Simplifying the error probability analysis in optical direct detection DPSK systems

Theoretical Insights Into the Impact of Coherent and Incoherent Crosstalk on Optical DPSK Signals

“…This can be done by choosing for the orthogonal functions a set of eigenfunctions of the integral equation (2) where are the corresponding eigenvalues. An additional advantage coming from using a Gaussian receiver configuration is the possibility of obtaining closed-form expressions for both the eigenfunctions and eigenvalues, without requiring the numerical evaluation of (2) [16].…”

“…The MGF of , conditioned on the optical power , can be expressed in terms of the MGF of the random variable , corresponding to the constructive port of the interferometer, and the MGF of the random variable corresponding to the destructive port, in the following way with [16] …”

“…This simplification is obtained by making the following approximations [16]: 1) , for and zero elsewhere; 2)…”

“…Therefore, the complex envelope of the total electrical field at the interferometer input can be given by (16) where the first term corresponds to the desired signal, the second term to the incoherent in-band crosstalk, and the third term, as in the coherent crosstalk case, to the ASE noise originated from the optical pre-amplifier.…”

“…The later reference also provides analytical and numerical probability density functions (PDFs) for the received powers and demonstrates that in the presence of coherent crosstalk the power penalties used to characterize the system performance are no longer deterministic, as happens in scenarios based on the incoherent crosstalk. Reference [15] uses some of the findings reported in [13] and [14], namely the fact of the received optical signal in presence of multipath interference could be described using Rician statistics, as the basis for developing a new treatment for evaluating the impact of coherent crosstalk on DPSK signals and derives analytical formulas for both the moment generating function (MGF) of the decision variable and error probability, by using the well-known wideband optical filtering assumption [16] to model the optical receiver.…”