On 64-APSK constellation design optimization

This paper investigates the design of power and spectrally efficient coded modulations based on amplitude phase shift keying (APSK) with application to broadband satellite communications. Emphasis is put on 64APSK constellations. The APSK modulation has merits for digital transmission over nonlinear satellite channels due to its power and spectral efficiency combined with its inherent robustness against nonlinear distortion. This scheme has been adopted in the DVB-S2 Standard for satellite digital video broadcasting. Assuming an ideal rectangular transmission pulse, for which no nonlinear inter-symbol interference is present and perfect pre-compensation of the nonlinearity takes place, we optimize the 64APSK constellation design by employing an optimization criterion based on the mutual information. This method generates an optimum constellation for each operating SNR point, that is, for each spectral efficiency. Two separate cases of interest are particularly examined: (i) the equiprobable case, where all constellation points are equiprobable and (ii) the non-equiprobable case, where the constellation points on each ring are assumed to be equiprobable but the a priory symbol probability associated per ring is assumed different for each ring. Following the mutual information-based optimization approach in each case, detailed simulation results are obtained for the optimal 64APSK constellation settings as well as the achievable shaping gain.