TAILIEUCHUNG - Optical Networks: A Practical Perspective - Part 80

Optical Networks: A Practical Perspective - Part 80. This book describes a revolution within a revolution, the opening up of the capacity of the now-familiar optical fiber to carry more messages, handle a wider variety of transmission types, and provide improved reliabilities and ease of use. In many places where fiber has been installed simply as a better form of copper, even the gigabit capacities that result have not proved adequate to keep up with the demand. The inborn human voracity for more and more bandwidth, plus the growing realization that there are other flexibilities to be had by imaginative use of the fiber, have led people. | 760 Receiver Noise Statistics L2 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 . The electric field at the input to the receiver may be written as E t V2P cos 27r ct 4 N t . Here P is the signal power fc is the carrier frequency and is a random phase uniformly distributed in 0 2tt . A t represents the amplifier spontaneous emission noise. For our purposes we will assume that this is a zero-mean Gaussian noise process with autocorrelation Rn t . The received power is given by P i P2 t 2P cos2 2ttfct D t cos 4 A2 i . The mean power is E P i P 0 . To calculate the autocovariance note that since A r is a Gaussian process E A2 t A2 i t R2N 0 2R r using the moment formula . Using this fact the autocovariance of P . can be calculated to be p2 Lp r 2R2n t 4PP v r cos 27t ct cos 47r cr . The corresponding spectral density is given by W y00 Lp T e-i2 rdr 2SN f SN f 2P SN f - fc SN J fc P2 8 f 2fc 8 f 2fc . The denotes the convolution operator where f x g x f u g x u du. After photodetection the last term in and can be omitted because the 2fc components will be filtered out. In order to derive the noise powers we return to and substitute for E P . and Lp . from and respectively to obtain r eR P Rn 0 5 r 1Z2 4PRn t cos 2tt ct R2 2R2n t . Amplifier Noise 761 We also have Si J eTl P Rn 0 K22P SN f - fc SN f c 1l2 2SN f SN f . 1-7 The first term on the right-hand side represents the shot noise terms due to the signal and the amplifier noise. The second term represents the signal-spontaneous beat noise and the last term is the spontaneous-spontaneous beat noise. Note that we have so far assumed that the amplifier noise is Gaussian but with an arbitrary spectral shape Sp tf . In practice it is appropriate to assume that the amplifier noise is centered at fc and is white over an optical .

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