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

Abstract

Abstract-In-band crosstalk, due to multiple interferers, has been identified as one of the most severe impairments in optical transparent networks, especially in the ones with a large number of nodes and a high wavelength density. Due to its robustness to in-band crosstalk differential phase-shift keying (DPSK) emerges as an attractive modulation scheme to be used in such environments. This paper proposes a rigorous formulation to estimate the performance of direct-detection DPSK receivers using an eigenfunction expansion technique in the time domain. The method takes into account both the in-band crosstalk, due to an arbitrary number of interfering terms, and the amplified spontaneous emission noise and is able to deal with any combination of optical and electrical filter shapes. Using this method the accuracy of an approximation based on the wideband optical filtering assumption was evaluated and shown that the approximation, although not providing reliable results for the error probabilities, can be used with confidence to compute power penalties due to in-band crosstalk. Furthermore, the crosstalk tolerance of DPSK over on-off keying was quantified and shown that this tolerance is reduced when the number of interferers increases.Index Terms-Differential phase-shift keying, eigenvalues and eigenfunctions, in-band crosstalk, optical networking.

Implications of in-band crosstalk on DQPSK signals in ROADM-based metropolitan optical networks

“…In the second case, the OOK format, θ x;i ðtÞ ¼ 0 and a x;i ¼ 1 for a bit "one" and a x;i ¼ r (0 rr o 1) for a bit "zero" (r is the ratio between the average optical power level of a bit "one" and the average optical power level of a bit "zero"). The random phase φ x;i describes the phase noise difference between the primary signal and the i-th crosstalk signal, which is assumed constant over the symbol period and is statistically modelled considering a uniform distribution over the interval [ À π,π] [8]. Throughout this paper, it is assumed a worst case interference scenario, i.e., all the interfering signals are assumed to be co-polarised and temporally aligned with the primary signal [8].…”

“…The random phase φ x;i describes the phase noise difference between the primary signal and the i-th crosstalk signal, which is assumed constant over the symbol period and is statistically modelled considering a uniform distribution over the interval [ À π,π] [8]. Throughout this paper, it is assumed a worst case interference scenario, i.e., all the interfering signals are assumed to be co-polarised and temporally aligned with the primary signal [8]. The crosstalk level of the i-th interferer, ε i , is defined as the ratio between the crosstalk power and the primary signal power (ε i ¼ P x;i =P s ), whereas the total crosstalk level is given by ε T ¼ P M i ¼ 1 ε i .…”

“…Next, the decision variables v Q ðt d Þ and v I ðt d Þ can be written as a sum of independent random variables. To achieve that goal an eigenfunction expansion technique to decompose the signal, the crosstalk, and the amplified ASE noise at the optical filter input, in a series of orthogonal functions is employed [8].…”

“…These leakage signals, usually known as crosstalk signals, interfere with the primary data signal at the optical receiver, contributing to degrade the signal quality [6]. The impact of these crosstalk signals, especially when the crosstalk has the same nominal wavelength as the primary signal -the in-band crosstalk -, has been the focus of widespread attention over the years, but mainly in the context of systems based on OOK [7], and differential phase-shift keying (DPSK) schemes [8]. The implications of this impairment on other modulation formats, like for example DQPSK with direct detection and QPSK with coherent detection, have been less investigated and require further studies.…”

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

“…Secondly, the obtained MGF is averaged over the distribution of , which is assumed to be uniformly distributed over . As a consequence the is obtained using (8) with [20] (19) and (20) In these equations the is given by (21) where , whereas is given by (21) with replaced by and replaced by . It is also expected that the fact of a certain interferer, for instance interferer , being at the state "one" , or at the state "zero" will condition the statistics of .…”