Improved Perfect Space-Time Block Codes

TL;DR

This paper introduces new space-time block codes that improve energy efficiency and normalized minimum determinants over existing perfect STBCs by relaxing the unitarity requirement of the generator matrix.

Contribution

It demonstrates that unitariness is not necessary for energy-efficient STBCs and presents two new codes with larger normalized minimum determinants for 4 and 6 antennas.

Findings

New STBCs with larger normalized minimum determinants.

Relaxation of unitarity requirement improves energy efficiency.

Proven superiority over existing perfect STBCs.

Abstract

The perfect space-time block codes (STBCs) are based on four design criteria - full-rateness, non-vanishing determinant, cubic shaping and uniform average transmitted energy per antenna per time slot. Cubic shaping and transmission at uniform average energy per antenna per time slot are important from the perspective of energy efficiency of STBCs. The shaping criterion demands that the {\it generator matrix} of the lattice from which each layer of the perfect STBC is carved be unitary. In this paper, it is shown that unitariness is not a necessary requirement for energy efficiency in the context of space-time coding with finite input constellations, and an alternative criterion is provided that enables one to obtain full-rate (rate of $n_t$ complex symbols per channel use for an $n_t$ transmit antenna system) STBCs with larger {\it normalized minimum determinants} than the perfect STBCs. Further, two such STBCs, one each for 4 and 6 transmit antennas, are presented and they are shown to have larger normalized minimum determinants than the comparable perfect STBCs which hitherto had the best known normalized minimum determinants.