Optimal Spatial Signal Design for mmWave Positioning under Imperfect Synchronization

We consider the problem of spatial signal design for multipath-assisted mmWave positioning under synchronization errors and location uncertainties. First, the optimal precoder is shown to lie in a low-dimensional subspace spanned by directional and derivative beams pointing towards the existing paths. Under imperfect knowledge of path parameters, we propose an optimal robust design and a codebook-based heuristic design with optimized beam power allocation by exploiting the low-dimensional structure. Through numerical results, we characterize three 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.