Abstract: Low complexity methods for hard and soft bit level demapping in a receiver of QAM signals with non-square, Gray coded constellations created as per U.S. Pat. No. 8,422,579 B1. In these methods the received signal is equalized to remove channel distortion, demodulated into in-phase and quadrature phase related symbols, and these symbols converted into hard-bits or preliminary soft-bits bits via the application of bit decision rules. Further, if converted into preliminary soft-bits, they may be multiplied by a factor to account for the impact of the received signal's signal-to-noise ratio on bit reliability, thereby creating final-soft-bits.

Abstract: A square array of signal points forming a 22n-QAM signal constellation, where n=3, 4, is modified by relocating the inner most 22n/16 and outer 22n/16 constellation points to specific positions, resulting a modified-square constellation with a reduced peak to average power ratio (PAPR) at the modulator output relative to that of the square constellation while resulting in a receiver sensitivity that is degraded by less than the decrease in the modulator's PAPR and hence less than the possible improvement at the transmitter in average transmitted power.