Optimal Normalized Diversity Product of 2 × 2 Lattice-Based Diagonal Space–Time Codes From QAM Signal Constellations

摘要

In this correspondence, we prove that the optimal normalized diversity product of $2,times,2$ lattice-based diagonal space–time block codes with Gaussian integer (or QAM) signal constellations, i.e., $BBZ [{bf i}]$, and any generating matrices of complex entries (not necessarily algebraic extensions of $BBZ [{bf i}]$ as commonly used) is $1/sqrt {3}$ . This result implies that $2,times,2$ lattice-based diagonal space–time block codes with Gaussian integer signal constellations and generating matrices of entries from quadratic algebraic extensions of $BBZ [{bf i}]$ have already reached the optimal normalized diversity product.