Pricing-based distributed beamforming for weighted sum energy-efficiency in MISO ad hoc networks

In this paper, we consider the problem of maximizing the weighted sum energy efficiency (WS-EE) of a multi-input single-output (MISO) ad hoc network. To solve this problem, we develop one low-complexity distributed beamforming algorithm based on pricing mechanism. Specifically, each node updates its price information and broadcasts it to all the other nodes. Having collected all the information, each node selects its beam-vector in closed-form with low computational complexity. The convergence of this algorithm is strictly proved. Compared with the existing two-layer optimization algorithm, our algorithm has lower computational complexity without performance loss. Simulation results show that the proposed algorithm performs slightly worse than the centralized algorithm, but requires much less information exchange overhead.