Mathematical expression of the bit error ratio in terms of the SNR and laser linewidths in digital coherent optical communication systems

The development of high speed digital signal processors has enabled the migration from previous direct detection systems to digital coherent optical communication systems. The adoption of this technology in optical interconnects is subject to more stringent power consumption requirements that have been partially addressed by adopting periodic phase alignment. In this paper, we develop a mathematical expression for the bit error ratio (BER) in QPSK digital coherent optical systems in terms not only of the signal to noise ratio but also the linewidth of the lasers, which is not usually considered as it is often compensated digitally. The obtained expression is validated through simulation and applied to dimension the system for a target BER.