Impact of User and Relay Hardware Impairments on Spectral Efficiency of HD Massive MIMO Relay

Multi-pair two-way massive multiple-input multiple-output (mMIMO) relaying is being widely investigated. Most of the spectral efficiency (SE) investigations in mMIMO relaying assume ideal hardware. We consider a multi-pair two-way mMIMO half-duplex (HD) relay with user and relay hardware impairments. We derive a novel closed-form SE expression with maximum ratio relay processing and show that the SE, primarily due to the user hardware impairments, asymptotically saturates to a finite value despite the number of relay antennas N going to infinity. We also scale the HD relay hardware impairments as Nz with $z\geq 0$, and analyze the asymptotic SE limits for four different power scaling schemes. We use them to investigate the rate of increase in relay hardware impairments with increase in N that can be tolerated without compromising the SE.