Diversity Product Properties of Lu–Kumar's Space-Time Codes

In this paper, we show that the diversity products of the full transmit diversity space-time block codes proposed by Lu–Kumar (we call them Lu–Kumar's codes) with quadratic-amplitude modulation (QAM) constellations are lower bounded by $4$. We present a sufficient condition on the minimum Hamming weight of the linear binary full-rank space-time code such that this lower bound is met. We show that the special Lu–Kumar codes does satisfy the sufficient condition, and therefore, the diversity products of the special Lu–Kumar codes are $4$, where “special” means that the linear binary full-rank space-time codes are not general but specially constructed by Lu–Kumar.