In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the channel. Accepted requests must satisfy constraints on the signal-to-interference-plus-noise (SINR) ratio. The objective is to maximize the number of accepted requests. Using competitive analysis we study algorithms using distance-based power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1, ∆] and duration in [1, Γ] we derive a lower bound of Ω(...