On the Accuracy of the Gaussian Approximation for Performance Estimation in Optical DPSK Systems with In-Band Crosstalk

Abstract

The Gaussian approximation is known to be quite accurate for estimating the system performance of an optically pre-amplified on-off keying (OOK) system in the presence of multiple in-band interferers. This paper assesses if similar accuracy can be also achieved in an optically pre-amplified differential phase-shift keying (DPSK) system. The probability density function of the decision variable at the receiver is computed as a function of the number of interferers, and it is observed that this variable statistic is clearly non-Gaussian even for a large number of interferers. It is also shown that, for a 1 dB power penalty and a 16 interferer scenario, the Gaussian approximation over-estimates the real value of the total crosstalk level by as much as 3.7 dB for DPSK signals, while for OOK signals this gap shrinks by approximately 2 dB.

Estimating the Performance of Direct-Detection DPSK in Optical Networking Environments Using Eigenfunction Expansion Techniques

“…Taking into consideration the fact that the optimum decision threshold for an ideal balanced receiver is zero [24], then in that situation an observed negative value leads to a decision error. As a consequence, the error probability can be evaluated by integrating (28) from to 0 and can be written, for the specific case that of the interferers are "ones", in the following form: (29) where denotes probability, is the upper limit of the region of convergence of the integral, and is the conditional MGF given that the signal symbol is "one" and the number of interferers at the state "one" is . Bearing in mind that for interferers in the state "one" there are in the state "zero", and using (24), the conditional MGF is .…”

“…The average error probability is evaluated by applying a binomial symbol conditioning on the interfering signals. As a result, and for the case of the "one" and "zero" interfering symbols being equally likely, the average error probability is given by (30) The integral in (29) can be evaluated numerically by using the saddle point integration method [44]. According to this method a possible contour of integration is a straight line parallel to the imaginary axis, which is required to pass through the saddle point of the integrand of (29) It should be noted that the same strategy can be used to solve the integral in (28) in order to obtain the PDF of the decision variable , although in this case the phase function (31) must be replaced by .…”

“…Nevertheless, this analysis relies on a simplified assumption, since it considers an idealized receiver resulting from the combination of an ideal rectangular optical filter with large bandwidth-time product and an integrate-and-dump electrical filter, the so-called wideband optical filtering assumption [27], [28]. It is also worth noting that due to the complex nature of the statistics of the decision variable, the Gaussian techniques can not be applied to give accurate results with DPSK signals, even when the number of interferers is high [29], restricting considerably the space of solutions in comparison with OOK. In our recent work we have also developed some theory to deal with coherent in-band crosstalk originated from multipath interference, but once again its foundation relies on the wideband assumption [30].…”

Complementary Approaches to Accurately Evaluate the Performance in Optically Pre-Amplified DPSK Receivers with Direct Detection

“…More recently, some advantages of using this modulation format in the broader context of optical networks were also unveiled, namely its greater tolerance to in-band crosstalk when compared with the OOK format [2]. In this way, the performance modeling of optically pre-amplified DPSK receivers using direct detection has been an active research topic [1]- [6].…”

“…However, they differ on the way how the orthogonal functions are obtained. In particular, in [2]- [4] the authors used, as a simplified assumption, the fact that for a combination of a wide-band ideal optical filter and an integrate-and-dump electrical filter the complex exponential functions are an appropriate set of orthogonal functions [7], while [1] and [6] treat the case of arbitrary optical and electrical filtering, and in this case the orthogonal functions are obtained as the eigenfunctions of an integral equation.…”