Spectrum and Energy Efficiencies for Multiuser Pairs Massive MIMO Systems With Full-Duplex Amplify-and-Forward Relay

Abstract

To achieve insights about the impact of amplified loop interference, we consider a dual-hop full-duplex (FD) massive multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying system in terms of achievable ergodic rates for each user pair as well as spectrum and energy efficiencies. It is assumed that the base station (or relay) is equipped with $M_{Rx}$ receive antennas and $M_{Tx}$ transmit antennas, while all sources and destinations have a single antenna. For such FD massive MIMO AF relaying systems, the closed-form expressions of the lower bounds of achievable ergodic rates are derived first with a finite number of receive and transmit antennas at base station. Then, the asymptotic performance analysis is performed by considering three different power-scaling schemes: 1) $P_{S} =E_{S} /M_{Rx} $ and $P_{R} =E_{R} $ ; 2) $P_{S} =E_{S} $ and $P_{R} =E_{R} /M_{Tx} $ ; and 3) $P_{S} =E_{S} /M_{Rx} $ and $P_{R} =E_{R} /M_{Tx} $ , where $E_{S} $ and $E_{R} $ are fixed, and $P_{S} $ and $P_{R} $ denote the transmit powers of each source and relay, respectively. Our results show that only when the power-scaling 2) is utilized, do the FD massive MIMO AF relay systems have the ability to restrict the loop interference, so that the system performance is free of loop interference when the number of antennas at the relay is large enough. On the contrary, with the power-scaling cases 1) and 3), the systems have no ability to cancel the loop interference even if $M_{Rx} $ or $M_{Tx} $ (or both) goes to infinity. The insight is different from the results in the FD massive MIMO decode-and-forward relaying systems where the loop interference can be entirely eliminated for the three power-scaling cases.