Spectral and Energy Efficiency for Large-Scale Multiple-Input-Multiple-Output Two-Way Hybrid Relaying With Multi-Pair Users Under Imperfect Channel State Information

Herein, we investigate the system spectral efficiency (SSE) and system energy efficiency (SEE) for massive two-way multiple-input-multiple-output (MIMO) relaying networks while considering imperfect channel state information (CSI) with K-pair users in the presence of the hybrid relaying processing. First, we obtain the general expression of the signal-to-interference-and-noise-ratio (SINR) for the considered system when the antenna number of the relay station (RS) M tends to be significantly large. Next, we consider the power scaling scheme (PSS) and achieve asymptotic SSE and SEE. We set the pilot sequence transmit power P-p to be fixed P-p and variable P-p. For a nonvanishing SINR, we achieve different power scaling cases under fixed and variable P-p. For a fixed P-p value, the optimal PSS of the SSE can be obtained when the transmit power of each user can be scaled by M, whereas that of the SEE can be achieved when the transmit power of both the RS and each user terminal can be reduced by M. Based on the variable value of P-p, the optimal PSS' of both the SSE and the SEE can be used when the transmit power of both RS and each user can be scaled by M-1/3. Thus, we conclude that the required SSE and SEE performances can be attained in multi-pair massive MIMO two-way relaying networks with a considerably low transmit power at RS and/or the transmit power of each user. The analytical results for the same are validated via simulation.