On the Performance of Multi-Way Massive MIMO Relay With Linear Processing

Previous works on multi-way massive MIMO relay only consider either Matched Filter (MF)/Maximum Ratio Transmission (MRT) or Zero Forcing as the pairs for the detector (or receiver) and the precoder for the uplink and downlink transmissions, respectively. This paper considers a more complex linear receiver/precoder pair, i.e., the minimum mean square error (MMSE) receiver and the regularized zero-forcing (RZF) precoder. Obtaining the signal-to-interference plus noise ratio (SINR) or the spectral efficiency (SE) of this pair is difficult. In this work, this issue is resolved by performing the analysis in the large system regime, where the number of users (K) and the number of antennas (N) at the relay go unbounded with a constant ratio. We assume that perfect channel state information (CSI) is available at the massive MIMO relay and employ the time-division duplex (TDD) protocol with perfect channel reciprocity. We derived the large system SINR approximations not only for the MMSE-RZF pair but also for the ZF-ZF and MF-MRT pairs. Numerical simulations show that the large system results are accurate for practical finite system sizes. We also obtained the limiting SINR for all pairs in the massive MIMO regime where K is finite, but N goes unbounded ( $K/N\to 0$ ) for different power scaling laws. In this regime, it is interesting to see that when the uplink power is scaled by N, the limiting SINRs of all pairs become equal, and thus, the least complex pair, MF-MRT, becomes beneficial.