Systematic Construction of Full Diversity
Algebraic Constellations, Mohamed Oussama Damen, Hesham El Gamal, Norman C. Beaulieu · 2003
,the th cyclotomic number ring, all the possible dimensions that allow for achieving the optimal minimum product distances using the proposed approach are determined. It turns out that one can construct optimal unitary transformations using our construction if and only if factors into a power of and powers of the primes dividing .F or not satisfying these conditions, a method based on Diophantine approximation theory is proposed to “optimize” the minimum product distance. A lower bound on the product distance is given in this case, thus ensuring full diversity with “good” minimum product distances. Furthermore, the proposed approach subsumes the optimal unitary transformations proposed by Giraud et al. over and , while giving optimal unitary transformations for infinitely many new values of and . Index Terms—Constellations, Diophantine approximation, diversity methods, number fields, number rings.