Exact error probability of DQPSK signal with nonlinear phase noise

Exact Error Probability of DQPSK Signal with Nonlinear Phase Noise

Jen-An Huang and Keang-Po Ho

Graduate Institute of Communication Engineering,

National Taiwan University, Taipei 106, Taiwan

Tel: +886-2-2363-525

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+886-2-2368-3824

’

E-mail: koho@,cc.ee.ntu.edu.tw

Differential quadrature phase-shift keying (DQPSK) [1-3] signal has received renewed attention recently for spectral-efficiency transmission systems. Nonlinear phase noise [4] is the major degradation for phase-modulated signals [4--91. Correlated with received intensity [7-91, nonlinear phase noise can be compensated by the received intensity. The exact error probability of DQPSK signal is derived with and without linear compensation, taking into account the dependence between linear and nonlinear phase noise.

With Gray code, the bit-error probability is equal to ’

where 171

with parameters of 7

and Yo(v)= s e c G e x p b , f i t a n f i ) is the marginal characteristic function of nonlinear phase noise that depends solely on the signal-to-noise ratio (SNR) ps [IO], (Om) is the mean nonlinear phase shift, and a is the linear compensation factor. The optimal compensation factor is aOpt =

i ( ~ ~

+{h5

.

a = 0 is the case without linear compensation.

Figure 1 plot the SNR penalty for a BER of I O 9 = a function of nonlinear phase noise. For a SNR penally of less than 1 dB, the mean nonlinear phase shift must be less than 0.50 and 0.95 rad without and with linear compensation, respectively. The optimal operating point is for a mean nonlinear phase shift of (QNL) = 0.89 and 1.72 rad without and with linear compensation, respectively, such that the increases of launched power does not degrade the system performance due to nonlinear

phase noise.

5 , 1

REFERENCES

[I] R. A. Griffin et al. OFC ‘02, post-deadline paper FD6.

[2] P. S. Cho el al. PTL 15,473 (2003).

[3] H. Kim and R . 4 . Essiambre, PTL 15,769 (2003). 141 J. P. Gordon and L. F. Molienauer, Opt. Lett. 15, 1351 (1990).

[5] A. Mecozzi, JLT 12,1993 (1994).

[6] H. Kim and A. H. Gnauck, PTL.IS,320 (2003). [7] K.-P. Ho, e-print: physics/0303090.

[8] K.-P. Ho, PTL, Sept. 2003.

[9] X. Liu el al. Opt. Lett. 27, 1616 (2002). [IO] K.-P. Ho, Opt. Lett., Aug. I, 2003.

.

Fig. I . The SNR penalty of DQPSK signal with without linear compensation.

and

0-7803-7766-4/031$17.00 02003 IEEE