Abstract

When communicating optically through the clear atmospheric channel, not only is there atmospheric turbulence and background noise, but there may also be interference from other sources such as other users in a multiple access system. Even if the interference is off axis, its signal can couple into the receiver through scattering. We would like our communication system to perform well in the presence of interference, background noise, and fading. This paper investigates the performance of diversity coherent and incoherent receivers in the presence of fading, background noise, and various interference types. We find that diversity coherent detection provides significant power gain over diversity direct detection and that most of the benefit of diversity coherent detection can be achieved with a small amount of diversity. Moreover, we find that diversity always improves the performance of coherent detection, whereas in the presence of worst-case interference, diversity degrades the performance of direct detection. This paper also describes a sensible way to select the amount of diversity and power margin to deal with atmospheric turbulence and interference and quantifies the amount of interference that the system can handle while still achieving a given outage probability.

© 2009 Optical Society of America

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References

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  1. Laser Beam Propagation in the Atmosphere, J. H. Shapiro and J. W. Strohbehn, eds. New York, USA: Springer-Verlag, 1978, pp. 172–183.
  2. E. J. Lee, V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, Seoul, South Korea, 2005, pp. 333–339.
  3. E. J. Lee, V. W. S. Chan, “Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
    [CrossRef]
  4. E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” in IEEE Int. Conf. on Communications, Glasgow, Scotland, pp. 2485–2492, 2007.
  5. E. J. Lee, V. W. S. Chan, “The effect of an interferer on atmospheric optical communication that uses diversity incoherent or diversity coherent receiver,” Proc. SPIE, vol. 6709, paper 67090O, 2007.
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    [CrossRef]
  7. R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE, vol. 58, no. 10, pp. 1523–1545, Oct. 1970.
    [CrossRef]
  8. R. M. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.
  9. V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 6, pp. 959–975, Nov./Dec., 2000.
    [CrossRef]
  10. R. L. Mitchell, “Permanence of the log-normal distribution,” J. Opt. Soc. Am., vol. 58, pp. 1267–1272, Sept. 1968.
    [CrossRef]

2007 (1)

E. J. Lee, V. W. S. Chan, “The effect of an interferer on atmospheric optical communication that uses diversity incoherent or diversity coherent receiver,” Proc. SPIE, vol. 6709, paper 67090O, 2007.

2004 (1)

E. J. Lee, V. W. S. Chan, “Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

2000 (1)

V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 6, pp. 959–975, Nov./Dec., 2000.
[CrossRef]

1976 (1)

1970 (1)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE, vol. 58, no. 10, pp. 1523–1545, Oct. 1970.
[CrossRef]

1968 (1)

Chan, V. W. S.

E. J. Lee, V. W. S. Chan, “The effect of an interferer on atmospheric optical communication that uses diversity incoherent or diversity coherent receiver,” Proc. SPIE, vol. 6709, paper 67090O, 2007.

E. J. Lee, V. W. S. Chan, “Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 6, pp. 959–975, Nov./Dec., 2000.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” in IEEE Int. Conf. on Communications, Glasgow, Scotland, pp. 2485–2492, 2007.

E. J. Lee, V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, Seoul, South Korea, 2005, pp. 333–339.

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE, vol. 58, no. 10, pp. 1523–1545, Oct. 1970.
[CrossRef]

Lee, E. J.

E. J. Lee, V. W. S. Chan, “The effect of an interferer on atmospheric optical communication that uses diversity incoherent or diversity coherent receiver,” Proc. SPIE, vol. 6709, paper 67090O, 2007.

E. J. Lee, V. W. S. Chan, “Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” in IEEE Int. Conf. on Communications, Glasgow, Scotland, pp. 2485–2492, 2007.

E. J. Lee, V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, Seoul, South Korea, 2005, pp. 333–339.

Mitchell, R. L.

Shapiro, J. H.

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE, vol. 58, no. 10, pp. 1523–1545, Oct. 1970.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

E. J. Lee, V. W. S. Chan, “Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. W. S. Chan, “Optical space communications,” IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 6, pp. 959–975, Nov./Dec., 2000.
[CrossRef]

J. Opt. Soc. Am. (2)

Proc. IEEE (1)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE, vol. 58, no. 10, pp. 1523–1545, Oct. 1970.
[CrossRef]

Proc. SPIE (1)

E. J. Lee, V. W. S. Chan, “The effect of an interferer on atmospheric optical communication that uses diversity incoherent or diversity coherent receiver,” Proc. SPIE, vol. 6709, paper 67090O, 2007.

Other (4)

R. M. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.

E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” in IEEE Int. Conf. on Communications, Glasgow, Scotland, pp. 2485–2492, 2007.

Laser Beam Propagation in the Atmosphere, J. H. Shapiro and J. W. Strohbehn, eds. New York, USA: Springer-Verlag, 1978, pp. 172–183.

E. J. Lee, V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, Seoul, South Korea, 2005, pp. 333–339.

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Figures (18)

Fig. 1
Fig. 1

Diagram showing that outage occurs when the operating point moves above an error probability threshold.

Fig. 2
Fig. 2

Signals in direct detection when the interference (gray) is on as a constant signal for only the first half of the symbol. The communication signal is shown in white.

Fig. 3
Fig. 3

Signals in direct detection when the interference (gray) is on as a canceling signal for (a) the entire symbol and (b) only the first half of the symbol. The communication signal is shown in white.

Fig. 4
Fig. 4

Signals in homodyne detection when the interference is on as a 0. The communication and interference signals are shown in white and gray, respectively.

Fig. 5
Fig. 5

Block diagram of multiaperture incoherent detection (direct detection) with receiver diversity N.

Fig. 6
Fig. 6

Block diagram of multiaperture coherent detection with receiver diversity N.

Fig. 7
Fig. 7

Error probability in the absence of interference and fading when N n = 1 .

Fig. 8
Fig. 8

Outage probability in the absence of interference when P e thresh = 0.1 , σ χ = 0.3 , and N n = 1 .

Fig. 9
Fig. 9

Outage probability in the absence of interference when P e thresh = 10 4 , σ χ = 0.3 , and N n = 1 .

Fig. 10
Fig. 10

Received signal constellation.

Fig. 11
Fig. 11

(a) Interference worst-case duty cycle and (b) error probability of direct and homodyne detection in the presence of interference that uses the worst-case duty cycle: no fading, N = 1 , N n = 1 .

Fig. 12
Fig. 12

(a) Communication (white) and interference (gray) signals and (b) net signal in direct detection when the canceling interference is on for the entire symbol.

Fig. 13
Fig. 13

(a) Communication (white) and interference (gray) signals and (b) net signal in direct detection when the canceling interference is on for only the first half of the symbol.

Fig. 14
Fig. 14

(a) Interference worst-case duty cycle and (b) outage probability of direct detection and homodyne detection in the presence of interference that uses the worst-case duty cycle: σ χ = 0.3 , P e thresh = 0.1 , N = 1 , and N n = 1 .

Fig. 15
Fig. 15

Outage probability (in the presence of fading) of direct detection and homodyne detection in the presence of interference that uses the worst-case duty cycle: σ χ = 0.3 , P e thresh = 0.1 , N = 4 , and N n = 1 .

Fig. 16
Fig. 16

Error probability (in the absence of fading) of direct detection in the presence of Gaussian interference that turns on for only the first half symbol and uses the worst-case duty cycle: N n = 1 .

Fig. 17
Fig. 17

Outage probability (in the presence of fading) of direct detection in the presence of interference that turns on for only the first half symbol and uses the worst-case duty cycle: σ χ = 0.3 , P e thresh = 0.1 , and N n = 1 .

Fig. 18
Fig. 18

Power gain of homodyne detection over direct detection (if interference is present and it uses the worst-case duty cycle) for outage probability of 0.01 when σ χ = 0.3 , P e thresh = 0.1 , N n = 1 , and N opt = 6 .

Tables (3)

Tables Icon

Table 1 Worst-Case Interference Duty

Tables Icon

Table 2 Error and Outage Probability When the Interference Uses the Worst-Case Duty Cycle

Tables Icon

Table 3 Power Gain of Homodyne Detection (Homo) in the Presence of Canceling Interference Over Direct Detection (DD) in the Presence of Gaussian Interference That Is On for Half the Symbol

Equations (62)

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i = 1 N γ i 2 = 1 .
P e , DD , noInterference = exp { ( ( 1 N i = 1 N α i ) N S + N N n 2 N N n 2 ) 2 } ,
P outage , DD , noInterference 1 2 exp { 1 2 σ U 2 [ m U ln ( θ thresh + 2 θ thresh N N n N S ) ] 2 } ,
e U = 1 N i = 1 N α i ,
m U = 1 2 ln ( 1 + e 4 σ χ 2 1 N ) , σ U 2 = ln ( 1 + e 4 σ χ 2 1 N ) .
P e , Homo , noInterference = 1 2 exp [ ( 1 N i = 1 N α i ) 2 N s ( 1 + N n ) ] ,
P outage , Homo , noInterference 1 2 exp { 1 2 σ U 2 [ m U ln ( ( 1 + N n ) ( ln 2 + θ thresh ) 2 N s ) ] 2 } .
P outage , Homo , noInterference 1 2 exp { c N } ,
N S * = ( 1 + N n ) ( ln 2 + θ thresh ) 2 exp { 2 ln ( 2 p ) ln ( 1 + e 4 σ χ 2 1 N ) + 1 2 ln ( 1 + e 4 σ χ 2 1 N ) }
P ( e ) = ( 1 β ) P ( e | interf. is not on ) + β P ( e | interf. is on ) β P ( e | interf. is on ) ,
P outage = ( 1 β ) P ( outage | intef. is not on ) + β P ( outage | interf. is on ) β P ( outage | interf. is on ) .
N n N I β ,
N n 2 N I β ,
N N I β ( N N I β ) 2 .
P ( e ) = β 2 P ( e | interf. is on , sender sent 0 ) + β 2 P ( e | interf. is on , sender sent 1 ) β 2 exp ( ( m N S * + N N I β + N N n 2 N N n 2 ) 2 ) + β 2 exp ( ( m N S * + N N n 2 N N I β + N N n 2 ) 2 ) .
P outage β Pr ( 1 2 exp ( ( 1 N i = 1 N α i m N S * + N N n 2 N N I β + N N n 2 ) 2 ) > e θ thresh ) β 2 exp ( 1 2 σ U 2 [ m U ln ( ( ln 2 + θ thresh + N N I β + N N n 2 ) 2 N N n 2 ( m N S * ) ) ] 2 ) .
N N I β ( ln 2 + θ thresh )
m = N N I 2 β + N N n 2 ,
σ 2 = N N I 2 β + N N n 2 + 2 [ N N I 2 β + N N n 2 ] 2 ,
P ( e ) = β P ( N S + n 0 < n 1 | interference is on , H 0 ) = β Q ( m N S * 2 σ 2 ) β 2 exp ( ( m N S * ) 2 ( 2 ( N N I β + N N n + [ N N I β + N N n ] 2 ) ) ) ,
P outage β 2 exp ( 1 2 σ U 2 [ m U ln ( 2 ( N N I β + N N n + [ N N I β + N N n ] 2 ) ( ln 2 + θ thresh ) ( m N S * ) ) ] 2 ) .
m = N N I β + N N n 2 ,
σ 2 = N N I β + N N n 2 + 2 [ N N I β + N N n 2 ] 2 ,
P ( e ) = β 2 P ( e | interference is on , H 1 ) = β 2 Pr ( n 1 > m N S * | interference is on ) β 2 exp ( ( m N S * ( N N I β + N N n 2 ) ) 2 2 ( N N I β + N N n 2 + 2 [ N N I β + N N n 2 ] 2 ) ) .
P outage β 2 exp ( 1 2 σ U 2 [ m U ln ( 1 m N S * ( 2 ( N N I β + N N n 2 + 2 [ N N I β + N N n 2 ] 2 ) ( ln 2 + θ thresh ) + ( N N I β + N N n 2 ) ) ) ] 2 ) .
P ( e ) = β P ( N 1 N 0 | interferer is on , H 0 ) β E [ e s ( N 1 N 0 ) | H 0 ] = β exp ( ( m N S * + N N I 2 β 2 N N I m N S * β + N N n 2 N N I 2 β + N N n 2 ) 2 ) ,
P outage β 2 exp ( 1 2 σ U 2 [ m U ln ( θ thresh ( N ( m N S * N 2 N I β ) ) 2 ) ] 2 ) .
P ( e ) = β 2 P ( e | interf. is on , sender sent 0 ) + β 2 P ( e | interf. is on , sender sent 1 ) β 2 exp ( ( m N S * + N N I β 2 N N I m N S * β + N N n 2 N N n 2 ) 2 ) + β 2 exp ( ( m N S * + N N n 2 N N I β + N N n 2 ) 2 ) .
P ( e ) = β exp ( ( m N S * N N I β ) 2 ) .
P outage = β Pr ( exp ( ( i = 1 N α i m N S * N i = 1 N α i N I β ) 2 ) > e θ thresh ) .
P ( e ) = β 2 exp { 2 m N S * 1 + N I β + N n }
P outage β 2 exp ( 1 2 σ U 2 [ m U ln ( ( 1 + N I β + N n ) ( ln 2 + θ thresh ) 2 m N S * ) ] 2 ) .
P ( e ) = β [ 1 2 Pr ( n > a S a I | H 1 ) + 1 2 Pr ( n < ( a S + a I ) | H 0 ) ] β 4 exp ( ( a S a I ) 2 N 0 ) + β 4 exp ( ( a S + a I ) 2 N 0 ) ,
a S = E S = 2 ( q η h ν ) 2 P L P S T ,
a I = E I = 2 ( q η h ν ) 2 P L P I β T ,
N 0 2 = q 2 η h ν P L + ( q η h ν ) 2 P L N 0 , background   ,
P ( e ) = β 4 [ exp ( 2 ( m N S * N I β ) 2 ( 1 + N n ) ) + exp ( 2 ( m N S * + N I β ) 2 ( 1 + N n ) ) ] .
P outage β 2 exp ( 1 2 σ U 2 [ m U ln { 1 m N S * ( ( 1 + N n ) ( ln 4 + θ thresh ) 2 + N I β ) 2 } ] 2 ) ,
N I β ( 1 + N n ) ( ln 4 + θ thresh ) 2
1 > ln 2 + θ thresh 2 P e thresh > 1 2 e 2 = 0.068 .
P outage = N N I ( 2 ln 2 + θ thresh + 1 ) 2 m N S * ( 1 + e 4 σ χ 2 1 N ) .
mN S * = N I ( 2 ln 2 + θ thresh + 1 ) 2 P outage ( N + e 4 σ χ 2 1 ) .
N opt , GaussianHalfBitInterf. = 1 .
N S , DD = ( θ thresh + 2 N N n θ thresh ) 1 + e 4 σ χ 2 1 N exp { 2 ln ( 1 + e 4 σ χ 2 1 N ) ln ( 2 P out , DD ) } .
0 = a 3 N opt 3 2 + a 2 N opt + a 1 N opt 1 2 + a 0 ,
a 3 = 2 N n ,
a 2 = 2 N n ( e 4 σ χ 2 1 ) ln ( 2 P outage ) ,
a 1 = θ thresh ( e 4 σ χ 2 1 ) ln ( 2 P outage ) ,
a 0 = θ thresh 2 ( e 4 σ χ 2 1 ) ,
P outage , DD , GaussHalfBitInterf. ( β worstcase , DD ) = P outage , Homo , CancelingInterf. ( β worstcase , Homo ) ,
N N I ( 2 ln 2 + θ thresh + 1 ) ( 1 + e 4 σ χ 2 1 N ) 2 m D D , GaussHalfBitInterf. N S * = N I ( 1 + e 4 σ χ 2 1 N ) 2 m Homo , CancelingInterf. N S * .
P outage , DD , noInterference = P outage , Homo , noInterference ,
1 N S , DD [ θ thresh + 2 θ thresh N N n ] = ( 1 + N n ) ( ln 2 + θ thresh ) 2 N s , Homo .
Power Gain N = c N ,
c = 2 2 θ thresh N n ( 1 + N n ) ( ln 2 + θ thresh ) .
N S , Homo = ( 1 + N n ) ( ln 2 + θ thresh ) 2 exp { 2 ln ( 1 + e 4 σ χ 2 1 N ) ln ( 2 P outage , Homo , noInterference ) + 1 2 ln ( 1 + e 4 σ χ 2 1 N ) } .
Power Gain N = k 1 exp ( k 2 N ) ,
Power Gain N = c 1 exp ( k 2 N ) ,
N I = 2 m N S * P outage , required ( 1 + e 4 o χ 2 1 N ) .
N I m N S * = 2 P outage , required ( 1 + e 4 o χ 2 1 N ) .
N I m N S * 2 P outage , required ,
m N S * N I / 2 P outage , required .