Full-Diversity Finite-Constellation 4 x 4 Differential STBC Based on Finite Quaternion Groups

This paper presents a novel way to construct unitary space-time block codes suitable for differential modulation. The new codes rely on quaternionic algebra to achieve finite constellation. Among these, a particular code with a codebook of size 48 is studied and shown to be differentially decodable by means of two symbol-by-symbol decoders (each symbol having 2 bits) and one larger decoder for a size 16 constellation. Simulations in a realistic WiMAX environment show the proposed code to outperform an optimized size 48 diagonal MPSK code by 1 dB. Ways to counter reduced performance in highly mobile environments are also suggested