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.