009). [CrossRef]

23. N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Optical Wireless Communications with Adaptive Subcarrier PSK Intensity Modulation,” (2010). Accepted for publication in IEEE Global Telecommunications Conference (GLOBECOM ’10), URL http://users.auth.gr/nestoras.

## 6. Conclusions

**11**(5), 390–392 (2007). [CrossRef]

**21**(14), 1017–1019 (2009). [CrossRef]

**18**(6), 5356–5366 (2010). [CrossRef] [PubMed]

37. A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications,” Opt. Express **18**(**16**), 17,346–17,363 (2010). [CrossRef]

21. I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express **17**(20), 18,250–18,262 (2009). [CrossRef]

22. I. B. Djordjevic, “Adaptive Modulation and Coding for Free-Space Optical Channels,” IEEE/OSA Journal of Optical Communications and Networking **2**(5), 221–229 (2010). [CrossRef]

*P*= 10

_{b}^{−8}requires a considerably high value of SNR about 150 dB which can be remarkably reduced to a value of SNR about 74 dB at the expense of a reduction of capacity of 0.5 bits/channel use or a value of SNR about 68 dB at the expense of a lower capacity of 0.25 bits/channel use for a TDO=2. In this way, when a value of TDO=4 is available, this target BER requirement of

*P*= 10

_{b}^{−8}can be satisfied with a value of SNR about 37 dB at this same capacity value of 0.25 bits/channel use.

47. A. Garcia-Zambrana and A. Puerta-Notario, “Novel approach for increasing the peak-to-average optical power ratio in rate-adaptive optical wireless communication systems,” IEE Proceedings -Optoelectronics **150**(5), 439–444 (2003). [CrossRef]

37. A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications,” Opt. Express **18**(**16**), 17,346–17,363 (2010). [CrossRef]

35. A. García-Zambrana and A. Puerta-Notario, “Large change rate-adaptive indoor wireless infrared links using variable silence periods,” IEE Electronics Letters **37**(8), 524–525 (2001). [CrossRef]

## Acknowledgments

## References and links

1. | J. M. Kahn and J. R. Barry, “Wireless Infrared Communications,” Proc. IEEE |

2. | L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid Optical RF Airborne Communications,” Proc. IEEE |

3. | W. Lim, C. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under Gamma-Gamma turbulence channels,” Opt. Express |

4. | L. Andrews, R. Phillips, and C. Hopen, |

5. | X. Zhu and J. M. Kahn, “Free-Space Optical Communication through Atmospheric Turbulence Channels,” IEEE Trans. Commun. |

6. | J. Anguita, I. Djordjevic, M. Neifeld, and B. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. |

7. | M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. |

8. | I. B. Djordjevic, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel using Q-ary pulse-position modulation,” Opt. Express |

9. | I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-Coded MIMO Optical Communication Over the Atmospheric Turbulence Channel,” IEEE/OSA Journal of Lightwave Technology |

10. | F. Xu, A. Khalighi, P. Caussé, and S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express |

11. | S. G. Wilson, M. Brandt-Pearce, Q. Cao, I. Leveque, and J. H., “Free-Space Optical MIMO Transmission With |

12. | S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER Performance of Free-Space Optical Transmission with Spatial Diversity,” IEEE Trans. Wireless Commun. |

13. | T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. |

14. | M. Simon and V. Vilnrotter, “Alamouti-Type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. |

15. | A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett. |

16. | C. Abou-Rjeily, “Orthogonal Space-Time Block Codes for Binary Pulse Position Modulation,” IEEE Trans. Commun. |

17. | E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. |

18. | A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection Transmit Diversity for FSO Links Over Strong Atmospheric Turbulence Channels,” IEEE Photon. Technol. Lett. |

19. | A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express |

20. | J. Li and M. Uysal, “Achievable information rate for outdoor free space optical communication with intensity modulation and direct detection,” in Proc. IEEE Global Telecommunications Conference GLOBECOM ’03 , vol. |

21. | I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express |

22. | I. B. Djordjevic, “Adaptive Modulation and Coding for Free-Space Optical Channels,” IEEE/OSA Journal of Optical Communications and Networking |

23. | N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Optical Wireless Communications with Adaptive Subcarrier PSK Intensity Modulation,” (2010). Accepted for publication in IEEE Global Telecommunications Conference (GLOBECOM ’10), URL http://users.auth.gr/nestoras. |

24. | A. A. Ali and I. A. Al-Kadi, “On the use of repetition coding with binary digital modulations on mobile channels,” IEEE Trans. Veh. Technol. |

25. | S. Trisno, I. I. Smolyaninov, S. D. Milner, and C. C. Davis, “Delayed diversity for fade resistance in optical wireless communication system through simulated turbulence,” in Proc. SPIE , pp. 385–394 (2004). [CrossRef] |

26. | S. Trisno, I. I. Smolyaninov, S. D. Milner, and C. C. Davis, “Characterization of delayed diversity optical wireless system to mitigate atmospheric turbulence induced fading,” in Proc. SPIE , pp. 589,215.1–589,215.10 (2005). |

27. | C. H. Kwok, R. V. Penty, and I. H. White, “Link Reliability Improvement for Optical Wireless Communication Systems with Temporal-Domain Diversity Reception,” IEEE Photon. Technol. Lett. |

28. | M. K. Simon and M.-S. Alouini, |

29. | S. Hranilovic and F. R. Kschischang, “Optical intensity-modulated direct detection channels: signal space and lattice codes,” IEEE Trans. Inf. Theory |

30. | 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,” Optical Engineering |

31. | I. S. Gradshteyn and I. M. Ryzhik, |

32. | R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE |

33. | 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. |

34. | H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average Capacity of Optical Wireless Communication Systems Over Atmospheric Turbulence Channels,” IEEE/OSA Journal of Lightwave Technology |

35. | A. García-Zambrana and A. Puerta-Notario, “Large change rate-adaptive indoor wireless infrared links using variable silence periods,” IEE Electronics Letters |

36. | A. García-Zambrana and A. Puerta-Notario, “RZ-Gaussian pulses reduce the receiver complexity in wireless infrared links at high bit rates,” IEE Electronics Letters |

37. | A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications,” Opt. Express |

38. | A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient lognormal channel model for turbulent FSO communications,” IEE Electronics Letters |

39. | N. D. Chatzidiamantis, G. K. Karagiannidis, and D. S. Michalopoulos, “On the Distribution of the Sum of Gamma-Gamma Variates and Application in MIMO Optical Wireless Systems,” in Proc. IEEE Global Telecommunications Conf. GLOBECOM 2009 , pp. 1–6 (2009). [CrossRef] |

40. | V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in |

41. | Wolfram Research Inc., “The Wolfram functions site,” URL http://functions.wolfram.com. |

42. | N. L. Johnson, S. Kotz, and N. Balakrishnan, |

43. | A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “On the Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels Using OOK Signaling,” EURASIP Journal on Wireless Communications and Networking |

44. | J. C. Diels and W. Rudolph, |

45. | A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express |

46. | Wolfram Research Inc., |

47. | A. Garcia-Zambrana and A. Puerta-Notario, “Novel approach for increasing the peak-to-average optical power ratio in rate-adaptive optical wireless communication systems,” IEE Proceedings -Optoelectronics |

**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: October 13, 2010

Revised Manuscript: November 11, 2010

Manuscript Accepted: November 13, 2010

Published: November 19, 2010

**Citation**

Antonio García-Zambrana, Carmen Castillo-Vázquez, and Beatriz Castillo-Vázquez, "Rate-adaptive FSO links over atmospheric turbulence channels by jointly using repetition coding and silence periods," Opt. Express **18**, 25422-25440 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25422

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