Characterization of Totally Real Subfields of 2-Power Cyclotomic Fields and Applications to Signal Set Design

Abstract

A classification of all totally real subfields K of cyclotomic field Q(zeta_{2^r}), for any r ≥ 4, and the fully-diverse related versions of the Z^n-lattice are presented along with closed-form expressions for their minimum product distance. Any totally real subfield K of Q(zeta_{2^r}) must be of the form K=Q(zeta_{2^2} + zeta_{2^2}^{-1}), where s = r − j for some 0 ≤ j ≤ r − 3. Signal constellations for transmitting information over both Gaussian and Rayleigh fading channels (which can be useful for mobile communications) can be carved out of those lattices.