5208 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 23, DECEMBER 1, 2017 Use of Extreme Value Statistics to Assess the Performance Implications of Cascaded ROADMs John C. Cartledge, Fellow, IEEE, Filipe Matos, Charles Laperle, Member, IEEE, Andrzej Borowiec, Maurice O’Sullivan, and Kim Roberts, Senior Member, IEEE Abstract—The performance implications of passband impair- ments and bandwidth narrowing caused by the cascading of op- tical filters are investigated using a 100 Gb/s dual polarization, quadrature-phase-shift-keyed (DP QPSK) transceiver. The overall responses for cascades of filters are emulated using the combination of a programmable optical filter and variable bandwidth optical filter. The statistical variations in the responses for a cascade are ad- dressed by considering 1000 realizations that result from randomly selected responses for each of the individual filters. To determine the impact on system margins, a methodology based on extreme value statistics is presented. The signal-to-noise ratios (SNRs) that correspond to real-time estimates of the pre-forward error correc- tion bit error ratio (pre-FEC BER) are quantified in terms of the probability that the minimum of n observations of the SNR is less than a specified value (maximum pre-FEC BER exceeds a speci- fied value). This approach improves the reliability of predicting the impact of cascaded filtering on system performance by removing the uncertainty about the underlying statistical distribution of the SNR. Index Terms—Optical filtering, Coherent optical fiber commu- nications. I. INTRODUCTION T HE performance of optical fiber transmission systems with direct or coherent detection can be affected by signal dis- tortion due to the overall frequency response of cascaded optical filters [1]–[36]. The cascading of reconfigurable optical add- drop multiplexers (ROADMs) in modern systems with coherent detection produces passband impairments, bandwidth narrow- ing and center frequency offset from the carrier frequency. The impact of cascaded filtering on system performance and tech- niques to mitigate the filtering penalties have been assessed by simulation [14], [15], [18], [23], [25], [28], [29], [32], [36] and by experiments that have used both offline signal process- ing [12], [15], [20], [21], [24], [26]–[28], [36] and real-time processing [13], [17], [19], [22], [31], [33]–[35]. Experiments have either used a recirculating loop to repeatedly apply an op- tical signal to the same optical filter(s) [15], [18]–[21], [24], Manuscript received August 22, 2017; revised October 16, 2017; accepted October 23, 2017. Date of publication October 31, 2017; date of current version November 20, 2017. (Corresponding author: John C. Cartledge.) J. C. Cartledge and F. Matos are with the Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON K7L 3N6, Canada (e-mail: john.cartledge@queensu.ca; filipe.matos@queensu.ca). C. Laperle, A. Borowiec, M. O’Sullivan, and K. Roberts are with the Ciena Corp., Ottawa, ON K2K 0L1, Canada (e-mail: claperle@ciena.com; aborowie@ciena.com; mosulliv@ciena.com; kroberts@ciena.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2017.2768962 [25], [28], or straight-line cascades of distinct optical filters [12], [13], [15], [17], [22], [31], [35]. These results have, for the most part, focused on bandwidth narrowing and consider a relatively small number of possible realizations for the overall frequency response of a cascade. The performance implications of (i) passband impairments and bandwidth narrowing [33] and (ii) bandwidth narrowing and center frequency offset [34] have recently been investigated by considering emulated realizations of the cascaded response and real-time processing. In this paper, the performance implications of passband im- pairments and bandwidth narrowing caused by the cascading of optical filters are investigated. Overall responses for ten cas- caded filters were emulated using the combination of a pro- grammable optical filter (POF) and variable bandwidth optical filter (VBOF). The results focus on the impact of the statistical variations in the overall responses by considering 1000 realiza- tions that result from randomly selected responses for each of the ten filters. The performance is assessed using estimates of the pre-forward error correction bit error ratio (pre-FEC BER) for a 100 Gb/s dual polarization, quadrature-phase-shift-keyed (DP QPSK) transceiver. The signal-to-noise ratios (SNRs) that correspond to the pre-FEC BERs are interpreted using extreme value statistics in order to reliably quantify the expected impact on system performance. This is done in terms of the probability that the minimum of n observations of the SNR is less than a specified value (or equivalently the maximum of n observations of the pre-FEC BER is greater than a specified value). II. EMULATION OF THE CASCADED RESPONSE The overall responses of the cascaded filters were realized using a programmable optical filter with a resolution of 1 GHz (Finisar WaveShaper 1000S) and a variable bandwidth optical filter (Yenista XTA-50). The POF was used to set the passband impairment over a frequency range of 75 GHz and the VBOF was used to set the 3-dB bandwidth and center frequency (in the absence of passband impairments). The VBOF has a steep 500 dB/nm roll-off with a flat passband and is able to approxi- mate the sharp roll-off required for the cascaded filter response. In combining the two filters, the VBOF carved out the center portion of the POF passband response. The overall passband responses for 1000 cascades of ten fil- ters were first generated offline using Matlab. The passband impairment for each filter is characterized by a slope about the carrier frequency with amplitude A s , and ripple with ampli- 0733-8724 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.