We consider the problem of spatial signal design for multipath-assisted mmWave positioning under limited prior knowledge on the users location and clock bias. We propose an optimal robust design and a codebook-based heuristic design with optimized beam power allocation by exploiting the low-dimensional precoder structure under perfect prior knowledge. 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.
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