The Partially-Coherent AWGN Channel: Transceiver Strategies for Low-Complexity Fibre Links

Carrier phase estimation (CPE) is one of the key requirements to perform intradyne coherent detection in optical communication systems. Residual errors in the phase estimation at the receiver, also known as residual phase noise (RPN), follow the so-called Tikhonov distribution. In the digital domain, a channel where the phase has already been estimated by the CPE is generally known as a partially-coherent additive white Gaussian noise (PCAWGN) channel. Herein, we present a joint strategy to modulate and demodulate a 2-dimensional (2D) signal in a PCAWGN channel.

Using a low-complexity demapper, we geometrically shape (GS) 8- to 64- ary modulation formats for a PCAWGN channel. Through numerical simulations, we then assess the bit-wise achievable information rates (AIRs) and post forward error correction (FEC) bit error rates (BER) of the presented constellations with the: theoretical optimum model, Euclidean model and the low-complexity PCAWGN model.

The resulting constellations are shown to be tolerant to a significant amount of RPN and are therefore applicable to coherent optical communication systems using high linewidth lasers (e.g., >500 kHz) and/or lower symbol rates. Moreover, we demonstrate that shaped PCAWGN constellations combined with a low-complexity demapper can either significantly relax laser linewidth (LW) or carrier phase estimation (CPE) requirements. Assuming a rate-9/10 LDPC scheme, we demonstrate post-FEC BER shaping gains of up to 2.59 dB and 2.19 dB versus uniform 64QAM and 64-ary constellations shaped for the purely AWGN channel, respectively.