Understanding the Paradox of Power Control on the Capacity of Wireless Networks

It is well-known that power control can affect the wireless network capacity. However, recent works show conflicting results: network capacity may increase or decrease with higher transmission power under different scenarios. In this work, we want to explore this paradox and provide fundamental understanding on power control. Specifically, we want to explore the following questions: (1) Theoretically, should we increase or decrease transmission power to maximize network capacity? (2) Theoretically, how much network capacity gain can we achieve when using power control? (3) Under realistic situations, how do power control, link scheduling and routing interact with each other? Under which scenarios can we expect a large capacity gain by using higher transmission power? To answer these questions, firstly, we prove that the optimal network capacity is a non-decreasing function of transmission power. Secondly, we prove that the optimal network capacity can be increased unlimitedly by higher transmission power in some network configurations. However, when nodes are distributed uniformly, the gain of optimal network capacity by higher transmission power is upper-bounded by a positive constant. Thirdly, we discuss why network capacity in practice may increase or decrease with higher transmission power under different scenarios using carrier sensing and the minimum hop-count routing. Extensive simulations are carried out to verify our analysis. This work provides a deeper understanding on how power control can affect network capacity. Besides the theoretical contributions, it offers some design intuitions to wireless network researchers.