Multi-dimensional phase/frequency coded modulation with nonuniform signal constellations

Multi-dimensional trellis coded frequency-shift key/phase-shift keyed (FSK/PSK) uniformly-spaced phase frequency modulation formats defined over an expanded set of signals varying both in phase and frequency have been shown to improve error performance over uncoded modulation. Nonuniformly spaced (or asymmetric) M-PSK (M-APSK) can have advantages over traditional uniformly spaced M-PSK. The author shows that by combining FSK with nonuniformly-spaced M-PSK modulation (2-FSK, 4-FSK)/M-APSK are using trellis coding and Viterbi decoding, one can, in some instances, obtain a performance gain over coded (2-FSK, 4-FSK)/M-PSK. The asymptotic performance gains due to coding, frequency-shift, and nonuniformity are evaluated in terms of the minimum free Euclidean distance d_free of the trellis. A few example are given to show the performance gain