Abstract

A gradual multi-pulse pulse-position modulation (gradual MPPM) scheme is proposed as a new modulation scheme to improve both the performance and bandwidth-utilization efficiency of the conventional optical multi-pulse pulse-position modulation (MPPM) scheme in deep-space optical communications. Whereas in the conventional MPPM scheme, a fixed number of optical pulses is transmitted in every signal block, a variable number of pulses are transmitted in the proposed scheme. Information is represented by different combinations of the positions of these pulses. The transmission characteristics, bandwidth utilization, and power requirements for the proposed scheme are studied in this paper. Several performance measures are derived and compared with those of the conventional MPPM scheme in deep-space optical communications. Our results reveal that, at the same average power, the proposed gradual MPPM scheme achieves much lower levels of symbol-error rates than those of the ordinary MPPM scheme, whereas, at the same peak power levels, the ordinary MPPM outperforms the gradual scheme. Also, in terms of bandwidth-utilization efficiency, the proposed modulation scheme achieves higher efficiency than the ordinary MPPM by allowing many more symbols to be transmitted per frame.

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References

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  1. J. Singh and V. K. Jain, “Performance analysis of BPPM and M-ary PPM optical communication systems in atmospheric turbulence,” IETE Tech. Rev., vol. 25, no. 4, pp. 146–153, July–Aug.2008.
    [CrossRef]
  2. M. Simon and V. Vilnrotter, “Performance analysis and tradeoff for dual-pulse PPM on optical communications channels with direct detection,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1969–1979, Nov.2004.
    [CrossRef]
  3. H. Sugiyama and K. Nosu, “MPPM: A method for improving the band utilization efficiency in optical PPM,” J. Lightwave Technol., vol. 7, no. 3, pp. 465–471, Mar.1989.
    [CrossRef]
  4. H. Park, “Performance bound on multiple-pulse position modulation,” Opt. Rev., vol. 10, no. 3, pp. 131–132, May2003.
    [CrossRef]
  5. M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.
  6. K. Sato, T. Ohtsuki, and I. Sasase, “Performance of coded multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel,” in Proc. IEEE Int. Communications Conf. (ICC), 2004, vol. 1, pp. 121–125.
  7. R. M. Gagliardi and S. Karp, Optical Communications. 2nd ed., John Wiley & Sons, 1995.
  8. S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, “Capacity of pulse-position modulation (PPM) on Gaussian and Webb channels,” The Telecommunications and Mission Operations Progress Report 42–142, Apr.–June 2000, Jet Propulsion Laboratory, Pasadena, California, Aug.15, 2000, pp. 1–31.
  9. A. Biswas and W. H. Farr, “Laboratory characterization and modeling of a near–infrared enhanced photomultiplier tube,” The Interplanetary Network Progress Report 42–152, Oct.–Dec. 2002, Jet Propulsion Laboratory, Pasadena, California, Feb.15, 2003, pp. 1–14.
  10. J. Hamkins and B. Moision, “Multipulse PPM on memoryless channels,” in Int. Symp. on Information Theory (ISIT), Chicago, Illinois, June 2004.
  11. S. Liu and F. R. Kschischang, “Coding for MPPM-like systems,” in 25th Biennial Symp. on Communications (QBSC 2010), Kingston, Ontario, Canada, May 12–14, 2010, pp. 365–368.

2008 (1)

J. Singh and V. K. Jain, “Performance analysis of BPPM and M-ary PPM optical communication systems in atmospheric turbulence,” IETE Tech. Rev., vol. 25, no. 4, pp. 146–153, July–Aug.2008.
[CrossRef]

2004 (1)

M. Simon and V. Vilnrotter, “Performance analysis and tradeoff for dual-pulse PPM on optical communications channels with direct detection,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1969–1979, Nov.2004.
[CrossRef]

2003 (1)

H. Park, “Performance bound on multiple-pulse position modulation,” Opt. Rev., vol. 10, no. 3, pp. 131–132, May2003.
[CrossRef]

1989 (1)

H. Sugiyama and K. Nosu, “MPPM: A method for improving the band utilization efficiency in optical PPM,” J. Lightwave Technol., vol. 7, no. 3, pp. 465–471, Mar.1989.
[CrossRef]

Barsoum, M. F.

M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.

Biswas, A.

A. Biswas and W. H. Farr, “Laboratory characterization and modeling of a near–infrared enhanced photomultiplier tube,” The Interplanetary Network Progress Report 42–152, Oct.–Dec. 2002, Jet Propulsion Laboratory, Pasadena, California, Feb.15, 2003, pp. 1–14.

Divsalar, D.

S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, “Capacity of pulse-position modulation (PPM) on Gaussian and Webb channels,” The Telecommunications and Mission Operations Progress Report 42–142, Apr.–June 2000, Jet Propulsion Laboratory, Pasadena, California, Aug.15, 2000, pp. 1–31.

M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.

Dolinar, S.

S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, “Capacity of pulse-position modulation (PPM) on Gaussian and Webb channels,” The Telecommunications and Mission Operations Progress Report 42–142, Apr.–June 2000, Jet Propulsion Laboratory, Pasadena, California, Aug.15, 2000, pp. 1–31.

Farr, W. H.

A. Biswas and W. H. Farr, “Laboratory characterization and modeling of a near–infrared enhanced photomultiplier tube,” The Interplanetary Network Progress Report 42–152, Oct.–Dec. 2002, Jet Propulsion Laboratory, Pasadena, California, Feb.15, 2003, pp. 1–14.

Fitz, M.

M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.

Gagliardi, R. M.

R. M. Gagliardi and S. Karp, Optical Communications. 2nd ed., John Wiley & Sons, 1995.

Hamkins, J.

M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.

J. Hamkins and B. Moision, “Multipulse PPM on memoryless channels,” in Int. Symp. on Information Theory (ISIT), Chicago, Illinois, June 2004.

S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, “Capacity of pulse-position modulation (PPM) on Gaussian and Webb channels,” The Telecommunications and Mission Operations Progress Report 42–142, Apr.–June 2000, Jet Propulsion Laboratory, Pasadena, California, Aug.15, 2000, pp. 1–31.

Jain, V. K.

J. Singh and V. K. Jain, “Performance analysis of BPPM and M-ary PPM optical communication systems in atmospheric turbulence,” IETE Tech. Rev., vol. 25, no. 4, pp. 146–153, July–Aug.2008.
[CrossRef]

Karp, S.

R. M. Gagliardi and S. Karp, Optical Communications. 2nd ed., John Wiley & Sons, 1995.

Kschischang, F. R.

S. Liu and F. R. Kschischang, “Coding for MPPM-like systems,” in 25th Biennial Symp. on Communications (QBSC 2010), Kingston, Ontario, Canada, May 12–14, 2010, pp. 365–368.

Liu, S.

S. Liu and F. R. Kschischang, “Coding for MPPM-like systems,” in 25th Biennial Symp. on Communications (QBSC 2010), Kingston, Ontario, Canada, May 12–14, 2010, pp. 365–368.

Moision, B.

J. Hamkins and B. Moision, “Multipulse PPM on memoryless channels,” in Int. Symp. on Information Theory (ISIT), Chicago, Illinois, June 2004.

M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.

Nosu, K.

H. Sugiyama and K. Nosu, “MPPM: A method for improving the band utilization efficiency in optical PPM,” J. Lightwave Technol., vol. 7, no. 3, pp. 465–471, Mar.1989.
[CrossRef]

Ohtsuki, T.

K. Sato, T. Ohtsuki, and I. Sasase, “Performance of coded multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel,” in Proc. IEEE Int. Communications Conf. (ICC), 2004, vol. 1, pp. 121–125.

Park, H.

H. Park, “Performance bound on multiple-pulse position modulation,” Opt. Rev., vol. 10, no. 3, pp. 131–132, May2003.
[CrossRef]

Pollara, F.

S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, “Capacity of pulse-position modulation (PPM) on Gaussian and Webb channels,” The Telecommunications and Mission Operations Progress Report 42–142, Apr.–June 2000, Jet Propulsion Laboratory, Pasadena, California, Aug.15, 2000, pp. 1–31.

Sasase, I.

K. Sato, T. Ohtsuki, and I. Sasase, “Performance of coded multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel,” in Proc. IEEE Int. Communications Conf. (ICC), 2004, vol. 1, pp. 121–125.

Sato, K.

K. Sato, T. Ohtsuki, and I. Sasase, “Performance of coded multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel,” in Proc. IEEE Int. Communications Conf. (ICC), 2004, vol. 1, pp. 121–125.

Simon, M.

M. Simon and V. Vilnrotter, “Performance analysis and tradeoff for dual-pulse PPM on optical communications channels with direct detection,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1969–1979, Nov.2004.
[CrossRef]

Singh, J.

J. Singh and V. K. Jain, “Performance analysis of BPPM and M-ary PPM optical communication systems in atmospheric turbulence,” IETE Tech. Rev., vol. 25, no. 4, pp. 146–153, July–Aug.2008.
[CrossRef]

Sugiyama, H.

H. Sugiyama and K. Nosu, “MPPM: A method for improving the band utilization efficiency in optical PPM,” J. Lightwave Technol., vol. 7, no. 3, pp. 465–471, Mar.1989.
[CrossRef]

Vilnrotter, V.

M. Simon and V. Vilnrotter, “Performance analysis and tradeoff for dual-pulse PPM on optical communications channels with direct detection,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1969–1979, Nov.2004.
[CrossRef]

IEEE Trans. Commun. (1)

M. Simon and V. Vilnrotter, “Performance analysis and tradeoff for dual-pulse PPM on optical communications channels with direct detection,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1969–1979, Nov.2004.
[CrossRef]

IETE Tech. Rev. (1)

J. Singh and V. K. Jain, “Performance analysis of BPPM and M-ary PPM optical communication systems in atmospheric turbulence,” IETE Tech. Rev., vol. 25, no. 4, pp. 146–153, July–Aug.2008.
[CrossRef]

J. Lightwave Technol. (1)

H. Sugiyama and K. Nosu, “MPPM: A method for improving the band utilization efficiency in optical PPM,” J. Lightwave Technol., vol. 7, no. 3, pp. 465–471, Mar.1989.
[CrossRef]

Opt. Rev. (1)

H. Park, “Performance bound on multiple-pulse position modulation,” Opt. Rev., vol. 10, no. 3, pp. 131–132, May2003.
[CrossRef]

Other (7)

M. F. Barsoum, B. Moision, M. Fitz, D. Divsalar, and J. Hamkins, “Iterative coded pulse-position-modulation for deep-space optical communications,” in Information Theory Workshop, Sept. 2007, pp. 66–71.

K. Sato, T. Ohtsuki, and I. Sasase, “Performance of coded multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel,” in Proc. IEEE Int. Communications Conf. (ICC), 2004, vol. 1, pp. 121–125.

R. M. Gagliardi and S. Karp, Optical Communications. 2nd ed., John Wiley & Sons, 1995.

S. Dolinar, D. Divsalar, J. Hamkins, and F. Pollara, “Capacity of pulse-position modulation (PPM) on Gaussian and Webb channels,” The Telecommunications and Mission Operations Progress Report 42–142, Apr.–June 2000, Jet Propulsion Laboratory, Pasadena, California, Aug.15, 2000, pp. 1–31.

A. Biswas and W. H. Farr, “Laboratory characterization and modeling of a near–infrared enhanced photomultiplier tube,” The Interplanetary Network Progress Report 42–152, Oct.–Dec. 2002, Jet Propulsion Laboratory, Pasadena, California, Feb.15, 2003, pp. 1–14.

J. Hamkins and B. Moision, “Multipulse PPM on memoryless channels,” in Int. Symp. on Information Theory (ISIT), Chicago, Illinois, June 2004.

S. Liu and F. R. Kschischang, “Coding for MPPM-like systems,” in 25th Biennial Symp. on Communications (QBSC 2010), Kingston, Ontario, Canada, May 12–14, 2010, pp. 365–368.

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Figures (12)

Fig. 1
Fig. 1

Frame structure in ordinary MPPM.

Fig. 2
Fig. 2

Frame structure in gradual MPPM.

Fig. 3
Fig. 3

Information rate ratio for M = 16 .

Fig. 4
Fig. 4

Bandwidth-utilization efficiency.

Fig. 5
Fig. 5

Symbol-error rate versus average received photons per frame at M = 8 .

Fig. 6
Fig. 6

Symbol-error rate versus average received photons per frame at M = 16 .

Fig. 7
Fig. 7

Average number of photons per signal slot versus average received photons per frame at M = 8 .

Fig. 8
Fig. 8

Average number of photons per signal slot versus average received photons per frame at M = 16 .

Fig. 9
Fig. 9

Symbol-error rate versus average received photons per signal slot at M = 8 .

Fig. 10
Fig. 10

Symbol-error rate versus average received photons per signal slot at M = 16 .

Fig. 11
Fig. 11

Average number of received photons per frame versus average received photons per signal slot at M = 8 .

Fig. 12
Fig. 12

Average number of received photons per frame versus average received photons per signal slot at M = 16 .

Tables (1)

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Table 1 Algorithm Steps

Equations (16)

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Information rate ratio = log 2 i = 1 n ( M i ) log 2 ( M n ) .
U M = log 2 ( M n M ) M ,
U G = log 2 i = 1 n G ( M i ) M .
P ( k | X ) = i = 1 M ( λ x i τ + K b ) k i k i ! e ( λ x i τ + K b ) .
P ( k | X ) P ( k | Y ) = i = 1 M ( λ x i τ + K b ) k i k i ! e ( λ x i τ + K b ) i = 1 M ( λ y i τ + K b ) k i k i ! e ( λ y i τ + K b ) = i = 1 M ( λ x i τ K b + 1 λ y i τ K b + 1 ) k i ,
P ( k | X ) P ( k | Y ) = ( K s K b + 1 ) k x 1 + k x 2 + + k x j k y 1 k y 2 k y j .
k x 1 + k x 2 + + k x j = k 1 + k 2 + + k j ,
P ( k | X ) P ( k | Y ) = i = 1 M ( λ x i τ + K b ) k i k i ! e ( λ x i τ + K b ) i = 1 M ( λ y i τ + K b ) k i k i ! e ( λ y i τ + K b ) = ( 1 + K s K b ) k l e K s .
T h = K s ln ( 1 + K s K b ) .
SER = 1 k max=0 l = 1 M n m = 0 n I ( l , m ) ( M n l ) p 0 ( k max ) l × P 0 ( k max 1 ) M n l ( n m ) p 1 ( k max ) m × ( 1 P 1 ( k max ) ) n m .
p ( c ) A = k max = 0 T h 1 l = 1 M 1 m = 0 1 I ( l , m ) ( M 1 l ) p 0 ( k max ) l × P 0 ( k max 1 ) M 1 l p 1 ( k max ) m × ( 1 P 1 ( k max ) ) 1 m .
p ( c ) B i = [ 1 P 1 ( T h 1 ) ] i [ P 0 ( T h 1 ) ] M i .
p ( c ) c = k min = T h l = 0 M n m = 1 n I ( l , m ) ( M n l ) × P 0 ( k min 1 ) M n l ( n m ) p 1 ( k min ) m × ( 1 P 1 ( k min ) ) n m .
SER = 1 p ( c ) = 1 1 j = 1 n ( M j ) [ ( M 1 ) p ( c ) A + i = 2 n 1 ( M i ) p ( c ) B i + ( M n ) p ( c ) C ] .
K a v M = K s M × n M .
K a v G = K s G × i = 1 n G i × ( M i ) i = 1 n G ( M i ) .