Phase-diversity method using phase-shifting interference algorithms for digital coherent receivers Thang M. Hoang n , Mohamed M. Osman, Mathieu Chagnon, Meng Qiu, David Patel, Mohammed Sowailem, Xian Xu, David Plant Department of Electrical and Computer Engineering, McGill University, Montreal, Canada article info Article history: Received 8 May 2015 Received in revised form 26 July 2015 Accepted 30 July 2015 Keywords: Coherent receivers Phase-diversity Optical hybrid Phase shifting interference abstract We describe phase-diversity optical coherent receivers (CRx) using the phase-shifting-interference (PSI) framework. The goals of the analysis are several-fold. First, we show that coherent detection can be realized with optical hybrids that have an arbitrary number of branches and phase shifts using a closed- form solution of the inphase-quadrature mapping. Second, we show that CRx with 2  4 90° hybrids using balanced detection (BD) and CRx with 2  3 120° hybrid using single-ended detection (SED) per- form optimally compared to alternative configurations. A proof-of-concept WDM colorless 10  132-Gb/s PDM-QPSK transmission experiment is conducted. We demonstrate that an example of arbitrary phase diversity CRx with a 2  3 90° hybrid SED operates with a 0.3 dB signal-to-noise-ratio (SNR) penalty relative to conventional CRx at 6400 km and 4480 km for bit-error-rates below the threshold of 2  10 2 and the threshold of 3.8  10 3 respectively. The sensitivity degradation of the 2  3 90° hybrid SED with respect to the 2  4 90° hybrid BD in the shot noise limited regime at a distance of 4480 km is 3 dB, which matches well with the predicted penalty from the PSI analytical model. To the best of our knowledge, this paper is the first attempt to model a CRx using the PSI model. & 2015 Elsevier B.V. All rights reserved. 1. Introduction Coherent fiber optic transmission systems are being developed to meet burgeoning capacity demands [1]. The ability to linearly map the in-phase (I) and quadrature (Q) components of the re- ceived optical signal to the electrical domain by mixing the re- ceived optical field with that of a local oscillator (LO) is the key advantage of a coherent receiver (CRx) [2]. This direct mapping enables digital signal processing (DSP), which then allows the use of spectrally efficient modulation formats as well as the mitigation of transmission impairments [2–9]. Furthermore, the recent interest in transparent networks has lead to the wide adoption of colorless reception using 2  4 90° hybrid balanced detection (BD) CRx to reject undesired direct- detection components in wavelength-division multiplexing (WDM) channels [10–12]. Since coherent detection is expected to be soon deployed in metro and shorter-distance network, reducing complexity front-end is highly desirable. To reduce complexity, optical front ends with single-ended detection (SED), such that they are still applicable for colorless reception, have been recently reported [13–17]. These proposals consist of using only a 120° hybrid. Those proposal offers several benefits. First, using SED may lower the total cost because of simpler transimpedance amplifier (TIA) and less radio-frequency connections between optical and electrical devices [17]. Second, compared to conventional 2  4 90° hybrid, 2  3 hybrid have broader optical bandwidth and larger fabrication tolerance [16,18]. Thus, there is a need for in-depth studies to explore the possibility in phase-diversity CRx. In this paper, we develop and experimentally validate a model of phase-diversity coherent detection using an optical hybrid with an arbitrary number of outputs and optical phase shifts (referred to as an arbitrary hybrid). This is achieved by applying phase- shifting interference (PSI) algorithms which originated in the field of optical measurement [19–21]. In Section 2, the theoretical description of traditional and al- ternate configurations of a CRx frond-end is reviewed. Section 3 describes the PSI signal processing and presents a general model and condition for an arbitrary phase-diversity CRx. In Section 4, a closed form expression for the signal-to-noise ratio (SNR) for a phase-diversity CRx under the assumption of an ideal receiver is presented. In the context of this paper, an “ideal receiver” means that there is no power imbalance, optical phase imbalance, and skew mismatch between the branches of the re- ceiver. The analytical solution indicates that a 2  4 90° hybrid BD and a 2  3 120° hybrid SED are the best phase-diversity receivers. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optcom Optics Communications http://dx.doi.org/10.1016/j.optcom.2015.07.086 0030-4018/& 2015 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: thang.hoang@mail.mcgill.ca (T.M. Hoang). Optics Communications 356 (2015) 269–277