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.