The Power of Consensus: Optimal Distributed Multichannel Wireless Transmitter Power Control

Consider a distributed network with N devices and K channels. Each device chooses a single channel and controls its transmission power on that channel. Our goal is to minimize the total transmission power while maintaining reliable communication between devices. Minimizing the total power consumption involves both the combinatorial optimization aspect of assigning channels to devices and the continuous optimization aspect of finding the optimal transmission powers. We present a distributed algorithm that solves the multichannel power control problem, and prove that it converges to the optimal solution. The algorithm is based on exploring new channel allocations by trial and error and running the best-response power control algorithm on the explored channel allocation. Using a novel wireless consensus phase, where devices use their transmission power as a consensus variable, all devices learn if the explored allocation is better than the current one. If the new allocation is better, all devices start using this allocation until the next trial and error. Finally, we provide simulations that support our analytical findings.