In Underwater Acoustic Sensor Networks (UASNs), the path loss of signal is serious due to the harsh underwater environment. Fractional power control algorithm has been widely used for the compensation of path loss. However, the randomness of underwater sensor nodes makes it hard to derive the performance index for UASNs. To address this issue, stochastic geometry theory is introduced to build an analysis model, which immediately gives the outage probability and transmission capacity for the fractional power control algorithm. Furthermore, the minimum transmission capacity for different power control factors is derived. This paper provides a huge incentive to improve the existing approaches to dynamically manage the power control scheme.
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