Abstract

In this paper a new hybrid wireless access system incorporating high bandwidth line-of-sight free space optical wireless and radio frequency localization is proposed and demonstrated. This system is capable of supporting several gigabits/second up-stream and down-stream data transmission and ideally suited for high bandwidth indoor applications such as personal area networks. A radio frequency signal is used to achieve localization of subscribers, offering limited mobility to subscribers within a practical office scenario. Even with the modest transmitted power of 5dBm, we demonstrate satisfactory performance of bit error rates better than 10−9 over the entire room in the presence of strong background light. Using simulations, the effectiveness of the proposed system architecture is investigated and the key performance trade-offs identified. Proof-of-concept experiments have also been carried out to validate simulation model, and initial experimental results successfully demonstrate the feasibility of the system capable of supporting 2.5Gbps over a 1-2m optical wireless link (limited by the length of the sliding rail used in the experiment) with a 45 degrees diffused beam in an indoor environment for the first time.

© 2010 OSA

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2009 (3)

F. Alsaadi and J. M. H. Elmirghani, “Performance evaluation of 2.5 Gbit/s and 5 Gbit/s optical wireless systems employing a two dimensional adaptive beam clustering method and imaging diversity detection,” IEEE J. Sel. Areas Comm. 27(8), 1507–1519 (2009).
[CrossRef]

F. Khozeimeh and S. Hranilovic, “Dynamic spot diffusing configuration for indoor optical wireless access,” IEEE Trans. Commun. 57(6), 1765–1775 (2009).
[CrossRef]

F. Alsaadi and J. M. H. Elmirghani, “Adaptive mobile line strip multibeam MC-CDMA optical wireless system employing imaging detection in a real indoor environment,” IEEE J. Sel. Areas Comm. 27(9), 1663–1675 (2009).
[CrossRef]

2007 (1)

C.-C. Lim, Y. Wan, B.-P. Ng, and C.-M. S. See, “A real-time indoor WiFi localization system using smart antennas,” IEEE Trans. Consum. Electron. 53(2), 618–622 (2007).
[CrossRef]

2005 (1)

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Performance comparison of LSMS and conventional diffuse and hybrid optical wireless techniques in a real indoor environment,” IEE Proc., Optoelectron. 152(4), 230–238 (2005).
[CrossRef]

2004 (2)

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Spot diffusing technique and angle diversity performance for high speed indoor diffuse infra-red wireless transmission,” IEE Proc., Optoelectron. 151(1), 46–52 (2004).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Line strip spot-diffusing transmitter configuration for optical wireless systems influenced by background noise and multipath dispersion,” IEEE Trans. Commun. 52(1), 37–45 (2004).
[CrossRef]

2000 (3)

J. B. Carruther and J. M. Kahn, “Angle diversity for nondirected wireless infrared communication,” IEEE Trans. Commun. 48(6), 960–969 (2000).
[CrossRef]

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multibeam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

S. T. Jovkova and M. Kavehard, “Multispot diffusing configuration for wireless infrared access,” IEEE Trans. Commun. 48(6), 970–978 (2000).
[CrossRef]

1999 (2)

J. Bellon, M. J. N. Sibley, D. R. Wisely, and S. D. Greaves, “Hub architecture for infra-red wireless networks in office environments,” IEE Proc., Optoelectron. 146(2), 78–82 (1999).
[CrossRef]

T. Ozugur, J. A. Copeland, M. Naghshineh, and P. Kermani, “Next-generation indoor infrared LANs: issues and approaches,” IEEE Personal Commun. 6(6), 6–19 (1999).
[CrossRef]

1998 (1)

H.-H. Chan, K. L. Sterckx, J. M. H. Elmirghani, and R. A. Cryan, “Performance of optical wireless OOK and PPM systems under the constraints of ambient noise and multipath dispersion,” IEEE Commun. Mag. 36(12), 83–87 (1998).
[CrossRef]

1997 (2)

B. Crow, T. Widjaja, J. Kim, and P. Sakai, “IEEE 802.11 wireless local area networks,” IEEE Commun. Mag. 35(9), 116–126 (1997).
[CrossRef]

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

1994 (1)

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

1993 (1)

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

1989 (1)

B. Leskovar, “Optical receivers for wide band data transmission systems,” IEEE Trans. Nucl. Sci. 36(1), 787–793 (1989).
[CrossRef]

1979 (1)

F. R. Gfeller and U. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” Proc. IEEE 67(11), 1474–1486 (1979).
[CrossRef]

Al-Ghamdi, A. G.

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Performance comparison of LSMS and conventional diffuse and hybrid optical wireless techniques in a real indoor environment,” IEE Proc., Optoelectron. 152(4), 230–238 (2005).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Spot diffusing technique and angle diversity performance for high speed indoor diffuse infra-red wireless transmission,” IEE Proc., Optoelectron. 151(1), 46–52 (2004).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Line strip spot-diffusing transmitter configuration for optical wireless systems influenced by background noise and multipath dispersion,” IEEE Trans. Commun. 52(1), 37–45 (2004).
[CrossRef]

Alsaadi, F.

F. Alsaadi and J. M. H. Elmirghani, “Performance evaluation of 2.5 Gbit/s and 5 Gbit/s optical wireless systems employing a two dimensional adaptive beam clustering method and imaging diversity detection,” IEEE J. Sel. Areas Comm. 27(8), 1507–1519 (2009).
[CrossRef]

F. Alsaadi and J. M. H. Elmirghani, “Adaptive mobile line strip multibeam MC-CDMA optical wireless system employing imaging detection in a real indoor environment,” IEEE J. Sel. Areas Comm. 27(9), 1663–1675 (2009).
[CrossRef]

Audeh, M. D.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

Bapst, U.

F. R. Gfeller and U. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” Proc. IEEE 67(11), 1474–1486 (1979).
[CrossRef]

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

Bellon, J.

J. Bellon, M. J. N. Sibley, D. R. Wisely, and S. D. Greaves, “Hub architecture for infra-red wireless networks in office environments,” IEE Proc., Optoelectron. 146(2), 78–82 (1999).
[CrossRef]

Carruther, J. B.

J. B. Carruther and J. M. Kahn, “Angle diversity for nondirected wireless infrared communication,” IEEE Trans. Commun. 48(6), 960–969 (2000).
[CrossRef]

Carruthers, J. B.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

Chan, H.-H.

H.-H. Chan, K. L. Sterckx, J. M. H. Elmirghani, and R. A. Cryan, “Performance of optical wireless OOK and PPM systems under the constraints of ambient noise and multipath dispersion,” IEEE Commun. Mag. 36(12), 83–87 (1998).
[CrossRef]

Copeland, J. A.

T. Ozugur, J. A. Copeland, M. Naghshineh, and P. Kermani, “Next-generation indoor infrared LANs: issues and approaches,” IEEE Personal Commun. 6(6), 6–19 (1999).
[CrossRef]

Crow, B.

B. Crow, T. Widjaja, J. Kim, and P. Sakai, “IEEE 802.11 wireless local area networks,” IEEE Commun. Mag. 35(9), 116–126 (1997).
[CrossRef]

Cryan, R. A.

H.-H. Chan, K. L. Sterckx, J. M. H. Elmirghani, and R. A. Cryan, “Performance of optical wireless OOK and PPM systems under the constraints of ambient noise and multipath dispersion,” IEEE Commun. Mag. 36(12), 83–87 (1998).
[CrossRef]

Djahani, P.

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multibeam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

Elmirghani, J. M. H.

F. Alsaadi and J. M. H. Elmirghani, “Adaptive mobile line strip multibeam MC-CDMA optical wireless system employing imaging detection in a real indoor environment,” IEEE J. Sel. Areas Comm. 27(9), 1663–1675 (2009).
[CrossRef]

F. Alsaadi and J. M. H. Elmirghani, “Performance evaluation of 2.5 Gbit/s and 5 Gbit/s optical wireless systems employing a two dimensional adaptive beam clustering method and imaging diversity detection,” IEEE J. Sel. Areas Comm. 27(8), 1507–1519 (2009).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Performance comparison of LSMS and conventional diffuse and hybrid optical wireless techniques in a real indoor environment,” IEE Proc., Optoelectron. 152(4), 230–238 (2005).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Line strip spot-diffusing transmitter configuration for optical wireless systems influenced by background noise and multipath dispersion,” IEEE Trans. Commun. 52(1), 37–45 (2004).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Spot diffusing technique and angle diversity performance for high speed indoor diffuse infra-red wireless transmission,” IEE Proc., Optoelectron. 151(1), 46–52 (2004).
[CrossRef]

H.-H. Chan, K. L. Sterckx, J. M. H. Elmirghani, and R. A. Cryan, “Performance of optical wireless OOK and PPM systems under the constraints of ambient noise and multipath dispersion,” IEEE Commun. Mag. 36(12), 83–87 (1998).
[CrossRef]

Gfeller, F. R.

F. R. Gfeller and U. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” Proc. IEEE 67(11), 1474–1486 (1979).
[CrossRef]

Greaves, S. D.

J. Bellon, M. J. N. Sibley, D. R. Wisely, and S. D. Greaves, “Hub architecture for infra-red wireless networks in office environments,” IEE Proc., Optoelectron. 146(2), 78–82 (1999).
[CrossRef]

Hranilovic, S.

F. Khozeimeh and S. Hranilovic, “Dynamic spot diffusing configuration for indoor optical wireless access,” IEEE Trans. Commun. 57(6), 1765–1775 (2009).
[CrossRef]

Jovkova, S. T.

S. T. Jovkova and M. Kavehard, “Multispot diffusing configuration for wireless infrared access,” IEEE Trans. Commun. 48(6), 970–978 (2000).
[CrossRef]

Kahn, J. M.

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multibeam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

J. B. Carruther and J. M. Kahn, “Angle diversity for nondirected wireless infrared communication,” IEEE Trans. Commun. 48(6), 960–969 (2000).
[CrossRef]

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

Kavehard, M.

S. T. Jovkova and M. Kavehard, “Multispot diffusing configuration for wireless infrared access,” IEEE Trans. Commun. 48(6), 970–978 (2000).
[CrossRef]

Kermani, P.

T. Ozugur, J. A. Copeland, M. Naghshineh, and P. Kermani, “Next-generation indoor infrared LANs: issues and approaches,” IEEE Personal Commun. 6(6), 6–19 (1999).
[CrossRef]

Khozeimeh, F.

F. Khozeimeh and S. Hranilovic, “Dynamic spot diffusing configuration for indoor optical wireless access,” IEEE Trans. Commun. 57(6), 1765–1775 (2009).
[CrossRef]

Kim, J.

B. Crow, T. Widjaja, J. Kim, and P. Sakai, “IEEE 802.11 wireless local area networks,” IEEE Commun. Mag. 35(9), 116–126 (1997).
[CrossRef]

Krause, W. J.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

Lee, E. A.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

Leskovar, B.

B. Leskovar, “Optical receivers for wide band data transmission systems,” IEEE Trans. Nucl. Sci. 36(1), 787–793 (1989).
[CrossRef]

Lim, C.-C.

C.-C. Lim, Y. Wan, B.-P. Ng, and C.-M. S. See, “A real-time indoor WiFi localization system using smart antennas,” IEEE Trans. Consum. Electron. 53(2), 618–622 (2007).
[CrossRef]

Marsh, G. W.

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

Messerschmitt, D. G.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

Naghshineh, M.

T. Ozugur, J. A. Copeland, M. Naghshineh, and P. Kermani, “Next-generation indoor infrared LANs: issues and approaches,” IEEE Personal Commun. 6(6), 6–19 (1999).
[CrossRef]

Ng, B.-P.

C.-C. Lim, Y. Wan, B.-P. Ng, and C.-M. S. See, “A real-time indoor WiFi localization system using smart antennas,” IEEE Trans. Consum. Electron. 53(2), 618–622 (2007).
[CrossRef]

Ozugur, T.

T. Ozugur, J. A. Copeland, M. Naghshineh, and P. Kermani, “Next-generation indoor infrared LANs: issues and approaches,” IEEE Personal Commun. 6(6), 6–19 (1999).
[CrossRef]

Sakai, P.

B. Crow, T. Widjaja, J. Kim, and P. Sakai, “IEEE 802.11 wireless local area networks,” IEEE Commun. Mag. 35(9), 116–126 (1997).
[CrossRef]

See, C.-M. S.

C.-C. Lim, Y. Wan, B.-P. Ng, and C.-M. S. See, “A real-time indoor WiFi localization system using smart antennas,” IEEE Trans. Consum. Electron. 53(2), 618–622 (2007).
[CrossRef]

Sibley, M. J. N.

J. Bellon, M. J. N. Sibley, D. R. Wisely, and S. D. Greaves, “Hub architecture for infra-red wireless networks in office environments,” IEE Proc., Optoelectron. 146(2), 78–82 (1999).
[CrossRef]

Sterckx, K. L.

H.-H. Chan, K. L. Sterckx, J. M. H. Elmirghani, and R. A. Cryan, “Performance of optical wireless OOK and PPM systems under the constraints of ambient noise and multipath dispersion,” IEEE Commun. Mag. 36(12), 83–87 (1998).
[CrossRef]

Wan, Y.

C.-C. Lim, Y. Wan, B.-P. Ng, and C.-M. S. See, “A real-time indoor WiFi localization system using smart antennas,” IEEE Trans. Consum. Electron. 53(2), 618–622 (2007).
[CrossRef]

Widjaja, T.

B. Crow, T. Widjaja, J. Kim, and P. Sakai, “IEEE 802.11 wireless local area networks,” IEEE Commun. Mag. 35(9), 116–126 (1997).
[CrossRef]

Wisely, D. R.

J. Bellon, M. J. N. Sibley, D. R. Wisely, and S. D. Greaves, “Hub architecture for infra-red wireless networks in office environments,” IEE Proc., Optoelectron. 146(2), 78–82 (1999).
[CrossRef]

IEE Proc., Optoelectron. (3)

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Spot diffusing technique and angle diversity performance for high speed indoor diffuse infra-red wireless transmission,” IEE Proc., Optoelectron. 151(1), 46–52 (2004).
[CrossRef]

A. G. Al-Ghamdi and J. M. H. Elmirghani, “Performance comparison of LSMS and conventional diffuse and hybrid optical wireless techniques in a real indoor environment,” IEE Proc., Optoelectron. 152(4), 230–238 (2005).
[CrossRef]

J. Bellon, M. J. N. Sibley, D. R. Wisely, and S. D. Greaves, “Hub architecture for infra-red wireless networks in office environments,” IEE Proc., Optoelectron. 146(2), 78–82 (1999).
[CrossRef]

IEEE Commun. Mag. (2)

H.-H. Chan, K. L. Sterckx, J. M. H. Elmirghani, and R. A. Cryan, “Performance of optical wireless OOK and PPM systems under the constraints of ambient noise and multipath dispersion,” IEEE Commun. Mag. 36(12), 83–87 (1998).
[CrossRef]

B. Crow, T. Widjaja, J. Kim, and P. Sakai, “IEEE 802.11 wireless local area networks,” IEEE Commun. Mag. 35(9), 116–126 (1997).
[CrossRef]

IEEE J. Sel. Areas Comm. (3)

F. Alsaadi and J. M. H. Elmirghani, “Performance evaluation of 2.5 Gbit/s and 5 Gbit/s optical wireless systems employing a two dimensional adaptive beam clustering method and imaging diversity detection,” IEEE J. Sel. Areas Comm. 27(8), 1507–1519 (2009).
[CrossRef]

F. Alsaadi and J. M. H. Elmirghani, “Adaptive mobile line strip multibeam MC-CDMA optical wireless system employing imaging detection in a real indoor environment,” IEEE J. Sel. Areas Comm. 27(9), 1663–1675 (2009).
[CrossRef]

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Comm. 11(3), 367–379 (1993).
[CrossRef]

IEEE Personal Commun. (2)

J. M. Kahn, J. R. Barry, M. D. Audeh, J. B. Carruthers, W. J. Krause, and G. W. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Commun. 1(2), 12–25 (1994).
[CrossRef]

T. Ozugur, J. A. Copeland, M. Naghshineh, and P. Kermani, “Next-generation indoor infrared LANs: issues and approaches,” IEEE Personal Commun. 6(6), 6–19 (1999).
[CrossRef]

IEEE Trans. Commun. (5)

F. Khozeimeh and S. Hranilovic, “Dynamic spot diffusing configuration for indoor optical wireless access,” IEEE Trans. Commun. 57(6), 1765–1775 (2009).
[CrossRef]

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Figures (21)

Fig. 1
Fig. 1

Room configuration (four of the eight cubicles shown here).

Fig. 2
Fig. 2

Optical fiber distribution network.

Fig. 3
Fig. 3

Location of fiber ends and cells.

Fig. 4
Fig. 4

Fiber transmitter structure.

Fig. 5
Fig. 5

Gaussian beam transmission.

Fig. 6
Fig. 6

Angles between cell center and transmitter.

Fig. 7
Fig. 7

Received background light power.

Fig. 8
Fig. 8

Noise variance.

Fig. 9
Fig. 9

Impulse response.

Fig. 10
Fig. 10

1Gbps system performances. (a) SNR performance. (b) BER performance.

Fig. 11
Fig. 11

2.5Gbps system performances. (a).SNR performance. (b) BER performance.

Fig. 12
Fig. 12

Required transmitted power for different bit rates.

Fig. 13
Fig. 13

Structure of the transmitter for up-stream transmission.

Fig. 14
Fig. 14

Structure of transceiver at the ceiling.

Fig. 15
Fig. 15

SNR of up-stream transmission at different transmitted powers where the beam waist is fixed at 1m and bit rate is fixed at 400Mbps.

Fig. 16
Fig. 16

SNR of up-stream transmission under different bit rates where the beam waist is fixed at 1m and the transmission power is fixed at 5mW.

Fig. 17
Fig. 17

SNR of up-stream transmission with different beam waists where the bit rate is fixed at 200Mbps and the transmission power is fixed at 5mW.

Fig. 18
Fig. 18

Experimental setup.

Fig. 19
Fig. 19

1Gbps system experimental results.

Fig. 20
Fig. 20

Tradeoff in 1Gbps OW system. (a). BER at beam boundaries with respect to different transmission powers. (b). Minimum transmission power needed with respect to beam waists.

Fig. 21
Fig. 21

2.5Gbps system BER with respect to the distance from beam center.

Equations (20)

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I ( φ ) = n + 1 2 π × P t × cos n ( φ ) ,
ω (z)= ω 0 [ 1 + ( λ z π ω 0 2 ) 2 ] 1 2 ,
R(z)=z [ 1 + ( π ω 0 2 λ z ) 2 ] 1 2 ,
f = π ω 0 2 λ ,
f ' = F 2 f ( l F ) 2 + f 2 ,
l ' = l ( l F ) + f 2 ( l F ) 2 + f 2 F ,
ω 0 ' = F ( l F ) 2 + f 2 ω 0 ,
ω ' ( z ) = ω 0 ' 1 + ( λ z π ω 0 ' ) 2 .
α x = tan 1 ( d x h c e i l i n g h c f ) ,
α y = tan 1 ( d y h c e i l i n g h c f ) ,
θ x = 1 2 α x ,
θ y = 1 2 α y .
σ 0 2 = σ p r 2 + σ b n 2 + σ s 0 2 ,
σ 1 2 = σ p r 2 + σ b n 2 + σ s 1 2 ,
σ 0 2 = σ 1 2 = σ 2 = σ p r 2 + σ b n 2 .
σ p r 2 = ( 4 k T R F + 2 e I L ) I 2 B + 4 k T Γ g m ( 2 π C T ) 2 A F f c B 2 + 4 k T Γ g m ( 2 π C T ) 2 I 3 B 3 ,
σ b n 2 = 2 e R P b n I 2 B ,
h ( t ) = R x ( t ) h ( t ) + n ( t ) ,
S N R = ( R × ( P s 1 P s 0 ) σ 0 + σ 1 ) 2 ,
B E R = 1 2 erfc ( S N R 2 ) .

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