Journal of Computer Networks and Communications

Volume 2019, Article ID 2938653, 11 pages

https://doi.org/10.1155/2019/2938653

## Adaptive Filtering in Optical Coherent Flexible Bit-Rate Receivers in the Presence of State-of-Polarization Transients and Colored Noise

School of Electrical Engineering and Computer Science, The University of Ottawa, Ottawa, Ontario K1N6N5, Canada

Correspondence should be addressed to Ahmad Abdo; ac.awattou@310odbaa

Received 29 July 2019; Revised 18 September 2019; Accepted 10 October 2019; Published 3 November 2019

Academic Editor: Youyun Xu

Copyright © 2019 Ahmad Abdo and Claude D’Amours. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this article, we analyze the performance of adaptive filtering in the context of dual-polarization coherent optical flexible bit-rate transceivers. We investigate the ability of different adaptive algorithms to track fast state-of-polarization (SOP) transients in the presence of colored noise. Colored noise exists due to the concatenation of Wavelength Selective Switches (WSSs) and polarization dependent loss (PDL) which can be considered as spatially dependent noise. We consider the use of different modulation formats, and the practical limitation of error signal feedback delay in decision-directed adaptive filters is also taken into account. The back-to-back required signal-to-noise ratio (RSNR) penalty that can be tolerated determines the maximum SOP rate of change that can be tracked by the adaptive filters as well as the filter’s adaptive step size. We show that the recursive least squares algorithm, using the covariance matrix as an aggressive “step size,” has a much better convergence speed compared to the least mean squares (LMS) and normalized LMS (NLMS) algorithms in the presence of colored noise in the fiber. However, the three algorithms have similar tracking capabilities in the absence of colored noise.

#### 1. Introduction

The era of cloud-based computation has arrived. To be able to accommodate the increased data rates and increased number of communicating devices on the internet, new techniques in optical telecommunications are being developed. The main vehicles for high-capacity networks are flexible bit-rate transceivers that use coherent detection and dual polarization. Dual polarization, introduced in [1], effectively doubles the data rate compared to single polarization techniques. The core operator in dual-polarization communication systems is the adaptive filter which performs equalization to correct the time-varying state-of-polarization (SOP) as well as other linear channel impairments. Studying both the convergence and tracking performance of the adaptive filters used in this process is important in understanding the limitations of the system.

The linear impairments encountered in an optical channel are a mix of deterministic and stochastic impairments. Chromatic dispersion (CD) is a type of deterministic impairment while polarization mode dispersion (PMD), polarization dependent loss (PDL), and SOP are stochastic ones. A dual-polarization optical signal has amplitude and phase in one polarization (*X*) and another amplitude and phase in the orthogonal polarization (*Y*). The received optical signal is a rotated version of the transmitted one. The rotation caused by the channel is either static or slowly varying which allows the receiver to employ a linear adaptive filter to decouple the two polarizations from the received rotated optical signal. Algorithms such as the classical least mean squares (LMS) [2–4] and the constant modulus algorithm (CMA) [5] have been used to undo the effects of the channel rotation.

In this paper, we investigate the performance of the LMS, normalized LMS (NLMS), RLS, and MMA algorithms for the adaptive filter in coherent receivers for dual-polarization optical signals in the presence of SOP transients, PDL, and optical filters. Then, we provide an overview of the main sources of SOP transients in optical links. In the next section, we look at the related literature discoursing adaptive filtering in coherent receivers. We present the concept of flexible bit-rate transponders in emerging programmable optical networks. In Section 5, we present a theoretical overview of coherent receivers and adaptive filtering. The simulation environment details are given, and then, we present our simulation results where we focus on the effect of SOP rate of change on RSNR penalty, as well as the tradeoff between performance in back-to-back (i.e., patch cord fiber between the transmitter and receiver) link configuration versus PDL penalty versus SOP tracking capabilities. As well, we compare different adaptive algorithms by simulating their convergence speed and SNR penalty for different SOP transients’ speed. The main contributions of this paper are the following:(1)Study of SOP tracking in the context of flexible bit-rate optical transceivers with practical hardware limitation(2)Illustrating the tradeoff when equalizing static versus fast variant channel, i.e., back-to-back RSNR and PDL penalties versus SOP tracking penalty.(3)Presenting analysis and simulation, in both convergence and steady states, to compare the performance of LMS versus NLMS, MMA, and RLS in the presence of colored noise (PDL and Filtering) and SOP transients

The work presented in this paper is an extension of the work presented in [6]. The work presented in [6] focuses on the RSNR penalty when the LMS algorithm is used to correct for SOP, PDL, and ROADM filtering effects in dual-polarized networks using QPSK modulation. The data rate is fixed, and the results are presented as an RNSR penalty for a given SOP rate and PDL level. In this work, we consider the performance of different adaptive filtering algorithms for the correction of SOP transients, PDL, and ROADM filtering effects in flexible bit-rate transceivers in software-defined networks which employ different modulation formats (QPSK as well as MQAM, where *M* = 8, 16, 32, and 64). The results are presented in terms of maximum SOP rates that can be tracked by the different algorithms for a given RSNR penalty and for different levels of PDL and number of ROADMs. Therefore, this work is a much more comprehensive study of the use of adaptive filters in dual-polarized coherent networks in the presence of fast SOP transients, PDL, and ROADM filtering effects than [6].

#### 2. Causes of State-of-Polarization Transients

Optical ground wires (OPGW) are primarily deployed by the electrical utility industry. They shield the conductors from lightning strikes, while providing a telecommunications path for third party communications. High-voltage lines carry electricity from the utility to the consumers while fiber optic cables provide telecommunication capability. OPGWs are being increasingly deployed to reduce costs compared with buried fibers; however, lightning strikes and other phenomena can cause the transmitted data to be exposed to fast SOP transients. In [7], it is stated that a 100 km length of OPGW can experience roughly 30 lightning strikes per year in Central Europe. The external structure of OPGW is constructed to discharge the lightning, but the Faraday effect, [8], is observed on the two polarizations when a lightning strike occurs.

An in-depth study performed using Verizon aerial fiber in [9, 10] showed that aerial fibers typically encounter higher SOP transients than those buried in the ground. In [11], data were collected from an OPGW plant in order to determine the correlation between SOP transients and lightning strikes. They were able to demonstrate a high correlation between lightning strikes and the occurrence of fast SOP transients which could achieve rates of up to 5.1 mrads/sec. Laboratory experiments were conducted in [12, 13] to emulate the effect of lightning on SOP transients observed in OPGW fibers. They showed that the rate of change in SOP increases as both the electrical current created by the lightning strike and the length of the cable increases. They demonstrated through repeated trials that for a given lightning current and cable length, the variance of the measured SOP data was less than 0.5% about the mean. In [14], the authors report that wind speed and the high-voltage line current also have an effect on the SOP rate of change.

Temperature and other forces can also have an effect on SOP in fiber cables. For example, deep sea cables experience mean SOP variations of 200 Hz, [15], while the mean SOP rate of change is 50 Hz in submarine cables, as shown in [15]. The authors of [16] found that the rate of SOP change is correlated to variations in ambient temperature. Other causes of fast SOP variation are mechanical vibration of the fiber cable caused by the passage of trains or construction work in close proximity. In [17], a study of SOP induced by mechanical vibration of Dispersion Slope Compensation (DSC) modules was done. The special case about DSCs is that they contain long fibers that are typically meant to compensate for dispersion of a span of the DWDM network (80 km). Certain packaging methodologies were introduced in [18] to reduce the fluctuations of SOP in DSC modules.

Much work has been done on reducing the RSNR penalty to compensate for the different impairments that are typical in coherent dual-polarization communication systems over fiber cables. In [19], it was shown that PMD actually helps averaging the penalty due to PDL. This is due to the fact that PMD spreads both polarizations equally at the two extreme PDL axes of the fiber. In [20], coding on the *X* and *Y* polarizations is used to mitigate PDL to avoid worst case orientations, which in turn reduces the RSNR penalty due to PDL. However, neither study considered the effect of fast SOP transients.

#### 3. Overview of Adaptive Filters in Optical Coherent Receivers

In [21], the authors presented a field-programmable gate array implementation of a coherent dual-polarization receiver where quadrature phase shift keying (QPSK) modulation is used. Operating at a data rate of 2.8 Gb/s, their receiver’s adaptive filter was able to track SOP transients of 5 kHz in the presence of 3 dB PDL in the link with a RSNR penalty of 0.5 dB. The work in [22] compared LMS algorithm with the recursive least square (RLS) algorithm in a system that employs spatial-division multiplexing (SDM), where multiple modes travel in the fiber in order to increase channel capacity. They show that the RLS has the superior convergence properties. The authors of [23] considered the effects of error feedback delay, using CMA, on the performance of the coherent receiver in the presence of CD. The work done in [24] shows how pipelining and efficient implementation of the adaptive filter’s feedback loop in the receiver help reducing the delay of the error signal used in the LMS tap weight updates by 18%.

In [25], the authors looked at Kalman filtering to tracking SOP with some PDL and frequency offset. Beside the fact that Kalman requires processing complexity in the order *O* (N^{3}), which does not fit in the industry’s trend to reduce power consumption in optical transceivers, there are two issues: conversion from Jones to Stokes parameters introduces noise enhancement in fixed-point implementation and the prerequisite for a fiber model in order to get the prediction and then compare with measurement for correction makes it tough to generalize. Constant Amplitude Zero Auto-Correlation (CAZAC) sequence, [26], are popular in wireless studies, and they are used in long-term evolution (LTE). In [27], the authors performed a detailed study on the impact of CAZAC in a long-haul transmission system viewed as chirp signals. In the studies undertaken in [28, 29], frequency-domain equalization (FDE) is used to track the SOP transients, using only QPSK modulation, in the pilot-directed mode. The papers focused on the amount of averaging of the channel estimates in tradeoff of back-to-back penalty and SOP transients tracking. The authors in [28–30] did not consider other types of optical fiber impairments such as PDL and optical filtering.

#### 4. Flexible Bit-Rate Transceivers in Software-Defined Networks

Next generation coherent receivers are designed to support high-speed, reduction in power consumption, and flexible provisioning. They are an integral component in the migration to Software-Defined Networks [31]. The programmability is required so that network operators can switch between modulation formats, to support flexible bit-rates based on reach, optical link margin, and available spectrum bandwidth. Therefore, it is worth studying the performance of the adaptive filters with the same practical limitations for different constellations (different line rates). We consider QPSK and 16QAM as high-order modulation format deployed for long reach link, throughout most of the study. As well, we look at the SOP rate of change tracking, for a different SNR penalty, of LMS for QPSK and 8/16/32/64 QAM. The PDL values, associated with modulation formats shown in Figure 1, are estimates based on the possible number of spans per bit-rate.