Abstract

This paper presents a new ray tracing method, which contains a whole set of mathematic models, and its validity is verified by simulations. In addition, both theoretical analysis and simulation results show that the computational complexity of the method is much lower than that of previous ones. Therefore, the method can be used to rapidly calculate the impulse response of wireless optical channels for complicated systems.

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References

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  1. Wikipedia. “Ray_tracing_(physics)”. http://en.wikipedia.org/wiki/Ray_tracing_(physics) .
  2. F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, “Ray tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels,” Opt. Eng. 39(10), 1510–1512 (2000).
    [CrossRef]
  3. 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]
  4. O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
    [CrossRef]
  5. S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
    [CrossRef]
  6. D. Takase, and T. Ohtsuki, “Optical wireless MIMO communications (OMIMO),” in Proceedings of IEEE Grobal Telecommunications Conference (Institute of Electrical and Electronics Engineers, Dallas, 2004), pp. 928–932.
  7. D. Takase and T. Ohtsuki, “Spatial multiplexing in optical wireless MIMO communications over indoor environment,” IEICE Trans. E 89-B(4), 1364–1371 (2006).
    [CrossRef]

2006 (1)

D. Takase and T. Ohtsuki, “Spatial multiplexing in optical wireless MIMO communications over indoor environment,” IEICE Trans. E 89-B(4), 1364–1371 (2006).
[CrossRef]

2005 (1)

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[CrossRef]

2002 (1)

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

2000 (1)

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, “Ray tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels,” Opt. Eng. 39(10), 1510–1512 (2000).
[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]

Ayala, A.

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[CrossRef]

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

Barry, J. R.

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]

González, O.

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[CrossRef]

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

Kahn, J. M.

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]

Krause, W. J.

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]

López-Hernández, F. J.

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, “Ray tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels,” Opt. Eng. 39(10), 1510–1512 (2000).
[CrossRef]

Mendoza, B. R.

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[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]

Ohtsuki, T.

D. Takase and T. Ohtsuki, “Spatial multiplexing in optical wireless MIMO communications over indoor environment,” IEICE Trans. E 89-B(4), 1364–1371 (2006).
[CrossRef]

Perez-Jimenez, R.

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[CrossRef]

Pérez-Jiménez, R.

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, “Ray tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels,” Opt. Eng. 39(10), 1510–1512 (2000).
[CrossRef]

Rodriguez, S.

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[CrossRef]

Rodríguez, S.

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

Santamaría, A.

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, “Ray tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels,” Opt. Eng. 39(10), 1510–1512 (2000).
[CrossRef]

Takase, D.

D. Takase and T. Ohtsuki, “Spatial multiplexing in optical wireless MIMO communications over indoor environment,” IEICE Trans. E 89-B(4), 1364–1371 (2006).
[CrossRef]

IEEE J. Sel. Areas Comm. (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]

IEEE Trans. Commun. (1)

O. González, S. Rodriguez, R. Perez-Jimenez, B. R. Mendoza, and A. Ayala, “Error Analysis of the Simulated Impulse Response on Indoor Wireless Optical Channels Using a Monte Carlo-Based Ray-Tracing Algorithm,” IEEE Trans. Commun. 53(1), 124–130 (2005).
[CrossRef]

IEICE Trans. (1)

D. Takase and T. Ohtsuki, “Spatial multiplexing in optical wireless MIMO communications over indoor environment,” IEICE Trans. E 89-B(4), 1364–1371 (2006).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

S. Rodríguez, R. Pérez-Jiménez, F. J. López-Hernández, O. González, and A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm,” Microw. Opt. Technol. Lett. 32(4), 296–300 (2002).
[CrossRef]

Opt. Eng. (1)

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, “Ray tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels,” Opt. Eng. 39(10), 1510–1512 (2000).
[CrossRef]

Other (2)

Wikipedia. “Ray_tracing_(physics)”. http://en.wikipedia.org/wiki/Ray_tracing_(physics) .

D. Takase, and T. Ohtsuki, “Optical wireless MIMO communications (OMIMO),” in Proceedings of IEEE Grobal Telecommunications Conference (Institute of Electrical and Electronics Engineers, Dallas, 2004), pp. 928–932.

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Figures (3)

Fig. 1
Fig. 1

Impulse response obtained from MMCA and photon tracing method. (a) MMCA. (b) Photon tracing method.

Fig. 2
Fig. 2

The comparison of numbers to be traced after kth bounce.

Fig. 3
Fig. 3

The number of elementary calculations of MMCA and photons tracing method. (a) Photon tracing method. (b) Comparison of MMCA and photon tracing method.

Tables (2)

Tables Icon

Table 1 Parameters used in the simulation

Tables Icon

Table 2 Number of photons remained after kth bounce

Equations (16)

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S = { r S , n ^ S , m } ,
R = { r R , n ^ R , A R , F O V } .
h ( t ; S , R ) = h ( 0 ) ( t ; S , R ) + k = 1 h ( k ) ( t ; S , R ) ,
h ( 0 ) ( t ; S , R ) m + 1 2 π cos m ( θ ) A R d 2 cos ( ψ ) r e c t ( ψ F O V ) δ ( t d c ) ,
r e c t ( x ) = { 1 | x | 1 0 | x | > 1 .
d A = { r d A , n ^ d A , 1 } .
h d A ( 0 ) ( t ; d A , R ) M π N cos ( θ ) A R d 2 cos ( ψ ) r e c t ( ψ F O V ) δ ( t T P I d c ) ,
h i ( 0 ) ( t ; d A , R ) 1 π N cos ( θ ) A R d 2 cos ( ψ ) r e c t ( ψ F O V ) δ ( t T P I d c ) .
h ( k ) ( t ; S , R ) = i P ( k ) h i ( 0 ) ( t ; d A , R ) ,
C i k = { T i k , E i k } ,
C i k ( t ) = E i k δ ( t T i k ) .
p ˜ j = 1 T t s ( j 1 ) T t s j T t s i k C i k ( t ) d t = 1 T t s i k E i k ( j 1 ) T t s j T t s δ ( t T i k ) d t ,
( j 1 ) T t s j T t s δ ( t T i k ) d t = { 1 for T i k [ ( j 1 ) T t s , j T t s ) 0 for T i k [ ( j 1 ) T t s , j T t s ) .
N t = k = 0 + ρ ˜ k N = N 1 ρ ˜ .
N t = k = 0 K ρ ˜ k N = N 1 ρ ˜ K + 1 1 ρ ˜ .
k ˜ = N t N = 1 ρ ˜ K + 1 1 ρ ˜ 1 1 ρ ˜ .

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