  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 Cram\'er-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.
