Achieving full diversity and fast ML decoding via simple analog network coding for asynchronous two-way relay networks

In this paper, we propose a simple analog network coding (ANC) scheme for asynchronous two-way relay networks where two sources exchange information through the relay nodes. In our proposed scheme, we consider a wireless scenario with frequency selective fading channels. Orthogonal frequency-division multiplexing (OFDM) is implemented at the two sources and then the OFDM blocks are transmitted to the relay nodes in the first time slot. In the second time slot, at the relay nodes, the ANC that has a few simple operations are implemented on the received mixed signals and then the processed signals are broadcasted to the two sources to finish the information exchange. In this scheme, at each source, when recovering the designed information transmitted from another source, the received signals have the orthogonal space time block code (OSTBC) structure or the quasi-orthogonal space time block code (QOSTBC) structure on each subcarrier. By a proper power allocation, the two sources can achieve full spatial diversity and fast ML decoding without the requirement of symbol level synchronization. By the repetition across the subcarriers, multi-path diversity available in frequency selective fading channels can be also exploited. Moreover, the proposed ANC scheme is also valid for multi-way relay networks where multiple sources exchange information.