Constellations with better performance using FHT instead of FFT in ADSL systems

In this paper we propose a new constellation that has better performance (in BER) with respect to custom QAM constellation. We compare the new one and two kinds of circular constellations with QAM. For comparison we chose them so that they have the same power average. Also we used FHT instead of FFT for all constellations and compared them with each other. Based on the results DMT, without cyclic prefix, with FHT has better performance with respect to FFT. Also the new constellation has a minor better performance in the channels which have maximum SNR=20 dB. Also it is very attractive that in the channel with SNR greater than 27 dB circular constellation (form II) has better performance with respect to form I especially when we use FHT.