512 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS
10.9Derive the Rice distribution [Eq. (10.4.13)] for the signal currentIgiven Eq.
(10.4.12) for an asynchronous heterodyne ASK receiver. Assume that both quadra-
ture components of noise obey Gaussian statistics with standard deviationσ.10.10Show that the BER of an asynchronous heterodyne ASK receiver [Eq. (10.4.17)]
can be approximated as
BER=^12 exp[−I 12 /( 8 σ^2 )]whenI 1 /σ1 andI 0 =0. Assume thatID=I 1 /2.10.11Asynchronous heterodyne FSK receivers are commonly used for coherent light-
wave systems. What is the SNR required by such receivers to operate at a BER
of 10−^9? Calculate the receiver sensitivity (in dBm units) at 2 Gb/s in the shot-
noise limit by assuming 1.2-GHz receiver bandwidth, 80% quantum efficiency,
and a 1.55-μm operating wavelength.
10.12Derive an expression for the SNR in terms of the intensity noise parameterrI
by including intensity noise through Eq. (10.5.1). Prove that the optimum value
ofPLOat which the SNR is maximum is given byPLO=σT/(RrI)when the
dark-current contribution to the shot noise is neglected.
10.13Derive an expression for the power penalty as a function ofrIby using the SNR
obtained in Problem 10.12.
10.14Consider an optical carrier whose amplitude and frequency are constant but
whose phase is modulated sinusoidally asφ(t)=φ 0 sin(ωmt). Show that the
amplitude becomes modulated during propagation inside the fiber because of
fiber dispersion.
10.15Discuss the effect of laser linewidth on coherent communication systems. Why
is the homodyne PSK receiver most sensitive to phase fluctuations? How is this
sensitivity reduced for asynchronous heterodyne receivers?
References
[1] M. Schwartz,Information Transmission, Modulation, and Noise, 4th ed., McGraw-Hill,
New York, 1990.
[2] R. E. Ziemer,Principles of Communications; Systems, Modulation and Noise, Wiley,
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[3] L. W. Couch II,Digital and Analog Communication Systems, 5th ed., Prentice Hall, Up-
per Saddle River, NJ, 1995.
[4] M. S. Roden,Analog and Digital Communication Systems, Prentice Hall, Upper Saddle
River, NJ, 1995.
[5] B. P. Lathi,Modern Digital and Analog Communication Systems, Oxford University
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[7] J. Salz,AT&T Tech. J. 64 , 2153 (1985);IEEE Commun. Mag. 24 (6), 38 (1986).
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