By Christian Cuadrado-Laborde
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Extra info for Applications of Digital Signal Processing
At very weak optical powers, the induced polarization has a linear relationship with E such that; 2 E= ∝ x (1) (t − t`) · E (r, t`)dt` PL (r, t) = ε 0 −∝ (2) Digital Backward Propagation: A Technique to Compensate Fiber Dispersion and Non-Linear Impairments 31 Where ε 0 is the vacuum permittivity and x (1) is the ﬁrst order susceptibility. To consider non-linearities in the system, the Eq. 2 can be re-written as illustrated in Eq. 3 (Agrawal, 2001). P (r, t) = PL (r, t) + PNL (r, t) (3) Whereas, PNL (r, t) is the non-linear part of polarization.
38 Applications of Digital Signal Processing In a WDM transmission with large dispersion, pulses in different channels move through each other very rapidly. , 2003) between pulses in different channels the step-size in the walk-off method is chosen, so that in a single step two pulses in the two edge channels shift with respect to each other by a time that is a speciﬁed fraction of the pulse width. Mathematically it is depicted as in Eq. 19. h= C υg (19) Whereas, C is a error bounding constant that can vary from system to system, υg is the largest group velocity difference between the channels.
Fig. 11(a) shows the required number of steps per span to reach BER=10−3 at various launch powers for different SSFM algorithms. It is obvious that more steps are required for higher launch powers. Using logarithmic distribution of step sizes requires less steps to reach a certain BER than using uniform distribution of step sizes. At a launch power of 3dBm, the use of logarithmic step sizes reduces 50% in number of steps per span with respect to using the A-SSFM scheme with constant step sizes, and 33% in number of steps per span with respect to using the S-SSFM and M-SSFM schemes with constant step sizes.
Applications of Digital Signal Processing by Christian Cuadrado-Laborde