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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25422–25440
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Rate-adaptive FSO links over atmospheric turbulence channels by jointly using repetition coding and silence periods

Antonio García-Zambrana, Carmen Castillo-Vázquez, and Beatriz Castillo-Vázquez  »View Author Affiliations


Optics Express, Vol. 18, Issue 24, pp. 25422-25440 (2010)
http://dx.doi.org/10.1364/OE.18.025422


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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

2. Atmospheric turbulence channel model

Together with this distribution and considering a limiting case of strong turbulence conditions [4

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

, 15

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]

], a negative exponential model with PDF given by
fI(i)=exp(i),i0
(6)
is also adopted to describe turbulence-induced fading, leading to an easier mathematical treatment to evaluate error rate performance for different values of rate reduction and time-diversity order. In this case, since the mean value of this turbulence model is E[I] = 1 and the second moment is given by E[I2] = 2, the scintillation index is SI = E[I2]/(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.

We consider OOK formats with any pulse shape and reduced duty cycle, allowing the increase of the PAOPR parameter [15

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

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]

]. In spite of the atmosphere can cause pulse distortion and broadening during propagation at extremely high signalling rates and, especially, at high levels of turbulence strength when increasing either Cn2 or the path length 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

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]

]. A new basis function ϕ(t) is defined as ϕ(t)=g(t)/Eg where 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 Eg=g2(t)dt is the electrical energy. In this way, an expression for the optical intensity can be written as
x(t)=k=ak2TbPG(f=0)g(tkTb)
(7)
where 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 Tb parameter is the bit period. The random variable (RV) ak follows a Bernoulli distribution with parameter 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 d=2PTbξ where ξ = TbEg/G2(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.

3. Proposed rate-adaptive transmission scheme

Adaptive transmission here considered is based on reducing the initial bit rate, Rb = 1/Tb, for a rate reduction (RR) parameter as Rb/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.

In relation to the rate-adaptive transmission only based on repetition coding, the expression for the optical intensity can be written as
xRRrc(t)=k=ak2TbPG(f=0)l=0RRrc1g(tlTbkRRrcTb)
(9)
where RRrc represents the repetition of each information bit and, hence, a rate reduction of RR = RRrc is considered. From this expression, it is easy to deduce that an increase of the PAOPR is not achieved; however, unlike rate-adaptive transmission only based on variable silence periods, a potential diversity gain can be exploited based on the concept of temporal-domain diversity reception [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]

]. To the best of the authors’ knowledge, closed-form expressions for the error rate performance corresponding to this rate-adaptive scheme in the context proper to FSO systems where a limited time-diversity order is only available have not been reported in the open literature.

4. BER performance analysis

In this section, assuming channel side information at the receiver, we present closed-form expressions for the average BER when the scintillation follows negative exponential and gamma-gamma distributions, which cover a wide range of atmospheric turbulence conditions.

4.1. Gamma-gamma atmospheric turbulence channel

Fig. 1 Performance comparison of different rate-adaptive transmission schemes in FSO IM/DD links over the gamma-gamma atmospheric turbulence channel when different levels of turbulence (a) (α,β) = (4, 3) and (b) (α,β) = (4, 1) are assumed, corresponding to values of scintillation index of SI = 0.66 and SI = 1.5, respectively.

4.2. Exponential atmospheric turbulence channel

In this subsection, considering a limiting case of strong turbulence conditions [4

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

,15

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]

], a negative exponential model is adopted to describe turbulence-induced fading, leading to an easier mathematical treatment to evaluate error rate performance for different values of rate reduction and time-diversity order. Here, particularizing with the negative exponential distribution in Eq. (6) and knowing that this can be seen as a gamma distribution of parameters μ = 1 and λ = 1 [42

42. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, vol. 2, 2nd ed. (Wiley Series in Probability and Statistics, 1994).

], i.e. I ∼ G(μ = 1, λ = 1), the sum of Ωd i.i.d. RVs represented by IT=k=1ΩdIk is also a RV following a gamma distribution with parameters μ = Ωd and λ = 1, i.e. ITG(μ = Ωd,λ = 1) as
fIT(i)=iΩd1Γ(Ωd)exp(i),i0.
(23)

Fig. 2 Performance comparison of different rate-adaptive transmission schemes in FSO IM/DD links over the exponential atmospheric turbulence channel, corresponding to a value of scintillation index of SI = 1.

Fig. 3 (a) Performance of the sech2 pulse shape with κ = 0.25 for the rate-adaptive scheme (Rep&Sil) with TDO = 2 and RR = {1, 2, 4, 8} in FSO IM/DD links over the exponential atmospheric turbulence channel; (b) Performance of the rate-adaptive scheme (Rep&Sil) here proposed with TDO = 2, rectangular pulse shape with κ = 1 and RR = {1, 2, 4, 8} in FSO IM/DD links over the gamma-gamma atmospheric turbulence channel with analytical results in Eq. (20) when different levels of turbulence are assumed, together with the analytical results in Eq. (24), corresponding to the negative exponential distributed turbulence model.

Finally, analytical results in Eq. (20) for the rate-adaptive transmission scheme (Rep&Sil) here proposed with TDO = 2, rectangular pulse shape with 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

Fig. 4 Achievable information rate corresponding to the rate-adaptive transmission schemes Sil, Rep and Rep&Sil for two different target BER requirements, (a) Pb = 10−4 and (b) Pb = 10−8, and time-diversity orders of TDO={2, 4}, together with the ergodic capacity for the exponential atmospheric turbulent optical channel.

From this figure, it can be deduced not only the superiority of the rate-adaptive transmission scheme based on the joint use of repetition coding and variable silence periods but also that an adaptive transmission design approach based on taking advantage out of the potential time-diversity order available in the turbulent channel is required, corroborating the fact that the rate-adaptive transmission scheme only based on variable silence periods implies a remarkably inefficient performance from the point of view of information theory. In this way, it can be observed that even when the available time-diversity order is low (TDO=2) a relevant improvement in achievable information rate is obtained, especially when a lower target BER is demanded. In spite of high values of TDO cannot be possible because of the latency introduced by the interleaver, to achieve a time diversity order available of TDO=2, 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]

] for a rate reduction of 2. It must be commented that the rate-adaptive transmission scheme proposed is not based on an adaptive signal constellation where more complicated modulation techniques can be defined, being assumed the use of OOK signaling due to its simplicity and low implementation cost, and, hence, an achievable information rate not higher than 1 bit/channel use can be achieved, since this is determined by the signal constellation and how the coding technique is able to take advantage of it. At the expense of a greater simplicity in hardware implementation, lower values of capacity are achieved if compared to rate-adaptive transmission schemes based on adaptive modulation or coding techniques more sophisticated than repetition coding and the inclusion of variable silence periods [21

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

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

From the relevant results here obtained when an adaptive transmission scheme based on the joint use of repetition coding and variable silence periods is adopted, investigating in the atmospheric turbulent FSO case the design of trellis coding schemes, where not only the PAOPR is increased, as proposed in [47

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]

] for indoor optical wireless communications, but also the potential time-diversity order available in the turbulent channel is exploited, is an interesting topic for future research, emphasizing the fact that the analysis of the FSO scenario implies to take into account aspects different to those present in the study of indoor optical communications. In this sense, conclusions in [37

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]

] from the analysis by simulation results of the rate-adaptive transmission technique only based on variable silence periods, simply adapting to FSO scenario from the indoor optical communications [35

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]

], such as proposing the use of shortened pulses as the central core of this adaptive transmission scheme, and its superiority compared to schemes based on variable-rate repetition coding, must be revised in the light of the analytical results presented in this paper: firstly, in relation to the impact on performance of the pulse shape adopted, providing an additional coding gain with independence of the rate-adaptive scheme employed or even in absence of rate-adaptive transmission; and, secondly, in relation to the benefit of using the available time-diversity order, aspect ignored when the rate-adaptive scheme is only based on variable silence periods.

Acknowledgments

The authors are grateful for financial support from the Junta de Andalucía (research group “Communications Engineering (TIC-0102)”).

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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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References

  1. J. M. Kahn, and J. R. Barry, "Wireless Infrared Communications," Proc. IEEE 85, 265-298 (1997). [CrossRef]
  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]
  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]
  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. Wirel. Comm. 5(6), 1229-1233 (2006). [CrossRef]
  8. I. B. Djordjevic, "LDPC-coded MIMO optical communication over the atmospheric turbulence channel using Q-ary pulse-position modulation," Opt. Express 15(16), 10,026-10,032 (2007). [CrossRef]
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