QAM Constellations With Fractional Entropy to Gain in Margin Maximization for Frequency Selective Channels

This letter proposes two approaches to increase the energy gain for the procedure of bit and power allocation in the frequency selective channels. The first one is the use of QAM constellations with optimal probabilistic shaping (PS) instead of the conventional QAM constellations. The second approach is the use of an extended set of QAM constellations with fractional entropy, which is named FQAM. These FQAM constellations are first offered in this work. As the channel examples, we used ADSL channel, fiber optic channel with Bessel filter, and the one with chromatic dispersion. It is shown that for the observed use cases the use of QAM with PS provides the energy gain in the range of 0.25–0.40 dB with respect to the conventional QAM constellations, while FQAM provides the gain in the range of 1.05–1.30 dB.