We consider two-way amplify and forward relaying, where multiple full-duplexuser pairs exchange information via a shared full-duplex massive multiple-inputmultiple-output (MIMO) relay. Most of the previous massive MIMO relaying worksmaximize the spectral efficiency (SE). By contrast, we maximize the non-convexenergy efficiency (EE) metric by approximating it as a pseudo-concave problem,which is then solved using the classic Dinkelbach approach. We also maximizethe EE of the least energy-efficient user {relying} on the max-min approach.For solving these optimization problems, we derive closed-form lower bounds forthe ergodic achievable rate both for maximal-ratio combining and zero-forcingprocessing at the relay, by using minimum mean squared error channelestimation. We numerically characterize the accuracy of the lower boundsderived. We also compare the SE and EE of the proposed design to those of theexisting full-duplex systems and quantify the significant improvement achievedby the proposed algorithm. We also compare the EE of the proposed full-duplexsystem to that of its half-duplex counterparts, and characterize the self-loopand inter-user interference regimes, for which the proposed full-duplex systemsucceeds in outperforming the half-duplex ones.
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