We consider a single-anchor multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system with imperfectly synchronized transmitter (Tx) and receiver (Rx) clocks, where the Rx estimates its position based on the received reference signals. The Tx, having (imperfect) prior knowledge about the Rx location and the surrounding geometry, transmits the reference signals based on a set of fixed beams. In this work, we develop strategies for the power allocation among the beams aiming to minimize the expected Cramér-Rao lower bound (CRLB) for Rx positioning. Additional constraints on the design are included to ensure that the line-of-sight (LOS) path is detected with high probability. Furthermore, the effect of clock asynchronism on the resulting allocation strategies is also studied. We also propose a gridless compressed sensing-based position estimation algorithm, which exploits the information on the clock offset provided by non-line-of-sight paths, and show that it is asymptotically efficient.