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 letter, 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.