GABBA codes: Generalized full-rate orthogonally decodable space-time block codes

Constellation independent, systematically constructed, orthogonally decodable, full-rate and full-diversity space time block codes (STBCs) generalized to any number of transmit antennas are considered. The proposed codes generalize the ABBA STBC, also known as quasi-orthogonal STBC (QO-STBC) and are referred to as generalized ABBA (GABBA) codes. The construction of GABBA codes is systematic in which the encoding matrix for any given number of transmit antennas is obtained by successive operations of a generation and a wrapping functions'. GABBA codes admit a linear orthogonal (symbol-by-symbol) decoder which fully decouples all encoded symbols using only linear combinations of the received signals and relying solely on knowledge of the channel at the receiver. The exact bit error probability of the proposed codes in generalized fading channels with the maximum likelihood (ML) receiver is computed and compared against simulation results obtained with the proposed symbol-by-symbol decoder. The comparison reveals that the linear orthogonal decoder achieves nearly the same performance of the ML receiver, despite its remarkably low complexity.