Weighted Sum Energy Efficiency Optimization for Massive MIMO Two-Way Half-Duplex AF Relaying

We consider two-way amplitude and forward half-duplex massive multiple-input multiple output (MIMO) relaying with multiple user-pairs. Most of the existing massive MIMO relaying literature has optimized the network-centric global energy efficiency metric, which is a pseudo-concave (PC) function, and can be optimized using well-known Dinkelbach algorithm. We optimize the user-centric weighted sum energy efficiency (WSEE), which is defined as the weighted sum of energy efficiencies of all the users, and is not a PC function. We propose a successive convex approximation approach to optimize it, and analytically show that this approach yields a Karush–Kuhn–Tucker point of the original WSEE problem. We also reduce the computational complexity of the above approach by approximating it as a second order cone program. We numerically demonstrate the WSEE improvement achieved by the proposed algorithms over baseline equal- and random-power allocation algorithms.