3. Modulation and Constellations
Achieving high-capacity transmission requires multi-level symbol constellations with compact spectra. The modulation
considered in this study uses Nyquist signals having ‘box-like’ spectra with a square-root raised cosine shape (in the optical
field) and a roll-off of 20% (see Fig. 2a) [11]. The optical multiplexer and demultiplexer transfer functions are identical
and match the square-root raised cosine signal spectrum. The modulation is free from inter-symbol interference (ISI) as
seen in Figs. 2b and 2c. The raised cosine roll-off is chosen to reduce the large memory in the time domain associated with
perfectly square spectrum modulation using the ‘sinc’ temporal function [11]. The constellation uses a concentric N-ring
structure in field (amplitude shift-keying, N-ASK) with equal amplitude spacing and random phase (phase shift-keying,
PSK) on a high-resolution angular grid. For each symbol, amplitude and phase are randomly chosen within the underlying
constellation, with equal population of each ring. The actual number of phase states needed in practical implementation
follows from the capacity results and the coding used.