The metric expression for a generic linear space-time block code (STBC) is studied using a different approach to vectorization and a new representation of the metric. The new representation lends itself to a simple measure of reliability based on the sum of inner products, and provides a quantifiable definition for minimum distance of a STBC. This provides the framework for a new family of near-maximum-likelihood (ML) and ML decoding algorithms. It also has applications in the development of optimality test criteria for STBCs, as well as in the design of STBCs with low decoding complexity.

For the large family of quasi-orthogonal space-time block codes, it is not clear when is best to decode using an exhaustive search, and when the sphere decoding algorithm (SDA) should be applied. In investigating this practical issue, a generic maximum-likelihood metric expression is utilized which is more conducive to lowering the decoding complexity. It is then shown that for smaller constellations and/or number of transmit antenna, the complexity advantage of smart exhaustive search in comparison with sphere decoding can be significant.

This paper addresses the following question: for the large family of quasi-orthogonal space-time block code (QOSTBCs), when is it best to decode using an exhaustive search, and when should the sphere decoding algorithm (SDA) be applied? First, a simple and intuitive generic metric expression for QOSTBCs is proposed. The new metric expression makes it easier to find the simplified and partially decoupled metric than if working from the Forbenius norm. A new rate-one full-diversity 8 antenna QOSTBC is then constructed that has lower decoding complexity than that in [3]. Finally, the question of when to use the SDA is considered.