Multiple trellis-coded modulation, per-survivor processing and Reed–Solomon coding in the presence of phase noise

The aim of this paper is to consider trellis coded modulation (TCM) in the presence of phase noise. The starting point is a two-dimensional 32 point cross (32-CR) signal set that has served as a benchmark for other power and bandwidth efficient modulation schemes. Per-survivor processing (PSP) is used for carrier phase estimation, and both the phase acquisition (transient state) and phase tracking (steady state) performances are considered in an additive white Gaussian noise (AWGN) channel, in which phase offset or time varying phase noise is introduced. Based on the theoretical and simulation results it can be said that the 32-CR constellation is itself more sensitive to a phase error rather than the PSP algorithm. Due to the phase error the TCM scheme becomes a catastrophic code. Possible solutions include stringent phase noise requirements for oscillators, multiple trellis-coded modulation (MTCM) and concatenated TCM and Reed–Solomon (RS) coding. Our simulation results show that a simple combined MTCM, PSP and RS scheme has around 3 dB advantage compared to the pure TCM and PSP in the presence of phase noise. A semianalytical approach is used for performance evaluation, and the method is a particularly convenient tool to determine the rate of RS coding in detail.