Fourth power phase estimation with alternative two-dimensional odd-bit constellations

It is well established that the fourth power phase estimator does not perform well for QAM cross (i.e., odd-bit) constellations. In this paper, new two-dimensional rectangular constellations are presented that give much improved performance, at a reasonably low increase in required constellation energy. For example, the 128B-COB constellation reduces the variance by an order of magnitude, while increasing the constellation´s average energy by only 0.28 dB and the peak to average energy ratio by 1.25 dB, relative to 128-QAM.