Some Designs and Normalized Diversity Product Upper Bounds for Lattice-Based Diagonal and Full-Rate Space–Time Block Codes

摘要

In this paper, we first present two tight upper bounds for the normalized diversity products (or product distances) of $2,times,2$ diagonal space–time block codes from quadratic extensions on ${BBQ} ($i$)$ and ${BBQ} ( {mmb{zeta }}_{6})$, where i $=sqrt {-1}$ and ${mmb{zeta }}_{6}=exp ($ i ${2pi/6})$. Two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products. We present two new diagonal space–time block codes from higher order algebraic extensions on ${BBQ} ($i$)$ and ${BBQ} ( {mmb{zeta}}_{6})$ for three and four transmit antennas. We also present a nontight upper bound for normalized diversity products of $2,times,2$ diagonal space–time block codes with QAM information symbols,-n-n i.e., in ${BBZ} [$i $]$, from general $2,times,2$ complex-valued generating matrices. We then present an $n,times, n$-diagonal space–time code design method directly from $2n$ real integers based on extended complex lattices (of generating matrix size $n, times, 2n$) that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do. We finally use the optimal $2,times,2$ diagonal space–time codes from the optimal quadratic extensions to construct two $2,times,2$ full-rate space–time block codes and find that both of them have better normalized diversity products than the Golden code does.