Approaching the Gaussian channel capacity with APSK constellations

We consider the Gaussian channel with power constraint P. A gap exists between the channel capacity and the highest achievable rate of equiprobable uniformly spaced signal. Several approaches enable to overcome this limitation such as constellations with non-uniform probability or constellation shaping. In this letter, we focus on constellation shaping. We give a construction of amplitude and phase-shift keying (APSK) constellations with equiprobable signaling that achieve the Gaussian capacity as the number of constellation points goes to infinity.