Optimization of Fast-Decodable Full-Rate STBC with Non-Vanishing Determinants

TL;DR

This paper analytically optimizes full-rate space-time block codes with non-vanishing determinants, highlighting the impact of constellation topology on code performance and proposing specific constellation designs for APSK to achieve optimal diversity-multiplexing tradeoff.

Contribution

It introduces a simplified code structure and an analytical optimization method, revealing the critical role of constellation topology for non-vanishing determinants in full-rate STBCs.

Findings

APSK constellation points on a square grid with radius √(m²+n²) achieve non-vanishing determinants.

The simplified code structure enables faster decoding while maintaining optimal diversity-multiplexing tradeoff.

Methodology for optimizing codes with vanishing determinants at specific constellation dimensions.

Abstract

Full-rate STBC (space-time block codes) with non-vanishing determinants achieve the optimal diversity-multiplexing tradeoff but incur high decoding complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an STBC structure with special QR decomposition characteristics. In this paper, we adopt a simplified form of this fast-decodable code structure and present a new way to optimize the code analytically. We show that the signal constellation topology (such as QAM, APSK, or PSK) has a critical impact on the existence of non-vanishing determinants of the full-rate STBC. In particular, we show for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius $\sqrt{m^2+n^2} (m,n\emph{\emph{integers}})$ needs to be used. For signal constellations with vanishing determinants, we present a methodology to analytically optimize the full-rate STBC at specific constellation dimension.