Optical Networks - _I_1 Shot Noise_167

Optical Networks - _I_1 Shot Noise_167 - S I (f ) = L I ()e...

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I.1 Shot Noise 797 Removing the conditioning over P(.) yields E [ I(t) ] = E [ P(t) ] , (I.2) and E [ I(t 1 )I (t 2 ) ] = e E [ P(t 1 ) ] δ(t 2 t 1 ) + 2 E [ P(t 1 )P (t 2 ) ] . The autocovariance of I(t) is then given as L I (t 1 ,t 2 ) = E [ I(t 1 )I (t 2 ) ] E [ I(t 1 ) ] E [ I(t 2 ) ] = e E [ P(t 1 ) ] δ(t 2 t 1 ) + 2 L P (t 1 ,t 2 ), (I.3) where L P denotes the autocovariance of P(t) . I.1 Shot Noise First let us consider the simple case when there is a constant power P incident on the receiver. For this case, E [ P(t) ] = P and L P (τ) = 0 , and (I.2) and (I.3) can be written as E [ I(t) ] = P and L I (τ) = e P δ(τ), where τ = t 2 t 1 . The power spectral density of the photocurrent is the Fourier transform of the autocovariance and is given by
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Unformatted text preview: S I (f ) = L I ()e i 2 f d = e P. Thus the shot noise current can be thought of as being a white noise process with a at spectral density as given here. Within a receiver bandwidth of B e , the shot noise power is given by 2 shot = B e B e S I (f )df = 2 e P B e . Therefore, the photocurrent can be written as I = I + i s , where I = P and i s is the shot noise current with zero mean and variance e P B e ....
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This note was uploaded on 01/15/2011 for the course ECE 6543 taught by Professor Boussert during the Spring '09 term at Georgia Institute of Technology.

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