Energy-Efficient Spatially-Correlated Hardware Impaired Massive MIMO FD Relaying

Most of the existing massive multi-input-multi-output (mMIMO) relaying works assume ideal transceiver hardware and spatially uncorrelated channels. A practical mMIMO relay, however, due to limited antenna spacing and the use of cost-effective equipment, usually experiences spatially-correlated channels and hardware impairments, respectively. We consider a hardware-impaired two-way full-duplex (FD) spatially-correlated mMIMO relaying with multiple MIMO FD user-pairs, and derive a closed-form spectral efficiency (SE) expression which is valid for a practical number of finite relay antennas. We use this expression to develop a quadratic transformation approach to optimize the non-convex global energy efficiency (GEE) and weighted sum energy efficiency (WSEE) metrics, which are fractional functions of optimization variables. The proposed approach first converts the fractional problem into its equivalent fraction-free counterpart, and then uses novel transformations to make the problem concave, and solve it using an iterative algorithm. We use this optimization to i) investigate the impact of spatial correlation and hardware impairments on GEE; ii) decide hardware impairment values for a tolerable reduction in GEE; and iii) investigate the impact of weights in WSEE on the users energy efficiency.