An eight-dimensional phase invariant trellis coded modulation scheme with constant envelope

An eight-dimensional trellis-coded-modulation (TCM) scheme which uses 512 points to transmit two information bits per signaling interval is presented. The system has constant envelope and, with only eight states on the trellis, yeilds an asymptotic gain of 6.02 dB without expanding the bandwidth over that of the equivalent uncoded system. The size of the coded constellation is doubled, but the minimum squared Euclidean distance (MSED) and the peak and average energies remain identical to those of the uncoded system, therefore avoiding the 3 dB loss in Ungerboeck´s conventional codes. The novel constellation is formed by the union of an 8D QPSK and a rotated version of it. The new scheme achieves an effective gain of 5.64 dB and a small normalized redundancy of ρ=0.25, has constant envelope, achieves spectral efficiency of 2b/s/Hz if Nyquist filtering is used, and uses simple and small constituent 2D constellation