On the performance evaluation of Trellis-Coded 8-PSK systems with carrier phase offset.

Combined convolutional codes and M-ary phase modulation have been shown to be more power efficient than uncoded coherent phase modulation at equal or better spectral efficiency. These schemes are often referred to as trellis-coded M-PSK systems. For example, at the same rate of 2 information bits per symbol, a simple rate 2/3 trellis-coded 8-PSK system yields a coding gain of 3 dB compared to coherent 4-PSK on an ideal Gaussian channel. Up to 6 dB coding gain can be achieved at the expense of higher complexity. However, carrier phase offset and phase ambiguity can be more serious problems for trellis- coded 8-PSK than for uncoded 4-PSK. In this paper we present a detailed analysis of the bit error probability for trellis- coded M-PSK systems with and without carrier phase offset. An equivalent distance measure is used for studying the effect of phase offset on specific error events. The error events which are particularly sensitive to phase offset are identified. Methods to calculate the error event probability and distance spectrum (the number of error events having a certain distance or probability) and an upper bound on the bit error probability are given. A modified state diagram is used to arrive at these results.