We consider an asynchronous two-way relay network in which a few distributed relays assist in the communication between two single-antenna terminals through analog network coding. The asynchronous transmission between relays and terminals causes symbol misalignments and results in diversity loss in space–time codes (STCs). We propose a family of zero-padded time-reversal STC that can achieve full diversity with low-complexity maximum likelihood (ML) decoding, given a bound for the path delay difference. With ML decoding, the proposed code is decomposed into several independent parts, which greatly facilitate the decoding process. For two-relay scenarios, three code designs based on Alamouti code, quasi-orthogonal space–time block code, and multigroup decodable STC are provided for each relay with one, two, and four antennas, respectively. For three-relay scenarios, one code design based on quasi-orthogonal space-time block code is provided for each relay with one antenna. Proof of full diversity is established, and the decoding complexity order is analyzed for all four designs. Simulations confirm the full diversity gain of all designs. The bit-error-rate performance in asynchronous scenarios is almost similar to that in synchronous scenarios.
['Yun Liu', 'Wei Zhang', 'Pak-Chung Ching']
Time-Reversal Space–Time Codes in Asynchronous Two-Way Relay Networks