A new bound and algorithm for Star 16-QAM carrier phase estimation

The true Cramer-Rao lower bound (CRLB) is derived and evaluated for the estimation of carrier phase of Star 16-quadrature amplitude modulation (QAM) and can be simply applied to carrier frequency estimation. Different geometries are investigated by varying the ring ratio (RR). For signal-to-noise ratios (SNRs) between 6-15 dB, the CRLB with RR=3 is lower than that of Square 16-QAM. A modified phase estimator is presented, which closely follows the new CRLB. Investigation of symbol error performance in short packet length reveals Star 16-QAM to be superior to Square 16-QAM for SNR<13 dB, which is a reasonable operating range for a coded system. Although Square 16-QAM and Star RR=1.8 are optimum for a perfect receiver, when the effect of phase estimation is considered, we find Star RR=3 to be better for SNR below 10 dB.