In this letter, we present an exact analytic expression for the maximum signal-to-interference ratio (SIR) for receivers communicating with multiple transmitting nodes over a general time-varying channel, where one of the nodes is chosen as a desired signal source based on the instantaneous channel condition and the other nodes act as interference sources. As an illustrative example, the maximum SIR distribution of a mobile receiver surrounded by three base stations (BS) is determined in a closed-form formula for Rayleigh fading channels, and its accuracy is confirmed using simulation results.