2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134409Unitary space-time modulation is known to be an efficient means to communicate over non-coherent Multiple Input Multiple Output (MIMO) channels. In this letter, differential unitary space-time coding and non-coherent space-time coding for the training based approach of Kim and Tarokh are addressed. For this approach, necessary and sufficient conditions for multi-group decodability are derived in a simple way assuming a Generalized Likelihood Ratio Test receiver and a unitary codebook. Extending Kim and Tarokh's approach for colocated MIMO systems, a novel training based approach to distributed non-coherent space-time coding for wireless relay networks is proposed. An explicit construction of two-group decodable distributed non-coherent space-time codes achieving full cooperative diversity for all even number of relays is provided.10 pages, 3 figures, submitted to IEEE Transactions on Wireless CommunicationsInformation Theorytext