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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 6 — Mar. 15, 2010
  • pp: 5356–5366
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Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels

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


Optics Express, Vol. 18, Issue 6, pp. 5356-5366 (2010)
http://dx.doi.org/10.1364/OE.18.005356


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Abstract

Atmospheric turbulence produces fluctuations in the irradiance of the transmitted optical beam, which is known as atmospheric scintillation, severely degrading the link performance. In this paper, a scheme combining transmit laser selection (TLS) and space-time trellis code (STTC) for multiple-input-single-output (MISO) free-space optical (FSO) communication systems with intensity modulation and direct detection (IM/DD) over strong atmospheric turbulence channels is analyzed. Assuming channel state information at the transmitter and receiver, we propose the transmit diversity technique based on the selection of two out of the available L lasers corresponding to the optical paths with greater values of scintillation to transmit the baseline STTCs designed for two transmit antennas. Based on a pairwise error probability (PEP) analysis, results in terms of bit error rate are presented when the scintillation follows negative exponential and K distributions, which cover a wide range of strong atmospheric turbulence conditions. Obtained results show a diversity order of 2L-1 when L transmit lasers are available and a simple two-state STTC with rate 1 bit/(s∙Hz) is used. Simulation results are further demonstrated to confirm the analytical results.

© 2010 Optical Society of America

1. Introduction

It must be emphasized that a simple translation of the analysis of STCs from RF systems is not plausible due to peculiarities proper to FSO scenario. It is well known from the vast literature on wireless RF systems that simply sending the same signal from different antennas (i.e., repetition coding) does not realize any transmit diversity advantage. However, in [20

20. M. Safari and M. Uysal, “Do We Really Need OSTBCs for Free-Space Optical Communication with Direct Detection?” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008). [CrossRef]

] it was shown that simple RCs not only are able to extract full diversity but also always outperform OSTBCs, because of the fact that the transmitted signal is an intensity and, hence, it is subject to a nonnegativity constraint. In this way, unlike in the RF case [21

21. V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Information Theory 44(2), 744–765 (1998). [CrossRef]

], performance bounds and systematic design guidelines for general FSO STCs are not available. In [22

22. E. Bayaki and R. Schober, “On Space-Time Coding for Free-Space Optical Systems,” (2009). Accepted for future publication in IEEE Trans. Commun.

], a closed-form expression has recently been derived for the asymptotic pairwise error probability (PEP) of general FSO STCs for two lasers and an arbitrary number of photodetectors for channels suffering from Gamma-Gamma fading, showing the quasi-optimality of STC designs based on repetition codes and their superiority compared to conventional orthogonal space-time block codes.

2. Atmospheric turbulence channel model

y(t)=ηi(t)x(t)+z(t)
(1)

where η is the detector responsivity, assumed hereinafter to be the unity, Xx(t) represents the optical power supplied by the source, and Ii(t) the scintillation at the optical path; Zz(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 at detector. In this case, the noise can usually be modeled to high accuracy as AWGN with zero mean and variance N 0/2, i.e. Z ~ N(0,N 0/2), independent of the on/off state of the received bit [1

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

]. Since the transmitted signal is an intensity, X must satisfy ∀tx(t) ≥ 0. Due to eye and skin safety regulations, the average optical power is limited and, hence, the average amplitude of X is limited. Although limits are placed on both the average and peak optical power transmitted, in the case of most practical modulated optical sources, it is the average optical power constraint that dominates [31

31. S. Hranilovic and F. R. Kschischang, “Optical intensity-modulated direct detection channels: signal space and lattice codes,” IEEE Trans. Information Theory 49(6), 1385–1399 (2003). [CrossRef]

]. The received electrical signal Yy(t), however, can assume negative amplitude values. In this fashion, the atmospheric turbulence channel model consists of a multiplicative noise model, where the optical signal is multiplied by the channel irradiance. Considering strong turbulence conditions [5

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

,16

16. 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]

], negative exponential and K distribution for the i.i.d. channel irradiances can be assumed. The probability density function (PDF) corresponding to the K turbulence model is given by

fI(i)=2αα+12Γ(α)iα12Kα1(2αi),i0
(2)

SI=E[I2](E[I])21=1+2α
(3)

Together with this distribution and considering a limiting case of strong turbulence conditions [5

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

, 18

18. 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]

, 28

28. N. Letzepis and A. G. Fabregas, “Outage probability of the MIMO Gaussian free-space optical channel with PPM,” in Proc. IEEE International Symposium on Information Theory ISIT 2008, pp. 2649–2653 (2008).

], a negative exponential model with PDF given by

fI(i)=exp(i),i0
(4)

is also adopted to describe turbulence-induced fading, leading to an easier mathematical treatment to evaluate error rate performance for any diversity order. This distribution can be seen as the K-distributed turbulence model in (2) when the channel parameter α → ∞.

We consider OOK formats with any pulse shape and reduced duty cycle, allowing the increase of the PAOPR parameter [18

18. 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]

, 26

26. 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]

]. 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 = ∫ -∞ g 2(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)
(5)

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. 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
(6)

3. Proposed transmit diversity scheme

The use of optical arrays, similar to the use of antenna-array technology for microwave systems, is considered as a means of combatting fading. In particular, we adopt a MISO array based on L laser sources, assumed to be intensity-modulated only and all pointed towards a distant photodetector, assumed to be ideal noncoherent (direct-detection) receiver. The sources and the detector are physically situated so that all transmitters are simultaneously observed by the receiver, and the separation distance between the lasers is large enough so that the fading experienced between source-detector pairs Ij(t) is assumed to be statistically independent. Assuming channel state information at the transmitter and receiver, we propose the transmit diversity technique based on the selection of two out of the available L lasers corresponding to the optical paths with greater values of scintillation to transmit the baseline STTCs designed for two transmit antennas [21

21. V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Information Theory 44(2), 744–765 (1998). [CrossRef]

]. To illustrate the proposed scheme, we adopt in this paper the example shown in Fig. 1, where a two-state STTC with rate 1 bit/(s∙Hz) using OOK is displayed [33

33. H. Jafarkhani, Space-Time Coding: Theory and Practice (Cambridge University Press, New York, 2005). [CrossRef]

, Fig. 6.5.]. The incoming symbol stream is first encoded using the trellis structure and the encoded stream is then distributed among the two sources out of the available L lasers corresponding to greater values of scintillation, I (L)(t) and I (L-1)(t), where I (1)(t),I (2)(t),…, I (L)(t) is a new sequence of L auxiliary random variables obtained by arranging the random sequence I 1(t),I 2(t),…,IL(t) in an increasing order of magnitude. The labeling i/kk along each branch of the trellis refers to the input bit (i) and the corresponding pair of output symbols (kk) that result from the transition between the states at the beginning and end of the branch.

Fig. 1. Trellis diagram of two-state STTC, OOK, 1 bit/(s∙Hz)

4. Performance analysis

In this section, an optical array based on L = {1,2,4,8} laser sources, all pointed towards a distant photodetector, is considered. We present aproximate closed-form expressions for the bit error rate (BER) using a pairwise error probability analysis when the scintillation follows negative exponential and K distributions, which cover a wide range of strong atmospheric turbulence conditions. The PEP represents the probability of choosing the space-time sequence X̂ when in fact the sequence X was transmitted [30

30. M. K. Simon and M.-S. Alouini, Digital Communications Over Fading Channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

, Chapter 16]. Assuming that the correct path is the all-zeros sequence, then for the shortest error event path of length N = 2 illustrated by shading in Fig. 1, we have

X=[0000],X̂=[0dd0]
(7)

where each column of X and X̂ is associated with the two symbols transmitted from the two lasers in a given symbol interval (time slot) and d is the Euclidean distance in (6) corresponding to the OOK signaling (i.e., the OOK symbols are the elements of the X and X̂ matrices associated with the trellis). In the proposed scheme, for example, we associate the first and second rows with the (L-1)th and Lth order statistics corresponding to the scintillation. Under the assumption of perfect CSI, the conditional PEP with respect to scintillation coefficients of greater value, I (L) and I (L-1), is given as [30

30. M. K. Simon and M.-S. Alouini, Digital Communications Over Fading Channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

, Chapter 16]

P(XX̂{I(L),I(L1)})=Q((d/2)22N0(i12+i22))
(8)

P(XX̂{I(L),I(L1)})=Q(γξ2(i12+i22))
(9)

where γ = P 2 Tb/N 0 is the average receiver electrical signal-to-noise spectral density ratio (SNR) in the presence of the turbulence [6

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

], knowing that PDF in (2) or (4) is normalized. Under the assumption of perfect interleaving, we can exploit independency among fading coefficients to obtain the average PEP, P(XX̂), by averaging (9) as follows

P(XX̂)=00Q(γξ2(i12+i22))fI(L)(i1)fI(L1)(i2)di1di2
(10)

According to order statistics [34

34. H. A. David and H. N. Nagaraja, Order Statistics, 3rd ed. (John Wiley and Sons Inc., 2003). [CrossRef]

], for i.i.d. RVs of {Ij}j=1,2,⋯L, the PDF corresponding to I (L) and I (L-1) can be written as

fI(L)(i)=LfI(i)[FI(i)]L1
(11)
fI(L1)(i)=L(L1)fI(i)(1FI(i))(FI(i))L2
(12)

being FI(i) the cumulative density function (CDF) corresponding to the turbulence model. An union bound on the average BER can be found as [30

30. M. K. Simon and M.-S. Alouini, Digital Communications Over Fading Channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

, eq. (13.44)]

Pb(E)1ncXP(X)XX̂nXX̂P(XX̂)
(13)

where P(X) is the probability that the coded sequence X is transmitted, n(X,X̂) is the number of information bit errors in choosing another coded sequence X̂ instead of X and nc is the number of information bits per transmission. Next, if we were to choose to approximate the average BER by considering only error event paths of minimum length (i.e., N = 2) [30

30. M. K. Simon and M.-S. Alouini, Digital Communications Over Fading Channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

, Section 14.6.4], we can use (10) to obtain Pb(E) ≃ P(XX̂). To simplify the expression in (10), we use the approximation for the Q-function presented in [35

35. M. Chiani, D. Dardari, and M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun. 2(4), 840–845 (2003). [CrossRef]

, Eq. (14)] (i.e., Q(x) ≃ (1/12)exp(-x 2/2)+(1/4)exp(-2x 2/3)), finally obtaining

Pb(E)1120exp(γξi124)fI(L)(i1)di10exp(γξi224)fI(L1)(i2)di2
+140exp(γξi123)fI(L)(i1)di10exp(γξi223)fI(L1)(i2)di2
(14)

To evaluate the improvement in performance, we compare the proposed scheme, which is referred to as the TLS/STTC scheme, with the transmit diversity technique TLS presented in [26

26. 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]

] for uncoded FSO links, based on the selection of the optical path with a greater value of scintillation, where the average BER is given by

Pb(E)=0Q(2γξi2)fI(L)(i)di
(15)

In the same way, we also include the performance corresponding to the STTC scheme when no transmit laser selection is used, where, following an approach as in (13), the average BER can be written as

Pb(E)P(XX̂)=00Q(γξ2(i12+i22))fI(i1)fI(i2)di1di2
(16)

4.1. K atmospheric turbulence channel

Particularizing with the K distribution in (2) and using [36

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

, Eq. (03.04.21.0013.01)] together with the fact that Kv(∙) is a even function with respect to its parameter, the derived integral for the CDF of the K channel can be written as

FI(i)=12αα/2Γ(α)iα/2Kα(2iα)
(17)

The results corresponding to this FSO scenario are illustrated in the Fig. 2, when different levels of turbulence strength of α = 1 and α = 4 are assumed, corresponding to values of scintillation index of SI = 3 and SI = 1.5, respectively, and where rectangular pulse shapes with ξ = 1 are used. Additionally, a relevant improvement in performance must be noted as a consequence of pulse shape used, providing an increment in the average SNR of 10log10 ξ dB. So, for instance, when a rectangular pulse shape of duration κTb, with 0 < κ ≤ 1, is adopted, a value of ξ = 1/κ can be easily shown. Nonetheless, a significantly higher value of ξ = 4/κ√π is obtained when a Gaussian pulse of duration κTb as g(t) = exp (-t 2/2σ2) ∀|t| < κTb/2 is adopted, where σ = κTb/8 and the reduction of duty cycle is also here controlled by the parameter κ. In this fashion, 99.99% of the average optical power of a Gaussian pulse shape is being considered. Then, a Gaussian pulse shape with κ = 0.25 is also adopted when L = 2 in order to show the improvement in performance obtained with pulse shapes having a high PAOPR. Numerical results for TLS/STTC in (14), TLS in (15) and STTC without laser selection in (16) are computed using a symbolic mathematics package [37

37. Wolfram Research, Inc., Mathematica, version 7.0 ed. (Wolfram Research, Inc., Champaign, Illinois, 2008).

]. 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 for L = {2,4,8}, as well as the greater diversity order for the transmit diversity technique here proposed if compared with TLS and STTC, being superior to the number of available transmit lasers L.

4.2. Exponential atmospheric turbulence channel

In this subsection, considering a limiting case of strong turbulence conditions [5

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

,18

18. 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]

,28

28. N. Letzepis and A. G. Fabregas, “Outage probability of the MIMO Gaussian free-space optical channel with PPM,” in Proc. IEEE International Symposium on Information Theory ISIT 2008, pp. 2649–2653 (2008).

], a negative exponential model is adopted to describe turbulence-induced fading, leading to an easier mathematical treatment to evaluate error rate performance for any number of transmit lasers. Here, particularizing with the negative exponential distribution in (4), the derived integral for the CDF of the exponential turbulent channel can be written as FI(i) = 1 - exp (-i). Using the binomial theorem in (11) and (12), we obtain

fI(L)(i)=Ln=1L(L1n1)(1)n1exp(ni)
(18)
fI(L1)(i)=L(L1)m=2L(L2m2)(1)m1exp(mi)
(19)
Fig. 2. Performance comparison of TLS/STTC and TLS in FSO IM/DD link over the K atmospheric turbulence channel when different levels of turbulence strength (a) (α = 1) and (b) (α = 4) are assumed, corresponding to values of scintillation index of SI = 3 and SI = 1.5, respectively.

Next, substituting (18) and (19) in (14) and evaluating the integrals by using [38

38. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth ed. (Dover, New York, 1970).

, eqn. (7.4.32)], a closed-form solution for the aproximate average BER yields as

Pb(E)L2(L1)48γξn=1L(L1n1)m=2L(1)m+n3(L2m2)
(4πerfc(mγξ)erfc(nγξ)exp(m2+n2γξ)+9πerfc(3m2γξ)erfc(3n2γξ)exp(3(m2+n2)4γξ))
(20)

where erfc(∙) is the complementary error function. The results corresponding to this FSO scenario are illustrated in the Fig. 3, where rectangular pulse shapes with κ = 1 are used.

Fig. 3. Performance comparison of TLS/STTC and TLS in FSO IM/DD link over the exponential atmospheric turbulence channel, corresponding to a value of scintillation index of SI = 1.

5. Conclusions

Acknowledgments

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

References and links

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.

K. Tsukamoto, A. Hashimoto, Y. Aburakawa, and M. Matsumoto, “The case for free space,” IEEE Microwave Mag. 10(5), 84–92 (2009). [CrossRef]

5.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001). [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.

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun. 51(8), 1233–1239 (2003). [CrossRef]

8.

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]

9.

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]

10.

E. J. Shin and V. W. S. Chan, “Optical communication over the turbulent atmospheric channel using spatial diversity,” in Proc. IEEE GLOBECOM , pp. 2055–2060 (2002).

11.

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]

12.

I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-Coded MIMO Optical Communication Over the Atmospheric Turbulence Channel,” J. Lightwave Technol. 26(5), 478–487 (2008). [CrossRef]

13.

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]

14.

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

15.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER Performance of Free-Space Optical Transmission with Spatial Diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007). [CrossRef]

16.

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]

17.

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]

18.

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]

19.

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

20.

M. Safari and M. Uysal, “Do We Really Need OSTBCs for Free-Space Optical Communication with Direct Detection?” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008). [CrossRef]

21.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Information Theory 44(2), 744–765 (1998). [CrossRef]

22.

E. Bayaki and R. Schober, “On Space-Time Coding for Free-Space Optical Systems,” (2009). Accepted for future publication in IEEE Trans. Commun.

23.

Z. Chen, B. Vucetic, and J. Yuan, “Space-time trellis codes with transmit antenna selection,” Electron. Lett. 39(11), 854–855 (2003). [CrossRef]

24.

D. A. Gore and A. J. Paulraj, “MIMO antenna subset selection with space-time coding,” IEEE Trans. Sig. Process. 50(10), 2580–2588 (2002). [CrossRef]

25.

A. F. Molisch and M. Z. Win, “MIMO systems with antenna selection,” IEEE Microwave Magazine 5(1), 46–56 (2004). [CrossRef]

26.

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]

27.

B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, “Closed-form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels,” Electron. Lett. 45(23), 1185–1187 (2009). [CrossRef]

28.

N. Letzepis and A. G. Fabregas, “Outage probability of the MIMO Gaussian free-space optical channel with PPM,” in Proc. IEEE International Symposium on Information Theory ISIT 2008, pp. 2649–2653 (2008).

29.

S. Z. Denic, I. Djordjevic, J. Anguita, B. Vasic, and M. A. Neifeld, “Information Theoretic Limits for Free-Space Optical Channels With and Without Memory,” J. Lightwave Technol. 26(19), 3376–3384 (2008). [CrossRef]

30.

M. K. Simon and M.-S. Alouini, Digital Communications Over Fading Channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

31.

S. Hranilovic and F. R. Kschischang, “Optical intensity-modulated direct detection channels: signal space and lattice codes,” IEEE Trans. Information Theory 49(6), 1385–1399 (2003). [CrossRef]

32.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic Press Inc., 2007).

33.

H. Jafarkhani, Space-Time Coding: Theory and Practice (Cambridge University Press, New York, 2005). [CrossRef]

34.

H. A. David and H. N. Nagaraja, Order Statistics, 3rd ed. (John Wiley and Sons Inc., 2003). [CrossRef]

35.

M. Chiani, D. Dardari, and M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun. 2(4), 840–845 (2003). [CrossRef]

36.

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

37.

Wolfram Research, Inc., Mathematica, version 7.0 ed. (Wolfram Research, Inc., Champaign, Illinois, 2008).

38.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth ed. (Dover, New York, 1970).

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:
Atmospheric and Oceanic Optics

History
Original Manuscript: November 16, 2009
Revised Manuscript: January 9, 2010
Manuscript Accepted: February 21, 2010
Published: March 1, 2010

Citation
Antonio García-Zambrana, Carmen Castillo-Vázquez, and Beatriz Castillo-Vázquez, "Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels," Opt. Express 18, 5356-5366 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5356


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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. K. Tsukamoto, A. Hashimoto, Y. Aburakawa, and M. Matsumoto, "The case for free space," IEEE Microwave Mag. 10(5), 84-92 (2009). [CrossRef]
  5. L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001). [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. X. Zhu and J. M. Kahn, "Performance bounds for coded free-space optical communications through atmospheric turbulence channels," IEEE Trans. Commun. 51(8), 1233-1239 (2003). [CrossRef]
  8. 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]
  9. 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]
  10. E. J. Shin and V. W. S. Chan, "Optical communication over the turbulent atmospheric channel using spatial diversity," in Proc. IEEE GLOBECOM, pp. 2055-2060 (2002).
  11. 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]
  12. I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, "LDPC-Coded MIMO Optical Communication Over the Atmospheric Turbulence Channel," J. Lightwave Technol. 26(5), 478-487 (2008). [CrossRef]
  13. 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]
  14. S. G. Wilson, M. Brandt-Pearce, Q. Cao, and I. Leveque, J. H., "Free-Space Optical MIMO Transmission With Q-ary PPM," IEEE Trans. Commun. 53(8), 1402-1412 (2005). [CrossRef]
  15. S. M. Navidpour, M. Uysal, and M. Kavehrad, "BER Performance of Free-Space Optical Transmission with Spatial Diversity," IEEE Trans. Wireless Commun. 6(8), 2813-2819 (2007). [CrossRef]
  16. 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]
  17. 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]
  18. 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]
  19. C. Abou-Rjeily, "Orthogonal Space-Time Block Codes for Binary Pulse Position Modulation," IEEE Trans. Commun. 57(3), 602-605 (2009). [CrossRef]
  20. M. Safari and M. Uysal, "Do We Really Need OSTBCs for Free-Space Optical Communication with Direct Detection?" IEEE Trans. Wireless Commun. 7(11), 4445-4448 (2008). [CrossRef]
  21. V. Tarokh, N. Seshadri, and A. R. Calderbank, "Space-time codes for high data rate wireless communication: performance criterion and code construction," IEEE Trans. Information Theory 44(2), 744-765 (1998). [CrossRef]
  22. E. Bayaki and R. Schober, "On Space-Time Coding for Free-Space Optical Systems," (2009). Accepted for future publication in IEEE Trans. Commun.
  23. Z. Chen, B. Vucetic, and J. Yuan, "Space-time trellis codes with transmit antenna selection," Electron. Lett. 39(11), 854-855 (2003). [CrossRef]
  24. D. A. Gore and A. J. Paulraj, "MIMO antenna subset selection with space-time coding," IEEE Trans. Sig. Process. 50(10), 2580-2588 (2002). [CrossRef]
  25. A. F. Molisch and M. Z. Win, "MIMO systems with antenna selection," IEEE Microwave Magazine 5(1), 46-56 (2004). [CrossRef]
  26. 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]
  27. B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, "Closed-form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels," Electron. Lett. 45(23), 1185-1187 (2009). [CrossRef]
  28. N. Letzepis and A. G. Fabregas, "Outage probability of the MIMO Gaussian free-space optical channel with PPM," in Proc. IEEE International Symposium on Information Theory ISIT 2008, pp. 2649-2653 (2008).
  29. S. Z. Denic, I. Djordjevic, J. Anguita, B. Vasic, and M. A. Neifeld, "Information Theoretic Limits for Free-Space Optical Channels With and Without Memory," J. Lightwave Technol. 26(19), 3376-3384 (2008). [CrossRef]
  30. M. K. Simon and M.-S. Alouini, Digital Communications over Fading Channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).
  31. S. Hranilovic and F. R. Kschischang, "Optical intensity-modulated direct detection channels: signal space and lattice codes," IEEE Trans. Information Theory 49(6), 1385-1399 (2003). [CrossRef]
  32. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic Press Inc., 2007).
  33. H. Jafarkhani, Space-Time Coding: Theory and Practice (Cambridge University Press, New York, 2005). [CrossRef]
  34. H. A. David and H. N. Nagaraja, Order Statistics, 3rd ed. (John Wiley and Sons Inc., 2003). [CrossRef]
  35. M. Chiani, D. Dardari, and M. K. Simon, "New exponential bounds and approximations for the computation of error probability in fading channels," IEEE Trans. Wireless Commun. 2(4), 840-845 (2003). [CrossRef]
  36. Wolfram Research, Inc., "The Wolfram functions site," URL http://functions.wolfram.com.
  37. Wolfram Research, Inc., Mathematica, version 7.0 ed. (Wolfram Research, Inc., Champaign, Illinois, 2008).
  38. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth ed. (Dover, New York, 1970).

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