Rotationally invariant trellis-coded modulations with multidimensional M-PSK

Using a multidimensional approach, the author discovers a large family of rotationally invariant trellis-coded M-PSK (M-ary shift keying) schemes, M⩾8, with nominal coding gains ranging from 3 to 5 dB and with bandwidth requirements the same as, or even less than, those of uncoded M/2-PSK schemes at the same information bit rate. The rotationally invariant schemes have performance and complexities comparable to the best known nonrotationally-invariant trellis-coded two-dimensional M-PSK schemes. Computer simulation results for these schemes, assuming an additive white-Gaussian-noise (AWGN) channel, are reported