Abstract

Transferring wireless broadband services across extremely far distances on Earth is usually implemented nowadays either by ground-based or satellite communications. Terrestrial networks require, however, heavy installation and maintenance costs, whereas satellite networks suffer from excessively high power requirements. An alternative but highly challenging solution is to employ a network consisting of high-altitude platforms (HAPs). In this paper, we propose a way of delivering WiMAX traffic using a serial multi-hop HAP network configuration. HAPs are located at specific locations in the stratosphere, pick up the traffic from the Earth region they cover, and communicate with each other using optical links. In such a configuration, we determine the WiMAX quality of service by evaluating the outage probability for the entire HAP network. The overall performance is examined by using a channel model that takes into account laser path loss and pointing error effects. The findings of the present study indicate that the consideration of specific network and channel model parameters is crucial toward the design and implementation of future multi-hop HAP networks.

© 2013 Optical Society of America

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2010 (3)

F. Fidler, M. Knapek, J. Horwath, and W. R. Leeb, “Optical communications for high-altitude platforms,” IEEE J. Sel. Topics Quantum Electron., vol.  16, no. 5, pp. 1058–1070, Sept.–Oct. 2010.

A. Bekkali, C. B. Naila, K. Kazaura, K. Wakamori, and M. Matsumoto, “Transmission analysis of OFDM-based wireless services over turbulent radio-on-FSO links modeled by gamma-gamma distribution,” IEEE Photon. J., vol.  2, no. 3, pp. 510–520, June 2010.
[CrossRef]

D. Kedar, D. Grace, and S. Arnon, “Laser nonlinearity effects on optical broadband backhaul communication links,” IEEE Trans. Aerosp. Electron. Syst., vol.  46, no. 4, pp. 1797–1803, Oct. 2010.

2009 (3)

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol., vol.  27, no. 3, pp. 189–204, Feb. 2009.
[CrossRef]

S. Arnon, “Minimization of outage probability of WiMAX link supported by laser link between a high-altitude platform and a satellite,” J. Opt. Soc. Am. A, vol.  26, no. 7, pp. 1545–1552, July 2009.
[CrossRef]

2008 (4)

H. G. Sandalidis, “Optimization models for misalignment fading mitigation in optical wireless links,” IEEE Commun. Lett., vol.  12, no. 5, pp. 395–397, May 2008.
[CrossRef]

Z. Yang, A. Mohammed, T. Hult, and D. Grace, “Downlink coexistence performance assessment and techniques for WiMAX services from high altitude platform and terrestrial deployments,” EURASIP J. Wireless Commun. Netw., vol.  2008, 291450, 2008.
[CrossRef]

Z. Yang, A. Mohammed, and T. Hult, “Performance evaluation of WiMAX broadband from high altitude platform cellular system and terrestrial coexistence capability,” EURASIP J. Wireless Commun. Netw., vol. 2008, 348626, 2008.
[CrossRef]

J. Thornton, A. D. White, and T. C. Tozer, “A WiMAX payload for high altitude platform experimental trials,” EURASIP J. Wireless Commun. Netw., vol. 2008, 498517, 2008.
[CrossRef]

2006 (2)

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
[CrossRef]

G. K. Karagiannidis, T. A. Tsiftsis, and R. N. Mallik, “Bounds for multihop relayed communications in Nakagami-m fading,” IEEE Trans. Commun., vol.  54, no. 1, pp. 18–22, Jan. 2006.
[CrossRef]

2005 (2)

D. Grace, J. Thornton, G. Chen, G. White, and T. Tozer, “Improving system capacity of broadband services using multiple high altitude platforms,” IEEE Trans. Wireless Commun., vol.  4, no. 2, pp. 700–709, 2005.
[CrossRef]

P. Likitthanasate, D. Grace, and P. Mitchell, “Coexistence performance of high altitude platform and terrestrial systems sharing a common downlink WiMAX frequency band,” Electron. Lett., vol.  41, no. 15, pp. 858–860, 2005.
[CrossRef]

2004 (1)

2003 (3)

T. Ohtsuki, “Multiple-subcarrier modulation in optical wireless communications,” IEEE Commun. Mag., vol.  41, no. 3, pp. 74–79, Mar. 2003.
[CrossRef]

M. O. Hasna and M. S. Alouini, “Outage probability of multihop transmission over Nakagami fading channels,” IEEE Commun. Lett., vol.  7, no. 5, pp. 216–218, May 2003.
[CrossRef]

S. Arnon, “Optimization of urban optical wireless communications systems,” IEEE Trans. Wireless Commun., vol.  2, no. 4, pp. 626–629, July 2003.
[CrossRef]

2002 (1)

1994 (1)

K. Kiasaleh, “On the probability density function of signal intensity in free-space optical communications systems impaired by pointing jitter and turbulence,” Opt. Eng., vol.  33, no. 11, pp. 3748–3757, Nov. 1994.
[CrossRef]

1989 (1)

C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun., vol.  37, no. 3, pp. 252–260, Mar. 1989.
[CrossRef]

1982 (1)

J. C. Daly, “Fiber optic intermodulation distortion,” IEEE Trans. Commun., vol.  30, no. 8, pp. 1954–1958, Aug. 1982.
[CrossRef]

Abramovitz, M.

M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1972.

Ahson, S.

S. Ahson and M. Ilyas, The WiMAX Handbook—Three-Volume Set. CRC Press, 2008.

Alouini, M. S.

M. O. Hasna and M. S. Alouini, “Outage probability of multihop transmission over Nakagami fading channels,” IEEE Commun. Lett., vol.  7, no. 5, pp. 216–218, May 2003.
[CrossRef]

Alvarez, M.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Alvarez-Herrero, A.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Andrews, L.

L. Andrews and R. L. Philips, Laser Beam Propagation Through Random Media, 2nd ed. SPIE, 2005.

Apestigue, V.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Aragón-Zavala, A.

A. Aragón-Zavala, J. L. Cuevas-Ruíz, and J. A. Delgado-Penín, High-Altitude Platforms for Wireless Communications. Wiley, 2008.

Armstrong, J.

Arnon, S.

D. Kedar, D. Grace, and S. Arnon, “Laser nonlinearity effects on optical broadband backhaul communication links,” IEEE Trans. Aerosp. Electron. Syst., vol.  46, no. 4, pp. 1797–1803, Oct. 2010.

S. Arnon, “Minimization of outage probability of WiMAX link supported by laser link between a high-altitude platform and a satellite,” J. Opt. Soc. Am. A, vol.  26, no. 7, pp. 1545–1552, July 2009.
[CrossRef]

A. Polishuk and S. Arnon, “Optimization of a laser satellite communication system with an optical preamplifier,” J. Opt. Soc. Am. A, vol.  21, no. 7, pp. 1307–1315, July 2004.
[CrossRef]

S. Arnon, “Optimization of urban optical wireless communications systems,” IEEE Trans. Wireless Commun., vol.  2, no. 4, pp. 626–629, July 2003.
[CrossRef]

S. Arnon, “Optical wireless communications,” in Encyclopedia of Optical Engineering, R. G. Driggers, C. Hoffman, and R. Driggers, Eds. CRC Press, 2003, pp. 1866–1886.

Arruego, I.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Aviv, D. G.

D. G. Aviv, Laser Space Communications. Artech House, 2006.

Azcue, J.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Bekkali, A.

A. Bekkali, C. B. Naila, K. Kazaura, K. Wakamori, and M. Matsumoto, “Transmission analysis of OFDM-based wireless services over turbulent radio-on-FSO links modeled by gamma-gamma distribution,” IEEE Photon. J., vol.  2, no. 3, pp. 510–520, June 2010.
[CrossRef]

Chen, C.

C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun., vol.  37, no. 3, pp. 252–260, Mar. 1989.
[CrossRef]

Chen, G.

D. Grace, J. Thornton, G. Chen, G. White, and T. Tozer, “Improving system capacity of broadband services using multiple high altitude platforms,” IEEE Trans. Wireless Commun., vol.  4, no. 2, pp. 700–709, 2005.
[CrossRef]

Coupechoux, M.

M. Maqbool, M. Coupechoux, and P. Godlewski, “Comparison of various frequency reuse patterns for WiMAX networks with adaptive beamforming,” in Proc. of IEEE VTC Spring, Marina Bay, Singapore, 2008.

Cuevas-Ruíz, J. L.

A. Aragón-Zavala, J. L. Cuevas-Ruíz, and J. A. Delgado-Penín, High-Altitude Platforms for Wireless Communications. Wiley, 2008.

Cvijetic, N.

N. Cvijetic and T. Wang, “WiMAX over free-space optics-evaluating OFDM multi-subcarrier modulation in optical wireless channels,” in Proc. IEEE Sarnoff Symp., Princeton, NJ, Mar. 2006.

N. Cvijetic and T. Wang, “A MIMO architecture for IEEE 802.16d (WiMAX) heterogeneous wireless access using optical wireless technology,” in Next Generation Teletraffic and Wired/Wireless Advanced Networking. Springer-Verlag, 2006, pp. 441–451.

Daly, J. C.

J. C. Daly, “Fiber optic intermodulation distortion,” IEEE Trans. Commun., vol.  30, no. 8, pp. 1954–1958, Aug. 1982.
[CrossRef]

de Mingo, J.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Delgado-Penín, J. A.

A. Aragón-Zavala, J. L. Cuevas-Ruíz, and J. A. Delgado-Penín, High-Altitude Platforms for Wireless Communications. Wiley, 2008.

Diaz-Michelena, M.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Djordjevic, I.

W. Shieh and I. Djordjevic, OFDM for Optical Communications. Academic, 2010.

Dohler, M.

M. Dohler and Y. Li, Cooperative Communications: Hardware, Channel and PHY. Wiley, 2010.

Dominguez, J.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Fidler, F.

F. Fidler, M. Knapek, J. Horwath, and W. R. Leeb, “Optical communications for high-altitude platforms,” IEEE J. Sel. Topics Quantum Electron., vol.  16, no. 5, pp. 1058–1070, Sept.–Oct. 2010.

Gallego, P.

I. Arruego, H. Guerrero, S. Rodriguez, J. Martinez-Oter, J. Jimenez, J. Dominguez, A. Martin-Ortega, J. de Mingo, J. Rivas, V. Apestigue, J. Sanchez, J. Iglesias, M. Alvarez, P. Gallego, J. Azcue, C. Ruiz de Galarreta, B. Martin, A. Alvarez-Herrero, M. Diaz-Michelena, I. Martin, F. Tamayo, M. Reina, M. Gutierrez, L. Sabau, and J. Torres, “OWLS: A ten-year history in optical wireless links for intra-satellite communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1599–1611, Dec. 2009.
[CrossRef]

Gardner, C. S.

C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun., vol.  37, no. 3, pp. 252–260, Mar. 1989.
[CrossRef]

Godlewski, P.

M. Maqbool, M. Coupechoux, and P. Godlewski, “Comparison of various frequency reuse patterns for WiMAX networks with adaptive beamforming,” in Proc. of IEEE VTC Spring, Marina Bay, Singapore, 2008.

Goldsmith, A.

A. Goldsmith, Wireless Communications. Cambridge University, 2005.

Grace, D.

D. Kedar, D. Grace, and S. Arnon, “Laser nonlinearity effects on optical broadband backhaul communication links,” IEEE Trans. Aerosp. Electron. Syst., vol.  46, no. 4, pp. 1797–1803, Oct. 2010.

Z. Yang, A. Mohammed, T. Hult, and D. Grace, “Downlink coexistence performance assessment and techniques for WiMAX services from high altitude platform and terrestrial deployments,” EURASIP J. Wireless Commun. Netw., vol.  2008, 291450, 2008.
[CrossRef]

D. Grace, J. Thornton, G. Chen, G. White, and T. Tozer, “Improving system capacity of broadband services using multiple high altitude platforms,” IEEE Trans. Wireless Commun., vol.  4, no. 2, pp. 700–709, 2005.
[CrossRef]

P. Likitthanasate, D. Grace, and P. Mitchell, “Coexistence performance of high altitude platform and terrestrial systems sharing a common downlink WiMAX frequency band,” Electron. Lett., vol.  41, no. 15, pp. 858–860, 2005.
[CrossRef]

D. Grace and M. Mohorčič, Broadband Communications via High Altitude Platforms. Wiley, 2011.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. New York: Academic, 2008.

Guerrero, H.

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P. Likitthanasate, D. Grace, and P. Mitchell, “Coexistence performance of high altitude platform and terrestrial systems sharing a common downlink WiMAX frequency band,” Electron. Lett., vol.  41, no. 15, pp. 858–860, 2005.
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Figures (9)

Fig. 1.
Fig. 1.

HAP network configuration.

Fig. 2.
Fig. 2.

Block diagram of (a) OFDM laser Tx and (b) OFDM laser Rx.

Fig. 3.
Fig. 3.

One-hop OP versus HAP Tx half-beam divergence angle.

Fig. 4.
Fig. 4.

One-hop OP versus HAP Tx half-beam divergence angle and electrical SNR threshold.

Fig. 5.
Fig. 5.

OP versus the average received SNR per subcarrier for the ground Rx assuming two hops.

Fig. 6.
Fig. 6.

OP at the ground Rx versus the SNR threshold at RF ground Rx for several hops.

Fig. 7.
Fig. 7.

OP at the ground Rx versus distance between the destination HAP and the RF ground Rx for various hops.

Fig. 8.
Fig. 8.

OP at the ground Rx versus the SNR threshold at the RF ground Rx and distance between the destination HAP and the RF ground Rx.

Fig. 9.
Fig. 9.

OP at the ground Rx versus hop distance for several hops.

Tables (1)

Tables Icon

TABLE I Numerical Parameters

Equations (36)

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sOFDM(t)=n=0S1xnexp[j2π(nTs+fc)t],0tTs.
PTO(t)=PTOavnTGTO×(1+n=0S1mnxnexp[j2π(nTs+fc)t]).
PTO(t)=PTOavnTGTO[1+msOFDM(t)].
fI(I)=βIβ1,0I1,
I¯=ββ+1,
β=θ24σ2.
PRO(t)=PTO(t)nRGRO(λO4πdO)2I+nHAP(t).
i(t)=RnTnRGTOGROPTOav(λO4πdO)2I×[1+msOFDM(t)]+nopt(t),
Pn=m2R2nT2nR2GTO2GRO2PTOav2(λO4πdO)4I2.
GTO=8θ2,
GRO=(πArλO)2,
μ=m2R2nT2nR2PTOav2(8θ2)2(πArλO)4(λO4πdO)4I2NO,n.
μ=αθ4I2,
α=m2(8RnTnRPTOav(Ar4dO)2)2NO,n.
fμ(μ)=β2(αθ4)β2μβ21,0μαθ4,
fμ(μ)=β2kβ2μβ21,0μk,
Fμ(μ)=(μk)β2,0μk.
Pout,1,n(μth)=Pr(μ<μth)=Fμ(μth)=(μthk)β2,0μthk,
Pout,1,n(θ,μth)=(μthαθ2)θ24σ2,0θ(αμth)14.
θopt=αμth41e.
Pout,1(μth)=1Sn=0S1Pout,1,n(μth).
yN,n=i=1Ngi1hi,nxn+i=1Nni(t=i+1Ngt1ht,n),g0=1,
hi,n=mRnTnRPTOav(8θ2)(πArλO)2(λO4πdO)2Ii
μeq=i=1Nhi2gi12i=1NNO,n(t=i+1Nht2gt12).
μeq=(i=1N1μi)1,
μi=m2R2nT2nR2PTOav2(8θ2)2(πArλO)4(λO4πdO)4Ii2NO,n=kIi2
Pout,N,n(μth)=Pr(μeq<μth)=Pr(1μeq1μth)=1L1(M1/μeq(s)s)|s=1/μth.
M1/μeq(s)=i=1NM1/μi(s).
M1/μi(s)=β2kβ20kxβ21es/xdx.
M1/μi(s)=β2k(1β2)/2s(β21)/2es/2kW1β/22,β/22(s/k).
PRRF=LPTRF=(λRFGl4πdRF)2PTRF.
μRFT=μeqFN,
μRFR=LμRFT.
μRFR,th=2(M1)3(erfc1(SER2))2.
Pout,end,n=Pr(μRFR<μRFR,th)=Pr(LμRFT<μRFR,th)=Pr(LμeqFN<μRFR,th)=Pr(μeq<FNLμRFR,th)=Pout,N,n(FNLμRFR,th).
Pout,end=1Sn=0S1Pout,end,n.