Adaptive Digital Equalization in Optical Coherent Receivers With Stokes-Space Update Algorithm

Abstract

In this paper, we describe a novel update algorithm for the filter coefficients of the adaptive digital equalizer in coherent receivers, which is based on error signals evaluated in Stokes space and is insensitive to both phase-noise and frequency-offset. We also introduce an optimized decision rule in the Stokes space, which takes into account the exact statistics of noise and yields a performance improvement with respect to the minimum distance decision criterion. We compare the performance of the new algorithm to the standard constant-modulus algorithm (CMA) for polarization-multiplexed 16QAM modulation, achieving similar performance in the absence of phase noise, with comparable complexity. Differently from CMA, the proposed Stokes-space algorithm allows us to remove the phase offset between polarizations, thus enabling the use of a joint carrier-phase estimation algorithm on both polarizations, which in turns yields a nearly doubled phase noise tolerance.

Novel Equalization Techniques for Space Division Multiplexing Based on Stokes Space Update Rule

“…The update algorithms considered in this paper are based on the stochastic gradient update [1], where the equalized signal is compared with the expected transmitted signal by means of the equalizer's error function [6]. For the error functions considered in this paper, the stochastic gradient update can be expressed as:…”

“…Introduced by [6], the Stokes Space Algorithm (SSA) equalizer takes advantage of the Stokes transformation to calculate the error function in that domain. As a consequence of this non-injective transformation, the number of points of the constellation of the transformed stokes space are reduced by a factor of approximately four [23].…”

“…The advantages of Stokes space is that it is insensitive to frequency offsets and phase rotations simultaneously introduced in both polarizations [6]. The SSA computes the error function as described by:…”

“…Simplified approximations of the previous formula are also available for decreasing the computational complexity [6]. …”

“…In this paper, we provide a discussion of the different SDM approaches and the main DSP techniques needed for each case. We focus on different equalization methods including novel equalization techniques based on Stokes Space recently introduced in [6][7][8].…”