A Turbo-Coded, DPSK-Modulated System with TMT Implemented

An nth root transformation is used for generating near Gaussian metrics from non-Gaussian metrics for input into a conventional turbo decoder that is based on the assumption that the input sequence to the decoder has a Gaussian distribution. The nth root transformation transforms channel non-Gaussian statistics to near Gaussian statistics for use with conventional turbo decoding for improved noncoherent communications over a non-Gaussian channel, such as a fading channel. For a differential coherent PSK waveform, where the channel statistics of a demodulator are non-Gaussian, for example, in the presence of fading, the nth root transformation is used to transform the non-Gaussian statistics to near Gaussian statistics for generating near Gaussian metrics, for improved PSK communications.