Abstract

We present a comparison between the modified Monte Carlo algorithm (MMCA) and a recently proposed ray-tracing algorithm named as photon-tracing algorithm. Both methods are compared exhaustively according to error analysis and computational costs. We show that the new photon-tracing method offers a solution with a slightly greater error but requiring from considerable less computing time. Moreover, from a practical point of view, the solutions obtained with both algorithms are approximately equivalent, demonstrating the goodness of the new photon-tracing method.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Kahn, and J. R. Barry, "Wireless infrared communications," Proc. IEEE 85, 265-298 (1997).
    [CrossRef]
  2. 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]
  3. F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, "Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels," Electron. Lett. 34(19), 1819-1820 (1998).
    [CrossRef]
  4. 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), 2775-2780 (2000).
    [CrossRef]
  5. C. R. Lomba, R. T. Valadas, and A. M. de Oliveira Duarate, "Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces," IEE Proc., Optoelectron. 145, 191-197 (1998).
    [CrossRef]
  6. 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]
  7. O. González, S. Rodríguez, R. Pérez-Jiménez, 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]
  8. M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
    [CrossRef] [PubMed]

2010 (1)

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
[CrossRef] [PubMed]

2005 (1)

O. González, S. Rodríguez, R. Pérez-Jiménez, 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), 2775-2780 (2000).
[CrossRef]

1998 (2)

C. R. Lomba, R. T. Valadas, and A. M. de Oliveira Duarate, "Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces," IEE Proc., Optoelectron. 145, 191-197 (1998).
[CrossRef]

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, "Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels," Electron. Lett. 34(19), 1819-1820 (1998).
[CrossRef]

1997 (1)

J. M. Kahn, and J. R. Barry, "Wireless infrared communications," Proc. IEEE 85, 265-298 (1997).
[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. Rodríguez, R. Pérez-Jiménez, 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. M. Kahn, and J. R. Barry, "Wireless infrared communications," Proc. IEEE 85, 265-298 (1997).
[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]

de Oliveira Duarate, A. M.

C. R. Lomba, R. T. Valadas, and A. M. de Oliveira Duarate, "Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces," IEE Proc., Optoelectron. 145, 191-197 (1998).
[CrossRef]

González, O.

O. González, S. Rodríguez, R. Pérez-Jiménez, 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. M. Kahn, and J. R. Barry, "Wireless infrared communications," Proc. IEEE 85, 265-298 (1997).
[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]

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]

Lomba, C. R.

C. R. Lomba, R. T. Valadas, and A. M. de Oliveira Duarate, "Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces," IEE Proc., Optoelectron. 145, 191-197 (1998).
[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), 2775-2780 (2000).
[CrossRef]

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, "Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels," Electron. Lett. 34(19), 1819-1820 (1998).
[CrossRef]

Mendoza, B. R.

O. González, S. Rodríguez, R. Pérez-Jiménez, 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]

Pérez-Jiménez, R.

O. González, S. Rodríguez, R. Pérez-Jiménez, 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]

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), 2775-2780 (2000).
[CrossRef]

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, "Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels," Electron. Lett. 34(19), 1819-1820 (1998).
[CrossRef]

Rodríguez, S.

O. González, S. Rodríguez, R. Pérez-Jiménez, 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]

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), 2775-2780 (2000).
[CrossRef]

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, "Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels," Electron. Lett. 34(19), 1819-1820 (1998).
[CrossRef]

Valadas, R. T.

C. R. Lomba, R. T. Valadas, and A. M. de Oliveira Duarate, "Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces," IEE Proc., Optoelectron. 145, 191-197 (1998).
[CrossRef]

Yuan, X.

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
[CrossRef] [PubMed]

Zhang, J.

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
[CrossRef] [PubMed]

Zhang, M.

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
[CrossRef] [PubMed]

Zhang, Y.

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
[CrossRef] [PubMed]

Electron. Lett. (1)

F. J. López-Hernández, R. Pérez-Jiménez, and A. Santamaría, "Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels," Electron. Lett. 34(19), 1819-1820 (1998).
[CrossRef]

IEE Proc., Optoelectron. (1)

C. R. Lomba, R. T. Valadas, and A. M. de Oliveira Duarate, "Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces," IEE Proc., Optoelectron. 145, 191-197 (1998).
[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. Rodríguez, R. Pérez-Jiménez, 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]

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), 2775-2780 (2000).
[CrossRef]

Opt. Express (1)

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, "Mathematic models for a ray tracing method and its applications in wireless optical communications," Opt. Express 18(17), 18431-18437 (2010).
[CrossRef] [PubMed]

Proc. IEEE (1)

J. M. Kahn, and J. R. Barry, "Wireless infrared communications," Proc. IEEE 85, 265-298 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Geometry of emitter and receiver with reflectors. Reflection pattern of the surface is described by Phong’s model.

Fig. 2
Fig. 2

Impulse responses obtained with (a) photon-tracing (PTA) and (b) ray-tracing (MMCA) algorithms.

Fig. 3
Fig. 3

Relative error of both algorithms: PTA (blue) and MMCA (green).

Fig. 4
Fig. 4

Number of contributions (a) along the time and (b) at the kth reflection.

Tables (2)

Tables Icon

Table 1 Parameters for simulation

Tables Icon

Table 2 Comparison between PTA and MMCA

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

P R = 1 d 2 R E ( ϕ , n ) A eff ( φ )
R E ( ϕ , n ) = n + 1 2 π P E cos n ( ϕ ) , 0 ϕ π 2
A eff = A r cos φ rect ( φ FOV )
rect ( x ) = { 1 , | x | 1 0 , | x | > 1
P R = 1 d 2 R S ( θ , θ ) A eff ( φ )
R S ( θ , θ ) = ρ P i [ r d cos θ π + ( 1 r d ) m + 1 2 π cos m ( θ θ ) ]
N op PTA = N S × ( N + ρ ˜ 1 N N 1 + ρ ˜ 2 N 1 N 2 + ... + ρ ˜ K 1 N K 2 N K 1 )
N op PTA = N N S ( 1 ρ ˜ K ) 1 ρ ˜
var ( P j ) = i = 1 N j p i , j 2 1 N f , j ( i = 1 N j p i , j ) 2
P j = i = 1 N j p i , j
rel err ( P j ) = [ i = 1 N j p i , j 2 ( i = 1 N j p i , j ) 2 1 N f , j ] 1 / 2
mean relative error = j = 1 J P j × rel err ( P j ) j = 1 J P j

Metrics