Constant envelope eight-dimensional trellis coded modulation schemes

The authors present two 8-D TCM (trellis-coded modulation) schemes which use 512 points to transmit 2 b/s/Hz. The systems have constant envelope and yield asymptotic gains of 3.01 dB with only four or eight trellis states, without expanding the bandwidth over that of the equivalent uncoded system (QPSK over four consecutive time intervals). The size of the coded constellation is doubled but the minimum square Euclidean distance, the peak and average energies, and the modulation level remain identical to those of the uncoded system. The novel constellation is formed by the union of an 8-D QPSK (quadrature phase shift keying) and a rotated version of it. The present low-complexity schemes achieve small normalized redundancy, have constant envelope, and use simple and small constituent 2-D constellations