The performance of trellis-coded modulation

Trellis-coded modulation (TCM) in an 8-PSK (phase shift keying) scheme is more power efficient than uncoded QPSK at the same spectral efficiency on perfect coherent detection. For the same signal-to-noise ratio (SNR) of phase reference, the sensitivity to phase offset for 8-PSK is more serious than for uncoded QPSK. To analyze the effect of imperfect coherent detection, the equivalent distances under recovered carrier phase offsets are derived. The conditional event error probability and its upper bound with respect to recovered carrier phase offset are taken into account. The results for the average bit error probabilities of the 4-state, 2/3-TCM and uncoded QPSK schemes with noisy phase reference are given. It is shown that very high values of phase reference SNR are required for the efficient implementation of the TCM scheme