Generalization of the Σ0-rank criteria for space-time codes.

Recently, Liu et al., developed the Σ0-rank criteria for space-time codes. It provides a sufficient condition on codeword and generator matrices defined over finite rings Z2k(j) to ensure full spatial diversity with 22k-QAM modulation. Here, we generalize the Σ0-rank criteria and derive a sufficient condition on the generator matrices defined over finite rings Z2l(j) to ensure full spatial diversity with 22k-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 Mammons and El Gamal achieve full spatial diversity when used with 22k-QAM modulation. [ABSTRACT FROM PUBLISHER]