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Beamforming is an attractive technique to improve the system performance for multi-input multi-output (MIMO) communications. Previous works mainly focus on improving the data transmission quality. However, the potential of beamforming for improving the localization quality is not yet fully studied. In this paper, we focus on active beamforming to reduce the user equipment (UE) localization error for millimeter-wave MIMO systems. Such beamforming for localization is of challenge because its optimization cost function (e.g., the localization error bound) also depends on the actual UE location and instantaneous channel states, which are unknown in advance. To address this challenge, a novel successive localization and beamforming (SLAB) scheme is proposed, where the long-term UE location and the instantaneous channel state will be jointly estimated and then the beamforming vector will be successively optimized as per the obtained estimation results. The proposed SLAB scheme will yield a sequence of beamforming weights and UE location estimates, which will converge to the stationary point of the associated optimization problem. Simulation results show that the proposed SLAB scheme achieves a huge performance gain for UE localization compared with state-of-the-art baselines.
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