  We consider the problem of spatial signal design for multipath-assisted
mmWave positioning under limited prior knowledge on the user's location and
clock bias. We propose an optimal robust design and, based on the
low-dimensional precoder structure under perfect prior knowledge, a
codebook-based heuristic design with optimized beam power allocation. Through
numerical results, we characterize different position-error-bound (PEB) regimes
with respect to clock bias uncertainty and show that the proposed
low-complexity codebook-based designs outperform the conventional directional
beam codebook and achieve near-optimal PEB performance for both analog and
digital architectures.
