Abstract

Optical space code-division multiple access is a scheme to multiplex and link data between two-dimensional processors such as smart pixels and spatial light modulators or arrays of optical sources like vertical-cavity surface-emitting lasers. We examine the multiplexing characteristics of optical space code-division multiple access by using optical orthogonal signature patterns. The probability density function of interference noise in interfering optical orthogonal signature patterns is calculated. The bit-error rate is derived from the result and plotted as a function of receiver threshold, code length, code weight, and number of users. Furthermore, we propose a prethresholding method to suppress the interference noise, and we experimentally verify that the method works effectively in improving system performance.

© 1998 Optical Society of America

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References

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  1. P. Prucnal, M. A. Santoro, T. R. Fan, “Spread spectrum fiber-optic local network using optical processing,” J. Lightwave Technol. 4, 547–554 (1986).
    [CrossRef]
  2. S. Tamura, S. Nakano, K. Okazaki, “Optical code-multiplex transmission by gold sequences,” J. Lightwave Technol. 3, 121–127 (1985).
    [CrossRef]
  3. J. A. Salehi, “Emerging optical code-division multiple access communications systems,” IEEE Network 3(2), 31–39 (1993).
  4. P. E. Green, Fiber Optic Networks (Prentice-Hall, New Jersey, 1993), Chap. 13.
  5. K. Kitayama, “Novel spatial spread spectrum based fiber optic CDMA networks for image transmission,” IEEE J. Sel. Areas Commun. 12, 762–772 (1994).
    [CrossRef]
  6. K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
    [CrossRef]
  7. M. Nakamura, K. Kitayama, Y. Igasaki, K. Kaneda, “Four multiplexed, 8 × 8-bit 2-D parallel transmission based upon space-CDMA,” in Massively Parallel Processing Using Optical Interconnections (MPPOI’96), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (NEC Research Institute, Princeton, N.J., 1996).
  8. M. Ishikawa, “Optoelectronic parallel computing system with reconfigurable optical interconnection,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Vol. CR62 of SPIE Critical Reviews Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1996), pp. 156–175.
  9. J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part I: fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
    [CrossRef]
  10. J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part II: systems performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
    [CrossRef]
  11. H. Toyoda, M. Ishikawa, “Learning and recall algorithm for optical associative memory using a bistable spatial light modulator,” Appl. Opt. 34, 3145–3151 (1995).
    [CrossRef] [PubMed]
  12. G. Yang, W. C. Kwong, “Two-dimensional spatial signature patterns,” IEEE Trans. Commun. 44, 184–191 (1996).
    [CrossRef]

1997 (1)

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

1996 (1)

G. Yang, W. C. Kwong, “Two-dimensional spatial signature patterns,” IEEE Trans. Commun. 44, 184–191 (1996).
[CrossRef]

1995 (1)

1994 (1)

K. Kitayama, “Novel spatial spread spectrum based fiber optic CDMA networks for image transmission,” IEEE J. Sel. Areas Commun. 12, 762–772 (1994).
[CrossRef]

1993 (1)

J. A. Salehi, “Emerging optical code-division multiple access communications systems,” IEEE Network 3(2), 31–39 (1993).

1989 (2)

J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part I: fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[CrossRef]

J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part II: systems performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

1986 (1)

P. Prucnal, M. A. Santoro, T. R. Fan, “Spread spectrum fiber-optic local network using optical processing,” J. Lightwave Technol. 4, 547–554 (1986).
[CrossRef]

1985 (1)

S. Tamura, S. Nakano, K. Okazaki, “Optical code-multiplex transmission by gold sequences,” J. Lightwave Technol. 3, 121–127 (1985).
[CrossRef]

Fan, T. R.

P. Prucnal, M. A. Santoro, T. R. Fan, “Spread spectrum fiber-optic local network using optical processing,” J. Lightwave Technol. 4, 547–554 (1986).
[CrossRef]

Green, P. E.

P. E. Green, Fiber Optic Networks (Prentice-Hall, New Jersey, 1993), Chap. 13.

Igasaki, Y.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

M. Nakamura, K. Kitayama, Y. Igasaki, K. Kaneda, “Four multiplexed, 8 × 8-bit 2-D parallel transmission based upon space-CDMA,” in Massively Parallel Processing Using Optical Interconnections (MPPOI’96), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (NEC Research Institute, Princeton, N.J., 1996).

Ishikawa, M.

H. Toyoda, M. Ishikawa, “Learning and recall algorithm for optical associative memory using a bistable spatial light modulator,” Appl. Opt. 34, 3145–3151 (1995).
[CrossRef] [PubMed]

M. Ishikawa, “Optoelectronic parallel computing system with reconfigurable optical interconnection,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Vol. CR62 of SPIE Critical Reviews Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1996), pp. 156–175.

Kaneda, K.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

M. Nakamura, K. Kitayama, Y. Igasaki, K. Kaneda, “Four multiplexed, 8 × 8-bit 2-D parallel transmission based upon space-CDMA,” in Massively Parallel Processing Using Optical Interconnections (MPPOI’96), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (NEC Research Institute, Princeton, N.J., 1996).

Kitayama, K.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

K. Kitayama, “Novel spatial spread spectrum based fiber optic CDMA networks for image transmission,” IEEE J. Sel. Areas Commun. 12, 762–772 (1994).
[CrossRef]

M. Nakamura, K. Kitayama, Y. Igasaki, K. Kaneda, “Four multiplexed, 8 × 8-bit 2-D parallel transmission based upon space-CDMA,” in Massively Parallel Processing Using Optical Interconnections (MPPOI’96), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (NEC Research Institute, Princeton, N.J., 1996).

Kwong, W. C.

G. Yang, W. C. Kwong, “Two-dimensional spatial signature patterns,” IEEE Trans. Commun. 44, 184–191 (1996).
[CrossRef]

Nakamura, M.

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

M. Nakamura, K. Kitayama, Y. Igasaki, K. Kaneda, “Four multiplexed, 8 × 8-bit 2-D parallel transmission based upon space-CDMA,” in Massively Parallel Processing Using Optical Interconnections (MPPOI’96), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (NEC Research Institute, Princeton, N.J., 1996).

Nakano, S.

S. Tamura, S. Nakano, K. Okazaki, “Optical code-multiplex transmission by gold sequences,” J. Lightwave Technol. 3, 121–127 (1985).
[CrossRef]

Okazaki, K.

S. Tamura, S. Nakano, K. Okazaki, “Optical code-multiplex transmission by gold sequences,” J. Lightwave Technol. 3, 121–127 (1985).
[CrossRef]

Prucnal, P.

P. Prucnal, M. A. Santoro, T. R. Fan, “Spread spectrum fiber-optic local network using optical processing,” J. Lightwave Technol. 4, 547–554 (1986).
[CrossRef]

Salehi, J. A.

J. A. Salehi, “Emerging optical code-division multiple access communications systems,” IEEE Network 3(2), 31–39 (1993).

J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part II: systems performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part I: fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[CrossRef]

Santoro, M. A.

P. Prucnal, M. A. Santoro, T. R. Fan, “Spread spectrum fiber-optic local network using optical processing,” J. Lightwave Technol. 4, 547–554 (1986).
[CrossRef]

Tamura, S.

S. Tamura, S. Nakano, K. Okazaki, “Optical code-multiplex transmission by gold sequences,” J. Lightwave Technol. 3, 121–127 (1985).
[CrossRef]

Toyoda, H.

Yang, G.

G. Yang, W. C. Kwong, “Two-dimensional spatial signature patterns,” IEEE Trans. Commun. 44, 184–191 (1996).
[CrossRef]

Appl. Opt. (1)

IEEE J. Sel. Areas Commun. (1)

K. Kitayama, “Novel spatial spread spectrum based fiber optic CDMA networks for image transmission,” IEEE J. Sel. Areas Commun. 12, 762–772 (1994).
[CrossRef]

IEEE Network (1)

J. A. Salehi, “Emerging optical code-division multiple access communications systems,” IEEE Network 3(2), 31–39 (1993).

IEEE Trans. Commun. (3)

G. Yang, W. C. Kwong, “Two-dimensional spatial signature patterns,” IEEE Trans. Commun. 44, 184–191 (1996).
[CrossRef]

J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part I: fundamental principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[CrossRef]

J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—part II: systems performance analysis,” IEEE Trans. Commun. 37, 834–842 (1989).
[CrossRef]

J. Lightwave Technol. (3)

P. Prucnal, M. A. Santoro, T. R. Fan, “Spread spectrum fiber-optic local network using optical processing,” J. Lightwave Technol. 4, 547–554 (1986).
[CrossRef]

S. Tamura, S. Nakano, K. Okazaki, “Optical code-multiplex transmission by gold sequences,” J. Lightwave Technol. 3, 121–127 (1985).
[CrossRef]

K. Kitayama, M. Nakamura, Y. Igasaki, K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202–212 (1997).
[CrossRef]

Other (3)

M. Nakamura, K. Kitayama, Y. Igasaki, K. Kaneda, “Four multiplexed, 8 × 8-bit 2-D parallel transmission based upon space-CDMA,” in Massively Parallel Processing Using Optical Interconnections (MPPOI’96), J. Goodman, S. Hinton, T. Pinkston, E. Schenfeld, eds. (NEC Research Institute, Princeton, N.J., 1996).

M. Ishikawa, “Optoelectronic parallel computing system with reconfigurable optical interconnection,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Vol. CR62 of SPIE Critical Reviews Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1996), pp. 156–175.

P. E. Green, Fiber Optic Networks (Prentice-Hall, New Jersey, 1993), Chap. 13.

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Figures (15)

Fig. 1
Fig. 1

Block diagram of the space-CDMA system.

Fig. 2
Fig. 2

(a) Examples of 5 × 5 OOSP’s that have a weight of three. (b) Mutual orthogonality between OOSP 1 and OOSP 2.

Fig. 3
Fig. 3

Upper bound on the BER versus the threshold for N = 10, w = 5, and M = 16, 32, 64.

Fig. 4
Fig. 4

Upper bound on the BER versus the threshold for N = 10, M = 32, and w = 3, 5, 7, 9.

Fig. 5
Fig. 5

Upper bound on the BER versus the number of users for M = 32, w = 5, and Th = 1, 3, 5.

Fig. 6
Fig. 6

(a) PDF of the detected power. (b) PDF of the detected power in the special case of N - 1 < w.

Fig. 7
Fig. 7

(a) Multiplexed image of three OOSP’s (2, 3, and 4). (b) Intensity distribution of the multiplexed image. (c) Distribution correlated with OOSP 1.

Fig. 8
Fig. 8

Upper bound on the BER versus the threshold with and without prethresholding for N = 10, w = 5, and M = 16, 32, 64.

Fig. 9
Fig. 9

Upper bound on the BER versus the threshold with and without prethresholding for N = 10, M = 32, and w = 3, 5, 7, 9.

Fig. 10
Fig. 10

Upper bound on the BER versus the number of users with and without prethresholding for M = 32, w = 5, and Th = 1, 3, 5.

Fig. 11
Fig. 11

Experimental setup of the space-CDMA system. FOP, fiber-optic plate.

Fig. 12
Fig. 12

Bit planes to be multiplexed.

Fig. 13
Fig. 13

Encoded and multiplexed bit planes after propagation through an image fiber.

Fig. 14
Fig. 14

(a) Correlation output with OOSP 1. (b) Normalized intensity of the correlation output. (c) Prethresholded result.

Fig. 15
Fig. 15

Maximum number of users with the restriction of BER < 10-9.

Tables (1)

Tables Icon

Table 1 Specifications of the Image Fiber

Equations (26)

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i = 1 M j = 1 M   e i ,   j q e i + k ,   j + l q =   w q δ A   for   k = l = 0 for   1 k ,   l M - 1 ,
i = 1 M j = 1 M   e i ,   j q e i + k ,   j + l q δ C     for   q q ,   0 k ,   l M - 1 ,
E ( q ) = e 11 ( q ) e 1 M ( q ) e M 1 ( q ) e MM ( q ) .
N M 2 - 1 w w - 1 .
P u u = 1 - w 2 2 M 2   δ u + w 2 2 M 2   δ u - 1 ,
m u = m ij ,
σ ij 2 < σ u 2 .
I 1 = n = 2 N   I n 1 ,
P I 1 I 1 = i = 0 N - 1 N - 1 C i w 2 2 M 2 i 1 - w 2 2 M 2 N - 1 - i   δ I 1 - i .
m I 1 = N - 1 w 2 2 M 2 ,
σ I 1 2 = N - 1 w 2 2 M 2 1 - w 2 2 M 2 .
BER = 1 2 Th   P I 1 d I 1 ,
BER < 1 2 Th   P I 1 I 1 d I 1 ,
BER < 1 2 i = Th N - 1 N - 1 C i w 2 2 M 2 i 1 - w 2 2 M 2 N - 1 - i .
P I 1 I 1 i = 1 N - 1 w C i m = 1 i 1 - q c N - m δ I 1 - i ,
BER < 1 2 i = Th w w C i m = 1 i 1 - q c N - m .
w 1 2 + 4 M 2 + N - 4 4 N 1 / 2 ,
BER < 1 2 i = w N - 1 N - 1 C i w 2 2 M 2 1 - w 2 2 M 2 N - 1 - i , without   prethresholding ,
BER < 1 2 m = 1 w 1 - 1 - w 2 M 2 N - m , with   prethresholding .
Pr I 1 = 0 =   w C 0 1 - w 2 2 M 2 N - 1 .
Pr p 1 = 1 = 1 - q c N - 1 ,
q c = 1 - w 2 M 2 .
Pr I 1 = 1     w C 1 1 - q c N - 1 .
Pr I 1 = 2     w C 2 1 - q c N - 1 1 - q c N - 2 .
Pr I 1 = i     w C i m = 1 1 1 - q c N - m ,     1 i w .
P I 1 I 1 i = 1 N - 1 w C i m = 1 i 1 - q c N - m δ I 1 - i .

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