AbstractWe consider the power and rate allocation for a transmission in a wireless network where the transmitter knows the channel state of the desired receiver but only knows the statistics of the interferes. While this scenario is often encountered in practice, and extremely important in dense networks, its optimal solution was not yet known. The analysis considers nodes that are distributed according to a homogeneous Poisson point process, and hence applies both to cellular and to ad‐hoc networks. We derive (for the first time) the optimal power allocation at a node, based only on the channel gain to its desired receiver. We also derive the optimal rate allocation in networks that are characterized by the outage rate model. Considering sub‐optimal allocations, we advocate the use of the simple threshold scheduling scheme for power allocation and linear rate adaptation for rate allocation. We prove that these suboptimal schemes are close to optimal, for any channel fading. We also present simulation results over Rayleigh fading channels that show a maximum loss of 1.5% between the advocated schemes and the optimal schemes.