Power scaling for multi-pair massive MIMO two-way relaying system under Rician fading

In this work, we investigate a massive multi-input multi-output two-way relaying system, where K pairs single-antenna users exchange information through a relay station equipped with N ( $$N\ge 2K$$ N ≥ 2 K ) antennas, employing the amplify-and-forward protocol and maximum ratio combining/maximum ratio transmission beamforming. Considering Rician fading channel with imperfect channel state information (CSI), we study the achievable sum rate and energy efficiency (EE) performance of the considered system. Firstly, we obtain the asymptotic results of the achievable sum rate and the EE, assuming a general power scaling scheme. It is shown that when $$N\rightarrow \infty $$ N → ∞ , the pilot sequences’ power, i.e., $$P_P$$ P P , each user’s transmit power, i.e., $$P_U$$ P U , and the relay station’s transmit power $$P_R$$ P R can be scaled down proportionally to $$1/N^a$$ 1 / N a , $$1/N^a$$ 1 / N a and $$1/N^b$$ 1 / N b , respectively, where $$a\ge 0$$ a ≥ 0 and $$b\ge 0$$ b ≥ 0 . Specifically, when perfect CSI is known and Rician factor $$\kappa =0$$ κ = 0 , our derived results reduce to the existing results in Rayleigh fading channel. Furthermore, the closed-form expressions of the achievable sum rate and EE are obtained approximately. Finally, simulation results are provided to confirm the validity of our analysis.