Error-rate Floors in Differential n-level Phase-shift-keying Coherent Receivers employing Electronic Dispersion Equalisation

An analytical model for the phase noise influence in differential n-level phase shift keying (nPSK) systems and 2n-level quadrature amplitude modulated (2nQAM) systems employing electronic dispersion equalization and quadruple carrier phase extraction is presented. The model includes the dispersion equalization enhanced local oscillator phase noise influence. Numerical results for phase noise error-rate floors are given for dual polarization DQPSK, D16PSK and D64PSK system configurations with basic baud-rate of 25 GS/s. The transmission distance in excess of 1000 km requires local oscillator lasers with sub MHz linewidth. Introduction: Coherent optical communications research activities focuses currently on achieving system bit-rates of 100 – 1000 Gb/s and to apply electronic dispersion equalization to account for several thousand kilometers of transmission [1,2]. Practical high capacity system configurations have been polarization multiplexed n-level phase shift keying (nPSK) and quadrature amplitude modulation (nQAM) systems (n = 4, 8, 16, 32, 64,...) with differential detection. The demodulation in the receiver is coherent (with an optical transmitter (Tx) and local oscillator (LO) laser) and effectively homodyne since homodyne detection provides the closest possible channel stacking in wavelength division multiplexed (WDM) system implementations as well as the best system sensitivity. Phase noise becomes a prime system design parameter for high-constellation coherent systems since it affects the electronic carrier phase extraction [3,4] and furthermore the LO phase noise influence is enhanced by electronic dispersion compensation [5]. It is possible (and straightforward) to extend the analytical derivation for the enhanced LO phase noise in [5] to specify the BER floor for nPSK and 2nQAM systems with and without practical n-power carrier phase extraction by generalizing results from [3,4]. In [6] a similar study including the Viterbi-Viterbi carrier phase extraction has been presented. The purpose of our paper is to provide practically important system design considerations based upon simple and physically insightful system models. Theory outline: In [5] a theoretical treatment of the equalization enhanced phase noise influence from the Local Oscillator laser caused by electronic dispersion compensation in the receiver (Rx) is given. This derivation assumes that perfect carrier phase extraction is used. Furthermore, the electronic dispersion is implemented by optimal fixed configuration electrical filtering (such as a time domain Finite Impulse Response (FIR) filter or a frequency domain Blind Look-Up (BLU) filter [2]) meaning that adaptive (time domain) Least Mean Square (LMS) filters [2] are not covered by the treatment. Adaptive (LMS) filters may be expected to lead to enhanced phase noise penalty because the adaptive filter tap optimization is strongly dependent upon the laser coherence over many symbol time periods and this coherence is destroyed by the laser phase noise. The dispersion equalisation enhanced laser phase noise influence is due to the LO laser only and using [5] the total phase noise variance is specified as