  Recent works show conflicting results: network capacity may increase or
decrease with higher transmission power under different scenarios. In this
work, we want to understand this paradox. Specifically, we address 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 by 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.
