I. Introduction
M-ary hyper phase-shift keying (MHPSK) modulation for , and 64 was introduced in [1] as a new technique for use in satellite communications. Practical satellite communications systems use forward error correction coding to improve bit error rates at low received energy levels due to the large distances involved between satellites and earth terminals. In satellite communications, due to the large distances between transmitters and receivers, received signal strength is often comparable to that of noise. Additionally, high spectral efficiency techniques like 8-ary phase shift keying (8-PSK), 16-ary phase shift-keying (16-PSK) and 16-ary quadrature amplitude modulation (16-QAM) are commonly used in satellite communications systems. Frequency shift-keying (FSK) does achieve good probability of bit error performance but does not posses adequate spectral efficiency for broadcast requirements.