Optimal Normalized Diversity Product of $2,\times,2$ Lattice-Based Diagonal Space–Time Codes From QAM Signal Constellations

In this correspondence, we prove that the optimal normalized diversity product of lattice-based diagonal space-time block codes with Gaussian integer (or QAM) signal constellations, i.e., , and any generating matrices of complex entries (not necessarily algebraic extensions of as commonly used) is . This result implies that lattice-based diagonal space-time block codes with Gaussian integer signal constellations and generating matrices of entries from quadratic algebraic extensions of have already reached the optimal normalized diversity product.