Maximum Rate of 3- and 4-Real-Symbol ML Decodable Unitary Weight STBCs

TL;DR

This paper determines the maximum achievable rates for 3- and 4-real-symbol ML decodable unitary weight space-time block codes with square structure, providing constructions and conditions for full diversity.

Contribution

It extends the known maximum rate results from 2-real-symbol codes to 3- and 4-real-symbol codes, including code constructions and diversity conditions.

Findings

Maximum rate for 3-real-symbol codes: (3(a-1))/2^a cspcu

Maximum rate for 4-real-symbol codes: (4(a-1))/2^a cspcu

Derived conditions for full-diversity achievement

Abstract

It has been shown recently that the maximum rate of a 2-real-symbol (single-complex-symbol) maximum likelihood (ML) decodable, square space-time block codes (STBCs) with unitary weight matrices is $\frac{2a}{2^a}$ complex symbols per channel use (cspcu) for $2^a$ number of transmit antennas \cite{KSR}. These STBCs are obtained from Unitary Weight Designs (UWDs). In this paper, we show that the maximum rates for 3- and 4-real-symbol (2-complex-symbol) ML decodable square STBCs from UWDs, for $2^{a}$ transmit antennas, are $\frac{3(a-1)}{2^{a}}$ and $\frac{4(a-1)}{2^{a}}$ cspcu, respectively. STBCs achieving this maximum rate are constructed. A set of sufficient conditions on the signal set, required for these codes to achieve full-diversity are derived along with expressions for their coding gain.