  Despite of the known gap from the Shannon's capacity, several standards are
still employing QAM or star shape constellations, mainly due to the existing
low complexity detectors. In this paper, we investigate the low complexity
detection for a family of QAM isomorphic constellations. These constellations
are known to perform very close to the peak-power limited capacity,
outperforming the DVB-S2X standard constellations. The proposed strategy is to
first remap the received signals to the QAM constellation using the existing
isomorphism and then break the log likelihood ratio computations to two one
dimensional PAM constellations. Gains larger than 0.6 dB with respect to QAM
can be obtained over the peak power limited channels without any increase in
detection complexity. Our scheme also provides a systematic way to design
constellations with low complexity one dimensional detectors. Several open
problems are discussed at the end of the paper.
