Some lattice based diagonal and full rate space-time block codes

Based on the normalized diversity product criterion of space-time code designs, we present two optimal 2 x 2 diagonal algebraic space-time block codes based on field extensions. We then present an n x n diagonal space-time code design method directly from 2n real integers based on extended complex lattices. We also present a non-tight upper bound for normalized diversity products of 2 x 2 diagonal space-time block codes with QAM information symbols from general 2 x 2 complex-valued matrices. We finally use the optimal 2 x 2 algebraic diagonal space-time codes to construct two 2 x 2 full rate space-time block codes and find that both of them have better normalized diversity products than the Golden code does.