Ergodic sum rate analysis and efficient power allocation for a massive MIMO two-way relay network

The authors study the transmit power allocation (PA) problem for a network of two multi-antenna terminals (one of which is a massive multiple-input and multiple-output (MIMO) terminal) and a two-way, amplify-and-forward relay. The relay is limited to a single antenna. Using perfect channel state information, the terminals employ beamforming with maximum-ratio-transmission and maximum-ratio-combining for transmission and reception, respectively. The authors investigate two practical problems, namely; (i) maximising the sum rate subject to a total power constraint (ii) maximising the sum rate when one of the terminals must exceed a target signal-to-noise ratio (SNR). For the first case, the authors derive the closed-form optimal PA and for the second, the authors derive a sub-optimal PA. In both cases, the resulting sum rates are a function of instantaneous channel gains. Thus by averaging over the Nakagami-m distribution and exploiting the weak law of large numbers, the authors derive the closed-form ergodic sum rates. Finally, the simulation results validate the theoretical analysis and show the sum-rate improvements over uniform PA. For example, to achieve 4 bit/s/Hz, a uniform allocation needs 1 dB more than the authors’ optimal allocation. When one of the SNRs must exceed a target value, the gap between the authors’ sub-optimal PA and random PA increases to 2 dB.