GENERALIZATION OF THE SIGMA O RANK CRITERIA FOR SPACE-TIME CODES

Abstract

Recently, Liu et al. developed the Sigma(o)-rank criteria for space-time codes. It provides a sufficient condition on code-word and generator matrices defined over finite rings Z(2)k (j) to ensure full spatial diversity with 2(2k)-QAM modulation. Here, we generalize the Sigma(o)-rank criteria and derive a sufficient condition on the generator matrices defined over finite rings Z(2)l (j) to ensure full spatial diversity with 2(2k)-QAM modulation for any positive integer l <= k. We also show that generator matrices defined over GF(2) satisfying the BPSK stacking construction constraint of Hammons and El Gamal achieve full spatial diversity when used with 2(2k)-QAM modulation.