Optical Networks - _I_2 Amplifier Noise_168

# Optical Networks - _I_2 Amplifier Noise_168 - 798 Receiver...

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798 Receiver Noise Statistics I.2 Ampliﬁer Noise An optical ampliﬁer introduces spontaneous emission noise to the signal in addition to providing gain. Consider a system with an optical preampliﬁer shown in Figure 4.7. The electric ﬁeld at the input to the receiver may be written as E(t) = 2 P cos ( 2 πf c t + ±) + N(t). Here, P is the signal power, f c is the carrier frequency, and ± is a random phase uniformly distributed in [0 , 2 π ] . N(t) represents the ampliﬁer spontaneous emission noise. For our purposes, we will assume that this is a zero-mean Gaussian noise process with autocorrelation R N (τ) . The received power is given by P(t) = E 2 (t) = 2 P cos 2 ( 2 c t + ±) + 2 2 PN(t) cos ( 2 c t + ±) + N 2 (t). The mean power is E [ ] = P + R N ( 0 ). (I.4) To calculate the autocovariance, note that since is a Gaussian process, E [ N 2 (t)N 2 (t + τ) ] = R 2 N ( 0 ) + 2 R 2 N using the moment formula (H.1). Using this fact, the autocovariance of P(.) can be calculated to be L P = 2 R 2 N + 4 PR N cos ( 2 c + P 2 2 cos ( 4 c τ).

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Optical Networks - _I_2 Amplifier Noise_168 - 798 Receiver...

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