Energy Efficiency Optimization of Massive MIMO FD Relay With Quadratic Transform

We optimize the weighted sum energy efficiency (WSEE) of two-way amplify and forward relaying, where multiple full-duplex (FD) user-pairs exchange information via a shared FD massive multiple-input multiple-output (MIMO) relay. Optimization of user-centric WSEE metric, which prioritizes links of users with high energy efficiency (EE) requirements by suitably choosing their weights, is a non-convex problem due to its sum-of-ratio form. We optimize it by first approximating WSEE as a concave-convex fractional function, and then by using the quadratic transform. We then use Karush-Kuhn-Tucker (KKT) conditions to derive a closed-form solution to optimize WSEE. We numerically show that the i) proposed solutions achieve significant WSEE gains; and ii) suitable choice of weights can help prioritize EE requirements of different users.