A Bit-Labeling Design for Trellis-Shaped Single-Carrier PSK with PAPR Reduction

Band-limited single-carrier signals, even with a phase-shift keying (PSK) constellation, suffer from relatively high peak-to-average power ratio (PAPR) when a narrow pulse-shaping filter is used at the transmitter. In our recent work, an application of trellis shaping (TS) has been studied extensively for the purpose of reducing PAPR of band-limited single-carrier PSK signals, and it has been shown that a nearly constant envelope signal can be generated even with the use of nearly rectangular pulse-shaping filter. In this paper, we first demonstrate that the uncoded bit error rate (BER) and PAPR reduction capability of the TS considerably depend on the bit labeling. We then propose a new bit labeling for high-order PSK constellation that can efficiently reduce PAPR while achieving BER performance comparable to that of Gray labeling. Finally, the BER of each constellation is theoretically analyzed and compared with the simulation results.