Abstract

Digital communication systems using the narrow pulses generated by a mode-locked laser are extremely efficient in their use of average laser power. However, these narrow pulses require precise system timing and decision intervals matched to the pulse width. This paper extends previous work by Gagliardi in this area to consider the effects of pulse timing errors and pulse width mismatch on the probability of bit error for on-off keying, binary pulse position modulation, and quarternary pulse position modulation formats. The general expressions are derived, and a number of examples are plotted.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. B. Champagne, Appl. Opt. 5, 1843 (1966).
    [CrossRef] [PubMed]
  2. R. M. Montgomery, W. Metheny, R. R. Carter, P. J. Titterton, “Experimental Evaluation of Ultrafast Pulsed Laser Communication Techniques” Paper 13.5,” in IEEE Conference on Laser Engineering and Applications, Washington D.C., 26–28 May 1969.
  3. R. M. Gagliardi, IEEE Trans. Commun., COM-20, 87 (1972).
    [CrossRef]
  4. T. Curran, M. Ross, Proc. IEEE 53, 1770 (1965).
    [CrossRef]

1972 (1)

R. M. Gagliardi, IEEE Trans. Commun., COM-20, 87 (1972).
[CrossRef]

1966 (1)

1965 (1)

T. Curran, M. Ross, Proc. IEEE 53, 1770 (1965).
[CrossRef]

Carter, R. R.

R. M. Montgomery, W. Metheny, R. R. Carter, P. J. Titterton, “Experimental Evaluation of Ultrafast Pulsed Laser Communication Techniques” Paper 13.5,” in IEEE Conference on Laser Engineering and Applications, Washington D.C., 26–28 May 1969.

Champagne, E. B.

Curran, T.

T. Curran, M. Ross, Proc. IEEE 53, 1770 (1965).
[CrossRef]

Gagliardi, R. M.

R. M. Gagliardi, IEEE Trans. Commun., COM-20, 87 (1972).
[CrossRef]

Metheny, W.

R. M. Montgomery, W. Metheny, R. R. Carter, P. J. Titterton, “Experimental Evaluation of Ultrafast Pulsed Laser Communication Techniques” Paper 13.5,” in IEEE Conference on Laser Engineering and Applications, Washington D.C., 26–28 May 1969.

Montgomery, R. M.

R. M. Montgomery, W. Metheny, R. R. Carter, P. J. Titterton, “Experimental Evaluation of Ultrafast Pulsed Laser Communication Techniques” Paper 13.5,” in IEEE Conference on Laser Engineering and Applications, Washington D.C., 26–28 May 1969.

Ross, M.

T. Curran, M. Ross, Proc. IEEE 53, 1770 (1965).
[CrossRef]

Titterton, P. J.

R. M. Montgomery, W. Metheny, R. R. Carter, P. J. Titterton, “Experimental Evaluation of Ultrafast Pulsed Laser Communication Techniques” Paper 13.5,” in IEEE Conference on Laser Engineering and Applications, Washington D.C., 26–28 May 1969.

Appl. Opt. (1)

IEEE Trans. Commun. (1)

R. M. Gagliardi, IEEE Trans. Commun., COM-20, 87 (1972).
[CrossRef]

Proc. IEEE (1)

T. Curran, M. Ross, Proc. IEEE 53, 1770 (1965).
[CrossRef]

Other (1)

R. M. Montgomery, W. Metheny, R. R. Carter, P. J. Titterton, “Experimental Evaluation of Ultrafast Pulsed Laser Communication Techniques” Paper 13.5,” in IEEE Conference on Laser Engineering and Applications, Washington D.C., 26–28 May 1969.

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 (17)

Fig. 1
Fig. 1

Fraction of pulse energy between t = T and ∞ vs ratio of T to exp(−2) half-width.

Fig. 2
Fig. 2

BPPM: effect of pulse displacement on PE for pulse fit parameter = 0.8; N = 0.5.

Fig. 3
Fig. 3

BPPM: effect of pulse displacement on PE for pulse fit parameter = 0.9; N = 0.5

Fig. 4
Fig. 4

BPPM: effect of pulse displacement on PE for pulse fit parameter = 1.0; N = 0.5.

Fig. 5
Fig. 5

BPPM: effect of pulse displacement on PE for pulse fit parameter = 1.2; N = 0.5.

Fig. 6
Fig. 6

QPPM: effect of pulse displacement on PE for pulse fit parameter = 0.8; N = 0.5.

Fig. 7
Fig. 7

QPPM: effect of pulse displacement on PE for pulse fit parameter = 0.9; N = 0.5.

Fig. 8
Fig. 8

QPPM: effect of pulse displacement on PE for pulse fit parameter = 1.0; N = 0.5.

Fig. 9
Fig. 9

QPPM: effect of pulse displacement on PE for pulse fit parameter = 1.2; N = 0.5.

Fig. 10
Fig. 10

OOK: effect of pulse displacement on PE for pulse fit parameter = 0.8; N = 0.5; D = 30.

Fig. 11
Fig. 11

OOK: effect of pulse displacement on PE for pulse fit parameter = 0.8; N = 0.5; D = 20.

Fig. 12
Fig. 12

OOK: effect of pulse displacement on PE for pulse fit parameter = 0.9; N = 0.5; D = 30.

Fig. 13
Fig. 13

OOK: effect of pulse displacement on PE for pulse fit parameter = 0.9; N = 0.5; D = 20.

Fig. 14
Fig. 14

OOK: effect of pulse displacement on PE for pulse fit parameter = 1.0; N = 0.5; D = 30.

Fig. 15
Fig. 15

OOK: effect of pulse displacement on PE for pulse fit parameter = 1.0; N = 0.5; D = 20.

Fig. 16
Fig. 16

OOK: effect of pulse displacement on PE for pulse fit parameter = 1.2; N = 0.5; D = 30.

Fig. 17
Fig. 17

OOK: effect of pulse displacement on PE for pulse fit parameter = 1.2; N = 0.5; D = 20.

Tables (4)

Tables Icon

Table I BPPM Relation Between Ratio of Slot Width to Pulse Width and the Number of Photoelectrons per Pulse Required to Maintain PE = 10−8

Tables Icon

Table II QPPM Relation Between Pulse-Fit Parameter and # Photoelectrons/Pulse Required to Maintain PE = 10−8

Tables Icon

Table III Thresholds Calculated from Eq. (16) for Various Extinction Ratios D (Compare to Values in Figs. 1017)

Tables Icon

Table IV OOK Relation Between Pulse-Fit Parameter and Number Photoelectrons/Pulse Required to Maintain PE = 10−8

Equations (16)

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

P E ( S , N ) = k 1 = 0 k 2 = k 1 γ k 2 P ρ ( k 1 , S + N ) P ρ ( k 2 , N ) ,
P p ( k , X ) = [ ( X ) k / k ! ] exp [ - ( X ) ] .
P E ( S , N ) / Δ = ½ P E ( S , N ) + ¼ P E ( S , N ) + ¼ P E ( S , N ) ,
and             = Δ / ( 2 T ) ;
P E ( S , N ) = ½ k = 0 K γ k P p ( k , S + N ) + ½ k = K γ k P p ( k , N )
P E ( S , N ) Δ = ½ P E ( S , N ) + ½ P E ( S , N )
P = P 0 exp ( - 2 t 2 / τ 2 )
E = ( π / 2 ) 1 / 2 τ P 0 .
α E = P 0 - - T exp ( - 2 t 2 / τ 2 ) d t .
α = ½ erfc [ ( 2 ) 1 / 2 T / τ ] .
α 2 = ½ erfc [ B ( 1 - 2 ) ( 1.5172 ) ] ,
α 3 = ½ erfc [ B ( 1 + 2 ) ( 1.5172 ) ] ,
P E , B = ¼ P E [ A ( 1 - 2 α 2 - 2 α 3 ) , N + A ( α 2 + α 3 ) ] + P E [ A ( 1 - α 2 - α 3 ) , N + α 3 A ] + P E [ A ( 1 - α 2 - α 3 ) , N + α 2 A ] + P E [ A ( 1 - 2 α 2 - α 3 ) , N + A ( α 2 + α 3 ) ] + P E [ A ( 1 - α 2 - 2 α 3 ) , N + A ( α 2 + α 3 ) ] + P E [ A ( 1 - α 2 - 2 α 3 ) , N + α 3 A ] + P E [ A ( 1 - 2 α 2 - α 3 ) , N + α 2 A ]
P E , B = ( 11 / 32 ) P E [ A ( 1 - α 2 - α 3 ) , N ] + ( 47 / 192 ) P E [ A ( 1 - α 2 - 2 α 3 ) , N + α 3 A ] + ( 47 / 192 ) P E [ A ( 1 - 2 α 2 - α 3 ) , N + α 2 A ] + ( 1 / 24 ) P E [ A ( 1 - 2 α 2 - 2 α 3 ) , N + A ( α 2 + α 3 ) ] + ( 1 / 24 ) P E [ A ( 1 / α 2 ) , N ] + ( 1 / 48 ) P E [ A ( 1 - α 2 - α 3 ) , N + α 3 A ] + ( 7 / 192 P E [ A ( 1 - α 3 ) ] , N ] + ( 1 / 192 P E [ A ( 1 - 2 α 3 ) , N + α 3 A ] + ( 1 / 48 ) P E [ A ( 1 - α 2 - α 3 ) , N + α 2 A ]
P E , B = [ k = 0 K γ k { P p ( k , A D D + 1 + N ) + P p [ k , A D D + 1 ( 1 - α 3 ) + N ] + P p [ k , A D D + 1 ( 1 - α 2 ) + N ] + P p [ k , A D D + 1 ( 1 - α 2 - α 3 ) + N ] } + k = K γ k ( P p ( k , A D + 1 + N ) + P p [ k , A D + 1 ( 1 + α 3 D ) + N ] + P p [ k , A D + 1 ( 1 + α 2 D ) + N ] + P p { k , A D + 1 [ 1 + D ( α 2 + α 3 ) ] + N } ) ]
K = int { A [ 1 - ( 1 / D ) ] ln [ A + N / N + ( A / D ) ] } .

Metrics