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In this paper, we develop two kinds of novel closed-form decompositions onphase shift keying (PSK) constellations by exploiting linear congruenceequation theory: the one for factorizing a $pq$-PSK constellation into aproduct of a $p$-PSK constellation and a $q$-PSK constellation, and the otherfor decomposing a specific complex number into a difference of a $p$-PSKconstellation and a $q$-PSK constellation. With this, we propose a simplesignal design technique to blindly and uniquely identify frequency selectivechannels with zero-padded block transmission under noise-free environments byonly using the first two block received signal vectors. Furthermore, aclosed-form solution to determine the transmitted signals and the channelcoefficients is obtained. In the Gaussian noise and Rayleigh fadingenvironment, we prove that the newly proposed signaling scheme enablesnon-coherent full diversity for the Generalized Likelihood Ratio Test (GLRT)receiver.

Full Diversity Blind Signal Designs for Unique Identification of Frequency Selective Channels