On Achievable SNR Region for Multi-User Multi-Carrier Asynchronous Bidirectional Relay Networks

We study the problem of obtaining achievable signal-to-noise ratio (SNR) region and the corresponding rate region for an asynchronous bidirectional multi-carrier relay network which consists of two transceivers and multiple relays. We assume that each relaying path, corresponding to each relay, causes a delay in the signal transmitted by one of the transceivers when this signal goes through that relay and arrives at the other transceiver. This delay depends on the distance traveled by the signal. Hence, different relaying paths incur different delays in the signal time of arrival at each of the two transceivers. In our data model, we take into account that these delays are different for different relaying paths. Assuming distributed beamforming at the relays and power control at the transceivers, we characterize the achievable SNR region and the corresponding rate region for this network. Such a characterization is performed when each subcarrier is used to enable bidirectional communication between several outer transceivers. To do so, we present our optimization framework and examine its structure, thereby showing how it can be solved. We prove that for the case where the rates over different subcarriers at each transceiver are constrained to be equal, our approach leads to semi-closed-form solutions for the relay beamforming weights and transceivers' subcarrier powers and for the boundaries of the SNR region.