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We consider two-way amplify and forward relaying, where multiple full-duplex user pairs exchange information via a shared full-duplex massive multiple-input multiple-output (MIMO) relay. Most of the previous massive MIMO relaying works maximize the spectral efficiency (SE). By contrast, we maximize the non-convex energy efficiency (EE) metric by approximating it as a pseudo-concave problem, which is then solved using the classic Dinkelbach approach. We also maximize the EE of the least energy-efficient user relying on the max-min approach. For solving these optimization problems, we derive closedform lower bounds for the ergodic achievable rate both for maximal-ratio combining and zero-forcing processing at the relay, by using minimum mean squared error channel estimation. We numerically characterize the accuracy of the lower bounds derived. We also compare the SE and EE of the proposed design to those of the existing full-duplex systems and quantify the significant improvement achieved by the proposed algorithm. We also compare the EE of the proposed full-duplex system to that of its half-duplex counterparts, and characterize the self-loop and inter-user interference regimes, for which the proposed full-duplex system succeeds in outperforming the half-duplex ones.

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Two-way relaying (TWR) reduces the spectral-efficiency loss caused in conventional half-duplex relaying. TWR is possible when two nodes exchange data simultaneously through a relay. In cellular systems, data exchange between base station (BS) and users is usually not simultaneous e.g., a user (TUE) has uplink data to transmit during multiple access (MAC) phase, but does not have downlink data to receive during broadcast (BC) phase. This non-simultaneous data exchange will reduce TWR to spectrally-inefficient conventional half-duplex relaying. With infrastructure relays, where multiple users communicate through a relay, a new transmission protocol is proposed to recover the spectral loss. The BC phase following the MAC phase of TUE is now used by the relay to transmit downlink data to another user (RUE). RUE will not be able to cancel the back-propagating interference. A structured precoder is designed at the multi-antenna relay to cancel this interference. With multiple-input multiple-output (MIMO) nodes, the proposed precoder also triangulates the compound MAC and BC phase MIMO channels. The channel triangulation reduces the weighted sum-rate optimization to power allocation problem, which is then cast as a geometric program. Simulation results illustrate the effectiveness of the proposed protocol over conventional solutions. Index TermsAsymmetric two-way relaying (TWR), back-propagating interference (BI), infrastructure relays, non-simultaneous data flow, weighted sum-rate (WSR) maximization.A part of this work was presented in ICC-2013. The authors are with the

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