New Results in Unitary Space-Time Code Construction and Comparison to Upper Bounds

Abstract

Unitary space-time codes are a coding technique for unknown (i.e. non-coherent) multiple-input multiple-output (MIMO) channels. The unitary constellation symbol-error rate performance is determined by the diversity product and diversity sum metrics of the constellation. Numerous techniques have been presented over the last few years for constructing unitary space-time codes with continually improving diversity products and sums. Other work has focused on determining bounds on the optimal diversity product and sum for a given number of transmit antennas and constellation size. This paper presents a comprehensive survey of known construction techniques and bounds for unitary space-time codes, and also reports a variety of new constellations that have been constructed with improved diversity product or sum. These new constellations are documented along with a list of the currently best known codes and bounds. In many cases, a large gap between the bound and best known constellation exist. This result suggests areas of focus for improved constructions or tighter bounds.