Abstract

The performance of differential phase-shift keying signals with a balanced receiver is exactly analyzed by using a closed-form expression without approximation. The numerical results are well matched with previous results based on the saddle-point approximation. The error probability is calculated exactly using the well-known Marcum Q function.

© 2007 Optical Society of America

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References

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  1. A. H. Gnauck and P. J. Winzer, J. Lightwave Technol. 23, 115 (2005).
    [CrossRef]
  2. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).
  3. R. A. Linke and A. H. Gnauck, J. Lightwave Technol. 6, 1750 (1988).
    [CrossRef]
  4. P. J. Winzer, S. Chandrasekhar, and H. Kim, IEEE Photon. Technol. Lett. 15, 840 (2003).
    [CrossRef]
  5. G. Bosco and P. Poggiolini, IEEE Photon. Technol. Lett. 16, 665 (2004).
    [CrossRef]
  6. M. Mlejnek, Opt. Lett. 31, 2266 (2006).
    [CrossRef] [PubMed]
  7. C. W. Helstrom, IEEE Trans. Aerosp. Electron. Syst. 14, 630 (1978).
    [CrossRef]
  8. J. I. Marcum, IRE Trans. Inf. Theory IT-6, 56 (1960).
  9. K.-P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
    [CrossRef]
  10. S. Stein, IEEE Trans. Inf. Theory IT-10, 43 (1964).
    [CrossRef]
  11. G. Bosco and P. Poggiolini, J. Lightwave Technol. 23, 842 (2005).
    [CrossRef]
  12. P. J. Winzer and H. Kim, IEEE Photon. Technol. Lett. 15, 1282 (2003).
    [CrossRef]

2006 (1)

2005 (2)

2004 (2)

G. Bosco and P. Poggiolini, IEEE Photon. Technol. Lett. 16, 665 (2004).
[CrossRef]

K.-P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
[CrossRef]

2003 (2)

P. J. Winzer, S. Chandrasekhar, and H. Kim, IEEE Photon. Technol. Lett. 15, 840 (2003).
[CrossRef]

P. J. Winzer and H. Kim, IEEE Photon. Technol. Lett. 15, 1282 (2003).
[CrossRef]

1988 (1)

R. A. Linke and A. H. Gnauck, J. Lightwave Technol. 6, 1750 (1988).
[CrossRef]

1978 (1)

C. W. Helstrom, IEEE Trans. Aerosp. Electron. Syst. 14, 630 (1978).
[CrossRef]

1964 (1)

S. Stein, IEEE Trans. Inf. Theory IT-10, 43 (1964).
[CrossRef]

1960 (1)

J. I. Marcum, IRE Trans. Inf. Theory IT-6, 56 (1960).

Bosco, G.

G. Bosco and P. Poggiolini, J. Lightwave Technol. 23, 842 (2005).
[CrossRef]

G. Bosco and P. Poggiolini, IEEE Photon. Technol. Lett. 16, 665 (2004).
[CrossRef]

Chandrasekhar, S.

P. J. Winzer, S. Chandrasekhar, and H. Kim, IEEE Photon. Technol. Lett. 15, 840 (2003).
[CrossRef]

Gnauck, A. H.

A. H. Gnauck and P. J. Winzer, J. Lightwave Technol. 23, 115 (2005).
[CrossRef]

R. A. Linke and A. H. Gnauck, J. Lightwave Technol. 6, 1750 (1988).
[CrossRef]

Helstrom, C. W.

C. W. Helstrom, IEEE Trans. Aerosp. Electron. Syst. 14, 630 (1978).
[CrossRef]

Ho, K.-P.

K.-P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
[CrossRef]

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).

Kim, H.

P. J. Winzer, S. Chandrasekhar, and H. Kim, IEEE Photon. Technol. Lett. 15, 840 (2003).
[CrossRef]

P. J. Winzer and H. Kim, IEEE Photon. Technol. Lett. 15, 1282 (2003).
[CrossRef]

Linke, R. A.

R. A. Linke and A. H. Gnauck, J. Lightwave Technol. 6, 1750 (1988).
[CrossRef]

Marcum, J. I.

J. I. Marcum, IRE Trans. Inf. Theory IT-6, 56 (1960).

Mlejnek, M.

Poggiolini, P.

G. Bosco and P. Poggiolini, J. Lightwave Technol. 23, 842 (2005).
[CrossRef]

G. Bosco and P. Poggiolini, IEEE Photon. Technol. Lett. 16, 665 (2004).
[CrossRef]

Stein, S.

S. Stein, IEEE Trans. Inf. Theory IT-10, 43 (1964).
[CrossRef]

Winzer, P. J.

A. H. Gnauck and P. J. Winzer, J. Lightwave Technol. 23, 115 (2005).
[CrossRef]

P. J. Winzer and H. Kim, IEEE Photon. Technol. Lett. 15, 1282 (2003).
[CrossRef]

P. J. Winzer, S. Chandrasekhar, and H. Kim, IEEE Photon. Technol. Lett. 15, 840 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

P. J. Winzer, S. Chandrasekhar, and H. Kim, IEEE Photon. Technol. Lett. 15, 840 (2003).
[CrossRef]

G. Bosco and P. Poggiolini, IEEE Photon. Technol. Lett. 16, 665 (2004).
[CrossRef]

K.-P. Ho, IEEE Photon. Technol. Lett. 16, 308 (2004).
[CrossRef]

P. J. Winzer and H. Kim, IEEE Photon. Technol. Lett. 15, 1282 (2003).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

C. W. Helstrom, IEEE Trans. Aerosp. Electron. Syst. 14, 630 (1978).
[CrossRef]

IEEE Trans. Inf. Theory (1)

S. Stein, IEEE Trans. Inf. Theory IT-10, 43 (1964).
[CrossRef]

IRE Trans. Inf. Theory (1)

J. I. Marcum, IRE Trans. Inf. Theory IT-6, 56 (1960).

J. Lightwave Technol. (3)

Opt. Lett. (1)

Other (1)

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).

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Figures (1)

Fig. 1
Fig. 1

Required SNR as a function of the imbalanced factor. The solid curve is calculated from the exact error probability of Eq. (8), and the dashed curve is from the approximation of Eq. (10). The required SNR is independent of the sign of the imbalanced factor.

Equations (10)

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s ( t ) = ( 1 + β ) E ( t ) + E ( t T ) 2 ( 1 β ) E ( t ) E ( t T ) 2 ,
r 1 = 1 + β 2 A + n ( t ) + n ( t T ) ,
r 2 = 1 β n ( t ) n ( t T )
p 1 ( r 1 ) = r 1 2 ( 1 + β ) σ n 2 I 0 ( r 1 A 1 + β σ n 2 ) exp [ r 1 2 4 ( 1 + β ) σ n 2 A 2 σ n 2 ] ,
p 2 ( r 2 ) = r 2 2 ( 1 β ) σ n 2 exp [ r 2 2 4 ( 1 β ) σ n 2 ] ,
p e 1 = { d th p 2 ( r 2 ) d r 2 0 r 2 2 + d th p 1 ( r 1 ) d r 1 d th < 0 0 p 2 ( r 2 ) d r 2 0 r 2 2 + d th p 1 ( r 1 ) d r 1 d th 0 .
p e 1 = { 1 β 2 exp [ d th 4 ( 1 β ) σ n 2 ( 1 + β ) A 2 2 σ n 2 ] d th 0 1 Q ( 2 A σ n , d th 2 ( 1 + β ) σ n ) + 1 β 2 exp [ d th 4 ( 1 β ) σ n 2 ( 1 + β ) A 2 2 σ n 2 ] Q ( A 1 β σ n , d th 1 β 2 σ n ) d th > 0 ) ,
p e = 1 + β 4 exp [ d th 4 ( 1 + β ) σ n 2 ( 1 β ) A 2 2 σ n 2 ] + 1 2 [ 1 Q ( 2 A σ n , d th 2 ( 1 + β ) σ n ) ] + 1 β 4 exp [ d th 4 ( 1 β ) σ n 2 ( 1 + β ) A 2 2 σ n 2 ] Q ( A 1 β σ n , d th 1 β 2 σ n ) .
p e 1 = 1 0 p 2 ( r 2 ) Q [ 2 A σ n , r 2 2 + d th 2 ( 1 + β ) σ n ] d r 2 .
p e 1 1 Q [ 2 A σ n , d th + 2 ( 1 β ) σ n 2 2 ( 1 + β ) σ n ] ,

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