Geometric Weighted Sum Power Minimization for Energy-Efficient D2D Underlay Networks

This letter presents a computationally efficient weighted sum power (WSP) minimization framework for underlaid device-to-device (D2D) networks. Our approach circumvents the high complexity of fractional programming (FP) inherent in energy efficiency (EE) and weighted sum EE (WSEE) maximization. The core innovation lies in decoupling the problem into two tractable components: (i) closed-form geometric optimal power allocation with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(1) time complexity, eliminating iterative computations; (ii) optimal link matching via the Kuhn-Munkres (KM) algorithm. Integrated with an energy-aware heuristic for dynamic weight adaptation, the proposed scheme achieves ∼50% average network lifetime extension compared to FP-based EE maximization while maintaining real-time feasibility.