Abstract

We analyze the performance of a spectrally phase-encoded optical code division multiple access slotted packet network based on a simple protocol. The steady-state throughput and average packet delay are derived as two measures to assess the performance of the network. First, only multiple access interference is considered and other sources of noise are neglected. In this context, comparing different systems with the fixed bit rate and chip duration leads us to conclude that increasing the code length improves the performance of networks with small average activity; but in highly active networks, decreasing the code length results in a significant improvement in the throughput and average packet delay. Next, Gaussian approximation is used in our performance analysis to consider both shot noise and thermal noise as well as multiple access interference. The packet success probability is derived as a function of transmitted power. It is shown that in a fixed bandwidth and with a fixed bit rate, increasing the code length can lead to better performance in high average powers. But, in the low-power regime, decreasing code length leads to better performance due to the lower level of activity.

© 2009 Optical Society of America

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  1. C. H. Lee, W. V. Sorin, B. Y. Kim, “Fiber to the home using a PON infrastructure,” J. Lightwave Technol., vol. 24, pp. 4568–4583, Dec. 2006.
    [CrossRef]
  2. B. T. Coonen, “Fiber to the home/fiber to the premises: what, where, and when?,” Proc. IEEE, vol. 94, no. 5, pp. 911–934, May 2006.
    [CrossRef]
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    [CrossRef]
  4. M. Rochette, L. A. Rusch, “Spectral efficiency of OCDMA systems with coherent pulsed sources,” J. Lightwave Technol., vol. 23, pp. 1033–1038, Mar. 2005.
    [CrossRef]
  5. J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol., vol. 8, pp. 478–491, Mar. 1990.
    [CrossRef]
  6. A. M. Weiner, Z. Jiang, D. E. Leaird, “Spectrally phase-coded O-CDMA [Invited],” J. Opt. Netw., vol. 6, no. 6, pp. 728–755, Jul. 2007.
    [CrossRef]
  7. S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
    [CrossRef]
  8. R. P. Scott, Wei Cong, V. J. Hernandez, K. Li, B. H. Kolner, J. P. Heritage, S. J. B. Yoo, “An eight-user time-slotted SPECTS O-CDMA testbed: demonstration and simulations,” J. Lightwave Technol., vol. 23, pp. 3232–3240, Oct. 2005.
    [CrossRef]
  9. J. Zhi, D. E. Leaird, A. M. Weiner, “Experimental investigation of security issues in O-CDMA,” J. Lightwave Technol., vol. 24, pp. 4228–4234, Nov. 2006.
    [CrossRef]
  10. V. J. Hernandez, W. Cong, J. Hu, C. Yang, N. K. Fontaine, R. P. Scott, Z. Ding, B. H. Kolner, J. P. Heritage, S. J. Ben Yoo, “A 320-Gb∕s capacity (32-User 10 Gb/s) SPECTS O-CDMA network testbed with enhanced spectral efficiency through forward error correction,” J. Lightwave Technol., vol. 25, pp. 79–86, Jan. 2007.
    [CrossRef]
  11. Z. Jiang, D. S. Seo, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, A. M. Weiner, “Reconfigurable all-optical code translation in spectrally phase-coded O-CDMA,” J. Lightwave Technol., vol. 23, pp. 1979–1990, June 2005.
    [CrossRef]
  12. H. M. H. Shalaby, “Optical CDMA random access protocols with and without pretransmission coordination,” J. Lightwave Technol., vol. 21, pp. 2455–2462, Nov. 2003.
    [CrossRef]
  13. G. C. Clark, J. B. Cain, Error-Correcting Coding for Digital Communications. New York, NY: Plenum, 1981.
    [CrossRef]
  14. C.-S. Hsu, V. O. K. Li, “Performance analysis of slotted fiber-optic code-division multiple-access (CDMA) packet networks,” IEEE Trans. Commun., vol. 45, pp. 819–828, July 1997.
    [CrossRef]
  15. W. Turin, Performance Analysis and Modeling of Digital Transmission Systems, 3rd ed., New York, NY: Springer, 2004.
    [CrossRef]
  16. D. Raychaudhuri, “Performance analysis of random access packet-switched code division multiple access systems,” IEEE Trans. Commun., vol. 29, pp. 895–901, June 1981.
    [CrossRef]
  17. L. Kleinrock, Queueing Systems, Vol. I: Theory. New York, NY: Wiley-Interscience, 1975.
  18. S. Khaleghi, S. Khaleghi, K. Jamshidi, “Analysis of throughput and delay in a spectrally phase-encoded optical CDMA packet network,” in Proc. IEEE Int. Conf. Wireless and Optical Commun. Networks, Singapore, Jul. 2007, pp. 1–5.
  19. S. Khaleghi, S. Khaleghi, K. Jamshidi, “Power performance analysis of spectrally phase-encoded optical CDMA packet networks,” in Proc. IEEE Int. Conf. Signal Processing and Commun., Dubai, UAE, Nov. 2007, pp. 285–288.
  20. K. Jamshidi, J. A. Salehi, “Statistical analysis of coherent ultrashort light pulse CDMA with multiple optical amplifiers using additive noise model,” J. Lightwave Technol., vol. 23, pp. 1842–1851, May 2005.
    [CrossRef]
  21. K. Jamshidi, J. A. Salehi, “Performance analysis of spectral-phase-encoded optical CDMA system using two-photon-absorption receiver structure for asynchronous and slot-level synchronous transmitters,” J. Lightwave Technol., vol. 25, pp. 1638–1645, June 2007.
    [CrossRef]

2007 (4)

2006 (3)

2005 (5)

2003 (1)

1997 (1)

C.-S. Hsu, V. O. K. Li, “Performance analysis of slotted fiber-optic code-division multiple-access (CDMA) packet networks,” IEEE Trans. Commun., vol. 45, pp. 819–828, July 1997.
[CrossRef]

1990 (1)

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol., vol. 8, pp. 478–491, Mar. 1990.
[CrossRef]

1981 (1)

D. Raychaudhuri, “Performance analysis of random access packet-switched code division multiple access systems,” IEEE Trans. Commun., vol. 29, pp. 895–901, June 1981.
[CrossRef]

’Galli, S.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Banwell, T.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Ben Yoo, S. J.

Cain, J. B.

G. C. Clark, J. B. Cain, Error-Correcting Coding for Digital Communications. New York, NY: Plenum, 1981.
[CrossRef]

Clark, G. C.

G. C. Clark, J. B. Cain, Error-Correcting Coding for Digital Communications. New York, NY: Plenum, 1981.
[CrossRef]

Cong, W.

Cong, Wei

Coonen, B. T.

B. T. Coonen, “Fiber to the home/fiber to the premises: what, where, and when?,” Proc. IEEE, vol. 94, no. 5, pp. 911–934, May 2006.
[CrossRef]

Delfyett, P.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Ding, Z.

Etemad, S.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Fejer, M. M.

Fontaine, N. K.

Heritage, J. P.

Hernandez, V. J.

Hsu, C.-S.

C.-S. Hsu, V. O. K. Li, “Performance analysis of slotted fiber-optic code-division multiple-access (CDMA) packet networks,” IEEE Trans. Commun., vol. 45, pp. 819–828, July 1997.
[CrossRef]

Hu, J.

Jackel, J.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Jamshidi, K.

K. Jamshidi, J. A. Salehi, “Performance analysis of spectral-phase-encoded optical CDMA system using two-photon-absorption receiver structure for asynchronous and slot-level synchronous transmitters,” J. Lightwave Technol., vol. 25, pp. 1638–1645, June 2007.
[CrossRef]

K. Jamshidi, J. A. Salehi, “Statistical analysis of coherent ultrashort light pulse CDMA with multiple optical amplifiers using additive noise model,” J. Lightwave Technol., vol. 23, pp. 1842–1851, May 2005.
[CrossRef]

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Power performance analysis of spectrally phase-encoded optical CDMA packet networks,” in Proc. IEEE Int. Conf. Signal Processing and Commun., Dubai, UAE, Nov. 2007, pp. 285–288.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Analysis of throughput and delay in a spectrally phase-encoded optical CDMA packet network,” in Proc. IEEE Int. Conf. Wireless and Optical Commun. Networks, Singapore, Jul. 2007, pp. 1–5.

Jiang, Z.

Khaleghi, S.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Power performance analysis of spectrally phase-encoded optical CDMA packet networks,” in Proc. IEEE Int. Conf. Signal Processing and Commun., Dubai, UAE, Nov. 2007, pp. 285–288.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Power performance analysis of spectrally phase-encoded optical CDMA packet networks,” in Proc. IEEE Int. Conf. Signal Processing and Commun., Dubai, UAE, Nov. 2007, pp. 285–288.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Analysis of throughput and delay in a spectrally phase-encoded optical CDMA packet network,” in Proc. IEEE Int. Conf. Wireless and Optical Commun. Networks, Singapore, Jul. 2007, pp. 1–5.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Analysis of throughput and delay in a spectrally phase-encoded optical CDMA packet network,” in Proc. IEEE Int. Conf. Wireless and Optical Commun. Networks, Singapore, Jul. 2007, pp. 1–5.

Kim, B. Y.

Kleinrock, L.

L. Kleinrock, Queueing Systems, Vol. I: Theory. New York, NY: Wiley-Interscience, 1975.

Kolner, B. H.

Langrock, C.

Leaird, D. E.

Lee, C. H.

Li, K.

Li, V. O. K.

C.-S. Hsu, V. O. K. Li, “Performance analysis of slotted fiber-optic code-division multiple-access (CDMA) packet networks,” IEEE Trans. Commun., vol. 45, pp. 819–828, July 1997.
[CrossRef]

Menendez, R.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Price, C.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Raychaudhuri, D.

D. Raychaudhuri, “Performance analysis of random access packet-switched code division multiple access systems,” IEEE Trans. Commun., vol. 29, pp. 895–901, June 1981.
[CrossRef]

Rochette, M.

Roussev, R. V.

Rusch, L. A.

Salehi, J. A.

Scott, R. P.

Seo, D. S.

Shalaby, H. M. H.

Sorin, W. V.

Toliver, P.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Turin, W.

W. Turin, Performance Analysis and Modeling of Digital Transmission Systems, 3rd ed., New York, NY: Springer, 2004.
[CrossRef]

Turpin, T.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Weiner, A. M.

Yang, C.

Yoo, S. J. B.

Young, J.

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

Zhi, J.

IEEE Photon. Technol. Lett. (1)

S. Etemad, P. Toliver, R. Menendez, J. Young, T. Banwell, S. ’Galli, J. Jackel, P. Delfyett, C. Price, T. Turpin, “Spectrally efficient optical CDMA using coherent phase-frequency coding,” IEEE Photon. Technol. Lett., vol. 17, pp. 929–931, Apr. 2005.
[CrossRef]

IEEE Trans. Commun. (2)

D. Raychaudhuri, “Performance analysis of random access packet-switched code division multiple access systems,” IEEE Trans. Commun., vol. 29, pp. 895–901, June 1981.
[CrossRef]

C.-S. Hsu, V. O. K. Li, “Performance analysis of slotted fiber-optic code-division multiple-access (CDMA) packet networks,” IEEE Trans. Commun., vol. 45, pp. 819–828, July 1997.
[CrossRef]

J. Lightwave Technol. (10)

K. Jamshidi, J. A. Salehi, “Statistical analysis of coherent ultrashort light pulse CDMA with multiple optical amplifiers using additive noise model,” J. Lightwave Technol., vol. 23, pp. 1842–1851, May 2005.
[CrossRef]

K. Jamshidi, J. A. Salehi, “Performance analysis of spectral-phase-encoded optical CDMA system using two-photon-absorption receiver structure for asynchronous and slot-level synchronous transmitters,” J. Lightwave Technol., vol. 25, pp. 1638–1645, June 2007.
[CrossRef]

R. P. Scott, Wei Cong, V. J. Hernandez, K. Li, B. H. Kolner, J. P. Heritage, S. J. B. Yoo, “An eight-user time-slotted SPECTS O-CDMA testbed: demonstration and simulations,” J. Lightwave Technol., vol. 23, pp. 3232–3240, Oct. 2005.
[CrossRef]

J. Zhi, D. E. Leaird, A. M. Weiner, “Experimental investigation of security issues in O-CDMA,” J. Lightwave Technol., vol. 24, pp. 4228–4234, Nov. 2006.
[CrossRef]

V. J. Hernandez, W. Cong, J. Hu, C. Yang, N. K. Fontaine, R. P. Scott, Z. Ding, B. H. Kolner, J. P. Heritage, S. J. Ben Yoo, “A 320-Gb∕s capacity (32-User 10 Gb/s) SPECTS O-CDMA network testbed with enhanced spectral efficiency through forward error correction,” J. Lightwave Technol., vol. 25, pp. 79–86, Jan. 2007.
[CrossRef]

Z. Jiang, D. S. Seo, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, A. M. Weiner, “Reconfigurable all-optical code translation in spectrally phase-coded O-CDMA,” J. Lightwave Technol., vol. 23, pp. 1979–1990, June 2005.
[CrossRef]

H. M. H. Shalaby, “Optical CDMA random access protocols with and without pretransmission coordination,” J. Lightwave Technol., vol. 21, pp. 2455–2462, Nov. 2003.
[CrossRef]

C. H. Lee, W. V. Sorin, B. Y. Kim, “Fiber to the home using a PON infrastructure,” J. Lightwave Technol., vol. 24, pp. 4568–4583, Dec. 2006.
[CrossRef]

M. Rochette, L. A. Rusch, “Spectral efficiency of OCDMA systems with coherent pulsed sources,” J. Lightwave Technol., vol. 23, pp. 1033–1038, Mar. 2005.
[CrossRef]

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol., vol. 8, pp. 478–491, Mar. 1990.
[CrossRef]

J. Opt. Netw. (2)

Proc. IEEE (1)

B. T. Coonen, “Fiber to the home/fiber to the premises: what, where, and when?,” Proc. IEEE, vol. 94, no. 5, pp. 911–934, May 2006.
[CrossRef]

Other (5)

G. C. Clark, J. B. Cain, Error-Correcting Coding for Digital Communications. New York, NY: Plenum, 1981.
[CrossRef]

W. Turin, Performance Analysis and Modeling of Digital Transmission Systems, 3rd ed., New York, NY: Springer, 2004.
[CrossRef]

L. Kleinrock, Queueing Systems, Vol. I: Theory. New York, NY: Wiley-Interscience, 1975.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Analysis of throughput and delay in a spectrally phase-encoded optical CDMA packet network,” in Proc. IEEE Int. Conf. Wireless and Optical Commun. Networks, Singapore, Jul. 2007, pp. 1–5.

S. Khaleghi, S. Khaleghi, K. Jamshidi, “Power performance analysis of spectrally phase-encoded optical CDMA packet networks,” in Proc. IEEE Int. Conf. Signal Processing and Commun., Dubai, UAE, Nov. 2007, pp. 285–288.

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Figures (13)

Fig. 1
Fig. 1

System representation of SPE-OCDMA (a) transmitter and (b) receiver.

Fig. 2
Fig. 2

Spectral phase encoding of ultrashort light pulse. (a) Uncoded ultrashort light pulse. (b) Spectrum of uncoded pulse. (c) Encoded ultrashort light pulse. (d) Spectrum of encoded pulse.

Fig. 3
Fig. 3

SPE-OCDMA network architecture.

Fig. 4
Fig. 4

Network throughput S versus average activity A for code length 64 and different numbers of users.

Fig. 5
Fig. 5

Average packet delay D versus average activity A for code length 64 and different numbers of users.

Fig. 6
Fig. 6

Network throughput S versus average activity A for 30 users and different code lengths.

Fig. 7
Fig. 7

Average packet delay D versus average activity A for 30 users and different code lengths.

Fig. 8
Fig. 8

Network throughput S versus average activity A for 30 users and different code lengths.

Fig. 9
Fig. 9

Average packet delay D versus average activity A for different code lengths and fixed bit rate.

Fig. 10
Fig. 10

Network throughput S versus average photons per bit q 2 for different average activities A.

Fig. 11
Fig. 11

Average packet delay D versus average photons per bit q 2 for different average activities A.

Fig. 12
Fig. 12

Network throughput S versus average photons per bit q 2 for different code lengths and fixed bit rate.

Fig. 13
Fig. 13

Average packet delay D versus average photons per bit q 2 for different code lengths and fixed bit rate.

Equations (24)

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

P act , bl ( i m ) = ( m i ) ( 1 d ) i ( 1 1 d ) m i ,
P act , th ( j m ) = ( M m j ) ( A ) j ( 1 A ) M m j .
S ( m ) = i = 0 m j = 0 M m ( i + j ) P s ( i + j ) P act , bl ( i m ) P act , th ( j m ) ,
G ( m ) ( M m ) A + m d .
P m n = Pr { R bl t + 1 = n R bl t = m } ,
P m n = i = max { 0 , m n } m j = max { 0 , n m } M m P act , bl ( i m ) P act , th ( j m ) ( i + j j n + m ) P s j n + m ( i + j ) [ 1 P s ( i + j ) ] i + n m .
m = 0 M π m = 1 , π n = m = 0 M π m P m n , n { 0 , 1 , , M } .
S = m = 0 M S ( m ) π m ,
G = m = 0 M G ( m ) π m ,
R bl = m = 0 M m π m .
D = R bl S G + 1 .
P BE ( l ) = 1 2 ( 1 [ γ ( l ) ρ ( l ) ] ) ,
γ ( l ) = 1 exp ( I th N 0 l P 0 ) ,
ρ ( l ) = 1 Q ( 2 N 0 l , 2 N 0 I th l P 0 ) .
Q ( a , b ) b x exp ( a 2 + b 2 2 ) I 0 ( a x ) d x
P PS ( l ) = { 1 l = 0 ( 1 P BE ( l ) ) L l > 0 } .
Pr ( l ) = ( z 1 l ) ( 1 2 K ) l ( 1 1 2 K ) z 1 l ,
P s ( z ) = P PS ( l ) l = l = 0 z 1 Pr ( l ) P PS ( l ) = ( 1 1 2 K ) z 1 + [ l = 1 z 1 ( z 1 l ) ( 1 2 K ) l ( 1 1 2 K ) z 1 l ( 1 1 2 ( 1 [ γ ( l ) ρ ( l ) ] ) ) L ]
E { Y q } = η q + η F Γ ,
var { Y q } = E { Y q } + 2 η 2 q Γ + η 2 F Γ 2 + 4 k B T r T e 2 R L ,
Γ = l q N 0 ,
P e ( l , q 1 , q 0 ) = Q ( E { Y q 1 } E { Y q 0 } var { Y q 1 } + var { Y q 0 } ) ,
Q ( x ) = 1 2 π x e α 2 2 d α .
P s ( z ) = l = 0 z 1 ( z 1 l ) ( 1 2 K ) l ( 1 1 2 K ) z 1 l [ 1 P e ( l , q 1 , q 0 ) ] L ,