Page 251 - Optical Communications Essentials

Performance Measures

Performance Measures 241

For a sinusoidal received signal, the carrier power C at the output of the
2
receiver (in units of A , where A designates amperes) is
1 2
C (mR MP 0 ) (14.12)
2
where R is the responsivity of the photodetector, M is the photodetector gain,
and P 0 is the average received optical power. The carrier-to-noise ratio then is
given by
1 2
/ 2 (mR MP 0 )
CNR (14.13)
2
2
RIN(RP 0 ) B e 2qR M F(M)P 0 B e (4k B T/R eq ) B e F t
where the noise terms in the denominator are due to RIN, shot, and thermal
noises, respectively. For the other terms, F(M) is the photodetector noise figure,
k B is Boltzmann’s constant, R eq is the equivalent resistance of the photodetector
load and the preamplifier, and F t is the noise figure of the preamplifier.

Relative Intensity Noise RIN is defined in terms of a noise-to-signal power ratio.
This ratio is the mean-square optical intensity variations in a laser diode divided by
the average laser light intensity. The mean-square noise current resulting from these
variations is given by

2 2
i RIN σ RIN RIN(RP 0 )B e (14.14)
The CNR due to laser amplitude fluctuations only is CNR RIN C/σ RIN .
2

14.3.2. Limiting conditions on CNR
Let us now look at some limiting conditions. When the optical power level at the
receiver is low, the preamplifier circuit noise dominates the system noise. For
this
1 / 2 (mRMP 0 ) 2 C
CNR limit 1 (14.15)
2
(4k B T/R eq )B e F t i T B e
In this case the CNR is directly proportional to the square of the received optical
power. This means that for each 1-dB variation in received optical power, CNR
will change by 2dB.
For intermediate power levels the shot noise of the photodetector will dominate
the system noise. In this case we have
1 2
/ 2 m R P 0
CNR limit 2 (14.16)
2qF(M)B e
Here the CNR is directly proportional to the received optical power, so that for
each 1-dB variation in received optical power, the CNR will change by 1dB.

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