M-ary hyper phase-shift keying over non-linear satellite channels

Forward error correction (FEC) coding in conjunction with M-ary hyper phase-shift keying (MHPSK) is considered in order to improve the robustness of a high spectral efficiency, non-linear satellite communications link. MHPSK is a spectrally efficient modulation technique that uses four orthonormal basis functions to increase the Euclidean distance between different symbols in the signal space. The use of four orthonormal basis functions provides an advantage over traditional spectrally efficient modulation techniques such as M-ary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) that only possess two degrees of freedom. MHPSK offers an improvement in probability of bit error performance over other spectrally efficient modulation techniques for the same average energy per bit-to-noise power spectral density ratio and the same spectral efficiency. As a result, MHPSK offers a novel way to improve both throughput and reduce power requirements using easy to generate waveforms. MHPSK and two-subcarrier orthogonal frequency division multiplexing (OFDM) with 8-PSK or 8-QAM on each subcarrier are compared in terms of the effect of peak-to-average power ratio and required amplifier backoff on the probability of bit error. In this paper, long block length Reed Solomon (RS) codes are used to encode information symbols which are then transmitted with MHPSK. Additionally, a comparison is made with two-subcarrier OFDM that uses 8-PSK or 8-QAM on each subcarrier and utilizing the Digital Video Broadcast (DVB) standard rate 0.9 low density parity check (LDPC) code commonly employed in non-linear satellite communications. As such, MHPSK and two-subcarrier OFDM with 8-QAM or 8-PSK on each subcarrier are compared in terms of probability of bit error, peak-to-average power ratio, amplifier backoff, and bandwidth efficiency using long forward error correction code block lengths.