## 2 Coherent Burst-Mode Receivers for PDM-QPSK and PDM-16 QAM Modulated Payloads  
The vast majority of current optical networks follow the connection oriented network paradigm and hence both transmitter and receiver work in continuous-mode from the beginning until the end of the connection [3]. For example, in a wavelength routed optical network (WRON), a wavelength channel named lightpath is open and remains open for the duration of the connection [1]. In dynamic optical networks, however, the information stream is packetized at the optical level, and this introduces a series of challenges in the optical receiver compared to the continuous-mode case.  
A receiver capable of receiving optical packets is referred as a burst-mode receiver (BMRX) [23; 24]. Current optical packet networks, such as PONs [9], make use of non-coherent, analog BMRXs with OOK modulation format [23]. The main challenges of OOK BMRXs are the detection of the presence of an incoming optical packet and the quick estimation of the amplitude of the optical signal to establish a threshold to cope with different packet amplitudes on a packet-by-packet basis. The introduction of coherent modulations requires digital coherent burst-mode receivers (DCBMRXs). Compared with analog BMRXs, DCBMRXs perform the signal processing in the digital domain and new parameters should be estimated, including the SOP, differential group delay (DGD), carrier frequency offset and carrier phase. Moreover, for PDM modulated signals, the quick estimation of the SOP is of extreme importance for correct signal demodulation and requires new algorithms to be developed for DCBMRXs. For example, in continuous-mode receivers, the constant modulus algorithm (CMA) has been proposed and widely accepted as a practical solution due to its low computational complexity [25]. However, depending on the initial equalizer kernel and the SOP of the optical packet, the CMA equalizer may converge to a situation when one of the polarizations is output to both tributaries. This situation is known as the CMA singularity [25]. This singularity problem is not critical on continuous-mode systems where it can be solved by inspecting the equalizer output and resetting the convergence process. Furthermore, the CMA equalizer may take several hundredths symbols to converge, which is not acceptable in a BMRX where the equalizer convergence should be as rapid as possible in order to increase the network throughput, i.e., reduce the optical layer packet overhead.  
Several DCBMRX designs have been proposed in the literature to determine the SOP in a non-singular way. Ref. [26] transmits an optical packet header with only one polarization tributary and hence the SOP can be estimated with the algorithm proposed in [27]. However, this requires a more complex transmitter capable of nullifying one of the signal polarizations and additionally the lower energy in the packet header will impair the packet detection process due to additional noise compared to having a PDM header. Ref. [28] proposes to track the slope of the modulus of the CMA error signal, an operation that can be performed in parallel. However, this solution may have a high implementation complexity. In this section, we propose and experimentally characterize a novel DCBMRX that makes use of the Stokes parametrization in order to promptly initialize the equalizer with instantaneous convergence time and in a non-singular way.